Three Essays on Financial Stability

Thèse

Jean Armand Gnagne

Doctorat en économiquePhilosophiæ doctor (Ph. D.)

Québec, Canada

© Jean Armand Gnagne, 2018

Three Essays on Financial Stability

Thèse

Jean Armand Gnagne

Sous la direction de:

Kevin Moran, directeur de rechercheBenoît Carmichael, codirecteur de recherche

Résumé

Cette thèse s’intéresse à la stabilité financière. Nous considérons plusieurs modèles écono-métriques visant à offrir une meilleure compréhension des perturbations pouvant affecter lessystèmes bancaires et financiers. L’objectif ici est de doter les institutions publiques et régle-mentaires d’un éventail plus large d’instruments de surveillance.

Dans le premier chapitre, nous appliquons un modèle logit visant à identifier les principauxdéterminants des crises financières. En plus des variables explicatives traditionnelles suggéréespar la littérature, nous considérons une mesure des coûts de transactions (l’écart acheteur-vendeur) sur les marchés financiers. Nos estimations indiquent que des coûts de transactionsélevés sont généralement associés à des risques accrus de crises financières. Dans un contexteoù l’instauration d’une taxe sur les transactions financières (TTF) ferait augmenter les coûtsde transactions, nos résultats suggèrent que l’instauration d’une telle taxe pourrait accroîtreles probabilités de crises financières.

Dans le second chapitre, nous analysons la formation des risques financiers dans un contexte oùle nombre de données disponibles est de plus en plus élevé. Nous construisons des prédicteursde faillites bancaires à partir d’un grand ensemble de variables macro-financières que nousincorporons dans un modèle à variable discrète. Nous établissons un lien robuste et significatifentre les variables issues du secteur immobilier et les faillites bancaires.

Le troisième chapitre met l’emphase sur la prévision des créances bancaires en souffrance (non-performing loans). Nous analysons plusieurs modèles proposés par la littérature et évaluonsleur performance prédictive lorsque nous remplaçons les variables explicatives usuelles par desprédicteurs sectoriels construits à partir d’une grande base de données. Nous trouvons que lesmodèles basés sur ces composantes latentes prévoient les créances en souffrance mieux que lesmodèles traditionnels, et que le secteur immobilier joue à nouveau un rôle important.

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Abstract

The primary focus of this thesis is on financial stability. More specifically, we investigatedifferent issues related to the monitoring and forecasting of important underlying systemicfinancial vulnerabilities. We develop various econometric models aimed at providing a bet-ter assessment and early insights about the build-up of financial imbalances. Throughoutthis work, we consider complementary measures of financial (in)stability endowing hence theregulatory authorities with a deeper toolkit for achieving and maintaining financial stability.

In the first Chapter, we apply a logit model to identify important determinants of financialcrises. Along with the traditional explanatory variables suggested in the literature, we considera measure of bid-ask spreads in the financial markets of each country as a proxy for the likelyeffect of a Securities Transaction Tax (STT) on transaction costs. One key contribution ofthis Chapter is to study the impact that a harmonized, area- wide tax, often referred to asTobin Tax would have on the stability of financial markets. Our results confirm importantfindings uncovered in the literature, but also indicate that higher transaction costs are generallyassociated with a higher risk of crisis. We document the robustness of this key result topossible endogeneity effects and to the 2008 − 2009 global crisis episode. To the extent thata widely-based STT would increase transaction costs, our results therefore suggest that theestablishment of this tax could increase the risk of financial crises.

In the second Chapter, we assess the build-up of financial imbalances in a data-rich envi-ronment. Concretely, we concentrate on one key dimension of a sound financial system bymonitoring and forecasting the monthly aggregate commercial bank failures in the UnitedStates. We extract key sectoral predictors from a large set of macro-financial variables andincorporate them in a hurdle negative binomial model to predict the number of monthly com-mercial bank failures. We find a strong and robust relationship between the housing industryand bank failures. This evidence suggests that housing industry plays a key role in the build-up of vulnerability in the banking sector. Different specifications of our model confirm therobustness of our results.

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In the third Chapter, we focus on the modeling of non-performing loans (NPLs), one otherdimension along with, financial vulnerabilities are scrutinized. We apply different modelsproposed in the recent literature for fitting and forecasting U.S. banks non-performing loans(NPLs). We compare the performance of these models to those of similar models in whichwe replace traditional explanatory variables by key sectoral predictors all extracted from thelarge set of potential U.S. macro-financial variables. We uncover that the latent-component-based models all outperform the traditional models, suggesting then that practitioners andresearchers could consider latent factors in their modeling of NPLs. Moreover, we also confirmthat the housing sector greatly impacts the evolution of non-performing loans over time.

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Table des matières

Résumé iii

Abstract iv

Table des matières vi

Liste des tableaux viii

Liste des figures x

Remerciements xiv

Avant-propos xvi

Introduction 1

1 Securities Transaction Taxes and Financial Crises 41.1 Résumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 STT and transaction costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.5 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.6 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.8 Robustness analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2 Monitoring Bank Failures in a Data-Rich Environment 232.1 Résumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.4 Determinants of bank failures . . . . . . . . . . . . . . . . . . . . . . . . . . 262.5 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.6 Econometric framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3 On The Usefulness of Big Data in Modeling Non-Performing Loans 463.1 Résumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

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3.2 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.4 Recent empirical literature . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.5 Econometric framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.6 Data and preliminary analyses . . . . . . . . . . . . . . . . . . . . . . . . . 553.7 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.8 Out-of sample forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Conclusion 65

A Monitoring Bank Failures in a Data-Rich Environment 67A.1 Static HNB Model : additional analyses . . . . . . . . . . . . . . . . . . . . 67A.2 Dynamic HNB model : additionnal analyses . . . . . . . . . . . . . . . . . . 69A.3 Chapter 2 – list of explanatory Variables . . . . . . . . . . . . . . . . . . . . 71

B On The Usefulness of Big Data in Modeling Non-Performing Loans 75B.1 Preliminary analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75B.2 Chapter 3 – list of explanatory variables . . . . . . . . . . . . . . . . . . . . 79

Bibliographie 83

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Liste des tableaux

1.1 Descriptive statistics for the variable “Financial Crisis" . . . . . . . . . . . . . . 121.2 Definition and source of variables . . . . . . . . . . . . . . . . . . . . . . . . . . 131.3 Index of transaction costs and adverse selection markers . . . . . . . . . . . . . 151.4 Index of transaction costs and tests of reverse causation . . . . . . . . . . . . . 161.5 Results from estimation of the likelihood (1.4) . . . . . . . . . . . . . . . . . . . 171.6 Robustness I : lower threshold for asset price decline (20%) in crisis definition . 201.7 Robustness II : crisis defined by banking crises (Laeven and Valencia, 2012) only 201.8 Robustness III : sensitivity to country-specific financial openness (Chinn and

Ito, 2008) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.9 Robustness IV : countries selection . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.1 U.S. bank failures and assistances : descriptive statistics . . . . . . . . . . . . . 302.2 Data description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.3 Estimation of the number of commercial bank failures . . . . . . . . . . . . . . 372.4 Actual and fitted cumulative frequencies . . . . . . . . . . . . . . . . . . . . . . 382.5 Bank failures prediction with the HNB model : three-months-ahead horizon . . 412.6 Bank failures prediction with the dynamic HNB model : four-months-ahead

horizon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.7 Bank failures prediction with the HNB model : sensitivity analysis . . . . . . . 45

3.1 Descriptive statistics for non-performing loans ratios (%) . . . . . . . . . . . . . 553.2 Data description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.3 Static OLS estimation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.4 Dynamic OLS estimation results . . . . . . . . . . . . . . . . . . . . . . . . . . 593.5 VAR estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.6 VAR-X estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.7 Forecast error variance decomposition . . . . . . . . . . . . . . . . . . . . . . . 62

A.1 Static HNB predictors summary statistics . . . . . . . . . . . . . . . . . . . . . 68A.2 Correlation across predictors in the static HNB model . . . . . . . . . . . . . . 68A.3 Dynamic HNB model grid search . . . . . . . . . . . . . . . . . . . . . . . . . . 69A.4 Dynamic HNB predictors summary statistics . . . . . . . . . . . . . . . . . . . 70A.5 Correlation across predictors in the dynamic HNB model . . . . . . . . . . . . . 70A.6 Chapter 2 – list of explanatory variables . . . . . . . . . . . . . . . . . . . . . . 71

B.1 Descriptive statistics of the real estate loans proportion . . . . . . . . . . . . . 75B.2 Descriptive statistics of the explanatory variables . . . . . . . . . . . . . . . . 75B.3 Correlation across explanatory variables - Benchmark model . . . . . . . . . . . 76

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B.4 Correlation across estimated predictors - Factor model . . . . . . . . . . . . . . 76B.5 Unit root tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77B.6 Granger causality tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77B.7 Lag length criteria Test – VAR Benchmark model . . . . . . . . . . . . . . . . . 77B.8 Lag length criteria test – VAR Factor model . . . . . . . . . . . . . . . . . . . . 78B.9 Lag length criteria test – VAR-X Benchmark model . . . . . . . . . . . . . . . 78B.10 Lag length criteria test – VAR-X Factor model . . . . . . . . . . . . . . . . . . 78B.11 Explanatory variables (before transformation) - Benchmark model . . . . . . . 78B.12 Chapter 3 – list of explanatory variables . . . . . . . . . . . . . . . . . . . . . . 79

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Liste des figures

1.1 Probability of crises according to the model . . . . . . . . . . . . . . . . . . . . 19

2.1 Evolution of the U.S. banking industry : 1975 - 2013 . . . . . . . . . . . . . . . 282.2 U.S. bank failures and assistances (in levels and in proportion of total) . . . . . 292.3 Histogram of the U.S. monthly bank failures and assistances . . . . . . . . . . . 302.4 Predicted number of bank failures by model . . . . . . . . . . . . . . . . . . . . 392.5 Bank failures prediction with the HNB model : various forecasting horizons . . 402.6 Bank failures prediction with the dynamic HNB model : four-months-ahead

horizon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.1 Non-performing loans in the US banking sector . . . . . . . . . . . . . . . . . . 563.2 IRF of the VAR model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.3 IRF of the VARX model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.4 Forecasting performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

A.1 Static HNB forecasting performance through different horizons . . . . . . . . . 67

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To the One who strengthens me,To my family.

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To the loving memory of mybrother Jean Hugues Gnagne.

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Research is an organized methodfor keeping you reasonablydissatisfied with what you have.

Charles F. Kettering

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Remerciements

Cette thèse constitue l’aboutissement d’un travail plus collectif qu’individuel. Remercier demanière exhaustive toutes ces personnes physiques et morales qui auront contribué de prèsou de loin à la réalisation de ce travail s’avère pour moi une démarche bien périlleuse que jeme garde d’entreprendre. De fait, je tiens à exprimer ici ma plus profonde gratitude à tous ettiens particulièrement à m’excuser pour toute omission qui relèverait sans doute de la naturehumaine.

J’adresse d’entrée de jeu mes remerciements les plus sincères à mon directeur de thèse, leProfesseur Kevin Moran pour l’excellent travail d’encadrement, ses précieux conseils, sa grandedisponibilité et surtout son optimisme à toute épreuve. Son sens de la rigueur, sa grandecompréhension des sujets macro-économiques, et son perpétuel souci de clarté constituentpour moi des enseignements que je retiendrai tout au long de ma carrière professionnelle. Deces années de collaboration, je garde un excellent souvenir. Je remercie également le ProfesseurBenoît Carmichael d’avoir accepté de codiriger ma thèse. Je le remercie pour sa disponibilité,son encadrement, sa bonne humeur constante et nos longues heures de discussions qui aurontété déterminants lors des moments plus difficiles.

J’exprime également ma reconnaissance à tout le département d’économique de l’UniversitéLaval, et particulièrement au Professeur Sylvain Dessy pour avoir cru en moi en m’acceptant auprogramme de doctorat. Son regard bienveillant et ses nombreux conseils m’ont grandementaidé. Je remercie aussi l’honorable Professeur Jean-Yves Duclos qui, en tant que directeurdu département d’économie, m’a témoigné une grande confiance en m’octroyant mes premierscontrats de chargé de cours, et après lui, le Professeur Guy Lacroix. Je ne peux oublier de citerle Professeur Philippe Barla qui fut décisif dans notre cheminement. À travers lui, je remercieégalement le Centre de recherche sur les risques, les enjeux économiques, et les politiquespubliques (CRREP) pour toutes les bourses dont j’ai été le bénéficiaire.

Je souhaite de plus, marquer toute mon appréciation aux autres professeurs du départementd’économique de l’Université Laval, ainsi qu’à tout le personnel. Merci spécial à Ginette Ther-rien pour la dose de bonne humeur distillée quotidiennement durant ces années. Nos précieusesdiscussions existentielles me manqueront. Merci également à Jocelyne Turgeon et Josée Des-gagnés pour l’excellent travail.

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Merci à mes collègues, docteur(e)s et candidat(e)s au doctorat en économique, Gilles Koumou,Ali Yedan, Setou Diarra, Simplice Aimé Nono, Mbea Bell, Isaora, Ghislaine Sandra, Elfried,Bodel, Carolle et Marie Albertine. Je chérirai ces années de franche camaraderie et d’entraide.Soyez assurés de mes sentiments les plus affectueux.

Aussi, aimerais-je ici saluer mes collègues de la Direction de la Gestion de la Dette et dela Modélisation Financière du ministère des Finances du Québec. Je porte une mention spé-ciale à notre Directeur, M. Benjamin Calixte pour sa grande disponibilité, son ouverture et sacompréhension à mon égard. Son attitude bienveillante et ses encouragements m’ont permisde rapidement achever cette thèse. À mes autres collègues, Jean-David, Martin, Mireille etJean-Philippe, merci de m’avoir rappelé quasi quotidiennement que j’avais une thèse à ter-miner. Sans vous, peut-être, l’aurais-je oublié. Également, aux autres collègues et directeursdu ministère des Finances du Québec, grand merci : spécialement au Directeur Général del’Analyse et de la Prévision Économique, M. Daniel Floréa, au Directeur Raymond Fournier,au Directeur Francis Hébert, à la Directrice Debbie Gendron, merci d’avoir cru en moi. À moncollègue et ami, Jonathan Morneau-Couture, tu as auras été plus décisif et déterminant danscette thèse que tu ne le penses.

Enfin, à ma famille, ma mère Albertine, mes frères et soeurs, Marcellin, Marina et Alice, monépouse, May-Astrid et ma fille, Kayla, inutile de me répandre ici sur votre indéfectible soutienet amour. Vous le savez, je vous dois cette thèse.

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Avant-propos

Les chapitres de la présente thèse constituent des articles soumis ou à soumettre à des revuesscientifiques avec comité de lecture pour publication.

Le premier chapitre de cette thèse est un article réalisé avec mon directeur de recherche, KevinMoran, et mon co-directeur Benoît Carmichael. Cet article, dont je suis l’auteur principal, faitl’objet de quelques révisions pour être soumis à une revue scientifique.

Le deuxième chapitre est un article réalisé avec mon directeur Kevin Moran, et mon co-directeur Benoît Carmichael. Cet article, dont je suis l’auteur principal, fait l’objet de quelquesrévisions pour être soumis à une revue scientifique.

Le dernier chapitre de cette thèse est un article réalisé avec mon directeur Kevin Moran, etmon co-directeur Benoît Carmichael. Cet article, dont je suis l’auteur principal, fait l’objet dequelques révisions pour être soumis à une revue scientifique.

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Introduction

Over the last decades, achieving and maintaining financial stability has risen to prominence.The sequence of severe financial crises 1 of the years 1980’s and 1990’s put the need for a soun-der financial system at the top of the regulatory authorities priorities. Since, significant actionshave been undertaken to bolster financial regulation. With, for example, the implementationof the Basel Committee, important achievements have been made. More integrated channelsfor the exchange of information between countries on developments in the banking sector andthe build-up of imbalances have been set up. New global standards for the regulation and su-pervision of banks have been established, and a better cooperation with other financial sectorsstandard setters and international bodies have been fostered. 2 However, as a reminder, thebrutality of the subprime crisis unveiled significant loopholes in the financial regulation andrenewed the interest of the regulatory authorities for a tighter regulation framework.

A functional definition of financial stability represents a key step towards a suitable regulationframework as it helps identify the set of policies to develop and implement. Defining financialstability or conversely financial instability has been one of the main focus of the macro-financial literature. Many authors have sought to provide a comprehensible definition coveringall the principal aspects along with a sound financial system can be achieved and maintained.Still, defining financial stability proves a thorny issue since the literature lacks a clear andconsensual definition of financial stability. As underlined by Schinasi (2004), does financialstability mean the soundness of institutions, the stability of markets, the absence of turbulence,low volatility, or something else more fundamental ? Should defining financial stability be themain focus or rather, defining financial instability ? The literature diverges on this standpoint.Oosterloo et al. (2007), in a survey of central banks of the Organisation for Economic Co-operation and Development (OECD) countries, found that there is no unambiguous definitionof financial stability. One strand of the literature, largely dominated by central bankers favorsthe definition of financial stability. The preeminent view put forward is that achieving financialstability is to ensure the financial system is capable of playing its role of facilitating the

1. Some of the major financial crises were the Latin America sovereign debt crisis, the Savings and Loansin the United States, the Russian financial crisis, the Asian financial crises.

2. For more details about the Basel Committee activities, we refer the readers to the Basel CommitteeCharter available at https ://www.bis.org/bcbs/charter.htm.

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functioning of the economy, by channeling funds from depositors to investors, and impedingbuild-up of imbalances. For most central banks, defining financial stability rather than itsabsence is likely to be the more useful and avoid biased policy decisions. Another strand of theliterature, largely dominated by academics (Mishkin, 1999; Ferguson, 2003; Allen and Wood,2006; Goodhart, 2006; Borio and Drehmann, 2009) rather prefer to view financial stabilitythrough the lens of the absence of financial instability. These authors therefore focus on a listof potential characterizations of financial instability such as the incapacity of the financialsystem to perform its usual roles, the divergence of an important set of financial assets prices,the domestically or internationally rationing of credit, the emergence of financial distress inresponse to normal-sized shocks. As one example, Borio and Drehmann (2009) define financialdistress as an event in which financial institutions experience substantial losses leading toserious dislocations to the economy. To the extent that, we focus on several financial distresscharacterizations, it seems reasonable to relate this thesis to the latter strand of the literature.

This thesis adresses the issue of financial stability in several important ways. First, we considerdifferent financial instability characterizations. The first Chapter analyzes financial distressepisodes defined as a profound disruption of financial markets whose symptoms include sharpdeclines in asset prices and the failure of financial firms (Eichengreen and Portes, 1987). Thesecond Chapter examines the aggregate failures of the commercial banks and the third Chapterinvestigates the evolution of bank non-performing loans. Second, this thesis contributes to abetter and early identification of forthcoming financial distress episodes by proposing variousforecasting models. These models can be used by the regulatory authorities to monitor thebuild-up of financial imbalances. Third, throughout our work, we adopt an empirical approachwhich is aimed at providing regulatory authorities with workable tools to spot and addressunderlying financial vulnerabilities.

In the first Chapter, we focus on the impact that a harmonized, area-wide tax, often referred toas Tobin Tax could have on the stability of financial markets. We use the framework developedby Demirgüç-Kunt and Detragiache (1998) to identify the determinants of financial crises toa panel dataset of OECD countries over the sample 1973 − 2012. We add to the traditionalexplanatory variables suggested in the literature, a measure of bid-ask spreads in the financialmarkets of each country as a proxy for the likely effect of a securities transaction tax (STT)on transaction costs. We find that higher transaction costs are associated with a higher risk ofcrisis and we document the robustness of this key result to possible endogeneity effects and tothe 2008 − 2009 global crisis episode. To the extent that an STT would increase transactioncosts, the establishment of an STT could increase the risk of financial crises.

In the second Chapter, we model and forecast aggregate commercial bank failures. We constructkey sectoral predictors from the large set of macro-financial variables developed by McCrackenand Ng (2016) for the United States and incorporate them in a hurdle negative binomial modelto predict the number of monthly commercial U.S. bank failures. Our results indicate a strong

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and robust relationship between the factor synthesizing housing industry variables and bankfailures. This suggests a link between the housing sector and the vulnerability of commercialbanks to non-performing loans increases and asset deterioration.

In the third Chapter, we review different models applied in the recent literature for fitting andforecasting U.S. banks non-performing loans (NPLs). We compare the performance of thesemodels to those of similar models that we develop in a data-rich environment. We replacetraditional explanatory variables by key sectoral predictors, all extracted from a large setof potential U.S. macro-financial predictors suggested by McCracken and Ng (2016) for bigdata analysis, that we supplement with additional banking variables. We uncover that data-rich-models all outperform the traditional models. Our results suggest that practitioners andresearchers could consider latent factors in their modeling of NPLs. More specifically, for theU.S. case, we also point out that housing sector, which accounts only for almost 10% of theU.S. banks total loans in average, greatly impacts the evolution of NPLs over time.

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Chapitre 1

Securities Transaction Taxes andFinancial Crises

1.1 Résumé

Ce chapitre étudie l’impact qu’une taxe sur les transactions financières (TTF), comme celleenvisagée par la Commission Européenne, peut avoir sur la probabilité de crises financières.Nous appliquons la méthodologie développée par Demirgüç-Kunt and Detragiache (1998) auxdonnées de pays de l’OCDE, de 1973 à 2012, auxquelles nous ajoutons une mesure du coursacheteur-vendeur, comme proxy de l’impact probable d’une TTF sur les coûts de transac-tions. Nos résultats indiquent que des coûts de transactions élevés sont associés à un risqueaccru de crises financières. Nous montrons la robustesse de ce résultat important aux possibleseffets d’endogénéité et à la crise de 2008 − 2009. Dans la mesure où une TTF pourrait ac-croître les coûts de transactions, ce résultat suggère donc que l’établissement d’une telle taxeaugmenterait les risques de crises financières.

1.2 Abstract

This Chapter studies the impact that a harmonized Securities Transaction Tax (STT), likethe one considered by the European Commission, could have on the likelihood of systemicfinancial crises. We apply the methodology developed by Demirgüç-Kunt and Detragiache(1998) to identify the determinants of financial crises to a panel dataset of OECD countriesover the sample 1973− 2012, adding a measure of bid-ask spreads in the financial markets ofeach country as a proxy for the likely effect of an STT on transaction costs. Our results indicatethat higher transaction costs are associated with a higher risk of crisis and we document therobustness of this key result to possible endogeneity effects and to the 2008−2009 global crisisepisode. To the extent that a widely-based STT would increase transaction costs, our resultstherefore suggest that the establishment of this tax could increase the risk of financial crises.

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1.3 Introduction

Important changes to the global environment for regulating financial markets and institutionshave been undertaken in recent years. These changes, motivated by the 2008-2009 financialcrisis, aim to make financial markets more resilient and lessen the likelihood of systemic crises. 1

In this context, the establishment of a Securities Transaction Tax (STT), an ad-valorem taxon financial transactions, has generated renewed interest. An ongoing policy effort initiatedby the European Commission aims to introduce an area-wide, harmonized version of such atax across the European Union that would have two stated goals : (i) increase the resilienceof European financial markets by complementing other regulatory policies aimed at avoidingfuture crises, and (ii) generate revenue to help share the burden of future support to troubledfinancial institutions (European Commission, 2013). The implementation of the EU STT hasnot proceeded in an orderly fashion, however, because important differences of opinion persistabout its scope, magnitude and general appeal. As a result, 11 EU members have agreed tocontinue discussing a near-future implementation of the tax in their jurisdiction, while othershave not joined these efforts. 2

The present paper contributes to this debate by analyzing the impact that a harmonized, area-wide tax like the one envisaged would have on the stability of European financial markets.Our approach follows the framework introduced by Demirgüç-Kunt and Detragiache (1998)to study the determinants of financial crises and studies a significant panel of countries overa long, consistent historical sample, in order to filter out country and time-specific factors.The approach in Demirgüç-Kunt and Detragiache (1998) is related to an important body ofwork analyzing banking and financial crises in order to identify “early warning” variables –key factors associated with heightened crisis probabilities– signaling developing vulnerabilities(Kaminsky and Reinhart, 1999; Borio and Lowe, 2002; Bussiere and Fratzscher, 2006; Barrellet al., 2010; Schularick and Taylor, 2012; Duca and Peltonen, 2013; Betz et al., 2014).

The extension of Demirgüç-Kunt and Detragiache (1998) that we develop is structured asfollows. First, a binary financial crisis variable is constructed and an empirical logit model forthis variable is formulated. As in the literature, this model includes a wide range of explanatoryvariables potentially associated with the likelihood of crisis. Next, we construct and incorporateto the model a country-specific, time-series measure of transaction costs in financial markets ;this index is meant to proxy for the likely impact of an harmonized STT on transaction costs. 3

We show this proxy to be unrelated to other characteristics of financial markets, like turnoveror volatility, and provide evidence that reverse causation from financial crises to transaction

1. These regulatory changes include increased capital requirements for banks, tighter limits on loan-to-valueratios, and macroprudential policies.

2. Some individual EU members have chosen to introduce their own, country-level version of the tax (France,2012 ; Italy, 2013) even as planning for the harmonized, area-wide one continues.

3. Aliber et al. (2003) and Lanne and Vesala (2010) adopt a similar approach and assess the relationshipbetween a measure of transaction costs and the markets volatility to investigate the likely impact of an STT.

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costs is unlikely. The complete model is then estimated using a panel dataset for the 34 OECDcountries over the sample 1973− 2012.

Our results uncover a positive, statistically and economically significant link between transac-tion costs and the likelihood of financial crisis ; said otherwise, higher transaction costs areassociated with a higher risk of crisis. Benchmark results show that the odds of experiencinga crisis increase by 50 percent following one-standard deviation increase in these costs. Weshow this result to be robust to alternative measures of the crisis, estimation subsamples andthe occurrence of the 2008-2009 global crisis.

This main finding has two important implications : first, it suggests that the “early warning”literature associated with Demirgüç-Kunt and Detragiache (1998), Kaminsky and Reinhart(1999) and Borio and Lowe (2002, 2009) might benefit from adding variables related to tran-saction costs to signal developing or increased vulnerabilities. Second, this finding also suggeststhat to the extent it would induce a general rise in transaction costs for financial trades, theimplementation of a EU-wide STT could increase the likelihood of financial crisis, a resultdistinctly at odds with the effect envisaged by the framers of the EU proposal.

This intriguing result might be interpreted by noting that the establishment of an STT in-creases trading costs for all traders, both informed (rational) investors whose trades serveto stabilize markets and noise traders following ‘positive-feedback strategies’ (DeLong et al.,1990) chasing momentum. If the tax leads more of the former to exit markets than the latter,the tax could lead to the building of financial imbalances (Borio and Lowe, 2002, 2009) thatare precursors of crises. 4

Previous work analyzing the impacts of STTs has most often focused on specific countries,historical episodes, or markets where such taxes were present. In addition, it has concentratedon aspects of financial markets’ performance different from the occurrence of systemic financialcrises, such as trading volumes, individual asset volatility and market liquidity (Jackson andO’Donnell, 1985; Roll, 1989; Umlauf, 1993; Saporta and Kan, 1997; Pomeranets and Weaver,2011; Capelle-Blancard and Havrylchyk, 2016; Becchetti et al., 2014). The present paper the-refore contributes a novel set of results to the literature on the impact of STTs, by using along, historically-consistent and area-wide approach and examining the impact of STTs on thelikelihood of systemic financial crises.

The remainder of this paper is organized as follows. Section 1.4 discusses the theoreticalunderpinnings and available empirical results about STTs and their impact on transactioncosts. It also discusses how they might affect the resilience of financial markets. Section 1.5presents the econometric strategy we employ and Section 1.6 describes the data, providing

4. Relatedly, Friedman (1953) emphasizes the important stabilizing influence of informed traders for ex-change rate markets and Lanne and Vesala (2010) provide empirical evidence that the actions of these tradersmight be reduced by the establishment of a ‘Tobin tax’ in these markets.

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extensive details on how we construct the crisis variable and the proxy for the impact ofSTTs on transaction costs. Section 1.7 presents our results while Section 1.8 documents theirrobustness. Finally, Section 1.9 concludes.

1.4 STT and transaction costs

1.4.1 Securities transaction taxes

Establishing an ad-valorem tax on financial transactions was originally proposed by Keynesto reduce what he considered excess volatility and disruptive speculation in financial markets.The likely macroeconomic and financial impacts of such a tax has been the subject of animportant literature ever since. 5

Proponents of STTs (Tobin, 1978; Stiglitz, 1989; Summers and Summers, 1989) argue thatthese taxes can stabilize financial markets and increase their resilience. These authors suggestthat when a significant fraction of trades in a given financial market reflect non-informedviews or short-term (speculative) investing horizons, excess volatility obtains and leads pricesto diverge from fundamentals. The environment developed by DeLong et al. (1990) reflectsthat view, and assumes the presence of “noise traders” basing their investment decisions onmomentum rather than fundamentals, which amplifies movements in asset prices and increasesvolatility. By discouraging such trades, an STT could therefore stabilize financial marketswithout affecting long-term investors, whose trades reflect fundamentals and thus help betterallocate capital. 6

More skeptical views about the merits of STTs are advanced in Schwert and Seguin (1993),Kupiec (1996), Amihud and Mendelson (2003) and Song and Zhang (2005), among others.These authors remark that an STT increases trading costs and the cost of capital for allinvestors and may have adverse effects when trades beneficial to liquidity and stability arethus discouraged. Kupiec (1996) for example, shows that discouraging trades by informedtraders will accentuate the price-impact of non-informed trading, thus removing a stabilizinginfluence on financial markets. He further shows that return volatility unambiguously increasesfollowing the establishment of an STT because it causes a level-decrease in the average price ofsecurities that trumps any decrease in their volatility. In addition, the environment developedin Song and Zhang (2005) emphasizes the positive impact of fundamentalists on deepeningoverall liquidity and the associated decreases in this liquidity from the establishment of anSTT. Bloomfield et al. (2009) argue that the literature’s conflicted views of what constitutes“noise” trading may explain the lack of clear conclusions. They describe an experimental set-up where two types of “noise” traders co-exist -liquidity traders and uninformed traders–

5. Pomeranets (2012) provides a review of this literature.6. The Commission proposal for the EU-STT reflects this opinion and states that one of the goal of the tax

is to “create appropriate disincentives for transactions that do not enhance the efficiency of financial markets”(European Commission, 2013).

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and report that the establishment of STTs is unlikely to deliver the reductions in volatilityenvisioned by their proponents.

The impact of STTs on financial markets has also generated an important empirical literature.This literature has commonly used difference-in-difference frameworks contrasting the behaviorof assets traded on an exchange subjected to an STT to that of similar assets traded elsewhereand not subjected to the tax. Umlauf (1993), analyzing the STT present in Sweden between1984 and 1986, Pomeranets and Weaver (2011) (the New York state tax between 1932 and1981) and Saporta and Kan (1997) (the UK Stamp Tax, 1963 − 1986) are examples of thisstrategy ; although they all report that these STTs depressed trading volumes significantly,they fail to reach a consensus about their impact on volatility. More recently, the 2012 decisionby France to establish its own, country-specific STT has lead to renewed contributions to thisliterature (Becchetti et al., 2014; Capelle-Blancard and Havrylchyk, 2016; Gomber et al., 2016).Again, these studies uncovered no significant impact of the French STT on volatility, liquidity,or general market quality.

This lack of consensus, and the fact that the empirical literature has not focused on the impactof STTs on systemic vulnerabilities, makes it challenging to judge whether the planned EU-STT can help avoid future crises. Our paper makes a contribution towards this assessment,by explicitly considering whether STTs affect the likelihood of systemic crises, using a well-established methodology to study the determinants of systemic crises (Demirgüç-Kunt andDetragiache, 1998) and verifying if our proxy for the effects of an STT on transaction costs issignificantly related to the occurrence of crises.

1.4.2 Securities transaction costs

Since no harmonized STT currently applies to a large group of countries, a proxy for its effectis developed to test this proposition. One likely effect of the EU-STT would be to increase thegap between prices paid by buyers and those received by sellers of financial assets. We thereforeanalyze the impact of an STT on the probability of crisis by using an index of transactioncosts. We discuss below the conditions under which our index of the naturally dispersion intransaction costs in our data can be linked to the likely impacts of an STT on transactioncosts.

Suppose τ , a round-trip ad valorem tax as the one envisaged by the European Union. Afterintroduction of such a tax, an additional cost of τχ is charged to transfer titles ownership ofany asset i valued at χ. The change in the transacting costs is thus :

∆Costsi = τχ, (1.1)

The literature provides various definition for securities transaction costs (STC) depending onthe transaction activities included, as pointed out by Demsetz (1968) in his seminal paper

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on transaction costs. Transaction costs can be viewed as the total amount paid by agents toacquire ownership of assets and these costs fall into two components : the brokerage commis-sion (BC) and the bid-ask spread (SPRD). The brokerage commission broadly represents feespaid to intermediaries to convey money from investors to market-makers which may be flator proportionate to transaction volumes. 7 The bid-ask spread is the difference between theask (Pa) and bid (Pb) prices of the market-makers and represents the markup charged forimmediate transaction. As an ad valorem tax, the change in transaction costs induced by theestablishment of an STT is more likely to pass through the bid-ask spread than the brokeragecommission. Thus, from the market-maker side, after the establishment of an STT, an extracost of τPbit will be required to purchase an asset i at time t and a supplement of τPait willbe charged to sell the same asset. Consequently, the bid-ask spread is expected to increase byτSPRDit. 8

In order for our proxy to replicate as closely as possible the likely impact of an STT on tran-saction costs, it should ideally load heavily on the asset’s price (its value), and not be affectedby other components affecting the bid-ask spread. It seems then worth to present the maincomponents of bid-ask spread according to theoretical and empirical analyses. The seminalcontribution of Demsetz (1968) identifies inventory costs and the market-maker markup forpredictable immediacy of exchange as the main component of the bid-ask spread. Many theo-retical and empirical contributions following his research (Tinic, 1972; Branch and Freed, 1977;Stoll, 1978; Easley and O’hara, 1987; Glosten and Harris, 1988; Harris, 1994; Bollen et al.,2004) also discuss the importance of informational asymmetry in the bid-ask spread. Bollenet al. (2004) summarizes this research and write the bid-ask spread in the general form :

SPRDit = f(OPCit, IHCit, ASCit, COMPit), (1.2)

where OPC represents order-processing costs, IHC, the inventory-holding costs, ASC, theadverse selection costs and COMP , the competition level. Most empirical works on bid-ask determinants posit a linear function. Hereafter, some evidence on these bid-ask spreaddeterminants on which we will base our assumptions and construct our STC index are reviewed.

Bollen et al. (2004) point out that order-processing costs (OPC) are irrelevant for competitivemarkets. 9 They also show, in a theoretical model, that IHC is proportional to the asset’stransaction value. This finding is empirically confirmed by Tinic and West (1972), Benstonand Hagerman (1974), Tinic and West (1974) and Grant and Whaley (1978). Further, researchon adverse selection costs (ASC) in stock market uncovered important evidence about “smallfirm" and “trade size" effects (Banz, 1981; Reinganum, 1981; Stoll and Whaley, 1983; Easley

7. For some developed stock markets, brokerage commissions may quantitatively be negligible relative toother components of total transaction costs.

8. We assume that all the burden of this tax is transferred to customers. Assuming a tax burden sharedbetween customers, intermediaries and market-makers does not invalidate our strategy, as the bid-ask spreadshould still increase by τ ′SPRD, with τ ′ representing the share of the STT incurred by the market-maker.

9. OPC include exchange seat, floor space rent, computer costs, information acquisition, etc.

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and O’hara, 1987; Amihud, 2002). Small firms are more likely to experience high transactionscosts due to a perception of adverse selection and the trade size is sometimes interpreted as asignal of informational asymmetries. This “trade size" effect is heightened for small firms whosestocks are infrequently traded. Finally, Tinic and West (1972), Benston and Hagerman (1974),Tinic and West (1974) and Grant and Whaley (1978) found a negative relationship betweenbid-ask spread and market competition level. As the level of competition increases, bid-askspread decreases. Our approach to measure markets’ transaction costs will aim at mitigatingthe impacts of all components affecting the bid-ask spread often than those proportionate toasset values.

1.5 Methodology

We adopt the approach developed by Demirgüç-Kunt and Detragiache (1998) and first denoteYit as a binary variable indicating whether country i at time t experiences a crisis (Yit = 1)or not (Yit = 0). A logistic approach is used whereby

Prob(Yit = 1) = F (β′Xit) =eβ′Xit

1 + eβ′Xit, (1.3)

where Xit is a (k · 1) vector of explanatory variables for country i at time t, and β is the(k · 1) vector of associated coefficients. The vector of explanatory variables Xit includes ourconstructed measure of transaction costs (described below) as well as other control variablesused in the literature. Parameters of the model are estimated by maximizing the samplelikelihood

LogL =∑i

∑t

[YitlogF (β′Xit) + (1− Yit)log(1− F (β′Xit))

]. (1.4)

In the data described below, financial crises constitute relatively rare events and some countriesare considered not to have experienced any such crisis during the period reflected by our sample(1973 − 2012). We therefore abstain from including fixed-effects in our logistic approach, toprevent one variable (the fixed effect) to perfectly predict the dependent variable for thecountries with no crisis. 10

In a logistic model like (1.3), the magnitude of a parameter is not the variable’s marginalimpact on probabilities, although the parameter’s sign correctly indicates the direction ofprobability change. Instead, a change in a given explanatory variable has a non-linear impactthat is a function of all other variables and will tend to be smallest for country-period pairswith very low, or very high, initial crisis probabilities. In this context, the economic significanceof our results is assessed by measuring how much a one-standard deviation change in a given

10. This data characteristic is also present in Demirgüç-Kunt and Detragiache (1998), who motivate abs-tracting from fixed effects by a desire to avoid the bias caused if only countries having experienced at leastone crisis are included. They discuss using a probit model with random effects as an alternative, but note thatdoing so would require making the strong assumption that such random effects are uncorrelated with otherregressors.

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explanatory variable Xk modifies the odds of observing a crisis. 11 This is expressed by thelog-change in the odds ratio ∆OR, which is computed as

log∆OR = logProb(Yit = 1|Xitk + 1)

Prob(Yit = 0|Xitk + 1)/Prob(Yit = 1|Xitk)

Prob(Yit = 0|Xitk)= βk, (1.5)

where βk is the coefficient associated with the explanatory variable Xk. A reported value of0.5, say, for βk indicates that a one-standard deviation increase in Xk causes a 50% increasein the odds of experiencing a crisis.

Once a crisis occurs, it may produce an endogenous economic response that includes an in-verse causality loop between our dependent and explanatory variables. To limit the extent ofthis problem, we follow Demirgüç-Kunt and Detragiache (1998) and estimate our model byexcluding all observations from a country that are subsequent to the onset of the first crisishaving affected that country ; this strategy eliminates potential endogeneity and crisis memoryeffects convincingly. Note that our work does not aim at analyzing the severity or duration ofcrises but only to determine factors associated with the eruption of crisis. Consequently, wepurposely consider only contemporaneous variables (Demirgüç-Kunt and Detragiache, 1998).

1.6 Data

Our dataset covers the 34 OECD countries over the period 1973−2012 and the data are at anannual frequency. 12 The dependent variable – the occurrence of a financial crisis – is binaryand takes value 1 if a crisis is experienced and 0 otherwise. The main variable of interest isthe likely impact of an STT on transaction costs. We construct a proxy for this using annualaverages of the bid-ask spreads of large firms in the financial markets for all countries and allperiod-years in our sample. Explanatory variables are from the financial and macroeconomicrealm and are similar to those used in related literature.

1.6.1 Dependent Variable

One influential view for what constitutes a financial crisis characterizes it as a profound dis-ruption of financial markets whose symptoms include sharp declines in asset prices and thefailure of financial firms (Eichengreen and Portes, 1987). To operationalize this definition, weuse historical data on banking crises constructed by Laeven and Valencia (2012), a widely-usedbenchmark measure of banking crises, as well as data on OECD countries’ stock market indexes

11. Since our index of transaction costs, our explanatory variable of interest, is reported in normalized terms,so that a one-unit change reflects a one standard-deviation modification to the underlying variable.12. Restricting the analysis to the relatively homogenous countries comprising the OECD is an appropriate

strategy to assess the EU STT tax, which would apply to a relatively homogenous group of countries similarto the OECD members. In addition, data availability limitations, notably on the bid-ask spreads underlyingour proxy for the STT’s effect on transaction costs, limits our capacity to extend the analysis to a larger setof countries.

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Table 1.1 – Descriptive statistics for the variable “Financial Crisis"

Number of Financial Crises when Defined with Decline in Asset Prices of :Period 20% 50% 0% (Only Banking Crises)

USA Canada OECD USA Canada OECD USA Canada OECD1973− 1980 0 0 0 0 0 0 0 0 31981− 1990 0 0 2 0 0 0 0 0 31991− 2000 0 0 7 0 0 3 0 0 132001− 2011 1 0 19 0 0 12 2 0 19

Total 1 0 28 0 0 15 2 0 38

Source : Authors’ calculations based on Laeven and Valencia (2012) and Datastream data on major stock indexes

from Datastream. Specifically, we define the presence of a financial crisis in a country-year ob-servation when a banking crisis occurs in the country according to Laeven and Valencia (2012)and when the country’s stock markets experience a year-over-year decline at a pre-determinedthreshold (we experiment with declines of 20% and 50%). Considering that an STT wouldarguably affect asset markets as much as the banking sector, we consider it important to usea crisis definition that records disruptions in both sectors.

Requiring that both the banking sector and asset markets experience major disruptions tomeasure financial crises makes them relatively rare events in the OECD data. Table 1.1 showsthat some countries (e.g. Canada) are not considered to have experienced a financial crisisin the 1973 − 2012 period, whereas others (like the United States) are considered to haveexperienced only one. In total, 28 crisis events are recorded for the 34 OECD countries in oursample when the threshold decline in assets prices is 20%, and 15 when a decline of 50% inasset prices is required to define a crisis. 13 To assess the robustness of our results, we alsoestimate our model using only the banking crisis indicator from Laeven and Valencia (2012)(38 crisis events are then recorded, see Table 1.1). Importantly, Section 1.7 shows that ourkey result – a positive association between our STT proxy and the likelihood of crisis – is notaffected by these changes in the measurement of crises.

1.6.2 Explanatory variables

Three explanatory variables from the macroeconomic realm are added : GDP growth, theinflation rate, and a measure of real short-term interest rates. These variables have beenshown to be significantly associated to the occurrence of crisis by the previous literature(Demirgüç-Kunt and Detragiache, 1998; Davis and Karim, 2008; Duca and Peltonen, 2013).Demirgüç-Kunt and Detragiache (1998) provides an intuitive discussion to motivate the linkbetween these variables and banking crises, noting for example that lower levels of economicactivity depress the capital position of banking institutions and high real interest rates hurtthem by affecting the maturity mismatch of bank’ balance sheets. 14

13. The data analyzed by Demirgüç-Kunt and Detragiache (1998) and others similarly feature few crisisevents, even if they study samples of countries not limited to OECD members or cover longer time periods.14. They include other macroeconomic explanatory variables in their analysis (exchange rates, terms-of-

trade, and the fiscal health of governments) but these variables exhibit no statistically significant relation to

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Next, we add three variables controlling for the strength and the depth of a country’s bankingsector : the banks’ operating costs as a ratio of the sector’s income, total bank deposits andtotal liquid bank assets (both expressed in ratios to GDP). These variables have also beenstudied in the literature analyzing the determinants of financial crises ; for instance, Davis andKarim (2008) show that high values of liquid bank assets reduce these vulnerabilities whereasrapid expansions in the bank deposits (money) to GDP ratio increases them.

Finally, the quality and depth of a country’s assets markets are represented by four variables :total stock market capitalization and total value traded (both relative to the country’s GDP),turnover, and intra-period volatility. Once again these variables have been used previously toprovide early warning to future crises, and Borio and Lowe (2002, 2009) notably single outrapid increases in prices as important variables for such purposes. Table 1.2 summarizes allvariables used in the analysis and their source. 15

Table 1.2 – Definition and source of variables

Variable Definition Source

Dependent VariablesBanking Crisis Significant banking system distresses IMFAsset prices declines Annual variation in stock market indexes Datastream

Securities Transactions TaxSTT Index Weighted Average of bid-ask spreads of 30 largest firms DatastreamMacroeconomic VariablesGDP Growth Real GDP growth rate OECDInflation Consumer Price Index growth rate OECDReal Interest Rate Real 3-Month Treasury Bill Rate OECD

Banking VariablesBank Costs Bank Costs as a Ratio of Sector’s Income OECDTotal deposits Deposits in banks relative to GDP OECDLiquid Assets Bank Cash and Liquid Securities to GDP OECD

Stock Market VariablesCapitalization Stock market Capitalization to GDP DatastreamValue Traded Value of Stock Market Transactions to GDP OECDStock Turnover Value of Transactions as a Ratio of Capitalization OECDPrice Volatility Within-Year Standard Deviation of Stock Prices Datastream

the probability of crisis.15. Intra-period volatility refers to the intra-year, monthly standard deviation of the stock market index and

is therefore conceptually different from the year-over-year change we use to define a financial crisis. A stockmarket’s index could be volatile during a given year even though its year-over-year change is null.

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1.6.3 STT index

Assumptions

As a result of the emergence over the last decades of the Internet and technological advanceslike real-time stock market investing phone applications, the intermediation costs and brokercommissions components of intermediation costs have sharply decreased. We therefore assumeBCit to be negligible for all i, t. Given that the establishment of a securities transaction tax isnot aimed at affecting the broker commission (as the tax does not affect the broker commis-sion), abstracting from BCit in the design of our index appears natural. In our analysis, weregard OECD countries stock market as sufficiently developed to be able to assume, followingBollen et al. (2004), that order-processing costs and competition do not affect the bid-askspread, ie.

∂SPRDit

∂OPCit=∂SPRDit

∂COMPit≈ 0. (1.6)

In other words, OECD countries’ stock markets are sufficiently competitive to eliminate in-efficiency and operate at marginal costs. At this stage and after having eliminated BC, OPCand COMP, we can rewrite the securities transaction costs from (1.2) as

STCit = a2IHCit + a3ASCit + εit. (1.7)

As argued above, IHCit closely reflects asset values χ and ASCit is the premium charged forinformational asymmetry, particularly relevant for small firms. To ensure that our STT indexis not contaminated by such asymmetry, we therefore consider only large firms in the creationof our proxy so that our data reflects the following formula

STCit = a2χ, (1.8)

where χ again represents assets values. Comparing (1.8) and (1.1) shows that under ourmaintained assumptions, the dispersion in transactions costs present in our data is similar inspirit to the changes in such costs that the establishment of an STT would entail. As such, theimpact of our transaction cost index on the likelihood of crisis can be interpreted as reflectingthe potential impact of an STT on this likelihood.

Construction

We compute an average of the bid-ask spreads on the thirty largest publicly-traded companiesof every country in our sample, weighted by capitalization, for each period-year in our sample.Our proxy for country i at time t is thus constructed as

STCit =∑j

Djit

Dit(PAjit − PBjit

PBjit), (1.9)

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where Djit is firm j’s capitalization and Dit is the aggregate market capitalization for all firmsconsidered of country i in year t. 16 Over the complete sample, average computed transactioncosts stand at 1.7% while the within-country but across time average is 2.4%. Considerableheterogeneity exists in the index : the average figures for the United States and Canada arerelatively low (0.2%) while corresponding figures for countries like Sweden and Denmark aresignificantly higher. Before proceeding with our estimation, we verify our STC index is notaffected by adverse selection, reverse causation (running from crisis to the STC index) andnot driven by the 2009 global crisis episode.

Robustness of our measure

Adverse selectionAs discussed above, bid-ask spreads typically encompass a premium for adverse selection,which we have aimed to mitigate in the construction of our index. Stoll and Whaley (1983),Easley and O’hara (1987) found significant relationships between adverse selection and va-riables like price volatility, transaction turnover, value traded and market capitalization. Weempirically verify that adverse selection does not affect our transaction costs measure by re-gressing our index on these markers of adverse selection. Table 1.3 shows that no significantrelationship is present, which suggests that our index is exempt from influences owing toadverse selection.

Table 1.3 – Index of transaction costs and adverse selection markers

Marker of adverse selection Adj. R2 (%) Coef. p-value

Price Volatility 0.00 0.00 0.94Transaction Turnover 0.54 -0.09 0.12Value Traded/Mkt Cap. 0.00 0.00 0.84

Note : the table reports the results of regressing our index of transaction costs on three markers of informationalasymmetry like adverse selection.

Reverse causationWe now investigate further our index of transaction costs by considering whether reversecausation, by which the occurrence of a financial crisis would cause higher transaction costs,may affect the index. Following Furceri and Mourougane (2012), we estimate the equation

STCi,t = αi +4∑j=1

βjSTCi,t−j +4∑

k=1

δkDi,t−k + ei,t, (1.10)

where Di,t−k indicates whether country i has experienced a crisis or not in the past years.We consider an unbalanced panel data from 1987 to 2012 for 20 OECD countries. We includefour lags of each explanatory variables as in Furceri and Mourougane (2012). 17 As Table 1.4

16. Companies are added or deleted from the index for each country as their market capitalization evolvesthrough time.17. Including additional lags does not qualitatively change the findings.

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indicates, we uncover no significant relationship between past occurrences of financial crisesand current values of STT index. Our index of transactions costs thus does not appear to bestatistically linked to our financial crises measure, once the influence of their own past valuesis taken into account.

Table 1.4 – Index of transaction costs and tests of reverse causation

(1) (2) (3)

STT Index (t− 1) −0.37 0.10 *** −0.36 0.10 *** −0.35 0.10 ***

STT Index (t− 2) −0.38 0.10 *** −0.37 0.10 *** −0.37 0.10 ***

STT Index (t− 3) −0.34 0.11 *** −0.33 0.10 *** −0.33 0.10 ***

STT Index (t− 4) −0.27 0.10 ** −0.27 0.10 *** −0.27 0.10 ***

Crisis (t− 1) 0.01 0.01 0.00 0.02 −0.00 0.01Crisis (t− 2) 0.00 0.01 0.00 0.01 0.00 0.01Crisis (t− 3) 0.00 0.01 0.00 0.01 0.00 0.01Crisis (t− 4) 0.00 0.01 0.00 0.01 0.00 0.01Adj. R-Sq.(%) 13.87 13.49 13.46

Note : Regression of our index of transaction costs on its past values and past crises (Furceri and Mourougane, 2012).Standard errors are in italic. Symbols ∗,∗∗ and ∗∗∗ indicate statistical significance at 10%, 5% and 1% level. Results (1),(2) and (3) are arrived at with the different measures of the dependent variables described in Section 1.4.1.

As a synthesis, we consider both theoretical and empirical evidence to construct an indexaimed at reflecting the likely impact of an STT on transaction costs. The assumptions wemake, may in fact underestimate the true incidence of an STT. 18 Indeed, although small,brokerage commissions and order-processing costs do apply and increase transaction costs.Furthermore, STTs may also amplify adverse selection premia, especially in periods of turmoil.Insofar as we purposely purged our index from these components, the evidence we uncovermay downplay the effective impact of the imposition of an STT on transaction costs.

1.7 Results

Table 1.5 presents our estimates of the likelihood (1.4) according to several specifications.Recall that in our sample, all data subsequent to the first crisis experienced by a countryare deleted. The specifications analyzed incorporate first the STT index (column 1), then theexplanatory variables (macroeconomic, banking or financial) one block at the time (columns2-4) or simultaneously (columns 5-7). Table 1.5 reflects results arrived at with the benchmarkcrisis measure (a crisis is defined by the presence of a systemic banking crisis and a declineof 50% in asset prices), but we verify the robustness of our results to this assumption below.The key results in Table 1.5 concern the impact of the STT proxy on the likelihood of crises.

18. Note that the design of our index is in line with a strand of the literature favoring a measure of transactioncosts based on bid-ask spreads (Schultz, 1983; Stoll and Whaley, 1983; Glassman, 1987; Aliber et al., 2003;Lanne and Vesala, 2010).

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Table 1.5 – Results from estimation of the likelihood (1.4)

(1) (2) (3) (4) (5) (6) (7)

Trans. CostsSTT Index 0.4 0.1 ** 0.4 0.2 ** 0.5 0.2 ** 0.4 0.2 *** 0.4 0.2 ** 0.5 0.3 * 0.5 0.2 **

Macro. Var.GDP Growth — — — −0.9 0.4 *** — — — — — — −0.2 0.4 −1.0 0.4 ** 0.3 0.6Inflation — — — −0.4 4.9 — — — — — — −6.4 7.7 0.1 5.8 −4.7 8.7Real Interest Rate — — — 0.1 0.4 — — — — — — −0.2 0.6 0.7 0.5 −0.7 0.8

Bank. Var.Bank Costs — — — — — — 0.0 0.4 — — — — — — −0.1 0.4 — — —Total Depostis — — — — — — −3.3 3.5 — — — — — — −3.6 3.6 −10.2 5.9 *

Liquid Assets — — — — — — 3.1 3.3 — — — — — — 3.3 3.4 11.7 5.8 **

Stck. Mkt. Var.Capitalization — — — — — — — — — −2.3 1.1 ** −2.5 1.2 ** — — — −6.2 2.7 **

Value Traded — — — — — — — — — 1.9 1.1 * 1.9 1.1 * — — — 4.1 2.1 *

Stock Turnover — — — — — — — — — −1.1 1.0 -1.2 1.0 — — — −2.8 1.8Price Volatility — — — — — — — — — 0.7 0.2 *** 0.7 0.2 *** — — — 0.8 0.3 ***

N. Obs 287 266 188 262 246 179 217Dev. Expl.(%) 5.8 14.8 12.5 41.5 43.2 24.8 51.4Success Rate (%) 97.2 97.0 96.8 97.3 97.2 96.7 96.7Accuracy (%) 100 100 100 66.7 66.7 100 60Sensibility (%) 11.1 11.1 14.3 44.4 44.4 14.3 37.5

Notes : Standard errors are in italic. Symbols ∗,∗∗ and ∗∗∗ indicate statistical significance at 10%, 5% and 1% level.

The estimated coefficients are positive, have stable magnitude across the table and are statisti-cally significant. They indicate that a rise in the proxy for transaction costs is associated witha higher risk of financial crisis. In addition, the results are economically significant : column(7) of the table, our benchmark for discussion below, notably reports that a one standarddeviation change in the transaction cost index leads to a 50 percent increase in the odds ratio.These results suggest that the EU-STT could reduce the resilience of European financial mar-kets and increase their vulnerability to financial crises, an outcome at odds with the intent ofthe policy.

This intriguing result may be interpreted as follows. As discussed in Section 1.4.2, the esta-blishment of an STT increases transactions costs for all types of traders, both noise traderswhose transactions may favour the emergence of financial vulnerabilities and rational (funda-mental) traders that stabilise markets by buying when prices are low and selling when they arehigh (Friedman, 1953). If the STT entails a shift in the composition of these traders, perhapsbecause more rational (fundamental) traders exit relative to noise traders, the price impact ofnoise-traders’ transactions might increase and mean-reverting mechanisms guiding prices backto fundamentals might decline. In addition, transaction cost increases following the introduc-tion of an STT may trigger a shift in noise traders’ demand, towards cheaper and riskier ones.As discussed in Black (1986), some noise traders base transactions on mistaken information(noise) but others may trade because of its consumption (“fun”) value. The former may bediscouraged by the establishment of an STT but not the latter for whom, sound but expensiveassets might just become less attractive. This shift from sound assets towards cheaper and

17

weaker ones may increase vulnerabilities. 19

The results in Table 1.5 also indicate that other macroeconomic and financial variables im-portantly affect the probability of crisis. Among them, GDP growth is estimated to reducethe probability of crisis in a sizeable and statistically significant fashion, a result that confirmsthose in previous contributions to the literature on crisis prediction (Demirgüç-Kunt and De-tragiache, 1998; Kaminsky and Reinhart, 1999; Davis and Karim, 2008). Similarly, high realinterest rates are also associated with increased vulnerability to crises. Interestingly, the es-timated impact of the rate of inflation is not significant, in contrast to Demirgüç-Kunt andDetragiache (1998). This might be related to the fact that our dataset covers the relatively ho-mogenous countries forming the OECD and inflation was well-anchored in most such countriesduring a large proportion of the years covered by our sample. 20 Estimates for the bankingvariables have the signs predicted by the literature. For instance, higher bank costs are asso-ciated with poorer resilience of financial markets. However, these estimates most often lackthe statistical significance exhibited by the macroeconomic variables discussed above. Thismight stem from the relatively wide scope of our definition for financial crises, which requiresboth banking and asset markets to experience challenging conditions before a crisis is defined.Finally, the impact of some asset and stock markets variables is significant, notably marketcapitalization as a ratio of GDP and value traded, again as a ratio to GDP : increased ca-pitalization is linked to a lower probability of crisis, perhaps reflecting depth and liquidity,whereas large values for value traded indicate vulnerabilities to crises, possibly resulting fromexcessive growth in prices. Intra-period price volatility is also very significant and its posi-tive association with systemic crisis confirms theoretical and empirical work that focuses ona strong relation between higher volatility and financial turmoil (Umlauf, 1993; Jones andSeguin, 1997; Pomeranets and Weaver, 2011)

Four criteria measure model performance. First, “Deviance explained” is a goodness-of-fitmeasure assessing the value-added of the model in explaining crises relative to a constant-onlyspecification. The next three measures, – the “Success”, “Accuracy” and “Sensibility” rates –index the model’s capacity to correctly classify events. To construct them, for each country-period pair, we consider the model’s in-sample prediction to be Yit = 1 (a crisis event) ifF (β′Xit) ≥ 0.5 and Yit = 0 (a non-crisis event) if F (β′Xit) < 0.5. Using this prediction,the “Success Rate” is the fraction of times the model correctly predicts realized events, the“Accuracy” rate is the fraction of times the model was correct in predicting a crisis and the“Sensibility” rate is the proportion of realized crises correctly predicted by the model ; as such,“Accuracy” controls for type-II errors while “Sensibility” encompasses errors of type-I. Thefour criteria all indicate a good in-sample fit of our model : our baseline result in column 7of the table notably indicates high goodness of fit (52%) and strikes a good balance between

19. Liu et al. (2016) point out the sensitivity of investors to transaction costs in their stock selection.20. Using data from developed countries, Schularick and Taylor (2012) also fail to statistically associate

inflation to financial crises.

18

Figure 1.1 – Probability of crises according to the model

0.00

0.25

0.50

0.75

1.00

DE

08

GR

08

HU

91

HU

08

IS 0

8

IL 7

7

IT 0

8

KR

97

LU 0

8M

X 8

1M

X 9

1

NL

08

NO

91

NO

08

Crisis Probability

DE – Germany, GR – Greece, HU – Hungary, IS – Iceland, IL – Israel, IT – Italy, KR – Republic ofKorea, LU – Luxembourg, MX – Mexico, NL – Netherlands, NO – Norway

accuracy and sensibility. Figure 1.1 evaluates this performance graphically, by depicting thein-sample prediction of crises probability for some of the crisis episodes in our sample : itshows that our model captures well the majority of crises depicted.

Overall we interpret our results as confirming previous literature on the impact of variousmacroeconomic and financial variables on the risk of crisis, on the one hand, while puttingforward the new result that our index of transaction costs, proxying for the likely impact ofan STT, lowers resilience and increase that risk.

1.8 Robustness analyses

1.8.1 Alternative crisis definition

Our first robustness check involves the definition of financial crises. We re-estimate our modelto gauge how a less stringent definition of crisis could have on our results. In this context, Table1.6 reports results arrived at when the decline in asset prices necessary to define the presenceof a financial crisis is lower (20%) and Table 1.7 reports results obtained when banking crisessolely define the occurrence of crisis. Both tables shows that our results are also robust tothese alternative definitions : notably, the estimated coefficient associated to transaction costscontinues to be positive and statistically significant in most cases.

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Table 1.6 – Robustness I : lower threshold for asset price decline (20%) in crisis definition

(1) (2) (3) (4) (5) (6) (7)

Trans. CostsSTT Index 0.3 0.2 * 0.4 0.2 * 0.3 0.2 * 0.4 0.2 ** 0.5 0.2 ** 0.9 0.6 * 0.6 0.3 **

Macro. Var.GDP Growth — — — −2.1 0.5 *** — — — — — — −2.2 0.7 *** −4.2 1.2 *** −2.5 1.0 ***

Inflation — — — — — — — — — — — — 6.2 6.6 12.9 10.1 13.7 11.5Real Interest Rate — — — — — — — — — — — — 1.3 0.8 0.5 0.5 1.6 0.8 *

Bank. Var.Bank Costs — — — — — — — — — — — — — — — 0.9 0.5 ** — — —Total Depostis — — — — — — 0.6 2.0 — — — — — — 0.4 0.4 1.4 4.0Liquid Assets — — — — — — −0.4 2.0 — — — — — — — — −0.8 4.2

Stck Mkt. Var.Capitalization — — — — — — — — — −1.2 0.8 0.0 0.8 — — — — — —Value Traded — — — — — — — — — 1.2 1.0 0.3 1.0 — — — 0.4 0.8Stock Turnover — — — — — — — — — −0.6 0.8 0.0 0.8 — — — −0.0 0.8Price Volatility — — — — — — — — — 1.3 0.3 *** 1.7 0.5 *** — — — 1.8 0.5 ***

N. Obs 227 220 191 209 194 140 166Dev. Expl.(%) 2.3 24.1 3.5 46.4 60.4 53.3 64.6Success Rate (%) 93.8 94.1 93.2 95.7 96.4 95.0 97.6Accuracy (%) 0 66.7 0 85.7 81.8 83.3 84.6Sensibility (%) 0 14.3 0 42.9 64.3 45.5 84.6

Notes : Standard errors are in italic. Symbols ∗,∗∗ and ∗∗∗ indicate statistical significance at 10%, 5% and 1% level.

Table 1.7 – Robustness II : crisis defined by banking crises (Laeven and Valencia, 2012) only

(1) (2) (3) (4) (5) (6) (7)

Trans. CostsSTT Index 0.3 0.2 * 0.4 0.2 * 0.3 0.2 * 0.4 0.2 ** 1.0 0.4 ** 1.0 2.1 0.4 0.6

Macro. Var.GDP Growth — — — −1.9 0.6 *** — — — — — — −3.8 1.5 ** −6.2 2.6 ** −3.5 1.3 ***

Inflation — — — — — — — — — — — — 12.2 9.5 7.8 20.7 −12.9 12.4Real Interest Rate — — — 0.0 0.4 — — — — — — 3.1 1.6 * 0.6 1.5 −0.1 0.8

Bank. Var.Bank Costs — — — — — — — — — — — — — — — 2.0 1.2 * — — —Total Depostis — — — — — — −0.2 2.1 — — — — — — 0.9 5.5 1.3 4.4Liquid Assets — — — — — — 0.5 2.1 — — — — — — −0.0 5.3 0.9 4.9

Stck. Mkt. Var.Capitalization — — — — — — — — — −0.5 0.9 2.3 1.2 ** — — — −3.4 1.7 *

Value Traded — — — — — — — — — 0.6 0.9 −1.2 1.2 — — — 2.9 1.1 ***

Stock Turnover — — — — — — — — — −0.3 0.8 2.3 1.3 * — — — −0.7 0.9Price Volatility — — — — — — — — — 1.2 0.3 *** 3.1 1.2 *** — — — — — —

N. Obs 193 177 165 178 166 117 144Dev. Expl.(%) 2.7 25.4 5.4 41.6 75 72.4 62.5Success Rate (%) 94.3 94.9 93.9 96.1 96.4 97.4 97.2

Accuracy (%) 0 100 0 83.3 77.8 85.7 87.5Sensibility (%) 0 18.2 0 45.5 63.6 75 70

Notes : Standard errors are in italic. Symbols ∗,∗∗ and ∗∗∗ indicate statistical significance at 10%, 5% and 1% level.

1.8.2 Unobserved country-specific risks

Although OECD countries, as a group of developed economies, share many macro-financialcharacteristics, important unobserved heterogeneity may subsist. Consequently, we consider avariable that may proxy for unobserved country-specific risk, ie the financial openness. Finan-

20

cial openness conditions stock markets’ depth and quality, and may lead different reactions tocommon exogenous shocks (Canada, for instance, was less affected than other OECD countriesby the subprime crisis). To control for financial openness, we include in our model the financialopenness index developed by Chinn and Ito (2008). This index is based on the InternationalMonetary Fund’s Annual Report on Exchange Arrangements and Exchange Restrictions andis decreasing along with the financial openness. Due to possible collinearity between “PriceVolatility" and “Financial Openness", we abstain from including “Price Volatility" in thisestimation. Note that since the index developed by Chinn and Ito (2008) is decreasing withfinancial openness, results in Table 1.8 (where the estimated coefficient related to opennessis positive across all the specifications) suggest that financial openness contributes to preventfinancial crises, perhaps because foreign capital can provide liquidity of last resort in periodof crisis.

Table 1.8 – Robustness III : sensitivity to country-specific financial openness (Chinn and Ito,2008)

(1) (2) (3) (4) (5) (6) (7)

Trans. CostsSTT Index 0.3 0.1 ** 0.3 0.2 ** 0.5 0.2 ** 0.3 0.2 * 0.3 0.2 * 0.4 0.2 * 0.3 0.2 *

Macro. Var.GDP Growth — — — −1.2 0.4 *** — — — — — — −0.6 0.4 −1.4 0.5 *** −0.8 0.5Inflation — — — 3.4 4.9 — — — — — — 6.5 6.3 17.3 8.4 ** 16.0 9.3 *

Real Interest Rate — — — 0.6 0.5 — — — — — — 0.6 0.6 1.4 0.7 ** 0.9 0.7

Bank. Var.

Bank Costs — — — — — — 0.0 0.3 — — — — — — — — — — — —Total Depostis — — — — — — −2.8 4.2 — — — — — — −1.4 3.4 2.0 1.0 **

Liquid Assets — — — — — — 2.4 3.7 — — — — — — 2.3 3.2 — — —

Stck. Mkt. Var.Capitalization — — — — — — — — — −3.4 1.1 *** −3.3 1.3 ** — — — −3.9 1.9 **

Value Traded — — — — — — — — — 3.1 1.0 *** 3.1 1.2 *** — — — 3.3 1.6 **

Stock Turnover — — — — — — — — — −2.2 0.9 ** -2.3 1.1 ** — — — −2.6 1.3 **

Financial Openness 3.5 3.3 5.5 3.9 3.1 3.2 5.6 3.9 8.2 4.4 * 9.3 4.7 9.8 4.8 **

N. Obs 256 237 175 246 231 204 207Dev. Expl.(%) 10.3 21.8 15.0 30.6 35.4 27.5 37.7Success Rate (%) 96.9 96.2 96.6 96.3 96.1 96.6 96.6Accuracy (%) 100 50 100 50 50 100 100Sensibility (%) 11.1 11.1 14.3 11.1 11.1 12.5 12.5

Notes : Standard errors are in italic. Symbols ∗,∗∗ and ∗∗∗ indicate statistical significance at 10%, 5% and 1% level.

1.8.3 Countries selection bias and contagion effects

Country-specific selection bias may be present when important countries drive the results. Were-estimate the model after having removed some countries of economic importance to assesstheir impact. Table 1.9 presents the results we arrive at with the Benchmark specificationof the model when we remove some countries from the sample. We successively remove fromour sample (1) the United States (U.S.), (2) the U.S. and the United Kingdom (U.K.), (3)the U.S, the U.K. and Japan, (4) the U.S, Canada and Mexico (North American countries),(5) the U.K., Germany, France and Italy, (6) Australia, Japan, Korea and New Zealand, (7)

21

the North American countries and western European countries removed in (5). By removingthese countries, the results are less likely to be impacted by the contagion effect of crises. Thisexperiment also controls for the Asian crises in the late 1990. Our key results remain robustto these additional tests. Overall therefore, our proxy for the STT is found to be positivelyassociated to the likelihood of crisis and this effect is most often statistically significant andeconomically meaningful.

Table 1.9 – Robustness IV : countries selection

(1) (2) (3) (4) (5) (6) (7)

Trans. CostsSTT Index 0.6 0.3 ** 0.5 0.3 * 0.5 0.3 * 0.5 0.3 * 0.6 0.3 * 0.6 0.3 ** 0.7 0.5

Macro. Var.GDP Growth −0.8 0.5 −0.7 0.5 −0.7 0.5 ** −1.5 0.5 *** −0.5 0.6 * −0.8 0.5 −1.6 0.7 **

Inflation 0.7 5.9 −3.6 7.2 −3.7 7.3 12.0 7.67 −5.9 8.7 −0.0 6.3 3.6 11.3Real Interest Rate 0.6 0.6 −0.3 0.6 0.4 0.6 1.0 0.5 ** 0.3 0.7 0.7 0.6 0.2 0.7

Bank. VariablesBank Costs −0.1 0.4 0.1 0.5 0.1 0.5 0.1 0.3 0.2 0.5 −0.2 0.4 0.5 0.6Liquid Assets 0.2 0.4 −0.1 0.4 — −0.1 0.4 −0.1 0.4 −0.0 0.4 0.2 0.3 −0.7 0.6

Stck. Mkt. Var.Value Traded −0.1 0.6 −0.4 0.8 *** −0.4 0.8 0.2 0.5 −0.9 0.3 −0.1 0.7 — −0.9 1.5Stock Turnover 0.3 0.7 −0.3 0.9 *** −0.3 1.0 −0.2 0.7 0.2 0.8 0.2 0.8 — −1.3 1.4Price Volatility 0.6 0.2 ** 0.4 0.2 * 0.4 0.2 * — — 0.5 0.3 ** 0.5 0.2 — —

N. Obs 186 174 172 169 151 164 129Dev. Expl.(%) 34.6 32.9 32.7 29.3 36.4 34.0 37.5Success Rate (%) 96.2 96.0 96.2 94.7 96.0 95.1 94.6Accuracy (%) 60 50 96.0 33.3 50,0 50.0 33.3Sensibility (%) 37.5 28.6 28.6 12.5 33.3 25.0 16.7

Standard errors are in italic. Symbols ∗,∗∗ and ∗∗∗ indicate statistical significance at 10%, 5% and 1% level.

1.9 Conclusion

Proponents of the EU securities transactions tax (STT) have argued that it has the potential todiscourage uninformed and disruptive trading and help reduce the likelihood of financial crises.Using a logistic approach and a panel dataset covering the period 1973− 2012 for the OECDcountries and after including control variables from macroeconomic and financial realms, weshow that a proxy for the likely impact of an STT on transactions costs is positively associatedwith the occurrence of crisis, suggesting that such a tax could increase, rather than decrease,the risk of financial crisis. This effect is present in several empirical specifications analyzed andis economically meaningful. This result may suggest that the establishment of an STT maylead to more rational traders exiting markets or reducing their activities than noise traders andpossibly encourage a shift towards cheaper (riskier) assets, increasing vulnerabilities. Our workis thus an important contribution to the debate on the likely effect of an STT and provides aninteresting complement to the empirical literature analyzing the determinants of financial andbanking crises with the objective of developing “early-warning” models of vulnerability (Borioand Lowe, 2002; Demirgüç-Kunt and Detragiache, 2005; Duca and Peltonen, 2013).

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Chapitre 2

Monitoring Bank Failures in aData-Rich Environment

2.1 Résumé

Ce chapitre développe un modèle de prévision des faillites bancaires aux États-Unis. Nousconstruisons des facteurs sectoriels à partir d’une grande base de données macro-financièresproposée par McCracken and Ng (2016) que nous incorporons dans un modèle à variablediscrète afin de prédire le nombre de faillites bancaires mensuelles aux États-Unis. Nous éta-blissons un lien significatif et robuste entre le facteur construit à partir des variables issues dusecteur immobilier et les faillites bancaires. Ce résultat suggère l’existence d’une relation entrel’évolution du secteur immobilier et la vulnérabilité des banques commerciales aux créancesen souffrance et la dépréciation des actifs. Nous examinons différentes spécifications de nosmodèles qui confirment la robustesse de nos résultats.

2.2 Abstract

This Chapter develops a monitoring and forecasting model for aggregate commercial bank fai-lures in the United States. We extract key sectoral factors from the large set of macro-financialvariables proposed by McCracken and Ng (2016) and incorporate them in a hurdle negative bi-nomial model to predict the number of monthly commercial bank failures. We uncover a strongand robust relationship between the factor synthesizing housing industry variables and bankfailures. This relationship suggests the existence of a link between developments in the housingsector and the vulnerability of commercial banks to non-performing loans increases and assetdeterioration. We assess different specifications of our model to confirm the robustness of ourresults.

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2.3 Introduction

Banking crises and other episodes of distress in financial markets have important macroecono-mic consequences : they cause disruptions in the flow of credit, enhance risks of corporate orpersonal failures, lead to output losses relative to trend and to sharp declines in tax revenuesand other measures of the fiscal health of governments. The 2007-2009 subprime crisis hasreaffirmed this fact and caused significant and worldwide economic damage. 1

Considering the costs they generate, an important body of work has long sought to analyzebanking and financial crises and identify “early warning” variables –key factors associatedwith heightened crisis probabilities– signaling developing vulnerabilities. This body of work,originating in contributions such as Demirgüç-Kunt and Detragiache (1998), Kaminsky andReinhart (1999) or Borio and Lowe (2002), has been energized by the recent subprime eventsand has grown exponentially since. 2

One recurring challenge to this literature is the correct definition by which the presence ofa banking or financial crisis should be measured. As such events often stem from differentcauses, develop at differing speeds and have different lengths, it is perhaps unavoidable thatthey be identified with subjective criteria. One well-used database (Laeven and Valencia,2013) identifies banking crises as a dummy variable that takes the value 1 when “significantsigns” of financial distress in banking systems are observed, such as bank runs, losses andbank liquidations, or “significant banking policy interventions”. This is related to Reinhartand Rogoff (2013)’s measure, which codes the presence of a banking crisis by the occurrenceof bank runs or when government assistance, closure, merging and other large-scale regulatoryactions are taken. Other measures include threshold-based quantitative signals of distress,in additions to bank run, to identify banking crises : Demirgüç-Kunt and Detragiache (1998,2005) notably add the presence of abnormally high ratios of nonperforming asset in the bankingsystem as crisis signal.

The present paper provides an original and complementary contribution to the literature stu-dying banking crises and financial distress. We develop a count-data framework to analyze themonthly aggregate number of bank failures in the United States. This has several advantagesover the rest of the literature. First, using the number of bank failures as the proxy for cri-sis provides a complementary measure to the qualitative (binary) alternatives used elsewhere(Reinhart and Rogoff, 2013; Demirgüç-Kunt and Detragiache, 1998). Second, the monthlyavailability of our measure allows our monitoring framework to provide a finer, high-frequencyand real-time tool providing early insights about underlying financial threats to regulatory

1. Reinhart and Rogoff (2013) and Laeven and Valencia (2013) present assessments of the fiscal conse-quences of banking crises. In addition, Laeven and Valencia (2013) document the extent to which economiessuffer output and bank equity losses following such crises. See also (Hutchison and McDill, 1999).

2. A non-exhaustive review of recent contributions to this field includes Bussiere and Fratzscher (2006),Davis and Karim (2008), Borio and Lowe (2009), Barrell et al. (2010), Barrell et al. (2010), Duca and Peltonen(2013) or Betz et al. (2014).

24

authorities. Finally, a framework to monitor and predict the aggregate occurrence of bank fai-lures in the United States is interesting in its own right, particularly for institutions, such asthe Federal Deposit Insurance Corporation (FDIC), whose mandate includes such monitoringresponsibilities.

More specifically, we employ a hurdle-negative binomial model to analyze the number ofmonthly commercial bank failures. This extension of the standard Poisson process for countdata allows our analysis to accommodate the high frequency of zero counts (an absence ofbank failures) and the high dispersion in our data. The explanatory variables are drawn fromthe McCracken and Ng (2016) database, which includes more than one hundred differentmacro-financial variables, to which we add several banking sector variables.

Using such a large dataset has the advantage that most available information relevant tothe study of bank failures occurrences should be included. However, it poses some practicalchallenges in the estimation process, as standard estimation and inference techniques loseefficiency when employed on such a big group of explanatory variables. To circumvent thesechallenges, an established literature has analyzed and documented the ability of a few keyfactors extracted from larger databases to outperform more standard estimation frameworks(Stock and Watson, 2002a,b, 2006; Bai and Ng, 2008). One rationale behind this approachlies in the inability of only a handful of variables to uncover the multiple signals from thelarger economy (Ludvigson and Ng, 2009). To the best of our knowledge, our work is thefirst contribution to employ a factor-based framework to analyze banking crises and financialdistress.

Our results indicate that the factor related to the housing industry contains the most robust,statistically and economically meaningful information about future bank failures. This leadingresult confirms some previous findings in related research that have theorized a pattern linkingthe housing sector to bank failures (Barrell et al., 2010; Bernanke, 2013; Ghosh, 2015). Boomsand busts in housing sector generally go together with expansion and contraction in bankingactivities. During boom periods, home values go up, banks ease lending, refinancing and mort-gage terms, thus increasing their exposure to loan defaults. As an economy experiences shiftsin market conditions characterized by house price decreases and rising interest and mortgagerates, many households find themselves struggling to face their contractual obligations anda surge in mortgage defaults obtains, which may rapidly spread to other types of bank as-sets, such as credit card or car loans, leaving hence banks struggling with increased levels ofnon-performing loans and making them vulnerable to failure.

Our results also identify factors related to production, labor markets, interest rates and mo-ney variables as important forecasters for bank failures. Factors related to output growth(Demirgüç-Kunt and Detragiache, 1998; Kaminsky and Reinhart, 1999; Louzis et al., 2012)and low unemployment rates (Louzis et al., 2012; Ghosh, 2015) are negatively associated with

25

bank failures, as a dynamic economy usually enjoys a boyuant housing sector, while accom-modating monetary policies encourage banks to offer more loans. However, the statisticalsignificance of these other predictors appears irregular across our different experiments withforecasting horizons and other model specifications, while the result about the capacity ofhousing variables is robust throughout.

Our work is a broad contribution to the literature on banking crises and is more specificallyrelated to two strands of this literature. On the one hand, our work contributes to the studyof the determinants of bank failures. In that context, our monthly-data framework provides aclear improvement, for monitoring purposes, to previous papers that used annual data on bankfailures and only a few explanatory variables (Davutyan, 1989; Herger, 2008). On the otherhand, to the extent that the aggreagate number of bank failures respresents an alternativeproxy measure of banking crises, our paper relates to West (1985), Wheelock and Wilson(2000) and Canbas et al. (2005), who analyze the potential of factor models for explainingbanking and financial crises. We extend the scope of these works by considering a large set ofmacro-financial variables and by modeling explicitly the number of bank failures.

The rest of this paper is organized as follows. Section 2.4 briefly reviews the theoretical litera-ture on the determinants of bank failures. Section 2.5 describes the data. Section 2.6 presentsthe econometric framework and Section 2.7 the results. Section 2.8 concludes.

2.4 Determinants of bank failures

Monitoring of financial systems is one key task of regulatory authorities. This literature hasidentified three broad categories of determinants for bank failures : bank-specific, industry-specific and national determinants. We hereafter briefly review these three categories.

Among all bank-specific factors alleged to underlie bank failures, “bad management" is seen asplaying a major role (Berger and DeYoung, 1997; Salas and Saurina, 2002; Podpiera and Weill,2008). Profit-seeking banks encourage managers to take innovative actions that may sometimeslead to poor credit scoring, spurious collateral appraisal, inadequate borrowers monitoring andoverall bad loan quality. Moreover, a lack of diversification in banking activities may exacerbatethese problems. Usually proxied by the proportion of non-interest income as a share of totalincome, diversification is expected to be negatively related to non-performing loans. Finally,insufficient loan loss provisions reflect the overall disinterest of banks towards risks control :such provisions may be perceived by investors and shareholders as signals of trouble and badmanagement, which may make banks reluctant to increase them.

Researchers have also identified important industry-specific factors driving bank failures. Thesefactors may be related to monetary policy, or to banking regulation (Keeton, 1999; Bernanke,2013). An over-accommodating monetary policy stance characterized by low interest rates and

26

growing money supply is generally associated with quick expansion of credit and subsequentdeterioration in credit-allocation standards. In addition, weak banking regulation such as lowcapital requirements in a competitive industry as well as generous deposit insurance, mayencourage banks managers to take risky actions. A lively debate on that subject remainsongoing, about the impacts of deposit insurance and the role of central banks as lenders oflast resort during times of financial system instability (Boyd and Gertler, 1994; Stern andFeldman, 2004; Ennis and Malek; Bernanke, 2013). Too weak banking regulation is sometimesworsened by the inability of regulators to adequately monitor banking activities. Developmentof sophisticated financial instruments also add difficulties to the supervision of the bankingindustry by the regulatory authorities.

Finally, national macro-financial factors also play a key role in financial system stability(Demirgüç-Kunt and Detragiache, 1998; Kaminsky and Reinhart, 1999; Louzis et al., 2012).Sustained output growth and well-anchored inflation are generally positively associated withbanking system stability. Low unemployment rate and dynamic housing industry foster boomsin banking activities. Breuer (2006) suggests that other national factors such as corruptionmay also be important.

The literature proposes various measures to characterize and classify banking crises (Demirgüç-Kunt and Detragiache, 1998; Kaminsky and Reinhart, 1999; Borio and Lowe, 2002; Carmichaelet al., 2015), among others, non-performing loans increase, bank runs occurence, public rescueand bank failures. In this study, we assess banking crises with the number of commercial bankfailures.

2.5 Data

The goal of this paper is to provide a robust and workable monitoring and forecasting tool forthe aggregate number of commercial bank failures in the US. To this end, we analyze monthlyfrequency data on bank failures and relate them to the information contained in the McCrackenand Ng (2016) dataset, which comprises a large set of macro-financial explanatory variableswhile being easily available on a timely basis. Considering our objective, we supplement theMcCracken and Ng (2016) dataset with additional banking variables that are continuouslyupdated and publicly available from the Federal Reserve Bank of St. Louis website.

2.5.1 Response variable

Our variable of interest is the monthly number of bank failures and we measure it with the to-tal number of failures and assistances reported by the Federal Deposit Insurance Corporation(FDIC). 3 A bank failure is defined as the closing of a financial institution by its chartering

3. The FDIC is a government corporation providing deposit insurance to US banks depositors. As a primaryfederal deposit insurance provider, the FDIC supervises both federally-chartered banks as well as most state-

27

authority, while an assistance pertains to a situation where a failing institution is acquired byanother (healthy) institution, possibly with financial assistance from the FDIC. Our bench-mark results pertain to the sum of failures and assistances but our robustness analysis alsoassesses how our model performs with the separate components.

Figure 2.1 depicts the evolution of the U.S. banking industry since the mid 1970s. As depictedin Panel (a) of the figure, more than 14,000 commercial banks were operating in the UnitedStates in the mid 1970s, largely as a result of strict regulations on branching. In the 1980s,a progressive ease in the regulation on branching induced a significant period of mergers andthe number of banks with no branch steadily decreased whereas the number of banks withbranches increased till the late 1980s (but has slowly declined since). These two effects combineto create a a significant downward trend in the total number of commercial banks in the UnitedStates.

Panel (b) of Figure 2.1 provides the data on failures, assistances and mergers. The evolutionof failures and assistances clearly depict the two major disruptive episodes experienced by theU.S. banking system over the last 40 years, namely the Savings and Loans crisis (late 1980’s)and the subprime crisis (2007-2009).

Figure 2.1 – Evolution of the U.S. banking industry : 1975 - 2013

(a)

1980 1990 2000 2010

050

0010

000

1500

0

All banks Banks with no branchBanks with branch(es)

(b)

1980 1990 2000 2010

020

040

060

080

0

Failures MergersAssistances

Notes : Data on the U.S. banking industry are expressed in levels and retrieved from Federal DepositInsurance Corporation. Panel (a) depicts the progressive concentration of the U.S. banking industry.Panel (b) reports creation, mergers and failures of U.S. banks.

chartered banks. Each insured bank must report to the FDIC, which is involved in the large majority of bankfailures or assistances.

28

Next, Figure 2.2 scrutinizes the monthly number of bank failures and assistances further. InPanel (a) the level is reported while Panel (b) reports the number of bank failures and assis-tances in proportion of the total number of banks at the beginning of the year. The magnitudeof the 2007-2009 subprime crisis thus appears slightly amplified when the proportion of bankfailures is considered. However, since we are explicitly interested in modeling the number ofbank failures, our work below emphasizes the number of bank failures and not the proportion. 4

Figure 2.2 – U.S. bank failures and assistances (in levels and in proportion of total)

(a)

Jan−75 Mar−84 May−93 Jul−02 Sep−11

050

100

150

200

Failures Failures and Assistances

(b)

Jan−75 Mar−84 May−93 Jul−02 Sep−11

0.00

00.

005

0.01

00.

015

Failures (%) Failures and Assistances (%)

Source : FDIC

Table 2.1 provides additional information about the process of bank failures. From 1975 to2013, the U.S. banking system experienced an average of almost eight bank failures each month,with an important variability that suggests overdispersion (ie. a situation where the varianceis higher than the mean, see Section 2.6). The two distress episodes (the Savings and Loansand subprime crises) are also clearly perceivable : during the period 1985-1994, an average ofmore than 21 banks failed each month whereas in 2005-2103, an average of almost five bankfailed each month. The pattern of overdispersion also appears in all historical episodes.

Figure 2.3 depicts the data on the form of a histogram showing the number of failures on thex-axis and the number of months during which the corresponding number of bank failuresoccurred. The figure shows that bank failures remain a relatively rare event : nearly 150

4. Our results are not significantly modified if we consider the number of bank failures and assistancesin proportion of the total number, which is not surprising considering how similar the two panels of Fig. 2.2appear.

29

months in our samples experienced no bank failure. Conversely, the distress episodes implythat a relatively fat tail is present in the histogram with months experiencing importantnumbers of bank failures. In March 1989, for instance, 175 banks went into bankruptcy. Ourdependent variable is hence characterized by a large proportion of zeroes and overdispersion,features that our econometric strategy, discussed below, will take into account.

Table 2.1 – U.S. bank failures and assistances : descriptive statistics

Period Nb. of Failures Monthly Mean Std. Dev.

1975 - 1984 438 3.65 4.121985 - 1994 2550 21.25 20.921995 - 2004 55 0.46 0.662005 - 2013 505 4.68 5.82

1975- 2013 3548 7.58 13.81

Source : FDIC

Figure 2.3 – Histogram of the U.S. monthly bank failures and assistances

0 5 10 15 20 25 30 35 40 45 176

050

100

150

Note : U.S. monthly bank failures and assistances in levels : the x-axis reports the number of bank failuresand the y-axis the number of months in our sample during which the corresponding number of bank failuresoccurred. Data are retrieved from the Federal Deposit Insurance Corporation.

2.5.2 Explanatory variables

McCracken and Ng (2016) propose a comprehensive dataset of macroeconomic time series forthe United States, organized by sectors and purposely designed for factor model analyses.

30

Table 2.2 – Data description

Group ID Data ID Data Description

Variables considered by McCracken and Ng (2016)1 001 - 015 Production2 016 - 018 Consumption3 019 - 027 Orders and Inventories4 028 - 037 Housing Industry5 038 - 068 Labor Market6 069 - 088 Prices7 089 - 105 Interest Rates8 106 - 112 Exchange Rates9 113 - 126 Money10 127 - 131 Stock Market

Variables added by the authors11 132 - 153 Banking Industry

They aim to provide a convenient “starting point" for research on big data. To the extent thatour variable of interest is the number of commercial bank failures, we consider it importantto represent the banking sector in a more comprehensive manner. We thus add more bankingvariables to the McCracken and Ng (2016) dataset. These additional banking variables are allcontinuously updated and publicly available from the Federal Reserve Bank of St. Louis web-site. Overall, our database contains 153 different variables all observed at a monthly frequencyover the sample 1975M1 - 2013M12. Table 2.2 presents the thematic sectors around whichthese variables are classified, as well as the number of variables in each sector (a detailed listof all data used in presented in the Appedix). Considering the large number of variables consi-dered, a procedure by which the dimension of the estimation is reduced becomes necessaryand our analysis via principal components is designed to achieve this.

We favor monthly data as we advocate the use of rapidly available data to early anticipateforthcoming occurrence of banking difficulties. In turn, the large number of variables we consi-der ensures we take advantage of all available relevant information, through the use of keysectoral predictors extracted from the larger database (Stock and Watson, 2002b; Boivin andNg, 2006).

2.6 Econometric framework

This section discusses our econometric strategy for first, constructing and selecting our predic-tors, and second, modeling the occurrence of aggregate commercial bank failures in the UnitedStates.

31

2.6.1 Predictors

The modeling of a large set of variables as the one presented in Table 2.2 (more than onehundred) can prove challenging. We detail below the approach we use to construct and selectour predictors. The goal here is to fully exploit the relevant information contained in ourdataset.

Construction of the predictors

For each group of variables presented in Table 2.2, we perform a principal component analysis(PCA). Principal component analysis is a multivariate statistical procedure that transformsa set of N correlated variables into a new set of N uncorrelated variables, the principal com-ponents (PCs). By construction, the principal components are orthogonal to each other andrepresent linear combinations of the original variables. They exhibit no redundant informa-tion and form as a whole an orthogonal basis on which the observations are projected. Thesecomponents are ordered, in the sense that the first principal component explains the largestfraction of the overall covariance or correlation matrix of the N original variables. 5

Concretely, denoteXjt as the data matrix for theNj time series in sector j (one of the 11 present

in our dataset). A principal component decomposition of Xjt will uncover Fjit, i = 1, . . . , Nj

with each Fjit a linear combinations of the underlying data, such that

Fjit = Xjtci

j , (2.1)

where cji is the ith eigenvector associated to the variance-covariance or correlation matrix ofXjt . One can show (Stock and Watson, 2006) that a PCA such as (2.1) can be used to identify

and estimate unobserved meaningful predictors and as such, provide a collection of potentialpredictors for our modeling of bank failures.

Selection of the predictors

The principal component analysis (2.1) presented above yields Nj principal components Fjit,which can be viewed as potential predictors summarizing the information contained in sectorj. From this set of valuable predictors, one needs to select the principal components to keepin the model. In recent years, selection of the first principal components, those with thelargest variance, has been popularized in the macro-financial literature. Recall that the firstprincipal components explain the largest fraction of the overall covariance or correlation matrixof the N original variables. This selection of the first principal components pertains to thefactor analysis (FA) framework developed and applied in different works (Stock and Watson,2002a,b; Bai and Ng, 2006). The rationale behind the factor model is that a few latent factors(represented by the first PCs in some works) can summarize all the information contained in a

5. For an extensive discussion of principal component analysis see Jolliffe (1986), Timm (2002), Jackson(2005), Basilevsky (2009) and Abdi and Williams (2010).

32

set of variables. However, as noticed by Jolliffe (1982), some principal components with a lowvariance can be as important as those with large variance. This assertion is often linked to theprincipal component regression (PCR) in the literature. The underlying idea is to select theprincipal components according to their association with the dependent variable. We regardthese two methods (FA and PCR) as relevant for our work and apply both. However, giventhe aim of our paper (forecasting of the monthly number of commercial bank failures), wefavor principal component regression 6 and present hereafter the results arrived at with thismethod. Results arrived at with the factor analysis framework are qualitatively not differentand provide robustness evidence for our core findings. 7

2.6.2 Models

We present our econometric strategy for analyzing the monthly occurrence of aggregate com-mercial bank failures in the United States. We first discuss the standard Poisson model oftenused as a starting point in the count data literature, before introducing refinements to thismodel aimed at accommodating data features, such as overdispersion and excess zero counts.

Standard Poisson Model

The Poisson distribution generally represents the starting point in modeling count data. Itsprobability mass function (p.m.f) is given by :

fYt(yt) =e−λtλyttyt!

, (2.2)

where yt represents the realization of a count variable of interest Yt (the number of bank failureoccurrences during period t in our case) and λt is the corresponding expected mean and alsovariance, as both coincide in the standard model :

E[Yt] = V [Yt] = λt. (2.3)

The standard Poisson regression model uses (2.3) to relate predictors to the conditional meanof yt via the following :

E[Yt|Xt] = λt = exp(X ′tβ), (2.4)

with Xt the vector of predictors and β the vector of associated parameters.

6. We conduct a search of all the possible Fjit for each sector to identify the one that is most promisingfor explaining the monthly occurrence of bank failures. Concretely, we regress our dependent variable on eachprincipal component and keep the one with the best in-sample fit to represent the information contained in thecorresponding sector. It is that one Fjit that we enter into the various count data models we consider. As such,we obtain a specification that is both concise (one variable per sector j) and exhaustive, as that one variable isa linear combination of all others in the sector, as per (2.1), and thus reflects information from all the sector.

7. We select the first principal component as predictor for each sector. Unlike with the PCR framework,significance of some predictors appears quite irregular, providing hence empirical grounds to Jolliffe (1982)’sassertion. Results arrived at with the factor analysis framework are available upon request.

33

This framework has been used by a considerable literature analyzing the determinants ofhealth services demand, insurance and accident claims and several other types of count data ;see Cameron and Trivedi (2013) for a survey. It has, however, seldom been applied to thestudy of bank failures, with the notable exception of Davutyan (1989). 8

The standard Poisson regression model cannot be applied successfully to all count data ana-lysis. Notably, data features such as overdispersion (where the variance exceeds the man)and excess zero-counts are at odds with the implications of the standard model. We discussrefinements that can accommodate these features.

Negative binomial model

Equidispersion refers to the equality of the mean and the variance of a count data variable ofinterest. By constrast, overdispersion (underdispersion) occurs when this property is violatedand the variance exceeds (is less than) the mean. As stated above, Poisson regression modelsassume equidispersion and as such cannot account for overdispersion in data.

One class of count data model that can account for dispersion is the negative binomial (NB)model. Negative binomial models relax the strict assumption of equality of mean and varianceand instead work with models admitting the following relationship between the conditionalmean and the conditional variance of the variable of interest :

V [Yt] = λt +λptα, p ∈ R, α ∈ R∗, (2.5)

where the two common parameterizations specify p = 1 or p = 2. In the latter case, theexpression thus becomes

V [Yt] = λt +λ2tα, (2.6)

and α is an overdispersion parameter to be estimated. 9

Hurdle negative binomial model

Hurdle models were introduced by Mullahy (1986) and are a class of models designed tohandle count data featuring excess zeros and overdispersion. These two-part models workwith a process for the zero counts (the absence of bank failures in our case) that is different

8. Davutyan’s analysis studies the annual count of bank failures using the standard Poisson model. Bycontrast, our analysis pertains to the monthly count of bank failures, which requires that we use the refinementsto the Poisson model discussed below.

9. This specification is the NegBin2 model discussed in Cameron and Trivedi (2013) and is the one wewill use below. Note that expressions like (2.6) are obtained by introducing an idiosyncratic, unobserved andmultiplicative disturbance ε in the standard model, so that the p.d.f. now reads

fYt(yt) =e−λtεtλtεt

y

yt!.

Assuming a Gamma distribution for ε and solving for the unconditional first moments for y implies relationshipbetween V [Yt] and E[Yt] as in (2.6). See Cameron and Trivedi (2013) for details.

34

from the process for the positive counts (the number of bank failures when occurring). Aneconomic interpretation of this structure could therefore be that two regimes can affect bankingactivities, namely normal times, for which k = 0, and abnormal times with increasing severityaccording to which k = 1, 2, ....

More specifically, let f1(0) denote the probability that yt takes a zero value and f2(k), atruncated p.m.f. governing the intensity for values greater than zero (k = 1, 2, ...). Note thatthe two p.m.f. functions are not constrained to be the same processes and/or to depend onthe same predictors. The p.m.f of a such a “hurdle-at-zero" model is given by :

fYt(yt = k) =

f1(0) k = 0,

(1− f1(0))f2(k)

1− f2(0)k = 1, 2, ...

(2.7)

where the p.m.f. f1(·) and f2(·) then depend on the various predictors examined. The functionf2(·) is then typically defined as a Poisson or negative binomial model, while f1(·) can be abinomial or a geometric model. The expected value arising from model (2.7) is

E(Yt) =(1− f1(0))

1− f2(0)

∞∑k=1

kf2(k), (2.8)

while the variance obeys

V ar(Yt) =(1− f1(0))

1− f2(0)

∞∑k=1

k2f2(k)−

[(1− f1(0))

1− f2(0)

∞∑k=1

kf2(k)

]2. (2.9)

Parameters of hurdle models are estimated with maximum likelihood and the log-likelihoodfunction (L) of a hurdle-at-zero model can be expressed as follows :

L =

T∑t=1

I{yt=0}logf1(0; θ1,t) + I{yt>0}log(1− f1(0; θ1,t)) +

n∑t=1

I{yt>0}logf2(yt; θ2,t)

1− f2(0; θ2,t)(2.10)

with θ1,t = {Xt, β1}, θ2,t = {Xt, β2}, and T the number of observations. β1 and β2 respectivelyrepresent the parameters associated to the p.m.f f1 and f2.

The specific assumptions we use are as follows. We consider a hurdle with negative binomial(HNB) model in which we first postulate a binomial for the process generating the zeros(f1) and a negative binomial distributions for the generation of the positive counts (f2). The“hurdle-at-zero" feature of the model is designed to capture the high occurrence of zeros noticedin Figure (2.3), while the negative binomial aspect is intended to address the high dispersionof positive counts.

Now recall that the p.m.f of a binomial distribution is given by :

f1(s;n, ps) =n!

s!(n− s)!prs(1− ps)n−s, (2.11)

35

with n the number of trials, ps the success probability for each trial and s the number ofsuccess. Since we posit a logit link function for the binomial regression, this implies that theprobability ps of success for each trial is related to our predictors in the following manner :

log(ps

1− ps) = X ′β. (2.12)

Zero-inflated model

A related strategy to address high counts of zeros is known as the zero-inflated model (Cameronand Trivedi, 2013). This model considers that zeros can arise either from the occurrence ofRegime 1, which always results in a zero-count, or from Regime 2, a standard count modelwhich includes the possibility of zeros. One would thus get

fYt(yt = k) =

π + (1− π)f2(0) k = 0,

(1− π)f2(k) k = 1, 2, ...

(2.13)

where the unobserved probability π of belonging to the point mass component could be aconstant or itself depend on regressors via a binary outcome model such as a binomial model.Below we analyze a zero-inflated negative binomial (ZINB) model wherein f2(·) is the negativebinomial described above and π modelled by a binomial distribution. As we show below, resultsarrived at using the HNB and ZINB are very similar.

2.7 Results

This section presents our results. Section 2.7.1 first analyzes the contemporaneous link betweenour predictors and bank failures’ count. This allows us to single out the Hurdle negativebinomial model (HNB) as the most promising framework. Next, Section 2.7.2 studies the abilityof the HNB model to predict bank failures at horizons between one and 24 months ahead.Section 2.7.3 then allows dynamic elements to enter the analysis by including lagged values ofthe response variable, ie. past occurrences of bank failures. Finally, section 2.7.4 gauges thesensitivity of our results to different measures of bank failures, notably by separating bankfailures and assistances into separate components and moving to a quarterly specificationinstead of our benchmark (monthly) framework.

2.7.1 Benchmark

Table 2.3 reports the results from fitting the monthly occurrence of bank failures with thestandard Poisson process, the negative binomial and the two extensions to the standard mo-del discussed above, ie. the Hurdle negative binomial (HNB) and the zero-inflated negativebinomial (ZINB). For each model, the variable to be explained is the contemporaneous numberof bank failures, expressed in levels, while the predictors are one single principal component

36

for each sector, extracted by the procedure, discussed above, which identifies the principalcomponent most likely to help predict bank failures. Recall that in each of the extended mo-dels (HNB and ZINB), two probability mass functions, f1(·) and f2(·), are analyzed, one thatcontrols the number of zero-counts and the other governing positive counts, ie. the intensityof bank failures given that some are present. As such, two sets of parameter estimates arepresent for each of the extended models.

Table 2.3 – Estimation of the number of commercial bank failures

Poisson NB ZINB HNBFactor Zeros NB2 Zeros NB2Production 0.89∗∗∗ 1.97∗∗∗ 1.88 2.15∗∗∗ 1.40∗∗ 1.90∗∗∗

Consumption 0.02∗ 0.03 −0.35 0.02 0.21∗∗ −0.02Orders & Inventories 0.02∗∗ 0.08∗∗ −0.40∗ 0.02 0.15∗ 0.01Housing Industry −0.65∗∗∗ −1.04∗∗∗ 4.01∗∗∗ −0.80∗∗∗ −1.53∗∗∗ −0.84∗∗∗

Labor Market 0.15∗∗∗ 0.30∗∗∗ −0.58 0.22∗∗ 0.32∗ 0.24∗∗

Price −0.52∗∗∗ −0.67∗∗∗ −0.08 −0.63∗∗∗ −0.51∗∗ −0.58∗∗∗

Interest Rate 0.21∗∗∗ 0.41∗∗∗ −3.41∗∗∗ 0.18 1.01∗∗∗ 0.19Exchange Rate −0.09∗∗∗ −0.05 −0.99∗ −0.14∗∗ 0.23∗ −0.14∗

Money −0.22∗∗∗ −0.53∗∗∗ 1.33∗∗ −0.32∗∗ −1.14∗∗∗ −0.24∗

Stock Market 0.67∗∗∗ −0.88 1.84 −0.40 0.28 −0.78Banking Industry 0.18∗∗∗ 0.11 1.70∗∗∗ 0.33∗∗∗ −0.70∗∗∗ 0.42∗∗∗

−Log Likelihood 2834.06 1214.55 1188.89 1188.37AIC 5692.12 2455.10 2427.78 2426.73BIC 5741.85 2508.97 2531.39 2530.33

Symbols ∗,∗∗ and ∗∗∗ indicate statistical significance at 10%, 5% and 1% level.

We first analyze the significance of the different sector-specific predictors in the different modelsand then assess the models’ overall ability to explain the count of bank failures.

Significance of sector-specific predictors

One standout result reported in the table is the robust significance of some predictors. Indeedone can see that the predictor associated to the housing sector is significant at high levelsin each model analyzed and for both branches or regimes (extensive and intensive margins)associated with the two extended models. As shown below, this high significance of the housingsector predictor for bank failures is a robust result that will extend to all our experiments,notably when the variable to be explained becomes future values of bank failures. 10

Other sector-specific predictors do not exhibit an equivalent robustness. For example, thepredictors associated with the Production or Labor Market sectors are often statistically si-

10. Recall however that factors are identifiable only up to a square matrix and as such interpretation of theirsign may be misleading.

37

gnificant but not always and some others, such as the one associated with the Consumptionor even the Stock Market, show little promise for explaining bank failures’ counts.

Model selection

The three classic measures of model performance reported in Table 2.3 are the log likelihood,the Akaike Information criterion (AIC) and the Bayesian Information criterion (BIC). Thelog-likelihood is multiplied by -1, so that smaller values indicate better performance, as is alsothe case for the AIC and BIC criteria.

The three criteria agree in their assessments of the models. First, Table 2.3 indicates that thenegative binomial (NB) model represents a very significant improvement with respect to thestandard Poisson model. Further, the two extended models (ZINB and HNB) also improveperformance, but by less of a margin. Finally, the performance of the ZINB and HNB modelsare very similar, with the HNB model retaining a very small advantage. The nature of bankfailures’ data, with excess counts of zeros and significant dispersion of positive counts, clearlyrequires that the ZINB or HNB structures be used.

To gain further insight about the different models’ ability to match the monthly occurrence ofbank failures, Table 2.4 reports actual and predicted frequencies and cumulative frequencies.The relatively poor performance of the standard Poisson model for fitting zero counts is clearlydepicted, as are the improvements obtained by moving first to the NB model and next to theextended ZINB or HNB models. Looking at positive counts, the standard Poisson modelcontinues to perform relatively poorly for low counts (an 0.15 observed frequency of countsof 1, while the Poisson only predicts 0.03) ; meanwhile the NB has a tendency to overpredictthese low counts while the ZINB or HNB are shown to match them the best.

Table 2.4 – Actual and fitted cumulative frequencies

0 1 2 3-5 6-10 11-20 21-30 31-40 41-50 50+FrequencyObserved 0.32 0.15 0.09 0.09 0.10 0.14 0.08 0.01 0.01 0.02Poisson 0.00 0.03 0.11 0.42 0.25 0.12 0.05 0.02 0.00 0.00NB 0.03 0.19 0.15 0.25 0.14 0.09 0.05 0.02 0.03 0.06ZINB 0.06 0.17 0.11 0.25 0.17 0.11 0.05 0.03 0.03 0.02HNB 0.05 0.15 0.13 0.27 0.15 0.11 0.06 0.03 0.02 0.03CumulativeObserved 0.32 0.47 0.55 0.64 0.74 0.88 0.96 0.97 0.98 1.00Poisson 0.00 0.03 0.14 0.56 0.81 0.93 0.98 1.00 1.00 1.00NB 0.03 0.22 0.37 0.62 0.77 0.86 0.90 0.92 0.95 1.00ZINB 0.06 0.23 0.34 0.59 0.76 0.88 0.92 0.95 0.98 1.00HNB 0.05 0.20 0.33 0.61 0.76 0.87 0.93 0.96 0.97 1.00

Figure 2.4 depicts yet another dimension along which to compare results, by providing time-series plots of observed and predicted occurrence of monthly bank failures for the four model

38

considered.

The Poisson model (top left of the figure), first, is seen to face significant challenges to fitperiods of high counts of bank failures, such as the mid-1980s or 2008-2010 crisis episodes.Next, the NB model (top right) has the tendency to overpredict at times, most notably atthe beginning of the two main crisis episodes in our dataset. The two bottom panels of Figure2.4 show that the additional flexibility extended by the ZINB et HNB models allows themto match counts significantly better than the other two models. Since the differences betweenZINB et HNB appear modest, henceforth we consider the Hurdle Negative Binomial (HNB)as our main framework for analyzing and monitoring future counts of bank failures.

Figure 2.4 – Predicted number of bank failures by model

Poisson Model

Mar−75 Jul−82 Nov−89 Mar−97 Jul−04 Nov−11

050

100

150

200

500

NB Model

Mar−75 Jul−82 Nov−89 Mar−97 Jul−04 Nov−11

050

100

150

200

500

ZINB Model

Mar−75 Jul−82 Nov−89 Mar−97 Jul−04 Nov−11

050

100

150

200

500

HNB Model

Mar−75 Jul−82 Nov−89 Mar−97 Jul−04 Nov−11

050

100

150

200

500

Observed failures Predicted failures

2.7.2 Predicting future occurrences of bank failures

The results discussed so far pertain to the contemporaneous link between macroeconomicfactors and bank failures. We now perform a series of estimations aimed at predicting theoccurrence of bank failures at horizons ranging from 0 to 24 months ahead. Note that foreach forecasting horizon, the procedure described in Section 2.6 is repeated, with the mostpromising principal component of each sector chosen in a manner specific to the forecastinghorizon considered : as such, the principal component chosen might be different when the modelis required to predict at the three-month-ahead horizon, say, rather than six-months-ahead.

To identify predictive success we add the Pearson Statistic to the three performance criteria

39

already discussed above. The Pearson statistic measure of goodness of fit for count data isgiven by

P =n∑i=1

(yt − λt)2

ωt, (2.14)

where as before yt is the number of bank failures in month t while λt and ωt represent estimatesof the mean and variance of yt, respectively.

Figure 2.5 – Bank failures prediction with the HNB model : various forecasting horizons

H = 3 months

mar−75 jul−82 nov−89 mar−97 jul−04 nov−11

050

100

150

200

250

H = 9 months

mar−75 jul−82 nov−89 mar−97 jul−04 nov−11

050

100

150

200

250

H = 14 months

mar−75 jul−82 nov−89 mar−97 jul−04 nov−11

050

100

150

200

250

H = 19 months

jan−77 mai−84 sep−91 jan−99 mai−06 sep−13

050

100

150

200

250

Observed failures Predicted failures

Figure 2.5 presents results for the predictions horizons three-months ahead, 9-months ahead,14 months-ahead and 19 months ahead ; these horizons were chosen from intrinsic criteria–such as the need to identify a good near-term prediction of bank failures– or because themodel’s performance is relatively good for the horizons. The complete set of results for allhorizons (zero to twenty-four months’ ahead) are presented in Figure A.1 in the Appendix.Overall the graphs in Figure 2.5 and Figure A.1 illustrate the significant potential of ourframework as a workable predictor of future bank failures.

40

Table 2.5 – Bank failures prediction with the HNB model : three-months-ahead horizon

Zeros NB2

Coef. Std. Err. Signif. Coef. Std. Err. Signif.

Explanatory VariableProduction 1.57 (0.56) *** 1.69 (0.40) ***Consumption 0.11 (0.18) −0.05 (0.08)Order & Inventories 0.13 (0.09) 0.05 (0.04)Housing Industry −1.51 (0.28) *** −0.80 (0.11) ***Labor Market 0.53 (0.19) *** 0.27 (0.10) ***Price −0.27 (0.14) * −0.23 (0.07) ***Interest Rate 1.23 (0.35) *** 0.19 (0.15)Exchange Rate 0.18 (0.13) −0.11 (0.06) *Money 0.51 (0.34) 0.05 (0.16)Stock Market 0.28 (0.24) −0.23 (0.17)Banking Industry 0.08 (0.20) 0.50 (0.10) ***

Log Likelihood −1179Akaike Information Criterion 2407.91

Symbols ∗,∗∗ and ∗∗∗ indicate statistical significance at 10%, 5% and 1% level.

Table 2.5 presents further details about one specific experiment, whereby bank failures arepredicted at the three-months-ahead interval. We consider this experiment as one of “nearmonitoring” of bank failures. The table reveals that information drawn from the HousingIndustry sector retains its statistically significant signalling value, both for the extensive (zeroor non-zero counts) and intensive (number of positive counts) margins. 11 The informationcontained in the Housing Industry block of variables from the McCracken and Ng (2016)database is thus a meaningful predictor for future bank failures, a result congruent with otherfindings obtained in related theoretical and empirical work (Barrell et al., 2010; Ghosh, 2015).

It is perhaps natural to expect housing sector information to play a key role in explaining bankfailures. Typically, banks transform short-term deposits into long-term loans, with mortgageloans representing the major part of these loans. Booms in the housing industry, marked byaccelerating housing starts and home loans growth generally constitute periods of high pro-fitability and low rates of non-performing mortgage loans for the banking sector. However,housing conditions can evolve rapidly and interest rates increases or deteriorating labor mar-kets lead vulnerable households to default on bank loans. Banks with high exposition to suchrisky loans quickly experience important difficulties, some resulting in failures.

Table 2.5 additionally reports that information from the Production, Labor Market or InterestRates sectors also feature statistically significant impacts. This is also consistent with resultsobtained elsewhere in the literature on the determinants of banking crises ; Output growth

11. The statistically significant impact of information drawn from the Housing sector remains in all forecas-ting horizons considered, from 0 to 24-months-aheads. Full results are available on request.

41

(Demirgüç-Kunt and Detragiache, 1998; Kaminsky and Reinhart, 1999; Louzis et al., 2012)and a low unemployment rate (Louzis et al., 2012; Ghosh, 2015) are often negatively associatedwith bank failures, whereas loose monetary policy, such a periods of low interest rates andgrowing money base have been found to mitigate immediate banking systems’ vulnerabilities.Notice however that unlike the case for our housing industry predictor, statistical significancefor these other sectors appears irregular across the different estimations.

2.7.3 Dynamic HNB model

One implicit assumption of the static HNB model is that the residuals are independent andidentically distributed (i.i.d.). Time series generally generate autocorrelation however, espe-cially in the macro-financial realm. This section modifies our framework in order to allow forsuch effects.

Specifically, we assume that past occurrences of bank failures can induce further bank failures,over and above all the explanatory variables considered so far. A number of observations andtheories tend to support this assumption. First, recent trends in the banking industry, namelymovements towards consolidation and integrated communication technologies, have renderedbanks more intercorrelated than ever. Such connectedness among banks may have left themmore vulnerable in the sense that a collapse of one or many important banks can destabilizethe whole banking system. 12 Second, the self-fulfilling prophecies and bank run theory ofDiamond (1983) provides solid theoretical grounds for this type of phenomenon.

To account for this dependency between past and current bank failures, we follow Cameronand Trivedi (2013) and add lagged values of our dependent variable to the model. As above,we experiment with various forecasting horizons, between 0 and 24-months-ahead and for eachhorizon, we successively incorporate 1 to 12 lagged values of our response variable and assessthe forecasting improvement. 13

Table 2.6 reports a representative sample of the results obtained in this experiment : it cor-responds to a case where at of period t, bank failures are forecast four-months ahead, ie. upto period t+ 4, using our explanatory variables dated of period t and up to seven lags of thenumber of bank failures. Full results for all our (forecasting horizons, number of lags of bankfailures) specification pairs are presented in Table A.3 in the Appendix.

Table 2.6 has important findings. First, it largely confirms results obtained until now in ouranalysis about the signalling properties of information drawn from the Housing Industry sec-tor : they remain statistically significant, especially to explain the intensive margin (the num-

12. For example, the collapse of Lehman Brothers on September 15, 2008 is considered by many researchersto have sparked the Subprime crisis.13. As indicated above, for each of these iterations, the best principal component to represent information

from each sector j might be changing : The complete analysis described in Section 2.4 is thus repeated for eachpossible forecasting horizon and each lag for the dependent variable.

42

ber of bank failures conditional on them being positive). Additionally, the lagged dependentvalue also has important effects, with the date-t count being especially important in the de-termination of the extensive margin (the presence of at least one bank failure) three-monthshence. This provides confirmation that bank failures are interconnected. Finally, note thatthe presence of lagged values for the dependent variables has reduced the impact of someother sectoral variables such as Production, Price and Interest Rates while leaving HousingIndustry’s impact on bank failures unaffected.

Table 2.6 – Bank failures prediction with the dynamic HNB model : four-months-aheadhorizon

Zeros NB2

Coef. Std. Err. Signif. Coef. Std. Err. Signif.

Explanatory VariableProduction −0.14 (0.63) 1.24 (0.24) ***Consumption −0.36 (0.34) 0.01 (0.08)Order & Inventories 0.13 (0.09) 0.08 (0.02) ***Housing Industry −0.63 (0.35) * −0.46 (0.06) ***Labor Market −0.08 (0.23) 0.01 (0.06)Price 0.23 (0.19) −0.15 (0.05) ***Interest Rate 0.20 (0.35) 0.15 (0.08) *Exchange Rate −0.10 (0.10) 0.04 (0.02)Money 0.81 (0.42) * 0.17 (0.10) *Stock Market −1.28 (1.73) 0.01 (0.43)Banking Industry −0.05 (0.28) −0.07 (0.07)

Lagged Response VariableBank Failures (t) 0.38 (0.15) *** 0.01 (0.00) ***Bank Failures (t− 1) 0.04 (0.14) 0.00 (0.00)Bank Failures (t− 2) 0.13 (0.15) 0.01 (0.00) *Bank Failures (t− 3) −0.21 (0.08) *** 0.00 (0.00)Bank Failures (t− 4) 0.06 (0.14) 0.01 (0.00) **Bank Failures (t− 5) 0.13 (0.13) 0.011 (0.00) **Bank Failures (t− 6) 0.16 (0.14) 0.01 (0.00)Bank Failures (t− 7) 0.26 (0.13) * 0.01 (0.00) ***

Log Likelihood −987.26Bayesian Information Criterion 2225.45

Symbols ∗,∗∗ and ∗∗∗ indicate statistical significance at 10%, 5% and 1% level.

Figure 2.6 shows the in-sample forecasting of the specific dynamic-HNB model whose resultsare reported in Table 2.6. recall that this uses information as of period t to predict the ag-gregate number of bank failures at the four-months-ahead horizon. The figure depicts a veryencouraging fit, which appears able to capture not only the two systemic bank failures episodesin our sample but also the non-crisis periods.

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Figure 2.6 – Bank failures prediction with the dynamic HNB model : four-months-aheadhorizon

mar−75 sep−80 mar−86 sep−91 mar−97 sep−02 mar−08 sep−13

050

100

150

200

250

Observed failures Predicted failures

2.7.4 Sensitivity analysis

To gauge the robustness of our main findings, Table 2.7 considers three alternative specifica-tions of the benchmark HNB model. The first specification (Panel 1 of Table 2.7) considersonly effective bank failures (thus leaving our bank assistances in the definition of failure) ; thesecond (Panel 2) considers quarterly variables as opposed to the monthly frequency used in ourbenchmark analysis and, finally, the third specification (Panel 3) considers only assistances todistressed banks.

Overall, the statistically significant of information drawn from the Housing Industry sectorremains robust throughout the table. Housing Industry proves able to explain both the twoRegimes (non-occurrence and occurrence) of bank failures, confirming hence the robustnessof our key result. Moreover, the set of significant sectoral variables identified in the previousestimations also remain relatively unchanged.

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Table 2.7 – Bank failures prediction with the HNB model : sensitivity analysis

(1) (2) (3)Zeros NB2 Zeros NB2 Zeros NB2

Production 2.26∗∗∗ 1.61∗∗∗ −0.37 −1.37∗∗∗ 1.44 6.16∗∗∗

Consumption 0.12 0.01 0.54 −0.04 0.08 0.24Orders & Inventories 0.06 0.12∗∗∗ 0.39∗ 0.17∗∗∗ −0.26∗ −0.33∗∗∗

Housing Industry −1.31∗∗∗ −0.81∗∗∗ 2.27∗∗ 1.03∗∗∗ −1.56∗∗∗ −0.56∗∗∗

Labor Market 0.22 0.19∗ 0.43 0.15 −0.42∗∗∗ −0.26∗∗∗

Price −0.29 −0.65∗∗∗ 0.17 0.85∗∗∗ 0.07 −0.32∗∗

Interest Rate −0.43 −1.87∗∗∗ 1.60 0.02 1.85∗∗∗ 0.13Exchange Rate 0.06 −0.07 −0.64 0.08 −0.42 −0.25Money −0.70∗∗∗ −0.29∗∗ 1.32∗∗ 0.70∗∗∗ 1.53∗∗∗ 1.12∗

Stock Market 0.07 −0.02 0.31 −0.22 −1.62 0.29Banking Industry −0.01 0.18∗∗∗ −35.62∗∗∗ −7.16∗∗ 0.10 0.38∗∗∗

−Log Likelihood 1109.12 508.07 386.07AIC 1109.12 1066.15 822.14BIC 1109.12 1142.07 925.75

Symbols ∗,∗∗ and ∗∗∗ indicate statistical significance at 10%, 5% and 1% level.

2.8 Conclusion

This paper develops a monitoring and forecasting framework for the monthly aggregate oc-currence of bank failures in the United States. We extract key sectoral factors from a largeset of potential (macro-financial) explanatory variables and incorporate them in a hurdle ne-gative binomial model for bank failures counts. Our result uncover a strong and consistentrelationship between housing industry variables and banking failures. Besides this main fin-ding, we also find that production, labor market, interest rates and money variables displaysome forecasting power through different horizons of prediction. One important area for futureresearch would perform an out-of-sample forecasting experiments with repeated estimations ateach stage, to verify the real-time robustness of the link uncovered between housing industryvariables and bank failures.

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Chapitre 3

On The Usefulness of Big Data inModeling Non-Performing Loans

3.1 Résumé

Nous estimons différents modèles appliqués dans la littérature récente afin d’analyser et pré-voir les créances en souffrance aux États-Unis. Nous comparons la performance de ces modèlesà celles de modèles similaires dans lesquels nous remplaçons les variables explicatives par desprédicteurs sectoriels construits à partir d’une base de données macro-financières suggérée parMcCracken and Ng (2016). Nous trouvons que les modèles à composantes latentes ont demeilleurs performances prédictives. Ce résultat suggère que les professionnels du monde ban-caire et les chercheurs pourraient considérer les facteurs latents dans leur analyse des créancesbancaires en souffrance. Dans le cas des États-Unis, le secteur immobilier, qui compte pourseulement environ 10% du total des prêts aux États-Unis en moyenne, impacte significative-ment l’évolution des créances en souffrances.

3.2 Abstract

We estimate different models applied in the recent literature for fitting and forecasting U.S.banks non-performing loans (NPLs). We compare the performance of these models to those ofsimilar models in which we replace traditional explanatory variables by key sectoral predictors,all extracted from a large set of U.S. macro-financial variables suggested by McCracken andNg (2016) for big data analysis. We find that the latent-component-based models all outper-form the traditional models suggesting that practitioners and researchers could consider latentfactors in their modeling of NPLs. In addition, for the U.S. case, we also uncover that thehousing sector, which accounts only for almost 10% of the U.S. banks total loans in average,greatly impacts the evolution of non-performing loans over time.

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3.3 Introduction

Most industrialized economies rely heavily on their banking systems to transform deposits intolong-term loans, finance valuable projects, invigorate household consumption and contributeto overall economic development. As such, banks serve monetary policy’s goals by transmittingdecisions of monetary authorities on interest rates or money supply to the broader economy.As a result of the banking system’s central, any worsening in the extent of non-performingloans (NPLs) at banks is destined to have important overall economic consequences.

In such a context, the monitoring and forecasting of NPLs is an important policy objective.Banks overburdened by NPLs are likely to become less inclined to provide liquidity to the eco-nomy, with consequences on consumption and investment and a general decline in the economicactivity. Further, a surge in the level of non-performing loans generally entails a tighteningof monetary policy which may in turn worsen the economic activity. Finally, as argued byBarseghyan (2010), bad (private) loans represent a public loan since in most industrializedeconomies, governments provide a deposit guarantee.

This potentially public and national character of NPLs implies that efficient monitoring ofbanks activities is valuable. In addition, Beck et al. (2013) identifies the monitoring of NPLsas an important element of the macro-prudential surveillance, since NPLs reflect overall assetquality and credit risk in the financial sector. Finally, a strand of the literature associates asustained increase of non-performing loans with an imminent banking crisis (Demirgüç-Kuntand Detragiache, 1998; Laeven and Valencia, 2012; Ghosh, 2015).

The recent global financial crisis, which was marked by a significant upsurge in non-performingloans, has energized a growing body of empirical work analyzing non-performing loans determi-nants and the forecasting of their evolution (Ghosh, 2017; Tarchouna et al., 2017; Anastasiouet al., 2016; Konstantakis et al., 2016; Ghosh, 2015; Makri et al., 2014; Klein, 2013; Louziset al., 2012; Nkusu, 2011). However, an important gap exists, between models in applied ma-croeconomic research that consider data-rich environments (a very large number of potentialexplanatory variables) and the work implemented in the banking literature, which typicallyfocuses on a limited set of explanatory variables. Considering the enhanced computationalcapacities and econometric methods allowing one to consider large sets of variables to exploitall available information, this gap appears unnecessary.

In this context, the present paper takes a step towards bridging this gap by revisiting thequestion of NPLs using a factor analysis. To do so, we revisit popular econometric approachesapplied in the literature on NPLs and compare their fitting and forecasting performance tothose of similar models where key sectoral factors, extracted from the large set of variablesin the McCracken and Ng (2016) database, replace the traditional explanatory variables. Thefactors are for the U.S. case.

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We find that factor-based models outperform traditional models in fitting, forecasting per-formance and economic intuition. Factor-based models consistently have the better in-samplefit and appear more parsimonious than traditional ones. In addition while some individualpredictors identified both by previous theoretical and empirical models as important to ex-plain and forecast non-performing loans (such as interest rates) are hardly identified by thetraditional models, the factor-based approach always single out these predictors. This providesempirical support for Ludvigson and Ng (2009), who argue that latent economic conditionscannot be summarized by few observable variables. Further, an out-of-sample exercise showthat factor-based models continue to outperform their traditional conterparts.

Overall, our findings suggest that forecasters and regulatory authorities monitoring bankingsystems can achieve significant forecasting improvement by adopting factor-based frameworks.In addition, our results uncover a robust evidence about the signalling properties of the HousingIndustry block of variables in the McCracken and Ng (2016) database. This finding supportscommon assumptions that mortgage defaults can rapidly spread to other types of lending,such as auto or credit card loans, and can significantly undermine financial stability.

The scope of this work relates to two different but not mutually exclusive strands of theeconomic literature. On the one hand, the present paper naturally relates closely to the afo-rementioned empirical research on NPLs determinants. On the other hand, our paper alsorelates to a growing strand of empirical macroeconomic research promoting the use of factormodels to deliver superior insights on current or future economic developments.(Stock andWatson, 2002b; Camacho and Perez-Quiros, 2010; Bańbura and Modugno, 2014). We extentthe scope of their work by providing empirical evidence that factor models outperform tra-ditional models and advocate systematic use of factor model (when possible) to capture trueunderlying economic conditions. We regard our findings as relevant to not only explore theunderpinnings of NPLs but also investigate any variable of interest in the banking literaturesuch bank failures. 1

The remainder of this paper proceeds as follows. In Section 3.4, we review recent empiri-cal contributions on non-performing loans. Section 3.5 then presents the econometric modelswidely applied in this literature and we introduce our factor-based approach. Section 3.6 des-cribes our data and conduct some preliminary tests. In Section 3.7, we perform the estimationsand discuss the results. Section 3.8 presents an out-of-sample forecasting exercise and Section3.9 concludes.

1. To the best of our knowledge, the only use of factor approach to analyze NPLs is found in Tarchounaet al. (2017). They apply a principal component analysis (PCA) to construct a corporate governance index,which they then use in a GMM estimation.

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3.4 Recent empirical literature

Empirical work on NPLs typically ranges between cross-country analyses to country-specificcase studies. It usually draws on three categories of possible determinants as explanatory va-riables, as suggested by the theoretical literature : bank-specific, industry-specific and country-specific. We briefly review some of the recent empirical works.

3.4.1 Cross-country analysis

Anastasiou et al. (2016) opt for a general method of moments (GMM) framework to studythe determinants of non-performing loans in the euro-banking system over the period 1990Q1-2015Q2. Aside from the traditional explanatory variables common to most of the literature onNPLs, they consider fiscal policy and find that the fiscal authorities’ fiscal decisions may laythe foundations for financial instability. In that context, they stress the importance of optimalfiscal policies design. Makri et al. (2014) examine both banking and country-specific variablesto identify the determinants of the non-performing loans rate of the Eurozone’s banking systemfor the period 2000-2008. They also apply a GMM estimation on their data from 14 countriesand confirm the importance of both banking and country-specific factors on the evolutionof NPLs. Beck et al. (2013) also use GMM methodology to investigate the macroeconomicdeterminants of non-performing loans (NPLs) across 75 countries, using a sample that includesboth developed and developing countries. They find real GDP growth, share prices, exchangeand lending rates to be significant predictors of NPLs. Nkusu (2011), meanwhile, studies thelink between NPLs and macroeconomic variables in 26 advanced countries. He estimates botha panel-OLS and a Vector Autoregressive (VAR) model and identifies credit market frictionsas playing an important role for macro-financial vulnerability. Finally, Espinoza and Prasad(2010) concentrate their analysis on around 80 banks in the Gulf Cooperation Council regionand find significant impact of economic growth, interest rates and risk aversion on the volutionof NPLs. They also assess the feedback effect of increasing NPLs on growth via a panel-VARmodel.

3.4.2 Country-specific analysis

Ghosh (2017) use various econometric methods (fixed-effect, GMM and panel VAR estima-tions) widely-applied in the NPLs literature to investigate the sector-specific determinants ofnon-performing loans for the 100 largest U.S. commercial banks over the period 1992-2016.He finds an accentuated sensitivity of real estate loans to macroeconomic conditions as wellas an important feedback effect from the banking sector to the real economy. Tarchouna et al.(2017), in order to assess the effect of corporate governance system on NPLs, consider U.S.commercial banks data for the period 2000-2013 and build a corporate governance index witha principal component analysis (PCA) method that they use in a GMM estimation. They finda positive impact of corporate governance only for small banks. Corporate governance fails

49

to prevent medium and large U.S. commercial banks from excessive risk-taking. Konstantakiset al. (2016) apply Vector Autoregressive (VAR) and Vector Error Correction (VEC) modelson quarterly data spanning the years 2001-2015 to identify the determinants of NPLs in theGreek banking system. They show significant impact of both macroeconomic and financialfactors on Greek NPLs. Ghosh (2015) examines state-level determinants of non-performingloans for all commercial banks and savings institutions across the U.S. states over the period1984-2013. Using both fixed effect and GMM estimations, he uncovers a significant impact ofregional economic variables and suggests that state-level conditions should be considered tomonitor evolution of NPLs. Louzis et al. (2012) study separately, for the Greek banking system,the evolution of the consumer, business and mortgage non-performing loans during the years2003-2009. They apply a GMM estimation and find for each of these loan categories that bothmacroeconomic variables and management quality significantly drive the evolution of NPLs.Salas and Saurina (2002), using panel data on Spanish commercial and savings banks in theperiod 1985-1997, find significant impact of macroeconomic variables, namely GDP growth onevolution of NPLs.

3.5 Econometric framework

3.5.1 Models

The empirical literature on non-performing loans has widely favored Fixed-Effect estimations,General Method of Moments (GMM) and Vector Autoregressive (VAR) estimations. We brieflyreview these models before introducing the factor-based approach the present paper employs.

Fixed-effect estimationRecent papers on non-performing loans have considered panel data and applied a panel orfixed-effect frameworks based as follows :

yit = αyit−1 + β(L)Xit + χi + εit, |α| < 1, i = 1, ...N, t = 1, ..., T, (3.1)

with yit representing the extent of NPLs in country i at period t, Xit a k × 1 vector ofexplanatory variables other than yit with β(L) the associated 1 × k lag-polynomial vector ofcoefficients, χi the unobserved country-specific effect and εt, the error term.

Various versions of such models have been estimated. The static version assumes α = 0 whereasdynamic versions use α 6= 0. Inasmuch as the analysis of the present paper only considers U.S.data, the equivalent specification we estimate is as follows :

yt = αyt−1 + β(L)Xt + εt, |α| < 1, i = 1, ...N, t = 1, ..., T. (3.2)

We also estimate a static and dynamic version of this model which correspond in our case toan ordinary least squares (OLS) estimation.

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Arellano-Bond generalized method of momentsThe analysis of non-performing loans requires that potential endogeneity issues be taken intoaccount. This problem, common in the banking literature, may arise because of reverse causa-tion between NPLs and their main explanatory variables. To circumvent endogeneity, Arellanoand Bond (1991) suggest the following version of the generalized method of moments (GMM)estimator for panel data

∆yit = α∆yit−1 + β(L)∆Xit + ∆εit, (3.3)

where ∆ represents the first-difference operator. As insofar we do not consider a panel data,this method appears less relevant to our work. We then do not estimate a GMM model.

Vector autoregressive estimationAnother approach widely considered in the banking literature on non-performing loans is thefollowing panel-vector autoregressive model (VAR) specification

Yi,t = Γ0 +

n∑s=1

ΓsYi,t−s + β(L)Xt + χi + εit, (3.4)

where Yi,t denotes the vector of endogenous variables. We omit the fixed-effect parameterand estimate two equivalent versions of this model. In the first version (VAR), we imposethat β(L) = 0 and relax this assumption in the second version (VAR-X) and include a set ofexogenous predictors.

3.5.2 Factor models

Selection of predictors in empirical work is an issue of substantial importance. Due to datalimitation and computational feasibility, most previous contributions assessing NPLs haveconsidered only a handful of predictors. Howver, as noticed by Ludvigson and Ng (2009),this approach might be inappropriate for at least two reasons. First, latent macro-financialdriving components can hardly be summarized by few observables or measured variables.Second, important theoretical macroeconomic concepts are often imperfectly measured andthen difficult to meaningfully interpret. To circumvent these limitations, a growing body ofempirical macroeconomic literature has applied factor analysis.

Developed in the early 1900’s by the psychologist Charles Spearman to model human intel-ligence, factor analysis is a modeling procedure used to analyze co-movements among a setof observed (measured) variables with a small set of latent variables. The underlying idea isthat a large set of observed variables may share co-movements driven by only a small set ofunobserved variables. Most factor analyses posit a linear relationship expressed as follows :

Zt = HtFt + Et, (3.5)

51

where Zt is the vector of observed variables, Ft, the latent factors,Ht, the matrix of parameters(which may vary with time t)and Et a vector of idiosyncratic perturbations. Identification ofthe latent factors and estimation of the parameters generally require the specification of thedynamic process driving the latent factors, most often through an autoregressive pattern ofthe type :

Ft = BFt−1 + Ut, (3.6)

with Ut is a noise error term. Different methods of estimations are considered in the literature,with the most common being the Kalman filter and principal component analysis (PCA). Thepresent paper considers the latter, as it is simple, robust and widely applied in the literature.

3.5.3 Principal component analysis

BackgroundFirst introduced by Karl Pearson in the early 1900’s and later formalized by Hotelling (1933),principal component analysis (PCA) is a multivariate statistical procedure, which transformsa set of N correlated variables into a new set of N uncorrelated variables, the principal com-ponents (PCs). 2 By construction, the principal components are linear combinations of theoriginal variables, but are orthogonal to each other. As such they exhibit no redundant infor-mation and form, as a whole, an orthogonal basis on which the observations are projected.PCA allows visualization, investigation and interpretation of latent dependencies among a setof variables. One of its appeals is its ability to reduce the dimension of the data space andprovide a subspace maximizing the variance of the projected observations when N ′ (N ′ < N)components are selected.

NotationsLet W be a M×N matrix of rank L with L ≤ min {M,N}, representing the data table to ana-lyze, wij a generic element of W and Σ = W ′W a positive semi-definite matrix correspondingto the covariance or correlation matrix of W , depending on the preprocessing implemented onW . 3

As a positive semi-definite matrix, Σ always admits an eigen-decomposition of the form :

Σ = C∆C ′, (3.7)

where C collects the eigenvectors of Σ such that CC ′ = CC−1 = I, with I the identitymatrix and ∆ is a diagonal matrix whose elements are the corresponding eigenvalues listed in

2. An extensive discussion of principal component analysis is provided by Jolliffe (1986), Timm (2002),Jackson (2005), Basilevsky (2009) and Abdi and Williams (2010). This subsection follows Abdi and Williams(2010).

3. The data table to analyze is generally pre-processed before the analysis in order to avoid an overweightingof some variables. When the columns of W are centered to their mean and each element divided by

√M or√

M − 1, Σ corresponds to the covariance of W. In addition to the centering, when each variable is standardizedto unit norm, Σ corresponds to the correlation matrix of W.

52

descending order. Covariance and correlation matrices are all positive semi-definite matriceswhich admit a eigen-decomposition with that particular property that the eigenvalues arealways positive or null. An eigenvalue λ of the matrix Σ and its corresponding eigenvector cis a pair solution of the following equation :

Σc = λc. (3.8)

Written differently, λ and c are solutions of

(Σ− λ)c = 0. (3.9)

Note that the total variance of the data table W is also equal to the trace of the matrix Σ as(3.7) can be rewritten as :

Σ = W ′W = CΛC ′ =

N∑j=1

λjcjc′j . (3.10)

Construction and selection of the principal componentsPrincipal component analysis can be thought as a projection procedure, with the observationsprojected onto a new orthogonal basis, the principal components. The objective is to find aprojection matrix maximizing the variance of the projected data. Different matrices, admissiblesolutions to this optimization problem, exist and one of them is the matrix C defined in (3.7).The new observations, the matrix F, are also referred to as the scores and are computed asfollows :

F = WC. (3.11)

Several methods are proposed in the literature to determine the number of principal compo-nents (PCs) to select in order to maximize the variance of the projected observations. Sincethe matrix C is a collection of eigenvectors listed in descending order according to the ampli-tude of their eigenvalues, a rule of thumb consists in selecting the first PCs accounting for atleast 70-80% of the total variance in the original data. Denote the proportion of total varianceaccounted for by the first k PCs as ρ2k , which is

ρ2k =

∑kj=1 λj∑Nj=1 λj

=

∑kj=1 λj

tr(Σ)(3.12)

Another method recommends selecting the principal components whose eigenvalues are greaterthan the average eigenvalues, such that :

λi >1

N

N∑j=1

λj (3.13)

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Yet another, somewhat subjective, graphical procedure can be applied to select the number ofprincipal components. This procedure is often referred as to the scree or elbow test. It consistsof plotting the eigenvalues according to their size, with the objective to identify a point inthis graph (an elbow) where the slope of the graph becomes flat abruptly and to keep only thecomponents before the elbow.

Some researchers consider the prediction performance of the principal components (PCs). Asimple approach consists, for example, to stop adding components when the residual sum ofsquares (RESS) increases. The RESS is computed as :

RESSM = ||W − W k||2, (3.14)

with W k the prediction ofW with the first k principal components. In principle, the smaller theRESS the better the k first principal components fit the data. More elaborated approach suchas the predicted residual sum of squares (PRESS) for random effect model are also consideredin the literature. 4 The principal components selection methods described above all pertainto the literature of Factor Analysis (FA). Given our aim, the prediction of NPLs, we favoranother selection approach based on the predicting performance of the principal components.Principal components are selected according to their association with the dependent variable.This relates our estimations the Principal Component Regression. 5

Interpretation of the factorsSince a growing number of economic variables are now becoming available, the study and inter-pretation of dependencies among these potentially correlated variables is proving increasinglychallenging. Interpretation of these data in a more meaningful form requires an appropriatereduction of the number of variables. This dimension reduction is provided by the principalcomponent analysis, after a small number N ′ (N ′ < N) of components has been selected. Ho-wever, these components, designed as linear combinations (a weighted average) of the originalvariables, lack some clear interpretation.

One popular approach to facilitate the interpretation of the principal components selectedis to apply a rotation. Two main types of rotations are applied : orthogonal when the newset of covariates are required to be uncorrelated and oblique otherwise (for more details,see, e.g., Abdi and Williams (2010)). In the economic literature and more specifically in themacroeconomic field, to interpret a principal component, a correlation analysis is generallyperformed to determine the original variable to which this principal component loads themost and then apply the appropriate sign transformation. For example, if the first principalcomponent of a set of variables loads more on the industrial production with a correlation of

4. We refer the readers to Abdi and Williams (2010) for more details.5. Results based on Factor Analysis are not qualitatively different and are available upon request.

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−0.89, this component could be interpreted as the industrial production, and be mutiplied by−1 if used in other analysis.

3.6 Data and preliminary analyses

3.6.1 Non-performing loans

In the banking industry, a loan is labelled as non-performing if no scheduled payment has beenmade for at least 90 days and the odds of a full repayment are substantially low. The bankingliterature adopts a more flexible definition and measures non-performing loans as the total ofloans and leases past due 90 days or more plus non-accrual loans, divided by total loans. Wefollow this definition to ease comparison with previous works.

Table 3.1 – Descriptive statistics for non-performing loans ratios (%)

Period Min Mean Max Std. Dev.

1984 - 1988 2.69 3.15 3.81 0.311989 - 1993 1.98 3.25 4..01 0.521994 - 1998 0.94 1.17 1.86 0.241999 - 2003 0.94 1.21 1.50 0.202004 - 2008 0.70 1.14 2.97 0.602009 - 2013 2.67 4.30 5.64 0.60

1984- 2013 0.70 2.37 5.64 1.36

Notes : Non-performing loans (NPLs), defined as loans that banks categorize as 90-days or morepast due or nonaccrual in the Call reports, are expressed in percentage of total (gross) loans. Dataare from the Federal Financial Institutions Examination Council (US), retrieved from FRED,the website of the Federal Reserve Bank of St. Louis.

Table 3.1 provides some descriptive statistics on the monthly NPLs in the US banking industryfor the sample 1984Q1-2013Q4 (data on NPLs was retreived from the Federal Reserve Bankof St. Louis website). We notice that over the full sample period, the quarterly proportionof NPLs was around 2.4% of the total, on average. The Savings and loans crisis in the late1990’s, as well as the subprime crisis in the late 2000’s, where both characterized by substantialincreases of NPLs. During these episodes of distress, NPLs were respectively equal to 3.25%and 4.30% in average. Below, we use the first difference of this ratio as our main variable ofinterest, to ensure we work with a stationary dependent variable. 6

Figure 3.1 depicts the evolution of the U.S non-performing loans and bank failures over thepast decades. We observe a significant and positive relationship between NPLs and bank

6. Several papers on the determinants of NPLs work with logit transformation of NPLs, wherein Y =log( NPL

1−NPL ). This transformation ensures values in the interval [-∞ ;+ ∞] and also avoids non-normality inthe error term. We considered this logit transformation but unit root tests suggested it was not stationnary.Applying a first difference helps remove the trend in the data.

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failures. A surge of NPLs is always accompanied by an increase of bank failures as argued byDemirgüç-Kunt and Detragiache (1998) and Laeven and Valencia (2012).

Figure 3.1 – Non-performing loans in the US banking sector

Jul−84 Oct−87 Jan−91 Apr−94 Jul−97 Oct−00 Jan−04 Apr−07 Jul−10 Oct−13

050

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Bank Failures Non−Performing Loans

Notes : Data on the U.S. bank failures are retrieved from Federal Deposit Insurance Corporation andplotted against the left vertical axis. Data on NPLs (expressed as a ratio of the total loans, in percentage)are retrieved from FRED, Federal Reserve Bank of St. Louis website and plotted against the right verticalaxis.

3.6.2 Explanatory variables

This paper draws on U.S. data suggested by McCracken and Ng (2016) who aim to provide a“convenient starting point for empirical analysis that requires big data". They collect a largedatabase of macroeconomic variables at a monthly or quarterly frequency, thus covering alarge pan of the U.S. economy in a database dating from 1959 up to the present date. Thedatabase is updated monthly and publicly accessible. We retain the quarterly version of thisdata and in addition, add more variables related to the banking sector to help our analysisof non-performing loans. These additional data are also retrieved from the Federal ReserveBank of St.-Louis website. Our sample thus spans the period 1984-2013 and over 150 differentvariables are considered, categorized into 11 economic and financial sector. We transform thevariables as suggested by McCracken and Ng (2016), in order to remove trends. Table 3.2presents the explanatory variables and the sector covered by our data (a detailed list of allthe explanatory variables is available in the Appendix).

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Table 3.2 – Data description

Group ID Data ID Data Description

Variables considered by McCracken and Ng (2016)1 001 - 015 Production2 016 - 018 Consumption3 019 - 027 Orders and Inventories4 028 - 037 Housing Industry5 038 - 068 Labor Market6 069 - 088 Prices7 089 - 105 Interest Rates8 106 - 112 Exchange Rates9 113 - 126 Money10 127 - 131 Stock Market

Variables added by the authors11 132 - 153 Banking Industry

3.6.3 Preliminary analysis

To ensure that no trend remains in the data, we perform a pre-experiment analysis and applyappropriate transformations to the data following McCracken and Ng (2016). In our empiricalwork below, we refer to the benchmark model when discussing the framework including onlytraditional explanatory variables and to the factor model as the one making use of our latent-factor methodology. Table B.11 in the Appendix lists the variables selected for the benchmarkmodel.

Table B.2 presents some descriptive statistics of the transformed explanatory variables. Apartfrom the Order & Inventories variable used in the Benchmark model, we note no significantdisparity in the explanatory data both used in the Benchmark and the Factor models. We assessthe correlation across the predictors we used for the Benchmark and Factor models. TablesB.3 and B.4 respectively presents these correlations. We find no significant and abnormalcorrelation across the predictors. Recall for the rest of the analyses that since the factors areidentifiable up to a square matrix, the signs of the coefficients of the latent factors have noparticular interpretation. Interpreting their signs may be misleading.

One of the modeling framework analyzed below is a vector autoregressive (VAR) model inwhich some hypotheses about variable placement in the VAR are motivated by timing andcausation. We thus assess the causal direction between the predictors by testing whether NPLsGranger-cause the variable or vice-versa. Results for the Benchmark and Factor models arepresented in blue and black color in Table B.6, respectively. The table reports interestingreverse causality (in a Granger sense) between some predictors : variables from sectors suchas the housing industry cause and are caused, in the Granger sense, by the evolution of non-performing loans, suggesting then the need to account for endogeneity.

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3.7 Estimation

We estimate the models presented in Section 3.5 Recall that for each model considered bench-mark refers to the model with a few of the traditional variables used to analyze NPLs whilethe factor model is our framework with factors extracted from the McCracken and Ng (2016)database.

3.7.1 OLS models

The first model estimated posits a linear relationship between non-performing loans and a setof explanatory variables. Table 3.3 presents the results for the static version of this model.The two models identify a relatively similar set of statistically significant predictors. Theyeach point five predictors as significant, with three of them common to the two frameworks :namely predictors related to the housing industry, the labor market and to stock markets.

Table 3.3 – Static OLS estimation results

Benchmark Model Factor Model

Coef. Std. Err. Signif. Coef. Std. Err. Signif.

Explanatory VariableProduction 3.40 2.50 −0.01 0.01Consumption −8.45 3.69 ** 0.01 0.01Order & Inventories −0.00 0.01 0.00 0.01Housing Industry −0.48 0.19 ** 0.02 0.01 **Labor Market 0.43 0.10 *** 0.01 0.01 **Price 1.87 2.25 −0.25 0.12 **Interest Rate 0.02 0.05 −0.08 0.03 ***Exchange Rate −0.48 0.71 0.00 0.02Money 2.89 1.53 * −0.03 0.02Stock Market 0.64 0.28 ** 0.06 0.02 ***Banking Industry 0.17 1.05 0.02 0.01

N. Obs. 118 118Adj. R-Squared 43.58 54.43Residuals Std. Error 0.17 0.15F. Stat. 9.21 13.70

Symbols ∗,∗∗ and ∗∗∗ indicate statistical significance at 10%, 5% and 1% level.

Table 3.3 shows that the Factor model fits the data better, with an adjusted R-squaredgreater than that of the Benchmark. Conversely, the residuals’ standard error is smaller inthe Factor model, relative to the benchmark. The benchmark results suggest that increasesin household consumption are associated with decreases in non-performing loans. Accordingto the cyclical consumption theory, households increase their consumption level when theyanticipate good economic conditions ahead, which is consistent with a decrease in NPLs.

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As household consumption, a dynamic economic characterized by an increase of orders alsoaccompanies a decrease of the NPLs. A favorable exchange rate, another sign of expansion, isfound here as in the empirical literature to contribute to a decrease of NPLs.

We now report the results arising from a dynamic estimation of the OLS model, in Table 3.4.To do so, we follow the previous literature and incorporate past value of the dependent variablein the set of explanatory variables. Table 3.4 shows that the Benchmark model now identifiessix explanatory variables as significant, whereas the Factor model only identifies four. The twomodels’ only common pick for a significant variable is now the housing industry variable. TheFactor model retains a (smaller) advantage in fitting the data over the benchmark. The Factormodel is more parsimonious however, with only four significant predictors identified ; it is alsomore consistent in that the significant variables it identifies are similar to those signled out inthe staitc model case.

Table 3.4 – Dynamic OLS estimation results

Benchmark Model Factor Model

Coef. Std. Err. Signif. Coef. Std. Err. Signif.

Explanatory VariableNPL(-1) 0.12 0.09 −0.02 0.10Production 4.51 2.45 * −0.01 0.01Consumption −6.39 3.66 * 0.02 0.01Order & Inventories −0.00 0.00 0.03 0.01Housing Industry −0.57 0.19 *** 0.01 0.01 **Labor Market −0.34 0.11 *** 0.01 0.01Price 3.20 2.19 −0.23 0.13 *Interest Rate 0.04 0.04 −0.08 0.03 **Exchange Rate −0.21 0.69 −0.01 0.02Money 3.68 1.51 ** −0.02 0.02Stock Market −0.20 0.28 ** 0.06 0.03 **Banking Industry 0.41 1.02 −0.00 0.01

N. Obs. 116 116Adj. R-Squared 47.45 48.52Residuals Std. Error 0.16 0.16F. Stat. 9.73 10.11

Symbols ∗,∗∗ and ∗∗∗ indicate statistical significance at 10%, 5% and 1% level.

3.7.2 Vector autoregressive models

VAR modelOn the grounds of the evidence provided by the series of Granger causality tests presented inTable B.6, we estimate a vector autoregressive model. We consider as endogenous variables thenon-performing loans (NPLs), the housing industry (Hous), the interest rates (Int) and thebanking industry (Bank). The two models identify past values of NPLs and housing industry

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as significant in explaining and forecasting the dynamic of current NPLs value. Contrary tothe Benchmark model, the Factor model also identifies the interest rate variable as significant.Notice that the Factor model outperforms the Benchmark in the fitting of the NPLs witha greater adjusted R-squared (respectively 40.28% and 38.28%). The standard errors of theresiduals are of the same magnitude. Table 3.5 presents the results of the VAR model.

Table 3.5 – VAR estimation

Benchmark Model Factor Model

NPL Hous Int Bank NPL Hous Int Bank

NPL(-1) 0.34 -0.08 -0.15 -0.01 0.27 1.35 -0.35 1.07Housing Industry(-1) -0.71 0.58 0.29 -0.00 0.03 0.67 -0.05 0.02Interest Rate(-1) -0.04 -0.02 0.53 0.00 -0.07 0.01 0.17 -0.18Banking Industry(-1) 0.54 -0.06 1.31 0.62 0.01 -0.12 -0.03 0.46

N. Obs 117 117 117 117 117 117 117 117Adj. R-Squared 38.28 45.56 31.04 37.23 40.28 47.54 23.74 33.48Residuals Std. Error 0.18 0.08 0.37 0.02 0.18 1.972 0.44 1.24F. Stat. 18.99 25.27 14.05 18.20 20.56 27.28 10.03 15.59

Bold figures are significant at 10%.

VAR-X modelFinally, we estimate a VAR model with exogenous variables. We select as exogenous variables,the variables identified by the Granger test (Table B.6) to granger-cause the NPLs. Thevariables we retain are related to production, consumption, order & inventories and labormarket. The objective here is to control for a possible impact of these variables and increasethe in-sample fit. Inclusion of these exogenous variables improves both the Benchmark andthe Factor model. Their adjusted R-squared increase to 46.23% and 47.88% respectively forthe Benchmark and the Factor models. Their residuals standard errors also decrease to 0.17%and 0.16% respectively. Note that, here again, the Factor model outperforms the Benchmarkmodel. The two models both select the housing industry variables as significant in the set ofendogenous variables and the consumption and labor market variables in the set of exogenousvariables. The Benchmark model selects again the past values of NPLs as significant in the setof endogenous variables whereas the Factor model picks the interest variable. We consider asbest, the Factor model for both statistical performance and economic intuitive results. Increaseand decrease of interest rate are expected both on the theoretical and empirical grounds toimpact households payment capacity and influence the evolution of NPLs. Households adapttheir consumption path according to their capacity to pay back their loans. Jobless householdsare more susceptible to experience difficulties to reimburse their loans.

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Table 3.6 – VAR-X estimation

Benchmark Model Factor Model

NPL Hous Int Bank NPL Hous Int Bank

NPL(-1) 0.19 -0.04 0.02 -0.01 0.14 1.41 -0.38 0.78Housing Industry(-1) -0.45 0.44 -0.05 0.01 0.02 0.54 -0.05 -0.05Interest Rate(-1) 0.01 -0.04 0.33 0.00 -0.06 0.29 0.19 -0.04Banking Industry(-1) 0.87 -0.49 3.78 0.56 0.00 -0.11 -0.03 0.48

Exogeneous Variables

Production 1.86 2.77 1.69 -0.28 -0.01 0.19 -0.03 -0.00Consumption -5.96 1.09 -6.17 0.13 0.03 0.54 0.05 0.34Order &Inventories -0.00 -0.00 0.05 -0.00 0.01 -0.14 0.03 0.10Labor Market 0.29 -0.05 0.01 -0.01 0.01 -0.07 -0.01 -0.04

N. Obs 117 117 117 117 117 117 117 117Adj. R-Squared 46.23 53.29 46.86 37.96 47.88 56.88 22.56 43.37Residuals Std. Error 0.17 0.08 0.33 0.02 0.16 1.79 0.45 1.14F. Stat. 13.47 17.54 13.78 9.87 14.32 20.13 5.22 12.11

Bold figures are significant at 10%.

Figures 3.2 and 3.3 respectively presents the impulse response function (IRF) of the factor-based VAR and VAR-X models. We apply an appropriate transformation to match the signsof the Benchmark model. The IRF functions both shows that an improvement of the housingindustry significantly reduces the number of NPLs. The interest rate also has the same effect.On this subject, the empirical literature proposes two opposing views. A first view suggests thatan increase of interest rate implies an increase of NPLs in the extent that fragile householdsrapidly become unable to pay back their loans. A second view argues that an increase of theinterest rate disqualifies fragile households to get a loan, reducing then the level of NPLs.Another interesting result is the impact of the banking industry on the evolution of NPLs.Our result suggests that improvement of the banking industry conditions induces an increaseof NPLs, since dynamic banking environment can encourage banks to take more risks andlower their standard in allocation of loans.

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Table 3.7 – Forecast error variance decomposition

VAR Model VAR-X Model

h=1 h=2 h=3 h=4 h=1 h=2 h=3 h=4

NPL 1.00 0.89 0.81 0.76 1.00 0.94 0.91 0.90Housing Industry 0.00 0.08 0.16 0.21 0.00 0.04 0.07 0.08Interest Rate 0.00 0.02 0.02 0.02 0.00 0.02 0.02 0.02Banking Industry 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Figure 3.2 – IRF of the VAR model

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Table 3.7 presents the forecast error variance decomposition of the factor-based VAR and VAR-X models. Housing sector explains most of the forecast error variance of the non-performingloans after its own past values.

3.8 Out-of sample forecasting

We conduct an out-of-sample forecasting exercise of the performance of the VAR models(Benchmark and the Factor models). We start from the sample covering the year 1983-2011

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Figure 3.3 – IRF of the VARX model

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and estimate the VAR models to predict the outcome of the first period ahead. We updatethe sample with the observation of the next period and reestimate the model to forecast thevalue of the period ahead. We repeat this exercise over the year 2011-2013 and compute thefollowing performance criteria : root mean square error (RMSE), mean absolute error(MAE)and mean absolute percentage error (MAPE). Figure 3.4 shows the relative performance ofthe Factor model over the benchmark model. A ratio less than 1 indicates a performanceof the Factor model over the Benchmark model and vice versa. According to our result, theFactor model continuously outperforms the Benchmark model over the whole out-of-sampleforecasting period.

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Figure 3.4 – Forecasting performance

Jan−11 Jul−11 Jan−12 Jul−12 Jan−13 Jul−13

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3.9 Conclusion

In this paper, we revisited widely applied models to analyze and forecast evolution of non-performing loans in the banking literature. We considered as predictors key sectoral factorsextracted from the large data suggested by McCracken and Ng (2016). We found that factor-based models outperform all the standards models. More specifically, for the U.S. case, wealso uncover that variables related to housing industry are very significant to understand andpredict evolution of non-performing loans. This result suggests the importance of the mortgageloans for U.S banks.

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Conclusion

This thesis investigates different issues related to financial stability. The first Chapter ana-lyzes the determinants of financial crises and also assesses the likely impact that a SecuritiesTransaction Tax (STT) could have on the likelihood of financial crises. The second Chapteraddresses the question of the monitoring and forecasting of the monthly aggregate commercialbank failures. The third and last Chapter focuses on the modeling of the non-performing loans.

In the first Chapter, we apply a logit model to study the impact that a harmonized SecuritiesTransaction Tax (STT) could have on the likelihood of systemic financial crises. We considerthe traditional explanatory variables suggested in the literature to analyze financial crises andadd a proxy for the likely effect of an STT. Our results confirm some previous findings in theliterature and also uncover a positive relationship between of our proxy and the occurenceof financial crises. Higher transaction costs are associated with a higher risk of crisis. Wedocument the robustness of this key result to possible endogeneity effects. To the extent thata widely-based STT would increase transaction costs, our results therefore suggest that theestablishment of this tax could increase the risk of financial crises.

In the second Chapter, we model the monthly number of commercial bank failures. Weconstruct key sectoral predictors from the large set of U.S. macro-financial variables in McCra-cken and Ng (2016) which we incorporate in a hurdle negative binomial model. The objectivehere is to explain and predict the number of monthly commercial bank failures. We find thathousing industry variables display a strong and robust forecasting power particularly duringrelatively calm or normal periods characterized by no systemic failures episodes. This resultsuggests that pressures in the housing sector highly influence the banking sector stability byexacerbating banks exposure to abnormal non-performing loans increase and to rapid assetsdeterioration. The different specifications of our model confirm the robustness of our results.

Finally, in the third Chapter, we review different models proposed in the literature for fittingand forecasting banks non-performing loans (NPLS). We apply these models to the U.S. caseand compare their performance to those of similar models in which we replace traditionalexplanatory variables by key sectoral predictors. We extract all these key sectoral predictorsfrom a large set of potential U.S. macro-financial predictors suggested by McCracken and Ng(2016) for big data analysis, that we supplement with additional banking variables. The main

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focus is to assess the performance of factor-based models over traditional ones in analyzingnon-performing loans. Our findings indicate that the factor-based models all outperform thetraditional models, suggesting then that latent factors are more informational. Practitionersand researchers could therefore consider latent factors in their modeling of NPLs. Moreover,for the U.S. case, we also uncover a strong evidence. Housing sector, which accounts onlyfor almost 10% of the U.S. banks total loans in average, highly impacts the evolution of non-performing loans over time. This result provides empirical grounds to the common assumptionthat mortgage defaults rapidly spread to other types of loans such as car and credit card loansand can significantly undermine financial stability.

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Annexe A

Monitoring Bank Failures in aData-Rich Environment

A.1 Static HNB Model : additional analyses

A.1.1 Static HNB forecasting performance through different horizons

We compare the values of four criteria across the different horizons of prediction ranging from0 to 24 months.

Figure A.1 – Static HNB forecasting performance through different horizons

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No clear-cut result emerges, but we notice four local minimum for each criterion namely forpredictions of three, nine, fourteen and nineteen months ahead. We consider in a first attemptthese horizons and select the one with the best in-sample fit of the dependent variable. FigureA.1 presents the performance of the Static HNB model.

A.1.2 Static HNB predictors summary statistics

We assess the persistence of the extracted factors in the static HNB model with their first-order autoregressive coefficient. As shown in Table A.1, we find no persistence greater than0.84 and not much volatility within the estimated factors.

Table A.1 – Static HNB predictors summary statistics

Sectors Std. Dev. AR(1)Production 0.22 0.67Consumption 0.73 −0.37Orders and Inventories 1.39 −0.23Housing Industry 0.73 0.84Labor Market 0.72 0.28Prices 0.91 0.53Interest Rates 0.48 0.51Exchange Rates 0.99 0.28Money 0.41 0.58Stock Market 0.48 0.34Banking Industry 0.64 0.44

A.1.3 Correlation across predictors in the static HNB model

There is also no strong endogeneity across factors. Table (A.2) presents their correlation, withhousing industry and interest rates being the most correlated (−0.29). This lack of strongcorrelation across factors reinforces the robustness of our approach.

Table A.2 – Correlation across predictors in the static HNB model

Prod. Cons. Ord. Hous. Lab. Prices Int. Exch. Money Stck.

Cons. -0.03 1.00 -0.22 -0.05 0.07 0.11 0.10 -0.03 0.01 -0.02Ord. & Inv. 0.04 -0.22 1.00 0.01 0.05 -0.00 -0.02 -0.04 -0.05 -0.01Hous. -0.23 -0.05 0.01 1.00 -0.20 0.18 -0.29 -0.01 -0.26 0.07Lab. -0.07 0.07 0.05 -0.20 1.00 -0.04 0.09 0.03 0.02 -0.04Prices -0.08 0.11 -0.00 0.18 -0.04 1.00 0.02 0.05 -0.04 -0.00Int. Rates 0.20 0.10 -0.02 -0.29 0.09 0.02 1.00 0.08 0.16 0.08Exch. Rates 0.04 -0.03 -0.04 -0.01 0.03 0.05 0.08 1.00 0.13 -0.01Money 0.13 0.01 -0.05 -0.26 0.02 -0.04 0.16 0.13 1.00 0.02Stck. Mkt. -0.07 -0.02 -0.01 0.07 -0.04 -0.00 0.08 -0.01 0.02 1.00Bank. Ind. -0.06 0.03 -0.02 -0.08 0.19 -0.05 0.17 0.05 0.11 0.06

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A.2 Dynamic HNB model : additionnal analyses

A.2.1 Dynamic HNB model Grid Search

We compute for each specification the relative BIC. We divide the model’s BIC by the staticHNB model’s BIC. The row refers to the horizon of prediction and the column to the numberof lags of the dependent variable included. We select according to Table A.3, the model withseven lags used to forecast bank failures four months ahead. Other specifications perform aswell, but we favor for the sake of parsimony the model with seven lags used to forecast bankfailures four months ahead since it is the model with the less predictors which yields the bestresults in the near term.

Table A.3 – Dynamic HNB model grid search

l=0 l=1 l=2 l=3 l=4 l=5 l=6 l=7 l=8 l=9 l=10 l=11 l=12

h = 0 0.92 0.92 0.91 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89h = 1 0.92 0.91 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89h = 2 0.93 0.91 0.90 0.90 0.90 0.90 0.89 0.89 0.89 0.89 0.89 0.89 0.89h = 3 0.92 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.89 0.90h = 4 0.91 0.90 0.89 0.89 0.89 0.89 0.89 0.88 0.88 0.88 0.88 0.88 0.88h = 5 0.92 0.91 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.89 0.89 0.90 0.90h = 6 0.92 0.91 0.90 0.90 0.90 0.90 0.90 0.91 0.90 0.90 0.90 0.91 0.91h = 7 0.92 0.91 0.90 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.90 0.90h = 8 0.93 0.91 0.91 0.90 0.90 0.91 0.90 0.90 0.91 0.91 0.91 0.91 0.92h = 9 0.93 0.92 0.91 0.91 0.91 0.91 0.91 0.91 0.91 0.92 0.92 0.92 0.92h = 10 0.93 0.91 0.91 0.91 0.90 0.91 0.91 0.91 0.91 0.92 0.92 0.92 0.92h = 11 0.92 0.91 0.91 0.91 0.91 0.91 0.92 0.92 0.92 0.93 0.93 0.93 0.93h = 12 0.93 0.93 0.92 0.92 0.92 0.92 0.93 0.93 0.93 0.93 0.94 0.94 0.94h = 13 0.96 0.95 0.94 0.94 0.95 0.95 0.95 0.95 0.95 0.96 0.96 0.96 0.96h = 14 0.96 0.95 0.95 0.95 0.95 0.95 0.96 0.96 0.96 0.96 0.96 0.97 0.97h = 15 0.96 0.96 0.95 0.95 0.96 0.96 0.96 0.96 0.97 0.97 0.97 0.98 0.98h = 16 0.97 0.96 0.96 0.96 0.96 0.96 0.97 0.97 0.97 0.97 0.97 0.98 0.98h = 17 0.97 0.97 0.97 0.97 0.97 0.97 0.98 0.98 0.98 0.98 0.99 0.99 0.99h = 18 0.97 0.97 0.97 0.97 0.97 0.98 0.98 0.98 0.98 0.99 0.99 0.99 0.99h = 19 0.98 0.97 0.97 0.97 0.97 0.98 0.98 0.98 0.98 0.99 0.99 0.99 0.99h = 20 0.98 0.97 0.97 0.97 0.98 0.98 0.98 0.99 0.99 0.99 0.99 0.99 1.00h = 21 0.97 0.97 0.97 0.97 0.98 0.98 0.98 0.98 0.98 0.99 0.99 0.99 1.00h = 22 0.99 0.99 0.98 0.98 0.99 0.99 0.99 1.00 1.00 1.00 1.00 1.01 1.01h = 23 0.99 0.98 0.98 0.98 0.99 0.99 0.99 0.99 1.00 1.00 1.00 1.01 1.01h = 24 0.98 0.98 0.98 0.98 0.99 0.99 0.99 0.99 1.00 1.00 1.00 1.01 1.01

69

A.2.2 Dynamic HNB predictors summary statistics

Table A.4 presents the summary statistics of the factors selected in the dynamic HNB model.Once again, we uncover no significant persistence.

Table A.4 – Dynamic HNB predictors summary statistics

Sectors Std. Dev. AR(1)Production 0.22 0.67Consumption 0.46 −0.09Orders and Inventories 1.94 0.85Housing Industry 0.73 0.84Labor Market 0.72 0.28Prices 0.91 0.53Interest Rates 0.48 0.51Exchange Rates 1.76 0.32Money 0.41 0.58Stock Market 0.09 0.33Banking Industry 0.64 0.44

A.2.3 Correlation across predictors in the dynamic HNB model

Table (A.5) presents the correlation across factors in the dynamic HNB model. Here again,housing industry and interest rates display the highest correlation (−0.29).

Table A.5 – Correlation across predictors in the dynamic HNB model

Prod. Cons. Ord. Hous. Lab. Prices Int. Exch. Money Stck.

Cons. -0.04 1.00 0.01 0.04 -0.02 -0.01 0.02 -0.11 0.01 -0.03Ord. & Inv. 0.01 0.01 1.00 -0.02 0.22 0.15 0.28 -0.08 0.06 -0.06Hous. -0.23 0.04 -0.02 1.00 -0.20 0.18 -0.29 -0.06 -0.26 0.06Lab. -0.07 -0.02 0.22 -0.20 1.00 -0.04 0.09 -0.10 0.02 0.06Prices -0.08 -0.01 0.15 0.18 -0.04 1.00 0.02 -0.04 -0.04 -0.03Int. Rates 0.20 0.02 0.28 -0.29 0.09 0.02 1.00 -0.11 0.16 -0.13Exch. Rates 0.04 -0.11 -0.08 -0.06 -0.10 -0.04 -0.11 1.00 -0.07 -0.07Money 0.13 0.01 0.06 -0.26 0.02 -0.04 0.16 -0.07 1.00 0.09Stck. Mkt. -0.13 -0.03 -0.06 0.06 0.06 -0.03 -0.13 -0.07 0.09 1.00Bank. Ind. -0.06 0.06 0.22 -0.08 0.19 -0.05 0.17 -0.01 0.11 -0.09

70

A.3 Chapter 2 – list of explanatory Variables

Table A.6 – Chapter 2 – list of explanatory variables

N. VARIABLE DEFINITION UNIT

VARIABLES CONSIDERED BY McCracken and Ng (2016)PRODUCTION AND BUSINESS ACTIVITY1 INDPRO Industrial Production (IP) Index2 IPFPNSS IP : Final Products and Nonindustrial Supplies Index3 IPFINAL IP : Final Products (Market Group) Index4 IPCONGD IP : Consumer Goods Index5 IPDCONGD IP : Durable Consumer Goods Index6 IPNCONGD IP : Nondurable Consumer Goods Index7 IPBUSEQ IP : Business Equipment Index8 IPMAT IP : Materials Index9 IPDMAT IP : Durable Materials Index10 IPNMAT IP : Nondurable Materials Index11 IPMANSICS IP : Manufacturing (SIC) Index12 IPB51222S IP : Residentials Utilities Index13 IPFUELS IP : Fuels Index14 NAPMPI ISM Manufacturing : Production index Percent15 CUMFNS Capacity Utilization : Manufacturing Percent

CONSUMPTION16 DPCERA3M086SBEA Real Personal Consumption Expenditures Index17 CMRMTSPL Real Manufacturing and Trade Industries Services Millions USD18 RETAILx Retail and Food Services Sales Millions USD

ORDERS AND INVENTORIES19 NAPM ISM : PMI Composite Index Index20 NAPMNOI ISM : New Orders Index Index21 NAPMSDI ISM : Supplier Deliveries Index Index22 NAPMII ISM : Inventories Index Index23 AMDNOx New Orders for Durable Goods Millions of Dollars24 ANDENO New Orders for Nondefense Capital Goods Millions of Dollars25 AMDMUO Unfilled Orders for Durable Goods Millions of Dollars26 BUSINV Total Business Inventories Millions of Dollars27 ISRATIO Total Business : Inventories to Sales Ratio Ratio

HOUSING INDUSTRY28 HOUST Housings Starts : Total New Privately Owned Thousands of Units29 HOUSTNE Housing Starts, Northeast Thousands of Units30 HOUSTMW Housing Starts, Midwsest Thousands of Units31 HOUSTS Housing Starts, South Thousands of Units32 HOUSTW Housing Starts, West Thousands of Units33 PERMIT New Private Housing Permits (SAAR) Thousands of Units34 PERMITNE New Private Housing Permits, Northeast (SAAR) Thousands of Units35 PERMITMW New Private Housing Permits, Midwest (SAAR) Thousands of Units36 PERMITSx New Private Housing Permits, South (SAAR) Thousands of Units37 PERMITW New Private Housing Permits, West (SAAR) Thousands of Units

71

List of Explanatory Variables (Continued)

N. VARIABLE DEFINITION UNIT

LABOR MARKET38 HWIx Help-Wanted Index for United States Index39 HWIURATIOx Ratio of Help Wanted/Number of Unemployed Ratio40 CLF16OV Civilian Labor Force Thousands of Persons41 CE16OV Civilian Employment Thousands of Persons42 UNRATE Civilian Unemployment Rate Percent43 UEMPMEAN Average Duration of Unemployment Weeks44 UEMPLT5 Civilians Unemployed - Less Than 5 Weeks Thousands of Persons45 UEMP5TO14 Civilians Unemployed for 5 - 14 Weeks Thousands of Persons46 UEMP15OV Civilians Unemployed - 15 Weeks and Over Thousands of Persons47 UEMP15T26 Civilians Unemployed for 15 - 26 Weeks Thousands of Persons48 UEMP27OV Civilians Unemployed for 27 Weeks and Over Thousands of Persons49 CLAIMSx Initial Claims Units50 PAYEMS All Employees : Total nonfarm Thousands of Persons51 USGOOD All Employees : Goods-Producing Industries Thousands of Persons52 CES1021000001 All Employees : Mining and Logging : Mining Thousands of Persons53 USCONS All Employees : Construction Thousands of Persons54 MANEMP All Employees : Manufacturing Thousands of Persons55 DMANEMP All Employees : Durable Goods Thousands of Persons56 NDMANEMP All Employees : Nondurable Goods Thousands of Persons57 SRVPRD All Employees : Service-Providing Industries Thousands of Persons58 USTPU All Employees : Trade, Transportation and Utilities Thousands of Persons59 USWTRADE All Employees : Wholesale Trade Thousands of Persons60 USTRADE All Employees : Retail Trade Thousands of Persons61 USFIRE All Employees : Financial Activities Thousands of Persons62 CES0600000007 Average Weekly Hours : Goods-Producing Hours63 AWOTMAN Average Weekly Overtime Hours : Manufacturing Hours64 AWHMAN Average Weekly Hours : Manufacturing Hours65 NAPMEI ISM Manufacturing : Employment Index Percent66 CES0600000008 Average Hourly Earnings : Goods-Producing Dollars Per Hour67 CES2000000008 Average Hourly Earnings : Construction Dollars Per Hour68 CES3000000008 Average Hourly Earnings : Manufacturing Dollars Per Hour

PRICES69 PPIFGSx Personal Producer Index : Finished Goods Index70 PPIFCGx PPI : Finished Consumer Goods Index71 PPIITMx PPI : Intermediate Materials Index72 PPICRMx PPI : Crude Materials Index73 PPICMM PPI : Metals and Metal Products Index74 NAPMPRIx ISM Manufacturing : Prices Index Percent75 CPIAUCSL CPI : All Items Index76 CPIAPPSL CPI : All Urban Consumer : Apparel Index77 CPITRNSL CPI : Transportation Index

72

List of Explanatory Variables (Continued)

N. VARIABLE DEFINITION UNIT

78 CPIMEDSL CPI : Medical Care Index79 CUSR0000SAC CPI : Commodities Index80 CUUR0000SAD CPI : Durables Index81 CUSR0000SAS CPI : Services Index82 CPIULFSL CPI : All Items Less Food Index83 CUUR0000SA0L2 CPI : All Items Less Shelter Index84 CUSR0000SA0L5 CPI : All Items Less Medical Care Index85 PCEPI PCE : Chain Index Index86 DDURRG3M086SBEA PCE : Durable Goods Index87 DNDGRG3M086SBEA PCE : Nondurable Goods Index88 DSERRG3M086SBEA PCE : Services Index

INTEREST RATES89 FEDFUNDS Effective Federal Funds Rate Percent90 CP3Mx 3-Month AA Financial Commercial Paper Rate Percent91 TB3MS 3-Month Treasury Bill Percent92 TB6MS 6-Month Treasury Bill Percent93 GS1 1-Year Treasury Rate Percent94 GS5 5-Year Treasury Rate Percent95 GS10 10-Year Treasury Rate Percent96 AAA Moody’s Seasoned Aaa Corporate Bond Yield Percent97 BAA Moody’s Seasoned Baa Corporate Bond Yield Percent98 COMPAPFFx 3-Month Commercial Paper Minus FEDFUNDS Percent99 TB3SMFFM 3-Month Treasury C Minus FEDFUNDS Percent100 TB6SMFFM 6-Month Treasury C Minus FEDFUNDS Percent101 T1YFFM 1-Year Treasury C Minus FEDFUNDS Percent102 T5YFFM 5-Year Treasury C Minus FEDFUNDS Percent103 T10YFFM 10-Year Treasury C Minus FEDFUNDS Percent104 AAAFFM Moody’s Aaa Corporate Bond Minus FEDFUNDS Percent105 BAAFFM Moody’s Baa Corporate Bond Minus FEDFUNDS Percent

EXCHANGE RATES106 TWEXBMTH Trade Weighted $U.S. Index : Broad Index107 EXUSAL U.S./Australia Foreign Exchange Rate $U.S. to 1 Aus. $108 TWEXMMTH Trade Weighted $U.S. Index : Major Currencies Index109 EXSZUS Switzerland/U.S. Foreign Exchange Rate CHF to 1 U.S. $110 EXJPUS Japan/U.S. Foreign Exchange Rate Jap. Yen to 1 U.S. $111 EXUSUK U.S./U.K. Foreign Exchange Rate $U.S. to 1 U.K. £112 EXCAUS Canada/U.S. Foreign Exchange Rate CAD to 1 U.S $

MONEY113 M1SL M1 Money Stock Billions of Dollars114 TCDSL Total Checkable Deposits Billions of Dollars115 DEMDEPSL Demand Deposits : Total Billions of Dollars116 M1REAL Real M1 Money Stock Billions of Dollars

73

List of Explanatory Variables (Continued)

N. VARIABLE DEFINITION UNIT

117 OCDCBS Other Checkable Deposits at Commercial Banks Billions of Dollars118 CURRDD Currency Component of M1 Plus Demand Deposits Billions of Dollars119 M2SL M2 Money stock Billions of Dollars120 M2REAL Real M2 Money Stock Billions of Dollars121 M2OWN M2 Own Rate Percent122 MZMOWN MZM Own Rate Percent123 MZMSL MZM Money Stock Billions of Dollars124 AMBSL St. Louis Adjusted Monetary Base Billions of Dollars125 TOTRESNS Total Reserves of Depository Institutions Billions of Dollars126 NONBORRES Reserves of Depository Institutions, Nonborrowed Millions of Dollars

STOCK MARKET127 S&P 500 S&P’s Stock Price Index : Composite Index128 S&P : INDUSTx S&P’s Stock Price Index : Industrials Index129 S&P DIV YIELDx S&P’s Stock Composite : Dividend Yield Index130 S&P PE RATIOx S&P’s Stock Composite : Price-Earnings Ratio Index131 NASDAQCOM Nasdaq Composite Index Index

VARIABLES ADDED BY THE AUTHORS

BANKING INSDUSTRY132 SAVINGSx Total Savings Deposits at all Depository Insitutions Billions of Dollars133 RMFSL Retail Money Funds Billions of Dollars134 STDSL Small Time deposits - Total Billions of Dollars135 SAVINGSL Savings Deposits - Total Billions of Dollars136 SVGCBSL Savings Deposits at Commercial Banks Billions of Dollars137 SVSTSL Savings and Small Time Deposits - Total Billions of Dollars138 STDCBSL Small Time Deposits at Commercial Banks Billions of Dollars139 SVGTI Savings Deposits at Thrift Institutions Billions of Dollars140 BUSLOANS Commercial and Industrial Loans Billions of Dollars141 LOANSx Loans and Leases in Bank Credit Billions of Dollars142 REALLN Real Estate Loans Billions of Dollars143 TLAACBM027SBOG Total Assets Billions of Dollars144 IBLACBM027SBOG Interbank Loans Billions of Dollars145 CASACBM027SBOG Cash Assets Billions of Dollars146 TLBACBM027SBOG Total Liabilities Billions of Dollars147 FRPACBM027SBOG Fed Funds andd Reverse RPs with Banks Billions of Dollars148 INVEST Securities in Bank Credit Billions of Dollars149 RALACBM027SBOG Residuals (Assets Less Liabilities) Billions of Dollars150 BOWACBM027SBOG Borrowings Billions of Dollars151 NONREVSL Total Nonrevolving Credit Owned and Securitized Billions of Dollars152 CONSPIx Nonrevolving Consumer Credit to Personal Income Ratio153 DTCTHFNM Total Consumer Loans and Leases Outstanding Billions of Dollars

74

Annexe B

On The Usefulness of Big Data inModeling Non-Performing Loans

B.1 Preliminary analyses

Table B.1 – Descriptive statistics of the real estate loans proportion

Period Min Mean Max Std. Dev.

1984 - 1993 6.61 8.26 9.87 0.011994 - 2003 8.62 9.90 11.70 0.012004 - 2013 10.98 12.09 13.33 0.01

1984- 2013 6.61 10.10 13.33 0.02

Source : Reserve Federal Bank of St. Louis

Table B.2 – Descriptive statistics of the explanatory variables

Benchmark Model Factor Model

Min Mean Max Std. Dev. Min Mean Max Std. Dev.

NPL -0.41 -0.00 1.05 0.23 0.41 -4e-03 1.05 0.23Production -0.06 0.01 0.03 0.01 -5.14 -2e-17 15.87 3.16Consumption -0.01 0.01 0.02 0.01 -2.61 -2e-17 8.91 1.57Order & Inventories 35.47 51.87 60.83 4.75 -3.43 -6e-17 10.17 2.18Housing Industry -0.49 -0.01 0.21 0.11 -4.82 4e-17 11.73 2.73Labor Market -0.43 -0.00 1.40 0.28 -4.95 6e-17 19.07 3.94Price -0.03 0.01 0.03 0.01 -0.55 -2e-17 0.31 0.12Interest Rate -1.52 -0.08 0.81 0.45 -1.99 2e-17 1.10 0.52Exchange Rate -0.05 0.00 0.70 0.02 -1.78 2e-18 1.78 0.73Money 0.00 0.03 0.06 0.01 -1.86 3e-17 2.91 0.88Stock Market -0.32 0.02 0.14 0.07 -3.71 -1e-17 3.52 0.88Banking Industry -0.03 0.03 0.09 0.02 -3.25 -2e-17 8.95 1.51

75

Table B.3 – Correlation across explanatory variables - Benchmark model

Prod. Cons. Ord. Hous. Lab. Prices Int. Exch. Money Stck.

NPLs -0.49 -0.41 -0.47 -0.48 0.62 -0.10 -0.25 -0.09 0.27 -0.11Prod. 1.00 0.48 0.75 0.57 -0.77 0.24 0.45 -0.01 -0.40 0.34Cons. 0.48 1.00 0.36 0.37 -0.47 -0.03 0.16 -0.01 -0.05 0.39Ord. & Inv. 0.75 0.36 1.00 0.40 -0.71 0.20 0.62 -0.04 -0.43 0.26Hous. 0.57 0.37 0.40 1.00 -0.54 0.08 0.21 0.03 -0.12 0.32Lab. -0.77 -0.47 -0.71 -0.54 1.00 -0.25 -0.45 -0.04 0.27 -0.30Prices 0.24 -0.03 0.120 0.08 -0.25 1.00 0.09 0.30 -0.31 0.10Int. Rates 0.45 0.16 0.62 0.21 -0.45 0.09 1.00 -0.08 -0.31 0.21Exch. Rates -0.01 -0.01 -0.04 0.03 -0.04 0.30 -0.08 1.00 -0.21 0.03Money -0.40 -0.05 -0.43 -0.12 0.27 -0.31 -0.31 -0.21 1.00 -0.16Stck. Mkt 0.34 0.39 0.26 0.32 -0.30 0.10 0.21 0.03 -0.16 1.00Bank. Ind. -0.24 0.06 -0.22 -0.33 0.06 -0.14 -0.08 -0.12 0.43 -0.24

Table B.4 – Correlation across estimated predictors - Factor model

Prod. Cons. Ord. Hous. Lab. Prices Int. Exch. Money Stck.

NPLs 0.49 0.50 0.50 0.48 0.63 -0.25 -0.39 0.11 -0.34 0.54Prod. 1.00 0.68 0.79 0.55 0.75 -0.19 -0.26 -0.02 -0.14 0.36Cons. 0.68 1.00 0.55 0.57 0.62 -0.17 -0.15 -0.04 -0.13 0.35Ord. & Inv. 0.79 0.55 1.00 0.39 0.78 -0.13 -0.19 -0.07 -0.08 0.56Hous. 0.55 0.57 0.39 1.00 0.48 -0.12 -0.11 0.11 -0.26 0.14Lab. 0.75 0.62 0.78 0.48 1.00 -0.13 -0.34 0.09 -0.23 0.56Prices -0.19 -0.17 -0.13 -0.12 -0.13 1.00 0.05 -0.13 0.06 -0.15Int. Rates -0.26 -0.15 -0.19 -0.11 -0.34 0.05 1.00 -0.26 0.05 -0.25Exch. Rates -0.02 -0.04 -0.07 0.11 0.09 -0.13 -0.26 1.00 -0.07 -0.10Money -0.14 -0.13 -0.08 -0.26 -0.23 0.06 0.05 -0.07 1.00 -0.26Stck. Mkt 0.36 0.35 0.56 0.14 0.56 -0.15 -0.25 -0.10 -0.26 1.00Bank. Ind. 0.42 0.48 0.38 0.43 0.47 -0.08 -0.21 0.14 -0.30 0.21

76

Table B.5 – Unit root tests

Benchmark Model Factor Model

ADF Test PP Test ADF Test PP Testt-Stat Prob z(alpha) Prob t-Stat Prob z(alpha) Prob

NPL(-1) -3.76 0.02 -62.10 0.01 -3.76 0.02 -62.10 0.01Production -4.39 0.01 -35.99 0.01 -4.51 0.01 -37.95 0.01Consumption -3.31 0.07 -96.00 0.01 -3.53 0.04 -78.58 0.01Order & Inventories -3.97 0.01 -29.83 0.01 -4.18 0.01 -32.54 0.01Housing Industry -2.69 0.29 -36.93 0.01 -2.71 0.28* -34.65 0.01Labor Market -3.43 0.05 -34.13 0.01 -3.23 0.09 -20.24 0.06Price -3.41 0.06 -43.58 0.01 -3.33 0.07 -43.55 0.01Interest Rate -3.75 0.02 -57.96 0.01 -3.34 0.07 -92.03 0.01Exchange Rate -4.41 0.01 -77.31 0.01 -5.32 0.01 -73.14 0.01Money -2.74 0.27* -25.05 0.02 -3.21 0.09 -21.11 0.05Stock Market -4.19 0.01 -77.14 0.01 -4.82 0.01 -35.66 0.01Banking Industry -3.09 0.12* -41.07 0.01 -3.48 0.05 -49.00 0.01

∗ Unit root tests all rejected for number of lags less than 4.

Table B.6 – Granger causality tests

Granger-Caused by NPLs Granger-Causing NPLs

p=1 p=2 p=3 p=4 p=1 p=2 p=3 p=4

Production xx xx xx xxConsumption x x xx xx xx xxOrder & Inventories xx xx xx xxHousing Industry xx xx xx xx xxLabor Market x xx xx xx xxPriceInterest Rate x x x xExchange RateMoney x x xStock Market x x xx xx xx xxBanking Industry xx xx xx xx xx x x x

Table B.7 – Lag length criteria Test – VAR Benchmark model

Lag Akaike Hannan-Quinn Schwartz Final Prevision Error

1 -19.06 -18.87 -18.58 5.27e− 092 -19.45 -19.09 -18.58 3.59e− 093 -19.64 -19.13 -18.39 2.97e− 094 -19.60 -18.93 -17.96 3.11e− 09

77

Table B.8 – Lag length criteria test – VAR Factor model

Lag Akaike Hannan-Quinn Schwartz Final Prevision Error

1 -3.48 -3.29 -3.00 0.032 -3.98 -3.63 -3.11 0.023 -3.93 -3.43 -2.69 0.024 -3.96 -3.30 −2.33 0.02

Table B.9 – Lag length criteria test – VAR-X Benchmark model

Lag Akaike Hannan-Quinn Schwartz Final Prevision Error

1 -19.44 -19.08 -18.57 3.62e− 092 -19.79 -19.28 -18.54 2.55e− 093 -19.96 -19.29 -18.32 2.17e− 094 -20.05 -19.23 -18.03 1.99e− 09

Table B.10 – Lag length criteria test – VAR-X Factor model

Lag Akaike Hannan-Quinn Schwartz Final Prevision Error

1 -3.72 -3.37 -2.86 0.022 -4.18 -3.68 -2.94 0.023 -4.24 -3.58 -2.61 0.014 -4.37 -3.55 −2.35 0.01

Table B.11 – Explanatory variables (before transformation) - Benchmark model

Index Variables Min Mean Max Std. Dev.

1 Production 55.08 82.22 104.94 16.5316 Consumption 45.61 77.68 108.56 20.0919 Order & Inventories 35.47 52.00 60.83 04.8228 Housing Industry 525.67 1394.06 2120.33 418.0242 Labor Market 3.90 6.19 9.93 1.5075 Price 102.53 167.26 234.21 39.1790 Interest Rate 0.01 3.98 10.32 2.65106 Exchange Rate 59.07 95.04 129.07 20.55119 Money 2157.53 5191.85 10944.07 2407.69127 Stock Market 155.77 843.14 1770.45 461.48143 Banking Industry 1980.53 6373.18 13949.31 3623.02

Source : Reserve Federal Bank of St. Louis

78

B.2 Chapter 3 – list of explanatory variables

Table B.12 – Chapter 3 – list of explanatory variables

N. VARIABLE DEFINITION UNIT

VARIABLES CONSIDERED BY McCracken and Ng (2016)PRODUCTION AND BUSINESS ACTIVITY1 INDPRO Industrial Production (IP) Index2 IPFPNSS IP : Final Products and Nonindustrial Supplies Index3 IPFINAL IP : Final Products (Market Group) Index4 IPCONGD IP : Consumer Goods Index5 IPDCONGD IP : Durable Consumer Goods Index6 IPNCONGD IP : Nondurable Consumer Goods Index7 IPBUSEQ IP : Business Equipment Index8 IPMAT IP : Materials Index9 IPDMAT IP : Durable Materials Index10 IPNMAT IP : Nondurable Materials Index11 IPMANSICS IP : Manufacturing (SIC) Index12 IPB51222S IP : Residentials Utilities Index13 IPFUELS IP : Fuels Index14 NAPMPI ISM Manufacturing : Production index Percent15 CUMFNS Capacity Utilization : Manufacturing Percent

CONSUMPTION16 DPCERA3M086SBEA Real Personal Consumption Expenditures Index17 CMRMTSPL Real Manufacturing and Trade Industries Services Millions USD18 RETAILx Retail and Food Services Sales Millions USD

ORDERS AND INVENTORIES19 NAPM ISM : PMI Composite Index Index20 NAPMNOI ISM : New Orders Index Index21 NAPMSDI ISM : Supplier Deliveries Index Index22 NAPMII ISM : Inventories Index Index23 AMDNOx New Orders for Durable Goods Millions of Dollars24 ANDENO New Orders for Nondefense Capital Goods Millions of Dollars25 AMDMUO Unfilled Orders for Durable Goods Millions of Dollars26 BUSINV Total Business Inventories Millions of Dollars27 ISRATIO Total Business : Inventories to Sales Ratio Ratio

HOUSING INDUSTRY28 HOUST Housings Starts : Total New Privately Owned Thousands of Units29 HOUSTNE Housing Starts, Northeast Thousands of Units30 HOUSTMW Housing Starts, Midwsest Thousands of Units31 HOUSTS Housing Starts, South Thousands of Units32 HOUSTW Housing Starts, West Thousands of Units33 PERMIT New Private Housing Permits (SAAR) Thousands of Units34 PERMITNE New Private Housing Permits, Northeast (SAAR) Thousands of Units35 PERMITMW New Private Housing Permits, Midwest (SAAR) Thousands of Units36 PERMITSx New Private Housing Permits, South (SAAR) Thousands of Units37 PERMITW New Private Housing Permits, West (SAAR) Thousands of Units

79

List of Explanatory Variables (Continued)

N. VARIABLE DEFINITION UNIT

LABOR MARKET38 HWIx Help-Wanted Index for United States Index39 HWIURATIOx Ratio of Help Wanted/Number of Unemployed Ratio40 CLF16OV Civilian Labor Force Thousands of Persons41 CE16OV Civilian Employment Thousands of Persons42 UNRATE Civilian Unemployment Rate Percent43 UEMPMEAN Average Duration of Unemployment Weeks44 UEMPLT5 Civilians Unemployed - Less Than 5 Weeks Thousands of Persons45 UEMP5TO14 Civilians Unemployed for 5 - 14 Weeks Thousands of Persons46 UEMP15OV Civilians Unemployed - 15 Weeks and Over Thousands of Persons47 UEMP15T26 Civilians Unemployed for 15 - 26 Weeks Thousands of Persons48 UEMP27OV Civilians Unemployed for 27 Weeks and Over Thousands of Persons49 CLAIMSx Initial Claims Units50 PAYEMS All Employees : Total nonfarm Thousands of Persons51 USGOOD All Employees : Goods-Producing Industries Thousands of Persons52 CES1021000001 All Employees : Mining and Logging : Mining Thousands of Persons53 USCONS All Employees : Construction Thousands of Persons54 MANEMP All Employees : Manufacturing Thousands of Persons55 DMANEMP All Employees : Durable Goods Thousands of Persons56 NDMANEMP All Employees : Nondurable Goods Thousands of Persons57 SRVPRD All Employees : Service-Providing Industries Thousands of Persons58 USTPU All Employees : Trade, Transportation and Utilities Thousands of Persons59 USWTRADE All Employees : Wholesale Trade Thousands of Persons60 USTRADE All Employees : Retail Trade Thousands of Persons61 USFIRE All Employees : Financial Activities Thousands of Persons62 CES0600000007 Average Weekly Hours : Goods-Producing Hours63 AWOTMAN Average Weekly Overtime Hours : Manufacturing Hours64 AWHMAN Average Weekly Hours : Manufacturing Hours65 NAPMEI ISM Manufacturing : Employment Index Percent66 CES0600000008 Average Hourly Earnings : Goods-Producing Dollars Per Hour67 CES2000000008 Average Hourly Earnings : Construction Dollars Per Hour68 CES3000000008 Average Hourly Earnings : Manufacturing Dollars Per Hour

PRICES69 PPIFGSx Personal Producer Index : Finished Goods Index70 PPIFCGx PPI : Finished Consumer Goods Index71 PPIITMx PPI : Intermediate Materials Index72 PPICRMx PPI : Crude Materials Index73 PPICMM PPI : Metals and Metal Products Index74 NAPMPRIx ISM Manufacturing : Prices Index Percent75 CPIAUCSL CPI : All Items Index76 CPIAPPSL CPI : All Urban Consumer : Apparel Index77 CPITRNSL CPI : Transportation Index

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List of Explanatory Variables (Continued)

N. VARIABLE DEFINITION UNIT

78 CPIMEDSL CPI : Medical Care Index79 CUSR0000SAC CPI : Commodities Index80 CUUR0000SAD CPI : Durables Index81 CUSR0000SAS CPI : Services Index82 CPIULFSL CPI : All Items Less Food Index83 CUUR0000SA0L2 CPI : All Items Less Shelter Index84 CUSR0000SA0L5 CPI : All Items Less Medical Care Index85 PCEPI PCE : Chain Index Index86 DDURRG3M086SBEA PCE : Durable Goods Index87 DNDGRG3M086SBEA PCE : Nondurable Goods Index88 DSERRG3M086SBEA PCE : Services Index

INTEREST RATES89 FEDFUNDS Effective Federal Funds Rate Percent90 CP3Mx 3-Month AA Financial Commercial Paper Rate Percent91 TB3MS 3-Month Treasury Bill Percent92 TB6MS 6-Month Treasury Bill Percent93 GS1 1-Year Treasury Rate Percent94 GS5 5-Year Treasury Rate Percent95 GS10 10-Year Treasury Rate Percent96 AAA Moody’s Seasoned Aaa Corporate Bond Yield Percent97 BAA Moody’s Seasoned Baa Corporate Bond Yield Percent98 COMPAPFFx 3-Month Commercial Paper Minus FEDFUNDS Percent99 TB3SMFFM 3-Month Treasury C Minus FEDFUNDS Percent100 TB6SMFFM 6-Month Treasury C Minus FEDFUNDS Percent101 T1YFFM 1-Year Treasury C Minus FEDFUNDS Percent102 T5YFFM 5-Year Treasury C Minus FEDFUNDS Percent103 T10YFFM 10-Year Treasury C Minus FEDFUNDS Percent104 AAAFFM Moody’s Aaa Corporate Bond Minus FEDFUNDS Percent105 BAAFFM Moody’s Baa Corporate Bond Minus FEDFUNDS Percent

EXCHANGE RATES106 TWEXBMTH Trade Weighted $U.S. Index : Broad Index107 EXUSAL U.S./Australia Foreign Exchange Rate $U.S. to 1 Aus. $108 TWEXMMTH Trade Weighted $U.S. Index : Major Currencies Index109 EXSZUS Switzerland/U.S. Foreign Exchange Rate CHF to 1 U.S. $110 EXJPUS Japan/U.S. Foreign Exchange Rate Jap. Yen to 1 U.S. $111 EXUSUK U.S./U.K. Foreign Exchange Rate $U.S. to 1 U.K. £112 EXCAUS Canada/U.S. Foreign Exchange Rate CAD to 1 U.S $

MONEY113 M1SL M1 Money Stock Billions of Dollars114 TCDSL Total Checkable Deposits Billions of Dollars115 DEMDEPSL Demand Deposits : Total Billions of Dollars116 M1REAL Real M1 Money Stock Billions of Dollars

81

List of Explanatory Variables (Continued)

N. VARIABLE DEFINITION UNIT

117 OCDCBS Other Checkable Deposits at Commercial Banks Billions of Dollars118 CURRDD Currency Component of M1 Plus Demand Deposits Billions of Dollars119 M2SL M2 Money stock Billions of Dollars120 M2REAL Real M2 Money Stock Billions of Dollars121 M2OWN M2 Own Rate Percent122 MZMOWN MZM Own Rate Percent123 MZMSL MZM Money Stock Billions of Dollars124 AMBSL St. Louis Adjusted Monetary Base Billions of Dollars125 TOTRESNS Total Reserves of Depository Institutions Billions of Dollars126 NONBORRES Reserves of Depository Institutions, Nonborrowed Millions of Dollars

STOCK MARKET127 S&P 500 S&P’s Stock Price Index : Composite Index128 S&P : INDUSTx S&P’s Stock Price Index : Industrials Index129 S&P DIV YIELDx S&P’s Stock Composite : Dividend Yield Index130 S&P PE RATIOx S&P’s Stock Composite : Price-Earnings Ratio Index131 NASDAQCOM Nasdaq Composite Index Index

VARIABLES ADDED BY THE AUTHORS

BANKING INSDUSTRY132 SAVINGSx Total Savings Deposits at all Depository Insitutions Billions of Dollars133 RMFSL Retail Money Funds Billions of Dollars134 STDSL Small Time deposits - Total Billions of Dollars135 SAVINGSL Savings Deposits - Total Billions of Dollars136 SVGCBSL Savings Deposits at Commercial Banks Billions of Dollars137 SVSTSL Savings and Small Time Deposits - Total Billions of Dollars138 STDCBSL Small Time Deposits at Commercial Banks Billions of Dollars139 SVGTI Savings Deposits at Thrift Institutions Billions of Dollars140 BUSLOANS Commercial and Industrial Loans Billions of Dollars141 LOANSx Loans and Leases in Bank Credit Billions of Dollars142 REALLN Real Estate Loans Billions of Dollars143 TLAACBM027SBOG Total Assets Billions of Dollars144 IBLACBM027SBOG Interbank Loans Billions of Dollars145 CASACBM027SBOG Cash Assets Billions of Dollars146 TLBACBM027SBOG Total Liabilities Billions of Dollars147 FRPACBM027SBOG Fed Funds andd Reverse RPs with Banks Billions of Dollars148 INVEST Securities in Bank Credit Billions of Dollars149 RALACBM027SBOG Residuals (Assets Less Liabilities) Billions of Dollars150 BOWACBM027SBOG Borrowings Billions of Dollars151 NONREVSL Total Nonrevolving Credit Owned and Securitized Billions of Dollars152 CONSPIx Nonrevolving Consumer Credit to Personal Income Ratio153 DTCTHFNM Total Consumer Loans and Leases Outstanding Billions of Dollars

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