Investment-Specific Shocks and External Balances in a Small Open Economy Model (Chocs spécifiques...

Investment-Specific Shocks and External Balances in a Small Open Economy Model (Chocsspécifiques àl'investissement et balances extérieures dans une petite économie ouverte)Author(s): Marc-André Letendre and Daqing LuoSource: The Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 40, No. 2(May, 2007), pp. 650-678Published by: Wiley on behalf of the Canadian Economics AssociationStable URL: http://www.jstor.org/stable/4620624 .

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Investment-specific shocks and external balances in a small open economy model Marc-Andre Letendre Department of Economics, McMaster

University Daqing Luo School of Economics, Shanghai University of

Finance and Economics

Abstract. We set up a standard small open economy business cycle model driven by government spending shocks, neutral productivity (TFP) shocks, and investment-specific shocks. The model is calibrated to quarterly Canadian data and its predicted moments and sample paths are compared with their Canadian counterparts. We find that the model captures the dynamics in investment and in the trade balance better than special cases of the model where either one of the productivity shocks is omitted. More specifically, the model matches the variance of the trade balance-output ratio, its correlation with output and its autocorrelation. It also matches the output-investment correlation. JEL classification: F41, E32

Chocs specifiques a l'investissement et balances exterieures dans une petite economie ouverte. Les auteurs construisent un modele standard de cycle d'affaires dans une petite &conomie ouverte alimentee par des chocs de depenses gouvernementales, des chocs de productivite, et des chocs specifiques a l'investissement. On calibre le modele avec des donnees canadi- ennes trimestrielles, et on compare ses previsions et trajectoires suggerees 'a ce qui se passe au Canada. On decouvre que le modele 6pouse mieux la dynamique dans l'investissement et la balance exterieure que les cas particuliers du modele oui l'un ou l'autre des chocs de productivit6 est omis. Plus specifiquement, le modele epouse la variance dans le ratio balance commerciale-output, sa correlation avec la production, et son auto-correlation. II epouse aussi la correlation output-investissement.

Letendre thanks the Social Sciences and Humanities Research Council of Canada for support of this research. We would like to thank two anonymous referees and seminar participants at York University, the University of Calgary, The Canadian Economics Association (Toronto, 2004), and the Theory and Methods in Macroeconomics conference (Lyon, 2005). Email: letendre@mcmaster.ca

Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 40, No. 2 May/mai 2007. Printed in Canada / Imprim au Canada

0008-4085 / 07 / 650-678 / ? Canadian Economics Association

Investment-specific shocks and external balances 651

1. Introduction

Open-economy dynamic general equilibrium models like the small open economy (SOE) model of Mendoza (1991) and the multi-country model of Backus, Kehoe, and Kydland (1992) (and their many extensions) imply that changes in a country's trade balance (and current account) following a positive shock to total factor productivity (TFP) are mainly driven by two forces: a desire to smooth consumption and a desire to take advantage of the persistently higher productivity of investment. Consumption smoothing tends to make the trade balance pro-cyclical, since a country's representative household desires to lend part of its suddenly high income to finance future consumption. However, the country also desires to borrow from the rest of the world in order to finance a transitory investment boom, which tends to make the trade balance counter-cyclical. Backus et al. (1992) and others document that external balances (i.e., trade balance or current account) of developed countries are counter-cyclical. This suggests that the primary determinant of fluctuations in the trade balance is fluctuations in investment. Empirical evidence backing up this reasoning can be found in Glick and Rogoff (1995) and in Gregory and Head (1999), among others. Therefore, when looking for a way to improve the canonical SOE model's ability to match the trade balance dynamics, it seems natural to look at factors changing investment dynamics. In this paper we focus on one such factor, investment-specific productivity shocks.

A series of recent papers have investigated, mostly in a closed-economy con- text, the importance of investment-specific technological changes in accounting for growth and business cycle properties of output. Greenwood, Hercowitz, and Krusell (1997) find that investment-specific technological changes explain approximately 60% of growth in output per man-hour in post-war U.S. data. Greenwood, Hercowitz, and Krusell (2000) set up a closed-economy business cycle model where business cycle fluctuations are produced by investment- specific technological changes. They calibrate their model to the U.S. economy and find that these changes explain approximately 30% of the variation in output.

Rather than measuring the importance of investment-specific technological changes on output and hours worked using a calibrated model, Fisher (2003, 2006) uses vector autoregression models and variance decomposition to identify the share of the variations in hours worked (at business cycle frequencies) explained by investment-specific technological changes and the share explained by neutral technological changes. Neutral technological changes affect symmet- rically the productivity of the technology producing consumption goods and the productivity of the technology-producing investment goods. For example, in a standard RBC model where consumption and investment goods can always be exchanged one for one, shocks to total factor productivity represent neutral technological changes. Fisher (2003) finds that about 50% of the fluctuations in hours worked in the U.S. are explained by investment-specific technological changes,

652 M.-A. Letendre and D. Luo

whereas neutral technological changes account for about 6% of the variation in hours worked. Fisher (2006) concludes, 'The finding that investment-specific shocks contribute a lot to the overall effects of technology suggests that business cycle research might benefit from being directed toward studying these shocks and other factors that influence the efficiency of producing investment goods relative to consumption goods.'

Since there is mounting evidence that investment-specific shocks are empiri- cally important and that these shocks evidently affect investment dynamics (itself an important contributor to trade balance dynamics), it is of interest to include this type of shocks in an SOE model. The literature on investment-specific shocks has mostly focused on closed-economy settings. Very little is known about the implications of investment-specific shocks in open-economy settings.1 We spec- ify a general equilibrium small open economy model that is essentially extending the closed-economy model proposed by Greenwood, Hercowitz, and Krusell (2000) to a small open economy framework. This model includes the usual neutral productivity (TFP) shocks as well as shocks that change the productivity of the technology producing new machinery and equipment (investment-specific shocks). We calibrate our model to the Canadian economy.

We believe that including investment-specific shocks in an SOE model is important because their effects on the trade balance are potentially very different from those of neutral productivity shocks that are routinely included in SOE models. The key difference comes from the interplay between the consumption smoothing and the borrow-to-invest motives for trade. Following a neutral productivity shock, our model's prediction regarding the response of the trade balance depends on the extent of capital adjustment costs. However, in response to an investment-specific shock, the change in the country's current income is very small, which implies that the borrow-to-invest motive for trade clearly dominates the effects of consumption smoothing. As a result, the model predicts that the trade balance falls in response to an investment-specific shock.

After we started working on this paper, we became aware of a working paper by M. Mulraine, who is also working with a small open economy with investment- specific productivity shocks calibrated to Canada. While the two papers share common ground they differ on a number of dimensions. At this point, we simply highlight one important difference in the structure of the model. Other contri- butions that are specific to our paper are discussed in the paragraphs below. Our model treats the stock of machinery and equipment separately from the stock of structures, while Mulraine lumps machinery-equipment and structures in a unique capital stock. The empirical work in section 2.1 shows that the time path of the relative price of machinery and equipment and that of structures are quite different, which convinced us to include two types of physical capital. Moreover, as reported in section 4.5, treating machinery and equipment and structures

1 Exceptions are Boileau (2002), who works with a two-country model, and Mulraine (2006), who works with a small open economy model.

differently actually helps the model to fit the data better, a first contribution specific to our paper.

As is usually done in business cycle type studies, we contrast the model's implications for the case where neutral productivity shocks are included with the case where investment-specific shocks are included. This is in line with what is done in Boileau (2002) and in Mulraine (2006). A second novel contribution is to document the model's implications when neutral and investment-specific productivity shocks are included in the model.2 To our knowledge, there is currently no paper that does this. It turns out that the model with both types of productivity shocks matches the data better than special cases that include only one type of productivity shock, a third notable contribution. More specifically, our small open economy model including both types of productivity shocks matches the statistical moments of investment and the trade balance-output ratio much better than variants of this model where only one of the productivity shocks is included. While the model with neutral productivity shocks and investment-specific productivity shocks matches well the moments of output, investment, and the trade- balance-output ratio, it fails to match the moments of consumption and hours. Actually, the moments of consumption and hours worked in the model without investment-specific shocks are very similar to those in the model with both neutral and investment-specific shocks. Therefore, adding investment-specific productivity shocks to a standard small open economy model that already includes neutral shocks improves the model's ability to match the data, since investment-specific shocks improve the model's predictions for investment and the trade balance without worsening the model's predictions for consumption, hours, output, and the current account.

In addition to reporting statistical moments of the variables appearing in the model, we also produce sample paths produced by feeding realized shocks to our model. These simulated paths are then compared with Canadian historical paths. This is the paper's fourth original contribution, since, to our knowledge, no other paper compares historical paths with paths produced by a DGE model driven by investment-specific shocks. This exercise also finds that having investment- specific shocks in the model helps to match the observed dynamics in investment and the trade balance.

The paper is organized as follows. Section 2 presents the model. Section 3 provides details on the numerical solution methods and on the parameter values employed in the simulations. Section 4 compares the statistical moments calculated using our sample of Canadian data with those predicted by three variants of the model described in section 2. Section 5 compares historical and model- generated sample paths. Section 6 concludes.

2 After all, if the two types of disturbances truly hit a given small open country, a model including both sources of disturbances may be closer to the true data-generating process and therefore may better reproduce the moments measured in historical data. Also, Fisher (2006) shows that both neutral and investment-specific shocks play important roles in explaining business cycle fluctuations in hours and investment.

2. Small open economy model

2.1. Model with two sources of growth Our small open economy model builds on the closed economy model of Green- wood, Hercowitz, and Krusell (2000) and the small open economy model of Greenwood, Hercowitz, and Krusell (2004a) [whose model builds on Green- wood, Hercowitz, and Huffman (1988), Mendoza (1991), and Correia, Neves and Rebelo (1995)].

The small open economy is populated by a large number of identical households and firms. Therefore, we focus on the problem of a representative household/producer whose utility depends on consumption of a single good (denoted by C) and on hours worked (denoted by n).3

00 [Ct - grent-a Eo a> 0>, A > 0, v > 1, O < < 1, r > 1, (1)

where E0 denotes the rational expectation operator, P is a subjective discount factor, and F is a gross growth rate defined below. We need the term 't in the momentary utility function for the model to have a balanced growth path, where n is constant. The presence of rt in the utility function can be interpreted as representing technological progress in home production activities (see Hercowitz and Sampson 1991 for more details).

As in Greenwood, Hercowitz, and Krusell (2000), output is produced using a stock of machinery and equipment (KI), a stock of structures (K2), and hours worked according to the following Cobb-Douglas production function

Y= At(utKit)e K2t (Ynt)-01-02, 0 < 01,2 < 1, Yx > 1, (2)

where At is a stationary productivity shock, ut is the utilization rate of machinery and equipment, and yt is a labour-augmenting factor.

The representative agent in the small open economy can borrow and lend on world capital markets. We denote holdings of foreign assets at the beginning of period t by Bt. In each period, the representative agent must satisfy the budget constraint

C, + lit + I2t + Gt + B1+1 = Yt + RtB, (3)

where Ilt is investment in machinery and equipment, I2t is investment in structures, Gt is government consumption financed by lump-sum taxes, Yt is output,

3 We use the following convention regarding notation: uppercase letters denote endogenous variables that are growing along a balanced growth path, while lowercase letters denote endogenous variables that are not growing along a balanced growth path (including endogenous variables that have been detrended).

and Rt is the (gross) interest rate faced by the households in the small open economy. This rate is the sum of a constant world interest rate Rw and of a 'risk premium' that depends on aggregate assets (B) and aggregate output (Y)4

R, = R" + P(Bt/lt) = RW + *2(etl-Bt/Yt - 1), f2 > 0. (4)

The transition equation for the stock of machinery and equipment is

Kit+1 = (1 - 8tu)Kit +

yztlt -

-it(yz - 1) 2Kt, (5)

where 0 < 81 < 1, q > 1, ,z > 1, l1 _ 0. Note that y z and v denote, respectively,

the growth and stochastic components in the productivity of the technology producing new machinery and equipment.

The transition equation for the stock of structures is

012 t W2t 2

K2t+= (1 -82)K2t + I2t - - 2) K2 (6) 2 K2)t

where 0 < 82 < 1 and 42 > 0. As it is often the case in open-economy models, transition equations (5) and

(6) include capital adjustment costs, governed by the parameters 01 and #2 to slow down investment movements. The adjustment costs functions are set in such a way that the model with adjustment costs has the same steady state as the model without them.

The production function (2) and the transition equations (5) and (6) make clear that the stock of structures and the stock of machinery and equipment are treated differently in our model. First, owing to the more active role played by machinery and equipment in production, we allow for the possibility of vary- ing the utilization rate of the stock of machinery and equipment in response to shocks. Accordingly, we make the depreciation rate of the stock of machinery and equipment depend on the utilization rate of this capital. Second, we include the term yr vt in transition equation equation(5) to represent technological changes in the productivity of the technology producing new capital. The time paths of the relative price of structures and of machinery and equipment show a dramatic fall in the relative price of machinery and equipment but no obvious trend in the relative price of structures. Figures 1 and 2 plot the relative price of structures and of machinery and equipment for Canada for the period 1976:Q1-2003:Q4. Appendix A contains a description of the Canadian data used in the paper. In figure 1, the relative prices are calculated by dividing the implicit price deflator

4 This risk premium is strictly decreasing and is included to avoid the well-known problem associated with a unit root in asset accumulation. See Schmitt-Groh6 and Uribe (2003) for more details about modelling devices targeted at this specific problem.

o - - Res. Struct. (N Non-Res. Struct.

1977 1980 1983 1986 1989 1992 1995 1998 2001 2004

FIGURE 1 Relative prices of components of investment price of component relative to price of non-durable goods and services

for machinery and equipment (or structures) by the implicit price deflator for expenditures on non-durable goods and services. In figure 2, the relative prices are calculated by dividing the implicit price deflator for machinery and equipment (or structures) by the implicit price deflator for expenditures on non-durable goods. However the relative prices are calculated, the trend properties of the two relative prices are vastly different.5 We interpret figures 1 and 2 as evidence that there are significant technological changes specific to the machinery and equipment sector. Accordingly, we include the factor yt in transition equation (5). The time path of the relative price of machinery and equipment is not a smooth downward trend; that is, there is variation in the relative price at business cycle frequencies. Calculating the standard deviation of the relative price of machinery and equipment and that of output per capita, where both series have been detrended using the Hodrick-Prescott filter (with smoothing parameter equal to 1600) in order to isolate fluctuations at business cycle frequencies, shows that the relative price is twice as volatile as output. Clearly, there is a good deal of variation in the relative price of machinery and equipment at business cycle frequencies. Accordingly, we include the investment-specific technology shock vt in equation (5).

5 Similar patterns are documented in Greenwood, Hercowitz, and Krusell (2000), and Fisher (2003) for the United States, by Boileau (2002) for the United States and other G7 countries, and by Mulraine (2006) for Canada.

0 - - Res. Struct. N

.............

Non-Res. Struct.

1977 1980 1983 1986 1989 1992 1995 1998 2001 2004

FIGURE 2 Relative prices of components of investment price of component relative to price of non-durable goods

We complete the description of the model by presenting the transition equation for the exogenous variables. Define the growth rate F =

yxy01/1-1-02 and

detrended government expenditures by gt -- G,Irt. Neutral technology shocks (A), detrended government expenditures (g) and investment-specific technology shocks (v) evolve according to the following vector autoregressive process (in logs):

[ln At+, F InnA*(- pA) P [A 0 0 ln At [A,t+1 Ingt+1 = Ing*(l - pg) + 0 pg 0 Ingt + gt+ , (7) Invt+1 In v*(1 - p,) 0 0 p, v In vt , v,t+1

where the unconditional means A* and v* are normalized to unity and the unconditional mean g* will be calibrated below. It is assumed that PA, Pg, and pv lie between 0 and 1 and that the covariance matrix of the vector of innovations

Et+1 [SA,+1 Eg,t+1 Ev,t+1 T

is E[EET] = E, where the off-diagonal elements of E are not restricted to be zero.

2.2. Detrended model and optimality conditions In the deterministic version of the model represented by equations (1)-(7), the trends in labour productivity and in the production of new machinery and

equipment imply that, along a balanced growth path where n and u are constant, the variables Y, II, 12, C, B, G, and K2 grow at rate F, while K1 grows at rate y, z. For a derivation of the growth rates along a balanced growth path in the deterministic version of the model, please see appendix B, available online through the CJE journal archive, http://economics.ca/cje/en/archive.php. In order to work in a stationary environment, we define the following detrended variables

t 12t Ct Bt K2t KI

t Yt =

- i2t = , Ct = b , k2t =-

and the adjusted discount factor = •'-" In the detrended economy, the representative agent chooses contingency plans

for {Yt}t=o, {ilt}o0, {J2t}t0o, {C }t=0, {t}It=0, {ut}t=, {bt+1}t=, {kit+1}to, and {k2t+1 } 0 to maximize

Wt [ct -

n ]1-a Eo t(9) 1-a t=0

subject to

Yt = At(utkl,)olknl--et (10)

Ct + ill + i2t+ gt + Fbt+l = yt + RAbt (11)

R" + 2 (e-'tt

- 1) (12)

21 (k it _l kit

(13) F zkit+l

= (1 - 81u7)kit

+ vtilt - (

(FYk1+itu))2kt

02 i2t _ _ )k (14) Fk2t+l = (1 - 2)k2t +2 - 2 (14)

and subject to the transition equation for the exogenous stochastic variables (7), and given the initial conditions klo, k20, bo, Ao, go, and vo.

The dynamic programming problem solved by the representative agent (in the detrended economy) implies the first-order conditions

[ct- Infl]-a = 3t (15)

lyv [c, -

tnt]-a nt-'

= (1 - 01 - 02)3tt- (16)

(ilt tl- la3ty

- Ilt l -- 1k

- [Fy - 1 + 81u ] 8lu kt = 0

-lt Vt - 01 t- [I'yz -1+ 1(18)

X3t = 2t -2 2t2] (19)

F•3t =

- EtX.3t+l [RW +

*2 (eV -bt+l/Yt+1 - 1)] (20)

t+ i 41+1 ilt+i _'_zlt

1_3t+_Xkl

t+i01_(_-I1_u t

r/ 1lt~ l _

(~lk 1-+-yl -t+l k it+1 t+lt+l (21) + 1 - 8u10 -12(kir+1 8 +))1U J (21)

yt+l 22t+1 i2t+1

F'X2t = ,,Et 0233?13t+1 I

+1 [/2 t 2kI-( I + 82)) 2t+I

I 2t= Et2+k2t+1

b k2t+1 k2t+l

+1- 2 k2t+l ) (22)

where the equilibrium conditions it = yt and bt = bt have been imposed. 1, .2, and ,3 denote the Lagrange multipliers associated with the transition equations

(13) and (14) and the constraint obtained by combining (10), (11), and (12).

3. Solution method and parameter values

The solution to the model is a set of stochastic processes for the endogenous variables n, y, i1, i2, u, c, kl, k2, b, X.1, 2, and X3 that satisfy the relevant transversality conditions as well as equations (10)-(22) where equation (12) has been used to eliminate Rt from the system. Since the model does not have a closed-form solution for general values of the structural parameters, the system of equations is linearized (around its deterministic steady state) and solved numerically using the method explained in King, Plosser, and Rebelo (2002).

The parameter values used in our quantitative analysis are presented in table 1. Most values are calibrated or estimated using Canadian quarterly data for the sample 1976Q1 to 2003Q4. We now provide details on how these values were selected.

TABLE 1 Parameter values

Preferences:

f = 0.993, a = 2, v = 1.7, t = 2

Production function: 01 = 0.192, 02 = 0.128

Depreciation and utilization: 81 = 0.0550, 82 = 0.0131, q7 = 1.8353

Adjustment costs and risk premium: *" = -0.34, ?2 = 0.001 Values for

4l and q2 are reported in tables of results below.

Exogenous processes: PA = 0.9544, UA = 0.0065, p, = 0.9802, a, = 0.0161, g* = 0.0686, pg = 0.9501, ag = 0.0092, cor(eA, Eg) = 0.0482, cor(e,, g) = 0.0686, cor(SA, AE) = -0.1286, Yx = 1.0022, y, = 1.0127

The values for the parameters P, a, and v are taken from Letendre (2004a):

1 = 0.993, a = 2, and v = 1.7. The value of the remaining parameter appearing in the periodic utility function, A, is set based on data for hours worked per capita. In our sample of data, the fraction of non-sleeping time spent working by a Canadian is approximately 20%. Accordingly, we select a value for A to ensure that n is equal to 0.20 in steady state. When calibrating their closed-economy RBC model to the U.S. economy, King and Rebelo (2000) also choose parameter values in such a way that the fraction of time spent working is 20% in steady state.

Greenwood, Hercowitz, and Krusell (2000) use the values 01 = 0.18 and 02 =

0.12, which imply 01 + 02 = 0.30. Mendoza (1991), who calibrates his model to the Canadian economy, sets 1 - (01 + 02) = 0.68. Therefore, we set 01 = 0.192 and 02 = 0.128 to accord with 1 - (01 + 02) = 0.68, as calculated by Mendoza and with the ratios 0 i/(O + 02) for i = 1, 2 used by Greenwood et al.

Given parameter values for 01 and 02, we use data on GDP per capita, capital utilization (proxied by industrial capacity utilization), stock of machinery and equipment per capita, stock of structures per capita (calculated as total capital stock less stock of machinery and equipment), and labour input to construct a series of 'modified Solow residuals' as follows:

MSR = In t - 01(ln ut + In Kit) - 02 In K2t - (I - 01 - 02)ln nt. (23)

According to production function (2) these modified Solow residuals are related to the neutral shocks and the growth rate in labour productivity as follows:

MSR = In At + (l - 1 - 02) ln(yx) x t. (24)

Based on the equation above, we first regress the MSR on a time trend to find an estimate of yx. This estimate is yx = 1.0022 (this corresponds to an annual average net growth rate of about 1%). Then, residuals from that regression are regressed on their first lag to identify the estimates pA = 0.9544 and rA = 0.0065.

We calculate values for yz, p, and av, by using the fact that our model implies that the inverse of the relative price of machinery and equipment in period t

(pme, t) is given by y

z vt. We construct a time series for pme by dividing the implicit

price deflator for machinery and equipment by the implicit price deflator for consumption of non-durable goods and services. Then, we estimate the regression

Inp =o+ t+et-1 (25) Pn me,p t -"= 0 + i t + et

and use the estimate W^I to calculate Yz = exp ( i) = 1.0127. The residuals from the above regression are then regressed on their first lag to find p, = 0.9802 and aO = 0.0161.

We calculate values for g*, pg and ag using data on government expenditures and GDP per capita. We regressed the log of government expenditures per capita on a constant and a trend and interpret the residuals as estimates of gt. We regress the residuals on their first lag to find pg = 0.9501 and ag = 0.0092. We set g* to ensure that the steady-state G/ Yratio is equal to 0.2177, the average of the ratio of government expenditures to output in our sample.

We use data on depreciation and capital stocks to calculate average depreciation rate for the two types of capital. Using data on depreciation and the stock of machinery and equipment, we find an average annual depreciation rate of 0.1606, which corresponds to an average quarterly depreciation rate of 0.0379. Given numerical values for a, 3, y x, and yz, the value ri = 1.8353 is selected to ensure that the steady-state depreciation rate for machinery and equipment is 0.0379.

For structures, we calculate depreciation and the stock by subtracting machinery and equipment from total capital. We find an average annual depreciation rate of 0.0536, which corresponds to an average quarterly depreciation rate of 0.0131. Accordingly, we set 82 = 0.0131. Note that the average annual depreciation rates we calculated using Canadian data are similar to the those reported by Greenwood, Hercowitz, and Krusell (2000) for the U.S. economy. They find an annual depreciation rate of 0.056 for structures and 0.124 for equipment.

We use a measure of industrial capacity utilization to proxy for capital utilization. In our sample, the average capacity utilization rate is 81.6%. Given numerical values for a, , y x, yz, and r7, the value 81 = 0.0550 is selected to ensure that the steady-state utilization rate is 81.6%.

In our dataset, SD(i)/SD(y) = 2.91 and SD(i i)/SD(i2) = 1.60, where SD(x) denotes the standard deviation of x. The capital adjustment costs parameters #1 and /2 are set to ensure that the model matches SD(i)/SD(y) = 2.91 and

SD(il)/SD(i2) = 1.60. The values for 01 and 02 used in the simulations are reported in the tables of results. To verify the robustness of the results, we also considered imposing 01 = 02 and selecting a value for 01 = 02 to match SD(i)/ SD(y) = 2.91. We found that when 0 1 and 02 are set this way, the results discussed below are unchanged.

The parameter 1l appearing in the equity premium in (4) is equal to the steady-state value of the ratio B/ Y. Calculating the sample average for this ratio using annual Canadian data on net foreign assets and nominal GDP yields -0.34. Accordingly, we set *1 = -0.34. We follow Letendre (2004a) and set

1/*2 = 0.001.

Finally, the sample correlations between the empirical equivalents of 8A, Eg, and 8, are cor(eA, Eg) = 0.0482, cor(es, eg) = 0.0686, and cor(eA, E) = -0.1286. We use these correlations in our simulations.

4. Moments-based analysis

4.1. Historical moments Table 2 reports historical moments for consumption, hours, output, total investment (the sum of investment in structures, machinery, and equipment), the trade balance-output ratio, and the current account-output ratio computed using quarterly per capita Canadian data covering the sample 1976Q1 to 2003Q4. The trade balance-output ratio, the current account-output ratio, and the logs of consumption, hours, output, total investment were detrended using the Hodrick-Prescott filter with its smoothing parameter set to 1,600.

Table 2 and other tables discussed below show standard deviations, standard deviations relative to that of output, correlations with output, and first-order autocorrelations of the variables. Moments calculated using simulated data will be compared with the numbers in table 2. When calculating the moments implied by a theoretical model, we average moments over 1,000 replications. For each of these replications, we generate artificial time series of 212 periods in length and we discard the first 100 observations. Therefore, our artificial dataset has 112 observations, just like our sample of quarterly Canadian data. To make historical and artificial data comparable, we apply the HP filter to artificial data for consumption, hours, output, investment (all in percentage deviations from their steady-state values) and the trade balance-output ratio and the current account-output ratio (in levels).

To evaluate the fit of a particular statistical moment predicted by a theoretical model, we use the method proposed by Gregory and Smith (1991) to construct confidence intervals for each of the statistical moments shown in the tables discussed below. By simulating the model 1,000 times, we get 1,000 realizations of the statistical moments of interest. For each of these moments, the 1,000 realizations are sorted and stored in a vector. Then, the lower (upper) bound of a 95% confidence interval is given by the 25th (975th) element of the sorted vector.

TABLE 2 Moments from Canadian data (1976Q1-2003Q4)

SD SD/SD(y) Cor. with y Autocor.

c 0.92 0.56 0.74 0.85 n 1.74 1.06 0.89 0.86 y 1.64 1 1 0.90 i 4.76 2.91 0.65 0.86 tb/y 0.88 0.54 -0.11 0.71 caly 0.26 0.16 -0.22 0.66

NOTES: SD stands for standard deviation. c denotes consumption. n denotes the fraction of time spent working. y denotes output. i is the sum of investment in structures, machinery, and equipment. tbly denotes the trade balance-output ratio. caly denotes the current account-output ratio. All data are per capita. Except for the trade balance-output ratio and the current account-output ratio, all data are in logs. All data were detrended using the HP filter with smoothing parameter 1600. Appendix A provides more details on the data used to compute the moments in table 2.

Similarly, the lower (upper) bound of a 99% confidence interval is given by the 5th (995th) element of the sorted vector. In the tables showing the moments predicted by the theoretical models, the superscripts ** and * indicate that a moment is not statistically different from its empirical counterpart at the 5% and 1%, levels of significance respectively.

4.2. Model without investment-specific productivity shocks In order to compare the implications of neutral productivity shocks and investment-specific productivity shocks, we start our analysis by looking at models with only one type of productivity shocks affecting the small open economy. The first model we consider includes only government spending shocks and neutral productivity shocks. table 3 reports the moments for this version of the model for two sets of capital adjustment costs parameters.

The top panel of table 3 reports the results computed using the values 4 = 0.75 and 02 = 8.82 in the simulations. These values are selected to make the model without investment-specific shocks match SD(il + i2)/SD(y) = 2.91 and SD(il)/SD(i2) = 1.60. Alternatively, one can use a common value 01 = 02 = 2.48, selected to make the model match SD(il + i2)/SD(y) = 2.91. These two sets of values for

il and 02 yield similar results, so we report only the moments

computed using 0b1 = 0.75 and 02 = 8.82. The bottom panel of table 3 reports the results computed using the values

01 = 3.40 and 02 = 8.95. These values are selected to make the model with both types of productivity shocks (discussed in section 4.4) match SD(i1 + i2)/ SD(y) = 2.91 and SD(il)/SD(i2) = 1.60.

We start the discussion of the model without investment-specific shocks by fo- cusing on the statistical moments reported in the top panel of table 3. The model without investment-specific productivity shocks matches the volatility of output

TABLE 3 Moments from the model without investment-specific shocks

Variable SD SD/SD (y) Cor. with y Autocor.

01 = 0.75 02 = 8.82 c 1.62 0.95 1.00 0.70* n 1.00 0.59 1.00 0.71 y 1.70** 1.00 1.00 0.71 i 4.93** 2.91** 0.95 0.64 tb/y 0.50 0.29 -0.58 0.65** caly 0.48 0.28 -0.60 0.66**

41 = 3.40 42 = 8.95 c 1.60 0.96 1.00 0.69 n 0.98 0.59 1.00 0.69 y 1.67** 1.00 1.00 0.69 i 3.24 1.95 0.99 0.68 tb/y 0.19 0.12 0.15** 0.73** caly 0.19* 0.12* 0.19* 0.74**

NOTES: Moments from the model are averages of 1,000 replications of length 112 periods. They were computed using HP filtered percentage deviations from steady state. For symmetry with Canadian data, artificial data on the trade balance-output and current account-output ratios are not expressed in percentage deviation from steady state. The superscripts ** and * indicate that a moment is not statistically different from its empirical counterpart at the 5% and 1% levels of significance, respectively.

very well. The standard deviation of output is 1.70 in the model and 1.64 in Cana- dian data (this difference is not statistically different at the 5% level). Although the model reproduces well the volatility of investment, we must remind the reader that 041 and 42 are calibrated to control the relative volatility of investment. The model does less well at matching the volatility of the other variables, but it is consistent with the empirical fact that consumption, the trade balance-output ratio and the current account-output ratio are less volatile than output and that investment is more volatile than output.

Table 2 shows that consumption, hours and investment are highly but not perfectly correlated with output in Canadian data. It also shows that the trade balance-output ratio as well as the current account-output ratio are moderately countercyclical. The model without investment-specific productivity shocks does poorly at matching the correlation of the variables with output. It predicts perfect correlation of consumption and hours with output, a very large correlation of investment with output, and strongly countercyclical trade balance-output and current account-output ratios.

The model also has difficulties in generating fluctuations in consumption, hours, output, and investment that are as persistent as those observed in Cana- dian data, although it should be noted that the autocorrelation of consumption predicted by the model is not statistically different from its empirical counterpart at the 1% level. The model does very well at matching the autocorrelation of the

trade balance-output ratio and the current account-output ratio (both moments match their empirical counterparts at the 5% level).

A comparison of the statistical moments reported in the two panels of table 3 clearly demonstrates the influence of the behaviour of investment on the properties of the trade balance and on the current account. Not surprisingly, increasing investment adjustment costs reduces the volatility of investment. This reduction in the volatility of investment (from 4.93 to 3.24) greatly reduces the volatility of the trade balance-output ratio and current account-output ratio. It also dramatically changes the correlation of these variables with output. For example, table 3 shows that the standard deviation of tb/y goes from 0.50 to 0.19, while the correlation of tb/y with y goes from -0.58 to 0.15 when l1 and 02 are raised. This change in the correlation between tb/y and y can be understood by looking at the responses of tb/y and i/y to a one standard deviation productivity shock shown in figure 3. In the figure, tb/y is expressed in deviation from steady state while i/y is expressed in percent deviation from steady state. With the larger values for ~1 and 02, i/y increases less in response to a productivity shock. Therefore, tb/y falls less. Actually, as shown in figure 3, tb/y increases slightly in response to the shock when the larger values for 41 and 42 are used. The role played by capital adjustment costs in determining the initial response of tb/y to a positive shock is explained as follows. On the one hand, since the shock hits directly the production function, the country's income increases temporarily. The consumption-smoothing desire built into the model implies that the small country wishes to lend part of its extra income to finance future consumption. This tends to make the trade balance pro-cyclical. On the other hand, since the marginal product of capital is temporarily higher, the small country wishes to borrow form the rest of the world to finance a temporary investment boom. This tends to make the trade balance counter-cyclical. Evidently, the larger the adjustment costs, the weaker is the borrow-to-invest motive, making tb/y increase in response to a positive shock.

While it is true that the model with larger capital adjustment costs fits the moment of tb/y and caly better, it fails to produce realistic investment volatility. So the results displayed in table 3 show how important the properties of investment are for the properties of the trade balance and the current account. Hence, one should pay close attention to factors that affect the behaviour of investment. We now turn our attention to one such factor, investment-specific productivity shocks.

4.3. Model without neutral productivity shocks In this section we investigate the dynamic properties of a special case of the model described in section 2, where there are only government spending shocks and investment-specific productivity shocks. In this model, a positive productivity shock in period t increases the productivity of the technology producing future machinery and equipment. Not surprisingly, investment in machinery and equipment is extremely volatile in such a model. In order to demonstrate this point,

o- tb/y : low costs S- - - i/y : low costs

oo - tb/y : high costs

0I- - i/y high costs . d

2 0 4 8 12 16 20 24 28 32 Periods

FIGURE 3 Impulse response function trade balance/output and investment/output

table 4 reports two sets of statistical moments predicted by the model without neutral shocks. In the top panel, the moments reported are calculated using i = 3.40 and 02 = 8.95 in the simulations. In the bottom panel, the moments reported are calculated using 01 = 250 and 02 = 52 in the simulations. Even with the very large value for 01 and 42 that we use to produce the moments reported in the bottom panel of table 4, the volatility of investment in machinery and equipment relative to the volatility of investment in structures is 2.9, which is larger than 1.60 (the number calculated using Canadian data). If instead we used a common value 01 = 02 = 85.1 for the capital adjustment cost parameters to match the volatility of total investment relative to that of output, the results are very similar. Thus, we report only the results computed using 41 = 250 and /2 = 52.

Comparison of the moments in the top panel of table 4 and those in the bottom panel of table 3 shows that many of the predictions of the model depends importantly on the type of productivity shocks hitting the small open economy. Investment-specific shocks generate a great deal of volatility in investment, the trade balance-output ratio, and the current account-output ratio, but very little volatility in consumption, hours, and output. The low volatility of hours and output in the model without neutral shocks is hardly surprising. A positive investment-specific productivity shock increases directly the productivity of the technology producing new machinery and equipment but does not directly affect the productivity of structures and hours worked. So, as argued by Greenwood, Hercowitz, and Huffman (1988), a productivity shock of a given magnitude is

TABLE 4 Moments from model without neutral productivity shocks

01 = 3.40 02 = 8.95 c 0.58 1.16 0.97 0.74** n 0.29 0.59 1.00 0.78** y 0.50 1.00 1.00 0.78*

4.06** 8.23 0.82 0.67 tb/y 0.86** 1.74 -0.70 0.67** caly 0.85 1.72 -0.74 0.67**

1 = 250 42 = 52

c 0.52 1.23 0.97 0.70 n 0.25 0.59 1.00 0.70 y 0.43 1.00 1.00 0.70 i 1.24 2.91** 1.00 0.69 tb/y 0.25 0.59** -0.64 0.69** ca/y 0.24** 0.58 -0.64 0.69**

actually 'smaller' when it is an investment-specific shock (rather than a neutral shock), because it does not affect directly the productivity of all inputs used in the production of the final good. This argument is especially applicable in our set-up where we have the investment-specific productivity shocks affecting only a fraction of the capital sector. Figure 4 demonstrates this point very clearly. It shows the responses of output and hours worked (in percentage deviations from steady state) to a neutral shock (computed using the model discussed in section 4.2) and to an investment-specific productivity shock (using 4i1 = 3.40 and 02 = 8.95 in both cases). The figure shows that the response of hours and output to an investment-specific shock is much smaller than the response to a neutral productivity shock.

The top panel of table 4 also shows that the model without neutral productivity shocks fails dramatically to reproduce the ranking of standard deviations computed in Canadian data when we set 01 = 3.40 and 02 = 8.95. The model predicts that consumption, the trade balance-output, and the current account- output ratios are more volatile than output, while the opposite is true in our sample of Canadian data.

Comparing the autocorrelations reported in the bottom panel of table 3 to those in the top panel of table 4, we see that investment-specific shocks are ca- pable to generate more persistence in c, n, and y. This finding is consistent with the findings of Greenwood, Hercowitz, and Huffman (1988), who consider a

o6i i i I I

S- -y : A-shock

S... n : A shock

S-? y : v shock Sn : v shock

Oil (D 0 S

60 5 10 15 20 25 30 35 40 45 50

Periods

FIGURE 4 Impulse response function output and hours

closed-economy model with investment-specific shocks. Figure 4 shows that the response of output and hours to an investment-specific shock have a hump shape, which obviously makes the response of output and hours more persistent than their response to a neutral shock. This hump shape response of output is not found by Greenwood, Hercowitz, and Krusell (2000) in their closed-economy model, which is very closely related to our model. When q1 = 3.40 and 02 =

8.95, we find that the hump in the responses disappears when the parameter p, (first-order autocorrelation in investment-specific shocks) is set below 0.75. When 4 i = 250 and 02 = 52 (as in the bottom panel of table 4), we find that the hump in the responses disappears when the parameter p, is set below 0.95. Since Greenwood, Hercowitz, and Krusell calibrate their model to annual data, their estimated p, (0.64) is much lower than the one we estimated (0.9802), which explains why they do not find a hump shape in the impulse responses they compute.

Increasing the parameters controlling capital adjustment costs to 01 = 250 and 02 = 52 in order to have more realistic relative investment volatility yields the moments reported in the bottom panel of table 4. Except for the volatility of the current account-output ratio that matches the data at the 5% level, the macro aggregates we consider are much less volatile in the model with investment-specific shocks than in Canadian data. Contrary to the model with neutral shocks, the current model does not match the standard deviation of output and of investment (not even at the 1% level).

Looking at the relative standard deviations in the bottom panel of table 4, we see that the model matches the relative volatility of the trade balance at the 5% level. However, a notable shortcoming of the model (which is robust to the change in capital adjustment cost parameters) is its prediction that consumption is more volatile than output.

The correlations with output and the autocorrelations presented in the bottom panel of table 4 closely resemble those in the top panel of table 3. Therefore, aban- doning neutral productivity shocks in favour of investment-specific shocks (and updating the adjustment cost parameters to ensure realistic investment volatility relative to output along the way) does not change the co-movements between the trade balance (or the current account) and output sufficiently to make it less negatively correlated with output.

The poor performance of the model with investment-specific productivity shocks only at producing realistic volatilities suggests that these shocks are not able, on their own, to capture well the properties of Canadian data when these shocks replace neutral shocks in the structural model we use.

4.4. Model with both types ofproductivity shocks An important finding based on the discussion in sections 4.2 and 4.3 is that, in the structural small open economy considered in this paper, having neutral productivity shocks or investment-specific productivity shocks does not allow the model to match very well the statistical moments of the trade balance, consumption, and hours worked. Since both sources of changes in productivity might be relevant to explain business cycle fluctuations (there is evidence of this for the U.S. economy in the paper by Fisher 2003) and the dynamics of the trade balance (and current account), we now look at the predictions of the model described in section 2. This model incorporates government spending shocks, neutral productivity shocks and investment-specific productivity shocks.

Table 5 reports the moments calculated using our small open economy model with both types of productivity shocks. The top panel of table 5 reports the moments for /1 = 3.40 and 02 = 8.95. Again, these values for the capital adjustment cost parameters are selected to make the model with all shocks match SD(il + i2)/SD(y) = 2.91 and SD(il)/SD(i2) = 1.60.

As discussed in section 4.3, investment-specific shocks have little effects on consumption, hours worked, and output. So it comes as no surprise that the statistical moments for consumption, hours worked, and output reported in the top panel of table 5 are very close to those reported in table 3. Therefore, adding investment-specific shocks to an otherwise standard small open economy RBC model does not worsen the predictions of the model regarding consumption, hours worked, and output.

Given the nature of the investment-specific productivity shocks, they have important effects on the properties of investment and consequently on the properties of the trade balance and current account. To see this, consider the effects of a

TABLE 5 Moments from model with both types of productivity shocks

01 = 3.40 02 = 8.95 c 1.63 0.97 0.99 0.70 n 0.99 0.59 1.00 0.70 y 1.69** 1.00 1.00 0.70 i 4.87** 2.91** 0.73** 0.68 tb/y 0.87** 0.52** -0.06** 0.67** caly 0.86 0.52 -0.06** 0.67**

1 = 3.40 02 = 8.95 corr(A, E,)= 0

c 1.70 0.98 1.00 0.70 n 1.02 0.59 1.00 0.70 y 1.74** 1.00 1.00 0.70 i 5.21** 3.01** 0.77** 0.68 tb/y 0.87** 0.50** -0.17** 0.67** caly 0.86 0.50 -0.17** 0.67**

positive investment-specific shocks. Evidently, this shock raises the small country's desire to borrow from abroad to finance an investment boom. This tends to make the trade balance counter-cyclical. Because the shock does not appear directly in the production function, the small country's income rises very little compared with the rise observed in response to a neutral productivity shock. As a result, the consumption, smoothing factor that tends to make the trade balance pro-cyclical is very weak. Actually, in our setting, it is never the case that the consumption-smoothing motive is strong enough to induce a rise in the trade balance in the period of the shock, no matter how much or how little capital adjustment costs are fed into the model. This is in stark contrast to the fact that we can get a rise or a fall in the trade balance in response to a neutral productivity shock depending on how much or how little capital adjustment costs we feed into the model.

When investment-specific shocks are added to a model that already includes neutral productivity shocks, they greatly improve the model's predicted moments for investment and the trade balance-output ratio. To see this, compare the moments of investment and trade balance-output ratio reported in the bottom panel of table 3 with the moments reported in the top panel of table 5. The addition of investment-specific shocks raises the volatility of investment sufficiently to allow the model to match the standard deviation of investment observed in Canadian data.

Also, the addition of investment-specific shocks changes the co-movements between investment and output sufficiently to match well the correlation between output and investment. The model implies a correlation of 0.73, while this correlation is 0.65 in Canadian data. As indicated in table 5, the difference between the correlation implied by the model and that calculated in Canadian data is not statistically significant at the 5% level. The addition of investment-specific shocks, however, fails to increase the autocorrelation of investment so that is the only statistical moments of investment that the model fails to match.

As shown in tables 3 and 4, the models with only one type of productivity shocks do not very well match the statistical moments of the trade balance. For example, the model without investment-specific shocks is unable to generate enough volatility in the trade balance-output ratio to match the Canadian data, while the model without neutral shocks implies a strong negative correlation between output and the trade balance-output ratio. A very interesting feature of the model with both types of productivity shocks is that it matches remarkably well the statistical moments of the trade balance. Actually, as indicated in the top panel of table 5, the model matches all of the statistical moments of tb/y at the 5% level.

The standard deviation of tb/y is 0.87 in the model and 0.88 in the Canadian data. The standard deviation of tb/y relative to the standard deviation of y is 0.52 in the model and 0.54 in the Canadian data. The autocorrelation of tb/y is 0.67 in the model and 0.71 in the Canadian data. Very interestingly, the correlation of tb/y with y is -0.06 in the model and -0.11 in the Canadian data. The slight positive correlation (0.15) between tb/y and y predicted by the model without investment-specific shocks (bottom panel of table 3) and the large negative correlation (-0.70) predicted by the model without neutral shocks (top panel of table 4) combine just in the right proportion to come very close to match the correlation observed in the data.6 This point is clearly illustrated in figure 5. It shows the responses of tb/y (in deviation from its steady-state value) to a one standard deviation neutral productivity shock, a one standard deviation investment-specific shock, and a one standard deviation government spending shock. Given the values 01 = 3.40 and q2 = 8.95 needed to match SD(il + i2)/SD(y) = 2.91 and SD(ii)/SD(i2)=1.60, a neutral productivity shocks raises tb/y (which promotes a pro-cyclical tb/y), while an investment-specific productivity shock or a government shock lowers tb/y (which promotes a countercyclical tb/y). As explained in the introduction, the correlation of the trade balance with output depends importantly on the tension existing between the consumption-smoothing motive and the borrow-to-invest motive for trade. Given the adjustment costs used in the model with all shocks, the consumption-smoothing motive operating following a neutral productivity shocks turns out to slightly dominate the borrow-to- invest motive, which implies that the trade balance increases. Given that an investment-specific shockhas a muchsmaller effecton the small country's income, the

6 This explanation also applies to the current account-output ratio.

; 0 5 1 C) 0

E o d 0-o

oC o /

- Investment-specific shock - - - Government shock

C0 5 10 15 20 25 30 35 40 45 50

Periods

FIGURE 5 Impulse response function Trade balance over output

consumption-smoothing motive is small and dominated by the borrow-to-invest motive, which results in a sizeable fall in the trade balance, as shown in figure 5.7

We conclude this section by pointing that the moments of the trade balance and current account are extremely similar. In our model, the difference between the current account and the trade balance lies in the term (Rt - 1)Bt. Therefore, extensions of the model that affect the properties of that term may break the close link that exists between the trade balance and the current account in our model.

4.5. Some sensitivity tests As reported in table 1 and discussed in section 3, the correlation between the innovations in the neutral productivity shocks (eA) and the innovations in the investment-specific shocks (er) is -0.1286. Even though this correlation is not very large, it is certainly not zero. Since the interaction of the two types of productivity shocks is important for the properties of tb/y, we verify whether the results are robust to a change in this correlation. Table 5 (bottom panel) reports the moments for the model with both types of productivity shocks and a zero correlation between eA and e,. All of the moments matched by the model at the 5% level in the top panel of table 5 are also matched at the 5% level in the bottom

7 Government spending shocks influence the reported moments very little, so we do not discuss them.

panel. Therefore, the model's ability to match the statistical moments of investment and the trade balance-output ratio is robust to changes in the correlation between EA and e,.

The empirical evidence provided in section 2.1 makes a convincing case for following Greenwood, Hercowitz, and Krusell (2000) and treating machinery and equipment separately from structures. Also, as reported in section 4.2, investment in machinery and equipment is 60% more volatile than investment in structures in the sample period we consider. Therefore, treating machinery plus equipment and structures differently seems like a very reasonable thing to do. Is this assumption important for the results we get? Simplifying our model to include a single capital stock (composed of residential and non-residential structures and machinery and equipment) and recalibrating it to take into account of the unique capital stock we obtain a model that fits more poorly than the model presented in the paper.8 A basic accounting exercise shows that 7 of the 24 moments reported are getting noticeably worse, 2 are getting noticeably better, and the remaining moments are not much affected. Not surprisingly, having the investment-specific shocks affecting the productivity of newly formed structures and machinery and equipment makes these shocks bigger, which raises the volatility in the model. Given that the model with two capital stocks grossly over-predicted the standard deviation of c, slightly over-predicted the standard deviations of y, i, and caly, and got the standard deviation of tb/y just right, an increase in the volatility of those variables makes the model worse. Besides the standard deviations, the model with only one capital stock mis-predicts the sign of the correlation of tb/y and caly with output.

5. Sample paths

The moment-based analysis above shows that combining investment-specific and neutral productivity shocks greatly helps our SOE model to match the correlation of investment with output, the correlation of the trade balance-output ratio with output and its standard deviation. Another way to evaluate the fit of the model is to feed the realized government spendings shocks, investment-specific shocks, and neutral shocks to the model and compare the model-generated simulated paths with the historical Canadian paths. Given our particular interest in the trade balance dynamics, we present the sample paths of tb/y and its components: output, consumption, and investment. Plotting the time paths for the three models used to generate the results in tables 3, 4, and 5 would make the graphs hard to read or would lead to a proliferation of graphs. A reasonable compromise is to present, for each of the four variables of interest, the historical path together with the simulated paths generated by the following models: (a) model without neutral productivity shocks (identified as model M2); (b) model with all shocks

8 Results are available upon request.

(identified as model M3). A contribution of this paper is to produce the simulated paths generated by models driven in part by investment-specific shocks. To our knowledge, this has not been done for Canadian data. Simulated paths generated by models driven by neutral productivity shocks have been reported for Canada and other countries,9 which is why we decided to drop those paths to keep the graphs readable.

Producing the sample paths implied by the model necessitates finding the realized innovations EA,t+1, Eg,t+1, and 8,,t+1 appearing in equation (7). Equation (24) implies that the residuals obtained from regressing MSR on a time trend can be interpreted as the realized In A. Then, regressing the In AA series on its first lag gives us sA,t+1l Similar steps applied to equation (25) yield 8~,,t+. Fi- nally, we obtain the 8g,t+l by first regressing the log of government expenditures per capita on a constant and a trend and saving the residuals (eg say). Then we regress the eg series on its first lag to obtain 8g,t+l. Then the vector of innovations is fed into the decision rules calculated using the linearization method of King, Plosser, and Rebelo (2002). Since the historical paths for the trade balance- output ratio and the logarithms of consumption, output, and investment (all per capita) are detrended using the HP filter (parameter = 1600), so are the simulated paths.

We start our analysis by looking at the sample paths for output in figure 6a. By visual inspection, we see that the model with all shocks (M3) produces a sample path that fits the historical output path better than the model without neutral productivity shocks (M2). The correlation between historical and simulated paths is 0.61 for the model with all shocks but is -0.38 for the model without neutral productivity shocks. The model without investment-specific shocks (not appearing on the graph) does slightly better, having a 0.7 correlation. It is quite clear that the model driven by investment-specific shocks and government consumption shocks is very far from matching the dynamics observed in Canadian output.

We get similar results when we look at consumption in figure 6b. The correlation between historical and simulated paths is 0.43 for the model with all shocks but is -0.35 for the model without neutral productivity shocks. The model without investment-specific, does slightly better having a 0.6 correlation.

So far, looking at sample paths has not brought convincing evidence that investment-specific shocks should be included in the SOE model. The main- stream model driven by neutral productivity shocks and government consumption shocks is the one performing best. A different picture emerges when we look at investment (figure 6c) and the trade balance-output ratio (figure 6d). The model without investment-specific shocks produces a correlation of 0.06 between simulated and historical investment paths. The model without neutral productivity shocks produces a zero correlation. However, when all the shocks are included in the model, the correlation rises to 0.24.

9 See Letendre (2004b) and references therein. Nason and Rogers (2006) report simulated paths for the Canadian current account.

a-Simulated and Histarical Paths: Output b-Simulated and Historical Paths: Consumptoan

It t t I

t 'It I

.,r I',Z

Ott go i ll of I\ I

0 20 4160 50 0OO 120 1 0 20 40 60 so t0o 120

•.1 ,! ? .r l ?I \I

c-Simuloted and Historical Paths: Investment d-Simulated and Historical Paths: TB/Y d 1; r ill A Il 1h I

II ' • 1 " ' • 1 ", '

0 20 40 60 so o00o 120 0 20 40 so so 100 20

FIGURE 6 (a) Simulated and historical paths: Output, (b) Consumption, (c) Investment, (d) TB/Y

Finally, the model producing the highest correlation between simulated and historical trade balance paths is the model with all shocks having a 0.39 correlation. It follows the model without neutral shocks (0.19) and the model without investment specific shocks (-0.35). While we are still far from a perfect fit in the case of investment and the trade balance-output ratio, the significantly larger correlation obtained when all shocks are included is further evidence that having both types of shocks in the model is important.

The results from the analysis in this section reinforces the findings from the moment-matching exercise presented in section 4: having both neutral and investment-specific shocks in the SOE model helps it to capture the dynamics in investment and the trade balance-output ratio.

6. Conclusion

We set up a small open economy driven by government spending shocks, neutral (total factor) productivity shocks, and/or investment-specific productivity shocks. The model is calibrated to the Canadian economy. The analysis shows that factors affecting the response of investment in the model have significant effects on the statistical moments of investment and the trade balance.

We find that the model matches the data better when both types of productivity shocks are included. The model with both types of productivity shocks matches very well the historical moments of output and investment and matches remarkably well the historical moments of the trade balance-output ratio.

While the paper focuses mostly on investment and the trade balance, we also report statistical moments for consumption and hours worked. We find that the addition of investment-specific shocks to a model that already includes shocks to total factor productivity essentially leaves the moments of consumption and hours worked unchanged. Therefore, the model will need to be modified to explain fluctuations in these variables. All the models we use in this paper imply perfect or near perfect consumption-output and hours-output correlations. Letendre (2004a) found habit formation in consumption to be an effective way to lower the consumption-output correlation. The utility function we use implies that the log of output is proportional to the log of hours worked, producing a perfect correlation between these variables. 10 An avenue for future research would be to consider habit formation in leisure to break the tight link between hours worked and output. Johri and Letendre (2006) argue that some dynamic elements should be added to (closed-economy) RBC-type models to improve the labour market part of the model. They find that habit in consumption and learning-by-doing are serious candidates to consider.

At this point in time, we do not know how the extensions to the SOE model listed above and previously explored extensions [e.g., interest rate shocks, as in Blankenau, Kose, and Yi 2001, terms of trade shocks, as in Iscan 2000, would interact with investment-specific shocks.

Appendix A: Data

The common period covered by all series is 1976Q1-2003Q4. Thus, the sample used in our empirical work is 1976Q1-2003Q4. All data were downloaded from the CANSIM II web site. CANSIM II labels are shown in brackets. Un- less otherwise indicated, the series are calculated using 1997 constant prices (not chained-weighted 1997 prices).

Population: Estimates of population, Canada, both sexes, 18 years and over [V466677]. This series is available only at an annual frequency. It was converted to a quarterly frequency using the procedure interpol in RATS.

Output: Gross domestic product [V1992259]. Consumption: Personal expenditures on non-durable goods [V1992232] + per-

sonal expenditures on services [V1992233]. Government expenditure: Government current expenditure on goods and ser-

vices [V1992235].

10 To see this, combine equations (15) and (16).

Investment: Investment in residential structures [V1992239] + investment in non-residential structures [V1992241]. Investment in machinery and equipment [V1992242].

Exports: Exports of goods and controls [V1992249]. Imports: Imports of goods and controls [V1992253]. Capital: Straight-line end-year net stock of machinery and equipment

[V1078485]. The stock of structures is calculated as the difference between the total straight-line end-year net stock of capital [V1078482] and the stock of machinery and equipment. These series are available only at an annual frequency. They were converted to a quarterly frequency using the procedure interpol in RATS. The corresponding depreciation series are [V1078478] for total capital and [V1078481] for machinery and equipment.

Utilization: The rate of capital utilization is proxied using industrial capacity utilization rate constructed by combining [V142812] for the period before 1987 and [V4331081] for the period after 1986.

Hours: Labour force survey estimates, actual hours worked for all industries [V4391505].

Current account: Total current account balance at current prices [V114421] deflated using the GDP deflator.

GDP deflator: GDP at current prices [V498086] divided by GDP at 1997 constant prices [V1992259].

Net foreign assets: Canada's international investment position at current prices-year ends-all foreign countries [V235422]. This series and nominal GDP are used to calibrate the parameter * 1.

References

Backus, D., P. Kehoe, and F. Kydland (1992) 'International real business cycles,' Journal of Political Economy 100, 745-75

Blankenau, W., M.A. Kose, and K.M. Yi (2001) 'Can world real interest rates explain business cycles in a small open economy?' Journal of Economic Dynamics and Control 25, 867-89

Boileau, M. (2002) 'Trade in capital goods and investment-specific technical change,' Journal of Economic Dynamics and Control 26, 963-84

Correia, I., J.C. Neves, and S.T. Rebelo (1995) 'Business cycles in a small open economy,' European Economic Review 39, 1089-113

Fisher, J.D.M. (2003) 'Technology shocks matter,' manuscript, Federal Reserve Bank of Chicago - (2006) 'The dynamic effects of neutral and investment-specific technology shocks,' Journal of Political Economy 114(3), 413-51

Click, R., and K. Rogoff (1995) 'Global versus country-specific productivity shocks and the current account,' Journal of Monetary Economics 25, 159-92

Greenwood, J., Z. Hercowitz, and G.W. Huffman (1988) 'Investment, capacity utilization, and the real business cycle,' American Economic Review 78, 402-17

Greenwood, J., Z. Hercowitz, and P. Krusell (1997) 'Long-run implications of investment specific-technological change,' American Economic Review 87, 342-62

- (2000) 'The role of investment-specific technological change in the business cycle,' European Economic Review 44, 91-115

Gregory, A.W., and A.C. Head (1999) 'Common and country-specific fluctuations in productivity, investment, and the current account,' Journal of Monetary Economics 44, 423-51

Gregory, A.W., and G.W. Smith (1991) 'Calibration as testing: inference in simulated macroeconomic models,' Journal of Business and Economic Statistics 9, 297-303

Hercowitz, Z., and M. Sampson (1991) 'Output growth, the real wage, and employment fluctuations,' American Economic Review 81, 1215-37

Iscan, T.B. (2000) 'The terms of trade, productivity growth, the current account', Journal of Monetary Economics 45, 587-611

Johri, A., and M.-A. Letendre (2006) 'What do "residuals" from first-order conditions reveal about dge models?' Journal of Economic Dynamics and Control, forthcoming

King, R.G., and S.T. Rebelo (2000) 'Resuscitating real business cycles', NBER Working No Paper No. 7534

King, R.G., C.I. Plosser, and S.T. Rebelo (2002) 'Production, growth and business cycles: technical appendix,' Computational Economics 20, 87-116

Letendre, M.A. (2004a) 'Capital utilization and habit formation in a small open economy model,' Canadian Journal of Economics 37, 721-41

- (2004b) 'Semi-parametric predictions of the intertemporal approach to the current account,' Journal of International Economics 64, 363-86

Mendoza, E.G. (1991) 'Real business cycles in a small open economy,' American Economic Review 81, 797-818

Mulraine, M.L.B. (2006) 'Investment-specific technology shocks in a small open economy,' manuscript, University of Toronto

Nason, J.M., and J.H. Rogers (2006) 'The present-value model of the current account has been rejected: round up the usual suspects,' Journal of International Economics 68, 159-87

Schmitt-Groh', S., and M. Uribe (2003) 'Closing small open economy models,' Journal of International Economics 61, 163-85

Investment-Specific Shocks and External Balances in a Small Open Economy Model (Chocs spécifiques...

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