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I O D ` B V�LUV �mÌ O ACA)�Eg LN_` B Z c=g�G aEO)Z AHGnDwBED�c=gQBED�c�B MNM ~ ZLPan` F)��ëH¶0G TwO)v G Z¡WL D K B _tZ G O1_ GnD�G T�LU_ A)p�¶QGn@�A O1` G M c 8Z G6c�@ _ F L GnD^BED�c o aEaEZCO)a BmF O � M @ _ FC@�BmF L GnD�A)�¤í ��9Õ6ð5� ï ~��5��a~�ñr�rñ(� ï ~S�g�¢�9��9ë�� «E«�r� O1_tO1TWVjO)Z ¨1«E«6¨ ® �Ë¨1äEä � Ë¨1·nª4R

I Z G v D L D a � K B Z F L D��BED�c>��GnAHFCBEA K�O)an`�LUZ �QëHq `�O f x2O1_ FCA|GE] K B MPO BED�c³� O1T B MPO ��B V G Z ?�@�s�s M [bGnDæ��G Tu�T G�c L F;[J� O1T BED�c�A)�¤í ��9��aë{�1�rð¢ñ�� ïu�E«�°Ì,@ M [�¨1«E«6¨ ® �j« k � � «E�6¨mR

�:B T s V2O1MNM �QÌEG ` D��uRP�eBED�c¿?6[�c�D O [ò��@�c Y�LPa ACGnD��ëHf M BEAHF LU_)L F LPO A}GE]w?6@ V AHF L FC@�F L GnD L Dìg O B M I:@�A L D O AA��[ �_)MUOuK G�c O1M A v0L F ` ¶0G TwOw �Z G�c�@ _ F L GnD��¤íÎ°Ìn@�D O � kmlElEl ® � O1MUO1_ F Z GnD LU_W��MPO B Y B LUM B V�MPO BmF v�v�v R¤D4[ERê] ZV RêG ZCam�� Z¢T B an` G TwO � O1_ GnD�G T�L AHF � M @�c Y�LPa ACGnD � M @�c Y6LPa AHGnD�R ` F T{M R

�:B T s V2O1MNM �,ÌEG ` D��uRP�6BED�c�dWR © ZO)a G Z [ K BED ¡�LUv � ë�:GnD�AC@ T s�F L GnD�� ¥ D _ G TwO ��BED�c ¥ D4F O)ZCO AHF�gQBmF O A1p�g O1L D4F O)ZH�s ZCO F L D a F `�O q LUTwO ? O)Z¢LPO A�f Y6L c O D _tO �¤í L D=i=R3I M BED _¢` B Z c|BED�cu?2R3� L A _¢`�O)Z�O c�A1RP�N�� )Ô �Ëï �)ðH�3��¢�9��9ëuñ��t�� Õ ï ~ §¨1«E·E« ® ��:B TWV�ZL c aEO � K o p K%¥ q �ZCO ACA1��¨1·E� ��k ¨1ä�R

�:B T s V2O1MNM �9ÌnG ` D&�uRP�nBED�c=d�R © ZCO)a G Z [ K BED ¡6LPv �jëHq `�O g O ACs2GnD�A O GE]��GnD�AC@ T s�F L GnD|FHG ¥ D _ G T{O �¤í �/Õ6ð§�-�� ï ��9�2�9ëuñ(�WÔ��p�3ñ±��J>ã �%§¨1«E«6¨ ® p�ª kEã�� ªmänª4R�:B T s V2O1MNM �4ÌEG ` D��uRP��BED�c�d�R © ZO)a G Z [ K BED ¡6LPv ��ë �O)Z¢T BED O D4F ¥ D _ G T{O ��@ ZCZCO D4F ¥ D _ G TwO BED�cb��GnD�A@ T s �

F L GnD��¤í �6�aÕ�ð�� ï ~��5� � Õ��¢ñ��2�-�¢��9��aë=ñ�� ï �rñ��-�rñ��t� ·b°Ì,@ M [^¨1«E« l ® � k äE� ��k ªm«�R�:BED�G Y B6��B V�L GWBED�c o D aEO1M�X0V�L c O ��ë ¥ D4F O)Z D�BmF L GnD�B M I:@�A L D O ACA:��[ _)MUO A)�4� L D�BED _)L B M�K B ZC¡EO FCA:BED�c}¶QGn@�A O1` G M c

k ª

8Z G6c�@ _ F L GnD��¤í ��9Õ6ð5� ï ~ �5�~�g��a��9ëuñ(�WÍ��9� ï ëuñ��t� ï �c�{�y�9��rðH�9~�kEk o s ZLUM ¨1«E«E· ® �� u � � �nª k Rf LN_`�O D V BE@ T � K B Z F L D7?jRP��B Z A O F O)Z ¶eBED�A O D7BED�c³S O D�D O F ` Ì�R�? L D anMPO FHGnDµë o F LUTwO ? O)ZLUO A o D�B M [�A L A0GE]

g O s ZCO A O D4FCBmF LPYEO o aEO D4F K G6c O1M A�GE]��GnD�AC@ T s�F L GnD}BED�cb� O1L AC@ ZCO � ` G LN_tO�X D�c O)Z�X D _tO)Z FCB L D4F;[E�¤í$� Õ ï ð5��;�)ð5~�� 9Õ6ð�� ï ~ �*��g�¢�9��9ëuñ��t� ¨ lnã r� O)V�Z @�B Z [Î¨1«E·E· ® �j�6¨ � ªEª4R

© ZCO)O D v G4G6c��8Ì O)ZO1T [7BED�c�� Y6L ¶ O)Z_ G vQL F � �|ëHq `�O o MUM G _ BmF L GnDËGE]e��Bms L FCB M BED�c>q LNTwO G YEO)Z F `�O I:@�A L D O ACA�:[ _)MPO �¤í �6�9Õ6ð�� ï ~��*��9~ ñr�rñ(� ï ~��9��aë�� «E«^r� O1_tO1T�VjO)Z ¨1«E«6¨ ® ��Ë¨1·E· � ¨ k ¨ u R

© ZCO)O D v G4G6c��Ì O)ZCO1T [E��g LU_¢` B Z cbg�G aEO)Z AHGnD%BED�c%gQBED�c�B MNM ~ Z¢LPan` F)�hëH¶QGn@�A O1` G M c 8Z G�c�@ _ F L GnD L D�g O B M I:@�A L��D O ACA��[ _)MPO q `�O G Z [E�¤í L DÎq&R��G�G MPO [E� O c�RP�G ðH�9��rñ±�tð¢�J�5� � Õ��-ñZ�2�t��¡�u�&��~U�tÔ��t�)� ï ð+�� R �ZL D _tO FHGnD��d�Ì�p 8ZL D _tO FHGnD X D LPYEO)Z A L F;[ �ZO ACA�§¨1«E«E� ® ��¨1�nª � ¨3ª u R

¶eB MUM �6g�G VjO)Z FhfQRP�yë?�FHG _¢` BEAHF LU_e¥§T s MULN_ BmF L GnD�A�GE]�F `�O � L ] Ot� ��[ _)MUO0 O)ZT BED O D4F ¥ D _ G TwO ¶0[�s2GEF `�O A L A)p�q `�O G Z [BED�c�f Y6L c O D _tO �¤í ��9Õ6ð�� ï ~ �*�W��9~ ñ'�rñ�� ï ~��g�¢�9��9ë�� ·Eä%r� O1_tO1TWVjO)Z ¨1«nªm· ® �j«nª�¨ � «E·E«�R

¶eB MUM ��gQG VjO)Z F�f�RP��ë ¥ D,F O)Z F O1T s2G Z B M ?6@ V AHF L FC@�F L GnD L Dæ��GnD�AC@ T s�F L GnD��¤í ��9Õ6ð�� ï ~��*��a~�ñr�rñ(� ï ~G��9�2�9ë�� «Eä o s ZLNM ¨1«E·E· ® p ãEã « ��ã �nª4R

S O [6D O A)��ÌEG ` D K B3[�D�B Z c��:ëHf _ GnD�G T{LN_W GnACA LUV�LUMUL F LUO A:]�G Z i�@ Z © Z BED�c _¢`�LUM c ZCO D��¤íA�Wï �rñ°�9� ï �J� � ��6�� ï ��ÕÆë �i _ FHG V2O)Z Ë¨bBED�c¿¨1·��e¨1« ãml R rg O s ZL D4F O c L D£¢ �6�$�y�9~Z~U��3�;��¤bð-ñ'�rñ��¦¥m��5�1��6� �Ëï �9� ï ð��{§w��9�2�t� �¸ G M @ TwO&¥8¨ � �:�� ï �9�|ñZ�¡�Q�)ð��Õ ï �¢ñ°�9� ��GnD�c�GnD��¨1«nª k R ®

S L D a ��gQG V2O)Z F © RP�0� ` B ZMUO A ¥ R hM GnACA O)Z ��BED�cµ? O)ZCanL GËq|R8g O)VjO1M G��uë �Z G6c�@ _ F L GnD�� © Z G v F ` BED�c�I:@�A L D O ACA�:[ _)MPO A1p ¥ Rjq `�O I:BEA LU_ d O G _)M BEACA LN_ B M�K G6c O1M �¤í �6�aÕ�ð�� ï ~��5� � �a�2�)� ï ð��A�g�¢�9��9ëuñ��t�&k ¨} K B Z_` ¨1«E·E· ® p¨1«E� ��kEãEk R

K BED ¡�LUv �4dWR © ZCO)a G Z [E��ëHq `�Oe O)ZT BED O D4F ¥ D _ G TwO ¶0[4sjGEF `�O A L A8BED�cJF `�O g O B M�¥ D4F O)ZCO AHF:gQBmF O �¤í ��9��aë=ñ��t�©��)�°�;�)ð� ªb§¨1«E·6¨ ® � ãml ª �\ã Ë¨mRK BED ¡�LUv ��dWR © ZCO)a G Z [E��Ìn@ MNL GJÌ�R2g�GEF O1TWVjO)ZCa BED�c%��B v�ZCO D _tO Ì�R�?6@ T{TwO)Z A)�hë ¥ D4F O)Z F O1T sjG Z B M ?6@ V AHF L FC@�F L GnD

L D K B _tZ G O1_ GnD�G T{LN_ A)�¤ís� Õ ï ðt�;�tð�~ª�«��9Õ6ð5� ï ~��5��9��aë=ñ��t� ¨ lEl r� O)V�Z @�B Z [³¨1«E·E� ® � kEk � ��k �6¨mRK^_ © Z BmFHF O D��f MUMPO D��2g LU_¢` B Z c�g�G aEO)Z ACGnD³BED�c^g0BED�c�[�~ Z¢LPan` F)��ë o DÎf z @ LUMULPV�ZL @ T K G�c O1M GE]�F `�O I:@�A L D O ACA

�:[ _)MPOQvQL F ` ¶0Gn@�A O1` G M c �Z G�c�@ _ F L GnD{BED�c}� L A _ B M� G MULN_ [E�¤í�¬ ��;�)ð5� ï �rñr�a� ï ~w�g�¢�9��9ëuñ��Ô��p�3ñ±��JÎã ·� K B1[¨1«E«nª ® � k änª �\k « l R

k ·

Table 1a: Estimates of s

(1982:2-1999:2, rational expectations)

1( ) t tc n s r nτ µ τ ε θε −∆ − ⋅ ∆ = + − ⋅ ∆ + +

τ Estimated s p-value of restrictions First-stage F

0.4 0.61 (0.20) 0.62 4.64

0.6 0.64 (0.16) 0.80 4.09

0.8 0.67 (0.15) 0.92 3.78

1.0 0.71 (0.13) 0.98 3.62

1.2 0.74 (0.12) 0.99 3.53

Notes:

Instruments are ( ) ( ) ( )2 , 2 , and 2 .c n r∆ − ∆ − −

p-value is for the test of over-identifying restrictions.

Table 1b: Estimates of s

(1982:2-1999:2, survey expectations)

1( ) t tc n s r nτ µ τ ε θε −∆ − ⋅ ∆ = + − ⋅ ∆ + +


0.4 0.48 (0.12) 0.50 5.53

0.6 0.50 (0.12) 0.80 9.44

0.8 0.53 (0.12) 0.91 7.79

1.0 0.57 (0.11) 0.98 6.72

1.2 0.62 (0.10) 0.91 6.01

Notes:



Table 1c: Estimates of s


1( ) t tc n s r nτ µ τ ε θε −∆ − ⋅ ∆ = + − ⋅ ∆ + +


0.4 -0.005 (0.11) 0.41 21.15146

0.6 0.05 (0.12) 0.14 16.58089

0.8 0.13 (0.12) 0.04 13.79036

1.0 0.23 (0.11) 0.01 12.07342

1.2 0.30 (0.09) 0.004 10.98652

Notes:



Table 1d: Estimates of s


1( ) t tc n s r nτ µ τ ε θε −∆ − ⋅ ∆ = + − ⋅ ∆ + +


0.4 -0.03 (0.16) 0.50 9.87768

0.6 0.08 (0.15) 0.27 8.38787

0.8 0.18 (0.14) 0.13 7.44436

1.0 0.28 (0.13) 0.06 6.83415

1.2 0.37 (0.12) 0.04 6.42499

Notes:



Table 2a: Different Instrument Sets


1( ) t tc n s r nτ µ τ ε θε −∆ − ⋅ ∆ = + − ⋅ ∆ + +

Instrument Set Estimated s p-value of restrictions First-stage F

( ) ( )

( )2 , 2 ,

2

c n

r

∆ − ∆ −

−

0.67 (0.15) 0.92 3.78

( ) ( )

( )2 , 2 ,

2

c y

r

∆ − ∆ −

−

0.68 (0.18) 0.92 3.70

( ) ( )

( ) ( )2 , 2 ,

2 2

c r

c y

∆ − −

− − −

0.69 (0.18) 0.64 3.69

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

n

c y

∆ − −

∆ −

− − −

0.66

(0.15) 0.81 2.79

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

y

c y

∆ − −

∆ −

− − −

0.68

(0.18) 0.81 2.73

Note: p-value is for the test of over-identifying restrictions.

Table 2b: Different Instrument Sets


1( ) t tc n s r nτ µ τ ε θε −∆ − ⋅ ∆ = + − ⋅ ∆ + +


( ) ( )

( )2 , 2 ,

2

c n

r

∆ − ∆ −

−

0.53 (0.12) 0.97 7.79

( ) ( )

( )2 , 2 ,

2

c y

r

∆ − ∆ −

−

0.53 (0.12) 0.97 7.73

( ) ( )

( ) ( )2 , 2 ,

2 2

c r

c y

∆ − −

− − −

0.49 (0.13) 0.35 7.50

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

n

c y

∆ − −

∆ −

− − −

0.48

(0.11) 0.55 5.77

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

y

c y

∆ − −

∆ −

− − −

0.49

(0.12) 0.55 5.75


Table 2c: Different Instrument Sets

(1949:1:2-1999:2, rational expectations)

1( ) t tc n s r nτ µ τ ε θε −∆ − ⋅ ∆ = + − ⋅ ∆ + +


( ) ( )

( )2 , 2 ,

2

c n

r

∆ − ∆ −

−

0.13 (0.12) 0.04 13.79036

( ) ( )

( )2 , 2 ,

2

c y

r

∆ − ∆ −

−

0.17 (0.09) 0.21 18.33781

( ) ( )

( ) ( )2 , 2 ,

2 2

c r

c y

∆ − −

− − −

0.08 (0.12) 0.14 13.17301

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

n

c y

∆ − −

∆ −

− − −

0.12

(0.12) 0.04 10.29021

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

y

c y

∆ − −

∆ −

− − −

0.19

(0.08) 0.10 13.99726


Table 2d: Different Instrument Sets

(1949:1:2-1982:1, rational expectations)

1( ) t tc n s r nτ µ τ ε θε −∆ − ⋅ ∆ = + − ⋅ ∆ + +


( ) ( )

( )2 , 2 ,

2

c n

r

∆ − ∆ −

−

0.18 (0.14) 0.13 7.64102

( ) ( )

( )2 , 2 ,

2

c y

r

∆ − ∆ −

−

0.25 (0.10) 0.20 11.90749

( ) ( )

( ) ( )2 , 2 ,

2 2

c r

c y

∆ − −

− − −

0.14 (0.14) 0.44 7.23907

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

n

c y

∆ − −

∆ −

− − −

0.18

(0.13) 0.26 5.61802

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

y

c y

∆ − −

∆ −

− − −

0.25

(0.10) 0.33 9.03191


Table 3: Robustness Checks

1 2 ( )t t t tc r n 1tµ β β τ ε θε −∆ = + + ⋅ ∆ + +

1982:2-1999:2

Rational Expectations

1982:2-1999:2 Survey

Expectations

1949:1-1999:2 Rational

Expectations

1949:1-1982:1 Rational

Expectations

r 0.74 (0.24)

0.56 (0.16)

-0.02 (0.12)

-0.07 (0.20)

nτ ∆ 0.40 (0.23)

0.50 (0.21)

0.34 (0.20)

0.34 (0.28)

Restriction Rejected? No No Yes Yes

Notes:

τ is set to 0.8.


Table 4a: Adding Disposable Income (Restriction Imposed)


1( ) t tc n s r n yτ µ τ β ε θε −∆ − ⋅ ∆ = + − ⋅ ∆ + ∆ + +

Instrument Set Estimated s Estimated β

( ) ( )( )

2 , 2 ,

2

c n

r

∆ − ∆ −

− 0.70

(0.17) 0.08

(0.21)

( ) ( )( )

2 , 2 ,

2

c y

r

∆ − ∆ −

− 0.69

(0.19) 0.09

(0.23)

( ) ( )( ) ( )

2 , 2 ,

2 2

c r

c y

∆ − −

− − −

0.70 (0.20)

0.15 (0.31)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

n

c y

∆ − −

∆ −

− − −

0.70 (0.17)

0.11 (0.21)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

y

c y

∆ − −

∆ −

− − −

0.70 (0.19)

0.12 (0.23)

Note: τ is set to 0.8.

Table 4b: Adding Disposable Income (Restriction Imposed)




( ) ( )( )

2 , 2 ,

2

c n

r

∆ − ∆ −

− 0.54

(0.13) 0.03

(0.18)

( ) ( )( )

2 , 2 ,

2

c y

r

∆ − ∆ −

− 0.54

(0.13) 0.06

(0.22)

( ) ( )( ) ( )

2 , 2 ,

2 2

c r

c y

∆ − −

− − −

0.49 (0.13)

0.01 (0.29)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

n

c y

∆ − −

∆ −

− − −

0.49 (0.13)

0.01 (0.22)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

y

c y

∆ − −

∆ −

− − −

0.49 (0.13)

0.01 (0.22)


Table 4c: Adding Disposable Income (Restriction Imposed)




( ) ( )( )

2 , 2 ,

2

c n

r

∆ − ∆ −

− 0.38

(0.47) -1.45 (1.38)

( ) ( )( )

2 , 2 ,

2

c y

r

∆ − ∆ −

− 0.17

(0.15) -0.73 (0.70)

( ) ( )( ) ( )

2 , 2 ,

2 2

c r

c y

∆ − −

− − −

0.42 (0.44)

-1.44 (1.57)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

n

c y

∆ − −

∆ −

− − −

0.46 (0.44)

-1.60 (1.38)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

y

c y

∆ − −

∆ −

− − −

0.21 (0.17)

-0.77 (0.78)


Table 4d: Adding Disposable Income (Restriction Imposed)




( ) ( )( )

2 , 2 ,

2

c n

r

∆ − ∆ −

− 0.54

(0.47) -0.96 (0.89)

( ) ( )( )

2 , 2 ,

2

c y

r

∆ − ∆ −

− 0.42

(0.28) -0.75 (0.79)

( ) ( )( ) ( )

2 , 2 ,

2 2

c r

c y

∆ − −

− − −

0.47 (0.51)

-0.81 (0.99)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

n

c y

∆ − −

∆ −

− − −

0.53 (0.44)

-0.92 (0.83)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

y

c y

∆ − −

∆ −

− − −

0.41 (0.25)

-0.73 (0.72)


Table 5a: Adding Disposable Income (Unrestricted)


1 2 3( )t t t t tc r n y 1tµ β β τ β ε θε −∆ = + + ⋅ ∆ + ∆ + +

Instrument Set Estimated 1β Estimated 2β Estimated 3β

( ) ( )( )

2 , 2 ,

2

c n

r

∆ − ∆ −

− 0.83

(0.81) 0.60

(1.81) -0.17 (1.49)

( ) ( )( )

2 , 2 ,

2

c y

r

∆ − ∆ −

− 0.74

(0.35) 0.42

(0.75) 0.004 (0.52)

( ) ( )( ) ( )

2 , 2 ,

2 2

c r

c y

∆ − −

− − −

-7.01 (190.6)

-15.5 (391.7)

16.1 (393.0)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

n

c y

∆ − −

∆ −

− − −

0.71 (0.76)

0.37 (1.74)

0.05 (1.43)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

y

c y

∆ − −

∆ −

− − −

0.72 (0.34)

0.35 (0.75)

0.09 (0.53)


Table 5b: Adding Disposable Income (Unrestricted)




( ) ( )( )

2 , 2 ,

2

c n

r

∆ − ∆ −

− 0.61

(0.50) 0.71

(1.78) -0.16 (1.38)

( ) ( )( )

2 , 2 ,

2

c y

r

∆ − ∆ −

− 0.55

(0.21) 0.51

(0.76) 0.03

(0.51)

( ) ( )( ) ( )

2 , 2 ,

2 2

c r

c y

∆ − −

− − −

-1.45 (10.2)

-6.47 (36.1)

6.55 (34.1)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

n

c y

∆ − −

∆ −

− − −

0.28 (0.49)

-0.43 (1.71)

0.77 (1.36)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

y

c y

∆ − −

∆ −

− − −

0.47 (0.22)

0.32 (0.77)

0.13 (0.55)


Table 5c: Adding Disposable Income (Unrestricted)




( ) ( )( )

2 , 2 ,

2

c n

r

∆ − ∆ −

− 1.03

(6.29) 1.14

(5.05) -3.86

(23.00)

( ) ( )( )

2 , 2 ,

2

c y

r

∆ − ∆ −

− 0.01

(0.30) 0.53

(0.43) -0.07 (1.16)

( ) ( )( ) ( )

2 , 2 ,

2 2

c r

c y

∆ − −

− − −

-0.98 (8.10)

0.06 (3.91)

3.63 (29.89)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

n

c y

∆ − −

∆ −

− − −

0.31 (1.49)

0.47 (0.95)

-1.12 (5.18)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

y

c y

∆ − −

∆ −

− − −

-0.08 (0.28)

0.35 (0.37)

0.28 (1.08)


Table 5d: Adding Disposable Income (Unrestricted)




( ) ( )( )

2 , 2 ,

2

c n

r

∆ − ∆ −

− 0.71

(1.75) 0.51

(0.82) -1.20 (2.56)

( ) ( )( )

2 , 2 ,

2

c y

r

∆ − ∆ −

− 0.11

(1.23) 0.48

(0.41) -0.28 (1.91)

( ) ( )( ) ( )

2 , 2 ,

2 2

c r

c y

∆ − −

− − −

1.98 (38.88)

0.59 (2.29)

-3.15 (60.28)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

n

c y

∆ − −

∆ −

− − −

0.76 (1.68)

0.55 (0.75)

-1.26 (2.51)

( ) ( )( )

( ) ( )

2 , 2 ,

2 ,

2 2

c r

y

c y

∆ − −

∆ −

− − −

0.18 (1.18)

0.52 (0.37)

-0.36 (1.82)


Table 6: Robustness Checks: Michigan Survey Data

1 2 ( )t t tc r n tµ β β τ∆ = + + ⋅ ∆ +η

1961:2-1999:2 Annual, Survey

Expectations

1961:2-1999:2

Annual, Rational

Expectations

1961:2-1999:2 Quarterly, Rational

Expectations

1982:2-1999:2 Annual, Survey

Expectations

r 0.023 (0.11)

-0.079 (0.15)

0.09 (0.12)

0.34 (0.063)

nτ ∆ 0.56 (0.49)

0.58 (0.27)

0.48 (0.19)

0.60 (0.18)

Restriction Rejected? No Yes Yes No

Notes:

τ is set to 0.8.

Instruments are ( ) ( ) ( )2 , 2 , and 2c n r∆ − ∆ − − for quarterly differences.

Instruments are ( ) ( ) ( )5 , 5 , and 5c n r∆ − ∆ − − for annual differences.

tη is assumed to be MA(1) for quarterly differences.

tη is assumed to be MA(5) for annual differences.

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