C-CAPM. An Estimation of C-CAPM Considering Risk-free Rate and Money-in-utility MIU. Tatsuya Morisawa C-CAPM GMM C-CAPM

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1 C-CAPM An Esimaion ofc-capm Considering Risk-free Rae and Money-in-uiliyMIU Tasuya Morisawa C-CAPM GMM C-CAPMMIU Coninuous Updaing GMM Consumpion-based Capial Asse Pricing Model: C-CAPM C-CAPM C-CAPM Poerbe and Roemberg1987 Finn, Hoffman and Schlagenhauf1990Holman1998Baba2000Ono, Ogawa and Yoshida Baba2000 Ono e al * UMDS Research Associaion

2 16 2 MIUmoney-in-uiliy MIU CIAcash-in-advance Baba2000CIA MIU C-CAPM MIU C-CAPM 3 Weil Sock and Wrigh2000 GMMHansen, Heaon and Yaron1996 Coninuous Updaing GMM Coninuous Updaing GMM Hansen, Heaon and Yaron1996 C-CAPM MIU 0

3 17 max s E0 c, a 1, m 1 0 u( c, m ).. a 1 m 1 (1 r ) a m w c 1 2 (0,); 1 / (1+)(0,1); a m w r E () uc( c, m ) u( c, m ) / c, 2 2 u cc ( c, m ) u( c, m ) /[ c ], u ( c, m ) u( c, m ) / m, 2 2 u c, m ) u( c, m ) /[ m ], m 2 u ( c, m ) u( c, m ) /[ c m ]. cm mm ( c : uc ( c, m ) for [0, ) 3 a E [ (1 r )] 0 for [0, ) 1 : 1 1 m E { [ u ( c, m ) ]} 0 for [0, ) 1 : m (1) E (1 r ) 1] 0 for [0, ) [ (1) uc ( c 1, m 1) 7 1 u ( c, m ) c 35 (2) E ( 1) 0 for [0, ) 1 8 (2) 1 (1) 1 u m ( c 1, m 1) 1 9 uc ( c 1, m 1) 6Euler equaion 7 sochasic discoun facor

4 18 u c, m ) ( u( c, m ) c m, 0 1 and Consan Relaive Risk Aversion: CRRA x c m 1 = Arrow1951 Pra1964relaive risk aversion RRA x ) u ( x ) x / u ( x ) ( xx x 10 RRA ( c ) u ( c, m ) c / u ( c, m ) 1 (1 ) 11 cc c RRA ( m ) u ( c, m ) m / u ( c, m ) (1 ) 12 mm m C-CAPM MIU 10 u c, m ) 0 cm ( u c, m ) c ( wealh effec WE ( m ) u ( c, m ) m / u ( c, m ) (1 )(1 ) 13 cm c 13 1% 13

5 (1) 1 c 1 c (1 ) 1 m m 1 (1 )(1 ) 14 M p N (1) 1 c 1 c (1 ) 1 ( p 1 M 1 / M / p ) ( N 1 / N ) (1 )(1 ) (6) c 1 E c (1 ) 1 ( p 1 M 1 / M / p ) ( N 1 / N ) (1 )(1 ) (1 r 1 ) X12-ARIMA 1 p p c N p M Baba2000 CACA+CADM1CAD+M1+M1+QMA

6 r p c c /c M (CA) CA(CAD) M M1+(M1+QMA) M /M -1 CA CAD M M1+QMA r p p /p N N /N Generalized Mehod of Momens: GMM GMM Sock and Wrigh Two-sep GMM Ieraed GMM 7 Hansen, Heaon and Yaron1996 Coninuous Updaing GMMC-U 8 Newey and Wes1987 HACHeeroskedasic and Auocorrelaion Consisen GMM

7 GMM J-TEST RRA(c ) RRA(m ) WE(m ) CA Two-sep (0.486) %**5%*10( ) 3J-TEST[ ] p (0.050) [0.484] Ieraed (0.489) (0.050) [0.542] C-U (0.508) (0.048) [0.564] CAD Two-sep (0.282) (0.052) [0.047] Ieraed (0.261) (0.054) [0.052] C-U (0.512) (0.047) [0.075] M1 Two-sep (0.160) (0.038) [0.858] Ieraed (0.160) (0.038) [0.855] C-U (0.161) (0.038) [0.856] M1+QMA Two-sep (0.551) (0.047) [0.180] Ieraed (0.548) (0.047) [0.167] C-U (0.627) (0.044) [0.203] J CAD 10% CAD Ieraed GMM C-U GMM 5%

8 22 1% 1% 11 13RRA(c )RRA(m )WE(m ) RRA(c ) 1 RRA(m ) WE(m ) GMM J-TEST RRA(c ) RRA(m ) WE(m ) CA Two-sep (0.531) %**5%*10( ) 3J-TEST[ ] p (0.045) [0.787] Ieraed (0.531) (0.045) [0.793] C-U (0.537) (0.044) [0.796] CAD Two-sep (0.291) (0.052) [0.050] Ieraed (0.270) (0.054) [0.055] C-U (0.493) (0.045) [0.071] M1 Two-sep (0.160) (0.038) [0.514] Ieraed (0.160) (0.037) [0.513] C-U (0.162) (0.037) [0.523] M1+QMA Two-sep (0.631) (0.046) [0.388] Ieraed (0.631) (0.046) [0.370] C-U (0.687) (0.043) [0.399]

9 GMM J-TEST RRA(c ) RRA(m ) WE(m ) CA Two-sep (0.513) %**5%*10( ) 3J-TEST[ ] p (0.046) [0.724] Ieraed (0.514) (0.046) [0.735] C-U (0.521) (0.045) [0.741] CAD Two-sep (0.283) (0.052) [0.056] Ieraed (0.266) (0.054) [0.061] C-U (0.430) (0.046) [0.072] M1 Two-sep (0.155) (0.038) [0.703] Ieraed (0.156) (0.038) [0.700] C-U (0.157) (0.038) [0.704] M1+QMA Two-sep (0.578) (0.047) [0.320] Ieraed (0.577) (0.048) [0.299] C-U (0.636) (0.045) [0.332]

10 24 GMM J-TEST RRA(c ) RRA(m ) WE(m ) CA Two-sep (0.758) %**5%*10( ) 3J-TEST[ ] p (0.032) [0.574] Ieraed (0.763) (0.032) [0.640] C-U (0.786) (0.031) [0.650] CAD Two-sep (0.519) (0.052) [0.001] Ieraed (0.543) (0.049) [0.004] C-U (0.013) (3.147) (0.032) * [0.027] M1 Two-sep (0.339) (0.035) [0.297] Ieraed (0.344) (0.035) [0.333] C-U (0.372) (0.035) [0.351] M1+QMA Two-sep (0.722) (0.029) [0.547] Ieraed (0.723) (0.029) [0.548] C-U (0.745) (0.029) [0.556] J CAD 10% 1%CAD CAD RRA(c ) RRA(m ) CAD WE(m ) 25CADC-U 910

11 GMM J-TEST RRA(c ) RRA(m ) WE(m ) CA Two-sep (0.767) %**5%*10( ) 3J-TEST[ ] p (0.027) [0.928] Ieraed (0.767) (0.027) [0.930] C-U (0.770) (0.027) [0.930] CAD Two-sep (0.539) (0.052) [0.001] Ieraed (0.566) (0.047) [0.005] C-U (0.012) (2.983) (0.028) [0.026] M1 Two-sep (0.337) (0.034) [0.762] Ieraed (0.338) (0.034) [0.763] C-U (0.343) (0.034) [0.765] M1+QMA Two-sep (0.799) (0.026) [0.846] Ieraed (0.799) (0.026) [0.843] C-U (0.806) (0.026) [0.844] 7 5 6

12 26 GMM J-TEST RRA(c ) RRA(m ) WE(m ) CA Two-sep (0.755) %**5%*10( ) 3J-TEST[ ] p (0.030) [0.876] Ieraed (0.756) (0.030) [0.882] C-U (0.760) (0.030) [0.883] CAD Two-sep (0.530) (0.052) [0.001] Ieraed (0.554) (0.048) [0.006] C-U (0.011) (2.772) (0.031) ** [0.023] M1 Two-sep (0.328) (0.036) [0.666] Ieraed (0.329) (0.036) [0.669] C-U (0.337) (0.036) [0.673] M1+QMA Two-sep (0.749) (0.028) [0.801] Ieraed (0.749) (0.028) [0.796] C-U (0.758) (0.028) [0.798] J CAD M1 10% CADM1 CAD

13 27 1% CAD RRA(c ) RRA(m ) CAD CAD RRA(m ) WE(m ) 36CAD 1.8 GMM J-TEST RRA(c ) RRA(m ) WE(m ) CA Two-sep (1.166) %**5%*10( ) 3J-TEST[ ] p (0.029) [0.593] Ieraed (1.174) (0.029) [0.650] C-U (1.219) (0.028) [0.661] CAD Two-sep (0.572) (0.079) [0.001] Ieraed (0.324) (0.176) [0.005] C-U (0.317) (0.216) [0.006] M1 Two-sep (0.563) (0.041) [0.059] Ieraed (0.571) (0.041) [0.069] C-U (0.922) (0.041) [0.114] M1+QMA Two-sep (1.110) (0.029) [0.332] Ieraed (1.112) (0.029) [0.352] C-U (1.183) (0.028) [0.372]

14 28 9 M1 J 8 GMM J-TEST RRA(c ) RRA(m ) WE(m ) CA Two-sep (1.237) %**5%*10( ) 3J-TEST[ ] p (0.027) [0.977] Ieraed (1.237) (0.027) [0.978] C-U (1.239) (0.027) [0.978] CAD Two-sep (0.582) (0.083) [0.000] Ieraed (0.330) (0.181) [0.005] C-U (0.320) (0.221) [0.006] M1 Two-sep (0.630) (0.042) [0.304] Ieraed (0.636) (0.042) [0.299] C-U (0.765) (0.041) [0.337] M1+QMA Two-sep (1.219) (0.026) [0.625] Ieraed (1.218) (0.026) [0.624] C-U (1.259) (0.025) [0.631] 10 9

15 29 GMM J-TEST RRA(c ) RRA(m ) WE(m ) CA Two-sep (1.205) %**5%*10( ) 3J-TEST[ ] p (0.030) [0.959] Ieraed (1.205) (0.030) [0.961] C-U (1.209) (0.030) [0.961] CAD Two-sep (0.589) (0.080) [0.000] Ieraed (0.328) (0.183) [0.005] C-U (0.319) (0.226) [0.006] M1 Two-sep (0.566) (0.042) [0.214] Ieraed (0.569) (0.042) [0.207] C-U (0.712) (0.042) [0.244] M1+QMA Two-sep (1.133) (0.027) [0.568] Ieraed (1.132) (0.027) [0.564] C-U (1.175) (0.027) [0.574] C-CAPM 1 GMM +CAD C-CAPM CAD C-U

16 30 2 Baba2000 Baba2000 Ono e al.2004 Baba RRA(c )RRA(m ) RRA(c )C-CAPM RRA(m ) 4 WE(m ) RRA(c )RRA(m ) WE(m ) CADC-U CAD 1.8 C-CAPM GMM RRA(m ) Baba2000 +M1M1

17 31 SNA Mehra and Presco1985 C-CAPM 1 Poerbe and Roemberg1987 Ono e al , pp C-CAPM Poerbe and Roemberg1987 Ono e al.2004 Holman ) 2 89 C-CAPM C-CAPM M1+QMA M2 M2 M2+CD M1+QMA 5 6 Sock and Wrigh2000weak insrumen GMM Sock, Wrigh

18 32 and Yogo2002Sock and Wason2011, ch , 2 7 Two-sep GMM Ieraed GMM Two-sep GMM Ieraed GMM C-U Hansen, Heaon and Yaron1996C-U Two-sep GMM Ieraed GMM HP hps:// pp Arrow, K. J.1951, Alernaive Approaches o he Theory of Choice in Risk-Taking Siuaions, Economerica 194, pp Baba, N.2000, Exploring he Role of Money in Asse Pricing in Japan: Moneary Consideraions and Sochasic Discoun Facors, Moneary and Economic Sudies 182, pp Finn, M. G., D. L. Hoffman and D. E. Schlagenhauf1990, Ineremporal Asse-Pricing Relaionships in Barer and Moneary Economies, Journal of Moneary Economics 253, pp Hansen, L. P.,J. Heaon and A. Yaron1996, Finie-Sample Properies of Some Alernaive GMM Esimaors, Journal of Business & Economic Saisics 143, pp Holman, J. A.1998, GMM Esimaion of a Money-in-he-Uiliy-Funcion Model: The Implicaions of Funcional Forms, Journal of Money, Credi and Banking 304, pp Mehra, R. and E. C. Presco1985, The Equiy Premium: A Puzzle,Journal of Moneary Economics 152, pp Newey, W. K. and K. D. Wes1987, A Simple, Posiive Semi-Definie, Heeroskedasiciy and Auocorrelaion Consisen Covariance Marix, Economerica 553, pp Ono, Y., K. Ogawa and A. Yoshida2004, The Liquidiy Trap and Persisen Unemploymen wih Dynamic Opimizing Agens: Empirical Evidence, Japanese Economic Review 554, pp Poerbe, J. M. and J. J. Roemberg1987, Money in he uiliy funcion: an empirical implemenaion, in W. B. Barne and K. Singleon eds., New Approaches o Moneary Economics: Proceedings of he Second Inernaional

19 33 Symposium in Economic Theory and Economerics, Chaper 10, Cambridge: Cambridge Universiy Press, pp Pra, J. W.1964, Risk Aversion in he Small and in he Large, Economerica 321-2, pp Sock, J. H. and M. W. Wason2011, Inroducion o Economerics, 3rd ed., Pearson Sock, J. H. and J. H. Wrigh2000, GMM wih Weak Idenificaion, Economerica 685, pp Sock, J. H., J. H. Wrigh and M. Yogo2002, A Survey of Weak Insrumens and Weak Idenificaion in Generalized Mehod of Momens, Journal of Business & Economic Saisics 204, pp Weil, P.1989, The Equiy Premium Puzzle and he Risk-Free Rae Puzzle, Journal of Moneary Economics 243, pp

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