Abstract
In this paper, an information matrix (IM)-based test is developed for testing the hypothesis of constant relative risk aversion parameter in the GARCH-M set up. A detailed Monte Carlo study is then carried out to evaluate the performance of this test in terms of size and power. Further, a bootstrap technique is suggested to correct the over-size problem found in small samples. The proposed test is then applied to the time series of returns on stock markets of five important countries to examine whether this important hypothesis holds or not, and it is found that the relative risk aversion parameter is not time invariant for all the five time series.
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References
Baillie RT, Bollerslev T (1990) A multivariate generalized ARCH approach to modelling risk premia in foreign exchange markets. J Int Money Finance 9: 309–324
Baillie RT, DeGennaro RP (1990) Stock returns and volatility. J Financial Quant Anal 25: 203–221
Bera AK, Kim S (2002) Testing constancy of correlation and other specifications of the BGARCH model with an application to international equity returns. J Empir Finance 9: 171–195
Bera AK, Ullah A (1991) Rao’s score test in econometrics. J Quant Econ 7: 189–220
Bera AK, Ra S, Sarkar N (1998) Hypothesis testing for some nonregular cases in econometrics. In: Chakrabarty S, Coondoo D, Mukharjee R (eds) Econometrics: theory and practice. Allied Publishers, pp 319–351
Bickel PJ, Freedman DA (1981) Some asymptotic theory for the bootstrap. Ann Stat 9: 1196–1217
Bollerslev T, Engle RF, Wooldridge JM (1988) A capital asset pricing model with time varying covariances. J Political Econ 96: 116–131
Bose A (1988) Edgeworth correction by bootstrap in autoregressions. Ann Stat 16: 1709–1722
Chesher A (1983) The information matrix test: simplified calculation via a score test interpretation. Econ Lett 13: 45–48
Chesher A (1984) Testing for neglected heterogeneity. Econometrica 52: 865–872
Chesher A, Spady R (1991) Asymptotic expansions of the information matrix test statistics. Econometrica 59: 787–816
Chou R, Engle RF, Kane A (1992) Measuring risk aversion from excess returns on a stock index. J Econ 52: 201–224
Cox DR (1983) Some remarks on overdispersion. Biometrika 70: 269–274
Das S, Sarkar N (2000) An ARCH in the nonlinear mean (ARCH-NM) Model. Sankhya Ser B 62: 327–344
Engle RF (1982) Autoregressive conditional heteroscedasticity with estimates of variance of U.K. inflation. Econometrica 50: 987–1008
Engle RF, Lilien DM, Robins RP (1987) Estimating time varying risk premium in the term structure: the ARCH-M model. Econometrica 55: 391–407
Freedman DA (1981) Bootstrapping regression models. Ann Stat 9: 1218–1228
French KR, Schwert G, Stambaugh R (1987) Expected stock returns and volatility. J Financial Econ 19: 3–30
Horowitz JH (1994) Bootstrap-based critical values for the information matrix test. J Econ 61: 395–411
Lancaster T (1984) The covariance matrix of the information matrix test. Econometrica 52: 1051–1053
Moran PAP (1971) The uniform consistency of maximum-likelihood estimators. Proc Camb Philos Soc 70: 435–439
Nelson DB (1990) Conditional heteroscedasticity in asset returns: a new approach. Econometrica 59: 347–370
Orme C (1990) The small sample performance of the information matrix test. J Econ 46: 309–331
Pindyck RS (1988) Risk aversion and determinants of stock market behaviour. Rev Econ Stat LXX: 183–190
Rao CR (1948) Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Proc Camb Philos Soc 44: 50–57
Self S, Liang K (1987) Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J Am Stat Assoc 82: 605–610
Taylor L (1987) The size bias of White’s information matrix test. Econ Lett 24: 63–67
White H (1982) Maximum likelihood estimation of misspecified models. Econometrica 50: 1–25
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The authors are grateful to an anonymous referee for very insightful comments on an earlier draft of this paper.
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Das, S., Sarkar, N. Is the relative risk aversion parameter constant over time? A multi-country study. Empir Econ 38, 605–617 (2010). https://doi.org/10.1007/s00181-009-0281-y
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DOI: https://doi.org/10.1007/s00181-009-0281-y