Hostname: page-component-7b7567c8c-jswmv Total loading time: 0 Render date: 2026-11-15T21:58:51.134Z Has data issue: false hasContentIssue false
  • English
  • Français

Using Samples of Unequal Length in Generalized Method of Moments Estimation

Published online by Cambridge University Press:  08 February 2013

Anthony W. Lynch and
Jessica A. Wachter
Anthony W. Lynch
Affiliation:
alynch@stern.nyu.edu, Stern School of Business, New York University, 44 W 4th St, New York, NY 10012;
Jessica A. Wachter
Affiliation:
jwachter@wharton.upenn.edu, Wharton School, University of Pennsylvania, 3620 Locust Walk, Philadelphia, PA 19104.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

This paper describes estimation methods, based on the generalized method of moments (GMM), applicable in settings where time series have different starting or ending dates. We introduce two estimators that are more efficient asymptotically than standard GMM. We apply these to estimating predictive regressions in international data and show that the use of the full sample affects inference for assets with data available over the full period as well as for assets with data available for a subset of the period. Monte Carlo experiments demonstrate that reductions hold for small-sample standard errors as well as asymptotic ones.

Information

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 48 , Issue 1 , February 2013, pp. 277 - 307
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2013 

References

Ahn, S. C., and Schmidt, P. “A Separability Result for GMM Estimation with Applications to GLS Prediction and Conditional Moment Tests.” Econometric Reviews, 14 (1995), 19–34.Google Scholar
Ait-Sahalia, Y.; Mykland, P. A.; and Zhang, L. “How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise.” Review of Financial Studies, 18 (2005), 351–416.CrossRefGoogle Scholar
Amemiya, T. Advanced Econometrics. Cambridge, MA: Harvard University Press (1985).Google Scholar
Anderson, T. W. ‘‘Maximum Likelihood Estimates for a Multivariate Normal Distribution When Some Observations Are Missing.” Journal of the American Statistical Association, 52 (1957), 200–203.CrossRefGoogle Scholar
Andrews, D. W. K., and Fair, R. C. “Inference in Nonlinear Econometric Models with Structural Change.” Review of Economic Studies, 55 (1988), 615–640.CrossRefGoogle Scholar
Andrews, D. W. K., and Ploberger, W. “Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative.” Econometrica, 62 (1994), 1383–1414.CrossRefGoogle Scholar
Bandi, F. M., and Russell, J. R. “Separating Microstructure Noise from Volatility.” Journal of Financial Economics, 79 (2006), 655–692.CrossRefGoogle Scholar
Brandt, M. W. “Estimating Portfolio and Consumption Choice: A Conditional Euler Equations Approach.” Journal of Finance, 54 (1999), 1609–1645.CrossRefGoogle Scholar
Campbell, J. Y., and Shiller, R. J. “Stock Prices, Earnings, and Expected Dividends.” Journal of Finance, 43 (1988), 661–676.CrossRefGoogle Scholar
Campbell, J. Y., and Thompson, S. B. “Predicting Excess Stock Returns Out of Sample: Can Anything Beat the Historical Average?” Review of Financial Studies, 21 (2008), 1509–1531.CrossRefGoogle Scholar
Cavanagh, C. L.; Elliott, G.; and Stock, J. H. “Inference in Models with Nearly Integrated Regressors.” Econometric Theory, 11 (1995), 1131–1147.CrossRefGoogle Scholar
Cochrane, J. H. Asset Pricing. Princeton, NJ: Princeton University Press (2001).Google Scholar
Conniffe, D. “Estimating Regression Equations with Common Explanatory Variables but Unequal Numbers of Observations.” Journal of Econometrics, 27 (1985), 179–196.CrossRefGoogle Scholar
Duffie, D., and Singleton, K. J. “Simulated Moments Estimation of Markov Models of Asset Prices.” Econometrica, 61 (1993), 929–952.CrossRefGoogle Scholar
Fama, E. F., and French, K. R. “Business Conditions and Expected Returns on Stocks and Bonds.” Journal of Financial Economics, 25 (1989), 23–49.CrossRefGoogle Scholar
Ghysels, E.; Guay, A.; and Hall, A. “Predictive Tests for Structural Change with Unknown Breakpoint.” Journal of Econometrics, 82 (1997), 209–233.CrossRefGoogle Scholar
Ghysels, E., and Hall, A. “A Test for Structural Stability of Euler Conditions Parameters Estimated via the Generalized Method of Moments Estimator.” International Economic Review, 31 (1990), 335–364.CrossRefGoogle Scholar
Ghysels, E.; Santa-Clara, P.; and Valkanov, R. “There Is a Risk-Return Trade-Off After All.” Journal of Financial Economics, 76 (2005), 509–548.CrossRefGoogle Scholar
Goetzmann, W. N., and Jorion, P. “Re-Emerging Markets.” Journal of Financial and Quantitative Analysis (1999), 1–32.CrossRefGoogle Scholar
Goldberger, A. S. Econometric Theory. New York, NY: John Wiley and Sons (1964).Google Scholar
Green, W. H. Econometric Analysis. Upper Saddle River, NJ: Prentice-Hall, Inc. (1997).Google Scholar
Hansen, L. P. “Large Sample Properties of Generalized Method of Moments Estimators.” Econometrica, 50 (1982), 1029–1054.CrossRefGoogle Scholar
Hansen, L. P., and Singleton, K. “Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models.” Econometrica, 50 (1982), 1269–1286.CrossRefGoogle Scholar
Harvey, A.; Koopman, S. J.; and Penzer, J. “Messy Time Series: A Unified Approach.” In Advances in Econometrics, Vol. 13. Greenwich, CT: JAI Press Inc. (1998), 103–143.Google Scholar
Harvey, C. “Time-Varying Conditional Covariances in Tests of Asset Pricing Models.” Journal of Financial Economics, 24 (1989), 289–317.CrossRefGoogle Scholar
Little, R. J. A., and Rubin, D. B.Statistical Analysis with Missing Data, 2nd ed. Hoboken, NJ: John Wiley & Sons (2002).CrossRefGoogle Scholar
Lynch, A. W., and Wachter, J. A. “Using Samples of Unequal Length in Generalized Method of Moments Estimation.” New York University Working Paper FIN-05-021 (2004).Google Scholar
MacKinlay, A. C., and Richardson, M. P. “Using Generalized Method of Moments to Test Mean-Variance Efficiency.” Journal of Finance, 46 (1991), 511–527.Google Scholar
Nelson, C. R., and Kim, M. J. “Predictable Stock Returns: The Role of Small Sample Bias.” Journal of Finance, 48 (1993), 641–661.CrossRefGoogle Scholar
Pastor, L., and Stambaugh, R. F. “Investing in Equity Mutual Funds.” Journal of Financial Economics, 63 (2002a), 351–380.CrossRefGoogle Scholar
Pastor, L., and Stambaugh, R. F. “Mutual Fund Performance and Seemingly Unrelated Assets.” Journal of Financial Economics, 63 (2002b), 315–349.CrossRefGoogle Scholar
Patton, A. J. “Estimation of Multivariate Models for Time Series of Possibly Different Lengths.” Journal of Applied Econometrics, 21 (2006), 147–173.CrossRefGoogle Scholar
Phillips, P. C. “Time Series Regressions with a Unit Root.” Econometrica, 55 (1987), 277–301.CrossRefGoogle Scholar
Robins, J. M., and Rotnitsky, A. “Semiparametric Efficiency in Multivariate Regression Models with Missing Data.” Journal of the American Statistical Association, 90 (1995), 122–129.CrossRefGoogle Scholar
Schmidt, P. “Estimation of Seemingly Unrelated Regressions with Unequal Numbers of Observations.” Journal of Econometrics, 5 (1977), 365–377.CrossRefGoogle Scholar
Shiller, R. J. Market Volatility. Cambridge, MA: MIT Press (1989).Google Scholar
Singleton, K.Empirical Dynamic Asset Pricing: Model Specification and Econometric Assessment. Princeton, NJ: Princeton University Press (2006).CrossRefGoogle Scholar
Sowell, F. “Optimal Tests for Parameter Instability in the Generalized Method of Moments Framework.” Econometrica, 64 (1996), 1085–1107.CrossRefGoogle Scholar
Stambaugh, R. F. “Analyzing Investments Whose Histories Differ in Length.” Journal of Financial Economics, 45 (1997), 285–331.CrossRefGoogle Scholar
Stambaugh, R. F. “Predictive Regressions.” Journal of Financial Economics, 54 (1999), 375–421.CrossRefGoogle Scholar
Stock, J. H. “Unit Roots, Structural Breaks and Trends.” In Handbook of Econometrics, Vol. IV, Engle, R. and McFadden, D. L., eds. Amsterdam, The Netherlands: North-Holland (1994), 2740–2841.Google Scholar
Storesletten, K.; Telmer, C. I.; and Yaron, A. “Cyclical Dynamics in Idiosyncratic Labor Market Risk.” Journal of Political Economy, 112 (2004), 695–717.CrossRefGoogle Scholar
Swamy, P. A. V. B., and Mehta, J. S. “On Bayesian Estimation of Seemingly Unrelated Regressions When Some Observations Are Missing.” Journal of Econometrics, 3 (1975), 157–169.CrossRefGoogle Scholar
White, H. “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity.” Econometrica, 24 (1980), 817–838.CrossRefGoogle Scholar
White, H. Asymptotic Theory for Econometricians. San Diego, CA: Academic Press, Inc. (1994).Google Scholar
White, H., and Domowitz, I. “Nonlinear Regression with Dependent Observations.” Econometrica, 52 (1984), 143–162.CrossRefGoogle Scholar
Zhou, G. “Asset-Pricing Tests under Alternative Distributions.” Journal of Finance, 48 (1993), 1927–1942.Google Scholar
Zhou, G. “Analytical GMM Tests: Asset Pricing with Time-Varying Risk Premiums.” Review of Financial Studies, 7 (1994), 687–709.CrossRefGoogle Scholar