GMM Estimation with Noncausal Instruments

Lanne, Markku and Saikkonen, Pentti (2009): GMM Estimation with Noncausal Instruments.

Abstract

Lagged variables are often used as instruments when the generalized method of moments (GMM) is applied to time series data. We show that if these variables follow noncausal autoregressive processes, their lags are not valid instruments and the GMM estimator is inconsistent. Moreover, in this case, endogeneity of the instruments may not be revealed by the J-test of overidentifying restrictions that may be inconsistent and, as shown by simulations, its finite-sample power is, in general, low. Although our explicit results pertain to a simple linear regression, they can be easily generalized. Our empirical results indicate that noncausality is quite common among economic variables, making these problems highly relevant.

• Item Type: MPRA Paper
• Language: English
• Keywords: Noncausal autoregression; instrumental variables; test of overidentifying restrictions
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Breidt, J., R.A. Davis, K.S. Lii, and M. Rosenblatt (1991). Maximum likelihood estimation for noncausal autoregressive processes. Journal of Multivariate Analysis 36, 175-�198.

Brockwell, P.J., and R.A. Davis (1987). Time Series: Theory and Methods. Springer-Verlag. New York.

Campbell, J.Y., A.W. Lo, and A.C. MacKinlay (1997). The Econometrics of Financial Markets. Princeton University Press. Princeton, New Jersey.

Campbell, J.Y., and N.G. Mankiw (1990). Permanent income, current income, and consumption. Journal of Business and Economic Statistics 8, 265�-279.

Hansen, B.E., and K.D. West (2002). Generalized method of moments and macroeconomics. Journal of Business and Economic Statistics 20, 460�-469.

Hansen, L.P. (1982). Large sample properties of generalized method of moments estimators, Econometrica 50, 1029�-1054.

Lanne, M., and P. Saikkonen (2008). Modeling expectations with noncausal autoregressions. HECER Discussion Paper No. 212.

Newey, W. (1985). Generalized method of moments speci�cation testing. Journal of Econometrics 29, 229�-256.

Stock, J.H., and M.W. Watson (2004). Combination forecasts of output growth in a seven-country data set. Journal of Forecasting 23, 405�-430.

Stock, J.H., J.H. Wright, and M. Yogo (2002). A survey of weak instruments and weak identi�cation in generalized method of moments. Journal of Business and Economic Statistics 20, 518�-529.