GMM Estimation with Non-causal Instruments*
研究了当滞后变量遵循非因果自回归过程时，它们作为工具变量会导致GMM估计不一致，且过度识别检验可能失效，模拟显示有限样本检验力低。
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.