Gmm Estimation Of Dynamic Panel Data Models

Panel data are well suited for examining dynamic effects, as in the first-order model, yit = xitP + y yi,t-1 + a + eu = WitS + ai + Bit, where the set of right hand side variables, wit now includes the lagged dependent variable, yit-1. Adding dynamics to a model in this fashion is a major change in the interpretation of the equation. Without the lagged variable, the "independent variables" represent the full set of information that produce observed outcome yit. With the lagged variable, we now have in the equation, the entire history of the right hand side variables, so that any measured influence is conditioned on this history; in this case, any impact of xit represents the effect of new information. Substantial complications arise in estimation of such a model. In both the fixed and random effects settings, the difficulty is that the lagged dependent variable is correlated with the disturbance, even if it is assumed that eit is not itself autocorrelated. For the moment, consider the fixed effects model as an ordinary regression with a lagged dependent variable. We considered this case in Section 5.3.2 as a regression with a stochastic regressor that is dependent across observations. In that dynamic regression model, the estimator based on T observations is biased in finite samples, but it is consistent in T. That conclusion was the main result of Section 5.3.2. The finite sample bias is of order 1/ T. The same result applies here, but the difference is that whereas before we obtained our large sample results by allowing T to grow large, in this setting, T is assumed to be small and fixed, and large-sample results are obtained with respect to n growing large, not T. The fixed effects estimator of S = [p, y] can be viewed as an average of n such estimators. Assume for now that T > K + 1 where K is the number of variables in xit. Then, from (13-4),

Was this article helpful?

0 0

Post a comment