The Estimation of Distributed Lags in Short Panels

In this paper, we investigate the problem of estimating distributed lags in short panels. Estimates of the parameter of distributed lag relationships based on single time-series of observations have been usually rather imprecise. The promise of panel data in this context is in the N repetitions of the time that it contains which should allow one to estimate the identified lag parameters with greater precision. On the other hand, panels tend to track their observations only over a relatively short time interval. Thus, some assumptions will have to be made on the contributions of the unobserved presample x?s to the current values of y before any lag parameters can be identified from such data. In this paper we suggest two such assumptions; both of which are, at least in part, testable, and outline appropriate estimation techniques. The first places reasonable restrictions on the relationship between the presample and insample x?s, while the second imposes conventional functional form constraints on the lag coefficients associated with the presample x?s.