Estimating Distributed Lags in Short Panels with an Application to the Specification of Depreciation Patterns and Capital Stock Constructs

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 is in the N repetitions of the time-series 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 contribution 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 in sample x's while the second imposes conventional functional form constraints on the lag coefficients. The paper concludes with an example which investigates empirically how to construct a "capital stock" for profit or rate of return regressions.