"Estimation of Distributed Lags and Leads with End Point Constraints," (with D. K. Andrews), Journal of Econometrics, 1992.Paper: pdf file
This paper considers the use of the polynomial distributed lag (PDL) technique when the lag length is estimated rather than fixed. We focus on the case where the degree of the polynomial is fixed, the polynomial is constrained to be zero at a certain lag length q, and q is estimated along with the other parameters. We extend the traditional PDL setup by allowing q to be real-valued rather than integer-valued, and we derive the asymptotic covariance matrix of all the parameter estimates, including the estimate of q. The paper also considers the estimation of distributed leads rather than lags, a case that can arise if expectations are assumed to be rational.
This paper makes two contributions to the PDL literature. The first is to allow the lag length to be estimated (along with the standard error of the estimate), and the second is to consider the case of polynomial distributed leads. An extensive set of results using the method is in 1993#1.