From the help desk: Polynomial distributed lag models

Polynomial distributed lag models (PDLs) are finite-order distributed lag models with the impulse-response function constrained to lie on a polynomial of known degree. You can estimate the parameters of a PDL directly via constrained ordinary least squares, or you can derive a reduced form of the model via a linear transformation of the structural model, estimate the reduced-form parameters, and recover estimates of the structural parameters via an inverse linear transformation of the reduced-form parameter estimates. This article demonstrates both methods using Stata. Copyright 2004 by StataCorp LP.