Interpolating exogenous variables in continuous time dynamic models

The need to interpolate exogenous variables when estimating the parameters of open continuous time models involves a potential to undermine a careful specification based on economic theory. Finding standard forms of interpolation have deficiencies that affect estimation and inference, we outline a method to select an optimal interpolant on the basis of the data, The method involves extending the interpolating polynomial proposed by Bergstrom (Econometric Theory, 1986) using a transformation that facilitates applying order selection criteria to the exact discrete analogue of the continuous time model, Monte Carlo evidence suggests an inappropriate interpolant can bias the estimates of the endogenous variable parameters. (C) 2001 Elsevier Science B,V, All rights reserved.