The estimation of systems of joint differential-difference equations

This paper considers estimation of the parameters of systems of joint differential-difference equations. The existence and uniqueness of the solution to the model are demonstrated, and the properties of the continuous time and discretely sampled processes are derived. The focus is on frequency domain methods throughout, one of the main technical achievements being the derivation of a computable expression for the spectral density function of the discretely observed data, which are allowed to be mixtures of stock and flow variables. A frequency domain Gaussian estimator is proposed, and its consistency and asymptotic normality are established without requiring the assumption that the data are Gaussian. The finite sample properties of the estimator are assessed in a small simulation exercise.