Nonlinear Models with Lagged Dependent Variables

Abstract

Dealing with models containing lagged dependent variables, econometricians are faced with the problem that in general the observations are dependently distributed. Consequently standard laws of large numbers and central limit theorems can no longer be used for deriving the asymptotic properties of the estimators involved. It is well known that for linear regression models this difficulty can be overcome by imposing some stability conditions on the model [see for example Malinvaud (1970, Ch. 14)]. In the nonlinear case, Sims (1976) has proved the strong consistency and asymptotic normality of a class of nonlinear robust M-estimators, including nonlinear least squares estimators, under the condition that the errors and the regressors are stationary and ergodic. However in our opinion the stationarity assumption is too restrictive.