Abstract The influence of certain specification errors on estimates of parameters in economic models is examined using Monte Carlo techniques. Autonomous growth is a secular change in the endogenous variables not explained by the exogenous variables and parameters of the structural equations. Autonomous growth will therefore appear in the shocks, and this usually causes them to become correlated with the exogenous variables in economic models—a specification error. The influence of linear autonomous growth on least squares (LS) and limited information single equation (LISE) estimates is examined using simulated economic data. Estimates by both methods are badly biased when autonomous growth is present but ignored, and the use of probability theory tends to give very bad decisions. A simple change in the model removes the difficulty for the LISE estimates. Some procedures to improve estimates are suggested when linear autonomous growth is thought to be present. * The research reported here was made possibl...