Speed of adjustment and estimation of the partial adjustment model

The effect which the speed of adjustment parameter has on the statistical properties of the partial adjustment model, and estimates of its parameters, is investigated. It is shown that in the case of very rapid adjustment, the model approaches a classical (static) regression model, but in the case of very slow adjustment, the dependent (or state) variable displays near random walk behaviour. The finite sample performance of the nonlinear least squares estimator is investigated in a simulation study, and it is found that substantial bias and mean squared error can be a feature of the estimates in the model with very slow adjustment. This suggests that extreme caution should be exercised in situations where the estimated speed of adjustment parameter is found to be small.