Measures of Deterministic Prediction Bias in Nonlinear Models - Mariano, Roberto S. (Institutional Knowledge at Singapore Management University, 1989)
In this paper, techniques are developed for assessing the magnitude and importance of the prediction bias in deterministic predictions from an estimated nonlinear model. Since this bias results from the nonlinearity of the system, indirect measures are proposed which indicate the extent of nonlinearity with respect to the disturbances in the system. These measures are based on the proportion of the generalized variance of the endogenous variables explained by a linear relationship with the disturbances. Direct estimates of the deterministic prediction bias are obtained as the difference between the deterministic and the stochastic predictors. As a measure of the practical importance of the deterministic prediction bias, the estimates of the bias are compared with the variance of the endogenous variables in a quadratic form. Formal tests of the statistical significance of the estimated deterministic prediction bias are developed for specific and general values of the exogenous variables. The test statistics utilized here differ from the direct measures in that the quadratic forms are now based on the covariance matrix of the estimated biases rather than the covariance matrix of the endogenous variables. A particular specialization of these tests leads to correction of the common practice of regressing sample period forecast errors on observable variables for model diagnostics. Finally, the procedures developed are illustrated through application to a log-linear regression model.