Alternative Non-nested Specification Tests of Time Series Investment Models

This paper develops and compares nonnested hypothesis tests for linear regression models with first-order serially correlated errors. It extends the nonnested testing procedures of Pesaran, Fisher and MacAleer, and Davidson and MacKinnon, and compares their performance on four conventional models of aggregate investment demand using quarterly United States investment data from 1951:I to 1983:IV. The data and the nonnested hypothesis tests initially indicate that no model is correctly specified. The tests are also intransitive in their assessments. Before rejecting these conventional models of investment demand, we investigate the small sample properties of these different nonnested test procedures through a series of Monte Carlo studies. We find that nonnested tests for models without serially correlated residuals have significant finite sample size and power biases. These biases persist, but are somewhat diminished, for nonnested tests that recognize serial correlation in the disturbances. The direction of the bias in the size is toward rejection of the null model, although it varies considerably by the type of test and estimation technique. After revising our critical levels for this finite sample bias, we conclude that the accelerator model of equipment investment cannot be rejected by any of the other alternatives.