Testing for Stochastic Non-Linearity in the Rational Expectations Permanent Income Hypothesis

The Rational Expectations Permanent Income Hypothesis implies that consumption follows a random walk. However, most empirical tests have rejected the hypothesis. Those empirical tests are based on linear models. If the data generating process is non-linear, conventional tests may not be able to pick up some of the randomness. As a result, inference based on conventional tests can be misleading. This paper tests for the presence of stochastic non-linearity in aggregate consumption of non-durable goods and services, using U.S. and Canadian data. The two major tests applied are a test devised by Brock, Dechert, and Scheinkman, and a test based on an Artificial Neural Network model. The results support (do not reject) the hypothesis that there is no non-linearity in the data. The forecast results, however, suggest that even though the linearity hypothesis is not rejected, the non-linear ANN model tends to outperform the ARIMA model over three different horizons