Exact Nonparametric Orthogonality and Random Walk Tests

The hypothesis that a variable is independent of past information, such as its own past and past realizations of other observable variables, is a frequent implication of economic theory. Yet standard regression-based tests of orthogonality may not have the correct level if there is feedback from innovations to future values of the regressors. In this paper we develop nonparametric tests of orthogonality based on signs and signed ranks which are proved to reject at their nominal levels over a wide class of models admitting feedback. The tests are robust to problems of non-normality and heteroskedasticity. Further, in simulation studies of two specifications of feedback-a rational expectations model considered by Mankiw and Shapiro, and the random walk model-we find that the nonparametric tests display remarkable power. The paper concludes with an application which assesses the efficiency of survey data on interest rate expectations previously studied by Friedman. Copyright 1995 by MIT Press.