Small Sample Properties of Three Tests for Granger-Causal Ordering in a Bivariate Stochastic System

T HE purpose of this paper is to study the small sample performance of tests for causal ordering of time series in the sense of Granger (1969). Versions of three tests are studied: that based directly on Granger's definition of causality and suggested by Sargent (1976); that suggested by Sims (1972); and the modification of Sims suggested by Geweke, Meese, and Dent (1982). Tests for causal orderings of time series have been applied often in recent econometric work. Sims (1972) introduced his version of a causal ordering test to inquire whether money was exogenous (as monetarists might suggest) in the money income relationship. Sargent (1976) used Granger and Sims procedures to test the validity of the natural-rate hypothesis inherent in his model. Salemi (1980) employed the Granger test as a test of specification of a money demand equation in hyperinflation. A goal of our research is to conduct our study with data that closely resemble the types of quarterly time series that arise in applied research. The cost of this approach is a research design for which finitely parameterized versions of the tests are never exactly correct. It is our view that users of these tests are likely to encounter this potential source of bias. Indeed, the problem of truncation (of leading and lagging coefficients in the causality test regressions) arises whenever the vector ARMA representation of the time series studied has, in reality, a nontrivial moving average component. To our knowledge, this feature of our research design has not been used before, and is a major difference between our work and the work of Geweke et al. and Nelson and Schwert (1980). Answers to the following research questions interest us. First, how likely is a user of each version of the test to reach a correct decision regarding the causal ordering of the time series? Second, how accurately does each test procedure recover population values of the test regression coefficients? Third, how sensitive are answers to the first and second questions to sample size, contemporaneous correlation of the exogenous errors, and the strength of the causal interrelationship? Fourth, how important a source of bias is the finite parameterization of the test regressions that is required in small samples? Section II of the paper describes the versions of the tests studied. Section III describes the experimental design. The results of the experiments are in section IV, and conclusions are presented in section V.