The Casual Causal Relationship between Money and Income: Some Caveats for Time Series Analysis

T HE investigation of causal relationships between economic variables is the bread and butter of econometric analysis. It is therefore not surprising that Granger's (1969) contribution of an operational definition of "causality" in a time series context has stimulated great interest among econometric theorists and applied practitioners. The nexus between Granger's definition of causality based on a criterion of incremental forecasting value and the philosophers of science notion of causality has yet to be clearly established.1 Nevertheless, the Granger definition is now widely used and has been shown to have some very appealing properties. Heuristically, Granger's notion of causality states that X "causes" Y if the past history of X can be used to predict Y more accurately than simply using the past history of Y. While this definition differs from traditional conceptions, it has several attractive applications. First, as shown by Sims (1972), Granger-type causality is equivalent to econometric exogeneity so that unidirectional causality from the independent to the dependent variable is a necessary condition for the consistent estimation of distributed lag models involving variables other than lagged dependent variables. Hence testing for the direction of causality may allow the researcher to avoid the problems discussed by Goldfeld and Blinder (1972) which result from incorrectly assuming that a policy variable is exogenously determined. Reduced form distributed lag models such as the St. Louis model of Anderson and Jordan (1968) must first pass the causality test in order for the estimation and interpretation of these models to be meaningful.2 A second implication of Granger's causality notion is concerned with leading indicators and rational expectations. Pierce (1975) has suggested characterizing a variable as a leading indicator of another variable if the first causes the second, in the sense defined above. Similarly, Feige and Pearce (1976) have argued that, under certain assumptions about the relative costs of information, testing for Granger-type causality is a useful way to evaluate what information can be usefully employed in forming "economically" rational expectations.3 Moreover, Caves and Feige (1977) have demonstrated the equivalence between the Granger definition of causality and the concept of "incremental efficiency" which has direct applications for testing the efficient market hypothesis. Perhaps most importantly, the Granger definition has given rise to a set of procedures for testing the direction of causality between economic variables that avoids the problem of "spurious regression" described by Granger and Newbold (1974). The purpose of this paper is to examine the alternative procedures that have been proposed as practical tests for the presence and direction of causality and to investigate the robustness of substantive economic results when alternative test procedures are employed. We focus our attention on three test procedures now employed in the literature: a crosscorrelation technique suggested by Haugh (1972, 1976) and Pierce (1977), which is essentially a Received for publication May 6, 1974. Revision accepted for publication September 25, 1978. * University of Wisconsin and University of MissouriColumbia, respectively. This is a much revised version of an earlier paper given at the meetings of the Mid-West Economic Association, April 1974. We wish to thank John Geweke, David Pierce, and Christopher Sims for many helpful comments, Douglas Caves, Robert McGee and Spence Hilton for very able computation assistance. Financial support from the Graduate School of the University of Wisconsin-Madison and the National Science Foundation Grant SOC76-21439 is gratefully acknowledged. Any remaining errors in the paper are the sole responsibility of the authors. See Davidson and Weintraub (1973) and Zellner (1977). 2 Anderson and Jordan explicitly assume that their measure of fiscal policy is exogenously determined. I The basic assumption is that information on past inflation rates has the least cost.