A VARMA Analysis of the Causal Relations among Stock Returns, Real Output, and Nominal Interest Rates

Previous research has documented a negative relation between common stock returns and inflation. Recently, Fama [3] and Geske and Roll [6] have argued that this relation results from a more fundamental one between real activity and expected inflation. Stock returns, they argue, signal changes in real activity, which in turn affect expected inflation. However, unlike Fama, Geske and Roll argue that changes in real activity result in changes in money supply growth, which in turn affect expected inflation. Empirical tests have analyzed separately each link in the proposed causal chain. In this article, we investigate simultaneously the relations among stock returns, real activity, inflation, and money supply changes using a vector autoregressive moving average (VARMA) model. Our empirical results strongly support Geske and Roll's reversed causality model. THERE HAVE BEEN MANY attempts to explain the negative relations observed between stock returns and expected inflation, changes in expected inflation, and unexpected inflation.1 These phenomena, documented by Fama and Schwert [5], are troublesome because they appear contrary both to Fisher's theory that nominal asset returns are positively--related to expected inflation, and to received wisdom that common stocks are hedges against expected as well as unexpected inflation. Fama [3] suggests an explanation for the observed negative relation between stock returns and inflation based on money demand theory. An increase in anticipated real activity leads, he argues, to an increase in the demand for real money balances. Given the level of nominal money, the increased demand for real money balances must be accommodated by a fall in the price level. Because stock returns are assumed to be positively related to expected future real activity, a negative relation between inflation and stock returns is induced. However, this negative relation is merely a proxy for the more fundamental relation between anticipated real activity and stock returns. Therefore, Fama argues that the observed relation between stock returns and inflation is spurious. As noted by Fama and others, this line of reasoning cannot explain completely the negative relation between stock returns and inflation. Fama finds that measures of unexpected inflation are significant determinants of monthly stock returns in regressions where anticipated real activity is included as an explanatory variable. In addition, the explanatory power of expected inflation is eliminated