Linear asset-pricing relations, with raacroeconomic factors as state variables, have found wide use in empirical finance. Applications of such relations range from academic studies of market efficiency and market anomalies to practical uses such as risk management and estimation of the cost of capital. These applications make two key assumptions: that the relationship is exclusively linear and that the macroeconomic factors are exogenous to returns. For the set of macro factors commonly used in these applications, both assumptions run counter to economic intuition.
This paper demonstrates that the assumptions are also counter to empirical evidence by testing for linear and nonlinear Granger causality. The tests work as follows. Given two forecasts of a time series--a forecast from its own lags and a forecast from its own lags and the lags of a second series--if the second is more accurate than the first (if the improvement is statistically significant), the second time series is said to Granger cause the first. When two time series Granger cause one another, feedback is said to exist between them.
Linear and nonlinear feedback are found between stock returns and commonly used macroeconomic pricing factors as well as between residuals from linear pricing relations and returns. In addition, there is little evidence to suggest that neglected autoregressive or autoregressive conditionally heteroscedastic dynamics are responsible for these findings, implying that the underlying dynamics are complicated.
The evidence strongly suggests that macroeconomic factors are neither exogenous nor related to stock returns in a solely linear way. Thus, linear asset pricing relations omit interesting and potentially useful aspects of the relationship between stock returns and the macroeconomy, The evidence also sheds light on the literature on univariate nonlinear dynamics in stock returns. It suggests that such dynamics result from a complicated interrelationship between the stock market and the macroeconomy.