Interpreting the predictive power of the consumption–wealth ratio

Lettau and Ludvigson [Lettau, M., Ludvigson, S.C., 2001a. Consumption, aggregate wealth and expected stock returns. Journal of Finance 56, 815–849] find that the estimated consumption–wealth ratio (cay) is a strong predictor of U.S. stock returns, while Brennan and Xia [Brennan, M.J., Xia, Y., 2005. tay's as good as cay. Finance Research Letters 2, 1–14] argue that the predictive power of cay arises from a look-ahead bias. In a unified framework, we examine how the presence of deterministic time trends affects the estimation and forecasting power of cay. We show that ignoring the presence of a deterministic time trend in estimating the cointegrating relationship among consumption, asset wealth, and labor income leads to a biased estimate of the consumption–wealth ratio. In the presence of a deterministic time trend, cay is a combination of the highly persistent bias component and the unbiased cointegrating residual, and most of the predictive power of cay is attributable to the bias component, casting doubt on the robustness of the forecasting power of cay.