Lettau-Ludvigson vs. a Time Trend

Martin Lettau and Sydney Ludvigson’s “Consumption, Aggregate Wealth and Expected Stock Returns” finds that the ratio of consumption to wealth forecasts stock returns. In essence, consumption along with labor income form a more useful “trend” than the level of dividends or earnings. They find this factor can explain the 25 Fama-French portfolios, that is, the spread we observe when stocks are sorted by size and book/market value. Cochrane calls this a 'stunning result' in his new text on Asset Pricing.

But the Fama-French result was conspicuously absent in their ultimate Journal of Finance paper. And Brennan and Xia produced this devastating critique:

The empirical evidence that the consumption–wealth ratio, cay, has strong in-sample predictive power for future stock returns has been interpreted as evidence that consumers take account of future investment opportunities in planning their consumption expenditures. In this paper we show that the predictive power of cay arises mainly from a “look-ahead bias” introduced by estimating the parameters of the cointegrating regression between consumption, assets, and labor income in-sample. hen a similar regression is run, replacing the log of consumption with an inanimate variable, calendar time, the resulting residual, which we label tay, is shown to be able to forecast stock returns as well as, or better than, cay. In addition, both cay and tay lose their out-of-sample forecasting power when they are re-estimated every period with only available data.

Lettau and Ludvigson reply is threefold. First, they say that that the forecasting power of cay for future returns cannot be spurious merely because the full sample has been used to estimate the cointegrating coefficients. Second, tay likely contains more economic content that the authors realize. Lastly, they assert that that in-sample tests are more credible than out-of-sample tests for assessing forecasting power.

I think the bottom line is that when a time-trend does better than your economic variable as an explanation of the data, you're doing it wrong.