Data Revisions and Out-of-Sample Stock Return Predictability

I. INTRODUCTION Lettau and Ludvigson (2001;LL, thereafter) show that the consumption-wealth ratio (cay)--the error term from the cointegration relation among consumption, net worth, and labor income--is a strong predictor of stock market returns. Their findings are important because the forecasting power of cay is consistent with rational pricing theories, for example, Campbell and Cochrane (1999), and helps explain many puzzling phenomena in the equity market; see, for example, Lettau and Ludvigson (2003), for an overview. Moreover, by contrast with Bossaerts and Hillion (1999), Ang and Bekaert (2007), Goyal and Welch (2003), and others, cay also forecasts stock market returns out of sample. (1) This paper investigates the out-of-sample predictive power of cay using real-time data instead of using revised data (as in LL). The information content of the two data sets could be quite different because of periodic revisions in consumption and labor income data provided by the Bureau of Economic Analysis (BEA) and in net worth data provided by the Federal Reserve Board. Therefore, the analysis has important implications for practitioners, for example, mutual funds managers and monetary policy makers, who might want to use cay to improve their forecasts with real-time information. (2) Consistent with early studies, for example, Croushore and Stark (1999), I document substantial revisions to consumption and labor income data; consequently, cay varies considerably across vintages. For example, during the period 1996-97, cay is substantially below its sample average in real-time data, although it is above or around the sample average in the 2002:Q3 vintage, the latest release when this paper was written. That is, in hindsight, there was no irrational exuberance in stock markets until 1998, which is over 1 yr after the remarks by Fed Chairman Alan Greenspan. If investors had switched from stocks to bonds, as signaled by the low level of real-time cay, they would have missed the stock market run-ups over this period. The example illustrates the main finding of this paper that cay has negligible out-of-sample predictive power for stock market returns in real time. Similarly, given that stock prices continued to rise despite the irrational exuberance speech, Alan Greenspan adopted the new economy explanation in 1998 and stock prices rose further until the crash in 2000. This episode highlights the theoretical results in Bernanke and Gertler (1999, 2001): Although policy makers cannot ignore the dramatic movements in the equity market, it is tricky in practice for central banks to predict stock prices at the business-cycle frequency. It is tempting to attribute the poor performance of real-time cay to the look-ahead bias suggested by Brennan and Xia (2005) and Avramov (2002). However, Guo (2006) argues that their results actually reflect an omitted variable problem: Recursively estimated cay regains the out-of-sample forecasting power when combined with a measure of realized stock market variance. His results are also consistent with an equilibrium model by Guo (2004), who argues that, in addition to a risk premium in the Capital Asset Pricing Model, investors also require a liquidity premium because of limited stock market participation. That is, realized market variance and ca), forecast stock returns because they are proxies for the risk and liquidity premiums, respectively. To disentangle the effect of the look-ahead bias and data revisions, I make forecasts with recursively estimated cay obtained from (1) the current vintage data and (2) real-time data. The two approaches are identical if there were no data revisions. I confirm the early results that current vintage cay outperforms a benchmark model of constant stock returns when combined with realized market variance, although it does not do so by itself. However, cay has negligible out-of-sample forecasting power in real-time data even after adding realized market variance to the forecasting equation. …