Structural breaks in the mean of dividend-price ratios: Implications of learning on stock return predictability
Introduction
Attempts at predicting stock returns or equity premium have a long tradition in finance. The literature generally reports that, although stock returns are predictable in-sample, evidence of out-of-sample predictability appears to be much weaker.
Lettau and Van Nieuwerburgh (2008) argue that these seemingly incompatible results can be reconciled if the assumption for a fixed steady-state mean of the economy is relaxed.3Focusing on the dividend-price ratio as a predictor for stock returns, they first document that the mean of the dividend-price ratio is not time-invariant. They then show that the in-sample forecasting relationship of mean-adjusted dividend-price ratios and future returns is statistically significant and stable over time. They note, however, that poor out-of-sample predictability is inevitable and results from the uncertainty associated with the magnitudes and, to a lesser degree, the timing of the breaks.
In their procedure for out-of-sample predictions, they assume that economic agents do not know either the dates of the structural breaks or the magnitudes of shifts. Meanwhile, they assume economic agents’ perception of the regime-specific mean for the dividend-price ratio to be time-invariant within a regime. However, as Evans and Honkapohja (2001) and Sargent (2002) suggest, in the presence of occasional structural breaks in the economy, economic agents will have to continuously relearn the new economy. Under this situation, they propose adopting constant-gain learning, in order to appropriately estimate economic agents’ perception of the changing economy.
Several empirical works on macroeconomics and international finance have used constant-gain learning. For example, Orphanides and Williams (2005) show that the stagflation of the 1970s can be better explained by constant-gain learning than by rational expectations. Mark (2009) employs learning in the exchange market, and shows that learning algorithms fit the data better than the rational expectations assumption. Branch and Evans (2006) demonstrate that the constant-gain learning algorithm serves as a plausible model of economic agents’ adaptive learning when forecasting inflation and GDP growth.
In this paper, we employ the constant-gain learning procedure in order to estimate economic agents’ perception of the mean of the dividend-price ratios that changes over time with structural breaks. We then use the dividend-price ratio adjusted for these estimates to obtain out-of-sample forecasts of stock returns. The empirical results show that our model obtains better out-of-sample predictions than that of Lettau and Van Nieuwerburgh (2008).
The rest of the paper is organized as follows. In Section 2, we provide a brief review of Lettau and Van Nieuwerburgh (2008) and constant-gain learning. In Section 3, we report our empirical results. Section 4 concludes the paper.
Section snippets
Brief review of Lettau and Van Nieuwerburgh (2008) and discussion
Lettau and Van Nieuwerburgh (2008), hereafter LVN, show that, in the presence of structural breaks in the steady state of the economy, the present value model of Campbell and Shiller (1988) can be given bywhere is the dividend-price ratio; is the stock return; is the dividend growth rate; and , , and represent time-varying means for the dividend-price ratio, stock return, and dividend growth rate, respectively. Eq. (1) suggests that
Data description
In this section, we use the U.S. and Japanese data to compare the out-of-sample predictive performance of our learning model to that of the LVN model. For the U.S. data, we use the monthly return and the dividend-price ratio data, which are constructed from the VWRETD and VWRETX series – the monthly returns with and without dividend on the value-weighted portfolio of all NYSE, Amex, and Nasdaq stocks – in the CRSP files from January 1926 to December 2013. Dividends are computed as the
Summary and conclusion
The purpose of this paper is not to show that our learning model outperforms the random walk model in terms of out-of-sample forecasting. In fact, even though our learning model results in better out-of-sample forecasts than the random walk model, the difference in the forecasting performance was not statistically significant. We agree with Lettau and Van Nieuwerburgh (2008) in that the uncertainty of estimating the size of steady-state shifts is responsible for the difficulty of forecasting
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Cited by (0)
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1.Chang-Jin Kim acknowledges financial support from the Bryan C. Cressey Professorship at the University of Washington.
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2.This work was supported by the National Natural Science Foundation of China (No.71873056) and Research Foundation of Jilin University (451200330029).