Structural instability and predictability

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Highlights

  • We propose a structural break predictive regression model.

  • Model accounts for predictor persistency, endogeneity, heteroscedasticity, and a structural break.

  • Monte Carlo (MC) simulations indicate that this test performs satisfactorily.

  • A structural break–based predictive regression model fits the data reasonably well.

Abstract

We propose a structural break predictive regression model that accounts for predictor persistency, endogeneity, heteroscedasticity, and a structural break. Monte Carlo (MC) simulations indicate that this test performs satisfactorily compared to competitor estimators. We employ a popular U.S. data set (the period January 1927 to December 2016) that includes stock market returns and multiple predictors. We show, consistent with the MC results, evidence of a structural break. Our analysis reveals that a structural break–based predictive regression model fits the data reasonably well in predicting stock price returns.

Introduction

Stock return predictability has become a popular research topic. Two theories motivate this subject. The efficient market hypothesis (EMH) has been at the heart of the stock return predictability literature. Given that the EMH hypothesis claims that prices reflect all available information the implication is that future prices should not be predictable. Many recent applications of stock price data though reject the EMH; see Narayan and Bannigidadmath (2015) and the references therein. That prices are predictable owes to an opposing finance theory namely those with roots in behavioral finance. That investors are able to make abnormal profits (by predicting future price changes) owes to a number of hypotheses in behavioral finance such as to a conservative approach to investing (see DeBondt and Thaler, 1985); buying and selling prematurely (see Shefrin and Stateman, 1985); heuristics biases (see Kahnman and Tversky, 1974); overconfidence (see Gervais and Odean, 2001); and underreaction and overreaction (see Barberis et al., 1998); among others.

Nevertheless, the large volume of research, while identifying several insights on predictability, has failed to provide conclusive evidence that stock returns are predictable (see, for instance, Wolf, 2000, Lanne, 2002, Goyal and Welch, 2003; and Lettau and Van Nieuwerburgh, 2008). Some authors find in-sample evidence of predictability; nonetheless, out-of-sample evidence has been elusive (see Bossaerts and Hillion, 1999). This has prompted a stream of research aimed at improving our understanding of predictability. This literature has roots in the early work of Stambaugh (1999), who proposed a bias-adjusted slope parameter, complemented by the work of Lewellen (2004). Campbell and Yogo (2006) added to this literature by proposing a new Bonferroni test to identify predictability even when the predictors are characterized by a unit root or heteroskedasticity.2 In recent attempts, Westerlund and Narayan, 2012, Westerlund and Narayan, 2015 contributed to this methodology by proposing a model that accounts for persistency, endogeneity, and heteroscedasticity. Others, such as, Henkel et al., 2011, Kim et al., 2011, Guidolin et al., 2013, and Devpura et al. (2018) show that predictability exists but in a time-varying fashion.

A related issue in testing for stock return predictability has to do with the role of structural breaks. This is motivated by empirical evidence supporting instabilities in the time-series properties of financial data, including stock prices (see, for example, Pastor and Stambaugh, 2001, Lettau and Van Nieuwerburgh, 2008, Paye and Timmermann, 2006, Rapach and Wohar, 2006, Ang and Bekaert, 2007; and Narayan and Smyth, 2007), among others.3 The main source of such instabilities is changes in monetary policy or tax policy, and large macroeconomic shocks such as oil shocks (see, for instance, Paye and Timmermann, 2006).

In this paper, we focus on the issue of structural shift or instability in data series. Structural break(s) in the slope is known to be a very important empirical feature of macroeconomic data sets (see Rapach and Wohar, 2006). We choose, as our starting point, the Westerlund and Narayan (2015) predictive regression model, because in Monte Carlo simulations, as shown by Westerlund and Narayan, 2012, Westerlund and Narayan, 2015, their test outperforms competing models. Our choice of this model is also motivated by the fact that it allows us to control for predictor persistency, endogeneity, and heteroscedasticity of the model, which are important given that financial time-series data are characterized by these three features.4 Given this background, allowing for a structural break in the Westerlund and Narayan (2015) model forms an ideal extension to examine the importance of a break in testing the null hypothesis of no predictability.

Our approach is fourfold. First, we propose a structural break model that extends the bivariate predictive regression model of Westerlund and Narayan (2015). Our contribution is that we accommodate a single break point both in the slope and trend of the model. The structural break date is identified using the Narayan and Popp (2010) endogenous structural break test.

Second, we employ historical monthly time-series data from January 1927 to December 2016 to test the performance of the structural break predictive regression model. This rich data set allows us to pursue our objective of detecting a significant structural break. Third, we use a wide range of predictors to test the predictive regression model. We consider 14 predictors: dividend-price ratio (DP), dividend yield (DY), dividend payout ratio (DE), earnings-to-price ratio (EP), book-to-market ratio (BM), inflation (INFL), long-term bond yield (LTY), long-term bond return (LTR), term spread (TMS), T-bill rate (TBL), net equity expansion (NTIS), default yield spread (DFY), default return spread (DFR), and stock variance (SVAR). The motivation behind this approach is that these predictors are widely used in testing predictability of U.S. stock market returns (see, Devpura et al., 2018). Fourth, we also undertake an out-of-sample forecasting analysis and compare forecasts from our predictive regression model with those from a model without a break.

Our findings can be summarized as follows. First, evidence from Monte Carlo simulations reveals that having a structural break in the trend and slope of the model improves the power of the predictive regression model compared to models without a structural break.

Our second finding relates to the importance of a structural break. We discover that a break in the slope is statistically significant in the case of 5 out of 14 predictors (LTY, DFR, INFL, SVAR, and TBL). This finding also justifies our one-break treatment of the predictive regression model. The message here is that breaks are important, but it depends on the type of predictor used. Moreover, we find no evidence of a break in trend, suggesting that with our financial time-series data, a break in the trend is a non-issue.

Our approaches and results contribute in different ways to the literature on stock return predictability. Our first contribution is that we demonstrate via Monte Carlo simulation experiments that after controlling for commonly known econometric issues, the structural break model performs well. This supports the role of a structural break in tests for stock return predictability. Our empirical setup suggests that a one-break predictive regression model is sufficient to test for predictability in historical data, such as ours; this is what the bulk of the literature uses in applications of new models.5

Our second contribution directly relates to the stock return predictability literature. We find that six predictors predict U.S. stock market excess returns: DP, DY, EP, LTR, LTY, and TBL. Among these six predictors, three (DP, DY, and EP) are valuation ratios. Our data are an extension of the data used by Goyal and Welch (2008). Therefore, we can directly compare our results with the Goyal and Welch (2008) results. These authors find variables DP, DY, and EP are in-sample insignificant and thus conclude that they hold no predictive ability for stock returns. Nonetheless, our results are contrary to the Goyal and Welch (2008) results. We argue that by incorporating structural breaks into the model leads valuation ratios to perform well. Moreover, Campbell, 1987, Hodrick, 1992 show that TBL is a successful predictor of U.S. stock returns, while Devpura et al. (2018) document that LTR and LTY predict U.S. stock market returns. Our results show that this evidence of predictability hold even when a structural break is accounted for.

The remainder of this paper proceeds as follows. Section 2 explains the econometric approach we employ. Section 3 presents the Monte Carlo simulation results. Section 4 describes the data set and empirical findings. Finally, we present concluding remarks in Section 5.

Section snippets

Methodology—econometric approach

We implement two steps in developing a structural break predictive regression model. First, we identify a statistically significant structural break date. To accomplish this, we draw on the Narayan and Popp, 2010, Narayan and Popp, 2013 structural break test. Second, we incorporate into the Westerlund and Narayan (2015) model the chosen break date by interacting it with the predictor variable. We refer to this augmented model as the structural break predictive regression model. The model is

Monte Carlo simulations

In this section, we use Monte Carlo simulations to evaluate the small-sample performance of the proposed FQGLS-based test that allows for a structural break and, in doing so, we focus on the Wald test. All results are based on 1000 replications of sample size T=100. We consider a relatively small sample size because, if it works well when T=100, it will also work well when T is larger. We compare the structural break predictive regression model estimated by FQGLS with the corresponding FQGLS-

Data and empirical results

The data we use here are obtained from Amit Goyal’s web page (www.hec.unil.ch/agoyal). This is U.S. stock market monthly time series data over the period January 1927 to December 2016. Stock market excess returns are computed using Centre for Research in Security Prices (CRSP_VW) value-weighted index returns (including dividends) minus the risk-free rate, which we proxy using the U.S. 3-month T-bill rate. We consider 14 predictor variables that have been extensively studied in the return

Conclusion

In this paper we propose a structural break predictive regression model in the spirit of the Westerlund and Narayan (2015) FQGLS estimator. Our innovation is that we extend the Westerlund and Narayan (2015) model by including a structural break in the slope and in the trend. We test the performance of the FQGLS and OLS estimators with and without a break using Monte Carlo simulations. We conduct five simulation experiments that test both size and power properties. The simulations indicate that

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    Address: Deakin Business School, Deakin University, 221 Burwood Highway, Burwood, Victoria 3125, Australia.

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