World output gap and global stock returns

Accepted Manuscript World output gap and global stock returns Victoria Atanasov

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S0927-5398(18)30048-3 https://doi.org/10.1016/j.jempfin.2018.06.010 EMPFIN 1058

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Journal of Empirical Finance

Received date : 21 March 2018 Revised date : 20 June 2018 Accepted date : 29 June 2018 Please cite this article as: Atanasov V., World output gap and global stock returns. Journal of Empirical Finance (2018), https://doi.org/10.1016/j.jempfin.2018.06.010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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World Output Gap and Global Stock Returns Victoria Atanasov

Abstract This paper shows that world output gap exhibits substantial in-sample and out-of-sample predictive power for global excess stock market returns. High world output gap today signals low expected returns in the future, consistent with a countercyclical equity risk premium. In contrast to the global economic growth which in‡uences returns only at the end of the year, world output gap reveals stable and signi…cant predictability all over the calendar year. Also, world output gap contains important predictive elements for local stock markets and often captures a larger fraction of return variation than the national output gap. Both cash-‡ow and discount-rate channels strongly reinforce the forecasting power of the world output gap.

JEL Classi…cation: G12, G14, G15 Keywords: world output gap; global stock returns; predictability

Chair of Finance, University of Mannheim, L9 1-2, 68161 Mannheim, Germany; [email protected], phone: +49 621 181 2984.

email:

*Highlights (for review)

World output gap is a strong predictor of global stock returns both in-sample and out-of-sample. High world output gap today signals low expected returns in the future. World output gap reveals stable and signi…cant predictability all over the calendar year. Cash-‡ow and discount-rate channels reinforce the predictive ability of the world output gap.

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*Blinded Manuscript Click here to view linked References

World Output Gap and Global Stock Returns

Abstract This paper shows that world output gap exhibits substantial in-sample and out-of-sample predictive power for global excess stock market returns. High world output gap today signals low expected returns in the future, consistent with a countercyclical equity risk premium. In contrast to the global economic growth which in‡uences returns only at the end of the year, world output gap reveals stable and signi…cant predictability all over the calendar year. Also, world output gap contains important predictive elements for local stock markets and often captures a larger fraction of return variation than the national output gap. Both cash-‡ow and discount-rate channels strongly reinforce the forecasting power of the world output gap.

JEL Classi…cation: G12, G14, G15 Keywords: world output gap; global stock returns; predictability

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Introduction

Understanding the relation between macroeconomic aggregates and …nancial markets has long been one of the centerpieces of …nancial economics. One reason for the interest in this relation is that expected returns appear to vary in ways that are linked to the business cycle. This tantalizing stylized fact suggests that stock returns should be predictable by variables which re‡ect expected business conditions. The forecastability of stock returns by business cycle indicators is indeed well documented for the United States1 , but related international studies remain scarce. Three major shortcomings stand out in the literature on international stock return predictability. First, most international results are based on regressions which use local country-speci…c or the U.S. market based …nancial or macroeconomic indicators and very little analysis has been conducted with common global predictor variables. Second, most international studies examine the predictability of national equity market returns at the individual-country level. However, a recent rise in globalization and capital and product market integration across countries, and the reduction in potential gains from country-market based diversi…cation strategies (Lumsdaine and Prasad (2003) and Bekaert, Hodrick, and Zhang (2009)) suggest that measures of global market performance are becoming increasingly important.2 Third, because monthly returns are still perceived as "strikingly unpredictable" (Cochrane (1999)), many international studies document predictability for longer-horizon returns. To address these criticisms, the present paper examines predictability of stock returns 1

See, for instance, Fama and Schwert (1977), Keim and Stambaugh (1986), Fama and French (1988, 1989), Lamont (1998), Campbell and Shiller (1988, 1989), Lettau and Ludvigson (2001), Campbell and Vuolteenaho (2004), Rangvid (2006), Santos and Veronesi (2006), Cooper and Priestley (2009), and Rapach, Strauss, and Zhou (2013). 2 Perhaps apart from Hjalmarsson (2010), Cooper and Priestley (2013), and Møller and Rangvid (2018) there is virtually no compelling evidence on stock return predictability by global business cycle variables. Global economic risks, however, tend to dominate local information variables in capturing the time variation in international equity returns (Ferson and Harvey (1993) and Zhou and Zhu (2015)).

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in six major developed market regions around the world including the MSCI World, World ex USA, EAFE, Europe, Paci…c, and Far East. Our empirical analysis centers around developed markets because the link between global economic risk factors and stock market returns is considerably weaker among emerging economies (Bekaert (1995) and Nitschka (2014)). We document stock return predictability at business cycle frequencies varying from one month to one year over the longest available sample period covering almost one half of a century, i.e. from January 1970 until December 2016. We show that the world output gap, a global business cycle indicator, is a powerful predictor of aggregate stock market returns both in-sample and out-of-sample. World output gap signals high future expected returns when business conditions deteriorate and low future expected returns when the economic outlook improves. For example, a one-standard-deviation reduction in the world output gap leads approximately to a 8.5 percentage point increase in expected returns on the world stock market over the next year. This evidence is comforting because it suggests that predictability does not arise in a manner which is disconnected from the real economy as is the case when using traditional …nancial market based predictors such as the ratio of prices to fundamentals or various measures of interest rate spreads (see also, Cochrane (2005), Cooper and Priestley (2009), and Atanasov, Møller, and Priestley (2018)). Our results lend support to the notion that variation through time in expected returns emerges as a rational response to changing business conditions and re‡ects time-varying risk or risk aversion. Such countercyclical variation in equity risk premia is a key feature of leading asset pricing models including consumption-based speci…cations (Campbell and Cochrane (1999) and Bansal and Yaron (2004)) and production-based ones (Cochrane (1991) and Zhang (2005)). To the extent that the world output gap captures common business cycle related risks, our …ndings contribute to the debate over advanced integration in developed …nancial markets (Lumsdaine and Prasad (2003) and Kose, Otrok, and Whiteman (2003)).

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We identify the world output gap as a cyclical component of the global economic activity from international industrial production data in a similar fashion as for instance the output gap of Cooper and Priestley (2009). Our …ndings are robust to a battery of robustness checks including alternative measures of the world output gap, changes in the sample period, variation in the investment style and horizon, the frequency of the data, and the numeraire currency in which returns are denominated. We also show that our results uphold in a cross-section of sixteen individual-country market returns. In fact, world output gap often explains a larger fraction of return variation than the national output gap. The latter …nding echoes Møller, Nørholm, and Rangvid (2014) who show that the aggregate measure of the European business cycle dominates the local-country consumer con…dence in explaining time variation in annual European risk premia. To alleviate a potential concern that our statistical inference may be complicated by the Stambaugh (1999) bias, we compute wild bootstrapped p-values based on a procedure that accounts for the persistence in regressors and correlations between stock returns and predictor innovations and allows for general forms of heteroskedasticity. A novel IVX testing approach of Kostakis, Magdalinos, and Stamatogiannis (2015) which is robust to the predictor’s degree of persistence and has good size and power properties reinforces the predictive power of the world output gap. Following the criticisms in Welch and Goyal (2008) related to the potential fragility of in-sample results, we conduct several out-of-sample encompassing tests and tests of the equality of mean squared errors. In contrast to Welch and Goyal (2008) who accentuate that many popular business cycle predictor variables have been unsuccessful in out-ofsample tests in the last few decades, our tests indicate statistically superior accuracy of a model of time-varying expected returns based on the world output gap compared to the prevailing-mean model. Motivated by an established literature which hypothesizes that the relation between

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macroeconomic variables and expected returns is stronger at infrequent points in time (Jagannathan and Wang (2007), Jagannathan, Marakani, Takehara, and Wang (2012), Møller and Rangvid (2015, 2018), Da, Yan, and Yung (2016), and Da, Huang and Yun (2017)), we study the seasonality patterns in the predictive ability of the world output gap. We show that the predictive power of the world output gap is stable over time and calendar year seasons. This …nding is important and interesting because it stands in marked contrast to the predictability of the global economic growth which is con…ned to the fourth-quarter months of the year and does not apply to returns measured over horizons other than twelve months ahead (Møller and Rangvid (2018)). Finally, we investigate the economic mechanisms which make the expected returns change. Following Cochrane (2011) and Huang, Juang, Tu, and Zhou (2015), we ask whether the forecasting potential of the world output gap comes from its ability to anticipate time variation in future cash ‡ows or discount rates. Both positive predictability of the dividend-price ratio (standard discount rate proxy) and negative predictability of dividend growth (conventional measure of cash ‡ows) imply a negative predictability for excess stock returns, as we …nd in the data. These …ndings are consistent with the theoretical prediction of an approximate present value identity of Campbell and Shiller (1988). The paper proceeds as follows. Section 2 describes the data. Section 3 presents the insample predictability results. Section 4 shows results from out-of-sample tests. Section 5 investigates seasonal patterns in the predictability. Section 6 explores the economic driving forces of the predictive ability of the world output gap and Section 7 concludes. A separate appendix describes a bootstrap simulation and contains several additional results.

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2

Data

2.1

Stock returns

We calculate stock market returns from Morgan Stanley Capital International (MSCI) total return indexes available since January 1970. Our sample ends in December 2016. We focus our attention on major industrialized markets since the link between global business cycle and stock market returns is found to be considerably weaker among emerging economies (Bekaert (1995), Harvey (1995), and Nitschka (2014)). The regional portfolio returns are obtained from the following six MSCI index series: World, World ex USA, EAFE (Europe, Australasia, Far East), Europe, Paci…c, and Far East.3 In addition, we study individual-country return series in sixteen international developed countries for which we can obtain data on industrial production and stock market returns over the full sample. These countries include Austria, Belgium, Canada, France, Finland, Germany, Italy, Japan, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, the United Kingdom, and the United States. When examining the regional stock market portfolios, we analyze excess returns denominated in U.S. dollars (USD). To construct excess returns, we use the U.S. threemonth Treasury-bill rate from the economic research data base at the Federal Reserve Bank at St. Louis (FRED) as a proxy for the risk-free rate. When examining the individual-country stock market returns, we focus on actual returns in local currency because appropriate proxies for country-speci…c risk-free rates are not su¢ ciently available at a monthly frequency for all countries under study. 3

The MSCI World index represents a global large- and mid-cap equity index consisting of 23 developed markets countries. With 1,656 constituents, the World index covers approximately 85% of the free ‡oatadjusted market capitalization in each country. The MSCI World ex USA index captures 22 developed markets countries excluding the United States. The MSCI EAFE index represents 21 developed markets countries around the world, not including the United States and Canada. The MSCI Europe index consists of 15 major developed European countries. The MSCI Paci…c index consists of 5 developed markets countries including Australia, Hong Kong, Japan, New Zealand, and Singapore, and the MSCI Far East index includes Hong Kong, Japan, and Singapore.

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2.2

World output gap and other predictor variables

For each country i, we …rst calculate an output gap as a residual from a regression of the natural logarithm of the seasonally adjusted industrial production index of country i from the OECD database on a linear and quadratic time trend for the period from January 1970 to December 2016:

log(IPti ) = ai + bi t + ci t2 + vti ;

(1)

where t is a time trend and vti constitutes the output gap of country i as de…ned in Cooper and Priestley (2009). Our main measure of the world output gap is then constructed as a simple equal-weighted average of national output gaps for the sixteen countries in the sample, i.e. wogt = in each time period t.4

N 1 P vi N i=1 t

(2)

Figure 1 shows a time-series plot of the world output gap along with the OECD recession indicator for major seven countries for the 1970-2016 period. The world output gap is strongly procyclical, falling sharp during recessions and rising during expansions.5 We compare the predictive ability of the world output gap with three standard predictive variables from the literature (see also, Møller and Rangvid (2018)). The …rst is the dividend-price ratio on the world stock market, computed based on the MSCI world price indexes with and without dividend reinvestment as a ratio between the twelvemonth moving sum of lagged dividends and current prices (Campbell and Shiller (1988) and Fama and French (1988)). The second is the global in‡ation rate, computed as the equal-weighted average of the CPI in‡ation rates for the sixteen countries in our 4

Section 5 discusses a number of alternative empirical measures of the world output gap. The average length of the OECD contractions in the 1970-2016 period is 24 months. The OECD counts 10 cycles in this period. 5

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sample (Fama and Schwert (1977)). The third is the world risk-free rate conventionally proxied by a short U.S. Treasury bill rate (Campbell (1987) and Ang and Bekaert (2007)).

2.3

Sample properties

Table 1 presents summary statistics. It shows the time-series averages, standard deviations, minima, maxima, …rst-order autocorrelations and Ng and Perron (2001) test statistics for the presence of unit root. The upper panel shows statistics for regional excess stock returns. Average excess returns vary from 0.44% for the World index to 0.52% for the Far East index with associated standard deviations of 4.27% and 5.90%, respectively. All stock market returns show low persistence. The bottom panel summarizes descriptive statistics for the predictive variables. The world output gap has an unconditional mean of zero by construction and a standard deviation of 4.42%. The average dividend-price ratio of the world market portfolio is around 2.82%, the average global in‡ation rate and the average world risk-free rate are about 0.40% in monthly terms. Similar to most business cycle predictor variables, world output gap is highly persistent with a …rst order autocorrelation coe¢ cient of 0.98. The unit root tests of Ng and Perron (2001) give a mixed evidence regarding the stationarity properties of the world output gap and the global in‡ation rate. They reject the unit root hypothesis for the T-bill rate and indicate stationarity of the world dividend-price ratio at the 5% level. It is well known that persistent predictor variables can give rise to unreliable statistical inference in return predictive regressions (e.g. Stambaugh (1999) and Nelson and Kim (1993)). We employ two strategies to address this econometric concern. First, we compute empirical p-values from a wild bootstrap procedure that accounts for the persistence in regressors and allows for correlations between stock market returns and 8

predictor innovations as well as general forms of heteroskedasticity. For more powerful tests of predictability, we follow the recommendation of Inoue and Kilian (2004) and calculate p-values for a one-sided alternative hypothesis. In addition, we employ a novel testing procedure of Kostakis, Magdalinos, and Stamatogiannis (2015) that robusti…es the econometric inference in a return predictive regression to the regressor’s degree of persistence. The appendix details the bootstrap algorithm and shows results of the IVXestimation methodology of Kostakis, Magdalinos, and Stamatogiannis (2015).

3

Benchmark in-sample regressions

We start by assessing the in-sample predictive ability of the world output gap for regional excess stock market returns at business cycle frequencies:6

rt+h =

+ wogt + "t+h ;

(3)

where rt+h is h-month stock market return, wogt is the world output gap, and "t+h is the error term. If wog is a good indicator variable for the global business cycle, the estimate of

should be negative because expected returns are high in economic downturns and vice

versa (Fama and French (1988), Campbell and Shiller (1988), and Lettau and Ludvigson (2001)). The results are summarized in Table 2. For each regression, we report the slope estimate, heteroskedasticity- and autocorrelation robust t-value (computed using a lag of h months; our results are robust toward other choices of truncation lags), and the adjusted R2 statistic in percent. To increase the robustness of our statistical inference and provide a more powerful test of predictability, we compute wild bootstrapped p-values to test H0 :

= 0 against HA :

< 0. Details on the bootstrap procedure can be found in the

6

The average length of the OECD contractions in the 1970-2016 period is 24 months. The OECD counts 10 cycles in this period.

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appendix. We …rst describe the results from predictions of returns on the World MSCI index provided in the …rst row. The initial point to notice is that the estimates of

are

reassuringly negative, implying that a fall in the world output gap today is associated with higher expected returns in the future, consistent with a countercyclical risk premium. The estimate of the regression slope for monthly returns has a value of -0.16. Economically, this estimate suggests that a one-standard-deviation increase in the world output gap leads approximately to a 70 basis points drop in next month’s return. In annualized terms, this corresponds to a 8.5 percentage point reduction in expected returns. This e¤ect is strongly statistically signi…cant. The Newey-West t-statistic of -3.74 and the bootstrap p-values indicate signi…cance at the 1% level. Variation in the world output gap accounts for 2.7% of the variation in the monthly world market return. The world output gap pertains its predictive power at the quarterly and annual horizons with associated R2 statistics of 7.88% and 20.63%, respectively. Cooper and Priestley (2009) …nd similar evidence for the relation between U.S. returns and U.S. output gap. Since the U.S. stock market has a high weight in the world market portfolio (59% in June 2017), one might wonder whether the results for the world market portfolio are driven by the United States. Most likely this is, however, not the case. We …nd generally similar empirical evidence for the MSCI World ex USA index as well as the regions of the EAFE, Europe, Paci…c, and Far East that do not include the U.S. stock market. We …nd a pervasive e¤ect of the world output gap on future expected returns regardless of the time horizon and the market region. To test the signi…cance of

in Equation (3), we additionally employ the novel IVX

testing approach of Kostakis, Magdalinos, and Stamatogiannis (2015) that is robust to the regressor’s degree of persistence (including unit root, local-to-unit root, near-stationary or stationary persistence classes) and has good size and power properties. This approach

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alleviates practical concerns about the quality of inference under possible misspeci…cation of the (generally unobservable) time series properties of the regressor in long-horizon predictive regressions. The IVX estimator indicates that the null hypothesis of no predictability can be rejected at the 1% level for return horizons of one, three, and twelve months. The complete results are reported in Table A1 in the appendix. Taken together, we …nd a pervasive e¤ect of the world output gap on future aggregate expected returns regardless of the time horizon and the market region. This evidence is robust statistically and economically, and is not a statistical artifact of the persistence of our predictor variable. This …nding is important because it constitutes new evidence of time-varying risk premiums and highlights a relation between return predictability and economic fundamentals in international stock markets.

3.1

Taking into account publication delays

Regression results presented so far were based on a lag length of one month. For example, a predictive regression for monthly returns in Equation (3) related world output gap in the current month t to international returns in the next month t + 1. The estimates of seasonally adjusted industrial production index are, however, published with a lag whose length varies across countries. For instance, the OECD estimates for industrial production of Canada for December are usually not released before early March. To take these release delays into account in a conservative way, we conduct the following regression type

rt+h =

+ wogt

2

+ "t+h ;

(4)

where we use the third lag of wog when forecasting stock returns. Consider, for example, a forecasting horizon of one month, h = 1. In this case, the speci…cation in Equation (4) relates returns in the next month t + 1 to the world output gap in month t 11

2 rather

than in month t as in Equation (3). We therefore say that we move returns forward or, alternatively, lag the world output gap, by two additional months. This timing convention is consistent for instance with Cooper and Priestley (2009) and Møller and Rangvid (2015, 2018). The results are summarized in Table 3, and they are much in line with our benchmark …ndings. Overall, we …nd signi…cantly negative estimates of

for all regions and all hori-

zons, and R2 statistics which increase with the horizon. The consistency of the estimated sign, the magnitude of coe¢ cient, and the statistical signi…cance further reinforce that the world output gap is useful in tracking the variation in future market returns around the world.

3.2

Long-horizon forecasts

Table 4 assesses the examines the forecasting power of wog for excess stock returns at longer horizons of 24, 36, and 48 months. Consistent with our benchmark results at business cycle frequencies, we …nd that the world output gap negatively predicts excess returns on regional stock markets. The estimates for the MSCI indexes for World, World ex USA, EAFE, and Europe are signi…cant at the 5% level at any return horizon that we consider, while the estimates for the regions of Paci…c and Far East are signi…cant at horizons of up to three years. In economic terms, we …nd roughly similar coe¢ cient estimates, t-statistics, and R2 values across the di¤erent return horizons for each region under study. For example, the R2 statistics are in the tight ranges of 28-36%, 18-23%, 20-24%, 19-32%, 13-15%, and 1415% for the World, World ex USA, EAFE, Europe, Paci…c, and Far East MSCI indexes, respectively. To gain an economic sense of how far the actual R2 statistics of a predictive regression deviate from the simulated R2 statistics generated under the null hypothesis of no pre12

dictability and given the persistency of the regressor, Table 4 reports 90% bootstrapped con…dence intervals next to each R2 statistic in squared brackets. The simulated adjusted R2 estimates are obtained from the bootstrap procedure described in the appendix. Under the null of no return predictability, the calculated con…dence intervals are very narrow and center at values close to zero with a lower bound of -0.19% and an upper bound of no more than 0.65%. Remarkably, the con…dence intervals have no tendency to increase at longer horizons, consistent with the stable R2 statistics that we report. Importantly, the actual R2 statistics are all outside the con…dence bounds computed from the simulated distributions of the R2 statistics generated under the null. The fractions of the return variation captured by the world output gap are thus statistically signi…cant (see also, Rangvid (2006)). Moreover, the evidence we …nd does not appear to support, for instance, Boudoukh, Richardson, and Whitelaw (2008) who argue that predictive ability of persistent regressors might be very fragile at longer horizons because common sampling errors can lead to coe¢ cient estimates and R2 statistics that are roughly proportional to the horizon under the null hypothesis.

3.3

Comparison with economic predictors

In this subsection, we compare the forecasting power of the world output gap with three alternative predictor variables commonly applied in the literature: the world dividendprice ratio (dp), the global in‡ation rate (in‡), and the world risk-free rate (tbl).7 The left half of Table 5 shows results from simple monthly predictive regressions:

rt+1 =

+ ztk + "t+1 ;

7

(5)

Because the OECD has immensed international series for capital stock of the business sector back in 2013, it is not possible for us to construct the world’s capital-to-output ratio of Cooper and Priestley (2013).

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where z k is either dp, in‡ or tbl. The results indicate that none of these benchmark variables exhibits a robust predictive power for global excess stock returns. Apart from some predictability stemming from in‡ation, we typically record insigni…cant estimates and often negative R2 statistics. To investigate the incremental forecasting power of wog we also estimate predictive regressions with wog and z k jointly:

rt+1 =

+ wogt + ztk + "t+1 :

The right half of Table 5 shows that the estimates of

(6)

in Equation (6) are nega-

tive and economically similar to the estimates in Table 2. More importantly,

remains

strongly statistically signi…cant in a regression augmented by the benchmark economic predictors. These results demonstrate that wog contains sizable complementary forecasting information beyond that contained in the benchmark economic predictors.

3.4

Country-speci…c evidence of predictability

The evidence we present above shows that the world output gap is a strong predictor of global stock market returns. In what follows, we investigate the predictive power of the world output gap for individual-country stock market returns and compare it with the explanatory power of the respective local output gap at a country-level. The top panel of Table 6 shows results from monthly predictive regressions for stock market returns in sixteen developed countries over the full sample period, 1970-2016. We generally …nd that the world output gap negatively predicts future individual-country stock returns, consistent with the evidence for regional portfolios. According to the bootstrap p-values, the estimates are signi…cant for Belgium, France, Germany, Italy, Japan, the Netherlands, Spain, Sweden, Switzerland, the United Kingdom, and the United States

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at the 5% level, and for Canada and Finland at the 10% level. In addition, we also see some evidence of predictability by the local measure of the output gap in line with Cooper and Priestley (2009). A direct comparison of the coe¢ cient estimates, the associated tstatistics, and R2 measures indicates that in twelve out of sixteen cases there is stronger evidence of predictability stemming from global risks as opposed to local country-speci…c economic risks (see also, Nitschka (2014)). To estimate more precisely the relative importance of local and global versions of the output gap for capturing time-variation in future expected returns, we employ a forecast encompassing test of Harvey, Leybourne, and Newbold (1998). Column

shows the

estimated optimal weight of the predictive regression forecast of the global and local measures of the output gap in a combination forecast that takes the form of a convex combination of the two forecasts. Obviously, the estimates of

add up to unity for each

country. We can reject the null hypothesis that the local output gap forecast encompasses the information from the global output gap forecast at the 5% signi…cance level for Belgium, Japan, the Netherlands, Sweden, Switzerland, the UK and the US. For Canada, Finland and Norway, the estimated weight of the global forecast is close to unity but not statistically signi…cant (left half of the table). The reverse null hypothesis that the world output gap forecast encompasses the information from the local output gap forecast can be signi…cantly rejected only for Germany (right half of the table). Overall, the Harvey, Leybourne, and Newbold (1998) test reinforces that the world output gap captures a larger fraction of return variation than the individual-country output gap. Motivated by the literature documenting an advanced degree of globalization and regional market integration over the 1980s and 1990s, we further analyze the extent of predictability by the global and local measures of the output gap in the post-1990 data characterized by increased market interdependence, with equities displaying a high degree of comovement across countries (Baele (2005) and Kose, Otrok, and Whiteman (2008)).

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Our results in the bottom panel of Table 6 con…rm that the link between the global economy and ‡uctuations in local-country expected returns has become stronger in the recent decades, while we record no systematic di¤erences in the predictive ability of the local output gap measures over the two sample periods that we study. The Harvey, Leybourne, and Newbold (1998) test suggests that Finland, Germany, and, marginally, the Netherlands are the only three countries for which the optimal weight of the local output gap forecast exceeds that of the world output gap forecast. The optimal weight of the global output gap forecast is equal or very close to unity for Austria, Canada, France, Italy, Japan, Norway, Portugal, Spain, Sweden, the UK, and the US. Overall, two main results emerge. First, our analysis indicates that aggregate business cycle risks contain signi…cant information about expected returns on national stocks and often capture a larger fraction of return variation than local information variables. This …nding echoes several studies which suggest that aggregate multi-country business cycle variables are informative about local-country expected returns. For example, Møller, Nørholm, and Rangvid (2014) show that an aggregate measure of the European business cycle captures time variation in annual European risk premia over the 1990-2010 period well. Cochrane (1999), however, notes that monthly returns are "still strikingly unpredictable." Against this backdrop, our evidence is particularly important because it focuses of the predictability at a one-month horizon. Second, our results suggest that the relevance of global risks has increased with a recent rise in globalization and capital market integration across countries, consistent with Lumsdaine and Prasad (2003), Stock and Watson (2005), and Imbs (2006).

3.5

Robustness tests

To explore the sensitivity of our conclusions, we perform a battery of robustness checks with respect to the relation between global stock returns and the world output gap. 16

3.5.1

Evolution over time and temporal stability

To investigate whether our results are a¤ected by the choice of the sample period, we estimated the basic predictive regression over alternative sample periods. We considered di¤erent starting periods: 1970, 1975, 1980, 1985, 1990, 1995, and 2000, and di¤erent ending periods: 1985, 1990, 1995, 2000, 2005, and 2010. Our results did not change qualitatively. Especially, the performance of the world output gap does not appear to be a¤ected by the oil price crisis in the mid-1970s–a feature found for many U.S. business cycle predictor variables (Welch and Goyal (2008) and Campbell and Thompson (2008)). The estimates for the post-1980 period compare favorably with those for the full 19702016 sample. For example, the adjusted R2 statistics of 2.21%, 7.27%, and 21.43% for monthly, quarterly, and annual returns on the MSCI World index in the post-1980 subsample are very close to those in Table 2 (2.69%, 7.88%, and 20.63%, respectively). We …nd consistent evidence for all regional portfolios. Similar predictability patterns emerge in a sample which omits the data in the aftermath of the run-up in prices in the early 2000s. Splitting the sample in two parts of roughly similar lengths generates robust evidence of predictability in each subsample too. Elliott and Müller (2006) propose an alternative test of the temporal stability of the estimates in Equation (3) to structural breaks. Their qLL-statistic which tests the hypothesis that

t

=

for all t (at any …xed horizon h) is particularly useful in the

context of predictive regressions because it is asymptotically e¢ cient for a wide range of data-generating processes, has superior size control in small samples than other popular statistics, and is simple to construct. Moreover, the simulation analysis in Paye and Timmermann (2006) shows that the test of Elliott and Müller (2006) possesses excellent …nite sample size properties even in the presence of highly persistent lagged endogenous predictors. Table A1 in the appendix documents that the qLL-statistics for our benchmark estimates in Table 2 are never signi…cant. These results emphasize a stable relation 17

between world business cycle risks and global stock market returns around the world. 3.5.2

Alternative measures of the world output gap

We have considered several alternative ways to calculate the world output gap. First, we experimented with a GDP-weighted average of country-speci…c output gaps. Second, we computed the world output gap as a …rst principle component of national output gaps. Third, we extracted the …rst principle component of the sixteen industrial production indexes and constructed then a measure of the world output gap. Fourth, we computed the world output gap from the industrial production data of G7 countries. Fifth, we calculated the world output gap based on a single series of industrial production index for G7 countries provided by the OECD. Sixth, we calculated the world output gap by averaging the industrial production indexes of all sixteen countries or only of the seven major countries and conducted then regression (1). Seventh, we have also considered several empirical measures of the world output gap based on quarterly GDP data. We generally found the same qualitative results. 3.5.3

Alternative time trend speci…cations

To guard against the possibility that our results are due to a particular detrending method we use when computing the individual-country output gap, we experimented with four alternative time trend speci…cations. The …rst two are based on lower and higher order time polynomials, i.e. a linear and a cubic time trend models (see also, Cooper and Priestley (2009) and Rapach, Ringgenberg, and Zhou (2016)). In addition, we computed a "stochastically detrended" industrial production series based on a rolling three-year window, i.e. the output gap in month t is equal to the di¤erence between the natural logarithm of industrial production in month t minus the average of the natural logarithm of industrial production in months t-36 to t-1 (e.g., Campbell (1991) and Hodrick (1992)).

18

We also applied the Hodrick and Prescott (1997) …lter to compute the output gap as a di¤erence between the natural logarithm of actual industrial production and its implied trend.8 These measures of the world output gap strongly comove with each other and yield generally similar results. Thus, the predictive power of the world output gap is very robust to the trend speci…cation. The estimates of

in Equation (3) are measured very

precisely for each detrending method and every return horizon. These results demonstrate that the question of which method should be employed to detrend industrial production series is largely irrelevant since all methods reveal substantial return predictability. 3.5.4

Numeraire currency and characteristics

The benchmark results we document above are obtained for regional returns in USD. We tested the robustness of our estimates toward the use of alternative return currency denominations. For instance, the MSCI index returns can be retrieved in GBP for the full sample period, and in EUR for the post-1999 subsample. This allows us to conduct tests of predictability from the point of view of a British or a European investor. We …nd similar results independently of the numeraire currency and sample length. These results have an important implication: The predictive ability of the world output gap is not merely a re‡ection of exchange rate ‡uctuations over time but is rather due to common movements in global …nancial markets and thus consistent with a time-varying risk premium hypothesis (see also, Møller and Rangvid (2018)). In addition to the standard price indexes employed in this paper, the MSCI collects historical data on securities exhibiting overall growth and value style characteristics since January 1975. The construction of the value and growth indexes is based on a comprehensive and state-of-the art approach.9 Our results are robust to using returns sorted on 8 We set the smoothing parameter in the Hodrick-Prescott procedure to 14,400 as is standard when working with monthly data. 9 The value investment style characteristics are de…ned using three variables: book-value-to-price ratio, twelve-month forward-earnings-to-price ratio, and dividend yield. The growth investment style

19

growth and value style characteristics. Another important aspect of our estimates is their robustness to the market capitalization style. We verify the general validity of our results with MSCI Small Cap returns (available since January 2001) and MSCI Large Cap returns (available since June 1994). Interestingly, we …nd that the economic and statistical in‡uence of the world output gap is stronger for expected returns of low market capitalization …rms. This …nding is consistent with several contributions in the business cycle literature which show that small …rms su¤er stronger from aggregate economic shocks. For example, Bernanke and Gertler (1989) and Kiyotaki and Moore (1997) show theoretically that small …rms are a¤ected more severely by lower liquidity and higher discount rates following an economic shock. Gomes, Yaron, and Zhang (2006) …nd that the size premium in returns is inherently conditional on the business cycle conditions and likely countercyclical. Perez-Quiros and Timmermann (2000) show that expected returns of small …rms exhibit much higher sensitivity to the business cycle. Overall, these tests reinforce our interpretation of countercyclical variation in risk premia in international stock markets.

4

Out-of-sample tests

Welch and Goyal (2008) …nd that numerous economic variables with in-sample predictive ability fail to provide consistently reliable out-of-sample forecasts. This implies that insample predictability does not necessarily mean that investors can bene…t from a better portfolio allocation if they follow the signals of in-sample regressions. Against this backdrop, we perform several tests to study the ability of the world output gap to predict returns out-of-sample. characteristics are de…ned using …ve variables: long-term forward earnings per share growth rate, shortterm forward earnings per share growth rate, current internal growth rate, long-term historical earnings per share growth trend, and long-term historical sales per share growth trend. The indexes are reviewed in May and November each year with the objective to guarantee a timely re‡ection of current changes in the style characteristics of the underlying equity markets.

20

4.1

Forecasting procedure and out-of-sample tests

To start with, we take a subsample of the …rst s observations t = 1; :::; s of the entire sample of T observations and estimate country-speci…c output gaps as speci…ed in Equation (1) and compute the world output gap as de…ned in Equation (2). Conditional on the information available at time s, we then form a return prediction by estimating Equation (4).10 We refer to this forecasting model as the unrestricted model. We use recursive regressions to reestimate both world output gap and the forecasting model in each period, adding one month at a time, thereby generating a sequence of out-of-sample return forecasts for t = s + 1; :::; T . We specify a model of constant expected returns as a benchmark model. We refer to this forecasting model as the restricted model. Accordingly, we evaluate whether the return predictions based on world output gap are more precise than predictions from the prevailing mean model. To guard against possibility that our conclusions are a¤ected by any particular period, we consider three di¤erent out-of-sample forecast evaluation periods: 1990-2016, 1995-2016, and 2000-2016.11 We follow Cooper and Priestley (2009) and Atanasov, Møller, and Priestley (2018) and assess the out-of-sample predictability by means of four conventional metrics. The 2 …rst statistic we report is the out-of-sample ROS statistic of Campbell and Thompson

(2008) which gives the proportional reduction in the mean squared error (MSE) for the predictive regression model vis-à-vis the prevailing mean benchmark forecast. A positive 2 value of ROS indicates that the predictive regression forecast outperforms the historical

average in terms of MSE, whereas a negative value signals the opposite. The second 10

We move returns forward by two months to take publication lags of the OECD industrial production estimates into account and thereby closely resemble the situation of a real-time investor. Our results are qualitatively similar for other lag lengths. For most of the countries in our sample, long samples of vintage data of unrevised industrial production series are unfortunately not available until 1999. 11 Starting the out-of-sample period in 1990 (or later) provides a reasonably long initial in-sample period for reliably estimating the parameters used to generate the initial predictive regression forecast. This is especially relevant when generating forecasts based on the world output gap, as we also need to estimate the trend for the log of industrial production to construct the national output gap measures.

21

statistic we report is the powerful EN C-N EW test of Clark and McCracken (2001) which extends the encompassing test of Harvey, Leybourne, and Newbold (1998) by deriving a nonstandard asymptotic distribution under the null of nested forecasts. The EN CN EW statistic tests the null hypothesis that the restricted constant expected return model encompasses the unrestricted time-varying expected return model; the alternative is that the unrestricted model contains information that could be used to signi…cantly improve the forecast of the restricted model. The third statistic we report is the M SE-F statistic of McCracken (2007) which tests the null hypothesis that the restricted constant expected return model has a MSE that is less than or equal to that of the unrestricted time-varying expected return model; the alternative is that the unrestricted model has a smaller MSE. Finally, we also calculate the certainty equivalent return (CER) gain for a meanvariance investor who allocates between equities and risk-free bills using the time-varying expected returns model relative to the historical mean return forecast. This allows us to gauge the economic importance of our predictability results. We assume that a meanvariance investor calculates the optimal equity portfolio weights based on the forecasting model of expected excess returns:

wt =

1 rbt ; b2t

(7)

where rbt is a forecast of the excess return at time t, b2t is the estimated variance of the return, and

is the coe¢ cient of relative risk aversion. We follow Campbell and

Thompson (2008) and impose realistic portfolio constraints preventing the investor from shorting stocks or taking more than 50% leverage. We assume a risk aversion coe¢ cient of three and use a rolling …ve-year window of past returns to estimate the variance, which is typical in tests with monthly data. At the end of each period, the portfolio return is calculated as the weighted average 22

of the respective return on the equity stock market and the return on the risk-free rate. The portfolio CER can then be computed as

CER = bp

0:5 b2p ;

(8)

where bp and b2p are the mean and variance, respectively, for the investor’s portfolio

over the forecast evaluation period. The CER corresponds to the risk-free rate of return that an investor is willing to accept instead of adopting the given risky portfolio. The CER gain is then computed as a di¤erence between the CER for an investor who uses a predictive regression forecast and the CER for an investor who uses the historical average forecast. We multiply this di¤erence by 1200, so that it can be interpreted as the percentage portfolio management fee that an investor would be willing to pay each year to have access to the predictive regression forecast in place of a prevailing mean forecast.

4.2

Out-of-sample evidence

Table 7 presents the results of out-of-sample predictions of monthly excess stock returns for three forecast evaluation periods: 1990-2016, 1995-2016, and 2000-2016. We generally …nd that the forecasts based on the world output gap are better than those generated 2 by the constant. For every region and each evaluation period, the out-of-sample ROS

statistics are positive and statistically signi…cant, meaning that the unrestricted model 2 delivers a lower MSE than the historical average forecast. For example, the ROS statistic

for the World stock market index is 3.09% when we forecast from 1990, 2.82% when we forecast from 1995, and 4.89% when we forecast from 2000. In economic terms, these estimates imply that an investor with a unit risk aversion, would increase the average portfolio return by about 37, 34, or 59 percentage points per year, if relying on the forecast based on the world output gap since 1990, 1995, or 2000, respectively. A return

23

increase would correspond approximately to 12, 11, or 20 percentage points, respectively, for an investor with a relative risk aversion of three. The forecast encompassing test of Clark and McCracken (2001) further reinforces the out-of-sample forecasting ability of the world output gap. The EN C-N EW test statistic consistently rejects the null hypothesis that the forecasts from the constant expected return model encompass the forecasts from the time-varying expected return model. The EN C-N EW test statistics are signi…cant at the 5% level or better for every region and each evaluation period that we consider. Furthermore, the M SE-F test systematically rejects the null hypothesis that the MSEs from the unrestricted model are bigger than or equal to those from the historical average return. These estimates are throughout statistically signi…cant. Finally, we typically …nd positive and sizable CER gains demonstrating the substantial economic value of the predictive regression forecast compared to the historical average forecast. 2 statistics are at least partly Di¤erences between these estimates and out-of-sample ROS

due to the estimated variance of stock return that is necessary to calculate the CER gains. The utility gains reported in Table 7 are limited by the leverage constraint but do not take into account any transaction costs. In summary, the evidence presented in Table 7 provides strong indication of statistical and economic out-of-sample predictive ability of the world output gap.

5

End-of-the-year economic conditions and expected returns

A number of prominent studies document a signi…cant relation between business cycle activity at the end of the year and asset values. For example, Jagannathan and Wang (2007) and Jagannathan, Marakani, Takehara, and Wang (2012) …nd evidence of a so24

called "end-of-the-year" e¤ect in cross-sectional data. They show that end-of-the-year consumption growth improves the ability of the standard consumption-based capital asset pricing model (CCAPM) to explain patterns in average stock returns in the United States, the United Kingdom, and Japan. The performance of the CCAPM deteriorates remarkably when consumption growth is measured based upon other quarters. Da, Yang, and Yun (2016) use end-of-the-year electricity growth rates to capture the cross-sectional distribution of expected stock returns in the United States in a framework of a household production model. Several other papers document the end-of-the-year e¤ect in time series. Perhaps most notably, Møller and Rangvid (2015, 2018) …nd that end-of-theyear macroeconomic growth predicts future one-year-ahead returns on a wide spectrum of risky …nancial assets, whereas economic growth during the rest of the year does not. Relatedly, Da, Huang, and Yun (2017) use end-of-the-year growth rate of the aggregate industrial usage of electricity to predict future stock returns. The economic underpinnings for these intriguing …ndings range from seasonal patterns in risk preferences and habit formation (Møller and Rangvid (2015)), over infrequent portfolio adjustment due to e.g. cultural, institutional or news events, or informational or transaction costs (Jagannathan and Wang (2007)), to the ability of macroeconomic growth to predict future real economic activity (Møller and Rangvid (2018)).

5.1

Quarterly predictive regressions

Inspired by this literature, we regress one-year-ahead excess world stock market returns on lagged quarterly world output gap or lagged quarterly log growth rates in global industrial production in di¤erent quarters of a year. We compute global industrial production growth as a cross-country average for the sixteen countries in our sample (the data are from the OECD). Our sample runs from the …rst quarter of 1970 to the fourth quarter of 2016. 25

To explain Table 8, Column Q1 summarizes results of regressions of the one-year-ahead excess returns measured from the beginning of the second quarter to the end of the …rst quarter next year on the …rst quarter realizations of the world output gap (Panel A) or the …rst quarter growth rates of global industrial production (Panel B), i.e. the growth rates from the fourth quarter last year to the …rst quarter current year. Analogously, Column Q4 in Table 8 displays results of regressions of annual excess returns measured over the next calendar year, i.e. from the beginning of the …rst quarter to the end of the fourth quarter next year, on the fourth quarter realizations of the world output gap (Panel A) or the fourth quarter growth rates of global industrial production (Panel B). The estimates in Panel A of Table 8 indicate a strong performance of the world output gap regardless of the timing of returns and their geographical coverage. In general, we detect a stable relation between our predictor variable and future expected returns. The estimated sign of coe¢ cients is reassuringly negative, such that a deterioration (improvement) in business activity increases (decreases) next year’s expected returns. Hence, investors raise the required returns when economic conditions worsen, consistent with rational asset pricing. The predictive power of the world output gap is economically and statistically signi…cant. In numerical terms, the t-statistics are in the range of 2.5-4.0 in absolute terms. It is important to note that our estimates are apparently not indicative of any seasonal patterns in the predictive ability of the world output gap. Its forecasting power is similarly strong in the …rst, second, third, and fourth quarter of the year. Hence, the …rm performance of the world output gap found using all observations in Table 2 is not merely due to its …rm performance in any speci…c quarter. The estimates in Panel B of Table 8 tell a di¤erent story. Regardless of whether the global economic growth is strong or weak in the beginning or middle of the year, we …nd that subsequent returns are more or less the same. The estimates show that …rstquarter, second-quarter, and third-quarter growth rates are insigni…cant predictors of

26

future returns and generate low and often even negative R2 statistics. By contrast, a rise in the fourth-quarter economic growth is associated with systematically lower subsequent returns. In line with Møller and Rangvid (2018), the coe¢ cient estimates, t-ratios, and R2 statistics are bigger in the fourth quarter in numerical values compared to the other quarters. The results in Table 8 indicate that the predictive power of the world output gap tends to exceed that of the global industrial production growth in every quarter of the year, and importantly, also at the end of the year. For example, the coe¢ cients of determination in the fourth-quarter regressions are 18.84%, 10.97%, 12.86%, 8.66%, 11.21%, and 11.60% for the World, World ex USA, EAFE, Europe, Paci…c, and Far East portfolios, while the respective R2 statistics for the global industrial production growth are only 9.33%, 7.20%, 8.01%, 8.14%, 3.94%, and 1.90%, respectively. These results are not a¤ected by the timing of one-year-ahead returns we forecast, which is advantageous because macroeconomic data is released with a lag. In general, we …nd that the predictability becomes a little weaker when we incorporate the macroeconomic release delays, but our main conclusions remain valid. Our analyses con…rm that fourth-quarter growth rates signi…cantly predict returns, whereas growth rates in other quarters do not. In marked contrast to this evidence, the predictive ability of the world output gap is not con…ned to any speci…c (calendar) time period.

5.2

Monthly predictive regressions

Table 9 contains results from predictive regressions for one-year-ahead excess stock returns on the world market portfolio on monthly lagged world output gap or monthly lagged log growth rates in global industrial production over the period from January 1970 to December 2016. For example, when using the January values of predictor variables, the one-year-ahead return is measured from the beginning of February to the end of January 27

next year; when using the December values of predictor variables, the one-year-ahead return is measured over the next calendar year, etc. The timing convention follows Møller and Rangvid (2015, 2018). The left half of Table 9 reinforces that high world output gap today predicts low stock market returns in the future, consistent with a countercyclical risk premium. This e¤ect is strongly statistically signi…cant in every month of the year. In numerical terms, t-statistics range from -4.50 in September to -8.19 in June, and adjusted R2 statistics ‡uctuate between 12.45% in August to 28.44% in February. The strong and robust predictive ability of the world output gap stands in marked contrast to the predictive power of global economic growth which is typically concentrated in the fourth-quarter months of the year. The results in the right half of Table 9 are generally consistent with results reported in Panel B of Table 8. They reveal that economic growth is overall a rather poor predictor of returns. The coe¢ cient of the global industrial production growth switches sign, it is often insigni…cant, and the associated R2 statistics are in many cases negative. Most of the predictive power of the global economic growth is concentrated at the end of the year with predictability being strongest in December. For example Jagannathan and Wang (2007) argue that December could be more important for portfolio decisions than other months within the fourth quarter because of Christmas and the resolution of uncertainty about end-of-year bonuses and tax payments. Consistent with the …ndings of Møller and Rangvid (2015, 2018), December and to a lesser extent November and October growth rates have some predictive ability for global stock returns around the world. In summary, we …nd a remarkably strong systematic relation between world output gap and future one-year-ahead excess returns which is robust, consistent, and not con…ned to any particular season. These results are especially important in view of the fact that the predictive power of the global economic growth is usually revealed only in the end of

28

the year.

6

Economic interpretation of predictability

Simple valuation models point to two reasons why stock prices may change: either cash ‡ows change, discount rates change, or both. From this perspective, we aim to gain insights into the economic sources of the predictive ability of the world output gap that we document in Section 3. To study the relative importance of the two channels, we follow the approach of Cochrane (2011) and Huang, Juang, Tu, and Zhou (2015), and conduct the following predictive regressions:

yt+1 =

+ wogt + dpt + dgt + "t+1 ;

(9)

where y denotes either the log dividend-price ratio, dp, or the log dividend growth rate, dg. The intuition behind these regressions comes from the Campbell and Shiller (1988) approximate present value identity:

rt+1 where rt+1 denotes log return and

k + dgt+1

dpt+1 + dpt ;

(10)

is a positive constant of approximation. Equation

(10) implies that if wogt predicts next period market return rt+1 beyond the information contained in dpt , it must predict either dgt+1 or dpt+1 , or both. Since dp proxies for discount rates (Cochrane (2008, 2011)) and dg proxies for cash ‡ows (Campbell and Shiller (1988) and Cochrane (2008, 2011)), the forecasting power of wog for future stock returns should be associated with the forecasting power of wog for future cash ‡ows or expected discount rates. Table 10 summarizes results of the regressions in Equation (9). We construct dg 29

and dp from MSCI gross stock market indexes and MSCI stock market indexes that do not consider reinvestment of dividends. We use annual dividend growth to avoid spurious predictability from within-year seasonality. Annual dividends are computed as rolling sums of monthly dividends. In our regressions, we use January 1971 as the …rst observation because we require the …rst twelve months of the sample to compute past dividends for the dividend growth. Our last observation is December 2016. Panel A of Table 10 shows the results of dividend-price ratio forecasting regressions. The

estimate is throughout positive such that a rise in world output gap systematically

predicts a rise in the future dividend-price ratio. The estimates are signi…cant for each region under study. Keeping the dividend constant, an increase in dp indicates a decline in future prices, consistent with our …nding of a negative relation between wog and expected returns. Regarding the dividend growth predictability, we typically …nd negative and statistically signi…cant

estimates in Panel B of Table 10, in line with the theoretical prediction

of Equation (10). From Equation (10), positive predictability for dividend-price ratio and negative predictability for dividend growth jointly indicate that the world output gap should display a signi…cant negative predictive power for aggregate stock market returns, which is in accord with the evidence reported in Section 3. For comparison, Fama and French (1989) and Cochrane (2008, 2011), among others, argue that aggregate stock market predictability stems from time variation in discount rates. These conclusions stand in contrast to Huang, Jiang, Tu, and Zhou (2015) who …nd that the predictive power of their aligned investor sentiment index–extracted from the Baker and Wurgler’s (2006, 2007) six individual investor sentiment proxies by applying the partial least squares method–emanates from the cash ‡ow channel. The estimates in Panels A and B of Table 10 also show that a high dividend-price ratio today signals a high dividend-price ratio and a high dividend growth tomorrow.

30

By contrast, high past dividend growth has an opposing impact on future dividend-price ratios and future dividend growth rates: The former e¤ect is positive, while the latter is negative. In summary, both positive predictability of the world output gap for the dividend-price ratio, and negative predictability of the world output gap for the dividend growth, imply a negative predictive ability of the world output gap for aggregate stock market returns, as we …nd in the data. These predictability patterns emphasize that the predictive ability of the world output gap is consistent with the theoretical prediction of the approximate return decomposition of Campbell and Shiller (1988).

7

Conclusion

This paper documents new evidence of predictability of stock market returns around the world with a global business cycle indicator–the world output gap. World output gap displays clear business cycle patterns and signals high expected returns when business conditions deteriorate and low expected returns when the economic outlook improves. This evidence is comforting because it is concurrent with the notion that variation through time in expected returns emerges as a rational response to changing business conditions and re‡ects time-variation in the investment opportunity set or changes in investors’risk aversion. World output gap exhibits stable predictability in-sample and out-of-sample and often captures a larger fraction of return variation than the national output gap. The predictive power of the world output gap is robust at business cycle frequencies and is not con…ned to any speci…c sample period or time when the forecast is made. This property is appealing because it stands in stark contrast to the global economic growth, for example, whose forecasting power is known to become signi…cant only at the end of the calendar year

31

and apply only to one-year-ahead returns. In addition, our analysis suggests that the strong forecasting potential of the world output gap for aggregate stock market returns emanates from its ability to rationally anticipate both future changes in market discount rates and cash ‡ows. These results are important for two main reasons. First, our …ndings emphasize the role of deep macroeconomic fundamentals as a central determinant of asset prices, i.e. one of the key insights in …nancial economics. Second, to the extent that the world output gap captures common business cycle related risks, our …ndings indicate that risk premia in equity stock markets are internationally connected and point toward advanced …nancial integration across the borders.

32

Table 1: Descriptive statistics The table displays summary statistics for excess global stock returns and the world output gap. Returns are computed based on the MSCI total return indexes in U.S. dollars. We use the U.S. three-month T-bill rate to calculate excess returns. wog is the world output gap. dp is the dividend-price ratio on the world stock market index. in‡ is the global in‡ation rate. tbl is the world risk-free rate. (1) designates …rst order autocorrelation. M Z GLS and ADF GLS denote test statistics for the presence of unit root. Bold font indicates statistical signi…cance at the 5% level. The sample period runs from January 1970 to December 2016. Mean

Std

Min

Max

(1)

M Z GLS

ADF GLS

Excess Stock Returns World

0.44

4.27 -18.99 14.20 0.10

-94.92

-6.12

World ex USA

0.46

4.93 -20.85 16.39 0.12

-68.28

-5.95

EAFE

0.46

4.91 -20.23 17.36 0.11

-56.97

-5.79

Europe

0.50

5.04 -21.30 23.13 0.08 -187.86

-10.43

Paci…c

0.49

5.73 -18.65 21.03 0.12

-49.78

-5.60

Far East

0.52

5.90 -19.28 22.88 0.12

-43.34

-5.60

Predictive Variables wog

0.00

4.42

-8.61

10.81 0.98

-21.75

-2.78

dp

2.82

1.04

1.23

5.74

0.99

-10.41

-2.17

in‡

0.40

0.45

-0.63

5.71

0.65

-16.54

-3.54

tbl

0.40

0.28

0.00

1.36

0.99

-29.20

-3.58

33

Table 2: Benchmark predictive regressions The table shows results from predictive regressions of monthly, quarterly and annual excess stock returns on monthly world output gap: rt+h =

+ wogt + "t+h , where h

denotes the horizon in months, rt+h is h-month excess stock market return, and wogt is the world output gap. For each regression, the table reports OLS estimates of the regressor, Newey-West corrected t-statistics computed using h lags, and adjusted R2 statistics in percent. Bold font indicates statistical signi…cance at the 5% level according to wild bootstrap p-values. The sample period runs from January 1970 to December 2016.

h=1

h=3

t-stat.

R2

-0.16

-3.74

2.69

World ex USA -0.14

-2.79

EAFE

-0.16

Europe

h = 12

t-stat.

R2

-0.50

-4.08

7.88

1.51

-0.46

-3.15

-3.14

1.90

-0.50

-0.13

-2.61

1.22

Paci…c

-0.18

-3.16

Far East

-0.19

-3.20

World

t-stat.

R2

-1.71

-3.53

20.63

4.88

-1.60

-2.86

12.86

-3.44

5.88

-1.73

-3.06

14.72

-0.42

-2.78

3.96

-1.47

-2.45

10.95

1.79

-0.58

-3.69

5.56

-1.97

-3.54

12.03

1.78

-0.60

-3.83

5.54

-2.07

-3.76

12.02

34

Table 3: Taking account of publication delays The table shows results from predictive regressions of monthly, quarterly and annual excess stock returns on three-month lagged monthly world output gap: rt+h = wogt

2

+

+ "t+h , where h denotes the horizon in months, rt+h is h-month excess stock

market return, and wogt is the world output gap. For each regression, the table reports OLS estimates of the regressor, Newey-West corrected t-statistics computed using h lags, and adjusted R2 statistics in percent. Bold font indicates statistical signi…cance at the 5% level according to wild bootstrap p-values. The sample period runs from January 1970 to December 2016.

h=1

h=3

t-stat.

R2

-0.17

-3.69

2.86

World ex USA -0.16

-3.04

EAFE

-0.17

Europe

h = 12

t-stat.

R2

-0.49

-3.77

7.47

1.91

-0.46

-3.06

-3.31

2.27

-0.50

-0.14

-2.67

1.43

Paci…c

-0.20

-3.54

Far East

-0.21

-3.63

World

t-stat.

R2

-1.58

-3.24

17.44

4.90

-1.48

-2.66

10.99

-3.30

5.76

-1.59

-2.83

12.51

-0.42

-2.62

3.95

-1.37

-2.29

9.59

2.24

-0.57

-3.71

5.42

-1.80

-3.21

9.98

2.24

-0.59

-3.89

5.43

-1.91

-3.42

10.22

35

36

+ wogt + "t+h , where h denotes the horizon in months, rt+h is h-month

-3.23

-3.39

World ex USA -2.72

-2.94

-2.70

-3.09

-3.35

EAFE

Europe

Paci…c

Far East

-3.27

-3.15

-3.25

-4.18

-2.85

World

R2

14.03 [-0.19,0.53]

13.65 [-0.19,0.47]

18.91 [-0.18,0.56]

19.81 [-0.18,0.54]

17.73 [-0.18,0.65]

28.23 [-0.19,0.58]

h = 24

t-stat.

-4.15

-3.75

-3.65

-3.76

-3.45

-3.57

-2.73

-2.59

-4.24

-3.32

-3.31

-5.03

R2

15.45 [-0.19,0.50]

14.53 [-0.19,0.43]

26.46 [-0.19,0.53]

22.95 [-0.19,0.55]

21.09 [-0.19,0.49]

32.26 [-0.19,0.63]

h = 36

t-stat.

predictability. The sample period runs from January 1970 to December 2016.

-4.34

-3.85

-4.49

-4.28

-3.93

-4.18

-1.91

-1.77

-4.56

-2.80

-2.88

-5.01

R2

14.41 [-0.19,0.56]

12.68 [-0.19,0.51]

32.12 [-0.19,0.62]

23.88 [-0.19,0.58]

22.69 [-0.19,0.53]

35.83 [-0.19,0.53]

h = 48

t-stat.

square brackets next to the R2 statistics, we report 90% con…dence intervals bootstrapped under the null hypothesis of no

at the 5% level or better according to wild bootstrap p-values. The column R2 shows adjusted R2 statistics in percent. In

regressor along with Newey-West corrected t-statistics computed using h lags. Bold font indicates statistical signi…cance

excess stock market return, and wogt is the world output gap. For each regression, the table reports OLS estimates of the

returns on monthly world output gap: rt+h =

The table shows results from long-horizon predictive regressions of two-, three-, and four-year excess stock market

Table 4: Long-horizon forecasts

Table 5: Comparison with economic return predictors The left haft of the table shows results from predictive regressions of excess stock returns on benchmark variables: rt+1 =

+ ztk + "t+1 , where rt+1 is monthly excess

stock market return and ztk is one of the economic predictor variables named in the …rst column. The right half of the table shows results from predictive regressions of excess stock returns on the world output gap and the respective benchmark variable: rt+1 =

+ wogt + ztk + "t+1 . For each regression, the table reports OLS estimates of the

regressor, Newey-West corrected t-statistics, and adjusted R2 statistics in percent. Bold font indicates statistical signi…cance at the 5% level or better according to wild bootstrap p-values. The sample period runs from January 1971 to December 2016.

37

Univariate regressions t-stat.

Bivariate regressions

R2

t-stat.

t-stat.

R2

Dividend-price ratio World

0.11

0.56

-0.10

-0.17

-3.70

-0.09

-0.44

2.67

World ex USA

0.15

0.69

-0.00

-0.15

-2.78

-0.03

-0.12

1.48

EAFE

0.16

0.71

-0.00

-0.17

-3.12

-0.04

-0.18

1.87

Europe

0.08

0.33

-0.16

-0.14

-2.59

-0.09

-0.38

1.09

Paci…c

0.27

1.06

0.00

-0.19

-3.12

0.04

0.16

1.84

Far East

0.30

1.16

0.10

-0.19

-3.13

0.07

0.28

1.80

In‡ation World

-0.78

-1.99

0.51

-0.16

-3.67

-0.65

-1.69

3.11

World ex USA -0.94

-1.93

0.57

-0.15

-2.77

-0.83

-1.70

2.07

EAFE

-0.97

-1.97

0.62

-0.16

-3.11

-0.85

-1.71

2.47

Europe

-0.58

-1.31

0.00

-0.13

-2.55

-0.48

-1.09

1.24

Paci…c

-1.11

-1.79

0.59

-0.19

-3.18

-0.97

-1.54

2.42

Far East

-1.02

-1.57

0.43

-0.19

-3.21

-0.87

-1.33

2.24

Treasury bill rate World

-0.95

-1.39

0.23

-0.17

-3.75

-0.87

-1.25

2.97

World ex USA -0.94

-1.19

0.12

-0.15

-2.86

-0.86

-1.07

1.73

EAFE

-0.91

-1.15

0.00

-0.17

-3.21

-0.82

-1.03

2.09

Europe

-0.76

-0.91

0.00

-0.14

-2.60

-0.69

-0.82

1.20

Paci…c

-1.08

-1.29

0.00

-0.19

-3.28

-0.98

-1.15

2.07

Far East

-0.97

-1.16

0.00

-0.20

-3.29

-0.87

-1.01

1.96

38

Table 6: Predicting country returns The table presents results from monthly predictive regressions of individual country returns on the world output gap or the local-country output gap. For each regression, the table reports OLS estimates of the regressor, Newey-West corrected t-statistics computed using one lag, and adjusted R2 statistics in percent. Column

in left (right) half of the

table shows the estimated weight on the predictive regression forecast based on the world (local-country) output gap in a combination forecast that takes the form of a convex combination of a predictive regression forecast by the world output gap and a predictive regression forecast by the local-country output gap. Bold font indicates statistical signi…cance at the 5% level or better according to wild bootstrap p-values or the p-values of the Harvey, Leybourne, and Newbold (1998) statistic. The top (bottom) panel of the table shows results for the period running from January 1970 to December 2016 (from January 1990 to December 2016).

39

Sample period 1970-2016 World output gap t-stat.

R2

Local output gap t-stat.

R2

Austria

-0.07

-1.18

0.12

0.64

-0.05

-1.03

0.00

0.36

Belgium

-0.22

-4.00

3.48 0.75

-0.16

-2.77

2.04

0.25

Canada

-0.08

-1.52

0.34

1.00

-0.03

-0.89

-0.00

0.00

France

-0.16

-3.05

1.33

0.66

-0.16

-2.54

1.15

0.34

Finland

-0.17

-1.56

0.58

1.00

-0.06

-1.32

0.32

0.00

Germany

-0.13

-3.40

0.82

0.13

-0.17

-3.07

1.79

0.87

Italy

-0.14

-2.17

0.62

0.00

-0.12

-2.47

0.91

1.00

Japan

-0.17

-3.16

1.70 0.68

-0.09

-2.41

1.00

0.32

Netherlands -0.20

-4.05

2.83 0.72

-0.17

-3.37

2.11

0.29

Norway

-0.09

-1.16

0.13

0.98

-0.02

-0.67

-0.10

0.02

Portugal

-0.10

-1.31

0.27

0.36

-0.09

-1.49

0.41

0.64

Spain

-0.12

-1.99

0.54

0.30

-0.07

-2.23

0.64

0.70

Sweden

-0.22

-3.36

2.21 1.00

-0.08

-2.48

1.10

0.00

Switzerland

-0.15

-3.42

1.77 0.82

-0.10

-2.58

0.95

0.18

UK

-0.20

-4.49

2.40 1.00

-0.13

-3.30

1.22

0.00

US

-0.16

-3.93

2.55 1.00

-0.09

-3.14

1.46

0.00

40

Sample period 1990-2016 World output gap t-stat.

R2

Local output gap t-stat.

R2

Austria

-0.23

-1.69

1.18

0.98

-0.12

-1.32

0.61

0.02

Belgium

-0.32

-3.49

4.52 0.66

-0.20

-2.47

3.41

0.34

Canada

-0.14

-2.00

1.22

1.00

-0.04

-0.70

-0.00

0.00

France

-0.18

-2.07

1.23

1.00

-0.14

-1.80

0.84

0.00

Finland

-0.37

-2.67

1.95

0.00

-0.25

-3.52

2.76

1.00

Germany

-0.20

-2.15

1.16

0.00

-0.20

-3.05

2.65

1.00

Italy

-0.25

-2.45

1.71

1.00

-0.18

-2.20

1.40

0.00

Japan

-0.25

-2.56

2.26

1.00

-0.11

-1.95

0.96

0.00

Netherlands -0.23

-2.91

2.41

0.47

-0.28

-2.88

2.60

0.53

Norway

-0.24

-2.26

1.55 0.99

0.01

0.13

-0.31

0.01

Portugal

-0.26

-2.75

2.43 1.00

-0.11

-1.76

0.77

0.00

Spain

-0.21

-2.02

1.15

1.00

-0.08

-1.60

0.47

0.00

Sweden

-0.34

-3.16

3.02

1.00

-0.20

-2.81

2.25

0.00

Switzerland

-0.21

-2.75

2.43 0.68

-0.13

-2.42

1.56

0.32

UK

-0.15

-2.18

1.46

1.00

-0.10

-1.34

0.31

0.00

US

-0.17

-2.41

1.79 1.00

-0.05

-0.89

0.00

0.00

41

Table 7: Out-of-sample forecasting results The table presents results of comparisons of out-of-sample forecasts of monthly excess stock returns. The forecasts are based on a constant (the restricted model) and on a constant and world output gap (the unrestricted model). The world output gap is 2 computed recursively based on updated time trend parameter estimates. ROS is the

out-of-sample R2 in percent de…ned as in Campbell and Thompson (2008). We employ the Clark and West (2007) adjusted statistic for testing the statistical signi…cance of 2 the ROS statistics. EN C-N EW is the Clark and McCracken (2001) encompassing test

statistic. The 95% critical value associated with EN C-N EW is 2.69 as derived in Clark and McCracken (2001). M SE-F is the McCracken (2007) F -statistic. The 95% critical value associated with M SE-F is 1.52 as derived in McCracken (2007). CER gain is the annualized certainty equivalent return gain in percent. Bold font indicates statistical signi…cance at the 5% level or better. The out-of-sample evaluation period runs from January 1990, January 1995 or January 2000.

42

2 ROS

EN C-N EW

M SE-F

CER

Forecasting from 1990 World

3.09

15.83

10.33

2.56

World ex USA 2.37

13.48

7.88

1.05

EAFE

2.24

14.24

7.44

0.99

Europe

1.51

8.64

4.95

0.32

Paci…c

2.45

15.31

8.13

2.23

Far East

1.70

15.31

5.62

1.74

Forecasting from 1995 World

2.82

13.65

7.66

4.16

World ex USA 1.95

12.08

5.24

1.07

EAFE

1.67

12.76

4.50

1.09

Europe

1.42

7.57

3.80

0.42

Paci…c

1.78

16.23

4.77

2.97

Far East

0.63

15.12

1.66

2.84

Forecasting from 2000 World

4.89

14.31

10.48

3.38

World ex USA 3.11

11.81

6.54

-0.49

EAFE

2.88

12.48

6.06

-0.72

Europe

2.36

7.44

4.93

-1.04

Paci…c

2.06

16.80

4.29

1.64

Far East

0.19

15.64

0.38

1.12

43

Table 8: Predicting one-year-ahead world market returns The table presents results from regressions of one-year-ahead excess world stock market returns on lagged world output gap or lagged log growth rate in global industrial production. Q1 denotes the …rst-quarter realization of the world output gap or the …rstquarter log growth rate of global industrial production, i.e. the growth rate between the fourth quarter of last year and the …rst quarter of current year. Q2, Q3 and Q4 denote the second-, third- and fourth-quarter realizations of the world output gap or the second-, third- and fourth-quarter log growth rates of global industrial production. For Q1, the one-year-ahead excess stock return is measured from the beginning of the second quarter to the end of the …rst quarter next year. For Q2, the one-year-ahead excess stock return is measured from the beginning of the third quarter to the end of the second quarter next year. For Q3, the one-year-ahead excess stock return is measured from the beginning of the fourth quarter to the end of the third quarter next year. For Q4, the one-year-ahead excess stock return is measured over the next calendar year. For each regression, the table reports OLS estimates of the regressor, Newey-West corrected t-statistics computed using four lags, and adjusted R2 statistics in percent. Bold font indicates statistical signi…cance at the 5% level or better according to wild bootstrap p-values. The sample period runs from 1970Q1 to 2016Q4.

44

45

-3.02

-2.11

-1.87

-2.30

-2.38

EAFE

Europe

Paci…c

Far East

-1.37 -1.29

World ex USA -2.59

-2.50

-2.40

-2.48

-1.87

EAFE

Europe

Paci…c

Far East

-1.02

-1.33

-1.18

-1.67

-3.71

-3.42

-2.65

World

-2.86

World ex USA -2.02

-2.47

-3.19

-1.96

World

t-stat.

Q1 R2

-1.66

-1.58

-1.38

-1.51

-1.39

-1.48

-3.07

-2.95

-3.12

-3.19

-3.00

-3.97

7.23

7.51

8.35

12.01

9.72

16.48

-1.94

-1.77

-1.19

-1.48

-1.35

-1.56

Panel A: World output gap

t-stat.

-3.15

-2.81

-2.29

-2.60

-2.47

-3.23

t-stat.

Q3

-1.21

-0.16

0.74

0.87

1.15

2.80

-0.99

-1.01

2.01

0.43

0.91

-0.62

-0.29

-0.35

0.88

0.21

0.41

-0.34

-2.06

-2.01

-0.83

-2.20

-1.94

-2.06

-4.74

-5.03

-1.21

-3.04

-2.28

-3.10

-1.31

-1.41

-0.32

-0.97

-0.77

-0.96

Panel B: Global industrial production growth

12.41

13.04

13.27

16.70

15.43

21.36

R2

Q2

0.13

0.66

-1.96

-0.51

-1.26

0.00

7.78

6.72

5.25

8.02

6.52

12.41

R2

-3.81

-4.41

-4.51

-4.57

-4.27

-4.13

-2.24

-2.09

-1.49

-1.79

-1.63

-1.80

-2.51

-3.55

-3.64

-4.19

-4.76

-3.75

-3.64

-3.37

-2.71

-3.14

-2.93

-3.55

t-stat.

Q4

1.90

3.94

8.14

8.01

7.20

9.33

11.60

11.21

8.66

12.86

10.97

18.84

R2

Table 9: Monthly predictive regressions of one-year-ahead world market returns The table presents results from monthly regressions of one-year-ahead excess world stock market returns on monthly lagged world output gap or monthly lagged log growth rates of global industrial production. When using the December values of predictor variables, the one-year-ahead excess stock return is measured over the next calendar year; when using the November values of predictor variables, the one-year-ahead excess stock return is measured from the beginning of December to the end of November next year, etc. For each regression, the table reports OLS estimates of the regressor, Newey-West corrected t-statistics computed using twelve lags, and adjusted R2 statistics in percent. Bold font indicates statistical signi…cance at the 5% level or better according to wild bootstrap p-values. The sample period runs from January 1970 to December 2016. t-stat.

R2

World output gap

t-stat.

R2

Global IP growth

January

-1.98

-5.32

24.84

0.77

0.27

-2.07

February

-2.23

-5.04

28.44

-6.66

-2.38

3.96

March

-1.97

-4.84

22.15

0.72

0.28

-2.21

April

-1.70

-5.56

21.75

-1.90

-0.74

-1.03

May

-1.47

-8.17

17.56

0.15

0.04

-2.27

June

-1.44

-8.19

15.81

2.66

0.87

-1.15

July

-1.49

-7.00

16.17

1.06

0.42

-2.06

August

-1.33

-5.76

12.45

-1.85

-0.45

-1.29

September -1.68

-4.50

14.04

-1.01

-0.36

-2.05

October

-1.69

-5.98

16.94

-5.33

-2.01

1.35

November

-1.68

-5.46

16.92

-5.26

-3.15

3.26

December

-1.93

-5.57

23.78

-6.24

-5.90

10.44

46

Table 10: Forecasting dividend-price ratios and dividend growth rates The table presents results from monthly predictive regressions of the form yt+1 = + wogt + dpt + dgt + "t+1 , where yt+1 denotes either log dividend-price ratio (dpt+1 ) or log dividend growth rate (dgt+1 ), and wogt is the world output gap. Panel A shows dividend-price ratio forecasting regressions; Panel B shows dividend growth rates forecasting regressions. For each regression, the table reports OLS estimates of the regressor, Newey-West corrected t-statistics, and adjusted R2 statistics in percent. Bold font indicates statistical signi…cance at the 5% level or better according to wild bootstrap p-values. The sample period runs from January 1971 to December 2016. Panel A: Forecasting dividend-price ratio t-stat.

t-stat.

t-stat.

R2

World

0.36

4.08

1.00

95.75

-1.26

-3.54

96.91

World ex USA

0.36

3.58

0.99

84.40

-1.27

-5.03

96.14

EAFE

0.38

3.90

0.99

84.64

-1.30

-5.46

96.26

Europe

0.33

3.20

1.00

72.46

-1.42

-6.92

95.26

Paci…c

0.39

3.67

0.98

97.69

-0.80

-4.53

96.70

Far East

0.42

4.01

0.98

96.00

-0.75

-3.52

96.68

Panel B: Forecasting dividend growth rates World

-0.05

-3.61

0.00

0.58

0.31

2.69

16.09

World ex USA -0.08

-3.31

0.01

2.72

0.27

2.44

17.20

EAFE

-0.07

-2.91

0.01

3.01

0.25

2.31

15.45

Europe

-0.08

-3.05

0.01

2.61

0.23

2.67

13.68

Paci…c

-0.04

-1.28

0.00

2.55

-0.04

-0.53

0.92

Far East

-0.06

-2.00

0.01

3.22

-0.02

-0.18

2.88

47

0.1 0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 1. World output gap. The …gure shows a time-series plot of the world output gap. Shaded areas denote OECD recession indicator for G7 countries. The sample period is January 1970 to December 2016.

48

Appendix: Bootstrap procedure for computing empirical p-values This section describes the wild bootstrap algorithm used to compute empirical pvalues. Building on Mark (1995) and Kilian (1999), our procedure accounts for the persistence in the regressor and the correlation between equity risk premium and predictor innovations, thereby being valid under Stambaugh (1999) speci…cation. Following Neely, Rapach, Tu, and Zhou (2014) and Atanasov, Møller, and Priestley (2018) the algorithm consists of three steps.

1. The bootstrap distributions are built upon estimated values of the restricted vector autoregression (VAR). In particular, we estimate a long-horizon regression of the form

rt+h =

+ wogt + "t+h ;

(A1)

where h denotes the horizon in months, rt+h is h-month excess stock market return, and wogt is the world output gap. Assuming that the persistent predictor follows an AR(1) process wogt+1 =

0

+

1 wogt

+

t+1 ;

(A2)

we then de…ne bct+1 = wogt+1

(bc0 + bc1 wogt );

(A3)

where bc0 and bc1 are reduced-bias estimates12 of the AR(1) parameters in (A2) obtained as bc1

b1 +

1+3b1 T 1

and bc0 = wog t+1

residuals b "t+h and bt+1 , and t-statistics of

bc1 wog t . The parameters bc0 and bc1 , the …tted estimates are saved.

2. In each replication b = 1, ..., 2,000, we draw a vector sequence wtb from a standard 12

Iterating on the analytical second-order bias expression for the OLS estimates produces very similar results.

49

normal distribution and construct a pseudo-sample of observations for the excess stock market return and the world output gap under the null of no return predictability:

b b ; = rt+h + b "t+h wt+h rt+h

b b ; wogt+1 = bc0 + bc1 wogtb + bct+1 wt+1

(A4) (A5)

where rt+h is the sample mean of excess stock market return and wtb is a draw from the standard normal distribution. We use the …rst observation of wogt for the initial value of "t+h , and skip the …rst h values in wtb for wogtb and zeros for the initial values of bct+1 and b b b b . We then employ demeaned series b "t+h wt+h and bct+1 wt+1 as pseudo-residuals. Notice wt+h

that in the wild bootstrap, we multiply b "t+h and bct+1 in (A4) and (A5) by the same scalar from the vector wtb , when generating the pseudo-residuals. Thus, the wild bootstrap not only preserves the contemporaneous correlations in the data but also accounts for general forms of conditional heteroskedasticity.

3. In each replication, we use the arti…cial data from pseudo-samples for the equity premium and the world output gap to estimate long-horizon regressions of the form:

b rt+h =

b

+

b

wogtb + "bt+h :

(A6)

We estimate the slope coe¢ cients and save the corresponding heteroskedasticity-robust t-statistics in (A6). Repeating this process 2,000 times yields empirical distributions for each of the t-statistics. We follow Inoue and Kilian (2004) and compute one-sided empirical p-values as the proportion of the bootstrapped t-statistics smaller than the t-statistic from the original sample.

50

Table A1: IVX-Wald and qLL-statistics The table shows Kostakis, Magdalinos, and Stamatogiannis (2015) IVX-Wald and qLL-statistics of Elliott and Müller (2006) for the benchmark predictive regression model: rt+h =

+ wogt + "t+h , where h denotes the horizon in months, rt+h is h-month stock

market return, and wogt is the world output gap. The IVX-Wald statistic tests the hypothesis H0 :

= 0 against H1 :

6= 0. The 10%, 5%, and 1% critical values are 2.71,

3.84, and 6.64. The qLL-statistic tests the hypothesis H0 :

t

=

for all t. The 10%, 5%,

and 1% critical values are -12.80, -14.32, and -17.57. h=1

h=3

h = 12

IVX-Wald

qLL

IVX-Wald

qLL

IVX-Wald

qLL

World

17.51

-4.74

45.66

-4.76

94.23

-2.75

World ex USA

10.99

-3.75

29.18

-4.11

56.18

-2.79

EAFE

13.11

-4.35

34.69

-4.42

65.70

-2.93

Europe

8.20

-4.62

22.87

-4.48

52.63

-2.48

Paci…c

12.89

-3.25

33.29

-3.81

46.12

-3.70

Far East

13.01

-2.87

33.12

-3.51

49.65

-3.63

51

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