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TRANSCRIPT
The Dog Has Barked for a Long Time: Dividend
Growth is Predictable∗
Andrew Detzel†
University of DenverJack Strauss‡
University of Denver
September 19, 2016
Abstract
Motivated by the Campbell-Shiller present-value identity, we propose a new method of fore-casting dividend growth that combines out-of-sample forecasts from 14 individual predictiveregressions based on common return predictors. Combination forecast methods generate robustout-of-sample predictability of annual dividend growth over the entire post-war period as wellas most sub-periods with out-of-sample R2 up to 18.6%. The dividend-growth forecasts coupledwith the dividend-price ratio also significantly forecast annual excess returns with out-of-sampleR2 up to 12.4%. In spite of robust dividend predictability, we find that most variation in thedividend-price ratio is still attributable to variation in expected returns.
JEL classification: G12, G17Keywords: Dividend growth, Return predictability
∗We thank Yosef Bonaparte, John Elder, Yufeng Han, Ralph Koijen, Xiao Qiao, Harry Turtle, Tianyang Wang(Discussant), Guofu Zhou, and participants at the University of Colorado Denver Front Range Finance Seminar and2016 World Finance Conference for helpful comments. We thank Amit Goyal and Ivo Welch for making all necessarydata available.
The Dog Has Barked for a Long Time: DividendGrowth is Predictable
Abstract
Motivated by the Campbell-Shiller present-value identity, we propose a new method offorecasting dividend growth that combines out-of-sample forecasts from 14 individualpredictive regressions based on common return predictors. Combination forecast meth-ods generate robust out-of-sample predictability of annual dividend growth over theentire post-war period as well as most sub-periods with out-of-sample R2 up to 18.6%.The dividend-growth forecasts coupled with the dividend-price ratio also significantlyforecast annual excess returns with out-of-sample R2 up to 12.4%. In spite of robustdividend predictability, we find that most variation in the dividend-price ratio is stillattributable to variation in expected returns.
1. Introduction
Following the present value identity of Campbell and Shiller (1988), a large literature investigates
whether the dividend-price ratio forecasts returns or dividend growth.1 Regression-based tests
frequently fail to find that the dividend-price ratio predicts dividend growth and conclude that time
variation in the dividend-price ratio primarily results from variation in expected expected returns
(see, e.g., Cochrane (2008), Cochrane (2011)). However, these regression-based tests suffer from
at least two econometric problems that limit their inferences about dividend-growth predictability,
which is important as dividend forecasts are a key input to equity and contingent-claim valuation.
First, only using the dividend-price ratio in dividend-growth-forecasting regressions incorrectly
limits the set of candidate predictive variables. Under the present value identity, the dividend-price
ratio should only forecast dividend growth controlling for expected future returns (see, e.g., Golez
(2014)), and vice versa. By similar logic, any predictor of returns should also forecast dividend
growth and the prior literature finds that numerous variables forecast returns (see, e.g. Rapach,
Strauss and Zhou (2010) and Cochrane (2011))). Second, predictive regressions based on the
dividend-price ratio exhibit statistical biases due to the persistence of the dividend-price ratio as
well as structural breaks that limit their out-of-sample reliability (see, e.g. Stambaugh (1999),
Lettau and van Nieuwerburgh (2008) and Koijen and Van Nieuwerburgh (2011)).
In this paper, we investigate whether dividend growth is predictable out-of-sample by using
combination forecast methods. Our combination forecasts are weighted averages of out-of-sample
univariate dividend-growth forecasts using 14 common return predictors identified by Goyal and
Welch (2008). Stock and Watson (2004), Timmermann (2006), and Rapach et al. (2010) find
that combination forecast methods frequently overcome the two sets of econometric problems cited
above. They produce structurally stable and reliable out-of-sample forecasts of macroeconomic
time series and returns from relatively unstable univariate forecasts.
We find that the dividend-price ratio as well as other common return predictors fail to indi-
vidually predict dividend growth out-of-sample. However, we show that a variety of combination
1See for instance, work by Menzly, Santos and Veronesi (2004), Lettau and Ludvigson (2005), Ang and Bekaert(2007), Cochrane (2008), Chen (2009), van Binsbergen and Koijen (2010), Engsted and Pedersen (2010), Golez (2014),Rangvid, Schmeling and Schrimpf (2014).
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forecast methods generate significant out-of-sample evidence of dividend-growth predictability for
horizons of one or two years over the entire post-war sample period. The simple average of the
different combination forecasts predicts dividend growth with an out-of-sample R2 of more than
16% at the one-year horizon. Goyal and Welch (2008) find return forecasting relationships change
over time and we investigate whether the same is true for dividend growth. The combination
dividend-growth forecasts provide significant out-of-sample predictability over most subsamples.
The present value identity of Campbell and Shiller (1988) implies that return and dividend-
growth predictability are “two sides of the same coin” because controlling for the dividend-price
ratio, any predictor of returns must predict dividend growth, and vice versa (see, e.g., Cochrane
(2008), Koijen and Van Nieuwerburgh (2011), and Cochrane (2011)). Following this logic, we
combine our combination forecasts of dividend growth with the dividend-price ratio to forecast
excess returns. The resulting return forecasts have large and significant out-of-sample R2 (about
11% at the one-year horizon, for example) and at short horizons outperform combination forecasts
of returns based directly on the 14 Goyal and Welch (2008) return predictors.
The Campbell-Shiller identity implies that variation in the dividend-price ratio must be ex-
plained by the variances of, and covariances between, expected future returns and dividend growth.
The aforementioned out-of-sample tests show that combination forecasts of dividend growth and
returns provide relatively accurate proxies for expected dividend-growth and returns and therefore
we use these forecasts to decompose the variance of the dividend-price ratio. The standard alterna-
tive method of decomposing price variation into cash-flow and discount-rate components is based
on vector autoregressions (VAR) and depends critically on a Kitchen sink-like forecast of returns
that performs poorly out-of-sample. Empirically, this problem manifests in VAR-based decomposi-
tions yielding results that are highly sensitive to specification, and often exaggerate the importance
of cash-flow news (see, e.g. Chen and Zhao (2009)). Conversely, our decomposition is based on
forecasts that we show perform well out-of-sample. We find that in spite of robust out-of-sample
predictability of dividend growth, the variance of expected dividend growth explains about 10%
or less of the variance of the dividend-price ratio, with 74% or more explained by the variance of
expected returns. Covariance between expected returns and dividend growth explains the remain-
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ing variation. Our estimated decompositions are consistent with relatively persistent and volatile
expected returns and are close to the analogous results from the seminal study of Campbell (1991).
However, several more recent studies attribute significantly more price variation to the variance
of expected dividend growth (see, e.g., Bernanke and Kuttner (2005), Chen and Zhao (2009), and
Golez (2014)).
Besides combination forecast methods, another econometric approach that generates dividend-
growth predictability out-of-sample uses restrictions from present value models such as that of
Campbell and Shiller (1988) to analyze the joint dynamics of expected returns and dividend growth
(van Binsbergen and Koijen (2010), Rytchkov (2012), Kelly and Pruitt (2013), Golez (2014), and
Bollerslev, Xu and Zhou (2015)). Sabbatucci (2015) also finds evidence of dividend-growth pre-
dictability by defining dividends to incorporate cash flows to shareholders that arise from mergers
and acquisition activities. These papers focus on the predictive power of the dividend-price ratio
or similar valuation ratios. They also do not find out-of-sample dividend-growth predictability
over the entire post-war period. In contrast, our paper expands on these results by (i) finding
out-of-sample forecasting power of other predictors for dividend growth, (ii) showing it holds over
the entire post-war period, and (iii) doing so without redefining dividends.2
The remainder of this paper proceeds as follows. Following the review of related literature in
section 2, section 3 explains our data and empirical methods. Section 4 describes our data and
results and section 5 concludes.
2. Related Literature
Following the present value decomposition of Campbell and Shiller (1988), a vast literature inves-
tigates whether variation in the market dividend-price ratio represents discount-rate or cash-flow
news. The most common way to investigate this question is predictive regressions of future re-
turns and dividend growth of the aggregate U.S. stock market on the market dividend-price ratio.
These regressions generally attribute most, if not all, of the variation to discount-rate news (see,
2Contingent-claim valuation, for example, relies on dividend forecasts per se, not total payouts to shareholderssuch as repurchases.
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e.g., Koijen and Van Nieuwerburgh (2011) for a recent survey). This is commonly interpreted as a
stylized fact that aggregate stock returns are predictable by the dividend-price ratio but dividend
growth is not (see, e.g., Cochrane (1992), Lettau and van Nieuwerburgh (2008), Cochrane (2008),
and Cochrane (2011)).
While much of this literature has focused on return predictability,3 several recent studies find
evidence of dividend-growth predictability, though they typically use methods besides predictive
regressions with the dividend-price ratio. One exception is Chen (2009), who shows that dividend-
growth predictability from regressions on the dividend-price ratio is present in the U.S., but only
prior to 1945. However, Chen (2009) does not find evidence of dividend-growth predictability post-
war or over the full sample. In contrast, by combining other forecasts, we find robust out-of-sample
dividend-growth predictability in the post-1945 sample.
Using restrictions from present value models similar to those of Campbell and Shiller (1988),
several recent studies analyze the joint dynamics of expected returns and dividend growth (van
Binsbergen and Koijen (2010), Kelly and Pruitt (2013), Piatti and Trojani (2013), Golez (2014),
and Bollerslev et al. (2015)). Most of these find some evidence of dividend-growth predictability
and the first two find out-of-sample evidence of dividend-growth predictability. While we have
a similar result of out-of-sample dividend-growth predictability, we expand on these results in at
least two ways. First, the present value model-based approaches generate predictability from the
dividend-price ratio or other valuation ratios whereas our source of dividend-growth predictability
stems from other common predictors besides just valuation ratios. Second, these studies focus on a
single model specification, whereas we show robust predictability with multiple specifications over
multiple time periods.
van Binsbergen and Koijen (2010) model expected returns and dividend growth rates as latent
processes and use filtering techniques to show that both of them are predictable using a present-
value framework. Our paper extends their work in a number of ways. We demonstrate dividend-
3See, e.g., Pesaran and Timmermann (1995), Kothari and Shanken (1997), Lettau and Ludvigson (2001), Lewellen(2004), Robertson and Wright (2006), Campbell and Yogo (2006), Boudoukh, Michaely, Richardson and Roberts(2007), Goyal and Welch (2008), Campbell and Thompson (2008), Lettau and van Nieuwerburgh (2008), Koijen andVan Nieuwerburgh (2011), Ferreira and Santa-Clara (2011), Shanken and Tamayo (2012), Li, Ng and Swaminathan(2013), Johannes, Korteweg and Polson (2014) are some of the recent papers focusing on return predictability.
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growth predictability using predictive regressions, report out-of-sample results for a significantly
longer time period (1946-2014 compared to 1973-2007), and demonstrate robustness over multiple
subsamples and horizons as well as with multiple combination methods. We also show that excess
return forecasts based on dividend growth also outperform those based on combination forecasts
of the common return predictors of Goyal and Welch (2008). Kelly and Pruitt (2013) additionally
generate forecasts that incorporate a Campbell and Shiller (1988)-type present value relationship
and combine multiple valuation-ratio predictors to find evidence of return predictability. Zhu
(2015) finds evidence of a time-varying relationship between dividend growth and the dividend-price
ratio. Sabbatucci (2015) further finds out-of-sample evidence of dividend growth predictability by
constructing a dividend measure that includes cash flows from mergers and acquisitions.4
Several studies find dividend-growth predictability in different markets than the aggregate U.S.
stock market. Engsted and Pedersen (2010) and Rangvid et al. (2014) identify dividend-growth
predictability in markets outside of the U.S. using the standard predictive regression approach.
Maio and Santa-Clara (2015) show that while aggregate U.S. dividends are difficult to forecast
with the dividend-price ratio, those of small-cap and value stocks are much easier to forecast,
though they only present results in sample. Ang and Bekaert (2007) and Lettau and Ludvigson
(2005) also find in-sample evidence of dividend-growth predictability with predictors besides the
dividend-price ratio or other valuation ratios. We expand on this evidence by showing out-of-sample
dividend-growth predictability with a broader set of predictive variables.
3. Data and Methods
The Campbell and Shiller (1988) present value-identity yields the following relationship between the
log dividend-price ratio (dpt), expected future log returns (rt+u), and log dividend growth (dgt+u):
dpt = Et
∞∑j=1
ρjrt+1+j − Et
∞∑j=0
ρjdgt+1+j , (1)
4Our work extends their work similar to what is mentioned above - longer time period, multiple sub-samples andhorizons, and use multiple combination methods.
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where ρ is a log-linearization constant. In particular, Eq. (1) implies that controlling for the
dividend-price ratio, any predictor of the discounted sums of future returns must also forecast
the discounted sums of future dividend growth. Hence, to identify candidate dividend-growth
predictors, we use common return predictors. We describe these predictors below, as well as our
methods for efficiently combining the forecasting information in them.
3.1. Data
3.1.1. Market returns and dividend growth
We use the CRSP value-weighted index as a proxy for the market return and the three-month Trea-
sury bill for the risk-free rate. We identify monthly dividends via the difference between monthly
returns with and without dividends. Due to seasonality, it is necessary to aggregate dividends an-
nually, which in turn requires an assumption about dividend reinvestment. Following Chen (2009),
Koijen and Van Nieuwerburgh (2011), and Golez (2014) we form twelve-month dividend series
(D12) by summing dividends over the most recent twelve months D12t =
∑ts=t−11Ds, which implic-
itly assumes no re-investment of dividends. The two alternatives are reinvestment at the risk-free
rate, which is known to perform similarly, and reinvestment in the market return. The latter op-
tion is problematic for studying dividend growth predictability because it adds excess volatility to
dividend growth processes and conflates return predictability with dividend growth predictability.
One-quarter log dividend growth in quarter t (dgt) is defined by:
dgt = log(D12
t /D12t−1). (2)
With this definition, dividend growth over quarters t+1 through t+h (relative to quarters t−h+1
to t) is given by:
dgt+1,t+h =
t+h∑u=t+1
dgu. (3)
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3.1.2. Dividend and return predictor data
Following Goyal and Welch (2008), Rapach et al. (2010), and Kelly and Pruitt (2013) we use the
quarterly return predictors taken from Amit Goyal’s website5. Our goal is to forecast dividend
growth over the entire post-war period (1946-present) given that this sample shows the weakest
evidence of dividend-growth predictability (see, e.g. Chen (2009)). Hence, we require a substantial
pre-war time-series to form initial out-of-sample forecasts. However, Kelly and Pruitt (2013) find
that including highly volatile depression error observations reduces the performance of out-of-sample
forecasts much later on in history, so we wish to trim depression era observations. To balance these
trade-offs, we choose a sample start date 1936:1, 10 years before the desired out-of-sample period
begins, but excluding many of the most volatile depression-era observations. Thus, we choose the
14 Goyal-Welch predictor variables that are available since 19366:
• Log Dividend-price ratio, dp: Natural log of the ratio of the 12-month dividend to the currentprice on the S&P500 index.
• Log earnings-price ratio, ep: Natural log of the ratio of one-year summed earnings on theS&P 500 index to the price-level of the index.
• Log Dividend-payout ratio, de: Natural log of the dividends-to-earnings on the S&P 500 index.
• Stock variance, SV AR: Sum of squared daily returns on the S&P500 index.
• Book-to-market ratio, B/M : Book-to-market ratio of the Dow Jones Industrial Average.
• Net equity issuance, NTIS: Ratio of twelve-month moving sums of net issues by NYSE-listedstocks to total end-of-year market capitalization of NYSE stocks.
• Treasury bill rate, TBL: Yield on a three-month Treasury bill (secondary market).
• Long-term yield, LTY : Long-term government bond yield.
• Term spread, TMS: Difference between LTY and TBL.
• Default yield spread, DFY : Difference between BAA- an AAA-rated corporate bond yields.
• Default return spread, DFR: Difference between long-term corporate bond and long-termgovernment bond returns.
• Inflation, INFL: Calculated from the CPI (all urban consumers); following Goyal and Welch(2008), we use an extra one-month lag xi,t−1 of inflation because it is released the followingmonth.
5http://www.hec.unil.ch/agoyal/docs/PredictorData2015.xlsx6There are actually 15 variables available since 1936 but the dividend yield (which is the dividend/stock price
last year) and dividend price ratio (dividend/current stock price) are very highly correlated. Hence, we exclude thedividend-yield. All results are robust to this choice.
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• Investment-to-capital ratio, I/K: Ratio of aggregate (private nonresidential fixed) investmentto aggregate capital for the entire economy (Cochrane (1991)).
This set is not exhaustive of all known return predictors, however, they are widely used and available
over our long sample period, which is why Goyal and Welch (2008) investigate them. The Goyal
and Welch (2008) predictors are a standard and fixed set mitigating data mining concerns. Other
predictors are generally not available, or at least not out-of-sample, for our sample period (see, e.g.,
cay of Lettau and Ludvigson (2001), and the variance risk premium of Bollerslev, Tauchen and
Zhou (2009)).
Table 1 presents the pairwise correlations of the different return predictors. The average ab-
solute correlation between them is 0.23 and aside from high correlations between variables that
are conceptually similar (e.g. D/P , B/M , and E/P ) the correlations are almost always less than
0.5. The relatively low correlation indicates that each predictor generally adds non-redundant
information that combination forecasts can potentially extract and integrate.
3.2. Combination forecast methods
Combining information from multiple predictors is a common and nontrivial problem in Asset
Pricing. Regression-based return forecasts, especially multivariate ones, often exhibit structural
breaks that result in poor out-of-sample performance (e.g., Goyal and Welch (2008), Rapach et al.
(2010), and Kelly and Pruitt (2013)). In contrast, combination forecast methods, which we use to
predict dividend growth, tend to perform well out-of-sample in the presence of model uncertainty
and structural breaks when forecasting market returns and other economic time series (e.g., Stock
and Watson (2004), Rapach et al. (2010), or Timmermann (2006)).
3.2.1. Step 1: Univariate Predictive regressions
The basic building block for our combination forecasts are univariate out-of-sample forecasts of
dividend growth, estimated recursively in real time for each of the return predictors:
dgt+1,t+h = αi + βixi,t + εt+1,t+h, (4)
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where xi,t is the ith predictive variable (i = 1, ..., N), and h is the forecast horizon. To avoid
seasonality of dividends, h is always a multiple of 4 quarters. Following Goyal and Welch (2008),
we generate out-of-sample forecasts (d̂gi,t+1,t+h) by estimating (4) using only data available through
time t. The d̂gi,t+1,t+h therefore simulate real-time forecasts that market participants could form
based on predictive regressions with the predictor xi,t.
3.2.2. Step 2: Combining forecasts
A combination forecast of dgt+1,t+h made at time t is a weighted averages of the N individual
forecasts based on (4):
d̂gc
t+1,t+h =N∑i=1
wci,td̂gi,t+1,t+h. (5)
Different combination forecasts (denoted c) are defined by the choice of weighting schemes {wci,t}.
The different combination forecast weights can be simple functions such as an equal-weighted mean
(MEAN, wMEANj,t ≡ 1/N), or time-varying functions of prior forecast performance that give low
weight to forecasts that have large past errors, and vice versa. There is generally no ex ante optimal
combination method for a given time series, it is an empirical question (see, e.g. Timmermann
(2008)). We therefore compare several methods. We use the MEAN method, which is the simplest
and most common combination method, as well four performance-based combination forecasts. If
the forecast errors of the individual forecasts have equal variance and equal pairwise correlation,
the MEAN combination method is optimal in that it produces the combination forecast with the
minimum mean-squared forecast error. Further, MEAN involves no estimation error and therefore
often empirically outperforms estimates of theoretically “optimal” weights in finite samples (e.g.,
Timmermann (2008)).
The first performance-based method, the discounted mean-squared forecast error (DMSFE)
follows Bates and Granger (1969) and Stock and Watson (2004) and chooses weights:
wDMSFEi,t =
φ−1i,t∑nj=1 φ
−1i,t
, (6)
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where
φi,t =t−h∑s=m
θt−1−s(dgs+1,s+h − d̂gi,s+1,s+h)2, (7)
and θ ∈ (0, 1] is a discount factor. The DMSFE method works well in the case where correlation
between individual forecast errors is unimportant relative to the associated estimation error in
estimating ex-ante optimal weights (Bates and Granger (1969)). When θ = 1, DMSFE does not
discount forecast errors further in the past. When θ < 1, greater weight is attached to the more
recent forecast accuracy of the individual models. Discounting past observations more heavily works
well if the data-generating process is more time-varying. However, the cost of higher discounting is
greater volatility of estimated weights, which reduces forecast performance if the data-generating
process is more stable. Ex ante, it is not obvious what level of discounting is appropriate for
dividend growth and return forecasts, so we compare three levels of θ (1, 0.8, and 0.6).
Our second performance-based method, the Approximate Bayesian Model Averaging (ABMA),
follows Garratt, Lee, Pesaran and Shin (2003) and chooses:
wABMA(IC)i,t =
exp(∆i,t)∑nj=1 exp(∆i,t)
, (8)
where ∆i,t = IChi,t - maxj(IC
hi,t), and ICh
i,t is either the Akaike-Information-Criterion (AIC) or
Schwarz-Information-Criterion (SIC) corresponding to the fitted model. The ABMA thus gives
higher weight to models with better historical fit as measured by AIC or SIC.
The third of the performance-based forecast combination methods uses a clustering approach
following Aiolfi and Timmermann (2006). In the clustering approach Ck, we first sort the univariate
forecasts into k = 2, 3, or 4 clusters using a k-means algorithm applied to the mean-squared forecast
error (MSFE) of the univariate forecasts through time t. Then, we choose wit = 0 for i in each
cluster except for the one with the lowest MSFE and then wit = 1/N1, where N1 denotes the
number of forecasts in the cluster with the lowest MSPE (cluster 1). Intuitively, the cluster
method identifies and discards predictors that persistently perform poorly in predicting dividend
growth.
The fourth of the performance-based forecast combination methods is the principal components
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method of Stock and Watson (2004), denoted PCk with a choice of k principal components. The
first step of PCk is to estimate the first k principal components (F1t, ..., Fkt) of the individual
forecasts {d̂gi,s+1,s+h}t−hs=0 at each point in time t. The second step of PCk is to estimate the
regression:
dgs+1,s+h = β1tF1s + ...+ βktFks + εs+1,s+h, (9)
over s = 0, ..., t− h. The PCk dividend-growth forecast is then defined by:
d̂gPCk
t+1,t+h = β̂1tF1t + ...+ β̂ktFkt. (10)
The idea behind the principal components method is to identify the common factors driving the
different forecasts and then use the regression given by Eq. (10) to assign more weight to factors
that were historically more accurate.
Finally, we also report “Kitchen Sink” (KS) forecasts for dividend growth that include every
predictor in a single regression:
dgt+1,t+h = αKS,h,m +N∑j=1
βKS,j,h,mxj,t + εt+1,t+h. (11)
3.2.3. Step 3: Forecast evaluation
Following Campbell and Thompson (2008), we use the standard out-of-sample R2 statistic (R2OS)
to compare a given forecast of dividend growth, d̂gt+1,t+h, to the historical average dividend growth
forecast, the natural benchmark under the null of no predictability. The R2OS statistics is analogous
to the familiar in-sample R2 statistic and given by:
R2OS = 1−
∑T−hk=q (dgk+1,k+h − d̂gk+1,k+h)2∑T−hk=q (dgk+1,k+h − d̄gk+1,k+h)2
, (12)
where q denotes the end of an initial in-sample period used to generate the first out-of-sample
forecast. The R2OS measures the reduction in mean-squared forecast error (MSFE) for the forecast
d̂gt+1,t+h relative to that of the historical average-based forecast d̄gt+1,t+h. When R2OS > 0 the
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forecast d̂gt+1,t+h outperforms the historical average forecast in terms of generating lower MSFE.
To test significance of the R2OS , we follow Rapach et al. (2010) and Kelly and Pruitt (2013), and
use the Clark and West (2007) MSFE-adjusted statistic, which modifies the well-known statistic of
Diebold and Mariano (1995) to accommodate possibly nested models.
4. Results
4.1. Out-of-sample dividend-growth forecasts
Table 2 presents out-of-sample results for our four-quarter dividend-growth forecasts over 1946:1-
2015:4, and several subsamples: 1960:1-2015:4, 1976:1-2015:4 (following van Binsbergen and Koijen
(2010)) and 2000:1-2015:4 (a recent period which includes the dot-com bust and the financial crisis).
Panel A presents results for the individual-predictor forecasts d̂gi,t+1,t+h, where i denotes one of
the 14 Goyal and Welch (2008) variables described above. None of the individual predictors predict
dividend growth with an R2OS > 0 over the entire sample or most subsamples.
In contrast, Panel B shows that all of the combination forecasts significantly beat the historical
average out-of-sample over the post-war period as well as most subsamples.7 Over 1946:1-2015:4,
the R2OS are large and significant at the 1% level, ranging from about 12%-19%. In the out-of-
sample period of 1960:1-2015:4, almost all combination forecasts are significant at 5% and possess
R2OS statistics of 7%-18%. Over the two more recent sub-periods, most forecasts maintain their
high R2OS and even remain at least marginally significant as the number of observations diminish in
the shortest subsample (2000:1-2015:4). Unlike combination dividend-growth forecasts, the kitchen
sink model always earns very low R2OS emphasizing the importance of properly combining predictive
information and the hazards of overfitting.
The results in Panel B contrast sharply with those of Chen (2009) who finds that dividend
predictability vanishes in the post-war period. Comparing Panel B to Panel A also indicates
that the combination forecasts outperform all of the most common individual predictors from the
literature in predicting dividend growth. Several recent studies use econometric methods besides
7These results improve if we replace the historical-average forecast with one based on an out-of-sample AR(1)forecast.
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standard predictive regressions or a modified definition of dividends and find some out-of-sample
dividend-growth predictability. For ease of comparison, we summarize the out-of-sample dividend
and return predictability results from these studies in Table 3.8 Comparing Tables 2 and 3, we see
our average combination dividend-growth forecast “ALL” has a greater R2OS over every subsample
than even the best R2OS reported by the prior literature. The R2
OS of the different combination
dividend-growth forecasts generally exceed those from the prior literature, but are of comparable
magnitudes. The combination forecasts also show out-of-sample predictability over a much longer
time period (more than 30 years) than prior studies.
Figure 1 depicts the out-of-sample forecasting performance of the combination forecasts relative
to the random walk over time. Specifically, the figure plots the cumulative squared-prediction error
of the historical average forecast minus the cumulative squared-prediction error of each combination
forecast. An upward slope indicates the the combination forecast generates a lower squared error
that quarter than the historical average. The plots for the three combination forecasts possess
similar trends and are generally upward sloping. Notably, each combination forecast shares a couple
sub-periods of relatively high accuracy, notably the late 1940’s and the post-crisis era post-2008.
Most of the combination forecasts perform poorly following the market crash in the early 2000’s,
perhaps because most indicators incorrectly indicated high expected cash-flow growth. Comparing
Figure 1 to Figure 2 of Rapach et al. (2010), combination forecasts of dividend growth reliably
perform at least as well, if not better than, combination forecasts of returns.
To further illustrate the reliability of the combination forecasts’ performance, Table 4 reports
the percentage of observations the 4-quarter combination forecast has a smaller squared forecast
error than the historical average over the full 70 years, and five sub-periods, approximately defined
by decade. To provide a benchmark, the last column presents analogous statistics as the others,
but for the forecast based only on the dividend price ratio.9 Over the entire sample period, the
prototypical average combination forecast (ALL) outperformed the historical average in 63.2%
of observations. With the exception of the 1990’s, the average combination forecast beats the
8This list of studies is not intended to be exhaustive, but representative of recent success in dividend predictability.We discuss the return results below.
9To be clear, the forecast is generate by out-of-sample estimation of Eq. (4) with the dividend-price ratio as xi,t.
15
historical average forecast at least 60% of the time. Again excluding the 1990’s, other combination
forecasts outperform the historical average in most subsamples. In contrast, the dividend-price
ratio predicts dividend-growth much worse than the historical average over the whole sample and
in most subsamples. Overall, Figure 1 and Table 4 show that combination forecasts of dividend
growth perform reliably, not exhibiting pro-longed periods of inaccuracy, or secularly declining
performance.
Koijen and Van Nieuwerburgh (2011), among others, find that any predictability of dividend
growth based on the dividend-price ratio is greatest at short forecasting horizons, with the converse
holding for return forecasts. Hence, we investigate whether the same is true of our combination
dividend-growth forecasts based on other predictors. Table 5 reports the out-of-sample performance
of the dividend-growth forecasts from Table 2 but with forecast horizons of 2 to 5 years. As with
the one-year horizon, the individual predictors generally have insignificant or negative R2OS at the 2
to 5 year horizons. The R2OS of the combination forecasts are all significantly positive at the 2-year
horizon and mostly at the 3-year horizon, but insignificant thereafter. The R2OS of the combination
forecasts all generally decrease in magnitude with horizon, becoming economically insignificant
after 3 years. Evidently, long-run dividend-growth remains hard to predict.
Overall, the combination forecast methods deliver robust and stable out-of-sample dividend-
growth predictability over the post-war period, several of its subsamples, and over forecasting
horizons of 1 to 3 years. Several combination methods perform particularly well, especially in sub-
samples. At the 1-year horizon, the DMSFE methods that highly discount past performance (θ =.6
or .8 ) possess relatively high R2OS over each subsample, consistent with rapid and large structural
change in expected 1-year dividend growth. The cluster methods that discards half or more of the
predictors also have relatively large 1-year R2OS statistics, suggesting that only a subset of predic-
tors are useful for predicting 1-year dividend growth at any one time. In contrast, the combination
methods that don’t discount past performance more heavily (MEAN, both ABMAs, and D(1))
maintain their R2OS better as the horizon increases to 2 and 3 years, consistent with parsimony
enhancing robustness. Although, no combination forecast method dominates in every subsample
or horizon, they all provide robust evidence of out-of-sample dividend-growth predictability.
16
4.2. Return predictability
By the Campbell-Shiller identity, expected dividend-growth should predict returns (see, e.g. Lac-
erda and Santa-Clara (2010), and Golez (2014)). Hence, we investigate whether our dividend-
growth forecasts are useful return predictors.
To exploit the present value identity in Eq. (1) for return forecasting, we follow van Binsbergen
and Koijen (2010), Rytchkov (2012), and Golez (2014), among others, and assume that expected
returns (µrt = Et(rt+1) and dividend growth (µdgt = Et(dgt+1)) follow AR(1) processes:
µdgt = γ0 + γ1µdgt−1 + εdgt , (13)
µrt = δ0 + δ1µrt−1 + εrt . (14)
Then, taking time-t expectations of both sides of Eq. (1) yields:
dpt = φ0 + φrµrt + φdgµ
dgt , (15)
where the φi are constants. By definition of µrt and Eq. (15):
rt+1 = µrt + εrt+1 = c0 + c1dpt + c2µdgt + εrt+1, (16)
where the ci are constants related to the φi.10 Motivated by Eq. (16) we forecast returns using our
combination forecasts of dividend growth and the dividend-price ratio.
Panel A of Table 6 describes the out-of-sample performance of excess return forecasts generated
by regressions of the form given by Eq. (16) using our 4-quarter dividend-growth forecasts as proxies
for µdg.11 We refer to these return forecasts as “bivariate return forecasts”. We require an initial
estimation period to estimate Eq. (16) given our out-of-sample combination forecasts as proxies
for µdg which exist since 1946:1. We choose a 10-year initial estimation period resulting in out-of-
sample return forecasts over 1956:1-2015:4. Following Campbell and Thompson (2008), we impose
10Specifically, c0 = −φ0/φr, c1 = (1/φr)dpt, and c2 = −(φdg/φr)µdgt
11We report forecasting results for excess returns although the theory above pertains to total returns. In untabulatedresults, we find even higher R2
OS in predicting total returns.
17
the restriction that excess return forecasts must be non-negative as investors would not bear risk
for a negative risk premium.
Panel A shows that the bivariate return forecasts significantly predict returns out-of-sample
with R2OS that are significant at the 1% level over horizons of 1 to 12 quarters. The R2
OS generally
increase with horizon up to 8 quarters, and then decline at the 12-quarter horizon. Rapach et al.
(2010) find that combining forecasts from univariate predictive regressions predicts returns better
out-of-sample than using a single multivariate predictive regression. Hence, in Panel B, we form a
combination return forecast (r̂avg) as a simple average of the two out-of-sample forecasts from the
univariate regressions:
rt+1,t+h = αdp + βdpdpt + εt+1,t+h, (17)
rt+1,t+h = αdgc + βdgc d̂gc
t+1,t+4 + εt+1,t+h. (18)
To be clear, letting α̂im, β̂
im denote estimates of Eqs. (17) and (18) using data available through
time m, we define:
r̂avgc,m+1,m+h =1
2
((α̂dpm + β̂dpm dpm
)+(α̂dgcm + β̂dgcm d̂gc,m+1,m+4
)). (19)
Panel B shows the r̂avgc generally perform better than the bivariate forecasts given by Eq. (16), and
increase monotonically with horizon from 1 to 12 quarters. The prior studies discussed in Table 3
predict returns (only) at the 1-year horizon with R2OS of up to 13.1% but frequently under 10%.
The 4-quarter R2OS from the bivariate and r̂avgc are comparable to the best forecasts from the prior
literature, ranging from 7.2% to 12.9% with more than half of the R2OS greater than 10%.
To provide a natural benchmark for assessing the R2OS in Panels A and B, Panel C presents
combination forecasts of returns (r̂c,t+1,t+h) following Rapach et al. (2010) based directly on return
forecasts from the 14 Goyal and Welch (2008) variables. At horizons of 1 or 4 quarters, the bivariate
return forecasts outperform the combination forecasts of returns. The R2OS of the representative 4-
quarter ALL forecasts based on dividend growth in Panels A and B (11.0% and 11.5%, respectively)
are more than twice as large as the ALL combination return forecast in Panel C (4.9%). At the
18
8-quarter horizon, the bivariate return forecasts have about the same R2OS as the combination
forecasts in Panel C, but r̂avgc performs the best with R2OS that are a few percent higher than
those of the bivariate and combination forecasts in Panels A and C, respectively. In Panel C, the
combination return forecast’s performance improves with horizon, and at 12-quarters earns similar
R2OS as r̂avgc .
Overall, the evidence from Table 6 indicates that expected dividend growth is a significant pre-
dictor of returns, especially at short horizons (2 years or less). Moreover, at short horizons, return
forecasts based on dividend growth are more accurate than combination return forecasts based
directly on common individual predictors. These results provide further evidence that imposing re-
strictions such as those from the Campbell-Shiller present value identity can improve out-of-sample
return predictability.
4.3. What moves prices?
The out-of-sample evidence above shows that the combination forecasts of dividend growth and
the associated “bivariate return forecasts” are relatively accurate proxies of expected dividend
growth and returns. Via the Cambpell-Shiller identity, these forecasts can therefore help address
the fundamental question of how much variation in stock prices is attributable to that of expected
returns or future dividend growth.
Assuming µdgt and µrt follow the AR(1) processes in Eqs. (13) and (14), the Campbell-Shiller
identity yields the follow decompositions of the variance of the dividend-price ratio (see, e.g. Golez
2014):
σ2(dpt) =
(1
1− ρδ1
)cov(µdgt , dpt)−
(1
1− ργ1
)cov(µdgt , dpt) (20)
=
(1
1− ρδ1
)2
σ2(µrt ) +
(1
1− ργ1
)2
σ2(µdgt )− 2
(1
1− ρδ1
)(1
1− ργ1
)cov(µrt , µ
dgt ). (21)
The constant ρ arises from the Taylor approximation used in the Campbell-Shiller identity. We
assume ρ = 0.96 following Cochrane (2008). We use the (observable) dividend-price ratio along with
our forecasts of dividend-growth and returns as proxies for µdg and µr to estimate the parameters
19
on the right-hand side of Eqs. (20) and (21).
Many other studies perform conceptually similar decompositions of the variance of unexpected
returns into the variances and covariances of cash-flow and expected return shocks (see, e.g.
Campbell (1991), Campbell and Ammer (1993), Bernanke and Kuttner (2005), and Chen and
Zhao (2009)). These decompositions typically assume that the vector of returns and predictors
zt = (rt, xt)′ follows a first-order VAR process zt = Φ1zt−1 + εt+1 and then infer discount-rate and
cash-flow news from the estimated Φ1 and shocks εt+1. Empirically, VAR-based decompositions are
very sensitive to specification of predictors and often over-estimate the role of cash-flow news (see,
e.g., Chen and Zhao (2009)). The VAR approach relies crucially on identifying expected returns
via the first equation in the VAR system:
rt = ar + brrrt−1 + b′rxxt−1 + εt, (22)
which the reader will recognize as a kitchen sink-type predictive regression. Such regressions tend to
perform very poorly out-of-sample (see, e.g., Rapach et al. (2010) and Panel C of Table 6) and are
therefore questionable proxies for conditional expected returns. The VAR-based decomposition then
attributes movements in prices not explained by estimated changes in expected returns to changes
in expected dividend growth, making both estimates unreliable. In contrast, our decomposition
directly incorporates our real-time forecasts of dividend growth and returns that we show above
both perform well as proxies for conditional expectations.
Columns 2-4 of Table 7 present estimates of the decomposition in Eq. (21) using each of our
4-quarter forecasts of dividend growth as a proxy for µdg and the corresponding real-time return
forecast generated from Eq. (16). Columns 5-6 present estimates of the analogous decompositions
according to (20). The terms in the decomposition are normalized to sum to 1.
We use GMM to estimate parameters and their standard errors. The moments are exactly
identified and we use Newey West standard errors with 3 lags to account for heteroskedasticity and
3 quarters of overlap in quarterly frequency forecasts with a 4-quarter horizon. In columns 2-4, the
20
moment conditions used are:
E
r̂ct − µr
d̂gc
t − µdg
(d̂gc
t − µdg)2 − σ2dg(r̂ct − µr)2 − σ2r
d̂gc
t − γ0 − γ1d̂gc
t−1
(d̂gc
t − γ0 − γ1d̂gc
t−1)d̂gc
t−1
r̂ct − δ0 − δ1r̂ct−1
(r̂ct − δ0 − δ1r̂ct−1)r̂ct−1
= 0. (23)
In columns 5-6, the moment conditions are:
E
r̂ct − µr
d̂gc
t − µdg
(d̂gc
t − µdg)(d̂pt − µdp)− σdg,dp
(r̂ct − µr)(d̂pt − µdp)− σr,dp
= 0. (24)
We compute standard errors of the variance and covariance contribution terms of Eqs. (20)
and (21) with the delta method. For each estimate of the components of Eq. (20) or Eq. (21), we
present two t statistics. The first, in parentheses, is the standard test of the null hypothesis that
the associated point estimate is 0. The second t statistic, in brackets, tests the null hypothesis that
1 minus the sum of the other terms in the decomposition is 0. The former ignores the restrictions
that the terms must add up to 1. The latter does not directly depend on the precision of the
parameters in the associated term, but only on the precision of the other terms and the restriction
on the sum of the components. For example, given the GMM estimates of the parameters, the
t-statistic in parentheses in column 3 denoted σ2(µr) tests the null hypothesis that:
(1
1− ρδ1
)2
σ2(µrt ) = 0. (25)
21
However, the corresponding t-statistic in brackets tests the null hypothesis that:
var(dpt)−(
1
1− ργ1
)2
σ2(µdgt ) + 2
(1
1− ρδ1
)(1
1− ργ1
)cov(µrt , µ
dt ) = 0. (26)
The restricted t-statistic in brackets has higher power than the first (unrestricted) t-statistic when
the other terms in the variance decomposition are smaller and have higher precision than the direct
point estimate.
In each specification of Eq. (21), the variance in expected dividend growth explains 3%-12% of
variation in dpt, and the estimate is always at least marginally significant based on the individual
t-statistic. Between 74% and 105% of the variation in prices is due to variation in expected returns,
but the point estimates are generally not significant without considering restrictions. However,
returns must account for the variation in prices not accounted for by the relatively small and
precisely estimated dividend-growth term. As a result, the second t-statistic on the σ2(µr) produces
a larger t-statistic that is always significant at the 1% level.12
Column 4 shows that covariation between expected returns and dividend growth explains up to
23% of variation in prices, but the estimate varies across combination methods and the t-statistic
is often not significant. With one exception (ABMA(AIC)), the insignificant covariance terms in
column 4 all come from the forecasts with R2OS less than 10% in Table 6. Hence, any weakness in
the cov(µr, µdg) terms could result from imperfections in the return or dividend-growth forecasts.13
Over 1952-1988, the seminal VAR-based results of Campbell (1991) are comparable to those in
columns 2-4. Campbell estimates that the variance of expected dividend growth and return news
accounts for about 14% and 80% of the variation in returns, respectively. However, some follow
up studies with different VAR specifications estimate the importance of dividend news to be many
times greater than the 4% average from Table 7 and often even greater than the importance of
expected returns (see, e.g. Bernanke and Kuttner (2005) and Chen and Zhao (2009)). Golez (2014)
uses derivatives to forecast dividends and then also performs a decomposition that also does not
12The second t-statistic on the σ2(µdg) term is generally not significant. This does not mean the σ2(µdg) termis insignificant. It simply means that the σ2(µr) term is estimated less precisely - and is much larger than - theestimated σ2(µdg).
13Like the σ2(µdg) term, the cov(µr, µdg) does not have a large t-statistic in brackets. This also simply reflects theimprecision of the σ2(µr) term relative to the size.
22
use a VAR. In contrast to our results, Golez finds that the variance of expected dividend growth
explains 102% of the variance of the dividend-price ratio and the variance of expected returns
explains 270%. Covariance between expected returns and dividend growth explains the balance of
-272%.
Columns 5 and 6 of Table 7 show that up to 14% of the variance of the dividend-price ratio
is explained by covariance with expected dividend growth, and 4% on average, although the point
estimates are insignificant in six specifications. The estimates are significant, however, for the
prototypical MEAN and ALL forecasts, as well as as few others. Covariance with expected returns
always explains at least 86% of the variance of the dividend-price ratio, and this proportion is
consistently significant at the 5% level.
Overall, in spite of robust dividend-growth predictability, the variance decompositions in Table
7 indicate that variance in dividend growth by itself explains about 10% or less of variation in
prices, and the rest is explained by variation in expected returns. Table 8 presents the GMM
estimates of parameters underlying the decompositions in Table 7 that help explain the relative
importance of returns and dividend growth. The volatility of expected returns is always greater
than that of dividend growth, usually by several times. The persistence of expected returns is also
always higher that that of expected dividend growth and at least 50% higher in all but one case
(ABMA(AIC)). Relative to shocks to expected returns, shocks to expected dividend growth should
therefore impact prices less because they are not very large and dissipate relatively quickly.
5. Conclusion
In this paper, we propose a new method for forecasting dividend growth based on common return
predictors that should also predict dividend growth by the Campbell and Shiller (1988) identity.
Prior dividend-growth forecasting literature relies primarily on predictive regressions based on the
dividend-price ratio. We expand on the predictive-regression approach by combining forecasts from
regressions that use not just the dividend-price ratio, but also 13 other common return predictors
from Goyal and Welch (2008) that are easily available to market participants. The combination
forecasts incorporate the information in these forecasting variables, while also mitigating the econo-
23
metric instability inherent to univariate forecasts. Contrary to the common finding that dividend
growth is relatively unpredictable compared to returns, we find that these combination forecasts
generate significant out-of-sample dividend-growth predictability on the CRSP value-weighted in-
dex over the entire post-war sample with R2 up to 18.6%.
Many studies investigate whether the dividend-price ratio predicts returns, but this implicitly
assumes constant dividend growth. Consistent with the Campbell-Shiller identity, we find that the
combination dividend-growth forecasts help the dividend-price ratio to predict post-war returns,
and do so with out-of-sample R2 up to 12.4% at the one-year horizon. Further exploiting the
Cambbell-Shiller identity, and our relatively accurate proxies for expected returns and dividend
growth, we decompose the variance of the dividend-price ratio in expected returns and cash-flow
components. We estimate that about 10% or less of the variance of prices is attributable to the
variance of expected dividend growth, and 74% or more is attributable to the variance of expected
returns. This relative importance of expected dividend-growth in explaining price movements is
less than estimates from several prior studies and follows intuitively from relatively high persistence
and volatility of expected returns.
24
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0.05
.1.15
.2
1945q1
1950q1
1955q1
1960q1
1965q1
1970q1
1975q1
1980q1
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
2015q1
0.05
.1.15
.2
1945q1
1950q1
1955q1
1960q1
1965q1
1970q1
1975q1
1980q1
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
2015q1
0.05
.1.15
.2.25
1945q1
1950q1
1955q1
1960q1
1965q1
1970q1
1975q1
1980q1
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
2015q1
Mean DMSFE(1.0) DMSFE(0.8)
0.1
.2.3
1945q1
1950q1
1955q1
1960q1
1965q1
1970q1
1975q1
1980q1
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
2015q1
0.05
.1.15
.2
1945q1
1950q1
1955q1
1960q1
1965q1
1970q1
1975q1
1980q1
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
2015q1
0.05
.1.15
1945q1
1950q1
1955q1
1960q1
1965q1
1970q1
1975q1
1980q1
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
2015q1
DMSFE(0.6) ABMA(AIC) ABMA(SIC)
0.05
.1.15
.2.25
1945q1
1950q1
1955q1
1960q1
1965q1
1970q1
1975q1
1980q1
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
2015q1
0.05
.1.15
.2.25
1945q1
1950q1
1955q1
1960q1
1965q1
1970q1
1975q1
1980q1
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
2015q1
0.05
.1.15
.2.25
1945q1
1950q1
1955q1
1960q1
1965q1
1970q1
1975q1
1980q1
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
2015q1
C2 C3 PC1
0.05
.1.15
.2.25
1945q1
1950q1
1955q1
1960q1
1965q1
1970q1
1975q1
1980q1
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
2015q1
0.05
.1.15
.2.25
1945q1
1950q1
1955q1
1960q1
1965q1
1970q1
1975q1
1980q1
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
2015q1
PC2 All
Figure 1: Cumulative square prediction error for the historical average forecast minus those ofseveral combination forecasts of 4-quarter dividend growth (dgt+1,t+4), 1946:1-2015:4
28
Table 1: Correlations of predictors 1936:1-2015:4
BM TBL LTY NTIS INFL LTR SVAR IK DP EP DEF DE TMS
TBL 0.43LTY 0.32 0.90NTIS 0.25 -0.04 -0.12INFL 0.44 0.54 0.45 0.08LTR -0.03 0.00 0.07 -0.15 -0.21SVAR -0.11 -0.07 0.00 -0.25 -0.19 0.28IK -0.06 0.53 0.36 -0.05 0.33 0.00 -0.01DP 0.89 0.26 0.15 0.25 0.27 -0.04 -0.10 -0.24EP 0.79 0.34 0.20 0.20 0.38 -0.01 -0.27 -0.02 0.78DEF 0.25 0.35 0.51 -0.40 0.10 0.28 0.45 -0.09 0.10 -0.04DE 0.09 -0.14 -0.08 0.07 -0.19 -0.04 0.28 -0.32 0.28 -0.38 0.21TMS -0.31 -0.42 0.03 -0.16 -0.30 0.14 0.16 -0.46 -0.27 -0.36 0.26 0.14DFR 0.02 -0.06 0.01 0.09 -0.04 -0.41 -0.09 -0.15 0.02 -0.11 0.03 0.20 0.14
29
Table 2: Out-of-sample performance of one-year dividend-growth forecasts
R2OS is the Campbell and Thompson (2008) out-of-sample R2 statistic. Statistical significance for
the R2OS statistic is based on the p-value (p) for the Clark and West (2007) out-of-sample MSFE-
adjusted statistic which corresponds to a one-sided test of the null hypothesis that a given modelhas equal squared prediction error relative to the historical average benchmark model. The columnheadings state the out-of-sample forecasting periods. The table uses the following abbreviationsfor the combination forecasts: D(θ0) = DMSFE, θ = θ0, Ci = i-cluster forecast, PCi = i ForecastPrincipal Components Method, KS = Kitchen Sink. *, **, and *** denote p-values < 10%, < 5%,and < 1%, respectively.
Panel A: Individual Forecasts
1946:1-2015:4 1960:1-2015:4 1976:1-2015:4 2000:1-2015:4
Predictor R2OS (%) p (%) R2
OS (%) p (%) R2OS (%) p (%) R2
OS (%) p (%)
DP -117.90 - -106.10 - -55.54 - -27.20 -EP -19.40 - -3.24 - -3.42 - -1.00 -DE -28.07 - -18.40 - 0.36 *** 7.09 **SVAR -2.40 - -10.06 - -4.29 - 17.80 *BM -40.25 - -44.04 - -41.62 - -4.98 -NTIS -6.04 - -6.38 - -8.35 - -11.50 -TBL -5.33 - -4.21 - -2.84 - -5.51 -LTY -23.85 - -39.96 - -7.62 - -2.34 -LTR -3.42 - -2.57 - -2.86 - -0.74 -TMS -10.53 - -14.00 - -12.77 - -7.02 -DFY -3.20 - -9.15 - -3.90 - 15.68 -DFR -9.03 - -4.90 - -2.96 - -1.55 -INFL -3.99 - -1.47 - 3.75 ** -1.09 -IK -1.36 - 0.53 - 0.63 - -1.55 -
Panel B: Combination and KS Forecasts
1946:1-2015:4 1960:1-2015:4 1976:1-2015:4 2000:1-2015:4
Predictor R2OS (%) p (%) R2
OS (%) p (%) R2OS (%) p (%) R2
OS (%) p (%)
Mean 12.25 *** 8.65 ** 8.64 ** 11.09 *D(1) 11.85 *** 7.03 ** 6.92 ** 10.20 *D(0.8) 15.95 *** 13.62 *** 14.48 *** 13.57 **D(0.6) 18.55 *** 18.12 *** 18.14 *** 14.90 **ABMA(AIC) 12.54 *** 8.80 ** 8.85 ** 11.33 *ABMA(SIC) 10.23 *** 7.94 ** 7.68 ** 10.02 *C2 14.51 *** 14.57 *** 14.78 *** 15.45 ***C3 15.12 *** 16.71 *** 17.37 *** 18.99 ***PC1 14.52 *** 2.93 - 10.07 *** 1.70 -PC2 16.47 *** 13.11 ** 19.88 ** 11.25 -ALL 16.78 *** 13.20 *** 14.67 *** 15.72 *KS -129.60 - -171.50 - -109.10 - -6.91 -
30
Table 3: Out-of-sample performance of one-year dividend-growth and return forecasts from severalrecent studies
For comparison with our results, this table summarizes the out-of-sample return and dividend-growth predictability found by several recent studies over a forecasting horizon of 1-year. A *indicates that the authors also examined and found positive R2
OS over different samples than thatof the main out-of-sample period listed in the table.
Out-of-Sample Period R2OS(%)
Study Div growth Returns Div growth Returns
van Binsbergen and Koijen (2010) 1974-2007 1974-2007 5.8 1.1Kelly and Pruitt (2013) 1980-2010 1980-2010 -9.0-12.1* 3.5-13.1*Golez (2014) N/A 2000-2011 N/A 0-5.9Sabbatucci (2015) 1972-2012 1972-2012 6.8 7.7
31
Table
4:
Con
sist
ency
ofd
ivid
end-g
row
thco
mb
inat
ion
fore
cast
s
Eac
hco
lum
nb
ut
the
last
ofth
ista
ble
pre
sents
the
per
centa
geof
obse
rvat
ion
sw
ith
inea
chsu
b-p
erio
dof
1946:1
-2015:4
for
wh
ich
the
squ
ared
-for
ecas
ter
ror
ofth
eco
mb
inat
ion
fore
cast
of4-
qu
arte
rd
ivid
end
grow
thd
efin
edin
the
colu
mn
hea
din
gis
less
than
that
ofth
eh
isto
rica
lav
erag
efo
reca
ster
.F
orco
mp
aris
on,
the
last
colu
mn
pre
sents
anal
ogou
sre
sult
sto
the
oth
erco
lum
ns
bu
tu
sin
gon
lyth
ed
ivid
end
-pri
cera
tio
inli
euof
aco
mb
inat
ion
fore
cast
.A
LL
den
otes
the
sim
ple
aver
age
of
the
oth
erfi
veco
mb
inati
on
fore
cast
s.T
he
tab
leu
ses
the
foll
owin
gab
bre
via
tion
sfo
rth
eco
mb
inat
ion
fore
cast
s:D
(θ0)
=DMSFE
,θ
=θ 0
,Ci
=i-
clu
ster
fore
cast
,P
Ci
=i
For
ecas
tP
rin
cip
alC
omp
onen
tsM
eth
od
.
Mea
nD
(1)
D(0
.8)
D(0
.6)
AB
MA
(AIC
)A
BM
A(S
IC)
C2
C3
PC
1P
C2
AL
LD
P
1946:1
-1959:4
62.5
%64.3
%53.6
%44.6
%62.5
%64.3
%42.9
%50.0
%55.4
%48.2
%64.3
%35.7
%1960:1
-1969:4
57.5
%60.0
%57.5
%50.0
%57.5
%60.0
%52.5
%55.0
%50.0
%47.5
%60.0
%5.0
%1970:1
-1979:4
62.5
%62.5
%67.5
%72.5
%60.0
%62.5
%67.5
%72.5
%60.0
%70.0
%75.0
%32.5
%1980:1
-1989:4
75.0
%77.5
%67.5
%62.5
%75.0
%75.0
%52.5
%60.0
%75.0
%57.5
%72.5
%52.5
%1990:1
-1999:4
20.0
%27.5
%45.0
%45.0
%20.0
%20.0
%57.5
%47.5
%27.5
%47.5
%42.5
%0.0
%2000:1
-2015:4
57.4
%59.0
%60.7
%60.7
%59.0
%59.0
%62.3
%57.4
%62.3
%63.9
%63.9
%57.4
%A
LL
56.3
%58.8
%58.5
%55.6
%56.3
%57.4
%55.6
%56.7
%55.6
%56.0
%63.2
%32.6
%
32
Table 5: Out-of-sample performance of two-year to five-year dividend-growth forecasts
R2OS is the Campbell and Thompson (2008) out-of-sample R2 statistic. h denotes the forecasting
horizon in quarters. Statistical significance for the R2OS statistic is based on the p-value (p) for the
Clark and West (2007) out-of-sample MSFE-adjusted statistic which corresponds to a one-sidedtest of the null hypothesis that a given model has equal squared prediction error relative to thehistorical average benchmark model. The out-of-sample forecasting period is 1946:1-2015:4. Thetable uses the following abbreviations for the combination forecasts: D(θ0) = DMSFE, θ = θ0, Ci= i-cluster forecast, PCi = i Forecast Principal Components Method, KS = Kitchen Sink. *, **,and *** denote p-values < 10%, < 5%, and < 1%, respectively.
Panel A: Individual Forecasts
h=8 h=12 h=16 h=20
Predictor R2OS (%) p (%) R2
OS (%) p (%) R2OS (%) p (%) R2
OS (%) p (%)
DP -55.65 - -13.39 - -4.08 - -8.15 -EP -15.80 - -11.85 - -12.55 - -15.07 -DE -12.46 - 4.23 *** -4.44 - -9.09 -SVAR 5.29 *** 5.13 *** -0.10 - -2.16 -BM -9.07 - -8.66 - -31.74 - -65.95 -NTIS -18.88 - -30.97 - -40.23 - -40.86 -TBL -12.80 - -44.20 - -166.00 - -288.90 -LTY -48.97 - -73.81 - -183.00 - -284.00 -LTR -5.01 - -3.47 - -2.95 - -2.13 -TMS -2.53 - -5.46 - -41.05 - -81.69 -DFY 8.18 ** 0.37 * -6.58 - -14.06 -DFR -3.36 - -4.35 - -2.11 - -2.26 -INFL -0.92 - 5.34 * 2.44 - 4.95 -IK 2.26 * -1.17 - -4.51 - -4.68 -
Panel B: Combination and KS forecasts
h=8 h=12 h=16 h=20
Predictor R2OS (%) p (%) R2
OS (%) p (%) R2OS (%) p (%) R2
OS (%) p (%)
Mean 10.29 *** 6.52 ** 0.13 - -9.32 -D(1) 14.13 ** 6.37 ** 0.25 - -14.23 -D(0.8) 11.25 ** 4.88 * 4.42 - 7.75 *D(0.6) 11.91 ** 4.21 - 2.12 - 7.52 *ABMA(AIC) 10.47 *** 6.55 ** -0.01 - -10.56 -ABMA(SIC) 10.47 *** 6.55 ** -0.01 - -10.56 -C2 8.08 ** 3.43 - 4.03 - 6.56 *C3 5.54 ** 0.18 - 1.29 - 7.63 **PC1 9.51 ** 2.80 * -57.55 - -178.60 -PC2 8.09 *** -9.58 - -65.62 - -152.30 -ALL 13.11 *** 6.30 ** -1.57 - -15.53 -KS -162.10 - -81.56 - -19.17 - 1.10 ***
33
Table 6: Economic significance of out-of-sample return forecasts based on expected dividend-growth and the log dividend-price ratio
This table presents statistics related to out-of-sample forecasts of log excess returns rt+1,t+h, h = 1, 4, 8, 12over the out-of-sample period 1956:1-2015:4. R2
OS denotes the Campbell and Thompson (2008) out-of-sampleR2 using the restriction that expected excess returns must be non-negative. Statistical significance of R2
OS
is based on one-sided p-values (p) from the Clark and West (2007) out-of-sample MSFE-adjusted statistic.In Panel A, the return forecasts are out-of-sample predicted values from regressions of the form:
rt+1,t+h = a+ b · dpt + c · d̂gc
t+1,t+4 + εt+1,t+h, (27)
where dpt is the dividend-price ratio and d̂gc
t+1,t+4 is one of the combination dividend-growth forecasts.In Panel B, the return forecasts are the simple averages (see Eq. (19)) of the out-of-sample forecasts frompredictive regressions of the form:
rt+1,t+h = a+ b · dpt + εt+1,t+h, (28)
rt+1,t+h = a+ b · d̂gc
t+1,t+4 + εt+1,t+h. (29)
In Panel C, the return forecasts are combination forecasts (r̂c,t+1,t+h) of log excess returns using the Goyaland Welch (2008) 14 variables directly. *, **, and *** denote p-values < 10%, < 5%, and < 1%, respectively.
Panel A: Bivariate Return Forecasts
h=1 h=4 h=8 h=12
c R2OS(%) p(%) R2
OS(%) p(%) R2OS(%) p(%) R2
OS(%) p(%)
Mean 2.13 *** 11.93 *** 14.34 *** 9.29 ***D(1.0) 2.98 *** 12.92 *** 11.58 *** 6.39 ***D(0.8) 2.13 *** 8.93 *** 9.56 *** 5.62 ***D(0.6) 2.15 *** 9.65 *** 10.00 *** 6.14 ***ABMA(AIC) 2.08 *** 11.92 *** 14.55 *** 9.49 ***ABMA(SIC) 1.66 *** 11.03 *** 13.07 *** 8.16 ***C2 2.37 *** 9.88 *** 9.85 *** 6.49 ***C3 2.31 *** 9.52 *** 9.80 *** 6.75 ***PC1 2.19 *** 7.22 *** 9.01 *** 6.48 ***PC2 2.05 *** 10.44 *** 12.60 *** 8.78 ***ALL 1.66 *** 11.03 *** 13.07 *** 8.16 ***
34
Table 6: Continued
Panel B: Average of return forecasts based on dpt and d̂gc,t+1,t+4
h=1 h=4 h=8 h=12
c R2OS(%) p(%) R2
OS(%) p(%) R2OS(%) p(%) R2
OS(%) p(%)
Mean 2.75 *** 12.35 *** 18.90 *** 20.40 ***D(1.0) 2.95 *** 12.23 *** 17.73 *** 18.72 ***D(0.8) 2.20 *** 9.60 *** 15.69 *** 17.46 ***D(0.6) 2.01 *** 9.45 *** 15.12 *** 16.84 ***ABMA(AIC) 2.73 *** 12.39 *** 19.00 *** 20.45 ***ABMA(SIC) 2.35 *** 11.51 *** 18.46 *** 20.37 ***C2 1.89 *** 9.15 *** 15.06 *** 17.43 ***C3 1.94 *** 9.29 *** 15.61 *** 17.90 ***PC1 1.69 ** 8.06 *** 13.76 *** 14.71 **PC2 2.03 *** 10.33 *** 16.76 *** 18.68 ***ALL 2.35 *** 11.51 *** 18.46 *** 20.37 ***
Panel C: Combination forecasts of rt+1,t+4 based on Goyal and Welch (2008) variables
h=1 h=4 h=8 h=12
c R2OS(%) p(%) R2
OS(%) p(%) R2OS(%) p(%) R2
OS(%) p(%)
Mean 2.06 *** 6.96 *** 11.52 *** 14.05 ***D(1.0) 2.07 *** 6.89 *** 12.12 *** 13.31 ***D(0.8) 2.08 *** 5.18 *** 12.86 *** 18.21 ***D(0.6) 2.14 *** 3.76 ** 10.89 *** 17.85 **ABMA(AIC) 2.06 *** 7.03 *** 11.85 *** 14.52 ***ABMA(SIC) 2.06 *** 7.01 *** 11.75 *** 14.39 ***C2 0.72 - 2.03 ** 11.52 *** 18.86 ***C3 0.45 - 1.05 * 11.09 *** 22.75 **PC1 1.21 ** 1.82 - 5.44 ** 13.51 **PC2 -0.54 - -0.49 - 13.22 *** 18.90 ***ALL 1.66 *** 4.89 *** 13.44 *** 20.44 ***KS -9.04 - -23.59 - -26.41 - -24.95 -
35
Table 7: Variance decomposition of dividend-price ratio
This table presents estimated variance decompositions of the market dividend-price ratio according to Eq. (20) incolumns 2-4 and Eq. (21) in columns 5 and 6. We normalize the entries to sum to 1. As proxies for µr
t and µdgt ,
we use our four-quarter combination forecasts of dividend growth and the associated bivariate four-quarter totalreturn forecasts estimated similarly to the excess returns from Panel A of Table 6. The choice of combinationforecast method is listed in column 1. The sample period is 1956:1-2015:4. For each of the two decompositions,we estimate all parameters jointly via GMM, and compute t-statistics for the terms in the variance decompositionvia the delta method. t-statistics in parenthesis test the null hypothesis that the associate estimate above is 0. t-statistics in brackets test the null hypothesis that the estimate implied by the other components of Eq. (20) or (21) is 0.
Decomposition from Eq. (21) Decomposition from Eq. (20)
Forecasts σ2(µdgt ) σ2(µr
t ) cov(µdgt , µ
rt ) cov(µdg
t , dpt) cov(µrt , dpt)
Mean 0.03 0.74 0.23 0.13 0.87(2.25) (1.84) (2.08) (2.53) (2.66)[0.07] [6.02] [0.55] [0.38] [17.6]
D(1.0) 0.04 0.76 0.21 0.10 0.90(2.42) (1.9) (2.15) (2.46) (2.84)[0.07] [6.93] [0.51] [0.32] [21.93]
D(0.8) 0.10 1.05 -0.16 -0.05 1.05(2.04) (1.37) (-1.14) (-0.96) (2.38)[0.15] [9.44] [-0.2] [-0.1] [22.09]
D(0.6) 0.08 1.00 -0.08 -0.02 1.02(2.06) (1.38) (-0.88) (-0.62) (2.4)[0.11] [12.48] [-0.11] [-0.06] [27.13]
ABMA(AIC) 0.12 0.82 0.06 -0.04 1.04(2.06) (1.59) (0.75) (-0.62) (2.46)[0.23] [8.41] [0.11] [-0.1] [15.68]
ABMA(SIC) 0.04 0.77 0.19 0.11 0.89(2.25) (1.63) (2) (2.53) (2.59)[0.07] [7.18] [0.39] [0.32] [20.69]
C2 0.12 1.00 -0.12 -0.02 1.02(2.77) (1.37) (-1.17) (-0.53) (2.37)[0.19] [10.49] [-0.17] [-0.05] [23.5]
C3 0.08 1.01 -0.09 -0.01 1.01(2.78) (1.4) (-1.14) (-0.41) (2.42)[0.12] [13.92] [-0.12] [-0.03] [29.01]
PC1 0.07 0.82 0.11 0.14 0.86(1.85) (1.7) (1.56) (2.46) (2.79)[0.14] [8.78] [0.22] [0.46] [14.92]
PC2 0.07 0.79 0.14 0.03 0.97(1.68) (1.53) (1.79) (0.86) (2.49)[0.13] [6.97] [0.27] [0.08] [26.28]
ALL 0.04 0.77 0.19 0.11 0.89(2.25) (1.63) (2) (2.53) (2.59)[0.07] [7.18] [0.39] [0.32] [20.69]
36
Table 8: Parameters used in variance decomposition
This table presents estimated parameters from Eq. (20). All parameters are estimated jointly via GMM (See Section4.3 for details).
Forecasts σ(µdgt ) σ(µr
t ) δ1 γ1
Mean 0.011 0.034 0.40 0.60(7.11) (10.86) (3.41) (5.96)
D(1.0) 0.01 0.031 0.38 0.61(7.67) (11.76) (3.29) (6.22)
D(0.8) 0.018 0.024 0.51 0.82(10.14) (11.04) (5.09) (12.63)
D(0.6) 0.016 0.024 0.52 0.82(10.30) (11.24) (4.93) (12.65)
ABMA(AIC) 0.016 0.029 0.52 0.67(10.30) (11.40) (4.93) (6.69)
ABMA(SIC) 0.011 0.026 0.39 0.70(6.95) (11.94) (3.39) (7.76)
C2 0.023 0.024 0.43 0.82(12.59) (11.17) (4.29) (12.47)
C3 0.018 0.023 0.46 0.82(14.11) (11.39) (4.99) (12.66)
PC1 0.016 0.024 0.47 0.80(7.43) (14.95) (3.43) (13.20)
PC2 0.019 0.024 0.35 0.77(4.84) (12.61) (2.70) (10.19)
ALL 0.011 0.026 0.39 0.70(6.95) (11.94) (3.39) (7.76)
37