Growth of aggregate corporate earnings and cash-flows: Persistence and determinants

International Review of Economics and Finance 25 (2013) 13–23

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Growth of aggregate corporate earnings and cash-flows: Persistence and determinants Lawrence Kryzanowski a,⁎, Sana Mohsni b, 1 a University Research Chair in Finance, Department of Finance, John Molson School of Business, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, P.Q., Canada H3G 1M8 b The Sprott School of Business, Carleton University, 1715 Dunton Tower, 1125 Colonel By Drive, Ottawa, ON, Canada K1S 5B6

a r t i c l e

i n f o

Article history: Received 10 March 2011 Received in revised form 8 May 2012 Accepted 10 May 2012 Available online 16 May 2012 JEL classification: C21 C22 G10 M41

a b s t r a c t Consistent with economic intuition and the intuition behind momentum strategies for market timing and sector rotation based on accrual earnings (AE), we find persistence in AE growth rates at the market and industry levels in the short run, and neither persistence nor mean reversion at both levels in the long run. Forecasted industrial production, GDP growth, term premium and default premium exhibit predictive power for short- but not long-term AE growth rates at the market level, and capital intensity and product type exhibit predictive power for both short- and long-term AE growth rates at the industry level. In contrast for growth rates of cash flows (CF), we find mean reversion and neither mean reversion nor persistence in the short- and long-run, respectively, at the market and industry levels. © 2012 Elsevier Inc. All rights reserved.

Keywords: Persistence Mean-reversion Growth rates Earnings Cash flows

1. Introduction Although theoretical asset valuation models favor the use of cash-flow and cash-flow growth rates, earnings and earnings growth rates are widely used in share valuation and performance measurement settings by practitioners. 2 Evidence of persistence in the aggregate growth rates of metrics, such as accrual earnings (AE) and cash flows (CF), is useful for a variety of portfolio management decisions, such as those related to market and sectoral risk premiums, policy and tactical asset allocation, earnings quality assessment, market and industry forecasts of strategists and analysts, implementation of momentum or contrarian investment strategies, and sector rotational strategies. 3 In fact, asset allocation (i.e., the distribution of investment wealth among

⁎ Corresponding author. Tel.: + 1 514 848 2424, local 2782; fax: +1 514 848 4500. E-mail addresses: [email protected] (L. Kryzanowski), [email protected] (S. Mohsni). 1 Tel.: + 1 613 520 2600x2991. 2 If correctly developed, pricing models using discounted cash-flow, earnings or dividends lead to identical solutions. 3 Hong, Torous, and Valkanov (2007) find that the returns of a significant number of industry portfolios predict stock market movements by up to two months, and that this finding is robust for the eight largest non-US stock markets. Their findings suggest that stock markets react with a delay to information contained in industry returns about their fundamentals and that information diffuses only gradually across markets. 1059-0560/$ – see front matter © 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.iref.2012.05.003

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various asset classes), sector rotations, and momentum strategies are founded on precise relative valuations of one asset class to the others (e.g., stocks to bonds) or, alternatively, the relative risk premium for each risky asset class. 4 In turn, these relative valuations are dependent on the accuracy of forecasts of future earnings or cash-flow growth rates. The importance of the aggregate growth of the AE and CF metrics is reflected in the literature. For example, estimates of aggregate growth of AE and CF are used to predict the appropriate equity risk premium (e.g., Fama & French, 2002), to explain cross-sectional prices (Fama & French, 2002; Gebhardt, Lee, & Swaminathan, 2001), to estimate the cost of capital (Fama & French, 1999), to investigate the time-series relation between value and price (Lee, Myers, & Swaminathan, 1999) and to assess profitability (Fama & French, 2000) across various industries. Due to the signaling importance of current and expected future aggregate corporate profits in resource allocation, other studies (Baghestani & Khallaf, 2012) examine the accuracy of various predictions of the growth in aggregate corporate profits. Ball, Sadka, and Sadka (2009) find that a substantial portion of the variation in firm-level earnings is explained by a common (aggregate) earnings factor, which is priced because it is not fully diversifiable. 5 Bansal, Khatchatrian, and Yaron (2005) find that most of the variation in asset prices can be attributed to economic uncertainty and fluctuations in expected cash-flow growth. Chen and Zhang (2003) and Hirshleifer and Teoh (2003) show that differences in segment-level growth prospects are important in valuing multi-segment firms, and provide useful information for investors. Investment decisions should, therefore, improve with a better understanding of the time-series behavior and determinants of AE and CF growth rates. A better understanding of the growth in aggregate earnings reduces the reliance on analysts and/or management forecasts in predicting growth rates, since an extant literature shows that such forecasts suffer from systematic biases at various levels of aggregation (e.g., Chen, Lin, Wang, & Wu, 2010; La Porta, 1996) that differ for various economic environments (Agarwal, Chomsisengphet, Liu, & Rhee, 2007). Despite the importance of the growth in expected earnings and cash flows in investment (and financial management) decisions, research on the time-series behavior of AE and CF growth rates is scarce and unable to provide unambiguous evidence for or against the null hypothesis that changes in these metrics are distributed randomly so that past and future growth rates are essentially uncorrelated at the market and industry levels. The major argument for a random behavior for growth rates or changes in AE and CF is based on the economic presumption that little time-series persistence should exist in the profitability of firms due to competitive pressures. Tests that are unable to reject this null hypothesis include examinations of the time-series properties (such as persistence) of annual and quarterly earnings and/or their growth rates. These tests are primarily conducted at the crosssectional and individual firm (and not more aggregated) level. 6 Investigations of earnings persistence at an aggregate level are limited in number and focus on Box and Jenkins related methodologies with little exploration of the impact of market-/industry-wide factors on the behavior of AE or CF growth rates. Using a set of ARIMA-related processes and variance ratios, Gil-Alana and Pelaez (2008) find that shocks to earnings for the S&P 500 index persist over long quarters, consistent with business cycle characteristics. Bae and Nelson (2007) find no evidence of a permanent change in the growth rates of aggregate earnings during the bull market of the 1990s. We extend this literature by examining the persistence of earnings and cash-flow growth rates both at the overall market and industry levels, using an ARDL (AutoRegressive Distributed Lag) model and a set of macro-variables and industry attributes. We explicitly test for any short-/long-term persistence in growth rates and examine whether macro-variables such as GDP and industrial production and/or industry attributes such as concentration, capital intensity, and product type are useful in explaining the behavior of future growth rates. This paper makes two contributions to the current literature on earnings and cash flow growth rates. First, consistent with economic intuition and the intuition behind momentum strategies for market timing and sector rotation, we find evidence of short-term persistence in AE growth rates at the market and industry levels, but little persistence at both levels in the long run. Second, our results show that macro-variables such as forecasted industrial production, GDP growth, term premium and default premium exhibit power for explaining short-term AE growth rates at the market level. However, this explanatory power is lost at the long-run, which indicates that although market-wide factors seem to lead changes in aggregate earnings, they are not able to explain long-term AE growth. Consistent with the industrial organization literature, we find that industry attributes such as capital intensity and product type exhibit power for explaining both short- and long-term AE growth rates at the industry level. The data, the sample and the metrics used to measure the growth rates of both accrual and cash-flow earnings are discussed in the next section. Major results for growth rate persistence using time-series models for market and industry portfolios are presented and discussed in Section 3. Section 4 concludes the paper. 2. Sample, data and growth metrics 2.1. Sample and data Our initial sample consists of all public U.S. firms with data available in the Annual Industrial Compustat (active and research files). Firms are selected at the end of each calendar year from 1950 to 2006. Despite the existence of a backfill bias before 1973, 4 As shown by Ibbotson and Kaplan (2000), the percentage of performance attributable to the policy asset mix is material but varies substantially in magnitude depending upon the question asked. 5 For a test of the implications of Merton's (1987) theory on market information segmentation at the international level, Chung and Kryzanowski (2001) find that their proxy measures for the breadth and depth of investor cognizance are significantly related to various information environment- and industry-specific effects, and country-specific effects (for depth only). 6 For example, refer to Lintner and Glauber (1967), Beaver (1970), Ball and Watts (1972), Albrecht, Lookabill, and McKeown (1977), and Chan, Karceski, and Lakonishok (2003).

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the earlier years are included for the sake of completeness (see Fama & French, 1999; Kim, 1997). 7 Firms without data on income before extraordinary items and common shares outstanding for the base and current year and those with different fiscal and calendar year-ends (about 35% of the firms) are eliminated from further study. To explore the persistence in the AEs and CFs, we define the non-cash items of earnings or accruals as the change in working capital net of depreciation. Cash flows, Cj, t, are given by: C j;t ¼ Ej;t −Aj;t ;

ð1Þ

where Ej, t and Aj, t are reported earnings and accruals for firm j during year t, respectively. In (1), Ej, t is measured as Income before extraordinary items (i.e., Compustat item 18), and Aj, t is given by the Change in working capital (or ΔWC) minus depreciation and amortization (Compustat item #14). 8 The cash component of earnings is computed for all firms in our sample with the exception of financial companies (SIC codes 6000–6999) given the ambiguity between operating and financing activities for these firms. As in the prior literature (Sloan, 1996; Subramanyam, 1996), we censure data before 1962 due to the absence of certain data items necessary to compute the cash component of earnings and delete observations with CFs that exceed their mean plus three standard deviations. 2.2. Growth metrics To remove any persistence due to changes in the scale of the firm's operations, we measure growth on a per share basis after correcting for stock splits. Our perspective is that of an investor who buys and holds one share over some horizon (e.g., one year), and tracks the growth rate of a firm's reported income per share before extraordinary items (i.e., EPSG) and its CF counterpart. We use a more inclusive approach when computing growth rates which includes negative base- and subsequent year values forEPSG since about 17% of the firms in our sample, on average, have negative values of EPSG for each year. 9 Ignoring the existence of these negative earnings in base years not only induces a biased characterization of the distribution of EPSG rates through leftside truncation but also creates a material survivorship bias. When these negative earnings values are used to compute growth rates, we better account for the existence of distressed firms that continue to operate despite a series of negative earnings and enjoy some probability of recovery, and of start-up firms in industries such as biotechnology, which usually begin life with many years of negative earnings. Growth rates computed using negative values in base years are generally very informative. For instance, a series of successively greater negative EPS values (i.e., increasing in absolute magnitude) indicate that a firm has persistent troubles and including such growth rates provides a more realistic characterization of the distribution of the growth rates for that firm. Negative EPS values declining in absolute magnitudes are common for firms at the beginning of their life cycles, and usually imply that such firms are only beginning to realize the cash inflows from their initial investments. We propose that this should be interpreted as an indicator of positive growth. 10 EPSGj, t is only calculated when two successive EPS have the same sign using:
. EPSGj;t ¼ D EPSj;t −EPSj;t−1 EPSj;t−1 ;

ð2Þ

where D is a dummy variable that is equal to +1 or − 1 if EPSj, t − 1 (as defined earlier) is greater or less than zero, respectively. As in previous studies, the impact of outliers on our results are reduced by deleting firm-year observations where the absolute value of the one-year EPS growth rate exceeds 100% and by trimming the extreme one percent of the distribution of CF growth rates for the whole sample. These extreme EPS growth-rate observations generally occur when the base year EPS is near zero, as is the case for turnaround and start-up firms as they move to profitability. In the next two sections, EPSGj, t and EPSGj, t + 5 refer to the series of one- and five-year (annualized) growth rates for EPS, respectively, for firm j and time t. Similarly, CF1Gj, t and CF1Gj, t + 5 refer to the series of one- and five-year (annualized) growth rates for CFPS, respectively. To avoid problems of raising negative numbers to fractional powers for the five-year growth rates, annual CF growth rates are truncated to |100%|. 7 Due to data backfilling, firms that failed to report financial statements due to problems like thin trading and financial distress but recovered from the problem later could retroactively report financial statements, unlike their counterparts that did not recover from such problems. This time-dated flexibility might produce a selection bias for the earlier years. 8 ΔWC is equal to the change in current operating assets (Compustat item #4), net of cash and short-term investments (Compustat item #1), less the change in current operating liabilities (Compustat item #5), net of short-term debt (Compustat item #34). 9 Chan et al. (2003) delete these firms from their initial sample although a much higher percent (29) of their firms have negative values of earnings before extraordinary items. Contingent years with negative base-year values but sign changes, whose occurrence is much less frequent, are not included because the resulting growth rates cannot be unambiguously interpreted. 10 Ettredge and Fuller (1991) argue that the potential for recovery of firms initially reporting losses tends to be underestimated by the market. La Porta (1996) finds that a large fraction of firms with high expected growth rates based on the forecasts of analysts have negative earnings.

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3. Growth rate persistence for market and industry portfolios 3.1. Portfolio construction All portfolio growth series account for changes in the compositions of the market or industries as companies enter and exit the market on an annual basis. Aggregation results in the diversification of firm-specific variations and also reduces survivorship bias since some firms have shorter lives. 3.1.1. Market- and typical-firm-based portfolios The series of annual EPSGmean, t are computed using the annual mean (implicitly equal weighted) growth rates of all firms existing in the market at the end of each year t. Two alternative EPSG measures are formed by weighting each firm's growth by the relative proportion of its total assets and of its market capitalization for each year t to obtain EPSGvw, t and EPSGindex, t, respectively. Weights based on total assets should exhibit less volatility than those obtained from using market values. 11 The series of annual CF growth rates, CF1Gmean, t, CF1Gvw, t, and CF1Gindex, t are computed in a similar fashion. 3.1.2. Industry-based portfolios To investigate whether certain industries generate more predictable growth than others, we examine the time-series behaviors of annual equal-weighted AE and CF growth rates by industry (EPSGi, t and CF1Gi, t), where i stands for one of the 43 (out of the 48) industry groups used by Fama and French (1997). The five excluded industries are agriculture, banking, insurance, real estate, and trading. Three types of industry characteristics are studied to investigate the impact of industry attributes on growth persistence. The first two characteristics are averaged over the last three years to reduce the impact of potential data errors (Hou & Robinson, 2006). The concentration level as proxied by the Herfindahl index (HHI) is calculated using market shares in terms of sales revenue for the top five firms in each of the 43 industry classifications. Based on the Stigler (1963) argument that persistence in a firm's profitability is positively related to the degree of industry concentration, and the findings of Lev (1983) and Baginski, Lorek, Willinger, and Branson (1999) that the earnings for industries with low competition are persistent, we expect more persistent growth rates for highly concentrated firms and industries. The second industry characteristic is capital intensity, which is computed as the average ratio of net property, plant and equipment (PPE) divided by total assets for the top five firms in terms of market shares (Francis, LaFond, Olsson, & Schipper, 2004). 12 Findings by Lev (1983), Ismail and Choi (1996) and Baginski et al. (1999) find lower persistence in earnings for firms with high capital intensity, since demand fluctuations, for instance, have a higher impact on firms with higher fixed costs. The third industry characteristic is product type where a dummy variable TYPE is used for industries classified into nondurables and services (TYPE = 0) and durables (TYPE = 1) using the survey of current business classification that is available from the Bureau of Economic Analysis. Based on Friedman's permanent income theory, which assumes that the consumption of nondurables and services (durables) is a function of permanent (transitory) income, demand and growth rates for nondurable goods and services should be more stable and more persistent than that for durable goods (Lev, 1983). 3.2. The regression model and descriptive statistics Most work on earnings persistence focuses on modeling the time series of changes in earnings on cross-sections of firms and uses Box–Jenkins based methodologies. 13 In contrast, a model that includes both lagged growth rates and other predictive variables is used herein because it imposes fewer restrictions on the lagged response of the dependent variable, and it allows for the inclusion of other variables that may predict future growth as well as its persistence for each level of aggregation. Our approach is similar in spirit to Welch (1984) who examines quarterly earnings predictability using a distributed lag (DL) model. The DL model that we use is composed of three lags of the dependent variable to alleviate residual autocorrelation, and a set of macro-variables including both realized and forward-looking but not contemporaneous data: Gp;tþn ¼ γ p;0 þ

Q X q¼1

γp;q Gp;t−q þ

N X K X

βp;mv;k MV t−k þ εp;tþn

ð3Þ

mv¼1 k¼1

where Gp, t + n indicates earnings growth rate EPSGp, t + n or CF growth rate CF1Gp, t + n for portfolio p at time t when n = 0 or at time t + 4 when n = 4; q indicates the lag; Q is the number of lagged earnings or CF growth factors; MV indicates the forecast (or actual) macro-variable; N indicates the number of macro-variables included; K is the number of lags of each macro-variable; γp is the intercept; and the error term εpt + nis normally distributed with a mean of zero and a variance of σ 2. Like stock price returns (Fama & French, 1993), AE or CF changes are expected to be related to market-wide factors (Brown & Ball, 1967) or macro-variables. We use the annual forecast of industrial productivity growth or EIPG as a proxy for expected future 11

This is consistent with the use of weights based on metrics other than market capitalizations in fundamental indexing (e.g., Arnott, Hsu, & Moore, 2005). A similar classification occurs with the use of the ratio of gross PPE value to total sales, as in Zmijewski and Hagerman (1981). 13 Examples include Foster (1977) and Brown and Rozeff (1979). Exceptions include Lev (1983), Welch (1984), Freeman, Ohlson, and Penman (1982), Ismail and Choi (1996), and Fama and French (1999). 12

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Table 1 Descriptive statistics and unit root tests, 1950–2006.

EPSGmean EPSGvw CF1Gmean CF1Gvw EPSGindex CF1Gindex GDPG EIPG TERM DEF

Mean

Median

Std dev

Skew

Kurt

ADF1

ADF2

PP

N

0.043 0.020 0.185 0.081 0.065 0.050 0.034 0.041 0.015 0.004

0.056 0.024 0.177 0.068 0.061 0.007 0.035 0.038 − 0.001 0.011

0.070 0.067 0.063 0.076 0.134 0.130 0.022 0.031 0.097 0.030

− 0.187 0.051 0.861 1.331 0.459 1.091 −0.300 −0.263 0.601 −0.348

2.620 3.153 7.845 5.517 3.096 4.024 2.738 3.420 2.883 2.967

− 5.860c − 5.658c − 7.304c − 7.960c − 5.690c − 8.094c −7.263c −6.176c − 8.163c −8.274c

− 5.871c − 5.601c − 7.563c − 8.320c − 5.632c − 8.230c − 7.258c − 6.162c − 8.983c − 8.437c

− 5.193c − 5.563c − 8.742c − 7.711c − 5.322c − 7.872c − 7.098c − 5.333c − 8.206c − 7.605c

56 56 43 43 56 43 56 56 56 56

This table reports summary statistics and results of unit root tests for the time-series of mean and TA-weighted annual growth rates (decimal) of earnings per share (EPSG rates), cash flows per share (CFG rates) and four macro-variables using data for 1950–2006 for EPSG rates and the macro-variables and for 1962–2006 for CFG rates. Growth rates are computed for all publicly traded U.S. firms in the historical COMPUSTAT database that are incorporated in the United States, have a December fiscal year end, and have data to calculate EPS for at least two successive years over the 57-year period, 1950–2006. EPS values are computed using Income before extraordinary items and Number of common shares outstanding from COMPUSTAT. Summary statistics and unit root test results are reported for real EPSG for the average or mean firm portfolio (EPSGmean) and for the total-asset-weighted portfolio (EPSGvw). CF1G is the growth rate of the cash component of EPS obtained by reflecting the adjustments to accrual flows for changes in net working capital and depreciation to obtain cash flows. CFG rates are calculated using data from 1962 to 2006 since prior to 1962 there was not enough data to compute the cash-flow growth component of earnings. Summary statistics and unit root tests results are reported for real growth for the average or mean firm portfolio (CF1Gmean) and the total-asset-weighted portfolio (CF1Gvw). Index EPS growth rate (EPSGindex) is computed using the sum of the EPS of individual firms multiplied by the number of shares outstanding at the end of each year. A similar approach is used to compute the index cash-flow growth rate based on cash-flow adjustments (CF1Gindex). Expected industrial production growth (EIPG) is computed using median forecasts of IP from the Livingston forecasts from 1950 to 2006. The actual real GDP growth rate (GDPG) is extracted from the U.S. Bureau of Economic Analysis from 1950 to 2006. Term premium (TERM) and default premium (DEF) are extracted from Ibbotson Associates over the period 1950 to 2006. Unit root tests are conducted using the Augmented Dickey Fuller with intercept (ADF1), Augmented Dickey Fuller with trend and intercept (ADF2), and the Phillips and Perron (PP). Lag lengths are determined using SIC. a, b and c indicate significance at the 10%, 5% and 1% levels, respectively.

growth of the economy, where EIPGt-1 is the median 12-month forecast of inflation-deflated industrial production for year-end t-1 divided by the actual industrial production for year-end t-1. The data for EIPG are available from the Livingston survey through the Federal Reserve Bank of Philadelphia. A second measure of economic growth is based on actual values of annual real GDP growth or GDPG, extracted from the U.S. Bureau of Economic Analysis. The term and default premiums are included in our model, as aggregate growth rates are expected to be related to business cycle fluctuations. The historical values of the term structure of interest rates or TERM (yield difference of long-term treasuries and three-month T-bills) and the default premium or DEF (yield difference of long-term corporates and long-term treasuries) are extracted from Ibbotson Associates. A lag length k of one is used for all macro-variables, since our expectation is that any impact from prior macro-variable realizations will be reflected in the lagged dependent variables that appear on the right-hand side of our regression model. 14 Descriptive statistics and unit root tests for annual real values of the set of macro-variables and dependent variables are reported in Table 1. The mean EPSGmean is comparable to its counterpart for expected industrial production growth (EIPG). The mean and median EPSGvw are lower than their counterparts for GDP growth. This is consistent with the conjecture of Bernstein and Arnott (2003) that earnings of existing firms grow slower than GDP of existing and new firms. Means and medians of CF growth rates are higher than their counterparts for EPSG, which indicates that the average firm has higher CF than AE growth. 15 Based on the TA-weighted growth rates, firms with high total assets (usually mature firms) tend to have both lower AE growths and lower CF growths than small firms. The means and median for EPSGindex and CF1Gindex are different from their TA-weighted counterparts. The highest standard deviations occur for the growth rates for the indexes. The unit root hypothesis is rejected for all variables at the 0.05 level based on Augmented Dickey Fuller (1979) tests with intercept (ADF1) and with both trend and intercept (ADF2), and based on the Philips–Perron test (PP). 16 Pearson and Spearman correlations for the explanatory variables that are used in the aggregate regressions are reported in Table 2. Not surprisingly, EPSGmean is highly correlated with EPSGvw, as are the equal- and TA-weighted growth rates for CF. As expected, a positive and significant contemporaneous correlation exists between GDPG and all measures of EPSG. Unexpectedly, no significant correlation exists between GDPG and EIPG. Although multicollinearity risk is believed to be low in general, the results related to the GDP variable should be interpreted with caution when both lagged GDP and lagged growth rates are used in the same regression.

14 Since forecasts of GDP growth and actual equity risk premiums have insignificant coefficient estimates, these variables are excluded from the model. We also tested the interactive effect of recession and expansion periods on persistence, but the results are not significant for most series. 15 This could be due to a variety of reasons such as positioning in the latter stages of the firm's life cycle, low ratios of the value of growth prospects to assets in place, more conservative accounting practices, and higher accrual components of earnings. 16 Untabulated results show that the unit root hypothesis is rejected at the o.o5 level for all series when using the more efficient Ng-Perron (2001) test.

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Table 2 Correlation matrix, 1962–2006.

EPSGmean EPSGmed EPSGvw CF1Gmean CF1Gmed CF1Gvw EPSGindex CF1Gindex GDPG EIPG TERM DEF

EPSGmean

EPSGmed

EPSGvw

CF1Gmean

CF1Gmed

CF1Gvw

EPSGindex

CF1Gindex

GDPG

EIPG

TERM

DEF

1.000 0.981c 0.747c 0.088 0.482c 0.018 0.627c 0.132 0.651c 0.045 0.006 − 0.027

0.973c 1.000 0.719c 0.060 0.488c − 0.005 0.600c 0.110 0.611c 0.077 0.059 −0.024

0.799 c 0.757c 1.000 −0.002 0.293a 0.104 0.736c 0.273a 0.588c 0.110 0.002 − 0.140

0.173 0.193 0.142 1.000 0.810c 0.760c 0.102 0.592 c − 0.153 0.270a 0.036 0.236

0.466c 0.493c 0.318b 0.842c 1.000 0.596c 0.368b 0.535c 0.145 0.176 0.063 0.111

0.166 0.155 0.322 b 0.595c 0.554c 1.000 0.048 0.868c −0.006 0.407c − 0.011 0.262a

0.678c 0.676c 0.707c 0.229 0.354b 0.212 1.000 0.197 0.501c 0.098 − 0.118 − 0.021

0.197 0.183 0.372b 0.503c 0.466c 0.867c 0.257 1.000 0.088 0.417c 0.083 0.158

0.560c 0.521c 0.539c − 0.013 0.148 0.102 0.539c 0.128 1.000 − 0.127 − 0.208 − 0.058

0.222 0.224 0.224 0.042 0.099 0.297a 0.127 0.315b −0.054 1.000 0.250 0.390b

0.082 0.113 0.011 − 0.035 0.081 − 0.016 − 0.135 0.099 − 0.151 0.229 1.000 − 0.312b

0.005 − 0.005 − 0.079 0.172 0.096 0.217 0.016 0.130 0.042 0.377b − 0.354b 1.000

This table reports Pearson (not bolded) and Spearman (bolded) correlation coefficients for the time-series of mean, median and TA-weighted annual growth rates (decimal) of earnings per share (EPSG rates), cash flows per share (CFG rates) and four macro-variables using data for 1962–2006. Growth rates are computed for all publicly traded U.S. firms in the historical COMPUSTAT database that are incorporated in the United States, have a December fiscal year end, and have data to calculate EPS for at least two successive years over the 57-year period, 1950–2006. EPS growth values (EPSGmean;EPSGmed; and EPSGvw) are computed using Income before Extraordinary items, Number of Common shares outstanding and total assets from COMPUSTAT. CFPS1G (CFPS1Gmean; CFPS1Gmed; and CFPS1Gvw) are the mean, median and TA-weighted growth rates of the cash component of EPS obtained by reflecting adjustments to accrual flows for changes in net working capital and depreciation to obtain cash flows. CFPSG rates are calculated using data from 1962 to 2006 since prior to 1962 there was not enough data to compute the CFPS component of accrual earnings. Index growth rate (EPSGindex;CF1Gindex) is computed using the sum of the EPS and cash flows of individual firms, respectively, multiplied by the number of shares outstanding at the end of each year. The actual real GDP growth rate (GDPG) is extracted from the U.S. Bureau of Economic Analysis from 1950 to 2006. Term premium (TERM) and default premium (DEF) are extracted from Ibbotson Associates over the period 1950 to 2006. a, b and c indicate significance at the 10%, 5% and 1% levels, respectively.

Table 3 Regressions using market-based portfolios and one-year growth rates, 1950–2006. γ2

γ3

Panel A: mean firm growth-based portfolios 0.281a 0.043c EPSGmean (3.706) (1.911) 0.032a 0.592c (1.869) (5.370) CF1Gmean − 0.127 0.206c (3.154) (− 0.951) 0.199c − 0.038 (3.690) (− 0.300)

−0.130 (− 0.996) 0.099 (0.831) − 0.185 (− 1.322) − 0.207b (− 2.691)

− 0.107 (− 0.871) −0.045 (− 0.656) 0.184 (1.460) 0.329c (3.445)

Panel B: TA-weighted growth-based portfolios 0.188a 0.021c EPSGvw (2.263) (1.783) 0.004 0.348c (0.146) (2.876) CF1Gvw − 0.436c 0.134c (3.652) (−3.337) 0.131c − 0.522c (3.752) (−4.373)

−0.090 (− 0.657) 0.050 (0.379) −0.314b (− 2.389) −0.263b (− 2.465)

− 0.147 (− 0.743) −0.023 (− 0.104) 0.070 (0.367) 0.085 (0.668)

Panel C: index growth-based portfolios 0.428c 0.058c EPSGindex (3.046) (3.767) 0.016 0.533c (0.510) (4.454) CF1Gindex − 0.280a 0.071b (2.175) (−1.828) 0.061 −0.399b (1.105) (−2.431)

−0.222 (− 1.344) −0.170 (− 1.181) −0.263a (− 1.951) −0.160 (− 1.237)

− 0.175 (− 1.302) − 0.093 (− 0.707) − 0.073 (− 0.313) − 0.007 (− 0.047)

γ0

γ1

βGDPG

βEIPG

c

− 1.595 (− 4.402)

− 1.073 (−1.455)

− 0.519 (− 1.006)

a

−1.407 (− 1.729)

− 0.845 (− 1.175)

− 2.262 (− 1.613)

βTERM

c

0.733 (3.175)

0.188 (0.660)

0.581 (1.579)

c

1.357 (3.437)

1.244c (3.205)

2.053c (2.797)

βDEF

c

c

0.195 (3.597)

0.736 (3.645)

−0.074 (− 0.756)

− 1.146c (− 2.705)

0.768c (2.745)

0.096 (1.294)

a

−0.220 (− 1.771)

0.167 (1.013)

−0.200 (− 0.984)

− 0.841 (− 1.690)

0.570 (1.353)

− 0.297 (− 0.359)

N

Adj. R2

56

0.06

56

0.51

56

0.03

43

0.29

56

0.03

56

0.21

43

0.16

43

0.41

56

0.20

56

0.31

43

0.03

43

0.25

This table reports regression results for one-year market-based growth rates of earnings and cash flows on the lagged dependent variable and four macrovariables over 1950–2006 for EPS growth rates and 1962–2006 for cash-flow growth rates. Variables are as defined in Table 1. Panel A reports regression results on the mean firm-based portfolios, where the mean growth rates of individual firms at the end of each year are used to form the market-level growth rate. Panel B reports regression results on the TA-weighted growth rate portfolios, where total-asset-weighted growth rates of individual firms at the end of each year are used to form the market-level growth rate. Panel C reports results on index-based portfolios, where growth rates are computed on the total market index and not on the firms composing it. T-statistics, which are in the parentheses, are corrected for heteroscedasticity and autocorrelation using Newey and West. a, b and c indicate significance at the 0.10, 0.05 and 0.01 levels, respectively.

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3.3. Empirical findings All regressions are estimated using GMM and a Newey and West correction for heteroscedasticity and autocorrelation, which is necessary when lagged dependent variables are used as regressors. Pooled cross-section and time-series regressions are run at the industry level to account for contemporaneous cross-correlations in the error terms. 3.3.1. Empirical findings for one- and five-year growth for market-based portfolios Based on the empirical model (3), the following regression is run on the market-based portfolios of growth rates to investigate short- and long-term persistence: Gp;tþn ¼ γp;0 þ γ p;1 Gp;t−1 þ γp;2 Gp;t−2 þ γ p;3 Gp;t−3 þ βp;EIPG EIPGt−1 þ βp;GDPG GDPGt−1 þβp;TERM TERMt−1 þ βp;DEF DEF t−1 þ εp;tþn

ð4Þ

where all variables are as previously defined. Summary results are reported in Table 3. When regressed solely on the lagged dependent variables, EPSGmean shows evidence of persistence with a positive and statistically significant first-order lag (panel A). However, lags two and three are negative but not significant, which indicates that any persistence is short lived. Short-term persistence remains significant when macrovariables are added. All macro-variable coefficients are significant (and positive except for the negative sign for GDPG), and their inclusion dramatically improves model significance. The positive and statistically significant coefficient on EIPG indicates that an expected increase in industrial production is associated with a similar increase in earnings growth. The positive and statistically significant coefficient on the term (default) premium indicate that contractionary periods, which are generally characterized by high term (default) premium and negative growth in earnings, signal positive expected growth in earnings. The GDPG coefficient represents the highest economic significance and indicates that current negative GDPG is followed by positive aggregate AE growth. Untabulated results that involve the use of the residuals from a regression of GDPG on the EPSG for an examination of median growth rates, remain qualitatively unchanged. Overall, the results show that mean AE growth exhibits evidence of shortterm persistence and of sensitivity to the business cycle. Regression results for mean CF growth rates, CF1Gmean, show little evidence of persistence with consistently negative but nonsignificant coefficients on the lagged dependent variable. While the inclusion of macro-variables improves the model fit, not all macro-variables are significant. This may indicate that mean CF growth rates are less sensitive to the business cycle than mean AE growth rates. It could also indicate that possible earnings manipulation creates an artificial persistence in aggregate earnings growth rates, which is not observed in cash flow growth since the latter are less prone to management manipulation. 17 Results using TA-weighted growth rates are reported in panel B of Table 3 and confirm previous findings of short-term persistence of AE growth with evidence of mean-reversion in CF growth rates that is more pronounced for firms with large asset values. The CF results are consistent with Ismail and Choi (1996) who find negative autocorrelations in the first-order differences of CF. Term and Default coefficients which are positive for EPS growth are negative for CF growth and indicate that earnings increase and CFs decrease following business cycles declines. Table 4 reports summary results for regression (4) using 5-year annualized growth rates. We find little persistence in longterm aggregate equal- and TA-weighted AE and CF growth rates (panels A and B). Since the inclusion of macro-variables does not improve the predictive power of the models, this implies that macro-variables are not good predictors of these two types of longterm growth rates. However, we find some evidence of mean reversion in long-term, index-based AE but not CF growth rates (panel C). Since market-based weights are used to compute index growth rates, this result indicates that firms with large market capitalizations exhibit significant but low magnitude long-term mean-reversion in AE growth rates whereas most other firms, including the mean firm, exhibit little predictability in long-term growth rates. Overall, these results are consistent with a random walk behavior of AE and CF long-term growth rates. These results provide little support for the use of various models (e.g., Ohlson & Juettner-Nauroth, 2005) to calculate the intrinsic value of equity at the market level by using the annual growth rate of AE or variants thereof for the next few years followed by a geometric decline to a fixed perpetuity growth rate thereafter. In summary, our empirical investigation at the aggregate level provides evidence of persistence in mean and TA-weighted short-term AE growth rates and mean reversion in TA-weighted short-term CF growth rates. This discrepancy in persistence between AE and CF short-term aggregate growth rates is consistent with a number of possible explanations given that differences in contemporaneous aggregate AE and CF are captured by aggregate accruals [see the earlier Eq. (1)] and are due to timing differences. First, this discrepancy may be linked to earnings management through the use of accruals to smooth earnings and to meet analysts' forecasts (e.g., Bradshaw, Richardson, & Sloan, 2001; Dechow, Sloan, & Sweeney, 1996). 18 Second, this discrepancy is consistent with the findings by Richardson, Sloan, Soliman, and Tuna (2005) that the accrual component of earnings at the firm level is less persistent than the cash flow component of earnings, 19 and that earnings persistence is negatively related to accrual reliability at the firm level. Furthermore, Li and Zhang (2011) find that firm-level accounting conservatism conditioned on accrual 17 However, this interpretation may not be robust since we later report evidence of predictability of growth rates for earnings using macro-variables but not for cash flows. 18 This hypothesis is examined by the authors in a separate working paper that studies earnings persistence at the firm level. 19 Fairfield, Whisenant, and Yohn (2003) interpret their findings as suggesting that the lower persistence of accruals versus cash flows as being more likely to be due to the effect of growth on future profitability than earnings management.

20

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Table 4 Regressions using market-based portfolios and five-year growth rates, 1950–2006. γ0

γ1

γ2

γ3

Panel A: mean firm five-year growth-based portfolios − 0.048 − 0.077a 0.023c EPSGmean, ltg (3.146) (− 0.985) (− 1.696) 0.021a 0.064 − 0.031 (1.702) (0.690) (− 0.490) CF1Gmean, ltg 0.034 − 0.025 − 0.043 (1.176) (− 0.337) (− 0.774) 0.032 − 0.024 − 0.045 (1.078) (− 0.327) (− 0.746)

− 0.036 (− 0.745) − 0.001 (−0.041) −0.008 (− 0.131) 0.000 (0.011)

Panel B: TA-weighted five-year 0.009c EPSGvw, ltg (3.135) 0.004 (0.660) 0.006a CF1Gvw, ltg (1.958) 0.005 (1.880)

−0.019 (− 0.689) −0.000 (− 0.030) −0.006 (− 0.547) − 0.012 (− 0.947)

growth-based portfolios − 0.042 − 0.023 (− 1.561) (− 0.778) − 0.046 − 0.011 (− 1.368) (− 0.415) − 0.022 − 0.019 (− 1.204) (− 1.281) − 0.030a − 0.024 (− 1.720) (−1.474)

Panel C: index five-year growth-based portfolios − 0.057a 0.037b EPSGindex, ltg (2.059) (− 2.006) 0.047 −0.058b (1.694) (− 2.171) CF1Gindex, ltg 0.019 0.020 (1.206) (0.404) 0.014 0.008 (0.586) (0.227)

− 0.035 (−1.095) − 0.026 (−0.862) 0.033 (0.545) 0.039 (0.651)

− 0.023 (− 0.056) − 0.025 (− 0.601) 0.055 (1.086) 0.071 (1.206)

βGDPG

− 0.392 (− 1.448)

− 0.024 (− 0.228)

0.019 (0.186)

0.026 (0.753)

−0.696 (− 1.301)

−0.234 (− 0.518)

βEIPG

βTERM

0.186 (0.963)

0.004 (0.032)

a

0.112 (1.702)

0.027 (0.791)

0.446 (0.646)

0.337 (1.251)

0.023 (0.652)

0.032 (1.172)

0.002 (0.105)

− 0.000 (− 0.618)

−0.275c (− 2.897)

− 0.074 (− 1.087)

βDEF

− 0.021 (− 0.206)

− 0.020 (− 0.267)

− 0.023 (− 0.444)

0.007 (0.346)

− 0.155 (− 0.447)

− 0.291 (− 1.038)

N

Adj. R2

51

0.01

51

0.01

38

− 0.06

38

− 0.08

51

− 0.01

51

0.01

38

0.03

38

− 0.06

51

0.02

51

−0.01

38

− 0.06

38

− 0.07

This table reports regression results for five-year market-based growth rates of earnings and cash flows on multiple lagged one-year growth variables and four macro-variables over the period 1950 to 2006 for EPS growth rates and the period 1962–2006 for cash-flow growth rates. Variables are as defined in Table 1, and five-year growth rates are computed as annualized five-year growth for each variable. Panel A reports regression results on the mean firm-based portfolios, where the mean five-year growth rates of individual firms at the end of each year are used to form the market-level five-year growth rate. Panel B reports regression results on the TA-weighted growth rate portfolios, where total-asset-weighted five-year growth rates of individual firms at the end of each year are used to form the market-level five-year growth rate. Panel C reports results on index-based portfolios, where five-year growth rates are computed on the total market index and not on the firms composing it. T-statistics, which are in the parentheses, are corrected for heteroscedasticity and autocorrelation using Newey and West. a, b and c indicate significance at the 0.10, 0.05 and 0.01 levels, respectively.

reliability affects accrual persistence only to the extent that it reduces the persistence of reliable accruals. Third, the discrepancy may be due to accruals acting as a leading indicator of changes in aggregate firm prospects in the absence of managerial earnings management (Chan, Chan, Jegadeesh, & Lakonishok, 2001). Any power of macro-variables to explain short-term aggregate growth rates depends upon the method used to aggregate to the market level. Consistent with economic intuition and the averaging out of timing differences over time, long-term aggregate growth rates are neither persistent nor mean-reverting. The inclusion of macro variables does not improve the explanatory power of the model for long-term growth rates. Overall, the long-term results indicate that the behavior of the mean and TA-weighted growth rates is more consistent with a random walk as argued in a strand of the literature. 20 3.3.2. Empirical findings for one- and five-year growth for industry-based portfolios In this section, we run two types of regressions. The first applies the previously described ARDL model to the 43 industries considered herein for both one- and five-year growth rates. Specifically: Gi;tþn ¼ γ 0 þ γ 1 Gi;t−1 þ γ 2 Gi;t−2 þ γ 3 Gi;t−3 þ βEIPG EIPGt−1 þ βGDPG GDPGt−1 þβTERM TERMt−1 þ βDEF DEF t−1 þ εi;tþn

ð5Þ

where Gi, t indicates earnings growth rate EPSGi, t or cash-flow growth rate CF1Gi, t for industry i at time t; and all other variables are as previously defined. The regression (5) results using one-year growth rates are reported in Table 5. Based on panel A, the industry results confirm the previously discussed market-level results of short-term persistence in AE growth, and display heightened evidence of meanreversion in CF growth rates. The significance of the macro-variables is lower than that at the market level, and none of the macrovariables at the industry level are significant in explaining CF growth rates. 20

Examples include Lintner & Glauber, 1967; Beaver, 1970; Ball & Watts, 1972; Albrecht et al., 1977; and Chan et al., 2003.

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Table 5 Regressions using industry-based portfolios and one-year growth rates, 1950–2006. Panel A: mean industry growth-based portfolios

EPSGmean

CF1Gmean

γ0

γ1

γ2

γ3

0.046c (4.327) 0.024 (1.233) 0.230c (5.498) 0.281c (5.803)

0.124b (2.526) 0.180c (4.448) − 0.124c (− 3.711) − 0.119c (− 3.704)

− 0.042 (−0.869) 0.028 (0.684) − 0.031 (−1.075) − 0.028 (−0.987)

− 0.054 (− 1.146) − 0.032 (− 0.781) − 0.025 (− 0.865) − 0.021 (− 0.730)

βGDPG

βEIPG

βTERM

βDEF

Adj. R2 0.01

− 1.101c (− 2.858)

1.107c (3.962)

0.268c (3.298)

0.005 (0.018)

0.05 0.02

− 1.056 (− 1.504)

−0.475 (− 1.051)

0.034 (0.337)

0.225 (0.548)

0.03

Panel B: panel regressions of mean industry growth using industry characteristics γ0 EPSGmean

CF1Gmean

γ1 c

0.054 (4.170) 0.057c (4.203) 0.269c (7.713) 0.264c (8.267)

γ2 c

0.155 (3.068) 0.112 (1.371) −0.139c (−3.448) −0.196c (−3.047)

−0.039 (− 0.781) − 0.042 (− 0.836) −0.039 (− 1.107) −0.043 (− 1.239)

γ3 −0.049 (− 0.986) − 0.045 (− 0.915) − 0.010 (−0.301) − 0.006 (−0.185)

HHI 0.001 (−0.113) 0.000 (−0.010) − 0.003 (− 0.576) 0.003 (1.345)

CI

TYPE a

− 0.012 (− 1.885) − 0.013a (− 1.832) −0.061a (− 1.825) −0.474b (− 2.254)

Lag1* HHI

Lag1* CI

Lag1*Type

a

− 0.014 (− 1.852) − 0.017b (− 2.286) − 0.001 (− 0.033) − 0.017 (− 1.108)

Adj.R2 0.04

− 0.009 (− 0.478)

0.071 (0.903)

0.067 (1.407)

0.04 0.02

− 0.005 (− 1.293)

0.686 (1.101)

0.089 (1.565)

0.03

This table reports pooled cross-section and time-series regression results of industry-based growth portfolios. Mean growth rates of industries are computed using mean growth rates of individual firms for years for which at least five observations are available within the period 1950–2006 for EPSGmean and for 1962–2006 for CF1Gmean . Panel A reports pooled cross-section and time-series regression results from regressing mean industry growth rates on lagged dependent variables and four macro-variables (as defined in Table 1). Panel B reports pooled cross-section and time-series regression results from regressing mean growth rates on lagged dependent variables, the industry Herfindal index (HHI), the industry capital intensity (CI), industry type (TYPE) and their interactive effects with the dependent variable. The capital intensity (CI) for each industry is calculated as the average ratio of net property, plant and equipment divided by total assets for the top five firms in terms of market share; the Herfindal index (HHI) is a proxy of industry concentration and is measured using the top five firms in terms of market share in each industry; and TYPE is a dummy variable that classifies industries as durables or nondurables & services (takes the value of 1 for durables and 0 otherwise). GMM regression t-statistics corrected for heteroscedasticity and autocorrelation using Newey and West are reported in the parentheses. a, b and c indicate significance at the 0.10, 0.05 and 0.01 levels, respectively.

The second regression examines the explanatory power of industry characteristics, as well as their impact on growth rate persistence by regressing growth rates on lagged one-year growth rates, industry concentration, capital intensity, product type and a set of interactive variables. This leads to the following formulation where all variables are as previously defined: Gi;tþn ¼ γ0 þ γ 1 Gi;t−1 þ γ 2 Gi;t−2 þ γ 3 Gi;t−3 þ βHHI HHIi;t−1 þ βCI CIi;t−1 þ βTYPE TYPEi;t−1 þδHHIlag1; HHIi;t−1  Gi;t−1 þ δCIlag1; CIi;t−1  Gi;t−1 þ δTYPElag1; TYPEi;t−1  Gi;t−1 þ εi;tþn

ð6Þ

Regression (6) results based on mean one-year growth rates are reported in panel B of Table 5. The overall results of persistence and mean-reversion for AE and CF growth rates are unchanged with the addition of industry characteristics. The concentration level (HHI) does not explain the mean industry growth or influence its persistence. Product type (TYPE) and capital intensity (CI) have explanatory power for growth in AE with higher growth rates for nondurables versus durables, and for less versus more capital intensive industries. Capital intensity (CI) also has explanatory power for CF growth, with less capital intensive industries generating higher growths. Contrary to expectations, the inclusion of interactive variables shows no evidence of higher persistence or mean-reversion of growth rates attributable to such industry characteristics. To guard against the omitted variables problem, we also add the macro-variables to regression (7) and obtain qualitatively similar results. Based on panel A of Table 6 for regression (5), little evidence of long-term growth persistence exists for AE or CF based on lagged one-year growth rates or when lagged macro-variables are included in the predictive set. Based on panel B of Table 6 for regression (6), little persistence exists in mean long-term growth rates using lagged mean one-year growth rates. Product type (TYPE) shows explanatory power for long-term AE growth rates, with durables having lower long-term growth rates than services and non-durables. Interestingly, capital intensity (CI), which had a negative and significant coefficient for short-term CF growth, has a positive and significant coefficient for long-term CF growth rates. Thus, as expected, firms with higher capital intensity have lower CF growth in the short-run but end-up having higher long-term growth rates. Long-term growth persistence is not impacted by any of the industry characteristics. In summary, the industry results confirm the previous findings of short-term persistence for AE growth rates and little persistence in CF growth rates. Consistent with economic intuition, we find little evidence of persistence in long-term growth rates. However, product type (capital intensity) provides some explanation for AE (CF) growth rates. Short-term macro-variables do not explain growth rates beyond one-year.

22

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Table 6 Regressions using industry-based portfolios and five-year growth rates, 1950–2006. Panel A: mean industry growth-based portfolios

EPSGmean, ltg

CF1Gmean, ltg

γ0

γ1

γ2

γ3

0.060c (17.813) 0.063c (15.139) 0.069c (18.890) 0.068c (12.916)

0.002 (0.151) 0.004 (0.301) 0.009 (1.562) 0.009 (1.573)

0.002 (0.149) 0.0006 (0.045) − 0.001 (− 0.132) − 0.001 (− 0.160)

0.016 (1.396) 0.015 (1.258) 0.005 (0.883) 0.005 (0.908)

βGDPG

βEIPG

βTERM

βDEF

Adj. R2 −0.00

− 0.037 (− 0.372)

− 0.031 (− 0.472)

− 0.004 (− 0.294)

0.003 (0.048)

− 0.00 −0.00

0.004 (0.056)

0.011 (0.158)

0.021 (1.373)

0.044 (0.543)

− 0.00

Panel B: panel regressions of mean industry growth using industry characteristics

EPSGmean, ltg

CF1Gmean, ltg

γ0

γ1

γ2

γ3

HHI

CI

TYPE

0.067c (17.147) 0.065c (16.124) 0.060c (13.433) 0.061c (11.126)

− 0.001 (− 0.070) 0.023 (0.980) 0.009 (1.421) 0.002 (0.154)

− 0.006 (− 0.489) − 0.004 (− 0.340) 0.002 (0.302) 0.003 (0.344)

0.005 (0.589) 0.005 (0.477) 0.002 (0.317) 0.002 (0.300)

0.446 (1.380) 0.368 (1.086) − 0.143 (− 0.404) − 0.247 (− 0.644)

0.059 (1.220) 0.084 (1.557) 0.177c (3.104) 0.149a (1.924)

− 0.024c (− 4.773) − 0.024c (− 4.479) 0.0009 (0.825) 0.004 (0.943)

Lag1*HHI

Lag1*CI

Lag1*Type

Adj. R2 0.02

0.001 (1.033)

− 0.508 (− 1.599)

0.004 (0.131)

0.02 0.01

0.497 (0.612)

0.197 (0.835)

− 0.016 (−1.130)

0.01

This table reports pooled cross-section and time-series regression results for industry-based growth portfolios. Mean five-year growth rates of industries are computed using annualized mean growth rates of individual firms for years for which at least five observations are available within 1950–2006 for EPSGmean and for 1962–2006 forCF1Gmean. Panel A reports pooled cross-section and time-series regression results from regressing five-year mean industry growth rates on lagged one-year growth rates and four macro-variables (as defined in Table 1). Panel B reports pooled cross-section and time-series regression results from regressing five-year mean growth rates on lagged one-year growth rates, the industry Herfindal index (HHI), the industry capital intensity (CI), industry type (TYPE) and their interactive effects with the dependent variable. The capital intensity (CI) for each industry is calculated as the average ratio of net property, plant and equipment divided by total assets for the top five firms in terms of market share; the Herfindal index (HHI) is a proxy of industry concentration and is measured using the top five firms in terms of market share in each industry; and TYPE is a dummy variable that classifies industries as durables or nondurables & services (takes the value of 1 for durables and 0 otherwise). GMM regression t-statistics corrected for herteroscedasticity and autocorrelation using Newey and West are reported in the parentheses. a, b and c indicate significance at the 0.10, 0.05 and 0.01 levels, respectively.

4. Conclusion In this paper, we examined the persistence of short- and long-term growth rates for both accrual earnings (AEs) and cash-flows (CFs) at the market and industry levels. Unlike previous work, we use a long time series of data and a multivariate approach with both lagged growth rates and various other explanatory variables to better capture the behavior of growth across time at these two levels of aggregation. Our paper extends the existing literature on aggregate growth rates by exploring the usefulness of macro- and industry-related variables in explaining future earnings and cash-flow growth rates. Evidence of growth rate persistence has implications for investment management, such as risk premium estimation, asset allocation and sector rotation. Consistent with economic intuition and the intuition behind momentum strategies, we find persistence in AE growth rates at the market and industry levels in the short run (Tables 3 and 5, respectively), and neither persistence nor mean reversion at both levels in the long run (Tables 4 and 6, respectively). Economic indicators (such as forecasted industrial production, GDP growth, term premium and default premium) exhibit explanatory power for short- but not long-term growth rates at the market level. Industry attributes (such as capital intensity and product type) exhibit explanatory power for both short- and long-term earnings growth rates at the industry level. In contrast for CF growth rates, we find mean reversion or neither mean reversion nor persistence in the short- and long-run, respectively, at the market level (Table 3), and mean reversion (Table 6) and neither mean reversion nor persistence in the short- (Table 5) and long-run (Table 6), respectively, at the industry level. Future research should address whether the discrepancy in persistence between aggregate earnings and cash flows can be interpreted as indicating earnings manipulation or management.

Acknowledgment Financial support from the Concordia University Research Chair in Finance, IFM2 and SSHRC are gratefully acknowledged. We are grateful to an anonymous referee for helpful comments and suggestions. Our thanks also go to Sean Cleary, Gordon Fisher, Eugene Kandel, Simon Lalancette and Latha Shankar, and to the discussant (Joseph Marks) and the participants at the 2006 meeting of the Financial Management Association (Salt Lake City) for their many helpful comments on earlier versions of this paper. The usual disclaimer applies.

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