Predicting Restatements in Macroeconomic Indicators using Accounting Information

Transcription

1 Predicting Restatements in Macroeconomic Indicators using Accounting Information Suresh Nallareddy Columbia University Maria Ogneva University of Southern California March 2014 Preliminary and incomplete. Please do not circulate. We would like to thank John Donaldson, Trevor Harris, Urooj Khan, Nan Li, Emi Nakamura, Stephen Penman, and Gil Sadka for their helpful comments and suggestions. Any remaining errors are our own.

2 Abstract Initial announcements of macroeconomic indicators are based on imprecise and incomplete information. Government statistical agencies routinely restate the initial estimates over the course of several subsequent years as more information becomes available. We find that simple accounting-based aggregates, such as earnings dispersion, can predict future restatements in macroeconomic estimates, including nominal and real GDP growth and unemployment. Out-of-sample tests suggest early macroeconomic estimates can be significantly improved by incorporating accounting information. Early macroeconomic releases attract intense scrutiny from policy makers, capital market investors, business planners, and other economic agents. Therefore, improving the accuracy of early macroeconomic estimates has wide-ranging implications for the efficiency of a large spectrum of economic decisions.

3 1. Introduction We investigate whether real-time aggregate accounting information can predict errors in early announcements of macroeconomic indicators. Regulators, business planners, investors, and other interested parties heavily scrutinize the announcements of major macroeconomic indicators, such as gross domestic product (GDP). Macroeconomic expectations shaped by these announcements affect a large spectrum of decisions by government agencies and economic agents. However, initial announcements of macroeconomic indicators are based on imprecise and incomplete information. 1 The initial estimates are routinely restated over the course of several subsequent years as more information becomes available. 2 We find that simple accounting-based aggregates, such as earnings dispersion, can predict future restatements in macroeconomic estimates. Our out-of-sample tests suggest that incorporating accounting information can significantly improve early macroeconomic estimates. When estimating GDP for the quarter that just ended, the BEA (Bureau of Economic Analysis) is put in a position of a corporate controller tasked with reporting last quarter s earnings after receiving information from only a fraction of subsidiaries. Missing components of GDP have to be nowcasted by using trend estimates to extrapolate information from prior months, quarters, or years. 3 In addition, the non-missing hard data are based on limited-size 1 For example, 30% of the initial quarterly GDP estimate is based on a combination of the Census Bureau s monthly surveys from only the first two months of the quarter extrapolated for the third month, whereas 25% of the estimate is based solely on the trend data derived from various indicators (Grimm and Weadock 2006). The monthly Census Bureau surveys are not a 100% accurate. They cover approximately 35,500 reporting units compared to the annual coverage of 150,000 units (Landefeld et al. 2008). Further, respondents are not mandated to respond to monthly survey questionnaires, leading to a lower response rate. 2 For example, initial announcement of nominal GDP growth for the first quarter of 2008 is a positive 3.19%, which is subsequently revised to a negative 0.46%. Likewise, the initial announcement of real GDP growth for the first quarter of 2001 is a positive 1.98%, which is subsequently revised to a negative 1.14%. 3 An example of a trend-based estimate for which no monthly or quarterly hard survey data is available is spending in the personal care category (including health clubs, barbers, and beauty shops), where quarterly 1

4 surveys and thus represent a noisy estimate of the underlying macroeconomic construct. Precision of reported macroeconomic aggregates can be increased either by using more precise trend estimates or by adjusting the imprecise source data using accurate information from alternative sources. Overall, any information that is correlated with true underlying macroeconomic indicators or their trends can be used to increase the precision of macroeconomic nowcasts. Aggregated accounting data represent one such timely source of information. First, aggregate earnings may serve as a GAAP-based proxy for the Corporate Profits component of GDI (gross domestic income), which is an income-based counterpart of expenditure-based GDP. 4 In fact, the BEA incorporates selected GAAP earnings information in quarterly Corporate Profits estimates. However, if it does not consider GAAP earnings from a full spectrum of industries, ignores information contained in earnings from prior fiscal quarters, or uses earnings to estimate only GDI, aggregate earnings may be used to improve the accuracy of early GDP estimates. 5 Second, accounting information, aggregate earnings dispersion in particular, may serve as a leading indicator for changing economic conditions. For example, Jorgensen et al. (2011) and Kalay et al. (2014) link earnings dispersion to structural shifts in the economy and subsequent movement of labor or capital. In the presence of frictions, such movement takes time, which either directly leads to slower growth in corporate sector s output or leads to temporary increases estimates are based on a combination of population growth, consumer price index in personal care services, and data from prior Census Bureau Services Annual Survey (Landenfeld et al. 2008). 4 The NIPA definition of corporate profits BEA uses in calculating GDI is operationally derived from taxable income reported annually to the IRS. Complete tax data are available only with a two-year lag, so quarterly NIPA profit estimates are extrapolated from the most recent annual figure (Landefeld et al. 2008). 5 GDI estimates are announced with a lag relative to early GDP estimates, so early GDP estimates may not incorporate GAAP earnings information in a timely manner. 2

5 in unemployment, which decreases consumer demand, and subsequently GDP. 6 In both cases, higher earnings dispersion precipitates decreases in output and may thus be used to improve the precision of the trend estimates embedded in initial GDP estimates. Over time, statistical agencies obtain more complete and accurate information pertaining to past quarters. 7 Based on such information, the BEA restates previously reported estimates of GDP and its components. 8 If initial estimates do not fully incorporate past accounting information, then earnings-based variables should predict future macroeconomic restatements. Our sample includes restatements in real and nominal GDP growth for 160 quarters in the period. To confirm a link between the true underlying macroeconomic constructs and earnings aggregates, we regress final restated values for GDP growth on contemporaneous and lagged aggregate earnings and earnings dispersion. Nominal and real GDP growth is significantly associated with contemporaneous (but not lagged) aggregate earnings. These results are consistent with aggregate earnings being useful for estimating a component of the sameperiod GDP. Both nominal and real GDP growth are significantly associated with contemporaneous, and especially lagged, aggregate earnings dispersion, supporting economic theories linking performance dispersion to temporarily depressed output. 6 Earnings dispersion to some extent captures dispersion in productivity among private firms. Macroeconomics has a long history of linking such dispersion to changes in economic output. The creative destruction (Schumpeter 1942; Foster et al. 2000, 2006) and sectoral shift (Lucas and Prescott, 1974; Lilien 1982) theories suggest that higher productivity or performance dispersion precipitates reallocation of labor/capital from worse to better performing firms. Because of frictions, such reallocation takes time leading to lower output (or higher unemployment) in the economy in the short-run due to resource misallocation. The economic magnitude of the effect such misallocation can have on total output can be substantial (e.g., Hsieh and Klenow 2009). 7 Such information is derived from administrative sources, such as tax filings, from the Census Bureau s annual surveys with mandatory response requirements based on larger samples of respondents and, eventually, from the Census Bureau s benchmark surveys. The latter are conducted every five years and cover virtually all businesses and over 95% of expenditures included in GDP (Landefeld et al. 2008). 8 The initial quarterly estimates are followed by two restated estimates announced over the subsequent two months, which are further revised annually over the next three years and may undergo later revisions following the five-year benchmark surveys. 3

6 Our main restatement prediction tests suggest that prior quarter aggregate earnings dispersion is a robust restatement predictor, with higher earnings dispersion precipitating downward restatements in GDP growth. Specifically, a one standard deviation increase in prior quarter earnings dispersion predicts a 0.44% (0.43%) decrease in restatement for the nominal (real) GDP growth. These magnitudes correspond to 7% (17%) downward revisions in the corresponding average initial GDP growth estimates. However, predictability evidence based on lagged or contemporaneous aggregate earnings or contemporaneous earnings dispersion is mixed and is not robust to alternative test specifications. Information contained in earnings is incremental to the stock market or macroeconomic information. Earnings dispersion remains statistically significant after controlling for aggregate market returns, return dispersion, initial announcement-day market returns, macroeconomic variables, and a recession indicator. These results are robust to excluding the Great Recession period (the fourth quarter of 2007 to the first quarter of 2009) and using restatements accumulated over shorter horizons. 9 We conduct two additional analyses to gain insights into the mechanism that links past earnings dispersion to GDP restatements. First, under structural unemployment theory, dispersion in earnings leads to greater temporary unemployment, which lowers GDP. If the documented predictable restatements result from not fully incorporating a signal about increasing unemployment, dispersion in earnings should also predict restatements in unemployment figures. Our results confirm that greater earnings dispersion precedes upward restatements in 9 Namely, our main analyses use restatements accumulated between the initially announced and currently available estimates. The use of estimates available at the end of the sample period has pros and cons (see a similar discussion in Gilbert 2011). On the one hand, they represent more homogenously measured macroeconomic indicators that incorporate the latest methodological changes. On the other hand, the forecast horizons are unrealistically long, they vary in length depending on the vintage of the initial estimate, and very late revisions are less likely to result from the newly available information. We use two-year horizon restatements as an alternative that is sufficiently long term to accumulate most information-related revisions. All our results are robust to this change. 4

7 unemployment estimates. Second, under both the structural unemployment and creative destruction theories, across-industry dispersion in earnings is associated with higher frictions in labor and capital movements thus having a greater effect on unemployment and output. When we decompose earnings dispersion into across-industry dispersion and residual components, we find the across-industry dispersion component drives macroeconomic revision predictability. Finally, we conduct out-of-sample restatement prediction tests. Using only information available by the end of quarter t-1, we form regression-based forecasts of two-year- horizon restatements following the initial GDP growth announcements made in quarter t. 10 We evaluate our forecasts prediction performance relative to a naïve moving-average benchmark by estimating out-of-sample R 2 (Campbell and Thompson 2008). 11 Our results suggest a simple earnings-dispersion-based model significantly outperforms a naïve forecast for both real and nominal GDP growth, with greater restatement predictability observed in later periods. These findings have significant practical implications, suggesting that early GDP estimates can be improved in real time using accounting information. Our study is related to a recent stream of literature in accounting that investigates whether macroeconomic forecasters efficiently incorporate accounting information (e.g., Kothari et al. 2013; Konchitchki and Patatoukas 2013, 2014; Kalay et al. 2014). In this paper, we go beyond forecast efficiency and ask whether the realized values of macroeconomic indicators contain errors correlated with accounting information. This represents a more fundamental question because, while macroeconomic forecasts are available from a variety of sources characterized by 10 Specifically, we regress two-year GDP growth restatements on prior aggregate earnings and earnings dispersion within an expanding window ending with restatements made in quarter t-1. The obtained regression coefficients are combined with accounting variables available by the end of quarter t-1 to form restatement forecasts for GDP growth estimates initially announced in quarter t. 11 To ensure these tests have no look-ahead bias, we use restatements made over two-year horizons and allow for the appropriate gaps between the estimation and testing windows. 5

8 varying degrees of accuracy, macroeconomic indicator announcements represent a single most important source of information about the economy. Second, we contribute to a literature in macroeconomics that evaluates the quality of early macroeconomic estimates. 12 We show that accounting information can reliably predict macroeconomic restatements above and beyond previously suggested predictors. 2. Institutional Background and Related Literature 2.1. GDP Restatement Process The BEA (Bureau of Economic Analysis) issues the initial quarterly GDP estimate three weeks after the quarter end. The estimate is largely based on the data from monthly Census Bureau surveys that poll businesses and other economic agents, and cover about 35,500 reporting units (Landefeld et al. 2008). According to Grimm and Weadock s (2006) breakdown of initial GDP estimate by information source, approximately 45% of the estimate is based on the full three-months information. Another 30% is based on a combination of the Census Bureau s monthly surveys from the first two months of the quarter and trend extrapolations for the third month. The remaining 25% is based solely on the trend data derived from various indicators. The initial estimate is revised one and two months following the initial announcement due to either receiving information from additional sources (e.g., Census Bureau monthly surveys covering the last month of the quarter) or to receiving more precise information related to prior sources (e.g., questionnaires from late survey responders). It is further revised annually over the next three years when more information gets incorporated into the estimate, for 12 Depending on test specifications, this research finds that revisions in major macroeconomic indicators are either unpredictable (Faust et al. 2005) or can be predicted using macroeconomic variables (Arouba, 2008) or returns on initial announcement days (Gilbert, 2011). 6

9 example, coming from annual tax filings or annual Census Bureau surveys. Compared to monthly surveys, annual surveys cover a larger number of reporting units (approximately 150,000 units) and are mandatory. 13 Finally, every five years the BEA releases a comprehensive revision of accounts that is based on results from the recent economic census that covers virtually all businesses in the United States (in these years, no annual revisions are published). Based on the census results, the BEA revises its benchmark estimates for the structure of economy. GDP component estimates for the quarters following the census date are re-weighted based on the new benchmark data. Five-year comprehensive revisions may also include methodological or statistical changes. For example, starting in 1999 the BEA includes investment in computer software as part of fixed investment. Overall, early estimates of GDP and its components are based on limited data and rely in part on trend-based extrapolations and approximations. Any prior information helpful in predicting a given quarter s GDP should be incorporated in the initial macroeconomic estimate for that quarter. As explained in the next section, accounting earnings represent one such information source Accounting Information and GDP Estimates Accounting earnings are both directly and indirectly linked to GDP. The direct link stems from corporate profits being a component of GDI (gross domestic income), which is an incomebased alternative to final-expenditure-based GDP. Although the NIPA definition of corporate profits used by BEA is operationally derived from taxable income reported to the IRS, aggregate GAAP earnings and Corporate Profits are still highly correlated (e.g., Dichev (2013) reports a 13 Annual data are interpolated or extrapolated to prior quarters using quarterly or monthly source data. 7

10 correlation exceeding 0.89 prior to 1980). Complete tax data are available only with a two-year lag, so quarterly NIPA profit estimates are extrapolated from the most recent annual figure using a combination of the Census Bureau Quarterly Financial Report that samples manufacturing, trade, and mining companies, as well as publicly available corporate reports for the companies in industries not surveyed by the Census Bureau (Landefeld et al. 2008). However, BEA incorporates GAAP earnings from only a few industries and may ignore information contained in earnings from prior fiscal quarters. The indirect link between accounting earnings and GDP arises because the former serves as a leading indicator for economy-wide trends. Such indirect link is supported by two longstanding macroeconomic theories on creative destruction and sectoral shift. Creative destruction theory (Schumpeter 1942; Foster et al. 2000, 2006) suggests resources should be reallocated from lower to higher productivity firms, and the potential for reallocation is greater in the periods with high productivity dispersion. However, frictions slow down resource movements, leading to temporary resource misallocation and lower output. The loss in aggregate output due to such misallocation can be economically significant (e.g., Hsieh and Klenow 2009). According to the sectoral shift theory (Lucas and Prescott 1974; Lilien 1982), higher dispersion in performance causes migration of labor from worse performing to better performing firms. Frictions (e.g., costs related to job search and new skills acquisition) delay labor movement, leading to higher unemployment in the interim, which in turn depresses consumption and aggregate output (Okun, 1962; Abel and Bernanke, 2005). Recent studies in accounting (Jorgensen et al. 2011; Kalay et al. 2014) build upon these theories by linking dispersion in performance to aggregate GAAP earnings dispersion. They provide evidence consistent with earnings dispersion precipitating structural shifts in the 8

11 economy, subsequent movement of labor or capital, and aggregate output decreases Prior Research on Predictability in GDP Restatements The accuracy and efficiency of early GDP estimates have been a subject of a stream of literature in economics that debates a news versus noise interpretation of macroeconomic revisions. Under the news interpretation, revisions are completely unpredictable using any information available at the time of the initial estimate and thus only occur as a consequence of receiving new economic information. Under the noise interpretation, revisions reflect information that is already available at the time of the initial estimate and thus initial estimates are not rational. Conclusions from this literature are mixed. Early studies provide little evidence of predictability in GDP growth revisions in the United States. Mankiw and Shapiro (1986) conclude that revisions in real and nominal GNP growth estimates are unpredictable using initial GNP estimates, aggregate stock market returns, three-month treasury bills, and lagged GNP growth estimates. Faust et al. (2005) find that two-year restatements in real quarterly GDP growth are not predictable either in sample or out of sample, whereas restatements relative to the final estimate are predictable using the level of initial forecasts. Later studies find some evidence of restatement predictability. Aruoba (2008) finds that three-year restatements in both nominal and real GDP growth rates are predictable using initially announced estimates, past restatements, and unemployment rates (the latter are used to proxy for the stage of the business cycle). However, the real-time forecasting tests yield no evidence of out-of-sample predictability in either real or nominal GDP growth revisions hold-outregression-based forecasts do not provide a statistically significant improvement over a naïve extrapolation of the historical average restatements. Gilbert (2011) provides indirect evidence 9

12 consistent with predictability of GDP restatements. He finds that returns around the second and especially third restatement announcements (two and three months following the quarter end) are correlated with subsequent restatements. The signs of correlations, however, differ between expansions and recessions determined by the NBER ex post. Overall, evidence on GDP growth restatement predictability in the United States is mixed. Importantly, prior research does not consider accounting variables among GDP restatement predictors and provides no real-time out-of-sample predictability evidence Prior Research on Accounting Earnings and Macroeconomics The notion that accounting earnings contain macroeconomic information is widely recognized. 14 Studies that are closest to our research objective explore efficiency of macroeconomic forecasts with respect to accounting information. Specifically, Kothari et al. (2013) investigate the efficiency of inflation forecasts; Konchitchki and Patatoukas (2013, 2014) study nominal and real GDP growth forecasts; and Kalay et al. (2014) look at unemployment and industrial production forecasts. These studies argue that accounting earnings are relevant for forecasting future macroeconomic indicators and show that macroeconomists forecasts do not fully incorporate accounting information. Unlike these studies, we investigate whether the realized values of macroeconomic aggregates contain predictable errors, which is a more fundamental question compared to the forecast efficiency. Multiple economists issue macroeconomic forecasts and several surveys 14 Studies that explore macroeconomic content of aggregate earnings or earnings forecasts include, among others, Kothari et al. (2006), Anilowski et al. (2007), Shivakumar (2007, 2010), Sadka and Sadka (2009), Cready and Gurun (2010), Hann et al. (2012), Choi et al. (2011), and Gallo et al. (2013). A related stream of research examines the macroeconomic information content of firm-specific earnings, analysts, and/or management s forecasts, including Basu et al. (2010), Hutton et al. (2012), Bonsall et al. (2013), Ogneva (2013), and Hugon et al. (2014). Some of the above studies document the macroeconomic content of earnings indirectly through relating them to aggregate stock returns, whereas others explicitly link earnings or earnings forecasts to such macroeconomic indicators as GDP, consumption, industrial production, inflation, and interest rates. 10

13 aggregate such forecasts. These forecasts differ in efficiency and accuracy (e.g., Kothari et al. (2013) report different findings for CPI forecasts from MMS and SPF surveys). In contrast, a single realized value of each macroeconomic indicator is reported by a specific government agency and is heavily scrutinized by investors, policy makers, and economic forecasters. 3. Sample Selection and Variable Measurement 3.1. Sample We obtain all macroeconomic data from the Real-Time Data Set for Macroeconomists maintained by the Federal Reserve Bank of Philadelphia. 15 The main analyses use nominal and real GDP growth rates that represent seasonally adjusted percentage changes. 16 The additional analyses use the seasonally adjusted civilian unemployment rate measured and reported by the Bureau of Labor Statistics (BLS). All macro variables are measured at the quarterly frequency, annualized, and expressed in percent. Our accounting data come from the intersection of CRSP and Compustat datasets from 1972 to 2012, a period over which the quarterly accounting data are available. We impose the following restrictions on our sample. First, we include only ordinary common shares (share codes 10 and 11) that are traded on the NYSE, AMEX, or NASDAQ exchanges. Second, to align macroeconomic data with firm-level accounting data, we include only firms with fiscal year ends in March, June, September, or December. Finally, every quarter we winsorize the top and bottom two percent of firm-level observations before calculating aggregate measures. Our final firmlevel sample contains 472,158 firm-quarter observations Prior to 1992, the dataset includes the gross national product (GNP) instead of GDP. The initial GDP estimates are missing for the fourth quarter of 1995 due to the government shutdown; we omit this quarter from our sample. 11

14 3.2. Estimating Aggregate Earnings, Aggregate Returns, and Dispersion We estimate two aggregate measures of accounting information aggregate earnings and earnings dispersion. Because we are interested in new information related to aggregate earnings and dispersion, we perform estimation in several stages aimed at purging persistent components from both firm-specific and aggregate earnings. Specifically, we estimate aggregate earnings news in three steps. First, we estimate seasonal earnings changes (EC) for each firm-quarter as follows: ( X it X it 4) EC i, t =, (1) P it 1 where X it is realized earnings for firm i in quarter t, X it-4 is realized earnings for firm i in quarter t-4, and P it-1 is the price per share for firm i at the end of quarter t-1. Second, we estimate aggregate earnings changes (AEC) for each quarter as an equal-weighted average of firm-level earnings changes: N 1 t AEC t = ( ECi, t ), (2) N t i= 1 where AEC t is the aggregate earnings change for quarter t, and Nt is the number of firms in that quarter. 17 Third, because aggregate earnings are persistent (Sadka and Sadka 2009), we use the following AR (2) model to isolate the non-persistent component: AEC ρ + ρ AEC + ρ AEC + e, (3) t = 0 1 t 1 2 t 2 t Our aggregate earnings news measure (Ear t ) is the residual from equation (3) Our findings are robust to the use of the value-weighted average of firm-level earnings. 18 We verify that higher-order adjustment of aggregate earnings surprises for autocorrelation is unnecessary by estimating the AR(1) coefficient for the residual from (3). The obtained coefficient is equal to and is 12

15 We estimate aggregate earnings dispersion as the standard deviation of earning changes for a given quarter as follows: N 1 t 2 AEarDis t = ( ECi, t AECt ), (4) N t i= 1 where AEarDis t is the aggregate earnings dispersion for quarter t, AEC t is the aggregate earnings for quarter t, and Nt is the number of firms during that quarter. To isolate the non-persistent component of aggregate dispersion, we estimate an AR(2) model by substituting aggregate earnings dispersion instead of aggregate earnings into equation (3) above. Our aggregate earnings dispersion news measure (Ear_Disp) is a residual from the AR(2) model. 19 In addition to accounting-based measures, we estimate three stock-return-based aggregate measures aggregate return and aggregate return dispersion for the quarter, and market return on the initial GDP announcement day. Aggregate return (Mkt_Ret) is an equal-weighted average return estimated using all firms in our sample for a given quarter. 20 Aggregate return dispersion (Ret_Disp) is estimated using equations (2) and (4) after replacing earnings changes with stock returns for the quarter. Aggregate return dispersion is autocorrelation-adjusted and represents a residual from the AR(2) model. 21 However, we do not adjust aggregate return for autocorrelation because market returns are not persistent. The market return on the initial announcement day statistically insignificant (t-statistics of -0.08), suggesting the AR(2) estimation successfully isolates aggregate earnings surprises. 19 We verify that further adjustment for autocorrelation is not necessary, using a process similar to that described in footnote 18 for aggregate earnings surprises. Namely, we estimate the AR(1) coefficient for Ear_Disp and find it is equal to and is statistically insignificant (t-statistics of -0.16). 20 The results are robust to the use of the value-weighted average of firm-level stock returns. 21 We find that the AR(1) coefficient for Ret_Disp is equal to and is statistically insignificant (t-statistics of ), suggesting the AR(2) estimation successfully isolates a surprise component in return dispersion. 13

16 (Ann_Ret) is the S&P500 index return on the day of the BEA s announcement on the initial GDP estimate for the prior quarter Restatements of Macroeconomic Indicators The BEA releases initial GDP estimates for each quarter within one month of the quarter end. As described in section 2.1, initial estimates are then restated multiple times over the course of several years. Our main tests rely on cumulative restatements between the initially released values for quarter t and the final restated values as they appear today (our last vintage of macroeconomic data is from December 2013). We also track restatements accumulated at fixed time intervals following the initial estimate release. Namely, we use restated estimates as of the end of quarter t+2 (1 st restated estimate), quarter t+6 (2 nd restated estimate), and quarter t+10 (3 rd restated estimate), as described in Figure 1. We use currently available final estimates to measure restatements, because they represent homogenously measured macroeconomic indicators that incorporate all latest methodological changes (Gilbert 2011). However, evaluating the initially announced estimates relative to the current estimates has several disadvantages. Such evaluation impliesvery long forecast horizons that vary in length depending on the vintage of the initial estimate. Further, very late revisions are less likely to result from the newly available information and are more likely to be driven by methodological changes. Accordingly, we also report robustness tests using two-year horizon restatements (3 rd restated estimate initial estimate) that have fixed revision horizons that are sufficiently long to accumulate most information-related revisions. Our supplementary tests use delayed restatements accumulated between the 1 st restated estimate and the final estimate. Such a research design allows us to test whether accounting 14

17 information pertaining to the same quarter as GDP (and announced prior to the 1 st restated estimate) can predict GDP restatements. Figure 1 presents the timeline of restatement and other variables measurement. All total restatement predictors, including aggregate earnings and earnings dispersion, are estimated using information that is publicly available by the end of quarter t. Namely, we use earnings for fiscal quarter t-1 (released in quarter t) and stock market returns for quarter t. Likewise, delayed restatement predictors, including earnings for fiscal quarter t, are publicly available by the end of quarter t+1. Thus, we use only information that should be available to economists prior to the GDP estimate release Descriptive Statistics and Preliminary Results Descriptive Statistics Table 1 presents descriptive statistics. In our sample period, GDP estimates are on average revised upward total restatements are on average positive with the mean (median) restatement in nominal GDP growth (NGDP_Res) of 0.53% (0.43%) and mean (median) restatement in real GDP growth (RGDP_Res) of 0.43% (0.36%). Both mean and median restatements differ significantly from zero (results are untabulated). Although mean restatements are substantially smaller than mean initial estimates (e.g., the mean restatement in real GDP growth is about five times smaller than the mean initial real GDP growth estimate), they are highly variable. Specifically, the standard deviation of restatements in nominal (real) GDP growth is 1.97 (2.09), which is large compared to the standard deviation of initially announced nominal (real) GDP growth equal to 3.61 (3.18). That 15

18 is, standard deviations of restatements are at least 50% of standard deviations of the initial estimates. The ranges of restatements are also large. Specifically, the fifth percentile of restatements in nominal (real) GDP growth is -2.71% (-2.83%) and the 95 th percentiles is 3.65% (3.44%). In addition, we observe changes in the sign of growth from initial to current estimate. Specifically, nominal (real) GDP growth estimates switch signs from positive to negative and vice versa in 2.5% (7.5%) of quarters. For example, the initial announcement of nominal GDP growth for the first quarter of 2008 is 3.19%, which is subsequently revised to -0.46%. Likewise, the initial announcement of real GDP growth for the first quarter of 2001 is 1.98%, which is subsequently revised to -1.14%. The mean values of aggregate earnings (Ear), earnings dispersion (Ear_Disp), and return dispersion (Ret_Disp) are zero by construction, as these estimates are residuals from the AR(2) process. Overall, restatements in GDP estimates on average significantly deviate from zero. Further, variability of restatements, their magnitude ranges, and the presence of estimates sign changes between the initial and final revised values suggest restatements are also economically significant. Univariate Correlations Table 2 contains pairwise correlations for total restatements and restatement predictors. Correlation estimates suggest that higher lagged earnings dispersion robustly predicts downward restatements in both GDP growth estimates. Specifically, lagged earnings dispersion is significantly negatively correlated with restatements in nominal and real GDP growth with the Pearson (Spearman) correlation coefficients of and (-0.24 and -0.22), respectively. However, lagged aggregate earnings are not significantly correlated with total GDP restatements. 16

19 The evidence in Table 2 also confirms restatement predictability documented in prior research. Specifically, higher (lower) initially announced estimates are subsequently revised downward (upward). The Pearson (Spearman) correlations between restatements in real GDP growth and their initial announcement values are and (-0.20 and -0.33), respectively. However, initial announcement-day market returns have no ability to predict restatements in GDP estimates in our sample period. Likewise, neither aggregate return dispersion nor aggregate market returns are significantly correlated with subsequent GDP restatements. Finally, we find a significant downward trend in restatements over time restatements are significantly negatively correlated with the time variable. Preliminary Results Our restatement predictability tests rely on the assumption that accounting aggregates provide information about the true underlying GDP realizations. From the theory standpoint, both contemporaneous and lagged earnings information may be useful for producing an economic nowcast of GDP. For example, contemporaneous aggregate earnings should be informative about the same-quarter corporate profits component of GDI. At the same time, economic theories suggest that aggregate earnings dispersion can be a leading indicator of future aggregate output. To evaluate the strength of the links between the true underlying GDP values and earnings aggregates, we regress final restated GDP growth values on contemporaneous and lagged aggregate earnings and earnings dispersion. The regressions also include prior quarter GDP growth estimates to control for persistence in GDP growth. Specifically, we estimate the following regression: 17

20 FinalEstimate t = β 0 + β 1 Ear t + β 2 Ear _ Disp t + β 3 Ear t 1 + β 4 Ear _ Disp t 1 + β 5 FinalEstimate t 1 +ε t, (5) where FinalEstimate t is the final (currently available) estimate of nominal or real GDP growth for quarter t, Ear t-1 is aggregate earnings for fiscal quarter t-1 (estimated using earnings released in quarter t), Ear_Disp t-1 is earnings dispersion for fiscal quarter t-1, Ear t is aggregate earnings for fiscal quarter t (estimated using earnings released in quarter t+1), Ear_Disp t is earnings dispersion for fiscal quarter t, and FinalEstimate t-1 is the final (currently available) estimate of nominal or real GDP growth for quarter t-1. The results of estimation are reported in Table 3. Both nominal and real GDP growth estimates are significantly associated with contemporaneous (but not lagged) aggregate earnings. These results are consistent with aggregate earnings being useful for estimating a component of the same-period GDP. Both nominal and real GDP growth estimates are significantly associated with lagged aggregate earnings dispersion. However, the association between GDP growth and contemporaneous earnings dispersion is weaker and not robust to excluding quarters spanning the Great Recession (the fourth quarter of 2007 to the first quarter of 2009). This evidence supports economic theories suggesting performance dispersion precipitates temporarily depressed output. 4. Main Empirical Results 4.1. Aggregate Accounting Information and GDP Restatements In this section, we investigate whether initially announced GDP estimates contain errors predictable with accounting information available to macroeconomists at the time of the announcement. Specifically, we test whether aggregate earnings and earnings dispersion can 18

21 predict restatements in macroeconomic indicators. Predicting Total Restatements To verify that accounting variables ability to predict future macroeconomic restatements is incremental to other variables associated with restatements, we conduct multivariate tests by estimating the following time-series regression: 5 9 t = β0 + β1 Eart + β2 Ear _ Dispt + β3 [ Mkt _ rett ] + β4 [ Ret _ Dispt ] [ Ann _ rett ] + β6 [ Ini _ NGDPt ] + β7 [ Ini _ RGDPt ] + β8 [ Ini _ RConst ] [ Time _ Trend ] + β [ Recession] + ε, Restatement + β + β t 10 where Restatement t is the total restatement in nominal (real) GDP growth for quarter t, Ear is aggregate earnings (measured using earnings for fiscal quarter t-1 that are released in quarter t), Ear_Disp is earnings dispersion, Mkt_ret is quarterly market return, Ret_Disp is quarterly return t (6) dispersion, Ann_ret is the S&P 500 index return on the initial GDP announcement day, Ini_NGDP (Ini_RGDP) is the initially announced estimate of nominal (real) GDP growth, Time_Trend is the time trend (equal to 1 for 1972:Q3 and increasing by 1 every quarter), and Recession is a dummy variable that equals 1 for quarters classified as recessionary by the NBER. All independent variables are measured before the initial GDP estimate is announced, as shown in the Figure 1. Results are presented in Table 4. Earnings dispersion predicts restatements in both real and nominal GDP growth after controlling for aggregate earnings. The association is both statistically and economically significant. Specifically, the coefficients reported in columns (1) and (5) of Table 4 can be interpreted as one standard deviation increase in earnings dispersion predicting a 0.42% (0.40%) lower restatement in the nominal (real) GDP growth. These changes correspond to a 7% (17%) downward revision in the corresponding average initial GDP growth 19

22 estimates (i.e., 0.42%/6.12% (0.40%/2.42%)). These results are consistent with earnings dispersion containing useful information about the macro economy that government statistical agencies do not fully take into account. Table 4 also suggests that lagged aggregate earnings predict restatements, although predictability varies depending on the presence of controls, inclusion/exclusion of the financial crisis period, and on the type of macroeconomic indicator. Taken together, lagged aggregate earnings and earnings dispersion predict 3% (2%) of variation in nominal (real) GDP growth restatements. In untabulated results, we find that most predictability comes from lagged earnings dispersion, whereas the aggregate earnings share of explained restatement variation is statistically insignificant. In contrast, aggregate market return and dispersion in stock returns do not predict GDP restatements. Specifically, the R-squared from the model with market returns and returns-based dispersion (reported in columns (2) and (6) of Table 4) is indistinguishable from zero. Next, we control for other known predictors of macroeconomic restatements. Namely, we add initial GDP estimates, initial-announcement-day S&P 500 index return, and a recession dummy as control variables. The latter variable is motivated by prior research documenting that macroeconomic variables are especially difficult to predict during economic recessions (Swanson and Vandijk, 2006). We also control for the time trend in restatements. Regression results are reported in columns (3) and (7) of Table 4. We find that the coefficient on lagged earnings dispersion remains statistically significant and even increases marginally, suggesting that earnings-dispersion-based restatement predictability is incremental to predictability documented in prior research. Out of all additional restatement predictors, only initial estimates of real GDP growth significantly predict subsequent real GDP restatements. 20

23 Predicting Delayed Restatements Previously reported results use lagged (quarter t-1) aggregate earnings and dispersion to predict total restatements in quarter t GDP estimates. In this section, we examine whether aggregate earnings pertaining to the same quarter as GDP predict subsequent restatements. However, because same-quarter aggregate accounting information is not available at the time of the initial GDP estimate release, we examine predictability of delayed restatements (starting from the 1 st restated estimate shown in Figure 1 to the final restated value). Because the 1 st restated estimate for quarter t is announced approximately four months following the end of quarter t, accounting earnings for quarter t should be publicly available prior to the start of the delayed restatement accumulation. Accordingly, we re-estimate regression (6) after replacing total restatements with delayed restatements and adding contemporaneous (quarter t) aggregate earnings and earnings dispersion. Results are reported in Table 5. We find that aggregate earnings are positively related to delayed restatements in both real and nominal GDP growth, suggesting the BEA does not fully incorporate information contained in contemporaneous aggregate earnings even after they become publicly available. In contrast, contemporaneous aggregate earnings dispersion has no predictive ability with respect to future restatements. Similar to total-restatement-prediction results, lagged earnings dispersion is negatively associated with delayed restatements. Likewise, lagged aggregate earnings maintain a puzzling significantly negative relation with future restatements. Overall, contemporaneous aggregate earnings and lagged earnings dispersion predict restatements in the hypothesized direction, whereas lagged earnings are surprisingly negatively associated with future macro restatements. 21

24 Excluding the Great Recession Our sample period contains the most severe recession since the Great Depression. To verify that a single business-cycle episode does not drive our results, we re-estimate predictive regressions after dropping observations from the fourth quarter of 2007 to the first quarter of Results are reported in columns (4) and (8) of Tables 4 and 5. The ability of lagged earnings information to predict restatements is robust to excluding the crisis period. Specifically, lagged earnings dispersion continues to predict restatements in both nominal and real GDP growth. However, contemporaneous aggregate earnings are no longer predictive of restatements. Interestingly, the initial announcement returns S&P 500 index returns on the day of the initial GDP announcement remain significantly negative predictors for nominal and real GDP growth restatements even after excluding the Great Recession quarters. These results suggest the stock market does understand that initial announcements will be restated and incorporates expected restatements in stock prices (Gilbert, 2011). At the same time, initial announcement returns do not subsume the predictive ability of aggregate earnings dispersion, which suggests investors do not anticipate restatements that are associated with changes in aggregate earnings dispersion. Overall, we find that lagged earnings dispersion robustly predicts restatements in GDP growth estimates after controlling for alternative restatement predictors and after excluding quarters pertaining to the Great Recession Why Does Earnings Dispersion Predict GDP Restatements? We hypothesize that earnings dispersion provides useful information about the true state of the economy that government statistical agencies do not completely take into account 22

25 when compiling the initial estimate of GDP and its components. In this section, we attempt to pinpoint the nature of information conveyed by earnings dispersion. Across-Industry Earnings Dispersion and Macro Restatements The creative destruction (Schumpeter 1942; Foster et al. 2000, 2006) and sectoral shift (Lucas and Prescott 1974; Lilien 1982) hypotheses suggest that higher earnings dispersion indicates that resources (e.g., capital and labor) have to migrate from less to more profitable firms/sectors. Because of frictions, migration of resources takes time, leading to lower overall output in the interim. Such frictions should be higher when resources need to be redeployed in a different industry (e.g., workers need to acquire new skills, physical capital needs to be repurposed for new use, etc.). As a result of higher frictions, the loss of output should be higher due to higher earnings dispersion. All else equal, we should thus observe across-industry dispersion leading to greater downward restatements in GDP growth. We estimate across-industry earnings dispersion as follows. Every quarter, we assign firms to one of 49 Fama-French industries (Fama and French, 1997). 22 We estimate acrossindustry earnings dispersion as a standard deviation of average earnings from all industries. We remove the persistent component in across-industry earnings dispersion by estimating the AR(2) model and using residuals from the model as our measure of innovation in dispersion. To obtain two components of total dispersion (Ear_Disp) that pertain to across-industry and withinindustry dispersion, we regress total dispersion on across-industry dispersion from the previous step. The fitted value is the across-industry dispersion component of total dispersion (Ear_DispA). The residual is the component orthogonal to across-industry component of total 22 We obtain industry definitions from Kenneth French s website: 23

26 dispersion (Ear_Disp_Orth). Similarly, we also decompose return dispersion into across-industry component (Ret_DispA) and orthogonal component of total dispersion (Ret_Disp_Orth). Results based on dispersion decomposition are reported in Table 6. The evidence is consistent with our conjectures. Specifically, the marginal effect of across-industry dispersion is significantly larger than the marginal effect of remaining dispersion. A one standard deviation increase in prior quarter across-industry dispersion predicts a 0.47% (0.40%) decrease in restatement of nominal (real) GDP growth. Dispersion component that is orthogonal to acrossindustry dispersion does not predict macroeconomic restatements. Earnings Dispersion and Unemployment The sectoral shift (Lucas and Prescott, 1974; Lilien 1982) hypothesis states that higher dispersion in performance causes higher unemployment. Higher unemployment in turn leads to lower consumption and lower GDP (Okun, 1962; Abel and Bernanke, 2005). If earnings dispersion signals lower output because it is associated with increases in unemployment, and macroeconomists do not fully take that link into account, we should observe similar predictability in unemployment restatements. Unemployment figures are compiled and announced by the BLS. Similar to GDP figures, early unemployment estimates are based on incomplete and imprecise information. The initial estimates are then revised over several subsequent years. The BLS releases unemployment estimates on a monthly basis. To keep our research design in line with the GDP-based analysis, we use average quarterly estimates contained in the Real-Time Data Set for Macroeconomists maintained by the Philadelphia Federal Reserve. Table 7 reports results of regressing unemployment restatements on earnings dispersion and other predictors. Consistent with the sectoral shift hypothesis, earnings dispersion 24