Reconciling the divergence in aggregate U.S. wage series Julien Champagne

André Kurmann

Jay Stewart

Bank of Canada

Drexel University

Bureau of Labor Statistics

March 17, 2017

Abstract Average hourly wages from the Labor Productivity and Costs (LPC) program, the Current Population Survey (CPS) and the Current Employment Statistics (CES) have diverged, both in trend and volatility. Supplements and irregular earnings of high-income workers, included in the LPC but not in the two other datasets, have grown more rapidly and have become more volatile, accounting for most of the divergence between LPC and CPS earnings. The more restrictive worker coverage in the CES explains a large part of the divergence between CPS and CES earnings. The results have important implications for the choice of wage series in macroeconomic analysis. JEL codes: E01, E24, E30, J30 Keywords: Wages and salaries, Supplements, Irregular earnings, Worker coverage, Divergence in trend and volatility.

The views expressed in this paper do not necessarily represent those of the Bank of Canada or the Bureau of Labor Statistics. We thank John Schmitt, Shawn Sprague, Jean Roth, Barry Hirsch for invaluable help with the data; Christine Garnier for excellent research assistance; and sta¤ from the Current Employment Statistics, James Spletzer as well as seminar participants at the Bureau of Labor Statistics, the 2013 Canadian Economic Association conference, the Bank of Canada, the Fall 2013 Midwest Macro meetings, the 2014 Society of Economic Dynamics conference, and the 2014 Econometric Society European Meetings for comments. Contact information: [email protected], [email protected], [email protected].

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1

Introduction

The average hourly wage is a key macroeconomic variable and has been the focus of much research. Indeed, one of the most hotly debated topics in recent years concerns the slowdown in real wage growth experienced by the average worker in the United States and the associated decline in the labor share of income. Average wages also play a central role for business cycle analysis, both in terms of model evaluation and current economic outlook. Researchers working on these and other issues use di¤erent data sources. For example, Elsby, Hobijn and Sahin (2013) and Karabarbounis and Neiman (2014) study the evolution of the U.S. labor share with data from the Labor Productivity and Cost (LPC) program and the National Income and Product Accounts (NIPAs).1 In contrast, Bivens and Mishel (2015) report average wage growth based on data from the Current Employment Statistics (CES), while Lemieux (2006), Autor, Katz and Kearney (2008), and Acemoglu and Autor (2011), among many others, use data from the Current Population Survey (CPS) to analyze wage trends for di¤erent types of workers.2 For business cycle analysis, seminal studies such as Smets and Wouters (2007) and Christiano, Eichenbaum and Evans (2005) use wage data from the LPC to estimate Dynamic Stochastic General Equilibrium (DSGE) models. Yet, other prominent studies such as Gertler and Trigari (2009), Gali (2011), Haefke, Sonntag and Van Rens (2013), Basu and House (2016), and Daly and Hobijn (2017) use wage data from either the CES or the CPS. Business analysts and the popular press also often use CES wage data because the series is published on a monthly basis.3 In most cases, the decision to use one data source over another receives little or no discussion. However, as we document in this paper, the choice matters greatly because the three data sources tell very di¤erent stories. Looking at the CES, one would conclude that the average wage was largely stagnant since the 1970s and that the labor share of income dropped by almost 40%. According to the LPC, by contrast, average wage growth averaged about 1% per year and the labor share fell by only about 10% over the same period. And although the three wage series exhibit similar cyclical patterns when considered over the entire post World War II period, there are large di¤erences across subsamples. In particular, the volatility of the CES wage declined by about the same proportion as the volatility of output during the "Great Moderation" period that started in the mid-1980s. In 1

As we show below, the wages and salaries components of the LPC and the NIPAs are very similar. We refer to this data as the LPC data from hereon. 2 CES-based results such as the ones reported by Bivens and Mishel (2015) …gure prominently in policy debates. See, for example, The White House (2013), Clinton (2015), Scheiber (2015), or Sparshott (2015). The CES wage series is also a component of the Federal Reserve Board’s new Labor Market Conditions Index (e.g. Chung et al. (2014)). For policy papers based on CPS data, see Boddy et al. (2015) or Balls and Summers (2015). 3 Other data sources that can be used to compute average wage series include the Employment Cost Index (ECI), the Panel Study of Income Dynamics (PSID), and the Survey of Income and Program Participation (SIPP). We focus on the LPC, the CES and the CPS because they are among the most frequently used sources.

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contrast, the volatility of the LPC wage and the CPS wage increased more than two-fold relative to the volatility of output during the Great Moderation –an increase that represents an important challenge for competing theories of business cycle ‡uctuations.4 These di¤erences raise two important questions. What accounts for the divergence in the different wage series? And which data source is the most appropriate for the question at hand? The rest of the paper is devoted to answering these questions. We begin by decomposing the three average hourly wage series into average weekly earnings and average weekly hours components. The key result from this decomposition is that the majority of the divergence between the three hourly wage series –both in terms of trend growth and business cycle volatility –is due to average weekly earnings. Average weekly hours, by contrast, have evolved very similarly in the LPC and the CES; and they play only a limited role in explaining the di¤erences between the CPS wage and the other two wage series. Based on this …nding, we focus on the divergence of average weekly earnings in the three datasets. We identify two principal causes: (i) di¤erences in earnings concept (employer-paid supplements and irregular earnings of high-income individuals included in the LPC but not in the CES and the CPS); and (ii) di¤erences in worker coverage (all non-farm business workers for the LPC and the CPS versus production and non-supervisory workers in the CES).5 To quantify the importance of the two di¤erences, we exploit the fact that the average earnings series constructed from the CPS is based on a very similar earnings concept as the one used by the CES but at the same time is representative of all workers. Our analysis yields three important results. First, wages and salaries of high-income individuals and employer-paid supplements have both grown at a considerably higher rate than wages and salaries of the average worker, with supplements being driven primarily by the growth in employer contributions to private insurance funds. This di¤erence accounts for almost all of the divergence between the LPC and the CPS average earnings series. Second, when excluding the top 5% earners, the CPS average earnings series is almost exactly the same as the corresponding average earnings series reported by Piketty and Saez (2003) based on Internal Revenue Service (IRS) data. The CPS therefore provides a reliable estimate of the wages and salaries portion of compensation for 95% of the workforce, which is important given that the CPS is one of the most widely used micro data sets of individual earnings in the United States. Third, the historical earnings series from the CES is not representative of the average worker. According to our simulation of the CES series, about 80% of the lower growth rate and about 50% of the decline in volatility of the CES earnings series can be attributed to the fact that the historic CES data only covers production and non-supervisory workers. The remaining di¤erence is likely due to a combination of unique measurement issues that 4 5

See Champagne and Kurmann (2013), Nucci and Riggi (2013) and Gali and Van Rens (2014). The CES began publishing all-employee wages in March 2006. We discuss this series in Section 5.

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arise in the CES as a result of sample expansion, changes in collection methods, and non-response bias. The results have important implications for the appropriate choice of wage series. As we argue in the conclusion of the paper, our CPS earnings construct provides a useful alternative measure of average earnings because it abstracts from the large and volatile irregular wage and salary portion of high-income individuals but covers the entire working population. Moreover, it can be augmented with an estimate of supplements to take into account non-wage payments in labor compensation. The growth in these supplements plays a key role for trends in labor compensation and may be important, more generally, for the appropriate speci…cation of compensation in labor market models. For instance, the rise in contributions to private insurance funds, which apply primarily to full-time employees, may help explain the recent increase in part-time and temporary work. Our paper contributes to the literature describing the evolution of labor earnings in the United States. Despite the large volume of research, little e¤ort has been made to compare di¤erent measures. The paper closest to ours is Abraham, Spletzer and Stewart (1998, ASS henceforth) who document the divergence in trends of average hourly wage measures from the NIPAs, the CPS, and the CES. Like them, we decompose the hourly wage into weekly earnings and weekly hours, and take advantage of the industry and occupation information in the CPS to quantify the importance of the narrower worker coverage in the CES. Our paper makes several contributions relative to their work. First, we focus on LPC earnings, which includes employer-paid supplements, while ASS only consider the wages and salaries component of NIPA earnings. This is important because employer-paid supplements are one of the principal reasons for the divergence between the LPC wage and the other wage series. Second, our paper introduces a new way to compute average earnings from the CPS by augmenting regular earnings with an estimate for overtime, tips and commissions (OTC), and by using information from Piketty and Saez (2003) to properly take into account earnings of high-income individuals. This allows us to establish that di¤erences in earnings concept explain almost all of the divergence between LPC and CPS earnings. The inclusion of OTC in our CPS earnings construct also helps to show that the narrower worker coverage in the CES is responsible for much of the di¤erence between CPS and CES earnings. These conclusions di¤er from the ones reached by ASS who do not have data on OTC and earnings of high-income individuals, and therefore cannot reconcile the divergence in the di¤erent wage series as well as we do. Third, we document and reconcile not only the divergence in trends but also the divergence in volatility between the three wage measures, which has important implications for the proper choice of wage series for business cycle analysis.6 Fourth, we extend the analysis of trends in ASS by 20 years, thus providing crucial new information about the extent of the slowdown in wage growth, 6

The divergence in business cycle volatility of the LPC wage and the CES wage has been noted by Champagne and Kurmann (2013) and Gali and Van Rens (2014). Neither of the two papers analyze the sources of this divergence.

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which has been one of the key economic policy debates. Our results suggest that CES earnings and to a lesser extent regular CPS earnings understate the growth in average total labor compensation.

2

Data

For each of the data sources, we calculate the average real hourly wage as average real weekly earnings divided by average weekly hours. Average real weekly earnings are obtained by de‡ating nominal earnings with the Personal Consumption Expenditure (PCE) index from the NIPAs.7 Auxiliary data used later in the analysis are described as they are introduced. An online appendix contains additional details about the data as well as robustness checks. The …rst data source is the CES, which is a monthly establishment survey of employment, payroll, and hours that has been conducted by the BLS since 1915. Historical estimates for average weekly earnings, average weekly hours, and average hourly earnings are available for private non-agricultural establishments from 1964 on, but only for production workers in goods-producing industries and for non-supervisory workers in service-providing industries.8 Earnings comprise regular wages and salaries including overtime. Tips, commissions, and bonuses are included only if earned and paid regularly each pay period. Supplements and gains from exercising stock options are excluded. The average weekly hours series counts all hours paid during the pay period that includes the 12th of the month, including overtime and paid leave. The CES sample has increased over the years and currently covers about 588,000 establishments. The second data source is the LPC program of the BLS, which has reported labor productivity and compensation data for the non-farm business sector quarterly since 1948. Average weekly earnings consist of "wages and salaries" and "supplements". Wages and salaries come from the Quarterly Census of Employment and Wages (QCEW), a mandatory employer-based program for all employees covered by unemployment insurance (UI) that comprises about 98% of U.S. private sector establishments and jobs, excluding non-pro…ts, general government, and the private household sector. Wages and salaries from the QCEW include executive compensation, commissions, tips, bonuses, and gains from exercising non-quali…ed stock options. Supplements are based on estimates by the Bureau of Economic Analysis (BEA) and consist of employer contributions to government social insurance funds, private pensions, as well as private health, life and welfare insurance funds. The primary source of hours data is the CES. The LPC program converts CES estimates 7

As Abraham and Haltiwanger (1995) document, the choice of price de‡ator a¤ects the comovement of real wages with hours and output over the business cycle. None of our results are a¤ected by the use of alternative de‡ators because we are looking at the divergence in trend growth and business cycle volatility across di¤erent real wage series. 8 In 2006, the CES started collecting earnings data for all workers in private non-agricultural establishments. We use this information in Section 5.

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of production and nonsupervisory hours paid to hours worked using hours-worked-to-hours-paid ratios from the National Compensation Survey.9 Non-production/supervisory hours are estimated by calculating the ratio of non-production to production worker hours using data from the CPS. This ratio is then applied to the production and nonsupervisory average weekly hours. The LPC also includes estimates of earnings and hours of self-employed workers. To make the LPC data comparable to the CES and CPS universe, which does not include self-employed workers, Section 5 of the paper removes self-employment and some other small components from the LPC.10 The third data source is the CPS, a monthly survey of about 60,000 households conducted by the U.S. Census Bureau for the BLS. Data on earnings and hours are available from di¤erent extracts of the CPS. Following ASS and Lemieux (2006), we combine information from the annual CPS May extracts for 1973-78 with information from the monthly outgoing rotation groups (ORGs) from 1979 onward to construct annual series of average weekly earnings and hours for the private nonagricultural business sector (excluding self-employment as in the CES).11 As explained in full detail in the appendix, weekly earnings are computed di¤erently for salaried and hourly-paid workers. For salaried workers, we take reported weekly earnings at the main job, which is de…ned as compensation normally received and includes OTC and bonuses if earned and paid in each period. For hourlypaid workers, we have reported weekly earnings, the reported hourly wage times usual hours worked and, starting with the redesign of the CPS in 1994, a separate report of OTC. For 1994 onward, we compute weekly earnings as the higher of reported weekly earnings and the sum of the reported usual hourly wage times weekly hours worked plus OTC. For the period before 1994, we compute weekly earnings as the reported hourly wage times usual weekly hours worked and adjust this number with an OTC estimate based on 1996-2000 data that depends on gender and education.12 9

This ratio accounts for paid leave, but not o¤-the-clock work. The ratio has been fairly constant over time (0.93), although there is some variation across industries. See Eldridge, Manser, and Otto (2004). 10 The LPC estimates earnings of self-employed workers by assuming that they earn the same average hourly compensation as wage and salary workers and multiplying this average by an estimate of hours worked by selfemployed workers from the Current Population Survey (CPS). As shown by Elsby, Hobijn and Sahin (2013), this assumption may generate misleading results. Their analysis, based on a reasonable alternative method to calculate earnings of the self-employed, suggests that the LPC understates earnings growth of the self-employed. 11 After removing observations for self-employed individuals, the May supplements yield an average of 42,037 observations of earnings and hours per year between 1973 and 1978, and the ORG …les yield an average of 173,925 observations per year between 1979 and 2013. Alternatively, we could have constructed average wage series from the CPS March supplements. We prefer the May/ORG for di¤erent reasons. First, the earnings concept in the May/ORG is closer to the earnings concept in the CES. Second, the March supplements only contains information on total hours worked starting in 1976. Third, the ORG portion of the May/ORG contains two to three times as many observations as the March supplements (depending on the year). Fourth, as Lemieux (2006) shows, the March supplements poorly measure the wages of hourly-paid workers, which make up 60 percent of the workforce. 12 The OTC adjustment prior to 1994 is not sensitive to the sample period used to estimate the adjustment factors (e.g. 1994-2013 vs. 1996-2000, etc.).

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This provides us with earnings numbers that consistently include an estimate of OTC across both salaried and hourly-paid workers.13 Moreover, as is usual in the literature, we keep observations with imputed earnings and multiply topcoded weekly earnings by a constant factor of 1.3.14 In Section 5, we experiment with more sophisticated topcode adjustments. Finally, we convert the data from a person basis to a job basis by adjusting earnings and hours for multiple job holding (MJH) and aggregate the resulting micro data using the CPS Census weights.15 Table 1 summarizes the relevant characteristics of each data source.

LPC

CES

CPS

Source

* QCEW; covering 98% of privatesector jobs.

* Establishment survey from BLS. * Household survey from BLS and Census. * About 160,000 establishments per month * About 60,000 households per month. in early 1980s to 588,000 in 2015.

Sample

* 1948 onward; quarterly.

* 1964 onward; monthly.

* 1973 onward; annual. CPS May & ORGs. * 1979 onward; monthly. CPS ORGs.

Population coverage

* All employees in non-farm business sector, including estimate for selfemployed.

* Production and non-supervisory employees in private non-agricultural sector, excluding self-employed. * From 2006 on, all employees in private non-agricultural sector.

* All individuals in private non-agricultural sector, excluding self-employed (sample is made representative using Census weights).

Earnings concept

* Wages and salaries: * Wages and salaries: ** Includes commissions, tips and ** Overtime, commissions and bonuses bonuses. only if paid regularly. ** Gains from exercising stock options. ** No irregular bonuses, gains from stock * Supplements. options or supplements. ** No tips, unless reported on employee's tax form.

* Wages and salaries: ** Includes overtime, tips, commissions and bonuses only if paid regularly. ** No irregular bonuses, gains from stock options or supplements.

Table 1. Description of the main data sources.

The table highlights the di¤erences in population coverage and earnings concept, which are the main focus of our investigation. While the LPC data cover all workers in the non-farm business sector and have a very comprehensive earnings concept, the CES data only cover production and nonsupervisory workers employed in private non-agricultural establishments, and use a more restrictive 13

As the analysis in the appendix shows, using the higher of the reported weekly earnings and the reported hourly wage times weekly hours worked prior to 1994 leads to a discontinuity in the weekly earnings series for hourly-paid workers. This suggests that some hourly-paid workers did not include OTC when reporting their usual weekly earnings, which is consistent with the BLS’s rationale for introducing a separate OTC question in 1994 (Polivka and Rothgeb, 1993). 14 About 30% of observations have missing earnings in the CPS ORGs. For these cells, the CPS uses a "hot deck" procedure that randomly assigns data from "donor" observations that are in same demographic cell. See Hirsch and Schumacher (2004) for a description. We discuss possible consequences of this imputation procedure in Section 5. 15 The CPS does not collect earnings on second jobs. Following ASS, we set weekly earnings on second jobs to 30% of weekly earnings of the multiple jobholder’s main job, based on questions asked about multiple job holding in select CPS May supplements. Weekly hours on the second job are set to the average hours on the second job reported in the 1994-2013 ORGs. The results are not sensitive to the choice of sample period. See the appendix for details.

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earnings concept. In comparison, our earnings construct from the CPS covers all workers in the private non-agricultural business sector, similar to the LPC data (except for some small di¤erences that we will address below), but is based on an earnings concept that is, aside from tips, the same as the one employed by the CES.16 We will exploit this "in-between" characteristic of the CPS data relative to the LPC data and the CES data for our analysis.

3

The Divergence in Trends

Figure 1 shows the evolution of average real hourly wages from the three data sources.

Figure 1. Average real hourly wages.

Three observations stand out. First, in the early 1970s, the LPC wage is already about 30% higher than the CES wage and the CPS wage. Second, the LPC wage grows at a substantially higher rate over the sample, ending up, in 2013, 84% and 62% higher than the CES wage and the CPS wage, respectively. Third, while the LPC wage and the CPS wage grow consistently throughout the sample, the CES wage declines from the early 1970s to the early 1990s, returning to moderate growth thereafter. Figures 2 and 3 show the corresponding evolution for average real weekly earnings and average 16

According to ASS, tips represented only a very small part of total average earnings in the economy.

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weekly hours.

Figure 2. Average real weekly earnings.

The trends in average weekly earnings are similar to those for average hourly wages in Figure 1, except that there is a sharper decline in CES earnings between the early 1970s and the early 1990s

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and LPC earnings diverge more slowly from CPS weekly earnings.

Figure 3. Average weekly hours.

These di¤erences in hourly wage and weekly earnings trends can be accounted for by the declines in CES and LPC weekly hours whereas CPS hours exhibit a ‡at trend. That the CES and the LPC hours series exhibit the same pattern of decline over time is not surprising since the CES is the primary source for hours in the LPC. The di¤erence in levels is mainly due to the hours-worked-tohours-paid adjustment mentioned earlier. Frazis and Stewart (2010) examine possible explanations for the divergence in weekly hours in the CPS and CES. They …nd that di¤erences in worker coverage, the e¤ects of multiple jobholding, and di¤erences in concept account for nearly all of the di¤erence in levels, but almost none of the di¤erence in trends.17 Interestingly, they …nd that most of the divergence can be attributed to three services industries: Retail Trade, Hospitality and Leisure, and Business and Professional Services. The reasons for this divergence remain unknown but may at least in part be due to the measurement issues in the CES that we discuss in Section 5.4. 17

Frazis and Stewart (2010) also consider possible over-reporting of hours in the CPS, as hypothesized by Bostrom and Robinson (1994), as well as the interaction of changes in the average length of pay periods and the distribution of hours over the month. They …nd no evidence of over-reporting in the CPS, and the e¤ect of lengthening pay periods can explain only a small portion of the divergence.

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To quantify the importance of weekly earnings trends and weekly hours trends for the divergence in hourly wage trends, we express the 1973-2013 average log di¤erence of each of the hourly wage series, log wi , in terms of average log di¤erences of weekly earnings, log Wi , and weekly hours, log Hi , log wi = log Wi log Hi , (1) where i 2 fLP C; CES; CP Sg. We then decompose the di¤erence in average growth between pairs of hourly wage series into di¤erences in average growth of weekly earnings and average growth of weekly hours. Table 2 reports the results.

Differences in annual average growth rates Δlog(wi) - Δlog(wj )

LPC - CES

%

LPC - CPS

%

CPS - CES

%

0.85%

100.0%

0.56%

100.0%

0.29%

100.0%

Δlog(W i ) - Δlog(W j )

0.84%

99.0%

0.34%

61.0%

0.50%

172.1%

Δlog(Hi ) - Δlog(Hj )

0.01%

1.0%

0.22%

39.0%

-0.21%

-72.1%

Notes: The table decomposes average hourly w age log first-differences betw een 1973 and 2013 into w eekly earnings grow th and w eekly hours grow th, i.e. Δlog(w) = Δlog(W) - Δlog(H) , w here w , W, and H denote the average hourly w age, average w eekly earnings, and average w eekly hours, along w ith the contribution of each component in accounting for the difference in hourly w age average grow th betw een the data sources.

Table 2. Accounting for the divergence in hourly wage average growth.

The decomposition con…rms that the divergence in average hourly wage growth between the LPC and the CES is entirely accounted for by the di¤erence in average weekly earnings growth: according to the LPC, average weekly earnings grew on average by 1.0% per year, while according to the CES, weekly earnings grew on average by only 0.1% per year. This con…rms the …ndings of ASS for a substantially longer sample. In comparison, about two-thirds of the considerably smaller divergence in average hourly wage growth between the LPC and the CPS is due to smaller weekly earnings growth in the CPS (0.6% per year). The remaining third of the divergence in average hourly wage growth is due to the fact that LPC weekly hours decreased over time, whereas CPS weekly hours remained relatively constant.

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The Divergence in Business Cycle Volatilities

Next, we examine whether the three hourly wage series also di¤er with respect to their business cycle volatility, and whether these volatilities have changed over time. To compute business cycle volatilities, we take logarithms of the di¤erent series and subtract the trend component using the

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Hodrick-Prescott (H-P) …lter.18 We then compute the standard deviation of each series for the pre-1984 and post-1984 periods. The break is motivated by the Great Moderation literature, which …nds a signi…cant decline in output volatility around 1984 (e.g. McConnell and Perez-Quiros, 2000). Table 3 reports the standard deviations for each of the hourly wage series, together with the corresponding standard deviations of weekly earnings and weekly hours as well as the correlation between the two. As a comparison, the table also shows the standard deviation of non-farm business real chain-weighted GDP and reports the ratio of the standard deviation for each series to the standard deviation of GDP (denoted relative standard deviation).19 Standard errors are in 18

The H-P …lter constant is set to 6.25 as recommended for annual data by Ravn and Uhlig (2002). As shown in the appendix, results are robust to alternative …ltering methods. 19 All of these results pertain to annual data. For the LPC and the CES, we have also computed business cycle volatilities using quarterly data for the 1964-2013 period and …nd very similar results. See the appendix for details.

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parentheses.20

Standard Deviation Pre-84 Post-84 Post/Pre-84 Real non-farm GDP

LPC hourly wage LPC weekly earnings LPC weekly hours ρ(LPC earnings, LPC hours)

CES hourly wage CES weekly earnings CES weekly hours ρ(CES earnings, CES hours)

CPS hourly wage CPS weekly earnings CPS weekly hours ρ(CPS earnings, CPS hours)

3.92

2.22

(0.31)

(0.38)

0.96

1.52

(0.19)

(0.20)

1.30

1.40

(0.26)

(0.21)

0.72

0.64

(0.14)

(0.07)

0.69

0.03

(0.07)

(0.14)

1.47

1.08

(0.19)

(0.11)

1.97

1.08

(0.26)

(0.15)

0.70

0.53

(0.11)

(0.08)

0.80

0.24

(0.09)

(0.14)

1.24

1.28

(0.20)

(0.24)

1.17

1.26

(0.16)

(0.28)

0.52

0.46

(0.05)

(0.08)

0.09

0.15

(0.34)

(0.07)

Relative Standard Deviation Pre-84 Post-84 Post/Pre-84

0.57

1.58 1.07 0.89

1.00

1.00

1.00

0.25

0.69

2.79

(0.04)

(0.17)

0.33

0.63

(0.06)

(0.15)

0.18

0.29

(0.02)

(0.03)

1.89 1.58

-0.66

0.73 0.55 0.76

0.37

0.49

(0.05)

(0.08)

0.50

0.49

(0.06)

(0.11)

0.18

0.24

(0.02)

(0.02)

1.30 0.97 1.35

-0.56

1.03 1.08 0.88

0.32

0.58

(0.05)

(0.16)

0.30

0.57

(0.06)

(0.17)

0.13

0.21

(0.01)

(0.01)

1.83 1.91 1.56

0.06

Notes: Annual data 1973-2013, H-P filtered. PCE-deflated earnings (2009 dollars). Standard deviations are multiplied by 100. The first three row s in each of the above panels show standard deviations (and relative st.dev) for the series defined in the left column; the fourth row of each panel show s the correlation coefficient betw een earnings and hours for each data source. The last column show s the ratio of post-84 to pre-84 for standard deviations, and the post-84 to pre-84 difference in correlations. Standard errors computed using GMM and the delta method appear in parentheses below estimates.

Table 3. Business cycle volatilities.

In the pre-84 period, the LPC wage and the CPS wage exhibit only moderate volatility, whereas the CES wage is almost twice as volatile. In the post-84 period, the volatility of the LPC wage increases by 60% and the volatility of the CPS wage increases by 15%. In contrast, the volatility of the CES wage drops by almost 50%. Since the volatility of output drops by about 50% between the two periods, the relative volatilities of the LPC wage and the CPS wage increase by a factor of 3.3 and 2.4, respectively, whereas the relative volatility of the CES wage remains essentially unchanged. As for trend growth, there is therefore a divergence in business cycle volatilities across the three hourly wage series. 20

Standard errors are computed via the delta method based on Generalized Method of Moments (GMM) estimates. See the appendix for details.

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To understand the sources behind this divergence in hourly wage volatility, we turn to the business cycle results for weekly earnings and weekly hours reported in Table 3. Three observations stand out. First, from the pre-1984 to the post-1984 period, the standard deviation of weekly earnings increases slightly in the LPC and decreases slightly in the CPS; but overall, the two series exhibit similar volatility.21 In contrast, the standard deviation of CES earnings drops by more than 60%, from being the most volatile to being the least volatile. Second, the volatility of weekly hours is about the same in the three data sets and changes very little between the pre-1984 and the post-1984 periods. Third, the correlation between weekly earnings and weekly hours declines considerably in all three data sources.22 To quantify the e¤ects of these changes in business cycle properties of earnings and hours on the volatility of hourly wages, we express the variance of the H-P …ltered wage series from each data source, 2wi , as 2 2 2 2 Wi ;Hi Wi Hi , (2) wi Wi + Hi denotes the variance of H-P …ltered earnings; 2Hi the variance of H-P …ltered hours; and 23 We then decompose the change in the variance of hourly Wi ;Hi the correlation between the two. wages between the pre-1984 and the post-1984 periods into the change in the variance of earnings, the change in the variance of hours, and the change in the correlation between earnings and hours. Finally, we make pairwise comparisons of the "change-in-volatility" decompositions for data source i with the corresponding "change-in-volatility" decomposition for data source j.24 Table 4 displays

where

2 Wi

21

This is consistent with recent …ndings from micro data that, for most individuals, the volatility of labor earnings has remained approximately constant (e.g. Dynan et al., 2007; Jensen and Shore, 2008). 22 The decline in correlation between earnings and hours echoes results in Gali and Gambetti (2009) and Stiroh (2009) who document that hourly wages experience a substantial decline in correlation with output and hours starting in the mid-1980s. This decline in business cycle co-movement occurs for both the LPC wage and the CES wage, although it is more pronounced for the CES wage. See the results appendix Table A.2 23 This expression holds exactly for …rst-di¤erenced data. For H-P …ltered data, the decomposition holds only as an approximation. The resulting error is, however, of minor quantitative importance. 24 See Section F in the appendix for a detailed derivation of this volatility accounting formula.

14

the results based on the numbers in Table 3.

Differences in volatility change Δσ2w i - Δσ

LPC - CES

%

LPC - CPS

%

CPS - CES

%

1.27

100.0%

0.39

100.0%

0.88

100.0%

Wj

1.22

95.4%

0.19

49.0%

1.02

116.1%

Hj

0.00

-0.3%

0.02

6.3%

-0.03

-3.2%

0.06

4.9%

0.18

46.1%

-0.12

-13.4%

2

2

Δσ

2

Wi

- Δσ

Hi

- Δσ

2

Δσ

wj

2

ΔρWi,Hi - ΔρWj,Hj

Notes: This figure decomposes the difference betw een the change in variance (post-84 vs. pre-84) of hourly w age series i and hourly w age series j into contributions of changes in (1) the variance of w eekly earnings, (2) the variance of w eekly hours, and (3) the correlation betw een w eekly earnings and hours.

Table 4. Accounting for the divergence in business cycle volatility of average hourly wages.

As the decomposition makes clear, the decline in volatility of the CES wage relative to the LPC wage is almost entirely due to the drop in volatility of earnings in the CES. In turn, the larger increase in the volatility of the LPC wage relative to the CPS wage is accounted for by the increase in volatility of LPC earnings, and the fact that the average volatility of earnings and hours over the two subsamples is larger in the LPC, which implies that the drop in correlation between earnings and hours receives a larger weight in the LPC than in the CPS. Finally, the larger increase in volatility of the CPS wage relative to the CES wage is driven by the larger drop in the volatility of earnings in the CES than in the CPS.

5

Accounting for the Divergence in Weekly Earnings

The above decompositions show that weekly earnings are the primary source for the divergence in not only trend growth but also the business cycle volatility of the di¤erent hourly wage series. Weekly hours, by contrast, account for only a small part of the initial gap between the LPC wage and the CES wage, and play a somewhat more important but still limited role for trend growth and volatility of the CPS wage. The main task therefore consists of accounting for the divergence in weekly earnings. Like ASS, we focus on two key di¤erences between the series as possible explanations for the divergent earnings behavior: (i) di¤erences in earnings concept, and (ii) di¤erences in worker coverage. Unfortunately, the establishment records underlying the LPC do not distinguish between regular and irregular earnings and do not contain information on worker occupation. It is therefore impossible to directly quantify the importance of di¤erences in earnings concept and worker coverage by using micro data from the LPC and the CES. Moreover, the micro data from the CES and 15

the LPC are both con…dential and currently unavailable for research purposes prior to the 1990s. We instead exploit the similarity of our CPS construct with the LPC in terms of worker coverage, and with the CES in terms of earnings concept to quantify the importance of the two sources of di¤erences in weekly earnings. Just as important, the industry and occupation information in the CPS allows us to simulate the CES sample. Our analysis reveals that the two di¤erences can account for the bulk of the divergence in weekly earnings. We conclude the section with a discussion of measurement issues that are particular to the CES and may explain why our CES simulations with the CPS are not entirely successful at replicating the observed evolution of CES earnings.

5.1

Di¤erences in earnings concepts

As described in Section 2, LPC earnings are based on a broad concept that includes supplements as well as irregular compensation, both of which are excluded from CPS and CES earnings. We begin by comparing the wages and salaries component of LPC earnings with the supplements component. We then show that high-income individuals account for most of irregular earnings. Finally, we augment our CPS earnings series with estimates of supplements and earnings of highincome individuals. Supplements The LPC does not produce separate information on wages and salaries versus supplements. However, it is possible to construct an estimate of the two components from the NIPAs.25 Figure 4 compares the evolution of the resulting average weekly supplements series (right scale) to that of 25

See the appendix for details. As shown below in Table 7 and Figure 7, the sum of two components matches very closely the weekly series from the LPC that we have reported so far.

16

the weekly wages and salaries series (left scale).

Figure 4. Components of total compensation: average weekly wages and salaries and supplements.

The …gure reveals a stark di¤erence in the average growth of the two series. Between 1973 and 1994, supplements grew on average by 2.9% per year whereas wages and salaries grew on average by only 0.3% per year, which is just slightly more than the 0.2% weekly earnings growth in the CPS during the same time period. Thereafter, supplements grew on average at 1.04% per year while wages and salaries grew at a slightly higher rate of 1.4%. This suggests that, at least for the …rst part of our sample, supplements accounted for a large part of the faster growth of LPC earnings. To understand the sources of growth in supplements, we further decompose supplements into employer contributions to (i) government social insurance, (ii) private insurance funds, and (iii)

17

private pension plans.

Figure 5. Components of average weekly supplements.

As Figure 5 shows, contributions to private insurance funds increase at a substantially faster rate than contributions to government social insurance and pension plans, accounting for two thirds of the average growth rate of supplements of 1.84% per year over the 1973-2013 period. In addition to growing faster, supplements are also more volatile than wages and salaries. As Table 5 shows, the standard deviation of supplements is more than two and a half times higher than the standard deviation of wages and salaries during the pre-1984 period, primarily because of

18

the higher volatility of contributions to pension plans and insurance funds.26

Standard Deviation

Components of Total Compensation

Pre-84

Wages and Salaries

Supplements Pension plans Insurance funds Government Social Insurance

Post-84

Post/Pre-84

0.75

0.92

1.23

(0.11)

(0.10)

1.93

1.56

(0.37)

(0.28)

3.68

2.18

(0.95)

(0.36)

3.01

2.43

(0.50)

(0.43)

1.98

1.05

(0.24)

(0.16)

0.81 0.59 0.81 0.53

Notes: LPC and NIPA data. Real Weekly Earnings (2009 dollars). Annual data from 1973 to 2013. Private non-agricultural sector (see the appendix for construction). All series are H-P filtered. Standard errors computed using GMM and the delta method appear in parentheses below estimates.

Table 5. Business cycle volatility for various components of total compensation.

This di¤erence becomes smaller during the post-84 period as the standard deviation of the di¤erent components of supplements declines while the volatility of wages and salaries increases. Nevertheless, the volatility of supplements remains about 70% higher than the volatility of wages and salaries. Earnings of high-income individuals Irregular earnings in the LPC are composed of commissions, tips, bonuses, and gains from exercising non-quali…ed stock options. While all workers can, in principle, receive irregular earnings, we expect them to be concentrated among high-income individuals whose earnings are topcoded in the CPS. Using Internal Revenue Service (IRS) records, Piketty and Saez (2003) document that the top 1 percent’s share of total income was fairly stable at about 10% from the 1950s through the mid26

The business cycle variance of the supplements series can be approximated as 2 Supp

X

s2i

2 i

i

+2

X si sj

i;j

i6=j

where i 2 fGovSI; P ensions; Insuranceg and si is the share of the i th component of supplements in the total supplements earnings series. Note that the supplements components are, on average, more volatile than the total supplements series. The reasons are twofold: (1) in the …rst subsample, the largest components (pensions and government social insurance) are negatively correlated and the other covariances are very low; (2) in the second subsample, private insurance plans become the largest component and have very low covariances with the other components. Both factors pull down the total supplements’volatility in the above equation.

19

1980s and increased to over 20% by the mid-2000s, mainly due to strong growth in labor income. Much of this income growth has been driven by irregular, variable earnings, suggesting another potential explanation for the higher trend growth and the larger post-84 increase in volatility of weekly earnings in the LPC relative to the CPS.27 It also follows that adjusting topcoded (regular) earnings in the CPS by a constant factor, as we and most of the literature do (see Section 2 and the appendix), may fail to capture the e¤ect of irregular earnings on average earning trends and volatility. To examine this issue, we use the data made available by Piketty and Saez (2003) to calculate average weekly earnings for the top 5% earners and for the remaining 95% for 1973-2011, and compare those estimates to the corresponding estimates from the CPS.28 Since the earnings concept in the Piketty and Saez data is very similar to the one used by the LPC – with the important exception that supplements are excluded – the comparison allows us to assess the importance of irregular earnings and topcoding for high-income individuals in the CPS. Figure 6 shows the results 27

In particular, compensation from stock options may be highly variable because stock options are likely to be exercised in upturns when their value is higher than their fair-market value at the time they were granted. See Mehran and Tracy (2001), who argue that the growth of stock options in the 1990s and their inclusion in compensation at the time of exercise has biased the trend in compensation upward. The authors also conjecture that increased use of stock options may render compensation more variable. Also see Guvenen et al. (2015), who document that the top-income individuals experience the biggest percent decreases in labor earnings during recessions. 28 We use data from Piketty and Saez updated to 2011 (available on Emanuel Saez’s website). The 5%-95% split is motivated by the fact that the fraction of individuals with topcoded earnings in the CPS data never exceeds 5%. Other, more narrow de…nitions of high-income earners would lead to very similar conclusions. Since the Piketty and Saez data does not distinguish between di¤erent sectors, we can perform this comparison only on an "all economy" level. We therefore adjust our CPS sample accordingly. See the appendix for details.

20

of this exercise.

Figure 6. Average real weekly earnings for di¤erent earnings groups.

The results are striking. For the bottom 95% of workers, weekly earnings from the CPS ("CPS 0-95") and from Piketty-Saez ("P-S 0-95") lie on top of each other. For the top 5% of earners, by contrast, weekly earnings from the CPS ("CPS 95-100") are substantially below the Piketty-Saez counterpart ("P-S 95-100"). Moreover, the P-S 95-100 series grows faster and appears to be more volatile than the CPS 95-100 series. This suggests that the top code adjustment that we and other researchers use does not adequately account for the irregular earnings of high-income individuals.

21

Table 6 con…rms this observation about business cycle volatilities.

Percentiles

Pre-84

P-S P0-95 CPS P0-95 P-S P95-100 CPS P95-100

Standard Deviation Post-84 Post/Pre-84

0.87

0.58

(0.11)

(0.06)

0.86

0.61

(0.16)

(0.11)

1.03

2.75

(0.13)

(0.27)

1.15

1.51

(0.11)

(0.37)

0.67 0.71 2.68 1.31

Notes: CPS May-MORG data and Piketty-Saez "Top income shares" database. Real Average Weekly Earnings (2009 dollars). Annual data from 1973 to 2011. All economy. All series are H-P filtered.

Table 6. E¤ect of high-earnings workers on average weekly earnings volatility.

For the bottom 95%, the volatility of the CPS and the Piketty-Saez earnings data is almost identical, decreasing slightly from the pre-1984 to the post-1984 period. This stands in stark contrast with the top 5% for which the volatility of earnings is about the same in the two data sources pre-1984, but then increases by 168% post-1984 according to the Piketty-Saez data, compared to only 31% according to the CPS data. The results con…rm that irregular earnings are quantitatively important for high-income individuals –both for trend growth and business cycle volatility –but do not matter for the remaining 95%. The close …t of our CPS earnings construct with the Piketty-Saez data for 95% of workers indicates that despite well-documented non-response and imputation issues (e.g. Hirsch and Schumacher, 2004; Bollinger et al., 2015), CPS May/ORG earnings provide a reliable measure of average wages and salaries for all but the highest-paid individuals in the U.S. workforce. This is an important …nding because the CPS May/ORGs is one of the most widely used micro data sets of individual earnings in the United States. Augmented CPS earnings data The above results suggest that by augmenting CPS earnings with estimates of supplements as well as wages and salaries of high-income earners, we should get relatively close to LPC earnings. We start by adding average supplements in the private non-agricultural sector to our CPS series. Next, we replace topcoded earnings in the CPS with an extrapolation based on Piketty and Saez’ earnings data for top-income fractiles (top 0.01%, 0.1%-0.01%, 0.5%-0.1%,...to 1%-5%) for each year from 1973 to 2011 (the last year for which the Piketty-Saez data are currently available).29 29

As an example, in 2005, 1.21% of respondents in our CPS sample were topcoded. For a fraction 1/1.21 of

22

Finally, to make the LPC data comparable to the private non-agricultural universe of the CPS sample (which we de…ned to match the universe of establishments in the CES), we use information from the NIPAs to remove self-employment and some other small components.30 Figure 7 compares the original LPC earnings series with this adjusted LPC earnings series (labelled "LPC private non-agriculture"), the original CPS earnings series, and the two augmented CPS earnings series.

Figure 7. Average real weekly earnings.

There are three main messages. First, the original LPC earnings series and the LPC private nonagricultural earnings series are very close to each other, indicating that the di¤erence in universe between the LPC and the CES is not important. Second, supplements are the main driver in closing the gap between CPS and LPC earnings, accounting for 65% of the di¤erence in 1973 and 57% of the di¤erence in 2013. Third, earnings of high-income individuals matter primarily in the second half of the sample. Together, supplements and P-S topcoded earnings account for 95% of the higher growth of LPC earnings over the sample period. these respondents, we assign the average earnings value of the top 1% in the Piketty-Saez data; and for a fraction 0.21/1.21, we assign an extrapolated average earnings value based on average earnings information for the top 1% and the top 5%. See the appendix for details. 30 Speci…cally, the universe of the LPC includes, aside from the self-employed, agricultural services, forestry and …shing, and government enterprises. These components are not part of the CES. See the appendix for details of how we adjust the LPC universe for these components.

23

Table 7 compares the business cycle volatility of the di¤erent series.

Relative Standard Deviation Pre-84 Real non-farm GDP LPC total compensation LPC total compensation (private non-agri) CPS CPS + Supplements CPS + Supplements & P-S topcode

Standard Deviation

Post-84

Post/Pre-84

Pre-84

Post-84

Post/Pre-84

2.90

1.40

0.48

1.00

1.00

1.00

(0.19)

(0.20)

0.29

0.65

2.24

(0.05)

(0.15)

0.84

0.91

(0.12)

(0.12)

0.82

0.87

(0.11)

(0.12)

0.80

0.72

(0.15)

(0.12)

0.82

0.72

(0.13)

(0.14)

0.80

0.79

(0.13)

(0.10)

1.08 1.07 0.90 0.88 0.98

0.28

0.62

(0.05)

(0.15)

0.28

0.52

(0.05)

(0.13)

0.28

0.51

(0.04)

(0.15)

0.28

0.56

(0.04)

(0.13)

2.21 1.87 1.83 2.03

Notes: Total sample extends from 1973 to 2013, except for P-S topcode adjusted series, w hich ends in 2011. Annual data. PCE-deflated w ages 2009 dollars). HP-filtered data. Standard errors computed using GMM and the delta method appear in parentheses below estimates.

Table 7. Business cycle volatilities for di¤erent average weekly earnings series.

As is the case for trends, the original and the private non-agricultural LPC earnings series behave very similarly. The CPS earnings series and the CPS + supplements earnings series also exhibit very similar volatility. This may seem puzzling given that the volatility of supplements is substantially higher than the volatility of the original CPS earnings construct (see Table 5). But this can be explained by noting that supplements account for less than 20% in the CPS + supplements series and that the covariance between supplements and CPS earnings is relatively low.31 By contrast, replacing topcoded earnings with extrapolated earnings based on the Piketty-Saez data increases the volatility of the CPS earnings series in the post-84 period, accounting for about half of the larger increase in relative volatility of LPC earnings. What explains the rest of the increase in volatility of LPC earnings in the post-84 period? One possibility is that our replacement of topcoded earnings remains too conservative. First, our extrapolation based on the Piketty and Saez data may underestimate the volatility of earnings at the very top. Second, the Census imputation procedures may result in too few topcoded observations. Bollinger et al. (2015) …nd that earnings non-response in the CPS is widespread among high income individuals. If individuals whose actual earnings are above the topcode value are less likely to report, 31

The business cycle variance of the ’CPS + Supplements’series can be approximated as 2 CP S_Supp

s2CP Sw

2 CP Sw

+ s2Supp

2 Supp

+ 2sCP Sw sSupp Cov(CP Sw; Supp)

where sCP Sw and sSupp are the shares of the CPS weekly earnings and weekly supplements in ’CPS+Supplements’ weekly earnings.

24

then missing earnings of people in high-income demographic groups are more likely to be imputed with earnings that are below the topcode value, and hence would not be replaced with Piketty-Saez data. Both issues suggest that earnings of high-income individuals may account for a larger part of the increased volatility of LPC earnings in the post-84 period than accounted for by our CPS + Supplements & P-S topcode series.

5.2

Di¤erences in worker coverage

As noted in Section 2, average earnings from the LPC and the CPS are representative of nearly all workers in the non-farm business sector, whereas the CES historically covered only production and non-supervisory workers. To quantify the importance of this narrower worker coverage, we exploit industry and occupation information in the CPS to simulate the CES sample. Our …rst step is to construct a weekly earnings series for workers who …t the o¢ cial BLS de…nition of production workers in goods-producing industries and non-supervisory workers in service-providing industries (adjusting for OTC and MJH as described in Section 2). This simulation, labeled "CES simulation 1" in Figure 8, comes close to the actual CES levels in the 1970s but fails to replicate the pronounced downward trend of weekly earnings in the CES from the early 1980s through the mid-1990s and

25

increases at a faster pace thereafter.32

Figure 8. Average real weekly earnings for CPS, CES and the two CES simulations.

As discussed in Plewes (1982) and ASS, many establishments in service-providing industries historically interpreted non-supervisory workers as employees who are paid hourly or are nonexempt under the Fair Labor Standards Act.33 Following ASS, we therefore construct a second simulation that keeps the same de…nition of production workers in goods-producing industries as in CES simulation 1, but categorizes hourly-paid workers along with workers that are likely to be non-exempt as non-supervisory workers in service-providing industries (see the appendix for details). As Figure 8 shows, the resulting "CES simulation 2" tracks the actual CES earnings series more closely, exhibiting a downward trend from the late 1970s through the mid-1990s and then an increase from the mid-1990s onward. At the same time, CES simulation 2 lies somewhat below actual CES earnings, especially in the beginning and towards the end of the sample. We discuss possible explanations for this discrepancy below. Table 8 compares the business cycle volatility of the two CES simulations with the volatility of 32

The simulation stops in 2002 because of occupations classi…cation changes in 2003 which makes the construction of consistent occupation-speci…c series (as the CES simulations) di¢ cult. 33 This misreporting issue was particular to service-providing industries because the non-supervisory classi…cation is not one that establishments would naturally use for other purposes.

26

our CPS earnings series and the actual CES earnings series.

Pre-84 CPS CES simulation 1 CES simulation 2 CES

Standard Deviation Post-84

0.80

0.73

(0.15)

(0.16)

1.01

0.72

(0.15)

(0.14)

1.22

0.80

(0.09)

(0.18)

1.30

0.50

(0.18)

(0.09)

Post/Pre-84 0.92 0.71 0.65 0.39

Notes: CPS May-MORG and CES data. Real Average Weekly Earnings (2009 dollars). Annual, HP-filtered data. Sample: 1973 to 2002.

Table 8. Business cycle volatilities for the CES, CPS, and the two CES-simulated series.

As noted in Section 4, CES earnings are substantially more volatile than CPS earnings before 1984. The volatility of both series declines post-1984, but the much greater decline in the volatility of the CES series reverses their relative positions.34 CES simulation 1 accounts for part of the higher volatility of CES earnings in the pre-1984 sample and the larger drop in volatility in the post-1984 sample. CES simulation 2 improves upon this picture, accounting for 85% of the di¤erence in pre1984 volatility between CES and CPS earnings, and for about half of the drop in volatility of CES earnings. The simulations suggest that earnings of production and non-supervisory workers in the CES are not representative of average earnings in the non-farm business sector, and that this lack of representativeness accounts for a substantial part of the divergence in trend and volatility between CES and CPS earnings. We …nd further support for this conclusion by comparing the CES and CPS earnings series with the new CES "all employees" earnings series that starts in 2006. As shown in Figure A.2 of the appendix, the CES all-employees earnings series lies substantially above the historical CES series and is fairly close to our CPS earnings series.35 34

The CPS earnings volatility for the post-1984 period reported here is slightly di¤erent from the one in Table 3 because the sample stops in 2002 instead of 2013. 35 As we discuss at the end of this Section, the small remaining gap between the CES all employees series and the CPS series is likely to be attributable to non-response bias in the CES.

27

5.3

Taking stock

Table 9 summarizes our …ndings.

Level difference

Volatility difference

Initial (1973) level $

Change 1973-2013 $

1973-1984 stdev

Ratio post-84 / pre-84 stdev

LPC total compensation (private non-agri)

752.71

363.02

0.82

1.07

CPS + Supplements + P-S topcode

709.25

353.28

0.80

0.98

Weekly earnings series

CPS

620.35

174.93

0.80

0.90

CPS with CES worker coverage ("CES simul 2")

549.33

60.17

1.22

0.65

CES

601.89

29.48

1.30

0.38

Notes: Table show s initial 1973 levels and level changes (left) for various real w eekly earnings series, and the pre-84 volatilities and ratio of post-84 to pre-84 volatilities (right). Data sources: LPC, CES, CPS May/ORG, NIPA, and Piketty-Saez "Top income shares" database. Real average w eekly earnings (2009 dollars). Private nonagriculture sector. Annual data from 1973 to 2013. All series are HP-filtered w hen computing standard deviations.

Table 9. Accounting for the divergence in average weekly earnings.

Di¤erences in earnings concept and di¤erences in worker coverage account for a large part of not only the divergent evolution of the two earnings measures over time, but also their initial level and volatility di¤erences. In particular, supplements and earnings of high-income individuals account for 67% of the initial di¤erence and 95% of the higher trend in LPC earnings relative to CPS earnings. Di¤erences in worker coverage, in turn, account for almost 80% of the lower trend and about 50% of the larger drop in volatility of CES earnings relative to CPS earnings.36 It is also worth noting that the percent increase between 1973 and 2013 of our CPS + Supplements + P-S topcode series (50%) is almost exactly the same as that of the LPC series (48%), and that percent increase of the CES simulation 2 series (11%) is fairly close to that of the actual CES series (5%)

5.4

Other potential sources of divergence

In addition to di¤erences in earnings concepts and population coverage, the three datasets also di¤er in other respects that could have contributed to the divergence in earnings trends and volatility. In particular, the earnings data for the LPC series come primarily from the QCEW, an administrative dataset collected for UI purposes that covers nearly all private-sector establishments for which measurement and coverage has remained constant over time. In contrast, the CPS and the CES are 36

Since the Piketty-Saez earnings data currently stops in 2011, we compute the 1973-2013 change for "CPS + Supplements & P-S topcode" earnings by assuming that the growth rate of this series for 2012 and 2013 is the same as the growth rate of LPC earnings. Likewise, since occupations codes in the CPS change in non-trivial ways in 2002, we compute the 1973-2013 change for "CPS simulation 2" by assuming that the growth rate of this series for 2003-2013 is the same as the growth rate of CES earnings.

28

voluntary surveys of households and establishments that have changed over time and are subject to a number of potential measurement issues. For the CPS, the major change was the 1994 redesign, which a¤ected the earnings questions and added questions on multiple job holdings (MJH). As described in Section 2, we address these issues in various ways using the CPS microdata. While none of these adjustments is perfect, the resulting average earnings construct closely tracks the administrative IRS records from Piketty and Saez (2003) for 95% of the workforce. This indicates that our CPS earnings construct provides a reliable average measure of wages and salaries for all but the highest-paid individuals in the U.S. workforce. For the CES, the measurement issues that could bias average earnings are quite di¤erent in nature. Since these issues are not as well known in the literature, we devote more detail to describing them and their potential e¤ects. The sample size and industry coverage of the CES have expanded signi…cantly over time. Between 1964 and 1983, the CES sample increased from 135,000 to 190,000 establishments and contained data for more than 500 industries. But only 30 percent (155 industries) were serviceproviding, even though service-providing industries accounted for about 57 percent of private sector employment (about 70 percent of total employment). As a result, small establishments, which are disproportionately in services, were under-represented to the point where “the sample in the service sector falls short of representation in the smallest size categories” (Plewes, 1982).37 Partly in response to this concern, the BLS expanded the CES sample signi…cantly to about 425,000 establishments by 1989 (additional, smaller expansions occurred thereafter). This expansion improved sample representation and allowed the BLS to increase the number of estimation cells in the service-sector by an additional 82 industries. In the mid-1990s, the BLS started shifting survey collection from a mail-shuttle form to automated methods. Under the mail-shuttle method, the same form was mailed back and forth between establishments and the BLS, and the BLS did not provide feedback to respondents on how to …ll out the form correctly. Under current procedures, data for new respondents are collected via computer assisted telephone interviewing (CATI), whereby interviewers can help respondents provide the correct data. After several months of CATI interviews, respondents are transitioned to automated data collection methods. A …nal change arrived in the early 2000s when the BLS switched from a quota sample to a probability sample. Under quota sampling, the BLS speci…ed the number of establishments required for each industry-size cell and solicited new establishments until the quota was met. Moreover, 37

Large establishments account for a disproportionate fraction of employment in the U.S. The CES therefore samples larger establishments at a higher rate as this allows the survey to cover a larger fraction of total employment. See BLS (2014) for details.

29

establishments remained in the sample until they refused reporting or went out of business. As a result, establishments in the CES sample tended to be older than the universe of establishments. Under the new probability sampling, establishments in each industry-size cell are solicited at random without replacement; and reporting establishments are regularly rotated out of the sample. These changes improved the quality and representativeness of the CES data; but they may have also a¤ected the average earnings series in unexpected ways.38 Speci…cally, the under-representation of smaller establishments in service-providing industries in the early part of the sample may have biased upwards both the level and the volatility of average earnings in the CES.39 If that is the case, then the 1980s sample expansion, which made the sample more representative, could have caused the CES earnings series to trend downward and to decline in volatility. This could explain why in Figure 8, CES earnings start out above the CPS-based simulations but then decline at a faster pace during the 1980s; and why in Table 8, the volatility of CES earnings declines so much from the pre-84 to the post-84 sample. The change in survey collection methods in the mid-1990s, in turn, may have reduced misclassi…cation of non-supervisory workers, thereby shifting the worker coverage of the CES sample from the one assumed in CPS-based simulation 2 towards coverage resembling the one assumed in simulation 1. This could explain why the CES average earnings series exhibited stronger growth than simulation 2 during the second half of the 1990s. Ideally, we would like to simulate the e¤ects of these changes using data from the QCEW, which is the sample frame for the CES. Unfortunately, the micro data needed are not available for research purposes prior to the 1990s. And even if the micro data were available, the simulations would only be an approximation since the QCEW earnings concept and worker coverage do not match those in the CES. However, we can at least obtain an idea of the e¤ect of the early 1980s sample expansion, which occurred primarily in the service sector, by looking separately at goods and service sectors. We …nd that the CES average earnings series for service-providing industries starts out above the corresponding CES simulation 2 and then experiences a pronounced downward trend, closing most of the gap with its CPS-based simulation by 1980. For goods-producing industries, by contrast, the CES earnings series and its CPS-based simulation match each other closely in the beginning of the sample and there is no downward trend. This suggests that the decline in CES average earnings in the early part of the sample was at least partly driven by changes in the service sector. At the same time, it is worth noting that the decline in service sector earnings started prior to the mid-1980s 38

Since the di¤erent changes occurred gradually, they did not result in obvious breaks. Moreover, the published CES average earnings series are computed using a “link-and-taper” estimator, which tends to smooth the e¤ects of changes to the sample. See BLS (2014) for details. 39 In itself, oversampling of larger and older establishments, which tend to pay higher wage, does not bias average earnings since each industry-size-state cell in the CES is weighted with QCEW employment counts. An upward bias could occur, however, if within each cell, the sampled establishments are larger and older than their cell population average.

30

expansion of the CES sample. Hence, if this explanation is correct, the main improvements in representativeness of the service sector sample would have had to occur during the smaller sample expansions of the 1970s and early 1980s. Another factor that may have contributed to the di¤erence between the CES and CPS earnings series is non-response bias. As documented in a recent BLS study by Gershunskaya et al. (2013), the response rates for the CES earnings and hours questions are very low. Between 2007 and 2011, about 53 percent of all establishments sampled by the CES provided all-employee counts; and conditional on reporting the all-employee counts, the response rate for the earnings and hours questions was about 57 percent. This translates into an unconditional response rate of about 30 percent for the earnings and hours questions, which is substantially smaller than the response rate of 70% in the CPS ORGs. The CES does not impute earnings and hours for missing observations, but their estimation procedure amounts to reweighting. This procedure may lead to systematic bias in CES average earnings numbers if non-response is related to average earnings, conditional on cell characteristics.40 To assess the extent of non-response bias, the Gershunskaya et al. (2013) study matches all establishments sampled by the CES to the QCEW and compares the QCEW earnings of CES respondents to the earnings of the full sample (respondents and non-respondents).41 Overall, average earnings of sampled CES establishments that report earnings is 6.7 percent less than average earnings of all sampled establishments. There are a couple of drawbacks to the Gershunskaya et al. (2013) study. It covers a relatively short period, so it is impossible to determined how the bias may have changed over time. Moreover, as noted earlier, the QCEW earnings concept di¤ers from the CES earnings concept; and the comparison was done for all employee earnings and not earnings of production and non-supervisory workers, which is the historical coverage of the CES. Even so, the study suggests that non-response has resulted in a signi…cant downward bias in CES earnings in recent years and that this bias explains a large part of the di¤erence between the CPS and CES "all-employees" series in Figure A.3 of the appendix.42 The discussion above suggests that at least part of the remaining divergence between historical CES earnings and the LPC and CPS earnings series is due to the CES sample expansion, changes in 40

Non-response rates vary by establishment size, with response rates decreasing with establishment size. Response rates also vary by data collection method and length of pay period. In general, establishments either always respond to the earnings and hours questions (about 33 percent of establishments that report all-employee counts for 12 months) or they never respond (about 52 percent). 41 As noted above, the CES started collecting all-employee earnings and hours data starting in 2006. 42 Actually, non-response bias explains more than the di¤erence between the CPS and the CES "all-employees" series in Figure A.3. It is worth noting that, given the di¤erences between the CES and the QCEW, the estimated -6.7 percent bias should be viewed as a ball-park …gure.

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collection methods, and non-response bias in the CES earnings data. Investigating these di¤erences further would be of interest but would require access to historical CES microdata.

6

Conclusion

In this paper, we examine the historical trends of three commonly-used average hourly wage series from the LPC, the CES, and the CPS. We document that these series have diverged substantially in both trend growth and volatility over the past 40 years, and examine the sources of this divergence. We …nd that this divergence is due in large part to di¤erences in earnings concept and worker coverage. These di¤erences have important implications for the appropriate choice of average hourly wage series for macroeconomic analysis. The LPC series is the most inclusive of the three wage measures in terms of earnings concept, covering virtually all forms of wage and salary disbursements to workers as well as employer-paid supplements. As such, the LPC is the most appropriate series when the researcher needs a comprehensive measure of labor compensation, for example when calculating the total share of income going to labor. We show that an important part of the recent growth and increase in volatility of the LPC series is driven by the irregular earnings of workers in the top 5 percent of the earnings distribution. Thus, the LPC series underestimates the slowdown in wage growth and overestimates the increase in business cycle variability of wages as experienced by the majority of workers. Equally important, our analysis shows that supplements have been a major contributor to the growth of LPC earnings since the 1970s and that they now constitute a substantial portion of total labor compensation. It is therefore important to include supplements when analyzing trends in total labor compensation. At the same time, since a large fraction of supplements represent a per-worker …xed cost to …rms that applies to full-time employees (e.g. health bene…ts), their growing importance has potentially important implications for the speci…cation of wage setting in macroeconomic models that may account for a number of recent labor market phenomena; e.g. the increased use of part-time or temporary work. In contrast to the LPC, the historical CES wage series covers only production and nonsupervisory workers, and the earnings concept is limited to wages and salaries that are paid on a regular basis. These two properties explain much of the slow growth and decline in volatility of the CES earnings series. However, changes to the survey over time, while improving accuracy and representativeness, may also have a¤ected the evolution of CES average earnings. The CPS wage series, while not commonly used for macroeconomic analysis, o¤ers several advantages over the LPC wage and the CES wage. After adjusting for OTC, we …nd that our CPS earnings series is a reliable measure of the wage-and-salary portion of compensation for all but the top 5 percent of earners. This is important because the CPS is one of the most widely-used publicly 32

available micro data sets in the United States, and it has been used, among many other things, to document the divergent wage growth of di¤erent subpopulations. More generally, our …ndings suggest that our CPS earnings series can be used for macroeconomic analysis in situations where researchers have used either the CES or the LPC. CPS earnings do not include the volatile and growing “irregular” earnings of high-wage workers but are otherwise representative of the United States workforce. Furthermore, CPS earnings can be augmented with estimates of supplements to account for the growing importance of non-wage payments in total labor compensation. The usefulness of the CPS does not imply that the LPC and the CES series should be abandoned for macroeconomic analysis. The LPC earnings series is still the most inclusive and most comprehensive measure of total labor compensation; and the new CES "all employees" series provides a measure of regularly-paid wages and salaries that covers all non-self-employed workers in the private non-agricultural sector of the United States workforce. This is important because the CES is available monthly and is released by the BLS on the …rst Friday of the month following the reference month. In comparison, the LPC earnings series is available quarterly and a preliminary estimate is released about 5 weeks after the end of the reference quarter.43 Moreover, the LPC data are subject to several revisions that can sometimes be large whereas revisions to the CES tend to be smaller, with the largest revisions occurring in the two months following the initial release.44 For policy-makers such as the Fed and the business press where timeliness is key, the CES series will therefore continue to be among the most relevant data sources.

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