State and Time Dependence in Wage Dynamics: New Evidence from Administrative Payroll Data

Transcription

1 State and Time Dependence in Wage Dynamics: New Evidence from Administrative Payroll Data John Grigsby Erik Hurst Ahu Yildirmaz Preliminary and Incomplete Please do not cite without author permission April 16, 2018 Abstract Using administrative payroll data from the largest U.S. payroll processing company, we document a series of new facts about the extent of nominal wage rigidity in the U.S.. First, we document that nominal wage cuts are exceedingly rare. Over the pooled period, only 2% of workers who remain in a continuous employment relationships receive a nominal wage cut during a given year. Second, nominal wages are much more flexible (both up and down) for job changers. Third, the extent of wage rigidity is state dependent. Nominal wage adjustments are lower during recessions, in regions that suffered larger house price declines, and for firms that shed large amounts of workers. Moreover, nominal wage cuts are substantially higher during recessions. During the Great Recession, nearly 8 percent of salaried workers received a nominal wage cut. Finally, we document that wage changes within a firm vary substantially in response to firm level shocks. Those at the top of the wage distribution have nominal wages that respond more to firm level shocks. While some of the qualitative patterns have been documented in the prior literature, the exact quantitative magnitudes we document differ markedly. We end by discussing how measurement error in household level data and missing measures of hours in firm level data substantially bias existing measures of nominal wage rigidity. We thank Mark Aguiar, John Haltiwanger, Alan Krueger, and John Shea as well as seminar participants at the 2018 American Economic Association meetings and the University of Maryland for helpful comments. Authors contact information: jgrigsby@uchicago.edu, erik.hurst@chicagobooth.edu. and Ahu.Yildirmaz@ADP.com.

2 1 Introduction The extent to which wages are flexible is a key input into understanding macroeconomic fluctuations. For example, Yellen (2014) discussed the possibility that nominal wage rigidities could have resulted in pent-up wage deflation during the Great Recession which then contributed to slower than expected wage growth as the economy recovered. However, compared to the literature on price changes, there is only a relatively small literature which uses micro data to measure the extent to which nominal wages adjust. Contributing to the small literature is the fact that most micro data sets are not well suited to measure nominal wage changes. Household surveys with a panel component like the Current Population Survey (CPS), the Panel Study of Income Dynamics (PSID), and the Survey of Income and Program Participation (SIPP) often define the nominal wage by dividing self-reported earnings by self-reported hours. Any measurement error in either earnings, hours worked, or the self-reported hourly wages can result in a substantial upward bias in the volatility of individual level wage changes. Administrative datasets from the Internal Revenue Service (IRS), Social Security Administration, or state level unemployment records, on the other hand, measure individual earnings at the quarterly or annual frequency with little measurement error. However, these datasets hardly ever include measures of individual hours worked. When individual hours worked are collected, they are often reported not by the individual but instead by a payroll administrator. 1 While the administrative datasets provide high quality measures of quarterly or annual earnings, the lack of administrative data on hours worked makes them less than ideal to study nominal wage fluctuations. In this paper, we use administrative data from ADP one of the world s largest payroll processing companies to document a series of facts about individual nominal wage adjustments. Hundreds of thousands of firms per year contract with ADP to administer a variety human resource and payroll activities. 2 Most of ADP s clients use their payroll processing services, with ADP currently processing payroll checks for roughly 20 million workers each year, one-seventh of the U.S. workforce. For hourly workers, the data show administrative measures of their hourly wage. For salaried workers, we observe administrative measures of their earnings per pay period. We use these two objects as our measures of nominal wages. Using earnings per pay period for salaried workers avoids the need to measure hours worked. 1 Washington is one state that uses hours worked in the prior year to determine UI eligibility. According to Unemployment Insurance Tax Information: A Handbook for Washington State Employers (2014), employers in Washington state are required to report all hours worked for employees during the quarter. If, however, hours are not tracked, employers are instructed to report 40 hours per week. 2 The companies that contract with ADP are roughly representative by firm size and industry. As we discuss below, we re-weight the ADP data each year so that it matches identically the firm size and industry distribution within the United States. 1

3 Three additional features are worth noting about the ADP data. First, our data starts in 2008 and goes through Second, given our very large sample sizes, we can explore wage adjustment patterns at disaggregated levels such as region or narrow industry. Finally, given ADP s large firm coverage, we can track workers as they move from one ADP company to another ADP company. All three of these features allow us to explore how nominal wage adjustments vary with aggregate, sectoral and local business cycle conditions. We begin the paper by documenting patterns for a sample of job stayers. We define job stayers as those workers who remain attached to the same firm during the frequency of wage change we are exploring. Pooling together our data over the entire sample, we find that roughly 20 percent of job-stayers receive a nominal wage change over a quarter and about two-thirds of job stayers receive a wage change during a year. Unlike other studies in the literature, we find that nominal wage cuts are exceptionally rare. For our sample of job stayers during the period, only 0.9 percent of workers received a nominal wage cut during a given quarter and only 2.4 percent received a nominal wage cut during a given year. Essentially all wage changes within a given employment relationship are wage increases. Given the extensive nature of the ADP data, we can also measure wage changes for individuals who transition across firms. This is only possible for workers that transition from one firm who uses ADP payroll services to another firm that uses ADP payroll services. Given our large sample sizes, we have many workers who transition across ADP firms. For workers that transition across jobs, essentially all experience a nominal wage change. Given that job switchers are a non-trivial share of the economy, we can create a broader measure of nominal wage flexibility pooling together both job stayers and job changers. Doing so, we find that roughly 35 percent experience a wage change during a given quarter and 80 percent experience a wage change during a given year. Including both the job stayers and job changers, roughly 4 percent of workers experience a nominal wage decline with essentially all of the declines being driven by job changers. We find that wage adjustment patterns are correlated with both firm size and industry. Smaller firms are much less likely to adjust wages than larger firms. Additionally, the frequency of wage adjustment is higher in the manufacturing, FIRE and services industries and lower in construction, retail trade and wholesale trade. These differences persist even conditional on a vector of individual and firm level controls. At the heart of our paper is the use of our data to show a set of stylized facts supporting the importance of both time dependent and state dependent wage setting behavior. The evidence in favor of time dependence most reflects a model of Taylor (1980) staggered wage contracts at the individual level. Using the panel nature of our data, we show that in a sample of job stayers, wage adjustments occur primarily at 12 month intervals. There is a 2

4 small and constant probability of wage changes between 1 and 10 months and between 14 and 22 months suggesting that even at the individual level, some wage changes occur at frequencies other than a year. The nature of these wage changes are different in that they are much larger than the wage changes that occur at annual frequencies. While, for the most part, workers receive a wage change every 12 months, the wage changes at the aggregate level are mostly smoothed out across individuals. Exploring the seasonality in wage changes, we do find that wage changes are more common in January, April and July than in other months during the year. However, aggregating to quarters, the fraction of wage changes is roughly constant across quarters. At first blush, these patterns seem to support a Calvo model of wage setting commonly used in our aggregate macro models. However, we exploit a variety of empirical specifications to show that wage setting behavior is state dependent. We begin by exploiting business cycle variation. Even though nominal wage cuts are very rare over our entire sample period, roughly 9.1 percent of salaried workers and 3.3 percent of hourly workers received nominal wage cuts during the Great Recession. Moreover, we show that nominal wage cuts were much more likely in parts of the country that received large housing price declines. This suggests that any model with a constant fraction of wage adjustments (either in general or with respect to downward adjustment) will fail to match the wage setting patterns over a business cycle. The fact that wages adjust more on the downside during recessions only serves to strengthen the puzzle of increased unemployment at business cycle frequencies. To complement our business cycle results, we also explore cross-firm variation in wage setting in response to underlying firm level shocks. We document that firms with sharply declining employment are much more likely to reduce the nominal wages of their workers relative to either firms with constant employment or firms with sharply increasing employment. Moreover, even firms with sharply declining employment raise the wages of some of their employees by a large amount. The wage dynamics of growing and contracting firms display a large amount of heterogeneity in wage change patterns across employees. To further shed light on how firms adjust the wages of their workers, we exploit shocks to the manufacturing sector. Using a shift share strategy, we aggregate manufacturing shocks up to the level of an MSA. We then ask, for manufacturing jobs in regions more exposed to a manufacturing shock, what happens to wages of workers at different points in the firm wage distribution. Additionally, we can then compare the wage structure in retail and service industries in response to a local manufacturing shock. Our results further support a large state dependent component of individual wage setting. We find evidence that in response to shocks to local labor demand, wages of those at the top of the wage distribution adjust more. 3

5 We end the paper by showing the importance of using administrative payroll data to measure the extent of nominal wage changes among workers. To do so, we create two additional measures of nominal wages throwing away some of the strength of our data. First, we measure changes in quarterly earnings for a given worker who remains with a given firm. Then we measure quarterly earnings per hour. Both of these approaches use administrative data on earnings. The latter adjusts earnings by administrative measures of hours worked. We show that both of these measures lead to substantially higher amounts of wage adjustment for workers who remain on the same job. The reason is that hours vary substantially for a given worker across quarters and wages are measured with error for salaried workers even in administrative datasets. Collectively, our results highlight the importance of using administrative payroll data to accurately measure wage adjustments. Furthermore, we show a large amount of complementary evidence supporting state dependence in wage setting. Finally, given the high frequency of job changes, we show that nominal wages are fairly flexible. While there is no doubt that there is some short run stickiness, particularly on the downside, most workers do receive a wage change within a year. 2 Literature Our work contributes to a growing literature examining nominal wage stickiness. Across most papers, a consensus has emerged that most people experience a nominal wage change during a given year and that wages are more downward rigid than upward rigid. Across papers, the differences are in the magnitudes of the results. These differences stem from the fact that measuring nominal wage changes in household and administrative datasets is notoriously difficult given the presence of measurement error (household surveys) or missing hours (administrative datasets). One of the earliest papers to estimate the extent of nominal wage rigidity using household level data was Kahn (1997). Kahn (1997) used data from the Panel Study of Income Dynamics (PSID) to find that about 92% of workers receive a nominal wage change during a given year. More recently, Daly and Hobijn (2014) use data from the Current Population Survey (CPS) and find that 85% of workers who remain in a continuous employment relationship receive a nominal wage change during a given year. 3 Barattieri et al. (2014) recognize the problems that measurement error poses for accurate measurement of nominal wage rigidity. Using data from the Survey of Income and Program Participation (SIPP), they employ the 3 For early examples of research using the CPS to measure wage stickiness with similar conclusions, see Card and Hyslop (1997) and Elsby (2008). 4

6 methodology of Gottschalk (2005) to adjust for measurement error in wages. While their adjustments reduce the frequency of wage changes in the underlying household data, they still find that roughly 12% of all wage changes were negative, that there was no seasonality in wage changes, that the frequency of wage changes did not vary with industry, and that nearly one-quarter of job changers did not change their wage. These results contrast with the results we show in this paper. Although Barattieri et al. (2014) was among the first to address the problem of measurement error in self-reported wages, our administrative payroll data allow us to remove this problem altogether. A more recent literature has emerged using firm level data to measure wage stickiness. 4 Both Lebow et al. (2003) and Fallick et al. (2015) use data from the BLS s Employment Cost Index (ECI) to measure nominal wage rigidity. Unlike the household surveys or the payroll data, the unit of analysis in the ECI is a job not a worker. To the extent that workers who populate a specific job are heterogeneous with respect to underlying skills, nominal wage variation could occur due to shifting sampling of different quality workers over time. fact, the nominal wage variation in the ECI is larger than what we document in the payroll data. Le Bhan et al (2012) and Sigurdsson and Sigurdardottir (2016) use administrative establishment level data from France and Iceland, respectively, to measure nominal wage rigidities. Both datasets have administrative measures of earnings for a given employee. To make hourly wages, they divide administrative earnings by an administrative report of hours. The extent to which hours vary over time at either the extensive or intensive margins will generate a larger amount of measured nominal wage flexibility. Likewise, Kurmann and McEntarfer (2017) use data from the US Longitudinal Employer Household Dynamics (LEHD) to examine nominal earnings per hour adjustments for a sample of job stayers who reside in Washington state over a two year period. They focus their sample on residents of Washington state because Washington requires employers to report the hours worked of their employees as part of their Unemployment Insurance program. The hours measures are reported at the quarterly level and are self reported by the firm administrator filling in the unemployment insurance records. For salaried workers, the reported hours worked are often set to 40 hours per week. Relative to our findings, Kurmann and McEntarfer find lower amounts of earnings per hour rigidity and higher amounts of declines in earnings per hour. As we discuss in the last part of the paper, earnings per hour includes any earnings showing up in a paycheck including overtime payments, holiday, sick and vacation days, commissions, reimbursed meal and travel expenses, and bonuses. Within 4 There are many additional studies examining the nature of earnings dynamics using high-quality administrative data. See, for example, Postel-Vinay and Robin (2002), Bonhomme and Robin (2010), and Guvenen et al. (2014). In 5

7 our data, we can recreate a measure of earnings per hour and compare it to our measures of nominal wage changes using detailed payroll data. We show the pattern of changes in earnings per hour and nominal wage changes differ substantively from each other because of combination of mis-measured hours and year-to-year variation in overtime hours and other payments that move with unmeasured hours worked. Elsby, Shin, and Solon (2013) use data from the CPS and a British survey administered to employers to measure the cyclicality of wage rigidity. They show that approximately 4.5% of British workers received no wage change between 2008 and They postulate that the relatively infrequent changes in the United States may be an artifact of rounding error endemic to US survey data. Our payroll-based longitudinal hourly wage data show that this is not the case - indeed, we find more realized wage rigidity once one removes measurement error from U.S. data sources. 5 Our paper is closest in spirit to Altonji and Devereux (2000) and Sigurdsson and Sigurdardottir (2016). Altonji and Devereux use administrative payroll data similar to ours for one large financial service company during 1996 and The patterns of wage adjustment they document within this large financial company closely match the patterns we document for the whole U.S. economy during the period. In particular, they document that only 0.5% of workers receive a nominal wage cut during a given year. The fact that payroll data from an earlier period broadly matches the results from the recent ADP data highlights the importance of using administrative payroll data to measure wage stickiness. Sigurdsson and Sigurdardottir (2016) use their Iceland administrative firm earnings data to highlight the importance of state dependence in wage setting. Our results complement their results by using our administrative payroll data to emphasize the importance of state dependence in wage setting within the United States. Moreover, we can use a variety of identification strategies to isolate state dependence in wage adjustments. These same strategies allow us to also explore within firm heterogeneity in wage adjustments. 5 There is a long literature, surveyed by Bewley (2004) and Howitt (2002), examining the root causes of nominal wage rigidity. In a series of interviews with business managers responsible for compensation policy, they discuss a series of studies have documented that the primary resistance to wage cuts arises from concerns over damaging worker morale. See, for instance, Kaufman (1984), Blinder and Choi (1990), Agell and Lundborg (1995, 1999), Campbell and Kamlani (1997), and Bewley (1999). 6

8 3 Data 3.1 Overview of ADP Data We use administrative individual panel data provided by the ADP Corporation. ADP is a large, international provider of human resources services including payroll processing, benefits management, tax services, and compliance. ADP has over 650,000 clients worldwide, and currently covers payroll for over 20 million workers in the United States. The data to which we have access starts in May 2008 and extends through December During that period, we observe payroll information for approximately 12% of the American workforce. The data contain monthly aggregates of individual paycheck information, as well as all relevant pieces of information needed for human resources management. Most crucially, we observe, without measurement error, the per-period payment rate for all employees. For hourly workers, this payment rate is simply the worker s hourly wage, while for salaried workers, this constitutes the pay that a worker receives each pay period - either each week for workers paid weekly, every two weeks for workers paid biweekly, or each month for workers paid monthly. For much of our analysis, we consider hourly and salaried workers separately. Given the data is aggregated to the monthly level, the per period payment rate is measured as of the last day of the month. In addition to the administrative wage information, the data contain all other information that would appear on the worker s paycheck, such as the worker s gross earnings, taxes paid, and any benefits or bonuses provided by the firm. Additionally, the data contains other payroll information including whether the worker is paid hourly, the frequency at which the worker is paid and the number of hours worked during the month. For hourly workers, this is the exact number of hours worked. For salaried workers, this data is provided by the firm s HR administrator and is often set to 40 hours. We also observe various additional worker characteristics including their zip code of residence, sex, and age, as well as details about the job, such as the start date of employment (and thus worker tenure), firm size, and industry. Selection into the ADP data is at the firm level. As a result, given unique firm identifiers, we can measure wage distributions within and across firms over time. 6 Finally, the presence of consistently defined worker identifiers permits the careful study of individual worker dynamics across firms. The one caveat is that we are only able to track workers if they move to another ADP-covered firm. However, given our sample size, movements from 6 Strictly speaking, our definition of a firm is an ADP-provided client code. This will usually be an autonomous firm, rather than any individual establishment. One possible exception to this rule arises if particularly large conglomerates have multiple subsidiaries, all of which separately hire ADP to handle their payroll. In this case, each subsidiary would count as a separate ADP client. 7

9 one ADP firm to another ADP firm are quite common. We make two major sample restrictions for our analysis. First, we restrict ourselves to workers aged 21 through 60 years old. This restriction focuses our analysis on prime age workers. Second, we only make use of data from ADP s Autopay payment product, which is marketed principally towards firms with over 50 employees. Autopay is ADP s primary payroll processing product. Even though it is marketed to firms with more than 50 employees, the Autopay data does include some smaller firms. 7 The full dataset that we have access to includes over 50 million unique individuals and over 141 thousand firms. To reduce computational burden, we create two random subsamples of the full data. The first chooses one million unique employees, and follows them through their entire tenure in the sample. This is the primary dataset for analysis. However, this dataset is ill-suited to study questions at the firm level; we therefore construct a second subsample of one thousand unique ADP clients, drawing all workers from those firms in the process. The random employee-level and firm-level subsamples remain large, with roughly 25 million and 13 million unique employee-month observations, respectively. 3.2 Representativeness of ADP Data Table 1 highlights the firm size distribution for employees in our employee sample (column 1) and employees in our firm sample (column 2). For the results in this table, we pool our data together over the entire period. For comparison, we include data from the U.S. Census s Business Dynamics Statistics (BDS) over the same time period. The table also shows the number of employees and the number of firms in each of our samples. By design, we randomly drew 1 million employees for our employee sample and 1,000 firms for our firm sample. Our employee sample includes roughly 91,500 distinct firms while our firm sample includes roughly 980,000 distinct employees. The number of actual observations is much larger for each sample because we observe employees for multiple months. For our employee sample, we track all employees across all months between 2008 and 2016 that they are employed at any ADP firm. For our firm sample, we track all employees in that firm across all months that they remain employed at that firm. Given the ADP business design, it is not surprising that, as shown in Table 1, the ADP data under-represents both very small and very large firms. As discussed above, we have access over the entire period for ADP s product that is marketed to firms with 7 ADP does have a separate product called Run marketed to smaller firms. We have access to this data but only starting in July In the online appendix, we document that the many of the main patterns documented for the smaller firms in our primary sample match the patterns for smaller firms in the Run sample for overlapping time periods. 8

10 Table 1: Firm Size Distribution in ADP Samples and the BDS, Pooled Data Pooled ADP Employee Sample ADP Firm Sample BDS Data Number of Employees 1,000, ,523. Number of Firms 91,577 1,000. Number of Observations 24,831,244 12,994,801. % Firm Size: % Firm Size: % Firm Size: % Firm Size: % Firm Size: % Firm Size: Note: more than 50 employees. Given this, less than 4 percent of the employees in our sample come from firms with less than 50 employees. The comparable number for the aggregate economy is 18 percent. Likewise, very large firms tend to have their own human resource department that processes their payroll. Despite this, ADP still has a large amount of employees working in firms with over 5,000 employees (20 percent of the data). We also explore the industry distribution of our sample. Our data has a slight over-representation amongst the manufacturing and broad service sectors, and a complementary underweight in retail trade, construction, and agriculture, relative to data from the Census s Business Dynamics Statistics (BDS). To account for the concern that the data do not perfectly represent the universe of U.S. firms, all subsequent analyses in this paper have been weighted so as to match the BDS s firm size by industry mix of employment shares. We compute our weights for each year between 2008 and By re-weighting the data, we control for sample selection along these key observable dimensions. Although there may yet remain selection into the sample along unobservable dimensions (e.g., firms with high cash flow are more likely to hire ADP or the very small firms that are in ADP s autopay system are selected on some dimension), we consider these potential selection issues to be small once controlling for firm size and industrial mix. 8 Table 2 shows some additional summary statistics for our employee sample pooling across 8 In the Online Appendix that accompanies the paper we show a series of additional results. In particular, we show sample statistics for each individual year and report our sample weights. We also show our key results without imposing sample weights. Finally, we show that ADP is truly a national firm in that it has a very representative geographic coverage. 9

11 all years (column 1) and for selected individual years (columns 2-4). In particular, we show statistics for 2008 (our first year of data), 2012 (a middle year of data), and 2016 (our last year of data). As discussed in the Online Appendix, the age, sex, and tenure distributions in our ADP sample matches well the age, sex, and tenure distributions of workers in nationally representative surveys such as the Current Population Survey (CPS). About one-fifth of our sample is paid weekly while three-quarters is paid bi-weekly. Less than five percent are paid monthly. For our sample, roughly 64 percent are paid hourly with the remaining 36 percent being classified as salaried workers. According to data from the CPS monthly supplements, only 57 percent of employed workers in the U.S. between the ages of 21 and 60 report being paid hourly during this time period. When thinking about what explains the difference between the CPS and ADP data it is worth noting that the distinction between hourly and salaried workers is sometimes unclear within the ADP dataset. From talking with ADP staff, some workers are automatically entered as having worked 40 hours each week at a given hourly wage. These workers are therefore classified as wage workers. However, on many levels, these workers operate as if they were salaried in the sense that their actual hours are never recorded and their weekly wage rate is just their weekly salary divided by 40. Furthermore, these workers may report being salaried in survey data such as the CPS. For our purposes, however, we consider these workers as hourly, matching the ADP-provided definition. Additionally, with respect to wage changes, all changes in per-period earnings will be associated with a change in the hourly wage given that from the payroll system s perspective hours are fixed at 40 hours per week. Despite these differences in classification, the fraction reporting being paid hourly in the ADP data is not that different from the CPS averages. Given that ADP is growing over time, so too is our sample over individual years. Of our 1 million workers, only 202,000 are in our sample in 2008 while 343,000 are in our sample in Despite the growing sample size over time as ADP expands its business, the demographic composition of workers is essentially constant over time. One distinction is that average tenure is falling over time. Given that the Great Recession occurred early in our sample, it is not surprising that as many workers became displaced during the recession average tenure subsequently fell. 3.3 Measuring Wages and Wage Rigidity The focus of this paper is on the frequency and size of wage changes. We consider changes in the worker s per-period payment rate as our measure of changes in the worker s nominal 10

12 Table 2: Statistics for Employee Sample, Selected Years All Number of Workers 1,000, , , ,991 Number of Firms 89,350 89,350 89,350 89,350 Number of Observations 22,642,878 1,319,797 2,744,414 2,778,947 Age (%) Age (%) Age (%) Age (%) % Male Average Tenure % Paid Weekly % Paid Bi-Weekly/Semi-Monthly % Paid Monthly % Hourly wage. To reiterate, our nominal wage measure is the hourly wage for hourly workers and per-period earnings for salaried workers. We aggregate our unit of observation to the month. Specifically, our nominal wage measures are defined as the wage paid to the individual during the last pay period of the month. Throughout the paper, we explore both one-month, threemonth (one-quarter) and twelve-month (annual) wage changes. Given that our nominal wage measures come from the individual s actual paycheck, there should be little, if any, measurement error in our wage measures. Despite this, there are some exceptionally small wage changes in our data resulting from salaried individuals earning annual amounts that do not easily divide into twelve months. As a result, we consider only wage changes of at least 0.1%. That is, if worker i earns wage w it in period t, we consider the object wit k = log w it log w it k for some k, and say that an individual has experienced a wage change in the previous k months if wit k > Throughout the paper, we report both the frequency of wage changes and the size of the wage change conditional on a wage change occurring. As noted above, our default is to analyze separately hourly and salaried workers. However, when we discuss the level of wages in the economy, we pool together hourly and salaried workers by converting all wage measures to hourly wages. We only do this when benchmarking the wages in our sample to other nationally representative datasets. Specifically, for salaried workers we divide the per 11

13 pay-period nominal wage by the reported hours worked during the pay period. As noted above, most salaried workers are reported as working 40 hours per week. By pooling hourly and salaried workers, we can create a measure of the average wage in our sample of year olds for each year between 2008 and Figure 1 compares the average hourly wages in our ADP sample to average hourly wages in a similarly defined sample of year olds in the CPS. The bottom two lines in the figure compare the wages of workers paid hourly in both the ADP and CPS. To get the hourly wage in the CPS, we use data from the outgoing rotation of respondents from the CPS monthly surveys. In the outgoing rotation, workers are asked if they are paid hourly and if so their hourly wage. The top two lines compare the hourly wages of all workers in both the ADP and CPS. To get hourly wages for all workers in the CPS we use the March Supplement and divide annual earnings from the prior year by annual hours worked from the prior year. For hourly workers, hourly wages are slightly higher in the ADP sample than in the CPS. This may be the result of the fact that, as discussed above, some salaried workers are classified as being hourly within the ADP data. The differences are small and the trends are very similar. When moving to the full sample of workers, the differences are larger; but again the trends are similar. One reason that that the ADP wages could be higher on average is that we are missing workers at smaller firms despite our attempts at re-weighting. However, we take it as a good sign that level and trends in hourly wages are roughly similar between the ADP and CPS samples suggesting that the ADP data is representative of the entire U.S. population 4 Distribution of Wage Changes Figure 2 highlights the first key set of facts of the paper. The figure plots the distribution of 12-month wage changes for workers who remain with the same firm during the period. We refer to such workers as job stayers. Panel A plots the distribution for hourly workers, while Panel B plots the distribution for salaried workers. Three key observations are apparent from the figure. First, a large share of workers - 33% of hourly, and 35% of salaried do not receive a wage change in a given year. Second, there is a clear asymmetry in the wage change distribution, with the overwhelming majority of changes being wage increases. Indeed, of the roughly 66% of all individuals who receive a 9 Additionally, to limit the effect of extreme outliers when computing mean wage changes, we winsorize both the top and bottom 1% of nominal wages and the top and bottom 1% of wage changes. We only do this when computing the size of wage changes conditional on a wage change occurring. This does not affect our frequency of wage change results in any way. 12

14 Figure 1: Hourly Wage Comparison ADP vs. CPS, Average Demographically Adjusted Nominal Wage CPS: All Workers ADP: All Workers CPS: Paid Hourly ADP: Paid Hourly Note: Figure shows the average hourly wage in our ADP sample and in a sample of CPS workers between the ages of 21 and 60. The top two lines show the average wage for all workers while the bottom two lines show the average wage for only workers paid hourly. For the average hourly wage for all workers in the CPS, we use data from the March CPS and create a measure of wages which divides annual earnings divided by annual hours worked. For the average hourly wage for workers paid hourly in the CPS, we data from the monthly outgoing rotation files from the CPS. In the outgoing rotation files, workers paid hourly are asked to report their hourly wage. The ADP data is weighted so it is representative of the aggregate industry size distribution. The CPS data is weighted by the corresponding survey weights for the respective samples. 13

15 wage change over a given 12-month period, only 3.6% received a wage cut (2.4/66). Finally, there are very few small wage changes for either hourly or salaried workers. Just 8.6% of workers receive a wage change of between 0.1 and 2 percentage points, compared with 27.1% receiving between 2 and 4 percentage points. This missing mass of very small wage changes is consistent with the random menu cost models that are so prevalent in the price setting literature. Figure 2: Wage Change Distribution for Job Stayers Percent Wage Change (%, 12-month) Percent Wage Change (%, 12-month) Panel A: Hourly Workers Panel B: Salaried Workers Table 4 provides a set of moments on the probability of wage changes, wage increases and wage declines for three frequencies. Columns (1)-(3) show monthly, quarterly and annual frequencies, respectively. The annual frequencies correspond to the underlying data shown in Figure 2. We show moments for three samples: our sample of hourly workers, our sample of salaried workers and a sample that pools the two together. A few things are of note from the table. First, the frequency of wage changes is roughly similar between salaried and hourly workers. Roughly two-thirds of both receive annual wage changes over the entire sample period. Second, while the average probability of a wage change is similar between the two groups in our sample of job stayers, salaried workers are much more likely to receive a nominal wage cut. Over the entire sample, only 1.8% of hourly workers receive a nominal wage cut while 3.6 percent of salaried workers receive a nominal wage cut. Third, one cannot simply extrapolate monthly nominal wage changes to quarterly or quarterly wage changes to annual. The probability of a quarterly nominal wage change is less than four times the monthly wage change and the probability of an annual nominal wage change is less than four times the quarterly change. Table 4 shows the mean nominal wage change (in percent) conditional on a change occurring. During this period, nominal wages increased by roughly 6 percent per year, 14

16 Table 3: Probability of Wage Change, Pooled Sample of Job Stayers Monthly Quarterly Annual All Workers Probability of Wage Change (%) Probability of Positive Wage Change (%) Probability of Negative Wage Change (%) Hourly Workers Probability of Wage Change (%) Probability of Positive Wage Change (%) Probability of Negative Wage Change (%) Salaried Workers Probability of Wage Change (%) Probability of Positive Wage Change (%) Probability of Negative Wage Change (%) Figure 3: Number of Changes over 12 month period Percent Number of Wage Changes within Year Percent Number of Wage Changes within Year Panel A: Hourly Workers Panel B: Salaried Workers 15

17 Table 4: Mean Conditional Wage Change, Pooled Sample of Job Stayers Monthly Quarterly Annual All Workers Mean Wage Change (%) Mean Positive Wage Change (%) Mean Negative Wage Change (%) Hourly Workers Mean Wage Change (%) Mean Positive Wage Change (%) Mean Negative Wage Change (%) Salaried Workers Mean Wage Change (%) Mean Positive Wage Change (%) Mean Negative Wage Change (%) conditional on a wage change taking place. The fact that the wage change is relatively constant across frequencies is indicative of the fact that most job stayers who receive a wage change only receive one wage change per year. While the frequency of wage increases is much higher than wage cuts, the size of a wage increase conditional on it happening is nearly identical to the size of a wage cut conditional on it happening. In both cases, the average wage adjustment is about 6 percent. Figure 4 shows the distribution of annual wage changes over the period by firm size and industry. The top panel shows patterns for hourly workers while the bottom patterns for salaried workers. The figure shows that wage changes are monotonically increasing in firm size. In a given 12-month period, 48.4% of hourly workers and 53.6% of salaried workers in firms with under 50 employees receive a wage change. The comparable numbers for firms with employees are 78.9% and 76.8%, respectively. The fraction of employees receiving wage changes is increasing monotonically in size for both hourly and salaried workers. Larger firms are much more likely to adjust wages during a given year. Figure 4 also shows that there is a fair degree of heterogeneity across industries with respect to wage changes. Both hourly and salaried workers in the manufacturing industry are much more likely to receive a wage change than workers in construction. Given that firms within different industries also differ by size, a natural question is how much of the variation across industries is due to differences is size. Columns 1 and 2 of Table 16

18 Share with Wage Change over Prior 12 Months Share with Wage Change over Prior 12 Months Share with Wage Change over Prior 12 Months Share with Wage Change over Prior 12 Months Figure 4: Share with Wage Change by Firm Size and Industry, All Years 85% 80% 75% 70% 65% 63.4% 67.9% 72.0% 78.9% 80% 75% 70% 65% 64.1% 64.7% 65.2% 67.3% 71.0% 75.1% 75.6% 60% 55% 60% 55% 55.4% 50% 45% 40% 48.4% Firm Size: Number of Employees 50% 45% Panel A: Hourly Workers by Size Panel B: Hourly Workers by Industry 85% 80% 75% 70% 65% 66.5% 72.9% 76.3% 76.8% 75% 70% 65% 60% 64.2% 65.4% 66.1% 69.9% 72.8% 60% 55% 50% 53.6% 55% 50% 50.8% 54.2% 55.2% 45% 40% Firm Size: Number of Employees 45% Panel C: Salaried Workers by Size Panel D: Salaried Workers by Industry 17

19 5 present a conditional regression of the probability of any nominal wage change during a year on a vector of size dummies and a vector of industry dummies. Column 2 also includes a vector of additional controls including a quadratic in worker age, a quadratic in worker tenure, an indicator of whether the worker is paid hourly, and a vector of state of residence * month-year fixed effects. The results of the regression still show that there is a large and statistically significant gradient between firm size and the propensity of a nominal wage change. Workers in firms with over 5,000 employees are 10 percentage points more likely to experience a nominal wage change than workers in firms with employees (column 2). Columns (3) and (4) show the result of similar regressions except the dependent variable is now the probability of receiving a nominal wage cut. Column 4 shows that conditional on controls, there is no difference at all in the propensity to receive a nominal wage cut between workers in big and small firms. Even conditional on firm size and worker controls, there is variation across industries in the extent to which workers receive a nominal wage change. During this time period, workers in public administration were 20 percentage points less likely to receive a nominal wage change than were workers in manufacturing. Workers in recreation and accommodation and in construction were roughly 9 percentage points and 7 percentage points less likely to receive a nominal wage change relative to workers in manufacturing. Table 6 is similar to Table 5 except we examine the size of the wage change conditional a wage change. Larger firms give slightly smaller wage changes conditional on changing wages but the gradient is much smaller than with the fraction of workers getting a wage change. There is much less variation in the size of the wage change across industries. Of course workers need not realize wage changes within a job in order to achieve earnings growth. Figure 5 plots the distribution of wage changes for individuals who change firms. That is, we compare the wage earned by the individual in the first month of employment at her new firm to the wage earned in her last month at her previous firm. We should note that it is sometimes hard to measure job changers in the ADP data because, as noted above, different units of an organization may contract separately with ADP. In that case, moving from one unit in an organization to another unit may look like a job change, but it is actually just mobility with an organization. To mitigate the effect of these inter-organization movements, we restrict our sample to workers who either (1) change their 4 digit industry or (2) change their Census Bureau Statistical Area (CBSA). In Panel A, we plot the wage changes for all job switchers. As one would expect, job changers experience a much more dispersed wage change distribution, with many job switchers experiencing both large raises and cuts. Roughly 90 percent of job changes receive a nominal wage change upon their changing jobs. We are looking into 18

20 Table 5: Regression Coefficients: Has Wage Change over Previous 12 Months Dependent Variable: Has Any Has Negative Wage Change (12-mo) Wage Change (12-mo) (1) (2) (3) (4) Employees (0.3) (0.3) (0.1) (0.1) Employees (0.5) (0.4) (0.1) (0.1) Employees (0.5) (0.4) (0.1) (0.1) Employees (0.6) (0.5) (0.2) (0.1) Mining, Utilities, Cons (1.7) (1.1) (0.3) (0.3) Manufacturing (1.6) (1.0) (0.2) (0.2) Wholesale/Retail Trade (1.5) (1.1) (0.2) (0.2) FIRE (1.6) (1.0) (0.2) (0.2) Health and Education (1.8) (1.2) (0.1) (0.2) Recreation and Accom (1.2) (1.0) (0.2) (0.2) Other Services (1.5) (1.1) (0.2) (0.2) Public Administration (3.3) (3.1) (2.4) (0.7) Controls N Y N Y State Date FE N Y N Y Observations 12,920,569 12,690,071 12,920,569 12,690,071 Notes: Omitted categories are firms with less than 50 employees, and Agriculture, and Forestry industries. Standard errors clustered at state-year level. Controls include a quadratic in age and tenure, an indicators for hourly pay, payment frequencies, and wage deciles. 19

21 Table 6: Regression Coefficients: Mean Size of Wage Change over Previous 12 Months Dependent Variable: Mean Size of Any Mean Size of Negative Wage Change (12-mo) Wage Change (12-mo) (1) (2) (3) (4) Employees (0.04) (0.04) (0.11) (0.10) Employees (0.06) (0.05) (0.13) (0.12) Employees (0.06) (0.05) (0.14) (0.12) Employees (0.07) (0.06) (0.15) (0.14) Mining, Utilities, Cons (0.17) (0.14) (0.37) (0.35) Manufacturing (0.15) (0.12) (0.35) (0.34) Wholesale/Retail Trade (0.13) (0.11) (0.35) (0.35) FIRE (0.13) (0.11) (0.34) (0.34) Health and Education (0.14) (0.11) (0.34) (0.33) Recreation and Accom (0.13) (0.12) (0.34) (0.33) Other Services (0.13) (0.11) (0.35) (0.35) Public Administration (0.43) (0.31) (0.55) (0.94) Controls N Y N Y State Date FE N Y N Y Observations 9,004,356 8,855, , ,992 Notes: Omitted categories are firms with less than 50 employees, and Agriculture, and Forestry industries. Standard errors clustered at state-year level. Controls include a quadratic in age and tenure, an indicators for hourly pay, payment frequencies, and wage deciles. 20

22 Figure 5: Wage Change Distribution for Job Changers, All Years, By Time Between Jobs Percent % Change in Wages, Job Changers Percent % Change in Wages, Job Changers Panel A: All Job Changers Panel B: Starting Wages > $15/hour Percent % Change in Wages, Job Changers Percent % Change in Wages, Job Changers Panel C: Hourly-to-Hourly Changers Panel D: Salaried Changers the remaining 10 percent. We are wondering how much of this 10 percent spike is a real phenomenon, how much is due to potential misclassification and how much is due to policy constraints like the minimum wage. Panels B, C and D of the figure help refine our estimates. First, in Panel B, we restrict our sample to a set of workers initially making $15 per hour. Such workers are not bound by the minimum wage in any location during any period of our smaple. As seen from the figure in this panel, the spike completely disappears. In Panel C (D), we restrict the sample to workers who move from one hourly wage (salary) job to another hourly wage (salary) job. Here there is slightly more stickiness in the base case, suggesting that some of the flexibility in Panel A is workers moving across different types of jobs. Even with these potential measurement issues (which we are looking to refine), there is much more wage flexibility for job changers. 21

23 Table 7: Probability of Wage Change, Pooled Sample of Job Stayers and Job Changers Monthly Quarterly Annual All Workers, No Adjustment Probability of Wage Change (%) Probability of Positive Wage Change (%) Probability of Negative Wage Change (%) All Workers, Adjusting for Missing Switchers Probability of Wage Change (%) xx xx xx Probability of Positive Wage Change (%) xx xx xx Probability of Negative Wage Change (%) xx xx xx Table 7 combines the results from our job stayer and job switcher samples. The top panel pools all our data together with no other adjustments. The bottom panel re-weights the job switcher sample to account for the fact that we only observe a portion of job switchers in our data. Focusing on the top panel, roughly 80 percent of workers receive a wage increase over a year during our sample period. Recall that in our sample of job stayers, the probability of a wage change was only 65%. Before concluding this section, it is worth emphasizing how different our patterns are with respect to the frequency of wage adjustments relative to other studies in the literature. For example, using the panel component of the CPS, Daly, Hobijn and Lucking (2012) report that roughly 85 percent of wages change annually during this time period for job stayers. We find that only about two-thirds of workers receive a wage change during the period. Using the methodology of Daly et al. (2012), the San Francisco Federal Reserve has created a Wage Rigidity Meter. They report higher wage flexibility for salaried workers relative to hourly workers. Again, this finding is inconsistent with the findings in our paper. But, the fact that measurement error in earnings and hours is high in household surveys can explain the higher variance of wage changes in the CPS. Additionally, the fact that hours are likely measured with more error for salaried workers who are not required to track their hours, would generate more wage volatility for salaried workers relative to hourly workers. Using SIPP data, Barattieri et al (2014) try to account for the measurement error in wages and hours in household data by looking for structural breaks in their individual wage series. When they make their correction, the frequency of quarterly wage changes for job stayers falls from over 50 percent to about 15 percent. Our quarterly frequency of wage changes 22

24 for job stayers is about 20 percent. They also estimate a much larger fraction of downward wage adjustments even after making their measurement error correction. Specifically, they find that 12 percent of all quarterly wage changes for job stayers are downward changes. As discussed above, we estimate only 4.6 percent of all quarterly wage changes are downward changes (0.9/19.4). Finally, unlike our results, they find no differences in wage change probabilities across occupations and industries. The differences between our results and Barattieri et al (2014) are consistent with some residual measurement error remaining after their procedure. 5 Time Dependence in Changes Most modern macro models assume some time dependence in wage setting. For example, Taylor (1979, 1980) emphasizes that staggered wage contracts can amplify business cycle persistence in response to aggregate shocks. New Keynesian macro models in the spirit of Christiano et al. (2005) use a Calvo (1983) model of wage setting. In this section, we use our detailed micro data to explore evidence for both To begin studying time dependence in wage setting, we exploit the individual level micro data and estimate an individual duration model of wage changes. To do so, we the consider the subset of employees who experience at least two wage changes over our sample period. Figure 6 plots the resulting hazard functions for wage adjustment. Specifically, the figure shows the probability of a one month wage change between t 1 and t conditional on the worker surviving to month t. For this specification, we only include our job stayer sample. The figure rejects the Calvo prediction at the individual level that the probability of wage change is constant over time. In most months, the probability of a wage change is roughly constant at about 3-4%. However, roughly 12 months after the last wage increase, individuals are much more likely to get a wage increase. Conditional on making it to month 11 with no wage change, there is over a 50% probability than an individual gets a wage increase in month 12. Note, given a little bit of calendar variation, there are small spikes at 11 and 13 months as well. We also see another spike in the hazard at 24 months and a more modest spike at 36 months. Moving away from a hazard analysis, we can define a sample of individuals who remained on their job for the next 18 months after a prior wage change. We can then ask how many of these workers got their next wage change months later. Of consistently employed workers, 30% receive their next wage change one year after their prior wage change. Figure 6 provides some evidence of time dependence in wage adjustment. The majority of wage changes occur annually. However, basic models of purely time dependent wage setting 23

25 Figure 6: Hazard Function of Wage Change, Pooled Sample Panel A: Hourly Workers Panel B: Salaried Workers Note: Figure shows the hazard rate of a wage change between t 1 and t conditional on surviving to t. Sample only includes individuals with at least two wage changes. have predictions regarding the average size of wage changes. Under standard productivity processes with positive drift, individuals who are able to renegotiate their wage every month would negotiate smaller increases in their wages than those who renegotiate only once per year, on average. As a result, those who wait longer between wage changes should observe larger average changes in absolute value. We explore this prediction next. Figure 7 shows the average size of the wage change by the time since last wage change. For this picture, we only include those workers who received a positive wage change. But, as shown above, essentially all wage changes are positive. While most wage changes occur at 12 month frequencies, Figure 7 shows that the size of the wage changes at these annual frequencies are much smaller than wage changes that occur at other times of the year. These predictions are not consistent with a standard Calvo (or Taylor) model at the individual level. However, the patterns could be consistent with a broader model of selection. If the workers who get these wage changes that occur off-cycle are positively selected in some way, this could explain why they receive higher wage increases. For example, if the worker receives an outside offer, the firm may have to raise the worker s wage earlier than their annual cycle in order to retain the worker. While the Calvo predictions may be rejected at the individual level, Calvo may still be a good approximation for the aggregate macro economy if the initial dates of our wage contract are spread out across the year. In fact, this is the underlying intuition behind the staggered wage contract model. Instead of each individual probabilistically getting a wage change each period, individuals deterministically get a wage changed at a fixed frequency 24

26 Figure 7: Mean Size of Wage Changes by Time Since Last Change, Pooled Sample Panel A: Hourly Workers Panel B: Salaried Workers Note: Figure shows the hazard rate of a wage change between t 1 and t conditional on surviving to t. Sample only includes individuals with at least two wage changes. Additionally, we restrict our analysis to the job stayer sample. but a constant fraction of the wage contracts adjust each period. To see whether Calvo is a good approximation for the aggregate economy, we explore the extent to which wage changes are coordinated within a given calendar year. Figure 8 shows the probability of wage changes by month and the conditional size of the wage change by month. The top panel is hourly workers and the bottom panel are salaried workers. Overall, Figures 6-8 provide some evidence of time dependence in wage adjustment. The majority of wage changes occur annually, usually at the beginning of the fiscal year - either in January, April, or July. However, basic models of purely time dependent wage setting have predictions regarding the average size of wage changes which are not borne out in the data. Under standard productivity processes with positive drift, individuals who are able to renegotiate their wage every month would negotiate smaller increases in their wages than those who renegotiate only once per year, on average. As a result, those who wait longer between wage changes should observe larger average changes in absolute value. 6 State Dependence in Wage Setting State dependent pricing refers to the notion that the frequency of price changes might depend on the state variables relevant for a firm s decision. There are two principal reasons why one might observe state dependence in realized wage changes. The first is if there is some explicit 25

27 Share with Any Wage Change (%) Mean Size of Wage Change (%) Share with Any Wage Change (%) Mean Size of Wage Change (%) Figure 8: Seasonality in Wage Changes, Job Stayers, All Years Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 4 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Panel A: Hourly - Pr{Change} Panel B: Hourly Mean Change Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 4 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Panel C: Salaried - Pr{Change} Panel D: Salaried Mean Change 26

28 cost to adjusting wages. Non-convex adjustment costs, or menu costs, are commonly employed in New Keynesian models of price setting in order to match moments of the price data. The presence of fixed adjustment costs generates an inaction region in which firms that are close to their optimal price in a frictionless economy will not adjust their prices until they move sufficiently far away from their optimal price in a frictionless economy. Thus the state of the firm - its distance from the optimal pricing rule - is crucial in determining price adjustment decisions. As a result, price changes are infrequent, and relatively large when they occur. Although a theory of non-convex adjustment costs in wages has yet to be fully developed to our knowledge, principally due to challenges arising from wage bargaining, the intuition gained from the output pricing literature helps guide analysis of state dependence in wage setting. A second reason for state dependence might arise in a framework with asymmetric rigidity. For instance, suppose that is harder for firms to cut wages than to raise them, possibly due to concerns over morale or because of union pressure. Under this scenario, firms receiving a negative productivity shock would have a lower probability of being able to adjust wages to the desired level than firms receiving a positive productivity shock. This would imply that wages would then appear less flexible in downturns than in booms. We look for evidence of state dependence in wage setting using three sources of variation. First, we consider the time series cyclicality of realized wage rigidity, both for job stayers and new hires. Next, we use regional variation during the Great Recession and show that parts of the economy that were particularly negatively affected during the 2008 recession exhibit more rigid wages. Finally, we show that growing firms tend to increase their wages more frequently and by more than shrinking firms. 6.1 Time Series Variation Figure 9 plots the time series of wage rigidity. We use our sample of job stayers for this analysis, pooling together both hourly and salaried workers. The top panel plots the extensive margin of wage changes: the percent of all employees in month t who have a different wage from month t 12. Our data starts in May That means the first observation in each of the panels in Figure 9 is for May 2009 and measures the fraction of job stayers who received a wage change between May 2008 and May The fact that our data spans the Great Recession allows us to explore business cycle variation in the extent of wage adjustments. As seen from the left panel of Figure 9A, wage flexibility exhibits striking pro-cyclicality. Only about 55 percent of continuing wage workers received a wage change during the depths of the recession. However, after the recession ended, between 65 and 70 percent of workers 27

29 received a wage change. While most of the time series variation was between the recession and non-recessionary periods, there is still a slight trend upwards in the share of workers receiving a wage change during the year between 2012 and The top right panel of Figure 9 separates the the wage change into wage increases (solid line) and wage declines (dashed line). During the Great Recession, the propensity of wage increases fall sharply and the propensity of wage declines increases sharply. One of the key findings of the paper is that while nominal wage cuts are exceedingly rare during non-recessionary periods, nearly 6 percent of all workers received a nominal wage cut during late 2009 and early The bottom panel of Figure 9 plots the mean size of wage changes, restricting attention to those who have indeed received a wage change in the prior 12 months. The bottom left panel pools together all wage changes while the bottom right panel separately looks at wage increases and wage declines. The overall mean wage change size is highly pro-cyclical. Strikingly, however, the mean size of wage cuts or wage raises does not move substantially over the cycle. The large fall in mean wage change during the Great Recession is therefore almost entirely driven by an increased share of wage changes being negative, rather than changes in the size of cuts themselves. Table 8 summarizes the business cycle differences in wage rigidity. We separate the sample into two periods: a period representing the depths of the Great Recession (May 2009-June 2010) and a period well into the recovery (January December 2016). A few things are of note from the summary table. First, over 9.1 percent of salaried workers who remained on their job received a nominal wage cut during the Great Recession. Table 8: Summary of Wage Change Distribution During and After the Great Recession % Decline % Zero % 0-5 % 5-10 % 10+ Mean Cut Mean Raise May June 2010 Wage Salaried All January December 2016 Wage Salaried All Notes: The results in this subsection show that wage adjustment varies sharply over the business 28

30 Figure 9: Time Series of Wage Changes Share with 12-month Wage Change (%) m1 2010m7 2012m1 2013m7 2015m1 2016m7 Year Month Share with 12-month Positive Wage Change (%) m1 2010m7 2012m1 2013m7 2015m1 2016m7 Year Month Positive Changes Negative Changes Share with 12-month Negative Wage Change (%) Panel A: Has Wage Change Panel B: Has Wage Change: Pos. vs Neg Conditional Mean 12-month Wage Change (%) 2009m1 2010m7 2012m1 2013m7 2015m1 2016m7 Year Month Conditional Mean 12-month Positive Wage Change (%) m1 2010m7 2012m1 2013m7 2015m1 2016m7 Year Month Positive Changes Negative Changes Conditional Mean 12-month Negative Wage Change (%) Panel C: Mean Wage Change Size Panel D: Mean Wage Change Size - Pos. vs Neg. Figure 10: Time Series of Wage Changes by Industry Panel A: Positive Change Panel B: Negative Change 29

31 cycle. Any model that assumes a constant hazard of wage changes over the business cycle is at odds with the underlying wage setting data. 6.2 Regional Variation During Great Recession Although the time series variation is suggestive of state dependence in wage adjustment, it is by no means conclusive. One may easily conjure models without state dependence in wage adjustment that could generate the patterns observed above. Suppose, for instance, that wages are set according to a Calvo adjustment process, whose aggregate Calvo parameter evolves according to some stochastic process. One could rationalize the patterns observed in Figure 9 and Table 8 in such a model if the Calvo probability of receiving a wage change randomly draws a low value at the beginning of Wages would adjust less, not because wage adjustment is state dependent per se, but because the stochastic aggregate state was such that adjustment is randomly more difficult. To address this potential identification concern, we use regional variation to difference out aggregate shocks to wage stickiness. Specifically, we group CBSAs into three groups based on the severity of the recession in locations. We use the decline in house prices as our measure of the severity of the recession. 10 One group, which we dub the Deep Recession CBSAs, is made up of local areas which are in the top quintile of peak-to-trough house price declines from 2007 to Similarly, the Shallow Recession CBSAs are those whose house price declines are in the bottom quintile. 11 Our goal is to determine whether realized wage rigidity responds to local economic conditions. Figure 11 shows a simple scatter plot relationship between local house price declines at the CBSA level and various measures wage adjustment at the local level (before pooling states into their three groups). CBSA s with the largest declines in house prices were much less likely to raise nominal wage (panel A) and were much more likely to cut nominal wages (panel B) during the Great Recession. Unconditionally, a 20 percent decline in house prices was associated with a 4.5 percentage point decline in the probability of increasing wages and a 0.9 percentage point increase in the probability of a nominal wage cut. The base probability of increasing and decreasing wages during this time period was roughly 50 percent and 5 percent, respectively. There was no meaningful relationship between CBSA house price declines and the size of wage increases or wage cuts in the CBSA, conditional on changing 10 There is a large literature showing that housing price declines explain much of the regional variation in economic activity during the Great Recession. See, for example, Mian and Sufi (2013). 11 We define recession severity according to the depth of house price decline, as we wish to use a measure which is somewhat removed from the labor market. Using employment changes as a measure of recession severity, for instance, might pose a reverse causality problem if, as has been hypothesized, firms which are most unable to cut wages are most likely to lay off employees. 30

32 Figure 11: Probability of Wage Changes by Recession Severity 12-month Share with Pos. Wage Change ( ) CoreLogic HPI % Change ( ) Line of best fit equation: y = x P-value on slope coefficient: month Share with Neg. Wage Change ( ) CoreLogic HPI % Change ( ) Line of best fit equation: y = x P-value on slope coefficient: Panel A: Pr{Wage Increase} Panel B: Pr{Wage Decrease} Mean 12-month Neg. Wage Change ( ) CoreLogic HPI % Change ( ) Line of best fit equation: y = x P-value on slope coefficient: Mean 12-month Wage Change ( ) CoreLogic HPI % Change ( ) Line of best fit equation: y = x P-value on slope coefficient: Panel C: E[ w w > 0] Panel D: E[ w w < 0] Scatters and regressions weighted by 2007 CBSA population estimates from the Census Bureau. wages (panels C and D). These cross region patterns match well the aggregate time series patterns discussed above. Table 9 presents the distribution of 12-month wage changes in 2009 for job stayers living in these two groups of CBSAs. The top panel presents the distribution of wage changes, as well as the mean wage raise and mean wage cut living in deep recession CBSAs, while the bottom panel shows the similar distribution for those living in shallow recession CBSAs. Deep recession states observed more rigid wages in 2009, with 45.3% of employees receiving no wage change over the prior 12 months, compared with just 36.3% of employees in shallow recession states. This difference in rigidity is particularly concentrated amongst hourly workers % of hourly workers in deep recession areas worked at the same wage in 2009 as they did in 2008, compared with 32.5% of hourly workers in shallow recession areas. Not only were wages more rigid in deep recession areas, they were also more likely to be cut. In these hard-hit regions, 5.7% of all workers and 9.8% of salaried workers received 31

33 Table 9: Distribution of Wage Changes by Severity of Recession in CBSA % Decline % Zero % 0-5 % 5-10 % 10+ Mean Cut Mean Raise Deep Recession (based on CBSAs) Wage Salaried All Shallow Recession (based on CBSAs) Wage Salaried All Notes: Recession severity defined by change in CBSA house prices between 2007 and Deep recession CBSAs are defined to be the CBSAs in the top quintile of CoreLogic house price declines, while shallow recessions CBSAs are in the bottom quintile of house price declines. a wage cut, compared with 4.8% and 7.2% in areas with only minor house price drops. Conditional on receiving a wage cut, however, there was little difference between the regions - salaried workers received a wage cut of 6.7% and 6.1% on average in deep vs shallow recession groups. The size of this cut is remarkable - that almost one in ten workers in deep recession regions lost approximately one-fifteenth of their salary in 2009 is striking evidence that wages are able to downwardly adjust in the face of large unanticipated shocks. However, the large size of these cuts is consistent with the intuition of menu cost models of price setting with substantial costs to reducing wages. In such a model, firms would only find it worthwhile to pay the cost to cut pay if the desired wage is much lower than the worker s current wage. 6.3 Firm Level Variation Although suggestive of state dependence in wage setting, the regional evidence provided above does not precisely emulate the decision problem faced by an individual firm. We therefore consider state dependence at the firm level by comparing wage change distributions for firms receiving large positive shocks with firms receiving large negative shocks. To do this, we use our firm level sample and define three groups of firms. First, we define firms as growing if they added at least 10 percent employment during a given calendar year. Second, we define firms as shrinking if they reduced employment by at least 10 percent during a given year. We refer to all other firms as being neutral. Table 10 presents the distribution of firm changes for growing firms, shrinking firms, and firms with little employment changes, both during and following the recession in Several interesting patterns emerge. First, realized wage rigidity is monotonically decreasing 32

34 Figure 12: Probability of Hours Change by Recession Severity (Hourly Workers Only) 12-month Share with Pos. Hours Change: Hourly ( ) CoreLogic HPI % Change ( ) Line of best fit equation: y = x P-value on slope coefficient: month Share with Neg. Hours Change: Hourly ( ) CoreLogic HPI % Change ( ) Line of best fit equation: y = x P-value on slope coefficient: Mean 12-month Pos. Hours Change: Hourly ( ) Panel A: Pr{Hours Increase} CoreLogic HPI % Change ( ) Line of best fit equation: y = x P-value on slope coefficient: Mean 12-month Neg. Hours Change: Hourly ( ) Panel B: Pr{Hours Decrease} CoreLogic HPI % Change ( ) Line of best fit equation: y = x P-value on slope coefficient: Panel C: E[ h h > 0] Panel D: E[ h h < 0] Scatters and regressions weighted by 2007 CBSA population estimates from the Census Bureau. 33

35 in firm growth rates. Shrinking firms in 2009 kept over half % - of their employees wages fixed year over year. In comparison, neutral firms did not adjust wages for 44.2% of employees, while growing firms look as though they hardly experienced a recession, changing 67.2% of their employees wages in This monotonicity is not limited to the crisis year of Indeed, from , shrinking firms did not adjust wages for 36.4% of employees, compared with 33.1% and 36.4% of employees at neutral and growing firms, respectively. Furthermore, firms which shrank after the recession cut wages by 5.7% on average, compared with 4.5% for shrinking firms during the recession. Again, this may be due to selection: firms which shrink at a time when aggregate conditions are favorable are likely to be subject to worse idiosyncratic shocks than those which cut employment during the great recession. Note also that neutral firms cut wages at roughly the same rate (6.0%) than did shrinking firms (5.6%) during the crisis of 2009, but the mean size of those wage cuts was smaller (5.4% vs 5.7%). This hints that firms which are more able to cut wages - either because they face lower menu costs to do so, have more flexible contracting, or are lucky enough to receive a Calvo shock - do not need to lay off as many employees. The intuition from this can be seen from a simple first order condition from a neoclassical production function. A profit maximizing firm will choose labor to set its marginal revenue product equal to the wage: Af (L) = w. If the firm s productivity A falls, and w is fixed, then the firm will adjust its labor demand downwards substantially. If, however, w is allowed to adjust freely, L need hardly move at all. This idea will be examined further in the next section. Finally, note that those who receive a raise while working for a shrinking firm tend to realize very large wage increases relative to their peers at growing or neutral firms, just as workers receiving wage increases in areas heavily impacted by the recession receive larger raises on average. Table 10: Distribution of Wage Changes by Firm Growth Status % Decline % Zero % 0-5 % 5-10 % 10+ Mean Cut (%) Mean Raise (%) January - December, 2009 Growing Shrinking Neutral January December 2016 Growing Shrinking Neutral Notes: Shrinking firms defined as those firms with at least a 10% reduction in employment year over year. Likewise, growing firms have at least a 10% increase in employment, year over year. 34

36 This section illustrates the many pieces of evidence for state dependence in wage setting. To the extent that they occur, wage cuts tended to arise at the deepest point of the recession in Furthermore, firms and regions which receive large negative shocks are more likely to keep their wages fixed, and cut the wages of their employees. However, conditional on receiving a wage change, employees in these hard-hit firms and regions tend to observe larger swings in their payment rates. All of this is consistent with the menu cost view of price setting. Given that wage changes appear to depend on relevant state variables for the firm and worker, it is important to understand the nature of the shock process that gives rise to these states. With this in mind, we now turn to an analysis of within-firm heterogeneity in wage rigidity, with the goal of elucidating how wages evolve for various segments of the population, and understanding whether the relevant shocks for wage setting occur at the firm level, or at the worker level. 7 Within Firm Heterogeneity The extent to which a firm, when faced with a shock, is able to adjust the wages of its entire workforce may be a key determinant of aggregate wage rigidity. In this section, we examine the within-firm correlation of wage setting, and examine the characteristics of those whose wages are most flexible. By way of motivation, consider a firm which employs a unit mass of workers, all of which have fixed productivity A, and are paid a wage w. Suppose that the firm s workforce is hit with a productivity shock, so that the firm s average productivity changes to A. How would we expect the firm s wages to change? The answer of course depends on the nature of both the shock, and the wage setting process. Suppose, for instance, that the shock is a firm-specific shock, which affects all of its workers uniformly. Suppose further that if the firm elects to change the wage of any of its employees, it is allowed to change the wage of all of its employees for free. 12 In this case, we would expect the firm to adjust all of its employee s wages down by the same amount, so that there is perfect correlation between wage changes within a firm. Deviations from this perfect correlation benchmark therefore suggest workerlevel idiosyncrasies in either the productivity shock process or the wage rigidity process. Figure 13 shows the extent to which wage changes are correlated within a firm. Panel A plots the share of employees within a firm who receive a wage change, conditional on the firm changing at least one worker s wage in that month. We show this statistic for firms of differing size. The figure shows that a relatively small share of workers receive a wage 12 Midrigan (2011) provides an example of such a nominal rigidity in the context of output price setting. 35

37 change during a month even if other workers in the firm are. Approximately 7.5% of workers receive a wage change in a month in which the firm changes at least one worker s wage. This fraction is roughly constant by firm size. Basically, even within a firm, only about one-twelfth of workers receive a wage change each month conditional on one wage change occurring. This fraction is roughly constant by firm size. For comparison, if all wage changes were evenly spread throughout the year, then, since 60% of workers receive a wage change in a given year, 5% of employees would change wages each month. Given this, there is some degree of within-firm correlation in monthly wage rigidity but to the extent it exists, it is small. Panel B provides further evidence for idiosyncratic wage adjustment shocks. It plots the share of firms which simultaneously increase some workers wages, and decrease others, in a given month. If firms tend to receive shocks that move everyone inside the firm in one direction, then this share should be small. If, however, worker-level idiosyncratic shocks account for a large portion of the variation in both desired wage levels and adjustment ability, then this share may be quite large. This panel shows that almost every firm with over 5000 employees adjusts some employees wages upwards, and some downwards, each month. Similarly, 90% of large ( employees), and 62% of mid-sized ( employees) firms simultaneously give cuts and raises. This is particularly striking since wage cuts are so rare, and concentrated amongst shrinking firms. Smaller firms, unsurprisingly, are less likely to both increase and decrease wages in a given month. These patterns provide strong evidence that it is shocks to a match, rather than aggregate shocks to the firm per se, which are relevant for determining wage flexibility. Figure 13: Within Firm Wage Setting Panel A: Average Share of Employees Panel B: Share of Firms with w/ Monthly Wage Change Conditional Both Positive and Negative Changes on One Change, All Years in a Given Month, All Years 36