Wage Rigidity and Employment Outcomes: Evidencefrom German Administrative Data ∗

Joshua Montes

University of Michigan

Gabriel Ehrlich

Congressional Budget Office

August 26, 2013

-PRELIMINARY AND INCOMPLETE-

-PLEASE DO NOT CITE OR CIRCULATE-

∗We would like to thank Charles Brown, Susan Collins, Christopher House, and Matthew Shapiro, andseminar participants at the University of Michigan for helpful comments. We would like to thank StefanBender and Daniela Hochfellner of the German Institute for Employment Research (IAB) for their generoushelp. Please contact the authors by e-mail at montesj@umich.edu or by mail at University of Michigan,Department of Economics, 611 Tappan St. Ann Arbor, MI. The views expressed in this paper are theauthors’ and should not be interpreted as the views of the Congressional Budget Office.

Abstract

This paper examines the relationship between downward nominal wage rigidity and employmentoutcomes using linked employer-employee data from Germany. Establishment-level estimates sug-gest that wage rigidity prevents 25 percent of counterfactual wage cuts. Wage rigidity is estimatedto be most prevalent in the public administration supersector and least prevalent in the constructionand mining/manufacturing supersectors. A model of an establishment’s optimal employment andwage policies in the presence of wage rigidity implies that establishments with more rigid wagesshould exhibit higher layoff rates and lower quit and hire rates. Consistent with these predictions,an establishment with the sample average level of measured wage rigidity is predicted to have a 0.7percentage point increase in the layoff rate, a 1.8 percentage point reduction in the quit rate, and a1.3 percentage point decrease in the hire rate relative to an establishment with no measured wagerigidity. Wage rigidity interacts with movements in establishment revenue in economically mean-ingful ways, amplifying its relationship with employment outcomes. Model calibration impliesthat the average wage cut costs the establishment 1.75 percent of the average wage, suggestingthat even moderate costs of cutting nominal wages generate meaningful effects on employmentoutcomes.

JEL Codes: E24, J23, J63

You say, ‘We know from repeated experience that the money price of labour never fallstill many workmen have been for some time out of work.’ I know no such thing; and,if wages were previously high, I can see no reason whatever why they should not fallbefore many labourers are thrown out of work. All general reasoning, I apprehend, isin favour of my view of this question, for why should some agree to go without anywages while others were most liberally rewarded?

Letter of David Ricardo to Thomas Malthus, 1821

1 Introduction

A perennial debate in economics concerns the extent to which difficulties in reducing nominalwages affect employment outcomes. Theory suggests that downward rigidity in nominal wagesmay exacerbate layoffs and unemployment following an adverse economic shock. Additionally,such rigidities may lower the rates of quits and hires. Downward nominal wage rigidity thereforehas potentially important implications for macroeconomic policy, yet its extent and macroeco-nomic significance remain subjects of considerable uncertainty. This paper uses linked employer-employee data to estimate the extent of downward nominal wage rigidity at a sample of WestGerman establishments. It then examines the relationship between establishment-level estimatesof wage rigidity and employment outcomes, specifically layoff, quit, and hire rates. These resultsare shown to be consistent with the predictions of a theoretical model of establishment decision-making in the face of downward nominal wage rigidity. Using the empirical results to quantifythe costs of nominal wage cuts in the theoretical model implies that even moderate costs can havesignificant effects on employment outcomes.

Several studies have documented the existence of downward nominal wage rigidity (hereafter,wage rigidity for brevity) in microeconomic datasets. Prominent examples using U.S. data includeCard and Hyslop (1996), who estimate that over 15 percent of workers experience nominally rigidwages in a 5 percent inflation environment, and Kahn (1997), who estimates that wage earnersexperience nominal wage reductions 47 percent less often than they would in the absence of wagerigidity. Kahn’s estimate implies that wage rigidity prevented 9.4 percent of the wage earners in hersample from receiving wage cuts. Using European data, Knoppik and Beissinger (2009) concludethat wage rigidity prevents 37 percent of counterfactual wage cuts in the Euro area, and 28 percentof wage cuts in Germany specifically. Dickens et al. (2007) examine evidence in the United Statesand 15 European countries, and find that the fraction of workers covered by wage rigidity is 28percent on average, ranging from 4 percent in Ireland to 58 percent in Portugal.

However, it has been difficult to establish a link between wage rigidity and employment out-comes. Using micro data, Card and Hyslop (1996) find that “...nominal rigidities have a small

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effect on the aggregate economy...”, while Altonji and Devereux (2000) report, “Our estimates ofthe effect of nominal wage rigidity on layoffs and promotions ... are too imprecise for us to drawany conclusions.” Akerlof, Dickens, and Perry (1996) find that wage rigidity makes a statisticallyinsignificant difference in macroeconomic time series estimates of a Phillips Curve equation in thepostwar period. Lebow, Saks, and Wilson (1999) estimate that the non-accelerating inflation rateof unemployment is positively correlated with inflation, contrary to what would be predicted byan important role for nominal wage rigidity. They describe the apparent contradiction betweenthe evidence on the extent of wage rigidity and the lack of evidence that it affects employmentoutcomes as a “micro-macro puzzle”.

An exception to this pattern is Kaur (2012), who finds strong causal effects of wage rigidity onemployment levels in informal Indian village labor markets. However, employment relationshipsin these markets lack some important features of developed economy employment relationships,such as fringe benefits and long-lasting employer-employee matches, that have been argued tomitigate the effects of wage rigidity. Therefore, Kaur’s estimates may not be representative fordeveloped economies.

Some potential resolutions to the micro-macro puzzle have been proposed. Lebow et al. (1999)study the role of non-wage compensation such as bonuses and other fringe benefits in facilitatingreductions in total compensation when base pay is downwardly rigid. Elsby (2009) argues thatforward-looking, wage-setting firms will compress wage increases in the presence of downwardnominal wage rigidity, thereby minimizing the macroeconomic effects of such rigidity.

Previous empirical work has been unable to examine the empirical relationship between es-tablishment level wage rigidity and employment outcomes because of the lack of high qualitylinked employer-employee data. This paper aims to fill that gap using the Linked Employer-Employee Data of Integrated Labor Market Biographies assembled by the German Federal Em-ployment Agency’s Institute for Employment Research. This novel data set facilitates the study ofthe relationship between wage rigidity and employment outcomes by allowing for observation atthe individual and establishment levels, where employment and wage decisions are made.

Downward nominal wage rigidity prevents 24.5 percent of wage cuts at the average estab-lishment in the sample, similar to the aggregate estimates of Knoppik and Beissinger (2009) andDickens et al. (2007). The standard deviation is 23.5 percent across establishments. Wage rigidityis estimated to be highest in the public administration supersector, where wage rigidity prevents 49percent of wage cuts at the average establishment, and weakest in the construction sector, whereonly 3 percent of wage cuts are prevented at the average establishment. Further, the degree ofdownward nominal wage rigidity an establishment faces is empirically associated with key em-ployment outcomes. An establishment with the sample average level of wage rigidity experiencesa 0.8 percentage point increase in its average layoff rate, a 1.6 percentage point decrease in its

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average quit rate, and a 2.6 percentage point decrease in its average hire rate relative to an estab-lishment with no measured wage rigidity.1 The empirical estimates serve as moments to calibrate amodel of establishment wage setting and employment adjustment in the presence of wage rigidity,which implies that an average wage cut costs the establishment 1.75 percent of the average wage.Even this moderate level of rigidity generates economically meaningful movements in the layoff,quit, and hire rates, consistent with those observed in the empirical data.

The paper proceeds as follows: Section 2 provides an overview of the data set and basic descrip-tive statistics of key variables used in the analysis. Section 3 introduces the method of measuringwage rigidity, in both the aggregate and establishment levels, used throughout the analysis. Section4 provides extensive descriptive statistics of wage rigidty in the sample of the German economy,including a breakdown of wage rigidity by sector, occupation, and education. Section 5 provides asimple, partial equilibrium model yielding predictions of the relationships between wage rigidityand layoffs, quits, and hires. Section 6 presents reduced-form estimates on the relationship be-tween wage rigidity and the layoff, quit, and hiring margins of employment adjustment. Section 7calibrates the theoretical model presented in section 5 using indirect inference with the momentsof the reduced-form regressions in section 6 to estimate the structural cost of wage rigidity to anestablishment in the sample. Section 8 concludes.

2 Data Description

2.1 Overview of Dataset

The paper employs administrative and survey data from the Research Data Centre (FDZ) of theGerman Federal Employment Agency (BA) at the Institute for Employment Research (IAB). 2 Themain analysis uses the Linked Employer-Employee Data of Integrated Labor Market Biographies(LIAB), matched with the annual IAB Establishment Panel Survey. The LIAB includes 9,653establishments from both East (4,360 establishments) and West (5,293 establishments) Germany3

that participated in the annual IAB survey each year either from 1999 through 2001 or from 2000through 2002, and follows each such establishment every year of its existence from 1997 through2003.

The LIAB also provides complete labor market biographies for the period 1993-2007 of each

1For comparison, the average layoff rate in the sample is 4.5 percent, the average quit rate is 9.2 percent, and theaverage hire rate is 17.2 percent.

2http://fdz.iab.de/en.aspx3Germany has 16 states that span East and West Germany. West German states include Baden-Wurttemberg,

Bavaria, Berlin, Bremen, Hamburg, Hesse, Lower Saxony, North Rhine-Westphalia, Rhineland-Palatinate, Saarland,and Schleswig-Holstein. East German states include Brandenburg, Macklenburg-Vorpommern, Saxony, Saxony-Anhalt, and Thuringia.

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employee liable to social security who was employed at a sampled, surveyed establishment atany point between 1997 and 2003. The data set follows these workers’ entire employment andunemployment histories from 1993 through 2007, even if the workers move to an establishmentoutside the sample.4 The LIAB provides the exact dates that an employment spell begins and endsfor an employee at a given establishment.

The LIAB offers several advantages pertaining to the study of the macroeconomic implicationsof wage rigidity. First, because data on individual workers is administrative data provided byestablishments to the FDZ by law (and subject to penalty if misreported), the wage data for eachindividual should theoretically be without measurement error. Establishment identifiers and fullemployment samples for the surveyed establishments allow for the accurate calculation of thewage level and wage change distributions at the establishment level.

Reported wages are the average daily compensation over the employment spell and includebase salary and any bonuses, fringe benefits, or other monetary compensation received throughoutthe spell or year. Thus, the wage reported in the data corresponds more closely to a measure oftotal compensation than to a base wage rate. This paper’s use of total compensation in studying therelationship between employment adjustment and wage rigidity is a significant advantage in lightof Lebow et al.’s (1999) finding that establishments are able to circumvent wage rigidity partiallyby adjusting ancillary compensation.

Second, the employment biographies in the dataset allow for the calculation of labor flows intoand out of each establishment in a given period. As the biographies provide information suchas the start and end date of an employment spell and the reason for each employment notifica-tion (e.g. end of or break in employment, required annual notification, etc.), labor flows such aslayoffs, quits, and hires may be imputed with minimal assumptions. Third, the LIAB providesan extensive set of employment-related characteristics such as the type of employment spell (e.g.marginal or liable to social security), professional and occupational status (including detailed jobdescriptions), and white-collar versus blue collar. Fourth, the worker biographies include detailedindividual characteristics, such as gender, birth year, nationality, education, and vocational train-ing. Finally, the annual IAB Establishment Panel Survey that is linked to the LIAB provides arich set of establishment characteristics, including information on an establishment’s revenue orbusiness volume, and the presence or absence of a work council or wage bargaining agreement.

A disadvantage is that the dataset does not contain employee-level data on hours worked; there-fore, a reduction in hours may appear as a wage cut using the wage measure in the data, the daily

4Thus, the data set contains information on establishments not sampled in the survey from the 1999 through 2001or 2000 through 2002 periods. For these establishment, the LIAB only contains the worker biographes of employeeswho arrived at or moved from sampled establishments. As a result, the sample does not include worker biographies forall employees liable to social security in these establishments during the 1997 through 2003 window, and the analysisexclude these establishments from the proceeding analysis.

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average wage rate. The data do distinguish between part-time workers working less than half offull-time, those working more than half of full-time, and full-time workers. When calculating wagechanges for job stayers, the analysis requires that a worker’s hours status does not change to mini-mize the potential for measurement error. To the extent that this error still exists, it is likely to makewages appear less downwardly rigid than they would in the absence of hours variation.5 Anotherdisadvantage of the dataset is that reported compensation is top-censored at the contribution limitfor the German social security system. Top-censoring affects roughly 7 percent of workers in thesample; the analysis excludes these workers from the sample for the purpose of estimating wagerigidity.

The analysis also makes use of an additional data set, the Establishment History Panel (BHP).The BHP is a panel dataset covering the years 1975 through 2008 for West Germany and 1993through 2008 for East Germany, containing establishment level characteristics for all establish-ments with at least one employee liable to social security on the reference date of June 30th eachyear. Establishment characteristics in the BHP include employment levels broken down by severalemployee characteristics, three-digit industry classification codes for each establishment, state-and district6-level location identifiers for each establishment, and quartiles of the establishment’semployee age and wage distributions of full-time workers. In additon, the BHP contains two setsof extention files. The first extension file provides establishment level information on total yearlyemployee inflows and outflows, which are also broken down by full-time statues, gender, age,skill, and occupation.7 The second extension file contains information on establishment births,deaths, and reclassifications. Supplementary data in this extension allows for the identification ofestablishment closures that are likely to be spin-offs or takeovers as opposed to true closures.

2.2 Descriptive Statistics

The analysis below restricts the sample to West German establishments for the period spanning1997 through 2003 and includes only workers ages 20 through 60. The main unit of analysis in thepaper is the establishment-year. An establishment-year is excluded if the establishment has lessthan 50 employees or 10 valid wage changes in the year. An establishement is excluded altogetherif the establishment does not meet the criteria above for at least three years. Additionally, theanalysis requires data on establishment revenues in both the current and previous years in order tocalculate the establishment’s change in revenue. These restrictions leave 2,250 of the 5,293 WestGerman establishments available in the survey for the analysis.

5Our prior belief is that hour flexibility is more of an issue among part-time workers than full-time workers.However, when calculating wage rigidity at the establishment level as described in section 3, the wages of part-timeworkers show to be slightly more rigid than their full-time counterparts. For more details, please see section 3 below.

6Districts in Germany are similar in size and structure to counties in the United States.7The reference date for the end of each year in this context is June 30th.

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Appendix B discusses the representativeness of the sample for the West German economy.Broadly speaking, establishments in the Mining/Manufacturing and Public Administration super-sectors of the economy are over-represented in the sample, while establishments in Trade/FoodService and Real Estate are under-represented. Geographically the sample is fairly well-balanced,although Bavaria is notably under-represented in the sample while most other states are slightlyover-represented. Approximately 80 percent of West German establishments employ fewer than 20workers. Therefore, the sample includes disproportionately larger average establishments. How-ever, far less than 80 percent of employees work at establishments with fewer than 20 employees,so the sample is more representative in terms of establishment size than this simple comparisonsuggests. Nonetheless, it is worth noting that the analysis is limited to relatively large establish-ments.

Layoff, quit, and hire rates are measured as fractions of the establishment’s total workforce asof December 31st of the preceding year. Following a convention for distinguishing involuntarylayoffs and voluntary quits in the worker biographies similar to that of Blein and Rudolph (1989)and Haas (2000), a layoff is defined as an interruption between employment spells that resultsin the employee flowing into unemployment, as indicated by receipt of unemployment assistance,before beginning employment again. Conversely, a quit is an employment interruption that does notcontain an unemployment spell and results in an employee flowing into another job without receiptof unemploment assistance (i.e. a job to job transition). The beginning of a new employment spellis classified as a hire if the employee’s immediately preceeding spell was either unemploymentor employment at another establishment, that is, if the worker was not employed at her currentestablishment in the preceeding period.8 In the data, there are many instances of a spell reportedas ending, but after which the worker begins employment at the same establishment immediatelyor nearly so and count. These occurences are classified as neither quits nor hires. A separation isclassified as neither a layoff nor a quit if the worker’s biography does not extend past the end ofthe employment spell (for instance, if the worker dies).9

Table 1 shows the descriptive statistics of the layoff, quit, and hire rates and establishment levelestimate of wage rigidity, which is described in detail in section 3, for the sample of establishmentsfrom 1997 through 2003. The average annual layoff rate over the period is 6.8 percent with a stan-

8A fourth possibility of employment adjustment is that of a “spin”, which can take the form of either an inflowor an outflow. Spin employment flows are those that involve employment movements either between establishmentswithin a firm or a merger or acquisition of two establishments from different firms. An example of an employmentmovement between establishments covered under the former description is that of an establishment closure where alarge portion of employees from the closed establishment move directly to another establishment within the same firm.The FDZ provides an extension file on establishment births, deaths, and reclassifications, as described in section 2.1,that allows for the identification of spin employment flows. Since the study focuses on the relationship between wagerigidity and the traditional employment flows, spin flows are excluded from the analysis.

9The establishment-level anlysis considers the period 1997 through 2003, but the worker biographies span theperiod 1993 to 2007, so most worker biographies extend beyond the end of the analysis period.

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dard deviation of 12 percent across establishment-years. The average annual quit rate over theperiod is 11.1 percent with a standard deviation on 16.1 percent, and the average annual hire rate is21.8 percent with a standard deviation of 33.5 percent.10 The average establishment-level measureof wage rigidity is 23.9 percent, implying that wage rigidity prevents 23.9 percent of counterfactualwage cuts at the average establishment, with a standard deviation of 26.9 percent. The average es-tablishment has 549 employees, versus 219 employees for the median establishment. The averagewage level is 87 euros per day, with a standard deviation of 28.4 euros per day in nominal terms.

The empirical strategy described in section 6 uses changes in establishment revenues to controlfor shifts in the marginal revenue product of labor. Each year, the survey asks each establishmentto provide its total business volume (or sales) in the preceeding fiscal year (i.e. from January 1through December 31).11 The average establishment-level revenue growth in the sample is 3.5percent per year, with a standard deviation of 20.6 percent.

3 Estimating Wage Rigidity

Several methods of measuring downward nominal wage rigidity have been proposed in the lit-erature. However, previous studies have measured wage rigidity at the aggregate level, whereasthis study measures wage rigidity at the establishment level. The small size of many of the estab-lishments in the sample poses a problem for these approaches in the context of this paper. Theapproach in this paper is conceptually similar to the histogram-location approach of Kahn (1997),modified for the context of much smaller samples. Figures 1A through 1D illustrate the approach.

For each establishment i, let mit represent the median log wage change from time t− 1 to timet expressed in percentage points. Then measure the proportion of wage changes in each year in onepercentage point wide bins. Let propijt, for j ∈ {−10,−9,−8, ...,−1, 1, ..., 8, 9, 10}, denote thesize of the bin that is between j and j+1 percentage points away from the median wage change forthat year. Figure 1A provides an illustration of these measurements for a simulated establishment.For example, j = −1 represents the bin between the median wage change and the median wagechange minus one percent in each year, whereas j = 1 represents the bin between the medianwage change and the median wage change plus one percent. In year 1, the median wage changeis 2.9 percent, bin j = −1 contains wage changes between 1.9 percent and 2.9 percent, whereasbin j = 1 contains wage changes between 2.9 percent and 3.9 percent. The median wage change

10Larger establishments tend to have lower rates of layoffs, quits, and hires than smaller establishments, so thesestatistics overstate turnover for the average worker, as opposed to the average establishment. To address this issue,weighted statistics are discussed later in the paper.

11While the sample only covers establishments with full employment biographies from 1997 through 2003, thesurvey spans from 1993 through 2008. Thus, the 2004 survey records the establishment’s business volume from 2003,the 2003 survey records business volume from 2002, and so on and so forth.

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always divides bins j = −1 and j = 1. However, the bin j containing nominal zero will varywith the median wage change over time. For instance, in year 1 the nominal wage change of zerolies in bin j = −3, which includes wage changes between -0.1 percent and 0.9 percent; in year 2,the median nominal wage change is 6.8 percent, and the nominal wage change of zero lies in binj = −7. The analysis excludes all bins more than 10 percentage points from the median each year.

For each establishment, estimate the regression

propijt = δ0 + δ1|j|+ δ2j2 + εit, j +mit > 0, ∀t (1)

That is, the regression in equation (1) restricts the sample to bins that reflect nominal wage in-creases only, and excludes the bin containing wage changes of nominal zero, as illustrated infigure 1B. A data point in this regression is the proportion of wage changes in bin j, in year t,at establishment i. The regression pools the data across years within establishment. Thus, forthe sample establishment in figure 1B, the regression in (1) contains 74 data points as there area total of 74 nominally positive wage change bins across all six years. |j| and j2 represent thelinear and quadratic distances from the median wage change, respectively. Therefore, equation (1)expresses the nominally positive portion of the wage change distribution as a quadratic function ofthe distance from the median wage change each year.

Next, this estimated function is used to predict what the the nominally negative portion of thewage change distribution would be in the absence of wage rigidity. The estimated coefficients fromequation (1) are used to predict the values propijt for the bins that contain negative wage changes,again excluding the bin that contains wage changes of nominal zero.12 For example, in year 1 offigure 1C, proportions are predicted for bins j = −4 through j = −10.

These predicted values are used to estimate the regression

propijt = γi × propijt + uijt, j +mit + 1 < 0, ∀t (2)

Equation (2) regresses the observed proportion of wage changes in bins corresponding to nominalwage cuts on the proportions that would be predicted from the regression using only nominal wageincreases. Figure 1D illustrates the regression. The dark bars in the nominally negative portion ofthe distribution represent the observed proportion of wage changes in these bins, while the lightbars represent the predicted proportions of wage changes in these bins. γi represents the fractionof predicted wage cuts observed in the data. The proportion of counterfactual wage cuts that are‘missing’ from the data, the measure of establishment-level of wage rigidity, is then

wri = 1− γi (3)12In cases where propijt would be predicted to be negative, propijt is set to zero.

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Therefore, the wage rigidity estimate in equation (3) is a time-invariant characteristic of the es-tablishment. wri has the natural interpretation that a value of 0.25 implies that 25 percent ofcounterfactual nominal wage cuts at establishment i were prevented by downward nominal wagerigidity over the sample period.13

There are three major advantages to this approach to estimating wage rigidity. First, it usescross-sectional and time variation in the position of the wage change distribution to identify wagerigidity, rather than relying solely on cross-sectional variation within each period. Second, in con-trast to typical histogram location approaches to estimating wage rigidity in the literature, this wagerigidity estimator uses wage changes both above and below the median to estimate the counterfac-tual distribution. Third, it performs well regardless of whether the median wage change is aboveor below zero, a situation that can be problematic for estimators that rely only on cross-sectionalvariation in the wage change distribution within a period. This situation arises in xx percent of theestablishment years in the sample. Appendix C discusses this issue in more detail in.

This approach imposes more structure on the counterfactual wage change distribution thanalternative approaches. It implicitly assumes that an establishment’s counterfactual wage changedistribution is symmetrical and has a constant variance across years. A potential drawback of thisapproach is that it implicitly assumes the nominally positive portion of the wage change distributionof the wage change distribution is unaffected by wage rigidity in order to predict the nominallynegative portion of the distribution. As emphasized by Elsby (2009), theory suggests that wagerigidity should affect the nominally positive portion of the wage change distribution as well as thenominally negative portion. Specifically, wage increases should be compressed in the presenceof wage rigidity. This compression is evident in simulations of the theoretical model presentedin section 5, as well. Monte Carlo simulations of the estimator in equation (3) suggest that it isunbiased both with and without compression in the wage change distribution. Intuitively, this isbecause the estimator only attempts to estimate the fraction of counterfactual wage cuts preventedby wage rigidity, and not their magnitude.

The Monte Carlo simulations suggest that there is some noise associated with the estimatorof wage rigidity in equation (3). This noise will lead to attenuation bias in the estimates of theassociation between wage rigidity and employment outcomes presented in section 6. Therefore,the estimates of these associations are likely to underestimate the strength of the true associations.Please see appendix C for a discussion of the Monte Carlo simulations.

13Nothing in this procedure prevents wri from being negative. A value for wri of -0.25 would imply that there are25 percent more wage cuts in the data than would be predicted by the distribution of nominally positive wage changes.

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4 The Distribution of Wage Rigidity in West Germany

To provide some context as to “where” and “how much” wage rigidity is present in the sample, thissection provides estimates of the prevalence of wage rigidity in each supersector, broad occupationclass, and education level before turning to the establishment-level analysis. The extent of wagerigidity is estimated using the methodology described in section 3, but taking these larger groupsas the unit of analysis rather than the establishment. For a wage change to qualify as valid in theseestimates, the employee must be classified in the same establishment and in either the same sector,occupation class, or education level for two consecutive years, with the employee’s hour statusunchanged between those years.

Table 2A shows wage rigidity estimates for each supersector, occupational class, and educationlevel in the sample. Among supersectors, public administration exhibits the highest degree of wagerigidity, with an estimated 46.6 percent of wage cuts prevented by wage rigidity over the sampleperiod.14 Finance and Administration also display large amounts of wage rigidty, with 28.8 and26.4 percent of wage cuts prevented, respectively. Construction and mining/manufacturing exhibitexhibit the least wage rigidity over the sample period, with -3.2 percent and 3.4 percent of negativewage cuts prevented due to wage rigidty. That is, the estimates suggest that there are more wagecuts in the construction sector than one would expect from the nominally positive portion of thewage change distribution, although this estimate is statistically indistinguishable from zero.

Occupational classes are classified according to the Blossfeld grouping, a common, broad clas-sification of occupations used in Germany. The middle portion of Table 2A shows that the highestdegrees of wage rigidity are concentrated among the semi-professional, simple commercial andadministrative, and engineer occupations, with 35.2, 34.5, and 32.9 percent of wage cuts preventeddue to wage rigidity, respectively, over the sample. On the other end of the spectrum, the lowestdegrees of wage rigidity are concentrated among simple manual, skilled manual, and simple ser-vice occupations with -0.6, 2.8, and 6.7 percent of wage cuts prevented, respectively. One odditythat emerges from the table is that the wage rigidity estimate for agricultural occupatons is 31.2percent, compared to an estimated 9.7 percent in the agricultural supersector. However, as docu-mented in Table ??, the agricultural supersector contains a large fraction of workers who are notemployed in agricultural occupations. Many of these workers are employed in simple and skilledmanual occupations that display low degrees of wage rigidity. Interestingly, skilled occupationsconsistently exhibit more wage rigidity than their less skilled counterparts.

Similarly, the bottom portion of table 2A shows that more educated groups generally exhibithigher degrees of wage rigidity. Workers whose highest educational attaintment is a secondaryschool leaving certificate with no vocation are estimated to have only 6.3 percent of counterfactual

14Appendix B describes the composition of supersectors in more detail.

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wage cuts prevented by wage rigidity. Graduates of a University of High Science are estimated tohave 41.3 percent of counterfactual wage cuts prevented. Workers who receive vocational trainingin both the secondary and upper secondary levels of education exhibit roughly 7 percent more rigidwages than their non-vocational counterparts.

Table 2B shows the mean, median, and standard devation of the distribution of wage rigidityestimates for individual establishments within each of the ten supersectors. The mean and medianlevels of wage rigidity vary widely across supersectors, with little difference between the meanand median within supersectors. The variation within supersectors, as measured by the standarddeviation across establishments, ranges from 19 percent to 34 percent. At the establishment level,construction remains the most wage flexible of all the supersectors, with an average of only 3.2percent of counterfactual wage cuts prevented by wage rigidity. The average amounts of wagerigidity estimated at the establishment level are qualitatively similar to the aggregate estimatesfrom table 2A.

5 Model of Establishment Decision Making with Wage Rigidity

This section examines the dynamic wage and employment policies of a single, representative es-tablishment15 with heterogeneous worker types in partial equilibrium facing an imperfectly com-petitive labor market. The establishment’s goal is to maximize its discounted stream of expectedfuture profits. The establishment experiences shocks to its marginal revenue product of labor andfaces costs of adjusting its stock of labor and wage rate.

5.1 Establishment Environment

The representative establishment has infinite life and uses one input of production, labor, of whichthere are J distinct types. The establishment maximizes the discounted stream of expected perperiod profits,

Π =J∑j=1

(pjn

αj − wjnj − ch(hj, nj,−1)hj − c``j − g(wj, wj,−1)nj

)where nj is the stock of type j labor used in production, α governs returns to scale in production,wj is the wage rate for type j labor, hj and `j are the number of type j employees the establishment

15The analysis refers to an establishment rather than a firm to be consistent with the data set, which providesestablishment identifiers rather than firm identifiers. Theoretically, however, the analysis would apply equally as wellto a firm’s problem.

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hires and lays off, and ch(·) and c` are costs of hiring and layoffs of type j labor, respectively. g(·)is the cost of wage adjustment for type j labor, while pj shifts the marginal revenue product oflabor. pj may be conceptualized as either type j’s level of labor productivity or the level of itsoutput price; the remainder of the paper refers to pj as productivity for concreteness’ sake. Theestablishment is assumed to be concerned exclusively with real payoffs, and all variables aboveare specified in real terms. The rate of price inflation enters the model through the cost of wageadjustments function as described below.

The establishment’s stock of type j labor evolves according to the equation:

nj = nj,−1 − δ(wj)nj,−1 + hj − 1+`j

where δ(wj) is the quit rate of type j labor from the establishment. The establishment choosesthe current stock of each type of labor by optimally setting the level of hires, the wage rate, andlayoffs.

The establishment faces an imperfectly competitive labor market for each type of labor. Thequit rate of type j labor is given by the function

δ (wj) = δ(wjw

)−γ, γ > 0 (4)

where δ is the economy-wide average quit rate. The quit rate is decreasing in the wage rate, wj .γ governs the degree of competition in the labor market: as γ increases, the quit rate becomesmore sensitive to wages. In the limit as γ approaches infinity, the labor market becomes perfectlycompetitive.

The establishment faces quadratic per-employee costs of hiring type j labor, given by the func-tion

ch(hj, nj,−1) = φ1

(hjnj,−1

)+ φ2

(hjnj,−1

)2

(5)

The quadratic hiring cost function allows for increasing or decreasing returns to scale. Most studiesof hiring costs indicate that hiring costs are subject to decreasing returns to scale, see for instanceBlatter, Muehlmann, and Schenker (2008).

Downward nominal wage rigidity enters the model through the wage adjustment cost function,g (wj, wj,−1), which is specified in per-employee terms as a quadratic polynomial in nominal wagereductions:

g (wj, wj,−1) = λ01(1+π)wj<wj,−1+ λ1 (wj,−1 − (1 + π)wj)1(1+π)wj<wj,−1

+λ2 (wj,−1 − (1 + π)wj)21(1+π)wj<wj,−1

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λ0 represents a fixed menu cost of cutting wages, while λ1 and λ2 represent linear and quadraticcosts of wage cuts, respectively. π represents the deterministic rate of price inflation. Both wj andwj,−1 are specified in real terms, but it is assumed that the establishment bears costs only when itcuts nominal wages. The nominal wage cut from the previous period to the present period is lastperiod’s real wage, wj,−1, less this period’s real wage, wj , times the increase in the price level 1+π,when this difference is negative, and zero otherwise. Thus, the cost of wage adjustment, g(·), ispositive when nominal wages are cut and zero otherwise. The cost of cutting nominal wages givesrise to downward nominal wage rigidity in the model.

Multiple theories which give rise to wage rigidity have been advanced in the literature. Ef-ficiency wage theory, as for instance in Shapiro and Stiglitz (1984), emphasizes that wage cutsmay reduce worker effort. Bewley (1999) emphasizes that wage cuts may reduce worker morale,thereby lowering productivity. Elsby (2009) and Kaur (2012) both model wage rigidity as aris-ing from reductions in morale associated with wage cuts. The wage adjustment cost functiong(·) provides a way of modeling costs of nominal wage cuts that is agnostic regarding the precisemechanism by which wage cuts are costly to the firm.

5.2 Solution to the Establishment’s Problem

Because the establishment’s profit function is a linear summation of the individual type j profitfunctions, the establishment’s dynamic optimization problem can be written separately for eachtype of labor. For each labor type j, the establishment chooses the wage rate, level of hires, andlayoffs to solve the following dynamic optimization problem:

Vj (z, uj, wj,−1, nj,−1) = maxwj ,hj ,lj

pjnαj − wjnj − ch(hj, nj,−1)hj − c``j

−g(wj, wj,−1)nj + βE[Vj(z′, u′j, wj, nj

)](6)

subject to

ln pj = ln z + lnuj (7)

ln z = (1− ψz) ln z + ψ ln z−1 + εz, εz ∼ N(0, σ2

z

)(8)

lnuj = (1− ψu) ln u+ ψ lnuj,−1 + εuj , εuj ∼ N(

0, σ2uj

)(9)

nj = (1− δ (wj))nj,−1 + hj − 1+`j (10)

g (wj, wj,−1) = λ01(1+π)wj<wj,−1+ λ1 (wj,−1 − (1 + π)wj)1(1+π)wj<wj,−1

+λ2 (wj,−1 − (1 + π)wj)21(1+π)wj<wj,−1

(11)

13

The Bellman equation has 4 state variables: establishment-level productivity, z, labor type j-specific productivity uj , last period’s type j wage rate, wj,−1, and last period’s type j labor stock,nj,−1. As specified in equations 8 and 9, both productivity levels evolve according to a meanreverting, AR(1) process. The errors εz and εuj are assumed to be independent.

The model solution uses standard value function iteration techniques to find the establishment’svalue and policy functions. The method of Tauchen (1986) approximates the autoregressive pro-cess for the productivity levels z and uj . A description of model calibration is deferred until section7, as the calibration uses the empirical results from section 6 of the paper. In the meantime, theproceeding section discusses the establishment’s policy functions and simulation results, whichgenerte the empirical predictions used to test the data in section 6.

5.3 Establishment Policy Functions and Simulations

Figure 1 displays the establishment’s policy functions using parameters calibrated as decribed insection 7, but setting the cost of wage cut parameters λ0, λ1, and λ2, to zero (and, hence, removingwage rigidity from the model). Each panel shows the policy functions for the lowest, middle, andhighest productivity levels in the discretized productivity space. Panel A illustrates the establish-ment’s employment policy function. As expected, the establishment’s desired employment levelincreases with productivity and the last period’s level of employment, but does not vary with thelast period’s wage. Panel B illustrates the establishment’s wage policy function. The establishmentpays higher wages when productivity is higher, and lower wages when last period’s employmentlevel is higher.16 As last period’s employment rises, the establishment can tolerate a higher quitrate while retaining enough employees to meet its desired employment level, reducing the estab-lishment’s incentive to pay high wages. Panel C illustrates the establishment’s quit rate policyfunction, which the firm controls deterministically by setting the wage rate. The quit policy func-tion varies inversely with the wage policy function. It is increasing in last period’s employmentlevel but decreasing with productivity, so that the flat policy surface at the bottom of the figurecorresponds to the high productivity level. The quit policy function does not vary with the previ-ous period’s wage. Finally, panel D illustrates the establishment’s layoff policy function. In theabsence of wage rigidity, the establishment essentially never finds it optimal to lay off employees:it is always more profitable for the establishment to decrease wages, thus increasing the quit rate,if it would otherwise have an employment level greater than desired.

Figure 2 displays simulated, period-over-period, wage change histograms using these policyfunctions. Each histogram represents a period for the establishment in the simulated data, whichcorresponds to an establishment-year in the empirical data. As expected, the histograms are widely

16Subject to approximation error.

14

dispersed around the median and roughly symmetrical. Wage cuts are as prevalent as would be beexpected given a symmetrical wage change distribution. The estimated level of wage rigidity usingthe estimator proposed in section 3 is close to zero.

Figure 3 illustrates the establishment’s policy functions using the calibrated parameters forwage rigidity. Panel A shows that the establishment’s employment policy continues to be increas-ing in productivity and the previous period’s employment level. However, the optimal employmentlevel now depends on the previous period’s wage, an effect that is especially visible for the middleproductivity level. When the previous period’s wage is above a certain level, the establishmentchooses to employ fewer workers as the wage rises. This is because downward nominal wagerigidity binds in this portion of the policy space, and the establishment pays a wage higher than inwould set in the absence of such rigidity. For the highest productivity level, wage rigidity is essen-tially never binding, so the employment policy function does not depend on the previous period’swage.

Panel B shows the establishment’s wage policy functions. The flat portions of the policy func-tion towards the front of the figure for each productivity level are the areas for which wage rigidityis not binding because the optimal new wage is above the previous period’s wage. The upwardsloping portions are the areas in which wage rigidity is binding and the establishment sets the cur-rent period’s wage equal to the previous period’s wage. Finally, the flat portions towards the rear ofthe figure are the areas in which the establishment is willing to incur the costs of adjusting wagesdownward.

Panel C illustrates the establishment’s quit rate function for the three productivity levels. Theflat quit rate policy surface at the bottom of the figure corresponds to the high productivity leveland reflects the establishment’s flat wage policy function for the high productivity level. Themiddle quit rate policy surface corresponds to the medium productivity level and also mirrorsthe establishment’s wage policy function. It is rising in last period’s employment level as theestablishment is more willing to tolerate quits, and it is falling with the previous period’s wagein the area where wage rigidity is binding. The top quit rate policy surface corresponds to thelowest productivity level. It also rises with the previous period’s employment level and falls inareas where wage rigidity is binding.

Panel D shows the establishment’s layoff policy function. For the highest productivity level,the establishment does not lay off employees. For the middle productivity level, the establishmentlays off employees only at high levels of the previous period’s wage and employment. For the lowproductivity level, the establishment’s layoff policy function is rising both in the previous period’swage and employment levels. This result is consistent with the intuition that downward wagerigidity leads to layoffs otherwise not enacted in flexible wage settings.

Figure 4 displays simulated wage change histograms using the calibrated wage rigidity param-

15

eters. The distribution of wage changes is notably compressed relative to the distribution in figure2, and there are fewer negative wage changes. The estimator of wage rigidity proposed in section3 can be applied directly to the simulated model data. The resulting estimate of the level of wagerigidity is 0.27, implying that wage rigidity prevented 27 percent of wage cuts that would otherwisehave occurred.

Figure 5 presents results from simulating the model holding all parameters fixed except thewage rigidity parameters, which are scaled proportionally by fractions ranging from zero to one.The simulation uses 1,100 periods for each level of the wage rigidity parameters and drops thefirst 1,000 periods to allow for burn-in. Panel A shows the average proportion of wage cuts,which decrease with wage rigidity. Panel B shows the average layoff rate, which is increasingwith wage rigidity. Panels C and D illustrate the average quit and hire rates, respectively. Bothrates are decreasing functions of the level of wage rigidity. Quits decline when wages are morerigid because under rigid wages the establishment sometimes finds itself paying wages above thelevel that would be optimal under perfectly felxible wages, which reduces worker turnover. Theslower pace of worker turnover reduces the establishment’s need to hire new workers as well.Additionally, more rigid wages increase the chance that the establishment will pay above optimalwages in the future, decreasing the incentive to hire today.

Therefore, the model generates three empirical predictions for the relationship between wagerigidity and employment adjustment:

1. Establishments with higher degrees of wage rigidity should exhibit higher layoff rates;

2. Establishments with higher degrees of wage rigidity should exhibit lower quit rates; and

3. Establishments with higher degrees of wage rigidity should exhibit lower hire rates.

Section 6 tests these predictions.

6 Wage Rigidity and Employment Adjustment

This section provides the estimates of the empirical relationship between wage rigidity and em-ployment adjustment. Section 6.1 describes the empirical strategy for estimating the reduced-formrelationship between wage rigidity and employment adjustment. Sections 6.2, 6.3, and 6.4 presentthe estimated relationship between wage rigidity and layoffs, quits, and hires, respectively, anddiscusses the results.

16

6.1 Empirical Approach

The theoretical model implies empirical regressions of the following form:

yit = β0 + β1wri +X ′itΥ + εit (12)

where the unit of observation is an establishment-year. yit represents an employment adjustmentvariable of interest: the layoff rate, the quit rate, or the hire rate. writ represents the estimatedpercentage of wage cuts prevented by downward nominal wage rigidity, as discussed in section 3.Xit represents a vector of control variables, including a dummy for the presence of a work council,the median year-over-year percentage wage change, a set of year, state, and sector fixed effects,dummies for establishment size groups, the fraction of the workforce that is female, and controlsfor workforce educational attainment and Blossfeld occupation. Estimates of equation (12) arepresented in column 1 of tables 3A, 4A, and 5A, for layoffs, quits, and hires, respectively. Theeconomic interpretation of these estimates is presented in tables 3B, 4B, and 5B.

It is natural to examine whether the employment effects of wage rigidity vary according to theeconomic shocks an establishment faces. In the theoretical model presented in section 5, wagerigidity binds more tightly in response to negative shocks to the marginal revenue product of laborthan in the absence of such negative shocks. While the data do not permit explicit observation ofmarginal revenue product of labor shocks, data on revenue growth is likely to be informative aboutsuch shocks. Assuming changes in revenue growth reflect primarily shifts in demand suggeststhe following additional specification for examining the relationship between wage rigidity andemployment outcomes:

yit = β0 + β1wri + β2posrevit + β3negrevit

+ β4 (wri × posrevit) + β5 (wri × negrevit) +X ′itΥ + εit (13)

The variables posrevit and negrevit denote the year-over-year change in revenue; posrevit is set tozero when this change is negative, while negrevit is set to zero when this change is positive. Spec-ifying the change in revenue this way allows us to estimate a linear spline function over revenuegrowth, allowing for disparate associations between revenue growth and employment adjustmentdepending on whether revenue growth is positive or negative.17 The variables (wri × posrevit)and (wri × negrevit) are interactions between estimated establishment wage rigidity and revenuegrowth, and allow us to capture possible interactions between wage rigidity and positive or negativemovements in revenue.

17The specification of revenue growth as a linear spline function with a kink at zero is similar to the specification ofHolzer and Montgomery (1993), who also interpret changes in sales growth as reflecting primarily shifts in demand.

17

Tables 3A, 4A, and 5A present five sets of results for each outcome variable. Column (1)presents estimates of equation (12), weighted by establishment employment. Column (2) presentsestimates of equation (13) without the wage rigidity-revenue growth interaction terms, also weightedby establishment employment. Column (3) presents estimates of equation weighted estimates ofequation (13) including wage rigidity-revenue growth interaction terms. Regression weights arelikely to be appropriate for two reasons: first, because the estimate of wage rigidity is likely tobe less noisy at larger establishments, and second, because larger establishments employ a largerpercentage of the total workforce, and thus their behavior has a larger effect on the aggregate econ-omy. Columns (4) and (5) present unweighted estimates of equation (13), splitting the sample intosmall and large establishments about the sample median employment level of 219 employees.

6.2 Layoffs

Table 3A shows results from the layoff regressions. In column (1), the estimated coefficient onthe wage rigidity variable is 2.9 percent and statistically significant. The sign is consistent withthe predictions presented in section 5: establishments with higher degrees of wage rigidity exhibithigher layoff rates. Adding positive and negative revenue growth as regressors in column (2),the coefficient on estimated wage rigidity is again 2.9 percent and statistically significant. Thecoefficient on negative revenue growth is negative 5.8 percent, which implies that a decrease inrevenue increases layoffs, as expected. The coefficient on positive revenue growth is estimated tobe close to zero and is not statistically significant. In column (3), which adds interactions betweenwage rigidity and revenue growth, the coefficient on the level of estimated wage rigidity is 2.5percent and statistically significant. The coefficients on the uninteracted revenue growth terms arestatistically insignificant, as is the coefficient on the interaction between wage rigidity and positiverevenue growth. However, the coefficient on the interactions between wage rigidity and negativerevenue growth is negative 19.3 percent and highly significant.

Table 3B shows the economic interpretation of these coefficients. Column (1) shows that anestablishment with the sample average level of wage rigidity is predicted to have a 0.7 percentagepoint higher layoff rate than an establishment with no wage rigidity. Column (2) shows that thisprediction does not change when positive and negative revenue growth are added as regressors.This difference corresponds to 15.9 percent of the sample average layoff rate. The magnitudesare similar in column (3), with a one standard deviation decrease in revenue associated with a 0.8percentage point higher layoff rate in response to a one-standard deviation decrease in revenue.

Columns (4) and (5) of table 3A, present the results from the split estimation sample. Theassociation between wage rigidity and layoffs differs meaningfully between small and large estab-lishments. The coefficient on the level of wage rigidity in column (4) is 2.9 percent and highly

18

significant, while the coefficient in column (5) is -1.0 percent and statistically insignificant. Thecoefficients on the wage rigidity-revenue growth interaction terms are not significant in either col-umn. Economically, the estimates in column (4) of table 3B show that large establishments wouldbe predicted to increase layoffs by 1 percentage point in response to a one standard deviation de-crease in revenue, similarly to the results in column (3). The estimates in column (5) imply thatsmall establishments would be predicted to decrease layoffs by 0.3 percentage points in responseto such a decrease in revenue, although this prediction is not statistically significant.

6.3 Quits

Table 4A shows results from the quit regressions. In column (1), the estimated coefficient on thewage rigidity variable is -7.2 percent and statistically significant. This sign is also consistent withthe predictions from the theoretical model, as establishments with higher degrees of wage rigidityexhibit lower quit rates. In column (2), the coefficient on estimated wage rigidity is also -7.2percent and statistically significant. The coefficient on positive revenue growth is 3.7 percent andstatistically significant, impyling counterintuitively that revenue growth is associaed with a higherquit rate. The coefficient on negative revenue growth is -21.5 percent and statistically significant,implying that a decrease in revenue also predicts a higher quit rate. In column (3), the coefficienton estimated wage rigidity is negative 5.2 percent. The coefficients on the interactions betweenwage rigidity and revenue growth also have the expected signs: firms with more wage rigidity arepredicted to experience fewer quits in response to an increase or decrease in revenue.

Table 4B shows the economic interpretation of the coefficients in the quit rate regressions. Col-umn (1) shows that an establishment with the sample average level of wage rigidity is predictedto have a 1.6 percentage point lower quit rate than an establishment with no wage rigidity. Again,column (2) shows that controlling for revenue growth does not change this prediction. This dif-ference corresponds to 19.3 percent of the sample average quit rate. The magnitudes are similarin column (3), with a one standard deviation decrease in revenue associated with a 1.6 percentagepoint lower quit rate in response to a one-standard deviation decrease in revenue, or 17.3 percentof the sample average quit rate.

Columns (4) and (5) of table 4A, present the results from the split estimation sample quit rateregressions. The association between wage rigidity and quits varies slightly between small andlarge establishments. The coefficient on the level of wage rigidity in column (4) is -5.5 percentcompared to -4.4 percent in column (5); both are statistically signficant. The coefficients on thewage rigidity-revenue growth interaction terms are generally statistically signifcant and have thesame, expected, signs in both columns. The economic interpretation of these results follows in ta-ble 4B. Column (4) shows that a large establishment with the sample average level of wage rigidity

19

would be predicted to experience a quit rate 2.5 percentage points lower than a large establishmentwith no wage rigidity in response to a one standard deviation decrease in revenue. The corre-sponding decrease for small establishments, shown in column (5), is 1.2 percentage points. Thesedifferences translate into 25.1 percent and 9.6 percent reductions in the sample average quit ratesfor large and small establishments, respectively.

6.4 Hires

Table 5A shows results from the hire regressions. In column (1), the estimated coefficient on thewage rigidity variable is -5.3 percent and statistically significant. This coefficient implies thatestablishments with greater wage rigidity exhbit lower hire rates, as predicted by the theoreticalmodel. In column (2), the coefficient on estimated wage rigidity is -5.9 percent and statisticallysignificant. The coefficient on positive revenue growth is 4.8 percent and statistically significantand the coefficient on negative revenue growth is 2.5 percent and not statistically significant. Bothof these signs imply that revenue growth is associated with more hires. In column (3), the coeffi-cient on estimated wage rigidity is negative 5.3 percent. The coefficient on the interaction betweenwage rigidity and positive revenue growth has the expected sign: firms with more wage rigidityare predicted to engage in fewer hires in response to an increase in revenue. The coefficient on theinteraction between wage rigidity and negative revenue growth has the counterintuitive sign: firmswith more wage rigidity are predicted to engage in more hires relative to firms with less wagerigidity when revenue decreases. It is worth noting that the estimates imply that establishmentswith average wage rigidity will still reduce hiring when revenue falls; however, this response willbe smaller when wage rigidity is higher.

Table 5B shows the economic interpretation of the coefficients in the hire rate regressions.Column (1) shows that an establishment with the sample average level of wage rigidity is predictedto have a 1.3 percentage point lower hire rate than an establishment with no wage rigidity. Incolumn (2), the corresponding difference is 1.4 percentage points, which corresponds to 8.4 percentof the sample average hire rate. The magnitudes are larger in column (3), with a one standarddeviation decrease in revenue associated with a 2.6 percentage point lower higher rate in responseto a one-standard deviation decrease in revenue, or 14.8 percent of the sample average hire rate.

Columns (4) and (5) of table 5A present the results from the split estimation sample hire rateregressions. The level association between wage rigidity and hires is roughly the same across smalland large establishments. The coefficient on the level of wage rigidity in column (4) is -4.8 percentcompared to -3.3 percent in column (5), though only the former is statistically significant. Thecoefficients on the wage rigidity-revenue growth interaction terms are statistically signifcant forpositive revenue growth and have the expected sign. These coefficients have the unexpected sign

20

for negative revenue growth but are not statistically significant.Table 5B presents the economic interpretation of these results. Column (4) shows that a large

establishment with the sample average level of wage rigidity would be predicted to have a hirerate 2.9 percentage points lower than a large establishment with no wage rigidity in response to aone standard deviation increase in revenue. The corresponding decrease for small establishments,shown in column (5), is similar in magnitude at 2.3 percentage points. As a fraction of the respec-tive sample average hire rates, the association in column (4), for large establishments, is larger at15.0 percent, compared to 9.4 percent for small establishments.

7 Model Calibration

This paper employs a combination of methods to calibrate the parameters of the theoretical modeldescribed in section 5. First, the parameters β and π are taken from German macroeconomic data.Second, the parameters α, δ, w, γ, ψz, and σ2

z are estimated directly from the LIAB microdata usedthroughout the paper. Then, the parameters ln z, λ0, λ1, ψu, σ2

uj, φ1, and φ2 are calibrated to match

a set of simulated moments to their empirical counterparts in the LIAB microdata. To simplify thecalibration, the parameters c` and λ2 are set to zero. The parameter u is normalized to 1. Table 8illustrates the parameters used to simulate the model.

The inflation rate, π, of 1.5 percent is calibrated as the rate of consumer price inflation inGermany over the period 1997 through 2003. The establishment discount rate β is calibaratedfrom the World Bank’s WDI tables to match the average German lending interest rate of 9.37percent per year for the period 1997-2002. The lending interest rate is defined as the bank rate thatmeets the short- and medium-term financing needs of the private sector.18 β is then calibrated as

11.0937

, or 0.914. The average quit rate δ and the average daily wage w are taken directly from themicrodata sample. δ is the average quit rate across establishment-years, 9.2 percent. The averagedaily wage is 89.1 euros.

The returns-to-scale parameter α is chosen to match labor’s average share of value added acrossall establishment-years in the microdata. For each establishment-year, the establishment’s totalwage bill is calculated from the worker biographies. The establishment’s value added is calculatedas total revenues minus intermediate inputs and external costs.19 The theoretical model in section

18See http://data.worldbank.org/indicator/FR.INR.LEND/countries?page=2 for more detail. The rate is not avail-able for 2003.

19Each year, the establishment survey panel includes a question regarding the share of revenue attributable to exter-nal costs. For instance, in the 2002 survey the question read:

What share of sales was attributed to intermediate inputs and external costs in 2001, i.e. all raw ma-terials and supplies purchased from other businesses or institutions, merchandise, wage work, externalservices, rents and other costs (e.g. advertising and agency expenses, travel costs, commissions, royal-ties, postal charges, insurance premiums, testing costs, consultancy fees, bank charges, contributions to

21

5 abstracts from intermediate inputs, so there is no distinction in the model between revenue andvalue added. However, in the microdata it is necessary to adjust for intermediate inputs to calculatelabor’s share of value added accurately. Therefore, labor’s share of value added per establishment-year is simply the establishment’s total wage bill divided by revenue less external costs. Averaginglabor’s share of value added across establishment-years yields an estimate of 0.65 for the parameterα.

The parameter γ is the elasticity of the quit rate with respect to wages in equation (4) fromsection 5.1. This equation is difficult to estimate directly due to its non-linearity in the wage. Afirst-order Taylor series yields the following linear approximation around the average wage, w:

δ(w)− δ ≈ −δγ(w − ww

)(14)

Equation (14) expresses the deviation of the establishment-year quit rate from the average quitrate as a decreasing function of the percentage deviation of the establishment-year wage from theeconomy average wage.20 Taking equation (14) to the data requires accounting for worker andestablishment heterogeneity that is not present in the theoretical model.21 A Mincer regression ofindividual log wages on worker and establishment observable characteristics allows for the removalof observable heterogeneity.22 Thus, the residual from this regression provides a cleansed measureof the deviation of individual log wages from the market average. Averaging these residuals at theestablishment-year level provides a log approximation to the term

(w−ww

)in equation (14).

To estimate equation (14), establishment-year quit rates minus the average qut rate were re-gressed on the average Mincer residuals, and a set of establishment and year fixed effects. Theinclusion of establishment fixed effects identifies γ off of time series variation in wages withinestablishments, rather than cross-sectional variation in wages across establishments, for reasonsdiscussed above. The estimated coefficient in regression equation (14) is -0.53, which correspondsto −δγ. Dividing the estimated coefficient by −δ yields an estimated γ of 5.75.

The persistence, ψz, and variance, σ2z , of establishment-wide productivity shocks are estimated

from the LIAB microdata using information on value added and the returns-to-scale parameterα calculated above. Taking logs of the theoretical establishment value added function yields the

chambers of trade and commerce and professional associations)?

20Although equation 4 is linear in logs, estimating the equation in logs is not feasible because quits are zero in someestablishment-years.

21Neglecting to account for heterogeneity may yield biased inference if wages are correlated with other determinantsof the quit rate. For example, if non-wage amenities such as pleasantness of the job are reflected in compensating wagedifferentials, a naive estimate of γ that does not account for heterogeneity will be biased toward zero.

22The covariates included in the Mincer regression are a set occupation dummies, a set of education dummies,gender, nationality, age and age squared, a set of year fixed effects, federal state, and a set of sector dummies.

22

equation:

ln(V Ait) = ln pit + α ln(nit) =⇒ ln(V Ait)− α ln(nit) = ln pit (15)

Using the measures of value added and the estimate of α described above, ln(V Ait) − α ln(nit)

is regressed on a set of worker covariates, year fixed effects, and establishment fixed effects. Theregression results allow for the calculation of annual establishment-level average productivity, pit.Assuming the law of large numbers holds, the average level of uijt in the sample wil be 1 eachyear, implying zit = pit. Regressing pit on pi,t−1 and a set of establishment fixed effects yieldsestimates for the persistence of the establishment-level productivity process, ψz, and the varianceof establishment-level productivity shocks, σ2

z .The wage cut cost function parameters λ0 and λ1, the average establishment-level productivity

ln z, the persistence and variance of shocks to worker-type productivity ψu and σ2u, and the hiring

cost function parameters φ1 and φ2 are calibrated to match a set of simulated moments from thetheoretical model to their empirical counterparts in the data sample. The target moments are theaverage hire rate in the data sample, the average wage level and the standard deviation of wagechanges for job stayers in the data sample, the average measured level of wage rigidity in the sam-ple, the average number of employees per establishment, the ratio between the average magnitudeof wage increases and wage decreases, and the increase in the layoff rate predicted by the averagelevel of wage rigidity in the sample.23 There is not a one-to-one correspondence between the targetmoments and the parameters they identify. However, intuitively, λ0 and λ1 are identified mainly bythe level of measured wage rigidity, the ratio between the average magnitude of wage increases andwage decreases, and the increase in the layoff rate. The worker-type productivity shock parametersψu and σ2

u are identified mainly by the increase in the layoff rate and the standard deviation of theaverage wage change. The average establishment-level productivity ln z is identified mainly bythe average establishment size. The hiring cost parameters φ1 and φ2 are identified mainly by theaverage hiring rate and average wage.

The parameters are calibrated by minimizing the sum of the squared percent deviations of thesimulated moments from their empirical counterparts. Table 8 shows the calibrated parameters,and table 9 shows the empirical and simulated moments using the calibrated parameters. Themodel performs well in matching the average wage rate, the standard deviation of percent wagechanges, measured wage rigidity, establishment size, and the ratio of the magnitudes of negativeand positive wage changes. The model underestimates worker turnover to some extent, as both theimplied increase in the layoff rate and the hire rate are below their target levels.

The estimated wage cut cost parameters λ0 and λ1 allow for the calculation of the cost of the

23This value is taken from column 2 of Table 5B.

23

average wage cut to the establishment. In the model simulations the average per worker cost of awage cut is 1.75 percent of the average wage. Roughly half of this cost is attributable to the fixedcos of wage cuts λ0 and roughly half is attributable to the linear cost λ1. Therefore, the modelsuggests that moderate costs of downward nominal wage adjustment can have noticeable effectson employment outcomes.

8 Conclusion

This paper explores the employment adjustment implications of downward nominal wage rigid-ity theoretically and empirically using German administrative data. A novel contribution of thepaper is the use matched establishment-employee data to measure wage rigidity and employmentadjustment at the establishment level. Establishment-level wage rigidity estimates document a sub-stantial amount of downward nominal wage rigidity in Germany, with 24 percent of counterfactualwage cuts on average per establishment-year missing from the observed data. The empirical anal-ysis shows that, consistent with the predictions of the theoretical model, establishments with moredownward nominal wage rigidity exhibit higher layoff rates and lower quit and hire rates.

24

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McLaughlin, Kenneth, “Are Wage Changes Skewed Away from Nominal Wage Cuts?”, mimeo

September, 1998.

Nickell, S., and Glenda Quintini, “Nominal Wage Rigidity and the Rate of Inflation”, Economic

Journal, October 2003, vol. 113, no. 490, pp. 762-781(20).

Ricardo, David. “Letters of David Ricardo to Thomas Robert Malthus, 1810-1823”, James Bonar(Ed.). London: Oxford University Press, 1887.

Shafir, Eldar, Peter Diamond, and Amos Tversky, “Money Illusion”, Quarterly Journal of Eco-

nomics, 112(2), May, 1997.

Tobin, James, “Inflation and Unemployment”, American Economic Review, vol. 62(1972), pp 1-18.

26

Table 1: Establishment-Level Descriptive Statistics

Number of Establishments 2,250

Sample Size, Establishment-Years 9,230

Mean Layoff Rate 0.068

(0.120)

Mean Quit Rate 0.111

(0.161)

Mean Hire Rate 0.218

(0.335)

Mean Employees per Establishment 549.381

(1,211.208)

Median Employees per Establishment 219

Mean Daily Wage, Level 87.176

(28.404)

Median Daily Wage, Level 87.262

Estimated Wage Rigidity 0.239

(0.269)

Average Revenue Growth 0.035

(0.206)

Standard deviations in parentheses where applicable.

27

Table 2A: Aggregate Wage Rigidity Estimates by Select Classifications

Classification Estimated Wage Rigidity

SupersectorAgriculture 0.097Mining/Manufacturing 0.034Energy/Water 0.063Construction -0.032Trade/Foodservice 0.058Transportation 0.050Finance 0.288Real Estate 0.170Public Administration 0.466Administration 0.264

Blossfeld Occupational ClassificationAgricultural occupations 0.312Simple manual occupations -0.006Skilled manual occupations 0.028Technicians 0.256Engineers 0.329Simple service 0.067Qualified service 0.191Semi-professions 0.352Professions 0.139Simple commercial and administrative occupations 0.242Skilled commercial and administrative occupations 0.345Manager 0.201

Educational AttainmentSecondary/Intermediate without Vocation 0.063Secondary/Intermediate with Vocation 0.138Upper Secondary without Vocation 0.308Upper Secondary with Vocation 0.373University of High Science 0.413University Degree 0.306

28

Table 2B: Establishment-Level Wage Rigidity Estimates by Supersector

SupersectorMedian Mean Standard Deviation

Agriculture 0.094 0.132 0.320Mining/Manufacturing 0.104 0.128 0.217Energy/Water 0.268 0.289 0.283Construction 0.034 0.032 0.190Trade/Foodservice 0.173 0.212 0.284Transportation 0.104 0.115 0.234Finance 0.303 0.311 0.222Real Estate 0.151 0.216 0.340Public Administration 0.490 0.459 0.270Administration 0.398 0.355 0.306

Estimated Wage Rigidity

29

Table 3A: Wage Rigidity and Layoffs – Regression Results

(1) (2) (3) (4) (5)

Wage Rigidity 0.029 0.029 0.025 0.029 -0.010

(0.005) (0.005) (0.006) (0.009) (0.008)

Positive Revenue Growth 0.005 0.012 -0.001 0.022

(0.005) (0.007) (0.011) (0.013)

Negative Revenue Growth -0.058 -0.015 -0.026 -0.121

(0.010) (0.014) (0.023) (0.021)

Wage Rigidity x Positive Revenue Growth -0.038 -0.014 0.019

(0.024) (0.036) (0.036)

Wage Rigidity x Negative Revenue Growth -0.193 -0.104 0.012

(0.044) (0.066) (0.058)

Work Council -0.058 -0.052 -0.058 -0.065 -0.040

(0.004) (0.003) (0.004) (0.006) (0.004)

Establishment Characteristics Yes Yes Yes Yes Yes

Individual Characteristics Yes Yes Yes Yes Yes

Year Dummies Yes Yes Yes Yes Yes

WeightsNo. of

EmployeesNo. of

EmployeesNo. of

EmployeesNone None

Sample RestrictionMin. 20

EmployeesMin. 20

EmployeesMin. 20

EmployeesMin. 220

EmployeesMax. 219 Employees

R-squared 0.339 0.342 0.344 0.450 0.226N 9,230 9,230 9,230 4,608 4,622

Dependent Variable

Standard errors in parentheses. Unit of observation is establishment-year. Wage rigidity is calculated as described in section 3, and is fixed by establishment over sample period Establishment characteristics include a set of controls for the median year-over-year wage change, occupational mix and dummies for sector, federal state, and establishment size. Individual characteristics include fraction female and controls for workers' education. Positive revenue growth is defined as the year-over-year percentage change in revenues when revenue growth is positive and zero otherwise. Negative revenue growth is defined as the year-over-year percentage change in revenues when revenue growth is negative and zero otherwise. All regressions cover the period 1997 to 2003.

Layoffs as a Percentage of Establishment Workforce

30

Table 3B: Wage Rigidity and Layoffs – Economic Interpretation

(a)

(b)

(a)

(b)

(a)

(b)

(a)

(b)

(a)

(b)

Wa

ge R

igid

ity L

eve

l0.

245

0.00

00.

245

0.00

00.

245

0.00

00.

255

0.00

00.

223

0.00

0(S

am

ple

Ave

rage

)(S

am

ple

Ave

rage

)(S

am

ple

Ave

rage

)(S

am

ple

Ave

rage

)(S

am

ple

Ave

rage

)

Layo

ff R

ate

, Sa

mpl

e A

vera

ge0.

045

0.04

50.

045

0.04

50.

045

0.04

50.

057

0.05

70.

079

0.07

9

Diff

ere

nce

in L

ayo

ff R

ate

s, L

eve

ls

Diff

ere

nce

in L

ayo

ff R

ate

s A

s a

Fra

ctio

n of

S

am

ple

Ave

rage

La

yoff

Ra

te

We

ight

s

Sa

mpl

e R

est

rict

ion

N

Est

abl

ishm

ent

La

yoffs

in R

esp

onse

to

a O

ne S

tand

ard

De

via

tion

De

cre

ase

in R

eve

nue

Gro

wth

, Ave

rage

Wa

ge

Rig

idity

ve

rsus

No

Wa

ge R

igid

ity, a

s a

Fra

ctio

n of

S

am

ple

Ave

rage

La

yoff

Ra

te

0.00

7

0.15

9

No.

of E

mpl

oye

es

Min

. 20

Em

ploy

ee

s

9,23

0

Uni

t of

obs

erv

atio

n is

est

abl

ishm

ent

-ye

ar.

Wa

ge r

igid

ity is

ca

lcul

ate

d a

s de

scri

bed

in s

ect

ion

3, a

nd

is fi

xed

by e

sta

blis

hme

nt o

ver

sam

ple

pe

riod

Est

abl

ishm

ent

cha

ract

eri

stic

s in

clud

e a

se

t of

con

trol

s f

or t

he m

edi

an

yea

r-ov

er-

yea

r w

age

cha

nge

, oc

cupa

tiona

l mix

and

dum

mie

s fo

r se

ctor

, fe

dera

l st

ate

, and

est

abl

ishm

ent

siz

e. I

ndiv

idua

l cha

ract

eri

stic

s in

clud

e fr

act

ion

fem

ale

and

con

trol

s fo

r w

orke

rs' e

duca

tion.

Pos

itive

re

venu

e g

row

th is

de

fine

d a

s th

e y

ea

r-ov

er-

yea

r pe

rce

nta

ge c

hang

e in

re

venu

es

whe

n re

venu

e g

row

th is

pos

itive

and

ze

ro o

the

rwis

e. N

ega

tive

re

venu

e g

row

th is

de

fine

d a

s th

e y

ea

r-ov

er-

yea

r pe

rce

nta

ge c

hang

e in

re

venu

es

whe

n re

venu

e g

row

th is

ne

gativ

e a

nd z

ero

oth

erw

ise

. All

regr

ess

ions

cov

er

the

pe

riod

199

7 to

20

03.

-0.2

15-0

.215

0.01

80.

010

0.01

60.

005

0.02

30.

026

No.

of E

mpl

oye

es

Min

. 20

Em

ploy

ee

s

0.00

80.

010

-0.0

03

Non

e

Min

. 220

Em

ploy

ee

s

Ne

gativ

e R

eve

nue

Gro

wth

, One

Sta

nda

rd

De

via

tion

of S

am

ple

Pre

dict

ed

Layo

ff R

ate

Ass

ocia

te w

ith O

ne

Sta

nda

rd D

evi

atio

n N

ega

tive

Re

venu

e G

row

th

-0.1

96-0

.196

(2)

-0.1

96-0

.196

0.01

80.

011

(1)

N/A

N/A

N/A

N/A

Non

e

Ma

x. 2

19 E

mpl

oye

es

9,23

04,

608

4,62

2

0.18

60.

182

-0.0

35

(3)

(4)

(5)

-0.1

96-0

.196

0.00

7

0.15

9

No.

of E

mpl

oye

es

Min

. 20

Em

ploy

ee

s

9,23

0

31

Table 4A: Wage Rigidity and Quits – Regression Results

(1) (2) (3) (4) (5)

Wage Rigidity -0.072 -0.072 -0.056 -0.055 -0.044

(0.008) (0.008) (0.009) (0.012) (0.011)

Positive Revenue Growth 0.037 0.079 0.083 0.065

(0.008) (0.012) (0.015) (0.017)

Negative Revenue Growth -0.215 -0.225 -0.130 -0.076

(0.015) (0.022) (0.030) (0.028)

Wage Rigidity x Positive Revenue Growth -0.192 -0.220 -0.070

(0.038) (0.047) (0.047)

Wage Rigidity x Negative Revenue Growth 0.043 0.220 0.042

(0.069) (0.088) (0.076)

Work Council -0.047 -0.047 -0.047 -0.040 -0.044

(0.006) (0.006) (0.006) (0.008) (0.005)

Establishment Characteristics Yes Yes Yes Yes Yes

Individual Characteristics Yes Yes Yes Yes Yes

Year Dummies Yes Yes Yes Yes Yes

WeightsNo. of

EmployeesNo. of

EmployeesNo. of

EmployeesNone None

Sample RestrictionMin. 20

EmployeesMin. 20

EmployeesMin. 20

EmployeesMin. 220

EmployeesMax. 219

Employees

R-squared 0.341 0.355 0.357 0.442 0.290N 9,230 9,230 9,230 4,608 4,622

Dependent Variable

Standard errors in parentheses. Unit of observation is establishment-year. Wage rigidity is calculated as described in section 3, and is fixed by establishment over sample period Establishment characteristics include a set of controls for the median year-over-year wage change, occupational mix and dummies for sector, federal state, and establishment size. Individual characteristics include fraction female and controls for workers' education. Positive revenue growth is defined as the year-over-year percentage change in revenues when revenue growth is positive and zero otherwise. Negative revenue growth is defined as the year-over-year percentage change in revenues when revenue growth is negative and zero otherwise. All regressions cover the period 1997 to 2003.

Quits as a Percentage of Establishment Workforce

32

Table 4B: Wage Rigidity and Quits – Economic Interpretation

(a)

(b)

(a)

(b)

(a)

(b)

(a)

(b)

(a)

(b)

Wag

e R

igid

ity L

evel

0.2

45

0.0

00

0.2

45

0.0

00

0.2

45

0.0

00

0.2

55

0.0

00

0.2

23

0.0

00

(Sam

ple

Ave

rage

)(S

ampl

e A

vera

ge)

(Sam

ple

Ave

rage

)(S

am

ple

Ave

rage

)(S

ampl

e A

vera

ge)

Qui

t Rat

e, S

ampl

e A

vera

ge0

.09

20

.09

20

.09

20

.09

20

.09

20

.09

20

.10

00

.10

00

.12

30

.12

3

Diff

eren

ce in

Qui

t Rat

es, L

evel

s

Diff

eren

ce in

Qui

t Rat

es A

s a

Fra

ctio

n o

f S

ampl

e A

vera

ge Q

uit R

ate

Wei

ghts

Sam

ple

Res

tric

tion

N

Est

ablis

hmen

t Qui

ts in

Res

pons

e to

a O

ne S

tand

ard

Dev

iatio

n D

ecre

ase

in R

even

ue G

row

th, A

vera

ge W

age

Rig

idity

ve

rsus

No

Wag

e R

igid

ity, a

s a

Fra

ctio

n o

f Sam

ple

Av

erag

e Q

uit R

ate

-0.0

18

-0.1

93

No

. of E

mpl

oye

es

Min

. 20

Em

plo

yees

9,2

30

(1)

N/A

N/A

N/A

N/A

(3)

(4)

(5)

-0.0

18

No

. of E

mpl

oye

es

Min

. 20

Em

plo

yees

9,2

30

(2)

-0.1

96

-0.1

96

0.0

25

0.0

42

Uni

t of o

bser

vatio

n is

est

ablis

hmen

t-ye

ar. W

age

rigid

ity is

cal

cula

ted

as

des

crib

ed in

sec

tion

3, a

nd

is fi

xed

by

esta

blis

hmen

t ove

r sa

mpl

e pe

riod

Est

abl

ishm

ent c

hara

cter

istic

s in

clud

e a

set o

f co

ntro

ls f

or

the

med

ian

year

-ove

r-ye

ar w

age

chan

ge,

occ

upat

iona

l mix

and

dum

mie

s fo

r se

cto

r, fe

der

al s

tat

e, a

nd e

stab

lishm

ent s

ize.

Ind

ivid

ual c

hara

cter

istic

s in

clud

e fr

actio

n fe

mal

e an

d c

ont

rols

for

wo

rke

rs' e

duc

atio

n. P

osi

tive

reve

nue

gro

wth

is d

efin

ed a

s th

e ye

ar-o

ver-

year

per

cent

age

chan

ge in

re

venu

es w

hen

reve

nue

gro

wth

is p

osi

tive

and

zer

o o

ther

wis

e. N

egat

ive

reve

nue

gro

wth

is d

efin

ed a

s th

e y

ear-

ove

r-ye

ar p

erce

ntag

e ch

ange

in r

even

ues

whe

n re

venu

e gr

ow

th is

neg

ativ

e an

d z

ero

oth

erw

ise.

All

regr

essi

ons

co

ver

the

perio

d 1

99

7 to

2

00

3.

Pre

dic

ted

Qui

t Rat

e A

sso

ciat

ed W

ith O

ne

Sta

ndar

d D

evia

tion

Neg

ativ

e R

even

ue G

row

th0

.02

80

.04

40

.00

00

.02

60

.01

6

No

. of E

mpl

oye

es

Min

. 20

Em

plo

yees

-0.0

16

-0.0

25

No

neN

one

Min

. 22

0 E

mpl

oye

esM

ax. 2

19

Em

plo

yees

-0.0

12

9,2

30

4,6

08

4,6

22

Neg

ativ

e R

even

ue G

row

th, O

ne S

tand

ard

D

evia

tion

of S

ampl

e-0

.19

6-0

.19

6-0

.19

6-0

.19

6-0

.21

5-0

.21

5

0.0

28

-0.1

73

-0.2

51

-0.0

96

-0.1

93

33

Table 5A: Wage Rigidity and Hires – Regression Results

(1) (2) (3) (4) (5)

Wage Rigidity -0.053 -0.059 -0.053 -0.048 -0.033

(0.015) (0.014) (0.015) (0.021) (0.021)

Positive Revenue Growth 0.048 0.103 0.157 0.235

(0.014) (0.019) (0.026) (0.035)

Negative Revenue Growth 0.025 0.106 0.119 0.001

(0.025) (0.036) (0.051) (0.055)

Wage Rigidity x Positive Revenue Growth -0.261 -0.335 -0.321

(0.064) (0.080) (0.094)

Wage Rigidity x Negative Revenue Growth -0.362 -0.287 -0.088

(0.116) (0.148) (0.152)

Work Council -0.115 -0.115 -0.115 -0.112 -0.123

(0.010) (0.010) (0.010) (0.013) (0.010)

Establishment Characteristics Yes Yes Yes Yes Yes

Individual Characteristics Yes Yes Yes Yes Yes

Year Dummies Yes Yes Yes Yes Yes

WeightsNo. of

EmployeesNo. of

EmployeesNo. of

EmployeesNone None

Sample RestrictionMin. 20

EmployeesMin. 20

EmployeesMin. 20

EmployeesMin 220

EmployeesMax. 219

Employees

R-squared 0.639 0.637 0.639 0.647 0.310N 9,230 9,230 9,230 4,608 4,622

Dependent Variable

Standard errors in parentheses. Unit of observation is establishment-year. Wage rigidity is calculated as described in section 3, and is fixed by establishment over sample period Establishment characteristics include a set of controls for the median year-over-year wage change, occupational mix and dummies for sector, federal state, and establishment size. Individual characteristics include fraction female and controls for workers' education. Positive revenue growth is defined as the year-over-year percentage change in revenues when revenue growth is positive and zero otherwise. Negative revenue growth is defined as the year-over-year percentage change in revenues when revenue growth is negative and zero otherwise. All regressions cover the period 1997 to 2003.

Hires as a Percentage of Establishment Workforce

34

Table 5B: Wage Rigidity and Hires – Economic Interpretation

(a)

(b)

(a)

(b)

(a)

(b)

(a)

(b)

(a)

(b)

Wa

ge R

igid

ity L

eve

l0.

245

0.00

00.

245

0.00

00.

245

0.00

00.

255

0.00

00.

223

0.00

0(S

am

ple

Ave

rage

)(S

am

ple

Ave

rage

)(S

am

ple

Ave

rage

)(S

am

ple

Ave

rage

)(S

am

ple

Ave

rage

)

Hire

Ra

te,

Sa

mpl

e A

vera

ge0.

172

0.17

20.

172

0.17

20.

172

0.17

20.

194

0.19

40.

242

0.24

2

Diff

ere

nce

in H

ire R

ate

s, L

eve

ls

Diff

ere

nce

in H

ire R

ate

s A

s a

Fra

ctio

n of

Sa

mpl

e

Ave

rage

Qui

t R

ate

We

ight

s

Sa

mpl

e R

est

rictio

n

N

-0.0

75

No.

of E

mpl

oye

es

Min

. 20

Em

ploy

ee

s

/

Est

abl

ishm

ent

Hire

s in

Re

spon

se t

o a

One

Sta

nda

rd D

evi

atio

n In

cre

ase

in R

eve

nue

Gro

wth

, A

vera

ge W

age

Rig

idity

ve

rsus

No

Wa

ge R

igid

ity,

as

a F

ract

ion

of S

am

ple

Av

era

ge H

ire R

ate

N/A

N/A

N/A

N/A

-0.0

13

-0.0

84

No.

of E

mpl

oye

es

Min

. 20

Em

ploy

ee

s

9,23

0

-0.0

23

Ma

x. 2

19 E

mpl

oye

es

-0.0

26-0

.029

-0.1

48-0

.150

-0.0

94

9,23

04,

608

4,62

2

-0.0

050.

009

-0.0

14

0.05

0

Uni

t of

obs

erv

atio

n is

est

abl

ishm

ent

-ye

ar.

Wa

ge r

igid

ity is

ca

lcul

ate

d a

s de

scrib

ed

in s

ect

ion

3, a

nd

is fi

xed

by e

sta

blis

hme

nt o

ver

sam

ple

pe

riod

Est

abl

ishm

ent

cha

ract

eris

tics

incl

ude

a s

et

of c

ontr

ols

for

the

me

dia

n ye

ar-

ove

r-ye

ar

wa

ge c

hang

e,

occu

patio

nal m

ix a

nd d

umm

ies

for

sect

or,

fede

ral s

ta

te,

and

est

abl

ishm

ent

siz

e.

Indi

vidu

al c

hara

cte

ristic

s in

clud

e fr

act

ion

fem

ale

and

con

trol

s fo

r w

orke

rs' e

duca

tion.

Pos

itive

re

venu

e g

row

th is

de

fine

d a

s th

e y

ea

r-ov

er-

yea

r pe

rce

nta

ge c

hang

e in

re

venu

es

whe

n re

venu

e g

row

th is

pos

itive

and

ze

ro o

the

rwis

e.

Ne

gativ

e r

eve

nue

gro

wth

is d

efin

ed

as

the

ye

ar-

ove

r-ye

ar

perc

ent

age

cha

nge

in r

eve

nue

s w

hen

reve

nue

gro

wth

is n

ega

tive

and

ze

ro o

the

rwis

e.

All

regr

ess

ions

cov

er

the

pe

riod

1997

to

2003

.

Pre

dict

ed

Hire

Ra

te A

ssoc

iate

d w

ith O

ne

Sta

nda

rd D

evi

atio

n P

ositi

ve R

eve

nue

Gro

wth

-0.0

050.

020

0.00

20.

031

0.02

8

No.

of E

mpl

oye

es

Non

eN

one

Min

. 20

Em

ploy

ee

sM

in.

220

Em

ploy

ee

s

Pos

itive

Re

venu

e G

row

th,

One

Sta

nda

rd

De

via

tion

of S

am

ple

0.19

60.

196

0.19

6

(2)

(3)

(4)

(5)

0.19

60.

196

0.19

60.

215

0.21

5

(1)

35

Table 6: Model Paremeter Values

Parameter Description Value Sourceα Returns to Scale in Production .65 Labor’s Share of Value Added

δ Average Quit Rate .092 Average Sample Quit Ratew Average Daily Wage 89.1 Average Sample Wageγ Wage Elasticity of Quit Rate 5.75 Empirical Regression

ln z Average Establishment-Wide Productivity 5.47x103 Empirical Regressionψz Persistence of Establishment-Wide Productivity .312 Empirical Regressionσ2z Variance of Establishment-Wide Productivity Shock .18 Empirical Regressionu Worker Type Productivity 1 Normalizationψu Persistence of Worker Type Productivity .789 Calibrationσ2u Variance of Worker Type Productivity Shock .626 Calibrationcl Firing Cost 0 Choiceφ1 Linear Hiring Cost 156.1 Calibrationφ2 Quadratic Hiring Cost 408.1 Calibrationλ0 Menu Cost of Downward Wage Adjustment .802 Calibrationλ1 Linear Cost of Downward Wage Adjustment .152 Choiceλ2 Quadratic Cost of Downward Wage Adjustment 0 Choice

Table 7: Calibration Moments

Moment Sample Value Simulated ValueIncrease in Layoff Rate Associated with Wage Rigidity 0.008 0.004

Average Hire Rate 0.172 0.128Average Wage Rate 89.1 90.7

Standard Deviation of Percentage Wage Change 0.08 0.07Measured Level of Wage Rigidity 0.245 0.273

Average Establishment Size 549 517Ratio of Magnitudes of Negative and Positive Wage Changes 0.83 0.78

36

Figure 1A: Illustration of Wage Rigidity Estimator

37

Figure 1B: Illustration of Wage Rigidity Estimator

38

Figure 1C: Illustration of Wage Rigidity Estimator

39

Figure 1D: Illustration of Wage Rigidity Estimator

40

Figure 2: Establishment Policy Functions with No Wage Rigidity

Stu

den

t V

ersi

on

of

MA

TL

AB

41

Figure 3: Wage Change Distributions with No Wage Rigidity

-0.2

00.

205101520253035

Relative Frequency of Wage Change

-0.2

00.

205101520253035

-0.2

00.

205101520253035

-0.2

00.

205101520253035

-0.2

00.

205101520253035

-0.2

00.

205101520253035

Relative Frequency of Wage Change

-0.2

00.

205101520253035

-0.2

00.

205101520253035

Wag

e C

hang

e, P

erce

nt-0

.20

0.2

05101520253035

-0.2

00.

205101520253035

Stu

den

t V

ersi

on

of

MA

TL

AB

42

Figure 4: Establishment Policy Functions with Wage Rigidity

Stu

den

t V

ersi

on

of

MA

TL

AB

43

Figure 5: Wage Change Distributions with Wage Rigidity

-0.2

00.

205101520253035

Relative Frequency of Wage Change

-0.2

00.

205101520253035

-0.2

00.

205101520253035

-0.2

00.

205101520253035

-0.2

00.

205101520253035

-0.2

00.

205101520253035

Relative Frequency of Wage Change

-0.2

00.

205101520253035

-0.2

00.

205101520253035

Wag

e C

hang

e, P

erce

nt-0

.20

0.2

05101520253035

-0.2

00.

205101520253035

Stu

den

t V

ersi

on

of

MA

TL

AB

44

Figure 6: Simulated Moments with Different Levels of Wage Rigidity

00.

20.

40.

60.

81

0.2

0.250.3

0.350.4

0.450.5

Wage

Rig

idity

Sca

leFact

or

Fraction of Periods with Wage Cut

Pan

el A

: Wag

e C

uts

00.

20.

40.

60.

81

0

0.00

5

0.01

0.01

5

0.02

0.02

5

0.03

0.03

5

Wage

Rig

idity

Sca

leFact

or

Average Layoff Rate

Pan

el B

: Lay

offs

00.

20.

40.

60.

81

0.17

0.18

0.190.2

0.21

0.22

Wage

Rig

idity

Sca

leFact

or

Average Quit Rate

Pan

el C

: Qui

ts

00.

20.

40.

60.

81

0.20

8

0.21

0.21

2

0.21

4

0.21

6

0.21

8

0.22

0.22

2

0.22

4

Wage

Rig

idity

Sca

leFact

or

Average Hire Rate

Pan

el D

: Hire

s

Stu

den

t V

ersi

on

of

MA

TL

AB

45

Appendix

A Simple Analytics of the Establishment Decision Making Modelwith Wage Rigidity

This section provides the simple analytics of the partial equilibrium, estbalishment decision mak-ing model with wage rigidity proposed in section 2 and calibrated in section 7. The model insections 2 and 7 contains J heterogeneous worker types within a representative establishment. Forsimplicity, however, the analytical results of this section will suppress the J worker types and solvethe establishment’s problem as if workers are homogenous. Since each of the worker types, j, insections 2 and 7 solve identical dynamic optimization problems, the analytical results presentedhere will be mostly identical24 to the dynamic optimization problem solved by each worker type, jin sections 2 and 7.

As discussed in section 2, the infinitely-lived, representative establishment uses one input ofproduction, labor, and maximizes the discounted stream of expected per period profits,

Π = pnα − wn− ch(h, n−1)h− c``− g(w,w−1)n

where n is the stock of labor used in production, α governs returns to scale in production, w is thewage rate labor, h and ` are the number of employees the establishment hires and lays off, and ch(·)and c` are costs of hiring and layoffs of labor, respectively. g(·) is the cost of wage adjustment forlabor, while p shifts the marginal revenue product of labor. p may be conceptualized as either thelevel of labor productivity or the level of its output price; for concreteness, as in sections 2 and 7,this section refers to p as productivity. The establishment is assumed to be concerned exclusivelywith real payoffs, and all variables above are specified in real terms. The rate of price inflationenters the model through the cost of wage adjustments function as described below.

As decribed in section 2.2, the establishment chooses the current wage rate, w, level of hires,h, and level of layoffs, `, to solve the following dynamic optimization problem:

V (p, w−1, n−1) = maxw,h,l

pnα − wn− ch(h, n−1)h− c``

−g(w,w−1)n+ βE [V (p′, w, n)] (A.1)

24The only difference between the optimzation problem solved in sections 2 and 7 and that solved in AppendixA comes in the form of the prodctivity process. With heterogeneous workers types, each worker type, j, has aproductivity process, uj , that interacts with an establishment-level productivity process, z, to give overall workerproductivity, pj . Since all workers are homogenous in this section, overall worker productivity will be p across allworkers. Accordingly, this section only models a productivity process, p, and makes no mention to processes z and u.This simplification does not affect the results.

i

subject to

ln p = (1− ψp) ln p+ ψ ln p−1 + εp, εp ∼ N(0, σ2

p

)(A.2)

n = (1− δ (w))n−1 + h− 1+` (A.3)

g (w,w−1) = λ01(1+π)w<w−1 + λ1 (w−1 − (1 + π)w)1(1+π)w<w−1

+λ2 (w−1 − (1 + π)w)2 1(1+π)w<w−1 (A.4)

where (A.2) is the establishment’s productivity process, which evolves according to a mean-reverting, AR (1) process with error term, εp, (A.3) is the labor stock equation of motion, and(A.4) is the cost function of cutting wages facing the establishment and is how downward wagerigidity enters the model.

Recall from section 2.1, the paramterized functional form of the quit rate of labor is

δ (w) = δ(ww

)−γ, γ > 0

where δ is the economy-wide average quit rate, and γ governs the degree of competition in thelabor market: as γ increases, the quit rate becomes more sensitive to wages. The establishmentalso faces quadratic costs of hiring labor, given by

ch(h, n−1) = φ1

(h

n−1

)+ φ2

(h

n−1

)2

which allows for increasing or decreasing returns to scale.The analytics of the estbalishment decision making model under wage rigidity on around the

wage cutting cost function, g (·), in (A.4). Note that (A.4) only takes a non-zero value when theestablishment cuts the nominal wage from the previous period (i.e. when (1 + π)w < w−1) andzero everywhere else. Thereoreg (·) is not a smooth function with a kink at the zero wage changeand not differentiable when (1 + π)w = w−1. It follows that the derivative of g (·) with respect tothe current period wage rate, w, takes the following piecewise form:

∂g (w,w−1)

∂w=

0 if (1 + π)w > w−1

undefined if (1 + π)w = w−1

−(

1 + π)[λ1 + 2λ2

(w−1 − (1 + π)w

)]if (1 + π)w < w−1

(A.5)

The intuition from (A.5) is straightforward: If the establishment rasies the workers’ wages, thenno cost of wage adjustment is incurred. If the establishment cuts the workers’ wages, then the costof wage adjustment increases linearly in λ1 and increases quadratically in λ2.

Similarly crucial to the analytics is how the labor stock equation of motion, (A.3), changes as

ii

the current period wage rate, w, changes. Differentiating (A.3) with resprect to w yields

∂n (w, h)

∂w= −∂δ (w)

∂wn−1

= −[(−γ) δ

(ww

)−γ−1( 1

w

)]n−1

=( γw

)δ(ww

)−γ (ww

)n−1

∂n (w, h)

∂w=

( γw

)δ (w)n−1 > 0 (A.6)

That is, the evolution of the establishment’s labor stock depends positively on the wage rate. Asthe current period’s wage rate increases, the number of quits in the current period (as a fractionof the end of the previous period’s employment, n−1) falls, and the establishment retains a largerportion of its workforce. The term,

(γw

), in (A.6) captures the effect that the establishment’s

competitiveness in the labor market has on the evolution of the labor stock: as the establishmentbecomes more competitive, it will retain more of its workers.

Since the model is a discrete choice problem, the establishment will never find it optimal toboth hire workers and lay off workers in the same period.25 Therefore, the analysis of this sectionis partitioned into five distinct cases: Case 1 presents the case of no layoffs and wage increases(` = 0, g (·) = 0). Case 2 presents the case with no layoffs and wage cuts (` = 0, g (·) > 0). Case3 presents the case of no layoffs and wages unchanged (` = 0, g (·) = 0, ∂g(·)

∂wis undefined). Case

4 presents the case of layoffs and wages unchanged ((` > 0, h = 0, g (·) = 0, ∂g(·)∂w

is undefined).Case 5 presents the case of layoffs and wage cuts (` > 0, h = 0, g (·) > 0).26

A.1 Case 1: No Layoffs, Wage Increases (` = 0, g (w,w−1) = 0)In the case of no layoffs (` = 0) and wage increases, (A.1) becomes

V (p, w−1, n−1) = maxw,h

pnα − wn− ch(h, n−1)h+ βE [V (p′, w, n)] (A.7)

The establishment chooses the current wage rate, w, and the level of hires, h, to solve its dynamicoptimization problem. Further, ` = 0 implies that the labor stock equation of motion constraint,(A.3), becomes

n = (1− δ (w))n−1 + h (A.8)

so that the current period labor stock, n, is simply the number of workers retained from the previousperiod plus the number of workers hired.

25The model presented in sections 2 and 7 achieves both hires and layoffs in the same period through the heteroge-neous J worker types. Distinct worker types experience hires and layoffs, but a single group worker type, j, will neverexperince both hires and layoffs in a given period.

26There is not a sixth case where an establishment both lays off workers and increases the wage. For an establish-ment that is laying off workers, wages must be less than or equal to w−1, as there is no need to keep wages high torecruit and keep workers while the establishment actively reduces its workforce. Therefore, an establishment layingoff workers must either keep wages unchanged or reduce wages in the model.

iii

Solving the establishment’s dynamic optimization problem yields the following first order con-dition with respect to the wage rate, w:

∂V

∂w: αpnα−1

∂n

∂w− n− w ∂n

∂w+ βE

[∂V ′

∂w

]= 0

: αpnα−1( γw

)δ (w)n−1 − n− w

( γw

)δ (w)n−1 + · · ·

βE

[∂V ′

∂ (p′n′α)

∂ (p′n′α)

∂n′∂n′

∂n

∂n

∂w+

∂V ′

∂ (w′n′)

∂ (w′n′)

∂n′∂n′

∂n

∂n

∂w+ · · ·

∂V ′

∂ch (h′, n)

∂ch (h′, n)

∂n

∂n

∂w+

∂V ′

∂ (g (w′, w)n′)

∂ (g (w′, w)n′)

∂w

]= 0

: αpnα−1( γw

)δ (w)n−1 − n− w

( γw

)δ (w)n−1 + · · ·

βE

[∂V ′

∂ (p′n′α)

∂ (p′n′α)

∂n′∂n′

∂n

∂n

∂w− w∂n

′

∂n

∂n

∂w+

∂V ′

∂ch (h′, n)

∂ch (h′, n)

∂n

∂n

∂w− · · ·

(n′∂g (w′, w)

∂w+ g (w′, w)

∂n′

∂n

∂n

∂w

)]= 0

: αpnα−1( γw

)δ (w)n−1 + · · ·

∂n

∂wβE

[∂V ′

∂ (p′n′α)

∂ (p′n′α)

∂n′∂n′

∂n+

∂V ′

∂ch (h′, n)

∂ch (h′, n)

∂n

]= · · ·

n+ γδ (w)n−1 + · · ·∂n

∂wβE

[(w′ + g (w′, w)

)∂n′∂n

]+ β

[n′∂g (w′, w)

∂w

]∂V

∂w: αpnα−1

( γw

)δ (w)n−1 + · · ·( γ

w

)δ (w)n−1βE

[αp′n′

α−1(

1− δ (w′))

+ φ1

(h′

n

)2

+ 2φ2

(h′

n

)3]

= · · ·

n+ w( γw

)δ (w)n−1 + · · ·( γ

w

)δ (w)n−1βE

[(w′ + g (w′, w)

)(1− δ (w′)

)]+ βE

[n′∂g (w′, w)

∂w

](A.9)

where

g (w′, w)

0 if (1 + π)w′ ≥ w

λ0 + λ1

(w + (1 + π)w′

)+ λ2

(w − (1 + π)w′

)2if (1 + π)w′ < w

(A.10)

iv

and

∂g (w′, w)

∂w

0 if (1 + π)w′ > w

undefined if (1 + π)w′ = w[λ1 + 2λ2

(w − (1 + π)w′

)]> 0 if (1 + π)w′ < w

(A.11)

The first order condition in (A.9) implies that the establishment sets the wage so that the marginalbenefit of the wage change equals the marginal cost. The left-hand side of (A.9) shows the marginalbenefit of a wage increase to the establishment. The first term on the left-hand side of (A.9) is theextra output associated with retaining more workers from a wage increase induced lower quit rate.The second term on the left-hand side of (A.9) is the continuation value of the extra output fromthose workers in future periods. An increase in the wage lowers this periods quit rate, and theestablishment carries those workers into the future period. Those workers produce output in thefuture period if the future wage rate, w′, does not induce those workers to quit in the future period.The third term on the left-hand side of (A.9) is the continuation value of the current period’s wageincrease on future hiring costs. Increasing wages today increases the establishment’s stock of labor,n, through reducing quits and carries that stock into the future period. A larger stock of labor, n,carried into the future period reduces the future period’s hiring costs, c (h′, n), as hiring costs aredecreasing in the stock of labor.

The right-hand side of (A.9) shows the marginal cost of a wage increase to the establishment.The first two terms on the right-hand side of (A.9) show the establishment’s total cost, this period,of the wage increase, as the establishment now pays all workers a higher wage. The second termon the right-hand side of (A.9) is the continuation cost of increasing wages today in the formof future wage costs. Increasing wages in the current period reduces the current period quit rateand increases the stock of labor, n, the establishment brings into the future period. When the wageincreases in the current period, fewer workers quit and the establishment’s stock of labor, n, carriedinto the future period increases. Of those workers who do not quit in the future given the futurewage, w′, the establishment pays them w′ and must pay g (w′, w) from (A.10) if the establishmentcuts the nominal wage from the current period to the future period. If the nominal wage changefrom the current to the future period is zero or positve, then g (w′, w) is zero as shown in (A.10),and the establishment only pays the wage rate, w′, to those workers in the future.

The third and final term on the right-hand side of (A.9) is the continuation cost of increasingwages today in the form of future costs to cutting wages that increasing the wage in the currentperiod imposes on the establishment in the future. The per worker cost of cutting wages in thefuture period, g (w′, w), is weakly increasing the the current period’s wage, w, as shown in (A.11).If the establishment finds itself in a future productivity state that requires a wage cut, the cost ofcutting the wage in the future period will be greater if the establishment increases the wage todaythan if the establishment did not increase the wage today. This term represents the Elsby (2007)effect of wage rigidity: forward-looking establishments will dampen wage increases in the currentperiod knowing that the establishment will have to pay a future cost of cutting wages in responseto a future adverse shock.

v

The first order condition with respect to hires, h, yields

∂V

∂h: αpnα−1

∂n

∂h− w∂n

∂h−[ch (h, n−1) +

∂ch (h, n−1)

∂hh

]+ βE

[∂V ′

∂h

]= 0

: αpnα−1 − w −

[φ1

(h

n−1

)+ φ2

(h

n−1

)2

+ φ1

(h

n−1

)+ 2φ2

(h

n−1

)2]

+ · · ·

βE

[∂V ′

∂ (p′n′α)

∂ (p′n′α)

∂n′∂n′

∂n

∂n

∂h+

∂V ′

∂ (w′n′)

∂ (w′n′)

∂n′∂n′

∂n

∂n

∂h+ · · ·

∂V ′

∂ (ch (h′, n)h′)

∂ (ch (h′, n)h′)

∂n

∂n

∂h+ · · ·

∂V ′

∂ (g (w′, w)n′)

∂ (g (w′, w)n′)

∂n′∂n′

∂n

∂n

∂h

]= 0

: αpnα−1 − w −

[2φ1

(h

n−1

)+ 3φ2

(h

n−1

)2]

+ · · ·

βE

[αp′n′

α−1[1− δ (w′)

]− w′

[1− δ (w′)

]− · · ·[

−φ1

(h′

n

)2

− 2φ2

(h′

n

)3]− g (w′, w)

[1− δ (w′)

]]= 0

∂V

∂h: αpnα−1 + βE

[αp′n′

α−1[1− δ (w′)

]+ φ1

(h′

n

)2

+ 2φ2

(h′

n

)3]

= · · ·

w +

[2φ1

(h

n−1

)+ 3φ2

(h

n−1

)2]

+ βE

[[w′ + g (w′, w)

][1− δ (w′)

]](A.12)

where ∂n∂h

= 1. The first order condition in (A.12) implies that the establishment will recruitworkers to the point where the marginal benefit of the hires equals the marginal cost. The left-hand side of (A.12) shows the marginal benefit of the hires. The first term is the extra outputproduced by the hired workers in the current period, and the second term is continuation valueof the hires through reducing the total hiring costs in the future. The right-hand side of (A.12)shows the marginal costs of the hires. The first term on the right-hand side of (A.12) is the costthe establshment incurs in the form of wages to employ the hires, whereas the second term is thehiring costs incurred by the establishment to hire the new workers.

vi

A.2 Case 2: No Layoffs, Wage Cuts (` = 0, g (w,w−1) > 0)When the establishment cuts wages but does not lay off workers, it incurs a cost g (w,w−1). Thus,the value function takes the form

V (p, w−1, n−1) = maxw,h

pnα − wn− ch(h, n−1)h

−g (w,w−1)n+ βE [V (p′, w, n)] (A.13)

The establishment chooses the current wage rate, w, and the level of hires, h, to solve its dynamicoptimization problem. Since ` = 0 as in section A.1.1, the labor stock equation of motion remainsas stated in (A.8).

Solving the establishment’s dynamic optimization problem in the case of wage cuts yields thefollowing first order condition with respect to the wage rate, w:

∂V

∂w: αpnα−1

∂n

∂w− n− w ∂n

∂w−(∂g (w,w−1)

∂wn+ g (w,w−1)

∂n

∂w

)+ βE

[∂V ′

∂w

]: αpnα−1

( γw

)δ (w)n−1 − n− w

( γw

)δ (w)n−1 − · · ·[

−(

1 + π)[λ1 + 2λ2

(w−1 − (1 + π)w

)]n− g (w,w−1)

( γw

)δ (w)n−1

]+ · · ·

βE

[∂V ′

∂ (p′n′α)

∂ (p′n′α)

∂n′∂n′

∂n

∂n

∂w+

∂V ′

∂ (w′n′)

∂ (w′n′)

∂n′∂n′

∂n

∂n

∂w+ · · ·

∂V ′

∂ch (h′, n)

∂ch (h′, n)

∂n

∂n

∂w+

∂V ′

∂ (g (w′, w)n′)

∂ (g (w′, w)n′)

∂w

]= 0

∂V

∂w: αpnα−1

( γw

)δ (w)n−1 + (1 + π)

[λ1 + 2λ2 (w−1 − (1 + π)w)

]n+ · · ·( γ

w

)δ (w)n−1βE

[αp′n′

α−1(

1− δ (w′))

+ φ1

(h′

n

)2

+ 2φ2

(h′

n

)3]

= · · ·

n+[w + g (w,w−1)

] ( γw

)δ (w)n−1 + · · ·( γ

w

)δ (w)n−1βE

[(w′ + g (w′, w)

)(1− δ (w′)

)]+ βE

[n′∂g (w′, w)

∂w

](A.14)

The intuition for (A.14) is similar to (A.9) in that the establishment will cut wages up until thepoint where the marginal cost of cutting wages equals the marginal benefit. The left-hand sideof (A.14) shows the marginal cost to the establishment of cutting wages. The first term on theleft-hand side of (A.14) represents the loss of output for the establishment as a result of a wagecut induced increase in quits. The second term on the left-hand side of (A.14) is the marginal costthe establishment pays in order to execute the wage cut for all workers, n. The third and finalterm on the left-hand side of (A.14) represents the continuation cost of the wage cut. As wageinduced quits increase this period, the establishment enters the next period with fewer workers, allelse equal. If the establishment experiences a high productivity state in the future, it will have to

vii

hire more workers to meet the labor needs of the high prouctivity state than if workers never quitoriginially. The additional hires lead to additional hiring costs.

The right-hand side of (A.14) shows the marginal benefit to the establishment of cutting wages.The first term on the right-hand side, n, is the number of workers in the current period that takea wage cut and thus represents the decrease in the establishment’s wage bill from all employedworkers. The second term on the right-hand side represents the decrease in the establishment’swage bill as a result of the wage cut induced quits. For the workers that quit, the establishment nolonger has to pay the wage rate, w, nor does the estbalishment have to pay the cost associated withcutting those workers’ wages. The final term on the right-hand side of (A.14) is the continuationvalue to the establishment for cutting wages this period. If the establishment cuts wages this period,it reduces the cost the establishment will pay in the future if it chooses to reduce future wages.

The first order condition with respect to hires, h, in the case of wage cuts yields

∂V

∂h: αpnα−1

∂n

∂h− w∂n

∂h−[ch (h, n−1) +

∂ch (h, n−1)

∂hh

]− g (w,w−1)

∂n

∂h+ · · ·

βE

[∂V ′

∂h

]= 0

: αpnα−1 − w −

[2φ1

(h

n−1

)+ 3φ2

(h

n−1

)2]− g (w,w−1) + · · ·

βE

[∂V ′

∂ (p′n′α)

∂ (p′n′α)

∂n′∂n′

∂n

∂n

∂h+

∂V ′

∂ (w′n′)

∂ (w′n′)

∂n′∂n′

∂n

∂n

∂h+ · · ·

∂V ′

∂ (ch (h′, n)h′)

∂ (ch (h′, n)h′)

∂n

∂n

∂h+ · · ·

∂V ′

∂ (g (w′, w)n′)

∂ (g (w′, w)n′)

∂n′∂n′

∂n

∂n

∂h

]= 0

∂V

∂h: αpnα−1 + βE

[αp′n′

α−1[1− δ (w′)

]+ φ1

(h′

n

)2

+ 2φ2

(h′

n

)3]

= · · ·

w + g (w,w−1) +

[2φ1

(h

n−1

)+ 3φ2

(h

n−1

)2]

+ · · ·

βE

[[w′ + g (w′, w)

][1− δ (w′)

]](A.15)

The left-hand side of (A.15) is the marginal benefit to the establishment for hiring, and the intuitionof the marginal benefit is the same as discussed with (A.12). The right-hand side of (A.15) is themarginal cost to the establishment for hiring workers. The intuition for the marginal cost of hiringis again the same as discussed with (A.12) with one exception: the marginal cost of hiring nowcontains an additional term, g (·), for the cost of cutting the hired workers’ wages.

viii

A.3 Case 3: No Layoffs, Wages Unchanged (` = 0, g (w,w−1) = 0)In the case of no layoffs and wages unchanged (w = w−1), the value function is the same as(A.7) in case 1. However, a wage first order condition does not exist when wages are unchanged.The function, g (w,w−1), is not smooth at w−1 and, thus, not differentiable. Therefore, the profitfunction is not differentiable in w at w−1. The hires first order condition is unchanged from (A.12)in case 1, and the intuition remains the same.

A.4 Case 4: Layoffs, Wages Unchanged (` > 0,h = 0, g (w,w−1) = 0)In the case of layoffs (` > 0) and no wage cuts from w−1, it must be the case that w = w−1 (wagesunchanged) and h = 0. When laying off workers, the establishment has no need to keep wageshigh to recruit workers and keep employees. Therefore, (A.1) becomes

V (p, w−1, n−1) = maxw,h

pnα − wn− c``+ βE [V (p′, w, n)] (A.16)

where g (w,w−1) = 0 since wages are unchanged fromw−1. The establishment chooses the currentwage rate, w, and the level of layoffs, `, to solve its dynamic optimization problem. Further, ` > 0and h = 0 imply that the labor stock equation of motion constraint, (A.3), becomes

n = (1− δ (w))n−1 − ` (A.17)

so that the current period labor stock, n, is simply the number of workers retained from the previousperiod less the number of workers the establishment lays off.

As in case 3, wages are unchanged (w = w−1), g (w,w−1) = 0, and ∂g(w,w−1)∂w

is undefininedat w−1. Therefore, the profit function is not differentiable at w−1 and a wage first order conditiondoes not exist.

The first order condition with respect to layoffs, `, yields

∂V

∂`: αpnα−1

∂n

∂`− w∂n

∂`− c` + E

[∂V ′

∂`

]= 0

: −αpnα−1 + w − c` + · · ·

βE

[∂V ′

∂ (p′n′α)

∂ (p′n′α)

∂n′∂n′

∂n

∂n

∂`+

∂V ′

∂ (w′n′)

∂ (w′n′)

∂n′∂n′

∂n

∂n

∂`+ · · ·

∂V ′

∂ (ch (h′, n)h′)

∂ (ch (h′, n)h′)

∂n

∂n

∂`+ · · ·

∂V ′

∂ (g (w′, w)n′)

∂ (g (w′, w)n′)

∂n′∂n′

∂n

∂n

∂`

]= 0

∂V

∂`: w + βE

[(w′ + g (w′, w)

)(1− δ (w′)

)]= αpnα−1 + c` + · · ·

βE

[αp′n′

α−1(

1− δ (w′))

+ φ1

(h′

n

)2

+ 2φ2

(h′

n

)3]

(A.18)

ix

where ∂n∂l

= −1.

A.5 Case 5: Layoffs, Wage Cuts (h = 0, g (w,w−1) > 0)In the case of layoffs (` > 0) and no wage cuts from w−1, it must be the case that w = w−1 (wagesunchanged) and h = 0. When laying off workers, the establishment has no need to keep wageshigh to recruit workers and keep employees. Therefore, (A.1) becomes

V (p, w−1, n−1) = maxw,h

pnα − wn− c``− g (w,w−1)n+ βE [V (p′, w, n)] (A.19)

where g (w,w−1) > 0 since the establishment cuts wages from w−1. The establishment choosesthe current wage rate, w, and the level of layoffs, `, to solve its dynamic optimization problem.Further, as in case 4 from section A.4, ` > 0 and h = 0 imply that the labor stock equation ofmotion constraint remains as is in (A.17), so that the current period labor stock, n, is simply thenumber of workers retained from the previous period less the number of workers the establishmentlays off.

Solving the establishment’s dynamic optimization problem in the case of wage cuts yields thesame first order condition with respect to the wage rate, w, as in (A.14) from case 2 in section A.2.

The first order condition with respect to layoffs, `, yields

∂V

∂`: αpnα−1

∂n

∂`− w∂n

∂`− c` − g (w,w−1)

∂n

∂`+ E

[∂V ′

∂`

]= 0

: −αpnα−1 + w − c` + g (w,w−1) + · · ·

βE

[∂V ′

∂ (p′n′α)

∂ (p′n′α)

∂n′∂n′

∂n

∂n

∂`+

∂V ′

∂ (w′n′)

∂ (w′n′)

∂n′∂n′

∂n

∂n

∂`+ · · ·

∂V ′

∂ (ch (h′, n)h′)

∂ (ch (h′, n)h′)

∂n

∂n

∂`+ · · ·

∂V ′

∂ (g (w′, w)n′)

∂ (g (w′, w)n′)

∂n′∂n′

∂n

∂n

∂`

]= 0

∂V

∂`: w + g (w,w−1) + βE

[(w′ + g (w′, w)

)(1− δ (w′)

)]= αpnα−1 + · · ·

c` + βE

[αp′n′

α−1(

1− δ (w′))

+ φ1

(h′

n

)2

+ 2φ2

(h′

n

)3]

(A.20)

where ∂n∂l

= −1.

B Sample RepresentativenessTo examine the representativeness of the sample for the West German economy, this appendixpresents the sample stratification of establishments across three dimensions and compare them tothe West German economy as a whole: sector, federal state, and size. Table 1, Panel A, shows

x

the fraction of establishments, by year, in each sector in both the sample and the West Germaneconomy as a whole. Table 1, Panel B, shows the fraction of establishments, by year, in eachfederal state in both the sample and the West German economy as a whole. Table 1, Panel C,shows the fraction of establishments, by year, broken down into 10 categories of establishmentsize by employees in both the sample and the West German economy as a whole. This measureuses the BHP employment statistics described in section 2.2, which contain employment statisticsfrom the 30th of June each year.

Lastly, Table 227 provides a breakdown of employment by broad occupation class, referredto as the Blossfeld Occupational classification system, for each sector, and shows the fraction ofemployees in each sector-Blossfeld occupation classification, averaged over the 1997 through 2003sample period.

C Monte Carlo Simulations of Wage Rigidity EstimatorThis section tests the performance of the estimator of wage rigidity proposed in section 3 usingMonte Carlo simulations. We simulate wage change distributions for 500 establishments facingdifferent levels of wage rigidity and generate the number of years’ worth of wage changes observedin the sample for each establishment as a random integer uniformly distributed between threeand seven. Next, we generate the number of employees per establishment as a random integeruniformly distributed between 15 and 500; the number of employees is fixed over the simulationperiod. For each establishment we generate the proportion of nominal wage cuts that will beprevented by downward nominal wage rigidity as a random variable uniformly distributed over theinterval [0, 1]: wri ∼ U [0, 1].

To simulate counterfactual nominally flexible wage change distributions for each establishment-year, begin by drawing the mean of the establishment-year wage change distribution from a nor-mal distribution with a mean of four percent and a standard deviation of four percent: µit ∼N(.04, .042). We draw the standard deviation of the counterfactual wage change distribution froma uniform distribution over the interval [0 .05]: σit ∼ U [0, .05]. We then draw the counterfactualflexible wage changes for each year from the normal distribution ∆ lnwcfijt ∼ N(µit, σ

2it), where

∆ lnwcfijt is the counterfactual flexible log wage change of individual j at establishment i from yeart− 1 to year t.

Wage rigidity is introduced by replacing proportion wri of the counterfactual negative wagechanges with positive wage changes that are distributed N(.001, .005) to allow for prevented wagecuts to result in wage changes that are not exactly equal to zero. Wage cuts are chosen to replacerandomly: there is no tendency for smaller wage cuts to be more likely to be prevented, for exam-ple. Finally, compression in the wage change distribution in the face of wage rigidity is introducedby multiplying counterfactual wage changes by a compression factor of 1− 0.5wri. That is, wagechanges at an establishment with no wage rigidity will not be affected by wage compression, whilewage changes at an establishment with 100 percent wage rigidity will be compressed by 50 percent.Introducing wage compression does not substantially change the simulation results.

The simulations use a reduced form method of simulating the wage change distributions inorder to test whether the estimator of wri provides unbiased estimates of the true wri in a setting in

27Currently omitted.

xi

which a constant fraction of counterfactual wage cuts are prevented by wage rigidity. In contrast,there is not a direct correspondence in the theoretical model presented in sections 5 and 7 betweenthe cost of wage adjustment parameters λ0, λ1, and λ2 and a fixed proportion of counterfactualwage cuts prevented.

Figure A displays the estimated and actual proportions of counterfactual wage cuts preventedby wage rigidity in these simulations. A regression of the form

wri = α + βwri + ui (A.21)

gives an estimate for α of 0.036 with a standard error of 0.024 and an estimate for β of 0.982 witha standard error of 0.041. Therefore, α and β are not statistically distinguishable from 0 and 1,respectively. We interpret these results as suggesting that this estimator of wage rigidity is likely tobe unbiased in this context. The standard error of the regression is 0.24, nearly equal in magnitudeto the standard deviation of the true amount of wage rigidity, which is 0.29. As discussed in themain text, this noise is likely to cause attenuation bias in the estimates of the relationship betweenwage rigidity and employment outcomes, meaning the true associations are likely to be larger thanestimated in this paper.

xii

Table 1: Sample Stratification Statistics

Panel A

1997 1998 1999 2000 2001 2002 2003 1997 1998 1999 2000 2001 2002 2003

Agriculture 0.025 0.021 0.017 0.010 0.011 0.014 0.016 0.030 0.030 0.032 0.032 0.031 0.031 0.032

Mining/Manufacturing 0.388 0.388 0.369 0.381 0.378 0.384 0.383 0.120 0.118 0.106 0.103 0.102 0.101 0.098

Energy/Water 0.028 0.025 0.021 0.014 0.012 0.014 0.016 0.002 0.002 0.002 0.002 0.002 0.002 0.002

Construction 0.044 0.047 0.048 0.053 0.047 0.044 0.044 0.118 0.117 0.102 0.100 0.098 0.096 0.093

Trade/Food Service 0.089 0.086 0.097 0.104 0.101 0.100 0.098 0.305 0.302 0.294 0.289 0.287 0.285 0.281

Transportation 0.035 0.034 0.033 0.036 0.032 0.028 0.024 0.050 0.049 0.047 0.047 0.047 0.046 0.046

Finance 0.068 0.067 0.063 0.054 0.054 0.056 0.056 0.022 0.023 0.024 0.024 0.024 0.024 0.024

Real Estate 0.065 0.060 0.058 0.061 0.063 0.060 0.063 0.137 0.141 0.175 0.181 0.185 0.186 0.188

Public Administration 0.222 0.233 0.252 0.244 0.256 0.256 0.258 0.134 0.135 0.124 0.124 0.126 0.128 0.129Administration 0.035 0.038 0.044 0.043 0.045 0.044 0.041 0.082 0.083 0.094 0.098 0.099 0.100 0.106

Panel B

1997 1998 1999 2000 2001 2002 2003 1997 1998 1999 2000 2001 2002 2003

Schleswig-Holstein 0.033 0.030 0.028 0.020 0.022 0.020 0.021 0.044 0.044 0.044 0.044 0.044 0.044 0.044

Hamburg 0.053 0.046 0.039 0.043 0.045 0.047 0.050 0.027 0.027 0.028 0.028 0.028 0.028 0.028

Lower Saxony 0.085 0.093 0.090 0.146 0.147 0.149 0.147 0.110 0.110 0.110 0.110 0.110 0.110 0.110

Bremen 0.025 0.021 0.017 0.036 0.040 0.016 0.017 0.009 0.009 0.009 0.009 0.009 0.009 0.009

North Rhine-Westphalia 0.276 0.264 0.260 0.236 0.234 0.241 0.243 0.242 0.243 0.242 0.243 0.244 0.244 0.245

Hesse 0.061 0.067 0.071 0.057 0.055 0.057 0.054 0.090 0.089 0.088 0.088 0.088 0.088 0.088

Rhineland-Palatinate 0.034 0.035 0.036 0.081 0.085 0.082 0.084 0.059 0.059 0.059 0.060 0.060 0.060 0.060

Baden-Wurttemberg 0.130 0.133 0.135 0.156 0.159 0.173 0.171 0.160 0.160 0.160 0.160 0.159 0.159 0.159

Bavaria 0.167 0.171 0.167 0.118 0.111 0.116 0.114 0.196 0.196 0.199 0.198 0.198 0.198 0.198

Saarland 0.025 0.021 0.018 0.012 0.012 0.014 0.017 0.015 0.015 0.015 0.015 0.015 0.015 0.015Berlin 0.110 0.119 0.139 0.093 0.090 0.086 0.083 0.047 0.047 0.046 0.046 0.046 0.046 0.045

Panel C

1997 1998 1999 2000 2001 2002 2003 1997 1998 1999 2000 2001 2002 2003

1 to 4 Employees 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.625 0.631 0.603 0.602 0.602 0.604 0.605

5 to 9 Employees 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.177 0.175 0.194 0.193 0.193 0.193 0.193

10 to 19 Employees 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.097 0.095 0.104 0.105 0.104 0.104 0.103

20 to 49 Employees 0.026 0.022 0.019 0.028 0.022 0.014 0.017 0.062 0.060 0.061 0.061 0.061 0.061 0.060

50 to 99 Employees 0.168 0.195 0.197 0.223 0.230 0.228 0.219 0.022 0.021 0.021 0.021 0.021 0.021 0.021

100 to 199 Employees 0.189 0.190 0.204 0.232 0.239 0.241 0.246 0.010 0.010 0.010 0.010 0.010 0.010 0.010

200 to 499 Employees 0.255 0.262 0.277 0.286 0.284 0.293 0.287 0.006 0.006 0.006 0.006 0.006 0.006 0.005

500 to 999 Employees 0.152 0.135 0.143 0.120 0.116 0.115 0.118 0.002 0.002 0.001 0.001 0.001 0.001 0.001

1,000 to 4,999 Employees 0.211 0.196 0.160 0.111 0.109 0.108 0.114 0.001 0.001 0.001 0.001 0.001 0.001 0.001

5,000-plus Employees 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Fraction of Establishments per Supersector, Sample Fraction of Establishments per Supersector, Economy

Fraction of Establishments per Federal State, Sample Fraction of Establishments per Federal State, Economy

Fraction of Establishments per Size Class, Sample Fraction of Establishments per Size Class, Economy

xiii

Figure A: Monte Carlo Simulations of Wage Rigidity Estimates-1-.50.51

0.2

.4.6

.81

(mea

n) w

r_am

t

(mea

n) w

r(m

ean)

wr_

amt

xiv