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Monopsony in Movers

The Elasticity of Labor Supply to Firm Wage Policies

Ihsaan Bassier, Arindrajit Dube and Suresh Naidu
Journal of Human Resources, April 2022, 57 (S) S50-s86; DOI: https://doi.org/10.3368/jhr.monopsony.0319-10111R1

Article Figures & Data

Figures

  • Changes in Hourly Wages across Job Separations for Firm Quartile-to-Quartile Transitions Notes: The legend indicates origin quartile to destination quartile, where quartiles are defined along the distribution of the average firm wage, using only workers who stay at the firm over the six-year period. The change in wage is shown for movers, who are defined as workers who make a between-firm job-to-job transition at any point during the period and are observed for at least nine consecutive quarters at the each firm before and after the move. The quarter of separation and the following quarter are omitted. This exercise is repeated for each six-year period (2000–2005, 2006–2011, and 2012–2017), the mover wage profiles are stacked, and the averages of the event quarter are plotted by quartile-transition categories.
    Figure 1

    Changes in Hourly Wages across Job Separations for Firm Quartile-to-Quartile Transitions

    Notes: The legend indicates origin quartile to destination quartile, where quartiles are defined along the distribution of the average firm wage, using only workers who stay at the firm over the six-year period. The change in wage is shown for movers, who are defined as workers who make a between-firm job-to-job transition at any point during the period and are observed for at least nine consecutive quarters at the each firm before and after the move. The quarter of separation and the following quarter are omitted. This exercise is repeated for each six-year period (2000–2005, 2006–2011, and 2012–2017), the mover wage profiles are stacked, and the averages of the event quarter are plotted by quartile-transition categories.

  • Separations and Firm Wage Effects Notes: The figure illustrates the split-sample approach using a control function. Residuals are calculated from a regression of own-sample firm effects on the complement-sample firm effects and used as a control in a regression of separations on own-sample firm effects. The plotted points show the binned scatter points of this latter regression (that is, depicting the partial correlation). The vertical axis is separations divided by mean separations such thatthe slope of the line represents the elasticity. The circles represent quantiles of the trimmed sample, which excludes the top and bottom 2.5 percent of the firm effects distribution. The diamonds represent quantiles of the excluded sample only, which we consider outliers. The trendline is a cubic polynomial fitted to the trimmed sample.
    Figure 2

    Separations and Firm Wage Effects

    Notes: The figure illustrates the split-sample approach using a control function. Residuals are calculated from a regression of own-sample firm effects on the complement-sample firm effects and used as a control in a regression of separations on own-sample firm effects. The plotted points show the binned scatter points of this latter regression (that is, depicting the partial correlation). The vertical axis is separations divided by mean separations such thatthe slope of the line represents the elasticity. The circles represent quantiles of the trimmed sample, which excludes the top and bottom 2.5 percent of the firm effects distribution. The diamonds represent quantiles of the excluded sample only, which we consider outliers. The trendline is a cubic polynomial fitted to the trimmed sample.

  • Binned Scatterplots of Separation and Firm-Component of Wages Notes: Panel A shows the first-stage relationship between Δln(wage i,t+1) and , where is the change in average firm wage for individual i at E-E separation date t – 1 compared to the intermediate firm at date t, and Δln(wage i,t+1) is (wage i,t+1) – (wage i,t–1). Panel B shows the relationship between separations and Δln(wage i,t+1), instrumenting by using a control function, that is, controlling for the residuals from a regression of Δln(wage i,t+1) on . Separation indicates the probability of separation from the intermediate firm. All specifications include fixed effects L(Historyi,t,d) corresponding to interacted event and calendar time by origin firm by worker tenure at origin firm (eight bins) by initial wage at the origin firm (eight bins), and are clustered at the level of origin firm by time. The sample consists of the first 16 quarters after initial separation from the origin firm. See text for sample construction.
    Figure 3

    Binned Scatterplots of Separation and Firm-Component of Wages

    Notes: Panel A shows the first-stage relationship between Δln(wage i,t+1) and Embedded Image, where Embedded Image is the change in average firm wage for individual i at E-E separation date t – 1 compared to the intermediate firm at date t, and Δln(wage i,t+1) is (wage i,t+1) – (wage i,t–1). Panel B shows the relationship between separations and Δln(wage i,t+1), instrumenting by Embedded Image using a control function, that is, controlling for the residuals from a regression of Δln(wage i,t+1) on Embedded Image. Separation indicates the probability of separation from the intermediate firm. All specifications include fixed effects L(Historyi,t,d) corresponding to interacted event and calendar time by origin firm by worker tenure at origin firm (eight bins) by initial wage at the origin firm (eight bins), and are clustered at the level of origin firm by time. The sample consists of the first 16 quarters after initial separation from the origin firm. See text for sample construction.

  • Event Study of Workers’ Wages and Separation Behavior Following Movement to a Higher-Wage Firm Notes: Panel A plots the first-stage regression β coefficients from , separately for each event-time period k ∈[-9, 16], where is the change in average firm wage for individual i at E-E separation date t -1 compared to the intermediate firm at date t, and Δln(wagei,t+k) is ln(wagei,t+k)–ln(wagei,t–k). Panel B reports coefficients from the reduced form specification , where Ri,t+k denotes retention at the intermediate firm, separately for each event-time period k ∈[1, 16]. All specifications include fixed effects L(Historyi,t,d) × 1t+k corresponding to interacted event and calendar time by origin firm by worker tenure at origin firm (eight bins) by initial wage at the origin firm (eight bins), and are clustered at the level of origin firm by time. Change in own wage is censored at the 1 percent tails. See text for sample construction.
    Figure 4

    Event Study of Workers’ Wages and Separation Behavior Following Movement to a Higher-Wage Firm

    Notes: Panel A plots the first-stage regression β coefficients from Embedded Image, separately for each event-time period k ∈[-9, 16], where Embedded Image is the change in average firm wage for individual i at E-E separation date t -1 compared to the intermediate firm at date t, and Δln(wagei,t+k) is ln(wagei,t+k)–ln(wagei,t–k). Panel B reports coefficients from the reduced form specification Embedded Image, where Ri,t+k denotes retention at the intermediate firm, separately for each event-time period k ∈[1, 16]. All specifications include fixed effects L(Historyi,t,d) × 1t+k corresponding to interacted event and calendar time by origin firm by worker tenure at origin firm (eight bins) by initial wage at the origin firm (eight bins), and are clustered at the level of origin firm by time. Change in own wage is censored at the 1 percent tails. See text for sample construction.

Tables

  • Table 1

    Separations and Recruits Elasticities to Firm Component of Wage Using AKM

    WageFirm FE
    (1)(2)(3)(4)(5)
    All separations-0.282-0.51-0.622-1.342-1.448
    (0.005)(0.01)(0.015)(0.085)(0.095)
    E-E separations-0.317-0.533-0.753-1.677-1.811
    (0.007)(0.013)(0.023)(0.127)(0.141)
    E-N separations-0.291-0.422-0.578-1.209-1.303
    (0.005)(0.01)(0.014)(0.075)(0.085)
    E-E recruits0.2660.1270.0670.4130.438
    (0.022)(0.031)(0.017)(0.059)(0.064)
    Pct. EE-recruits0.470.470.4640.4640.465
    Labor supply elasticity0.3550.8791.3452.692.912
    (0.024)(0.037)(0.039)(0.199)(0.221)
    Obs. (millions)7.3487.34869.07269.07268.553
    Log hourly wageYYYY
    Hazard spec.YY
    Firm FEYY
    Split sampleY
    F-statistic9,792

    • Notes: The unit of observation for the hazard specifications is an employment spell and for the linear specifications are both worker–quarter record. The Column 1 regressor is log quarterly wage. Elasticities are reported in each cell for the linear specifications, by dividing the regression coefficient by the corresponding sample mean of the outcome. Pct. E-E recruits indicates the average proportion of hires from employment. The first-stage F-statistic is given for the Row 1 regression. Firm fixed effects are censored at the 2.5 percent tails of the firm FE distribution. Standard errors are shown in parentheses.

  • Table 2

    Alternative Specifications for Separations and Recruit Elasticities to Firm Component of Wage Using AKM

    (1)(2)(3)(4)(5)(6)(7)(8)
    All separations-0.878-0.936-0.776-0.809-1.262-1.228-1.336-1.406
    (0.066)(0.071)(0.033)(0.039)(0.075)(0.065)(0.055)(0.063)
    E-E separations-0.866-0.913-0.946-0.987-1.607-1.535-1.545-1.553
    (0.057)(0.061)(0.053)(0.065)(0.115)(0.109)(0.08)(0.102)
    N-E separations-0.709-0.752-0.857-0.739-1.115-1.161-1.191-1.293
    (0.054)(0.058)(0.033)(0.034)(0.066)(0.053)(0.05)(0.048)
    E-E recruits0.7830.8320.4930.3490.3540.4420.3230.338
    (0.112)(0.121)(0.042)(0.045)(0.071)(0.064)(0.064)(0.075)
    Pct. EE-recruits0.4640.4650.430.4670.4630.4650.4660.465
    Labor supply elasticity0.8650.9081.3481.4932.5972.4292.5782.629
    (0.143)(0.154)(0.089)(0.107)(0.186)(0.174)(0.136)(0.169)
    Obs. (millions)7.3487.30416.4577.76770.60951.9241.79651.629
    Firm FEYYYYYYYY
    Split sampleYYYYYYY
    F-statistic4,58612,0438,6379,82011,0159,266
    Hazard spec.YY
    Annual earningsY
    Quarterly earningsY
    No trimmingY
    Controls
    Tenure trendY
    Indus. × County FEY
    Indus. × Tenure trendsY

    • Notes: The first-stage F-statistic is given for the Row 1 regression. The unit of observation for hazard specifications is an employment spell, and for the linear specifications, it is each job-quarter record. Column 2 uses the split sample in a control function for the hazard specification. Annual earnings indicates the annualized panel (one observation per worker–year), from which the AKM firm FEs (using log annual earnings) and separations variables are estimated. Quarterly earnings indicates AKM firm FEs estimated with quarterly earnings. Elasticities are reported in each cell for the linear specifications, by dividing the regression coefficient by the corresponding sample mean of the outcome. Tenure refers to the number of quarters since the job started, is coded as a continuous variable and includes control terms up to a quadratic power of tenure. Industry is defined at the one-digit level. Firm fixed effects are censored at the 2.5 percent tails of the firm FE distribution, except where “no trimming” is indicated. Standard errors are shown in parentheses are clustered at the firm level.

  • Table 3

    Falsification Test: Do Match Residuals Predict Future AKM Firm Quality of Movers?

    Future Firm FEPositive Change in Firm FE
    (1)(2)(3)(4)(5)(6)(7)(8)
    Match effect0.0580.0580.060-0.0030.1560.1580.1670.060
    (0.003)(0.003)(0.004)(0.000)(0.007)(0.006)(0.009)(0.001)
    Firm effect0.5130.4300.5040.444-1.045-1.202-1.037-1.174
    (0.011)(0.011)(0.011)(0.011)(0.029)(0.031)(0.029)(0.030)
    Obs.1,625,2091,497,1491,393,0701,386,5401,625,2091,497,1491,393,0701,386,540
    Controls
    Industry × countyYY
    TenureYY
    Industry × tenureYY

    • Notes: The match effect is calculated as the average residual from the AKM by worker–firm match. The sample is restricted to E-E separation quarters. The outcomes refer respectively to the AKM firm wage effect at the new firm (Columns 1–4) and an indicator for a positive change compared to the previous firm (Columns 5–8). Industry has eight categories, and tenure indicates a fourth-degree polynomial.

  • Table 4

    Separations Elasticities Based on Matched Event Study

    (1)(2)(3)(4)(5)(6)(7)(8)(9)
    First stage0.1220.1480.1480.1760.1730.0700.1650.1710.173
    (0.006)(0.001)(0.003)(0.004)(0.003)(0.009)(0.007)(0.006)(0.006)
    IV estimates
    Separations-0.761-2.431-2.475-2.100-2.014-1.293-2.084-2.085-2.163
    (0.051)(0.033)(0.059)(0.054)(0.040)(0.513)(0.096)(0.096)(0.080)
    E-E separations-1.352-4.000-4.341-4.031-3.606-1.754-4.326-4.379-4.201
    (0.096)(0.079)(0.144)(0.154)(0.108)(1.549)(0.304)(0.314)(0.234)
    E-N separations-0.693-2.409-2.415-2.048-1.955-0.761-2.001-1.969-1.956
    (0.057)(0.041)(0.072)(0.071)(0.052)(0.568)(0.123)(0.124)(0.099)
    Obs.8.2817.3803.0783.0684.1723.0681.5131.5111.868
    Movers852,341805,633347,418346,261474,817346,140160,606160,443194,976
    F-statistic (IV)282705318441397284746522582542
    Coarsened controlsY
    Interacted controls
    TimeYYYYYYYYY
    × FirmYYYYYYYY
    × wage 0 × tenureYYYYYY
    × 3 qtr wage lagsY
    Other controls
    O–I Firm-pair FEY
    AKM Worker FEY
    Sample restricted based on
    Column 4Y
    Column 8Y

    • Notes: See text for sample construction. The full instrumental variables specification is provided in Equations 12 and 13 in the main text. The outcomes Embedded Image indicate separation, E-E separation, and E-N separation such that s is missing for all periods after a single reseparation (and E-N reseparating workers are missing for the E-E separation outcome, similarly for the E-N separation outcome). Each of these regressions includes fixed effects as indicated, where “×” indicates that fixed effects are interacted. “Wage 0” indicates the wage at hire, and “3 qtr wage lags” indicates three quarters of pre-separation wages (Origin firm). Fixed effects are divided into eight equal bins, except where coarsened, which indicates that four bins are used instead. O–I Firm-pair FE indicate fixed effects for every Origin-Intermediate firm pair. AKM worker FE indicates a continuous control for the AKM worker fixed effect from the previous time period. The sample is restricted to the post-í period. Where indicated, the sample is additionally restricted for comparability to the estimable sample for the corresponding set of fixed effects. Change in own wage is trimmed at the 1 percent tails. All regressions are clustered at the level of origin firm by initial separation quarter. Only elasticities are reported by dividing regression coefficients by the average relevant sample reseparation rate.

  • Table 5

    Alternative Specifications for Separations Elasticities Based on Matched Event Study

    (1)(2)(3)(4)(5)(6)(7)
    First stage0.1760.1710.1770.3240.162
    (0.004)(0.004)(0.004)(0.004)(0.024)
    IV estimates
    Separations-2.100-1.961-1.992-2.027-0.272-1.536-2.322
    (0.054)(0.057)(0.054)(0.072)(0.012)(0.037)(0.527)
    E-E separations-4.031-3.771-3.803-3.996-0.445-3.083-4.100
    (0.154)(0.161)(0.153)(0.210)(0.026)(0.115)(1.068)
    E-N separations-2.048-1.958-1.968-3.178-0.385-1.489-3.228
    (0.071)(0.076)(0.072)(0.152)(0.026)(0.049)(1.035)
    Obs. (millions)3.0682.9992.9843.0693.0733.0820.112
    Movers346,261340,000338,562346,714347,193346,68411,044
    F-statistic (IV)1,3971,2791,3451964,44732
    Quarterly earningsY
    Mass Layoff IV
    Firm wageYYYYY
    BLM firm clusterY
    OLSY
    Firm value controlY
    Firm amenities controlY

    • Notes: Main spec. FE correspond to Table 4, Column 4 and are firm by event and calendar time by tenure bin by initial wage at hire, all for the origin firm, and where tenure and hire wage are divided into eight bins. Firm value, VEE. is estimated based on the procedure described in Sorkin (2018) over the full sample of observations in the worker–quarter panel, and for the separations regression in Column 2 above has elasticity -0.222 (SE = 0.033). The firm amenities value is calculated as the difference between the AKM firm effect and firm value, VEE, and the separations elasticity with respect to the amenities value in Column 3 is -0.291 (SE = 0.038). “BLM firm cluster” is estimated based on the procedure described in Bonhomme, Lamadon, and Manresa (2019) and is used as an alternative instrument in place of the firm wage. OLS indicates that the firm wage instrument is not used; that is, separations are regressed directly on the change in log own wage at initial transition. Quarterly earnings indicates the main specification with quarterly earnings instead of hourly wage, for both the firm and own wage changes. Mass layoffs correspond to the quarter of initial transition from the Origin firm and are defined in the full panel (before restrictions based on firm size and short spells) following the WARN Act definition: a firm with at least 100 full time workers has at least either (i) 500 fewer workers in the following four quarters or (ii) one-third fewer workers in the following four quarters. Standard errors shown in parentheses are clustered at the level of Origin firm by initial separation quarter.

  • Table 6

    Heterogeneity in Separation Elasticities Based on Matched Event Study

    First StageSeparationsE-E separationsMovers
    Panel A: Industry of Destination Firm
    Manufacturing0.178 (0.01)-2.287 (0.298)-4.136 (0.804)36,919
    Wholesale, trade & transport0.188 (0.008)-1.394 (0.159)-3.391 (0.487)63,158
    Prof., business & financial services0.117 (0.01)-3.91 (0.267)-7.974 (0.856)71,620
    Education and health0.154 (0.006)-2.148 (0.158)-3.777 (0.503)58,072
    Art, accommodation & food0.238 (0.021)-1.201 (0.255)-2.301 (0.786)22,999
    Panel B: Geographic Zone of Destination Firm
    Portland metro0.159 (0.005)-2.237 (0.132)-4.584 (0.397)92,123
    Non-Portland metro0.182 (0.007)-1.969 (0.142)-3.648 (0.472)51,957
    Panel C: HHI (Employment)
    0–5000.172 (0.007)-1.757 (0.154)-3.645 (0.5)46,675
    500–15000.163 (0.011)-1.668 (0.277)-2.701 (0.956)30,460
    1500+0.159 (0.007)-2.241 (0.231)-4.066 (0.732)48,489
    Panel D: HHI (Payroll)
    0–5000.182 (0.008)-1.712 (0.157)-3.597 (0.51)44,997
    500–15000.16 (0.01)-1.437 (0.311)-3.594 (1.183)29,222
    1500+0.158 (0.007)-2.372 (0.206)-4.086 (0.624)50,986
    Panel E: Period of Initial Separation
    2003–20060.17 (0.004)-2.353 (0.108)-4.489 (0.277)91,712
    2007–20090.171 (0.013)-2.044 (0.154)-4.194 (0.406)69,886
    2010–20120.178 (0.01)-2.481 (0.127)-4.687 (0.306)79,758
    Panel F: Quartile of Pre-separation Wage
    Quartile 10.194 (0.004)-1.46 (0.054)-2.337 (0.133)86,475
    Quartile 20.198 (0.009)-1.979 (0.1)-4.088 (0.294)68,597
    Quartile 30.168 (0.013)-2.451 (0.176)-5.438 (0.571)66,691
    Quartile 40.127 (0.006)-2.282 (0.2)-3.966 (0.502)81,470
    Panel G: Time horizon
    4-quarter out0.176 (0.004)-2.01 (0.051)-3.082 (0.116)346,261
    8-quarter out0.176 (0.004)-2.262 (0.057)-3.547 (0.132)346,261
    12-quarter out0.176 (0.004)-2.149 (0.054)-3.746 (0.141)346,261

    • Notes: Industry is defined at the one-digit level. “Agriculture,” “mining, utility and construction,” and “other”‘ industries have been excluded due to low number of movers. Professional, business and financial services includes the information industry. Period of separation indicates the year of initial separation: the worker is tracked over the following four years. Portland metro indicates the Portland metro commuting zone. HHI indicates the annual commuting zone by industry (four-digit) Herfindahl–Hirschman index using employment and payroll, respectively. Time horizon censors the sample at different maximum quarters and presents the average elasticity over that period. Standard errors shown in parentheses are clustered at the level of Origin firm by initial separation quarter.

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Monopsony in Movers
Ihsaan Bassier, Arindrajit Dube, Suresh Naidu
Journal of Human Resources Apr 2022, 57 (S) S50-s86; DOI: 10.3368/jhr.monopsony.0319-10111R1
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