LMS Statistical Extracts

This is a repository to help researchers use statistical extracts produced as part of two papers coauthored by Lamadon, Mogstad, and Setzler:

• “Imperfect competition, compensating differentials, and rent sharing in the US labor market” by Thibaut Lamadon, Magne Mogstad, and Bradley Setzler. American Economic Review 112.1 (2022): 169-212. [LMS] [bibtex]

• “How Much Should we Trust Estimates of Firm Effects and Worker Sorting?” by Stéphane Bonhomme, Kerstin Holzheu, Thibaut Lamadon, Elena Manresa, Magne Mogstad, and Bradley Setzler. Journal of Labor Economics 41.2 (2023): 291–322. [BHLMMS] [bibtex]

Aside from the statistical extracts described here, LMS papers also produced publicly-available software packages that may be useful to researchers:

• PyTwoWay: Provides implementations of all of the estimators considered by BHLMMS, including the two-way fixed-effect estimators of Abowd, Kramarz, and Margolis (1999, Econometrica); Bonhomme, Lamadon, and Manresa (2019, Econometrica); and Kline, Saggio, and Solvsten (2020, Econometrica). This package is written in Python and can be executed from Stata.

• eventStudy: Provides difference-in-differences estimation in R that accounts for staggered treatment onset using a “stacked data” approach. Importantly, it scales to very large datasets. This package is written in R.

• textables: Provides automated production of highly-customized LaTeX tables, including PDF compilation, directly from R. All tables in LMS and BHLMMS were produced using this package. This package is written in R.

Value Added and Wage Growth for Stayers in the US Tax Data

Here, we provide the estimates of the regional pass-through from firm productivity shocks to the earnings of workers. In particular, we provide the region-specific changes in log earnings and log value added relative to event time zero at which a log value added shock occurs using the approach described under the heading ``Difference-in-Difference Illustration of Internal Instruments” in subsection III.A of LMS. The provided variables are:

• EventTime: This is the number of years since the treated group received a positive log value added shock and the control group did not.
• LogVADiff_Unconditional and LogWageDiff_Unconditional: These variables are the mean difference in firm-specific log value added and log earnings among stayers, respectively, between the treated group and control group at a particular event time.
• LogVADiff_MarketLevel and LogWageDiff_MarketLevel: These variables are the mean difference in market-level averages of log value added and log earnings among stayers, respectively, between the treated group and control group at a particular event time.
• LogVADiff_FirmLevel and LogWageDiff_FirmLevel: These variables are similar to LogVADiff_Unconditional and LogWageDiff_Unconditional, respectively, but controlling for market-year fixed effects.

The statistical extract containing these estimates is available for download here. The first 3 rows of the statistical extract are as follows:

dd = setDT(read.csv(file="StatisticalExtracts/LMS-Stayer-Differences.csv"))

EventTime	LogWageDiff_Unconditional	LogVADiff_Unconditional	LogWageDiff_FirmLevel	LogVADiff_FirmLevel	LogWageDiff_MarketLevel	LogVADiff_MarketLevel
-6	0.0047330	0.0082319	0.0034821	0.0099495	0.0020086	0.0079590
-5	-0.0005126	-0.0013977	0.0008827	-0.0007460	-0.0047909	-0.0063824
-4	-0.0003985	0.0046383	0.0009619	0.0032093	-0.0051363	-0.0085800

Region-Sector Pass-through Measures for Stayers in the US Tax Data

Here, we provide the region-specific instrumental variables estimation of the pass-through from log value added to log earnings using the approach described under the heading ``Formal Identification Using Internal Instruments” in subsection III.A of LMS. Denoting log earnings by $w$ and log value added by $y$, the empirical equation is,

$$ \mathbb{E}[ \Delta y_t (w_{t+e} - w_{t-e'} - \gamma_r(y_{t+e} - y_{t-e'})) ] = 0 $$

which is estimated only among workers who are stayers and which is estimated separately for each broad market $r$. A similar equation is estimated using market-level means across all broad markets, in which case the parameter estimate is denoted $\Upsilon$.The preferred estimates of $\gamma_r$ are based on firm-level deviations from market-level means. The estimated $(\gamma_r,\Upsilon)$ parameters can then be transformed into the preference parameters $(\rho_r,\beta)$.

The statistical extract contains the following estimates:

• BroadMarket: This variable indicates the broad market, defined as a region and a sector of the economy.
• UnconditionalPassthrough: This variable is the IV estimate of $\gamma_r$ that does not control for market-year fixed effects.
• NetPassthrough: This variable is the preferred IV estimate of $\gamma_r$ that controls for market-year fixed effects.
• MarketPassthrough: This variable is the IV estimate of $\Upsilon$ using only market-level aggregate data; this estimate does not vary across broad markets.
• Parameter_rho: This variable is the estimate of the within-market preference parameter $\rho_r$, which varies across broad markets.
• Parameter_beta: This variable is the estimate of the between-market preference parameter $\beta$; this estimate does not vary across broad markets.

Estimating this equation requires population employer-employee data on earnings and firm value added. We provide estimates of the various terms in this equation. The statistical extract containing these estimates is available for download here. The first 3 rows of the statistical extract are as follows:

dd = setDT(read.csv(file="StatisticalExtracts/LMS-Regional-Passthrough.csv"))

BroadMarket	UnconditionalPassthrough	NetPassthrough	MarketPassthrough	Parameter_rho	Parameter_beta
Midwest_Goods	0.1562206	0.1558363	0.1795542	0.8435221	4.56935
Midwest_Services	0.1358427	0.1243210	0.1795542	0.6487151	4.56935
Northeast_Goods	0.1259046	0.1317955	0.1795542	0.6936381	4.56935

Region-Sector Rents in the US Tax Data

Here, we provide the region-specific rent estimation using the approach of Result 4 from subsection II.E of LMS. In particular, equation (9) of LMS shows that the firm technology parameter $\alpha_r$ can be recovered for each market using only the parameters $(\rho_r,\beta)$ discussed above and the (quasi) labor share. Then, given parameters $(\alpha_r,\rho_r,\beta)$, Result 4 of LMS shows that per-capita rents can be recovered from the per-capita wagebill and per-capita value added.

The statistical extract contains the following estimates:

• BroadMarket: This variable indicates the broad market, defined as a region and a sector of the economy.
• SampleWorkerYears: This variable is the count of worker-year observations used in the estimation, measured in 1,000 units.
• SampleFirmYears: This variable is the count of firm-year observations used in the estimation, measured in 1,000 units.
• LaborShare: This variable is the estimate of the (quasi) labor share defined as $\exp( \mathbb{E}[\ell + w - y])$, where $\ell$ is log labor, $w$ is log earnings, and $y$ is log value added.
• ValueAdded: This variable is the estimate of average value added, in per-capita units.
• Wagebill: This variable is the estimate of average wage bill, in per-capita units.
• Parameter_alpha: This variable is the estimate of the market-specific firm productivity parameter $\alpha_r$.
• WorkerRents_FirmLevel and FirmRents_FirmLevel: These variables are the estimates of rents at the firm-level that are captured by workers and by firms, respectively, measured as $1 per-capita.
• WorkerRents_MarketLevel and FirmRents_MarketLevel: These variables are the estimates of rents at the market-level that are captured by workers and by firms, respectively, measured as $1 per-capita.

We provide estimates of the various terms in this equation. The statistical extract containing these estimates is available for download here. The first 3 rows of the statistical extract are as follows:

dd = setDT(read.csv(file="StatisticalExtracts/LMS-Regional-Rents.csv"))

BroadMarket	SampleWorkerYears	SampleFirmYears	LaborShare	ValueAdded	Wagebill	Parameter_alpha	WorkerRents_FirmLevel	WorkerRents_MarketLevel	FirmRents_FirmLevel	FirmRents_MarketLevel
Midwest_Goods	42908.01	1945.136	0.6298813	91198.66	43647.52	0.2538398	6801.869	7837.094	4041.102	4940.472
Midwest_Services	69044.54	6636.190	0.6597992	90504.73	34054.24	0.2465285	4233.657	6114.580	3530.709	5734.364
Northeast_Goods	26699.95	1498.971	0.6630055	107545.25	50693.46	0.2363487	6681.169	9102.221	4197.952	6310.806

Earnings Inequality and Firm-Worker Clusters in the US Tax Data

Here, we provide the estimates of the equilibrium earnings expression presented in equation (14) of LMS using the empirical specification and estimation approach described in subsection IV.A of LMS. The empirical equation is,

$$w^a_{k}(x) = \psi_k + x\theta_k $$

where $k$ denotes a cluster of firms, $x$ denotes the measure of worker skill, $w^a$ is the predicted log wage after residualization and adjustment for productivity shocks, $\psi$ is the cluster-specific wage premium, and $\theta$ is the cluster-specific skill complementarity.

Estimating this equation requires population employer-employee data on earnings and firm value added. We provide estimates of the various terms in this equation, evaluated at quantiles $q$ in the $x$ distribution. In particular, the variables are:

• FirmCluster_k: This variable indicates the cluster $k$ of firms.
• Size_FirmCluster_k: This variable indicates the number of workers employed by cluster $k$.
• FirmPremium_psik: This variable indicates the firm premium $\psi_k$ for cluster $k$.
• SkillComplementarity_thetak: This variable indicates the skill complementarity $\theta_k$ for cluster $k$.
• WorkerDecile_q: This variable indicates quantile $q$ in the distribution of $x$.
• WorkerSkill_xq: This variable indicates the value of worker skill $x$ at quantile $q$.
• ExpectedLogWage_wkq: This variable indicates the expected log wage $w^a$ for cluster $k$ and worker skill quantile $q$, which is residualized on observables and adjusted for productivity shocks.

The statistics are available for download here.

dd = setDT(read.csv(file="StatisticalExtracts/LMS-Firm-Worker-Matches.csv"))

FirmCluster_k	Size_FirmCluster_k	FirmPremium_psik	SkillComplementarity_thetak	WorkerDecile_q	WorkerSkill_xq	ExpectedLogWage_wkq
1	11064786	0	1	0.1	-0.7989672	-0.7989672
1	11064786	0	1	0.2	-0.6709900	-0.6709900
1	11064786	0	1	0.3	-0.5787095	-0.5787095

In case the user prefers not to use the LMS adjustment for productivity shocks, the unadjusted version of these estimates are available for download here.

Between and Within Firm Inequality in Tax Data from the US and 4 European Countries

BHLMMS analyze employer-employee administrative data from 5 countries: Austria, Italy, Norway, Sweden, and the US. They take extensive steps to harmonize the various datasets to ensure cross-country comparability.

They characterize the role of firms in wage inequality by performing a within-between decomposition. Letting $w$ denote the log wage (or earnings), and letting $j(it)$ denote the firm at which worker $i$ is employed in year $t$, the average wage in firm $j$ is given by $w_j \equiv \mathbb{E}[w_{it} | j(it)=j]$. Then, we can write $w_{it} = w_j + (w_{it} - w_j)$, so the total variance in log wages can be expressed, $$\text{Var}(w_{it}) = \text{Var}(w_{j}) + \text{Var}(w_{it} - w_j)$$ where $\text{Var}(w_{j})$ is the between-firm variance and $\text{Var}(w_{it} - w_j)$ is the within-firm variance.

In addition to providing the within-between decomposition, BHLMMS describe the connectedness of each country’s firms by examining movers across firms and analyzing how many firms are workers are contained the full data, the connected subset of firms, and the leave-one-out connected subset of firms. The variables provided are:

• Country: This variable indicates the country represented by the data.
• YearRange: This variable indicates the number of years included in the sampling timeframe.
• Set: The set can be all firms, the connected subset of firms, or the leave-one-out connected subset of firms
• WorkerCount: This variable is the count of workers used in the estimation.
• MoverCount: This variable is the count of movers (i.e. workers who switch employers) used in the estimation.
• FirmCount: This variable is the count of firms used in the estimation.
• LogWageVariance: This is the variance in log wages (or earnings), $\text{Var}(w_{it})$.
• BetweenFirmVariance: This is the between-firm variance in log wages (or earnings), $\text{Var}(w_{j})$.
• WihtinFirmVariance: This is the within-firm variance in log wages (or earnings), $\text{Var}(w_{it} - w_{j})$.

The statistics are available for download here. The first 3 rows of the statistical extract are as follows:

dd = setDT(read.csv(file="StatisticalExtracts/BHLMMS-WithinBetween-Variance.csv"))

Country	YearRange	Set	WorkerCount	MoverCount	FirmCount	LogWageVariance	BetweenFirmVariance	WithinFirmVariance
Austria	3	connected	2844534	340754	116960	0.1830276	0.0798959	0.1031317
Italy	3	connected	863955	130469	54299	0.1762210	0.0791938	0.0970272
Norway	3	connected	986365	181415	63397	0.2292411	0.1021057	0.1271353

Firm Effects and Sorting in Tax Data from the US and 4 European Countries

Here, we provide the estimates of the two-way fixed-effects decomposition from equation (3) of BHLMMS using 4 estimators applied to data from 5 countries. Assuming that the residual log wage $w$ can be expressed as $w_{it} = x_i + \psi_{j(it)} + \epsilon_{it}$, where $j(it)$ denotes the firm at which worker $i$ is employed in year $t$, then the variation in the log wage can be expressed,

$$\text{Var}(w_{it}) = \text{Var}(x_i) +\text{Var}(\psi_{j(it)}) + 2\text{Cov}(\psi_{j(it)},x_i) + \text{Var}(\epsilon_{it})$$ The two key components of interest are $\text{Var}(\psi_{j(it)})$, which is the variance in log wages due to firm premia, and $2\text{Cov}(\psi_{j(it)},x_i)$, which is the variance in log wages due to the sorting of worker skill to firm premia.

Estimating this equation requires population employer-employee data on earnings from each of the countries. The 4 estimation methods are FE, CRE, FE-HO, FE-HE; see Section 4 of BHLMMS for discussion of the methods. The variables are:

• Country: This variable indicates the country represented by the data.
• YearRange: This variable indicates the number of years included in the sampling timeframe.
• Estimator: This variable indicates which of the methods was used in the estimation.
• LogWageVariance: This is the variance in log wages (or earnings), $\text{Var}(w)$.
• FirmEffectVariance: This is the variance in the firm effects, $\text{Var}(\psi)$.
• FirmWorkerEffectsCovariance: This is the covariance between the firm effects and the worker effects, $\text{Cov}( \psi , x )$.

The estimates using each of those methods are available for download here. The first 3 rows of the statistical extract are as follows:

dd = setDT(read.csv(file="StatisticalExtracts/BHLMMS-FirmEffects-Sorting.csv"))

Country	YearRange	Estimator	LogWageVariance	FirmEffectVariance	FirmWorkerEffectsCovariance
Austria	3	CRE	0.1830276	0.0185641	0.0160264
Austria	6	CRE	0.1865862	0.0218879	0.0182701
Austria	3	FE	0.1830276	0.0360737	-0.0048577

Licenses

The code is licensed under a MIT License.

The data is licensed under a Creative Commons Attribution 4.0 International License.