Income volatility, taxation and the functioning of the U.S.

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labor market∗

Thibaut Lamadon†

Magne Mogstad‡

Bradley Setzler§

This Version: April 19, 2021

Abstract

The goal of this report is to characterize income volatility in the U.S. labor market and

examine its causes and consequences. To achieve this goal, we analyze U.S. business and

household tax records. These administrative data sets allow us to match employees and

employers and to construct panel data on the outcomes and characteristics of U.S. firms,

individuals and households. The main insights from the empirical analysis may be summarized in four broad conclusions. First, income volatility rose steadily during 2001-2009,

peaked during the Great Recession, then dropped during 2010-2015. However, these national averages miss a lot. Income volatility is relatively high on the coasts and in the

Western part of the country, and lower socioeconomic areas tend to have higher income

volatility. Second, income volatility is lower if one considers income net of taxes and transfers. In particular, the Federal tax-transfer system attenuates both permanent shocks at the

worker level and the pass-through of firm shocks to workers’ earnings. Third, worker mobility across firms generates relatively small changes in income. By contrast, sorting of better

workers to better firms and the exit and entry of firms in local markets are empirically

important determinants of workers’ income. Fourth, income volatility, at the individual

and market level, may generate substantial changes in tax payments and the receipt of

tax credits. This indicates that income volatility in the U.S. labor market could make it

difficult to obtain accurate predictions of tax revenues.

∗ The opinions expressed in this report are those of the authors alone and do not reflect the views of the

Internal Revenue Service or the U.S. Treasury Department. This work is a component of a larger project on

income risk in the United States, conducted through the SOI Joint Statistical Research Program. We are grateful

to Victoria Bryant, Raj Chetty, Nathan Hendren, Kevin Pierce, Michael Weber, Danny Yagan, Owen Zidar, and

Eric Zwick for support and guidance in accessing and understanding the IRS data. We also appreciate the

constructive comments and suggestions from discussants and participants at various conferences and seminars.

Mogstad and Setzler acknowledge funding from the Washington Center for Equitable Growth.

† Department of Economics, University of Chicago. E-mail: lamadon@uchicago.edu

‡ Department of Economics,

University of Chicago; Statistics Norway; NBER; IFS. E-mail:

magne.mogstad@gmail.com

§ Department of Economics, University of Chicago. E-mail: bradley.setzler@gmail.com

Introduction

The aim of this report is to characterize income volatility in the U.S. labor market and examine

its causes and consequences. There are a number of key questions addressed. What is the

distribution of income volatility in the U.S. labor market? How large and persistent are the

year-by-year changes in the incomes of American workers? How much does the sorting of

workers to firms, regions, and industries matter for income volatility? How do the estimates of

income volatility change when we account for other sources of income such as spousal earnings?

To what extent does the Federal tax-and-tranfer system affect measures of income volatility?

Does income volatility make it difficult to predict tax revenues or receipt of tax credits?

Data challenges have made it difficult in the past to answer these questions. The ideal data

covers a large number of individuals, includes a sufficient number of years on each individual,

links each individual to her employer, and links individuals to households. While such data has

not previously been available for the U.S., administrative data has provided such information

for existing studies on some other countries. The advantages of these administrative data sets

are the accuracy of the income information provided, the large sample size, and the lack of

attrition, other than what is due to migration and death, as well as the possibility to link to

employers and households.

To investigate the above questions, we analyze U.S. business and household tax records.

These administrative data sets allow us to match employees and employers and to construct panel

data on the outcomes and characteristics of U.S. firms, individuals and households. The main

insights from the empirical analysis may be summarized in four broad conclusions. First, income

volatility rose steadily during 2001-2009, peaked during the Great Recession, then dropped

during 2010-2015. However, these national averages miss a lot. Income volatility is relatively

high on the coasts and in the Western part of the country, and lower socioeconomic areas tend

to have higher income volatility. Second, income volatility is lower if one considers income net of

taxes and transfers. In particular, the Federal tax-transfer system attenuates both permanent

shocks at the worker level and the pass-through of firm shocks to workers’ earnings. Third,

worker mobility across firms generate relatively small changes in income. By contrast, sorting

of better workers to better firms and the exit and entry of firms in local markets are empirically

important determinants of workers’ income. Fourth, income volatility, at the individual and

market level, may generate substantial changes in tax payments and the receipt of tax credits.

This indicates that income volatility in the U.S. labor market could make it difficult to obtain

accurate predictions of tax revenues.

Our work relates to a considerable literature on income volatility, risk, and inequality.1

DeBacker et al. (2013) use a panel of tax returns to study the persistent-versus-transitory nature

of rising inequality in individual male labor earnings and in total household income, both before

and after taxes, in the U.S. Their paper is the first to estimate error components models of

income dynamics using U.S. administrative data.2 Building on this work, we characterize the

1 See, for example, the recent review by Meghir and Pistaferri (2011), and the extensive list of studies referenced

therein.

2 See also Blundell et al. (2015) who perform a similar analysis for Norway.

variation over time and across areas in income volatility in the U.S. and explore the factors

correlated with high income volatility. Moreover, we separate between income volatility caused

by idiosyncratic shocks to individual workers and the volatility reflecting firm shocks common to

workers in that firm. We also explore how the sorting of workers to firms, regions, and industries

matters for the volatility and inequality in income. Our report also adds to existing work in

that we compare volatility in earnings, household gross income and household net income. This

allows us to draw inference about how the family and the tax-transfer system attenuate income

volatility.

Our analysis also contributes to a large and growing literature on firms, income volatility and

labor market inequality, reviewed in Card et al. (2018). A number of studies show that trends in

wage dispersion closely track trends in productivity dispersion across industries and workplaces

(Faggio et al., 2010; Dunne et al., 2004; Barth et al., 2016). While this correlation might reflect

that some of the productivity differences across firms spill over to wages, it could also be driven

by changes in the degree to which workers of different quality sort into different firms (see e.g.

Murphy and Topel, 1990; Gibbons and Katz, 1992; Gibbons et al., 2005). To address the sorting

issue, a growing body of work has taken advantage of matched employer-employee data. Some

studies use this data to estimate the pass-through of changes in the value added of a firm to

the wages of its workers, while controlling for time-invariant firm and worker heterogeneity (see

e.g. Guiso et al., 2005; Card et al., 2013a; Card et al., 2018; Carlsson et al., 2016; Balke and

Lamadon, 2020; Friedrich et al., 2019). These studies typically report estimates of pass-through

in the range of 0.05-0.20. We complement this work by providing evidence of pass-through for

a broad set of firms in the U.S. and by showing how the estimated pass-through of firm shocks

is confounded by market shocks and attenuated by the tax-transfer system.

Another set of studies use the matched employer-employee data to estimate the changes in

earnings caused by workers moving across firms. Following Abowd et al. (1999), these studies

typically use an additive worker and firm effects model. They tend to conclude that firms play

an important role in the determination of earnings, with a typical finding that about 15-20

percent of the variance of log earnings is attributable to the choice of firm (Card et al., 2018).

We show, however, that firm effects are small in the U.S. labor market, explaining only a few

percent of the variation in earnings. This finding contrasts with recent work from the U.S.

(Sorkin, 2018; Song et al., 2018) as well as many studies from other developed countries (Card

et al., 2018). The reason is that these studies do not address the concern that estimates of firm

effects will be biased upward and estimates of worker sorting will be biased downward in finite

samples, with the size of the bias depending inversely on the degree of worker mobility among

firms (Andrews et al., 2008). Following recent work by Bonhomme et al. (2019) and Kline

et al. (2020), we apply two alternative approaches to correct for the bias of the estimator of

Abowd et al. (1999). Both approaches show that firm effects explain very little of the variation

in earnings in the U.S. economy, once one corrects for bias due to limited mobility. Instead,

a substantial part of the variation in earnings is due to positive sorting of high wage workers

to high paying firms. Our report also differs in that we estimate the additive worker and firm

effects model both for earnings, household gross income and household net income. This allows

us to draw inference about how the progressive nature of the tax-transfer system attenuates the

income changes associated with moving across firms and reduces the incentives of better workers

to sort into better firms.

The remainder of the report is organized as follows. Section 2 describes the data and the

sample selection. Section 3 characterizes income mobility in the U.S. labor market and describe

how it varies over time and across areas. In Section 4, we use several complementary approaches

to examine causes and consequences of income volatility. Section 5 offers some concluding

remarks.

Data sources and sample selection

2.1

Data sources

Our empirical analyses are based on a matched employer-employee panel data set with information on the characteristics and outcomes of U.S. workers and firms. This data is constructed

by linking U.S. Treasury business tax filings with worker-level filings for the years 2001-2015.

Below, we briefly describe data sources, sample selection, and key variables, while details about

the data construction and the definition of each of the variables are given in Appendix A.

Business tax returns include balance sheet and other information from Forms 1120 (Ccorporations), 1120S (S-corporations), and 1065 (partnerships). The key variables that we draw

on from the business tax filings are the firm’s value added, commuting zone, and industry code.

Value added is the difference between receipts and the cost of goods sold. Commuting zone is

constructed using the ZIP code of the firm’s business filing address. Industry is defined as the

first two digits of the firm’s NAICS code. We define a market as the combination of an industry

and a commuting zone. At times we will aggregate these markets according to the combination

of Census regions (Midwest, Northeast, South, West) and broad sectors (Goods and Services).

We will refer to this classification as “broad markets”.

Earnings data are based on taxable remuneration for labor services for direct employees and

independent contractors. Earnings include wages and salaries, bonuses, tips, exercised stock

options, and other sources of income deemed taxable. These forms are filed by the firm on

behalf of the worker and provide the firm-worker link. Gross household income is constructed

using a definition similar to that of Piketty and Saez (2003). Net household income is given

by gross household income minus Federal taxes plus Federal benefits from Social Security and

unemployment. See Appendix A for further details.

We express all monetary variables in 2015 dollars, adjusting for inflation using the Consumer

Price Index.

2.2

Sample Selection

In each year, we start with all individuals aged 25-60 who are linked to at least one employer.

Next, we define the worker’s firm as the EIN that pays her the greatest direct (W-2) earnings

Workers

Panel A.

Full Sample:

Baseline Sample

Unique

89,570,480

Observation-Years

447,519,609

Unique

32,070,390

Observation-Years

207,990,422

Panel B.

Movers Only:

Unique

6,478,231

Observation-Years

39,163,975

Movers Sample

Panel C.

Complete Stayer Spells:

10 Stayers per Firm:

10 Firms per Market:

Firms

Unique

3,559,678

Observation-Years

23,321,807

Stayers Sample

Unique

10,311,339

6,297,042

5,217,960

6 Year Spells

35,123,330

20,354,024

16,506,865

Unique

1,549,190

144,412

117,698

6 Year Spells

6,533,912

597,912

476,878

Table 1: Overview of the Sample

Notes: This table provides an overview of the full sample, movers sample, and stayers sample, including the

steps involved in defining the stayers sample.

in that year. This definition of a firm conforms to previous research using the U.S. business tax

records (see, e.g., Song et al., 2018). The EIN defines a corporate unit for tax and accounting

purposes. It is a more aggregated concept than an establishment, which is the level of analysis

considered in recent research on U.S. Census data (see, e.g., Barth et al., 2016), but a less

aggregated concept than a parent corporation. As a robustness check, we investigated the

sensitivity of the estimated firm wage premiums to restricting the sample to EINs that appear

to have a single primary establishment. These are EINs for which the majority of workers live

in the same commuting zone. It is reassuring to find that the estimated firm wage premiums do

not materially change when we use this restricted sample.3

Since we do not observe hours worked or a direct measure of full-time employment, we

follow the literature by including only workers for whom annual earnings are above a minimum

threshold (see, e.g., Song et al., 2018). In the baseline specification, this threshold is equal to

$15,000 per year (in 2015 dollars), which is approximately what people would earn if they work

full-time at the federal minimum wage. As a robustness check, we investigate the sensitivity of

our results to other choices of a minimum earnings threshold. We further restrict the sample to

firms with non-missing value added, commuting zone, and industry. The full sample includes

447.5 (39.2) million annual observations on 89.6 (6.5) million unique workers (firms).

In parts of the analysis, we consider two distinct subsamples. The first subsample, which

we refer to as the stayers sample, restricts the full sample to workers observed with the same

employer for eight consecutive years. This restriction is needed to allow for a flexible specification

of how the worker’s earnings evolve over time. Specifically, we omit the first and last years

of these spells (to avoid concerns over workers exiting and entering employment during the

year, confounding the measure of annual earnings) and analyze the remaining six-year spells.

Furthermore, the stayers sample is restricted to employers that do not change commuting zone

3 In the baseline sample, the AKM (BLM) estimates of firm effects are around 10 (3) percent. By comparison,

the restricted sample gives AKM (BLM) estimates of approximately 9 (3) percent.

or industry during those eight years. Lastly, we restrict the stayers sample to firms with at least

10 such stayers and markets with at least 10 such firms, which helps to ensure sufficient sample

size to perform the analyses at both the firm and the market level. The stayers sample includes

35.1 (6.5) million spells on 10.3 (1.5) million unique workers (firms).

The second subsample, which we refer to as the movers sample, restricts the full sample to

workers observed at multiple firms. That is, it is not the same EIN that pays the worker the

greatest direct (W-2) earnings in all years. Following previous work, we also restrict the movers

sample to firms with at least two movers. This restriction might help reduce the limited mobility

bias. It also makes it easier to directly compare the AKM and BLM estimates of firm effects to

those produced by the approach of Kline et al. (2020) (which requires at least two movers per

firm). The movers sample includes 32.1 (3.6) million unique workers (firms).

Table 1 compares the size of the baseline, the stayers, and the movers samples. Detailed

summary statistics of these samples of linked firms and worker are given in Appendix Table

A.1. The samples are broadly similar, both in the distribution of earnings but also in firm-level

variables such as value added, wage bill, size, and the geographic distribution across regions and

sectors. The most noticeable differences are that the stayers have, on average, somewhat higher

earnings and tend to work in firms with higher value added.

Income volatility in the U.S.

In this section, we characterize income volatility in the U.S. labor market and describe how it has

changed over time and across areas. Following the literature, volatility is defined as movements

up or down in a household’s income over time, as measured by the variance of the year-by-year

changes in log household (annual) income. We construct this measure of volatility for three

different measures of income: individual earnings, gross household income, and net household

income. Following Blundell et al. (2015), we interpret the reduction in net household income

volatility relative to gross household income volatility as a measure of the protection provided by

the federal tax-transfer system. The transfers include Social Security benefits, unemployment

benefits, and the Earned Income Tax Credit (EITC).

Time trends in income volatility

Figure 1 presents estimates of income volatility across years. In Figure 1(a), we see that gross

income volatility rose steadily during 2001-2009, peaking during the Great Recession, then

dropped during 2010-2015. Net household income and earnings volatility followed similar trends,

but with smaller magnitudes. Figure 1(b) presents one minus the ratio of net household income

to gross household income, multiplied by 100%. This is a measure of the reduction in income

volatility, or protection, that is due to Federal taxes and transfers. The Federal tax-transfer

system provides substantial protection against income volatility. Federal taxes and transfers

reduce income volatility by about 21% on average, with a low of around 15% in 2001 and a peak

of around 23% in 2009.

0.15

●

Great

Recession

●

0.10

●

Net Income

●

Gross Income

●

Individual−level Tax Protection (%)

Variance in Within−individual Income Growth

Great

Recession

●

Earnings

0.05

●

0.00

2004

2008

2012

2004

Year

2008

2012

Year

(a) Earnings, Gross and Net Household Income(b) Percentage of Gross Income Volatility Attenuated

Volatility

by the Federal Tax-Transfer System

Figure 1: Income Volatility in the United States

Notes: This figure presents (a) the quantity of income volatility in the United States for gross household

income, net household income, and earnings, and (b) the percentage reduction in volatility attributable to the

federal tax-transfer system. Volatility is defined as movements up or down in a household’s income over time,

as measured by the variance of the year-by-year changes in log household (annual) income. The volatility

reduction due to the federal tax-transfer system is defined as 100% multiplied by one minus the ratio of net

household income volatility to gross household income volatility.

Geographical variation in income volatility

In Figure 2, we present the geographic distribution of the volatility measure when measured

separately for each commuting zone in the United States. We see that income volatility tends

to be higher on the coasts and in the Western part of the country, but lower in the Midwest

and along the Great Lakes. The patterns are broadly similar across income definitions with a

correlation of 0.78 between measures of local income volatility in earnings and gross household

income and a correlation of 0.99 between between measures of local income volatility in gross

and net household income.

Figure 3(a) presents correlations between gross income volatility and other local socioeconomic conditions within the commuting zone, where the measures of commuting zone conditions are from Chetty et al. (2015). Figure 3(b) presents these correlations for net income

volatility. Correlations are presented in absolute value, with the sign of the correlation indicated with a symbol of (+) for positive or (-) for negative. Overall, income volatility tends to

be larger in areas that are worse on other measures of economic and social conditions. Among

economic conditions, income volatility is most positively correlated with local income inequality

(as measured by the Gini coefficient) and the local poverty rate. It is negatively related to labor

force participation and the fraction of the population with income between the 25th and 75th

percentile (a proxy for the middle class). Among social conditions, income volatility is most

negatively related to the social capital index (which measures social resource availability) as well

as to our measures of short commute time to work, the marriage rate and the college graduation

rate. Moreover, local income volatility is positively related to the measures of violent crime rate,

segregation experienced by the impoverished, and the high school drop out rate.

(a) Earnings Volatility

(b) Gross Income Volatility

Figure 2: Geographic Distribution of Earnings and Income Volatility

Notes: These figures present the geographic distribution of volatility in individual earnings, gross household

income, and net household income. Volatility is defined as movements up or down in a household’s income over

time, as measured by the variance of the year-by-year changes in log household (annual) income.

Causes and consequences of income volatility

In this section, we use several complementary approaches to examine causes and consequences

of income volatility.

4.1

Income processes

In this subsection we follow a literature which explores income volatility by estimating a statistical process of income (see e.g. Blundell et al., 2015, Meghir and Pistaferri, 2011). These

analyses use the stayers sample. The estimated income process permits a decomposition of the

measure of income volatility into various components that capture different sources of volatility.

Appendix B.1 lays out and explains the income process and shows how it is identified and estimated. As explained in this appendix, one component of the income process reflects the trends

in income over time and across ages that are common to households, whereas the remaining

volatility in income can come from at least three sources: idiosyncratic permanent shocks to

the worker’s income; idiosyncratic transitory shocks to the worker’s income; and changes in

the firm’s performance or productivity (as measured by the value added) that are passed on to

workers within that firm.

Poverty Rate (+)

●

Unemployment Rate (+)

Economic

●

Gini (+)

Local Conditions

Fraction Between p25 and p75 (−)

Social Capital Index (−)

●

Unemployment Rate (+)

●

Segregation of Poverty (p < 25) (+)

●

High School Dropout Rate (Income Adj.) (+)

Social Capital Index (−)

●

Violent Crime Rate (+)

●

Fraction with Commute < 15 Mins (−)

●

Segregation of Poverty (p < 25) (+)

●

Fraction of Adults Married (−)

●

College Graduation Rate (Income Adj.) (−)

●

0.0

●

High School Dropout Rate (Income Adj.) (+)

●

Fraction of Adults Married (−)

College Graduation Rate (Income Adj.) (−)

●

Fraction Between p25 and p75 (−)

Social

Fraction with Commute < 15 Mins (−)

●

Gini (+)

●

Violent Crime Rate (+)

●

Labor Force Participation (−)

●

Local Conditions

Economic

Poverty Rate (+)

Labor Force Participation (−)

0.2

0.4

0.6

●

0.0

Correlation with Gross Income Risk

0.2

0.4

0.6

Correlation with Net Income Volatility

(a) Gross Income

(b) Net Income

Figure 3: Geographic Correlates of Income Volatility

Notes: This figure presents the correlations between (a) local gross household income variability and other local

conditions, and (b) local gross household income variability and local conditions. The local conditions are

divided into economic and social categories. The data on commuting zone conditions is from Chetty et al.

(2015). Commuting zones are weighted by the number of FTE worker observations with valid gross household

income measures when estimating the correlations and their standard errors. Correlations are presented in

absolute value, with the sign of the correlation indicated with a symbol of (+) for positive or (-) for negative.

Results from baseline model

Appendix B.2 presents the parameter estimates, and reports results from several specification

checks. In Table 2 under the column labeled “Firm Only,” we summarize the estimation results

from the baseline model and use these estimated parameters to quantify the contribution to

income volatility from the various sources. The full set of parameter estimates is available in

Appendix Table A.2. The standard deviation in log earnings growth is 0.17. Decomposing the

variance in log earnings growth, we find that almost 40 percent is due to permanent shocks at

the worker level, 58 percent can be attributed to transitory shocks at the worker level, and 3

percent is due to the pass-through of permanent shocks to value added at the firm level .

The estimated pass-through rate γ̂ is 0.14, suggesting that a 10 percent permanent increase

in the value added of the firm leads to a 1.4 percent permanent increase in the earnings of

incumbent workers. This pass-through rate is in the range of estimates reported by Card et al.

(2018). While permanent shocks to value added are transmitted to workers’ earnings, transitory

firm shocks are not. This finding is consistent with previous work (see e.g. Guiso et al., 2005;

Friedrich et al., 2019). A natural interpretation of this finding is that transitory changes in

value added reflect measurement error that does not give rise to economic responses. In the

remainder of the report, we will treat the transitory changes in value added as measurement

error and focus on the pass-through of the permanent shocks.

We repeat the analysis for gross household income and net household income. Appendix

Figure A.3 summarizes the estimation results and uses the estimated parameters to quantify

their contributions to volatility in gross and net household income. The standard deviation in

log gross income growth is 0.23, while it is 0.21 for log net income growth. We find that 33

percent of gross income volatility is due to permanent shocks at the worker level, 65 percent can

be attributed to transitory shocks at the worker level, and 1 percent is due to the pass-through

Parameters and Growth Decomposition

Firm Only

Accounting for Markets

Parameter

Var. (%)

Parameter

Var. (%)

Permanent Worker Shock (Std. Dev.)

0.10

(0.00)

39.5%

0.10

(0.00)

38.1%

Transitory Worker Shock (Std. Dev.)

0.13

(0.00)

57.6%

0.13

(0.00)

57.4%

Permanent Firm Shock Passed-through (Std. Dev.)

0.03

(0.00)

2.8%

0.02

(0.00)

1.8%

— Permanent Firm Shock Passthrough Coefficient

Transitory Firm Shock Passed-through (Std. Dev.)

0.14

(0.01)

0.00

(0.00)

— Transitory Firm Shock Passthrough Coefficient

Market Shock Passed-through (Std. Dev.)

-0.01

(0.01)

0.13

(0.01)

0.0%

0.00

(0.00)

0.00

(0.00)

0.02

(0.00)

— Market Shock Passthrough Coefficient

0.0%

1.1%

0.18

(0.02)

Table 2: Variance Decomposition in Baseline Passthrough Specification

Notes: This table presents the variance decomposition of the joint process for growth in value added and

earnings in the baseline specification. In the estimation sample, the standard deviation of log value added

growth is 0.31, and the standard deviation of log earnings growth is 0.17. The estimated moving average

coefficients are used to construct the variances of transitory shocks. The full set of parameter estimates is

available in Panel A of Appendix Table A.2.

of permanent shocks to value added at the firm level; these percentages are very similar for log

net household income. We also find pass-through rates of firm permanent shocks to gross and

net household income of 0.136 and 0.127, respectively. This indicates that the progressive nature

of the Federal tax-transfer attenuates more than 10 percent of the economic consequences of a

firm shock.

Contribution of firms versus markets

We have thus far followed the existing literature in assuming that all income volatility is specific

to the individual or the household, abstracting from aggregate regional or industry shocks. We

now take two steps to distinguish between shocks that are specific to individual workers versus

those that are common to workers in a market.

First, we estimate the earnings and value added processes conditional on a full set of year

times market fixed effects. The results are presented in Table 2 under the column labeled “Net

of Market.” Decomposing the variance in log earnings growth within markets, we find that

38 percent is due to permanent shocks at the worker level, 57 percent can be attributed to

transitory shocks at the worker level, and 2 percent is due to the pass-through of permanent

shocks to value added at the firm level. Conditional on the full set of year times market fixed

effects, the estimated pass-through rate γ̂ is 0.13. By comparison, the estimated pass-through

rate of permanent market shocks is as large as 0.18. This finding highlights the importance

of distinguishing between shocks that are specific to workers in a given firm versus those that

common to workers in a market. In Appendix Figure A.3, we control for a full set of year times

market fixed effects when analyzing gross household income and net household income, finding

also here an important role for shocks that are common to the market.

The second approach we use to examine the variability across regions and industries in income

volatility (and its sources) is to estimate the earnings and value added processes separately for

each broad market. This estimation generates market-specific parameters for the processes. We

perform this analysis separately for earnings, gross income, and net income. The results are

presented in Appendix Figure A.4. These results reveal that a pass-through rate of log value

added permanent shocks to workers’ earnings that is higher in the goods sector as compared

to the services sector. However, the Federal tax-and-transfer system attenuates some of these

differences.

Robustness checks

Appendix Figure A.2a explores how the pass-through rate varies across worker types by estimating the earnings and value added processes separately for each subgroup. Conditional on a

full set of year times market fixed effects, we find that the pass-through estimate does not vary

much by the worker’s age, previous wage, or gender. Moreover, the pass through rates do not

change materially if we restrict the sample to workers who were first hired at the firm in the

beginning of the eight year employment spell versus those that have stayed in the firm for a

longer time.

In Appendix Figure A.2b, we also present results from several other specification checks.

Following Guiso et al. (2005), our main measure of firm performance is value added. They

offer two reasons for using value added as a measure of firm performance. First, they argue,

value added is the variable that is directly subject to stochastic fluctuations. Second, firms have

discretionary power over the reporting of profits in balance sheets, which makes profits a less

reliable objective to assess. Nevertheless, it is reassuring to find that the estimates of the passthrough rates are broadly similar if we measure firm performance by operating profits, earnings

before interest, tax and depreciation (EBITD), or value added net of reported depreciation of

capital. We also show that the estimated pass-through is in the same range as our baseline result

if we exclude multinational corporations (for which it can be difficult to accurately measure value

added) or exclude the largest firms (which are more likely to have multiple plants).

Our analyses so far have relied on statistical processes of earnings and value added. While this

is common, the identification of shocks and pass-through rates relies on plausible but ultimately

debatable identifying assumptions. One concern is that individuals may change their behavior

in important ways in response to income shocks. For example, an exogenous increase in income

could cause workers to decrease labor supply, which could lead us to underestimate the passthrough to workers’ earnings of firm shocks. More indirect sources of bias in the estimation

of pass-through to workers could arise if individuals respond on margins that are correlated

with labor supply and earnings, such as capital investment, expenditure, marriage and fertility

decisions, geographic mobility, health investments, and retirement. To assess this, we analyze

information in Form W-2G on state lottery winnings. In particular, we leverage variation in

the timing of a lottery win, and form cohorts of lottery winners that win in different years. We

observe that prior to winning the lottery, the trend in employment, earnings, and other outcomes

evolve very similarly across lottery winning cohorts. This suggests a quasi-experimental research

design where we use later winners in the years prior to their lottery win as a control group

for current winners in the same calendar years. Concretely, this research design amounts to a

difference-in-differences analysis, where we use future winners to net out changes in the outcome

of interest due to common macroeconomic/time effects as well as common effects of the passage

of time, with the underlying identifying assumption that the exact timing of the lottery win

is unrelated to pre-existing outcome trends. We develop this identification strategy in greater

detail in Appendix D.1.

In Appendix D.1, we summarize difference-in-differences estimates of the the behavioral

responses to exogenous changes in income induced by lottery winnings in terms of earnings,

employment, and related behavioral response margins. Reassuringly, we find modest effects

on both employment and earnings per dollar won. On average, prize winners reduce their

employment by roughly $0.02 per dollar won. After estimating the average effects of income

changes induced by lottery winnings, we explore heterogeneity in impacts in various dimensions

such as age and prize size. Furthermore, Appendix D.4 summarizes related results, but in terms

of per-period income, where we use two distinct approaches to allocating one-time lottery income

shocks into annual income shocks.

Taken together, our analysis of lottery-induced changes in income lends support to the modeling of the income process. One remaining concern, however, is that the identification of firm

shocks and pass-through rates rely on plausible but ultimately debatable identifying assumptions. To critically examine and relax these assumptions – and thereby improve the quality

and credibility of our analyses – we extract observable firm shocks based on outcomes of public procurement auctions run by state governments, particularly departments of transportation

(DOTs). When two firms bid blindly for the same contract, and one firm happens to win by a

small margin, a (quasi)experiment is produced. The winning firm receives an as good as random

change in the demand for their products or services, producing exogenous shocks to their labor

demand. Using many such experiments from state government DOT public auction data, we

examine how these shocks transmit to workers.

We use the experiment of winning a procurement auction to estimate the pass-through of

firm-specific shocks. To do so, we match the records of firms that bid in procurement auctions

to their tax information using a matching algorithm. Appendix Table A.4(a) demonstrates

that the matching algorithm performs well in validation exercises. Appendix Table A.4(b)

provides an overview of the sample and shows that it is representative of the broader economy.

Nationally, the firms that were matched to procurement auctions represent around 10% of all

EBITD and employment in the construction industry. Appendix Table A.4(c) provides basic

sample characteristics on the main outcome variables of interest.

Given this data, Appendix Figures A.5(a-b) provide the pass-through effects of winning a

procurement auction on log earnings per worker and log number of employees, respectively. We

estimate these effects both prior to the auction announcement (“Before”) and after the auction

winner is announced (“After”). Since the auction should not affect the firm’s demand for labor

prior to the auction winner being announced, we expect to find no effects during the Before

period, so the Before period serves as a falsification test. In the bars labeled “Baseline”, we

compare auction winners to non-recipients that had never won an auction before and placed a

bid at the same time as the winners but lost. In the After period, we find that earnings per

worker increase by about 2% while the number of employees increases by about 8%. The ratio of

the effect on log employment to the effect on log earnings per worker recovers the labor supply

elasticity, which is presented in the “Baseline” bar of Appendix Figure A.8 to be about 4. We

show in Appendix Figure A.5 that these effects are similar if inferring the labor supply elasticity

from log receipts and using the shift-share design. We then use this labor supply elasticity

estimate to fit the rent-sharing model of Kroft et al. (2021). In Appendix Table A.41, we find

similar estimates when using GMM or OLS estimation for the key parameters, which are the

product demand elasticity 1/, the composite returns to labor ρ, the marginal returns to labor

βL , and the interquartile range of TFP estimates. Appendix Figure A.30 demonstrates that

these parameters are relatively similar across broad markets and years.

For robustness of the estimates based on procurement auctions, we consider a number of

alternative specifications. In Appendix Figures A.5(a-b), we consider restricting the control

sample to firms that had never bid in an auction before (bar labeled “Sample: First-timers”),

firms that would not go on to win an auction in the future (bar labeled “Sample: Never-winners”),

or firms that bid in the same auction as the winners (bar labeled “Sample: Same Auction”),

finding very similar effects in the After period and passing the falsification test in the Before

period. For the effect on mean log earnings in Appendix Figures A.5(a), we also consider reestimating these effects on the mean earnings of stayers or workers with longer tenure in the

firm, finding similar effects. The corresponding bars in Appendix Figure A.8 demonstrate that

the labor supply elasticity is not sensitive to these alternative specifications. Appendix Figure

A.6 demonstrates that the results are relatively stable across years after the auction occurs.

Appendix Figure A.7 demonstrates that the results are similar regardless of whether or not

the state in which the auction occurs has right-to-work or prevailing wage laws. Appendix

Figure A.9(a-b) demonstrates that the robustness of the results is not sensitive to the number

of years used when defining stayers and tenured workers, respectively. Appendix Figure A.9(c)

demonstrates that the effects on stayers are not sensitive to the minimum earnings threshold

required for workers to be included in the sample. Appendix Figure A.9(d) demonstrates that,

when we restrict the sample to winners and losers whose bids were within a close bandwidth of

one another, the results remain similar.

4.2

Mover analyses

So far, we focused on income volatility among workers who stay in the same firm over time. We

now turn attention to an approach which examines income changes associated with a worker

entering a new firm.

In the baseline results, we consider a special case which assumes that φij = xi + ψj and that

γ = Υ = 0. The first restriction imposes a log additive structure on the earnings that worker

i can expect to receive from working in firm j. Under this functional form, the worker fixed

effect captures the (time-invariant) portable component of earnings ability, whereas the firm

fixed effect can be interpreted as a firm-specific relative pay premium. The second restriction

assumes there is no pass through of firm or market level shocks. As a result, the firm effects

on earnings do not vary over time. By invoking these two restrictions, our statistical model

of earnings reduces to the two-way (worker and firm) fixed effect model of AKM. Appendix

C.2 presents results from relaxing these assumptions, and Appendix C.3 provides additional

robustness checks.

Under the above restrictions, the variance of log earnings can be written as:

V ar(log Wit ) = V ar(xi + Xit0 b) + V ar(ψj(i,t) ) + 2Cov(xi + Xit0 b, ψj(i,t) ) + V ar(it )

} |

} | {z }

Worker component

Firm component

Sorting component

(1)

Residual

where the worker and firm components tell us how much of the variation in log earnings can

be attributed to heterogeneity in worker and firm effects, respectively. The third component

captures the contribution to earnings inequality from the sorting of workers to firms. The goal

is to quantify these three components to draw inference about the determinants of earnings

inequality in the U.S. economy. The decomposition includes both workers who move between

firms and stayers. However, the firm and worker effects are only separately identified within a

connected set of firms that are linked by worker mobility. Consistent with previous work, we

therefore restrict our sample of workers (including stayers and movers) to those who work at a

firm in the largest connected set in each time interval (2001-2008 and 2008-2015). In the U.S.,

this set covers more than 90 percent of the workers (see Appendix Table A.6).

In Table 3, we present results from the variance decomposition in (1) based on data for

all firms and workers in the connected set (which includes both workers who move between

firms and stayers). This table reports estimates of the worker, firm and sorting components as

defined in equation (1). Appendix Table A.7 shows estimates of the subcomponents in the second

equality of (1). Consider first Panel A of Table 3 where we present estimates from the AKM

estimator for two different time periods (2001-2008 and 2008-2015) as well as pooled estimates

where we combine the data from these time periods. The results show that the worker, firm

and sorting components change little over time. Therefore, we focus attention on the pooled

estimates. These results suggest that the firm effects explain around 9 percent of the variation

in log earning, whereas worker sorting accounts for 5 percent. The correlation between firm

effects and worker effects is only 0.1.

Next, consider Panel B of Table 3 where we report the BLM estimates. As discussed in

Appendix C.1, a possible advantage of the BLM estimator is that it addresses limited mobility

bias. Once we correct for such bias we find that firm effects are very small in the U.S. labor

market, accounting for only 3 percent of the variation in log earnings. Instead, a larger part of

the earnings variation is explained by worker sorting. The correlation between firm effects and

Years:

2001-2008

Panel A.

Share explained by:

i) Worker Effects

ii) Firm Effects

iii) Sorting

Sorting Correlation:

Pooled

AKM Estimation

V ar(xi )

V ar(ψj(i) )

2Cov(xi , ψj(i) )

Cor(xi , ψj(i) )

Panel B.

Share explained by:

i) Worker Effects

ii) Firm Effects

iii) Sorting

Sorting Correlation:

2008-2015

75%

0.09

75%

0.11

75%

0.10

BLM Estimation

V ar(xi )

V ar(ψj(i) )

2Cov(xi , ψj(i) )

Cor(xi , ψj(i) )

72%

13%

0.43

72%

14%

0.46

72%

14%

0.44

Table 3: AKM and BLM Log Earnings Decomposition Estimates

Notes: This table presents the decomposition of log earnings variation using the AKM and BLM estimators for

two time periods.

worker effects exceeds 0.4 once we correct for limited mobility bias. This finding suggests that

sorting of better workers to better firms is an empirically important feature of the U.S. labor

market. Detailed sorting patterns are presented in Appendix Figure A.13.

In Table 4, we repeat the AKM and BLM analyses to understand the roles of firm effects,

worker effects, and the sorting of workers to firms in explaining gross household income and

net household income. We find that moving to a new firm causes even smaller changes in

gross and net income as compared to earnings. Moreover, sorting of better workers to better

firms contribute less to inequality in gross and net income than to dispersion of earnings. By

contrast, worker effects explain a larger part of the variation in gross and net income as compared

to gross earnings. Finally, the sorting of workers to firms explains about 5% of the variance in

each income measure compared to 9% for earnings, indicating that the Federal tax-and-transfer

system attenuates the incentives for better workers to move to better firms.

Inequality within and between firms

We now shift attention to describing the inequality within and between firms. To do so, we

follow Song et al. (2018) in expressing the variance of log earnings as:

Income Measure:

Earnings

Gross Income

Net Income

Panel A. AKM Estimation

Share explained by:

i) Worker Effects

ii) Firm Effects

iii) Sorting

Sorting Correlation:

V ar(xi )

V ar(ψj(i) )

2Cov(xi , ψj(i) )

Cor(xi , ψj(i) )

75.4%

8.8%

4.9%

0.09

83.6%

5.0%

2.6%

0.06

84.4%

4.7%

2.2%

0.05

Panel B. BLM Estimation

Share explained by:

i) Worker Effects

ii) Firm Effects

iii) Sorting

Sorting Correlation:

V ar(xi )

V ar(ψj(i) )

2Cov(xi , ψj(i) )

Cor(xi , ψj(i) )

72.4%

3.2%

12.9%

0.43

81.0%

0.4%

5.4%

0.45

84.0%

0.4%

4.8%

0.44

Table 4: AKM vs BLM by Income Measure

Notes: This table presents AKM and BLM decomposition estimates for log earnings, gross income, and net

income.

V ar(log Wit ) = V ar (log Wit − E [log Wit |j(i, t) = j]) + V ar (E [log Wit |j(i, t) = j])

} |

}

Within−firm

(2)

Between−firm

= V ar (xi + Xit0 b − E [xi + Xit0 b|j(i, t) = j]) + V ar(it ),

}

Worker heterogeneity within firms

+ V ar ψj(i,t) + 2Cov

} |

Firm effects

xi + Xit0 b, ψj(i,t)

Sorting

}

| {z }

Residual

+ V ar (E [xi + Xit0 b|j(i, t) = j])

}

Segregation

where the first equality expresses the variance of log earnings in terms of inequality within and

between firms, and the second equality decomposes these terms into economically interpretable

subcomponents. Our interest is centered on the last three subcomponents, which capture distinct

sources of inequality between firms: dispersion of firm pay premiums (“Firm effects”); sorting of

high earning workers into high paying firms (“Sorting”); and worker segregation which reflects

differences in the quality of the workforce across firms (“Segregation”). Both worker sorting

and segregation reflect non-random allocation of workers to firms. However, sorting matters for

aggregate inequality, whereas segregation does not. This is because an increase in segregation

will be offset by a reduction in within-firm inequality. Thus, changes in segregation by itself does

not affect earnings inequality; it does, however, matter for the relative importance of inequality

within versus between firms.

To perform the decomposition in (2), we use exactly the same sample as in Table 3 which

includes both workers who move between firms and stayers. The results are presented in Table

5. In Panel A, we report the terms in the first equality. We find that around one-third of the

variance of log earnings can be accounted for by the dispersion of average earnings between

firms. The remainder is due to heterogeneity across workers within firms. A comparison of the

estimates across the two first columns suggests the between firm component has become slightly

more important for inequality over time. This finding is broadly consistent with the results

reported in Song et al. (2018).4

In the next two panels of Table 5, we use the procedures of AKM and BLM to estimate

the subcomponents from the second equality. There are three main findings from this analysis.

First, a vast majority of the inequality within firms can be accounted for by the observable

characteristics and the fixed effects of the workers. Indeed, only 16 percent of the within-firm

inequality reflects time-varying unobservables of the worker. Second, once one addresses limited

mobility bias then firm effects explain only 10 percent of the inequality between firms. By

comparison, sorting of high earning workers to high paying firms accounts for 40 percent while

the remaining 50 percent can be attributed to worker segregation that is unrelated to firm pay

premiums. Third, there seems to be little if any changes in the relative importance of firm

effects, worker sorting and segregation over the time intervals we consider.

Our finding of the inequality contribution from firm effects changing little over time is consistent with Song et al. (2018), albeit their analysis uses AKM and thus suffers from limited

mobility bias. Table 5 reveals, however, that this bias does not change materially over the

time intervals we consider. As a result, bias correction seems to be empirically important for

accurately describing the cross-sectional distribution of earnings in the U.S., but not for understanding the growth in earnings inequality.5

Analyses of firm entry and exit

While the analyses discussed above allow us to understand the income volatility due to shocks

to or mobility between existing firms, they do not tell us how workers are affected by entry or

exit of firms in the same location. Intuitively, when a large factory opens or shuts down, we

expect it to impact the commuting zone as a whole rather than only its own workers, affecting

important economic outcomes like income variability, tax payments, and the unemployment rate.

As explained in Appendix E.1, we obtain an instrumental variable for firm entry and exit with

plausibly exogenous variation by analyzing how aggregate fluctuations in foreign economies may

affect foreign-owned firms’ decisions to enter or exit a location, making use of the information

on foreign ownership. In particular, when a foreign economy expands or contracts, we expect it

to result in more entry or exit of foreign-owned firms in the commuting zones with higher initial

concentration of activity by owners from that country, allowing us to draw causal inference

(under plausible identifying assumptions) by comparing those locations that do and do not

receive these shocks.

4 The analyses in Song et al. (2018) is based on data from 1978 to 2013. Over this longer time period, they

show that earnings inequaliy increased considerably, primarly due to a significant rise in the dispersion of average

earnings across firms. During the period we consider, however, Song et al. (2018) also report a modest increase

in earnings inequality, overall and between firms.

5 Song et al. (2018) also argue that increases in sorting and segregation caused a large increase in between-firm

inequality from 1981 to 2013. At first sight, it would seem like this is inconsistent with our findings. However,

most of these increases happen before our data start. During the intervals since 2001 that we consider, Song

et al. (2018) report modest increases in the contributions to between-firm inequality from sorting and segregation

and a modest decrease from firm effects, consistent with our AKM estimates.

Years:

2001-2008

Panel A.

2008-2015

Pooled

Total Decomposition

Within Firm Share:

Between Firm Share:

Panel B.

Shares of Within Firm Variance:

Worker Heterogeneity:

Residual:

Shares of Between Firm Variance:

Firm Effects:

Segregation:

Sorting:

V ar(wit − E[wit |j])

V ar(E[wit |j])

67%

33%

64%

36%

66%

34%

AKM Decomposition

V ar(xi + Xit

b − E[xi + Xit

b|j])

V ar(it )

84%

16%

85%

15%

84%

16%

V ar(ψj )

V ar(E[xi + Xit

b|j])

2Cov(xi + Xit

b, ψj )

27%

58%

15%

25%

59%

16%

26%

59%

15%

Panel C.

BLM Decomposition

Shares of Within Firm Variance:

Worker Heterogeneity:

Residual:

Shares of Between Firm Variance:

Firm Effects:

Segregation:

Sorting:

V ar(xi + Xit

b − E[xi + Xit

b|j])

V ar(it )

83%

17%

84%

16%

84%

16%

V ar(ψj )

V ar(E[xi + Xit

b|j])

2Cov(xi + Xit

b, ψj )

10%

50%

40%

10%

50%

40%

10%

50%

40%

Table 5: AKM and BLM Within and Between Inequality Decompositions

Notes: This table presents the decomposition of log earnings variation within and between firms using the

AKM and BLM estimators for two time intervals. The analysis uses both workers who move between firms and

stayers.

In Appendix E.2, we present and discuss the parameter estimates and the results from a

number of specifications and robustness checks. As shown in Appendix Table A.26, we find

a positive and statistically significant effect of a firm entering the market on the earnings of

workers at existing firms in the same commuting zone. To put the estimates in context, we

find that, if a firm employing 10 percent of employees in the commuting zone exits and lays

off its workers, then workers in existing employment relationships at other firms in the same

commuting zone experience a 4.5% decline in employment, a 4.7% decline in earnings payments

to workers, and a 6.4% decline in the firm’s value added. Interestingly, as shown in Appendix

Table A.32, we find that a layoff shock due to firm exit results in a substantial decrease in gross

and net income among workers at other firms in the same commuting zone. However, the impact

on net income is smaller than the effect on earnings and gross income, and the estimates imply

that the Federal tax-and-transfer system provides about a 9 percent rate of insurance against

shocks due to other firms entering and exiting.

4.3

Income volatility, tax revenues, and receipt of tax credits

So far, we have focused on documenting income volatility, quantifying its sources, and examining

the attenuation from the Federal tax-and-transfer system. We now shift attention to examining

how income volatility, at the individual and market level, may make it difficult to predict tax

revenues or receipt of tax credits.

Income processes and mover analyses

The goal is to use the estimates from the income processes and mover analyses to i) examine

how various sources of income volatility may generate change in tax revenues, and ii) illustrate

how the impact on tax revenues of income volatility may depend on the progressivity of the

tax system. As a first step, however, it is convenient to parametrize the tax schedule. Following Heathcote et al. (2014) and Blundell et al. (2016), we choose the following log-linear

parametrization to approximate the effective tax rates implicit in the Federal tax-and-transfer

system.

I˜i,t = τ Iit

where I denotes gross income and I˜ denotes net income. We estimate these parameters outside

the model. In each year, we regress log net household income (earnings plus other income minus

taxes) on log household gross income (earnings plus other income) for our sample. The construction of these income measures is detailed in Appendix A. The intercept from this regression

gives us τ while λ is identified from the slope coefficient. We estimate τ of around 0.89 whereas

λ is estimated to be about 0.92.6 In a proportional tax-transfer system, λ is equal to one and

(1 − τ ) is the proportional effective tax rate. By contrast, if 0 < λ < 1, then the marginal

effective tax rate is increasing in earnings. Appendix Figure A.17 shows how well our parsimo-

nious tax function approximates the effective tax rates implicit in the complex U.S. tax-transfer

system. Here we compare the predicted log net income from the regression to the observed log

net income across the distribution of log gross income, finding that this specification provides

an excellent fit.

First, we use the estimated tax schedule to understand how firm shocks are passed-through

to tax revenues. To do so, we simulate a one standard deviation shock to log value added at

the firm. Then, we use the estimated passthrough rates and the estimated tax-transfer system

to collect the implied changes in gross and net income, which in turn provide us the average

tax revenue response to a firm shock. Mean tax revenues rise in response to a firm shock in

the baseline tax system, as all workers have greater income and marginal tax rates are positive.

Finally, we change the parameter λ in order to investigate how the average tax revenue response

to the firm shocks depends on tax progressivity. Figure 4 presents the results of this exercise.

We find that the responsiveness of tax revenues to firm shocks is greater when the tax schedule

is more progressive.

Second, we use the estimated tax schedule to understand how sorting across firms affects

mean tax revenues. To do so, we use the AKM model for log gross income (it is the sum of

the firm effect, the worker effect, and the worker-year residual) but randomly re-assign firm

effects to construct log gross income without sorting. We then use the tax function to collect

6 These results mirror closely existing U.S. estimates of τ and λ (see e.g. Guner et al., 2014, Heathcote et al.,

2017).

●

Mean Tax Revenue Response to a 1SD Firm Shock

●

4000

●

3000

●

2000

●

Baseline

●

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Tax Progressivity

Figure 4: Mean Tax Revenue Responses to a Passed-through Firm Shock, by Tax Progressivity

Notes: In this figure, we consider the effect of a firm shock on mean tax revenues. To do so, we simulate a one

standard deviation shock to log value added at the firm. Then, we use the estimated passthrough rates and the

estimated tax-transfer system to collect the implied changes in gross and net income, which in turn provide us

the average tax revenue response to a firm shock. Finally, we change the parameter λ in order to investigate

how the average tax revenue response to the firm shock depends on tax progressivity.

implied net income and tax revenues for each worker, with and without sorting. Mean tax

revenues fall without sorting in the baseline tax system, as fewer workers receive high incomes

and high incomes face greater marginal tax rates. Finally, we change the parameter λ in order

to investigate how the average tax revenue response to sorting depends on tax progressivity.

Figure 5 presents the results of this exercise. We find that the tax revenue gains from sorting

are greater when the tax schedule is more progressive.

Analyses of firm entry and exit

Appendix Table A.32 uses the instrumental variables design described in Appendix E.1 in order

to estimate the effect that firm entries and exits has on tax payments made by workers employed

at other firms in the same commuting zone. It finds a positive and statistically significant effect.

To put the estimates in context, we find that, if a firm employing 10 percent of employees in the

commuting zone exits and lays off its workers, then workers in existing employment relationships

at other firms in the same commuting zone experience a 6.8 percent decline in tax payments.

In order to better understand the responsiveness of tax revenues, we highlight an important

component of the system, the Earned Income Tax Credit (EITC). We consider two margins

of EITC utilization – claiming any EITC deduction (the extensive margin) and the amount of

deduction claimed (the intensive margin).7 In Appendix Table A.32, we find negative effects of

7 Because the EITC is zero either at t or t − 1 for an observation that experiences a change in the EITC

extensive margin, we cannot explore log differences, as we do for other outcomes. Instead, we consider the

●

Mean Tax Revenue Gains from Sorting

●

1000

●

800

●

600

●

Baseline

●

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Tax Progressivity

Figure 5: Mean Tax Revenue Gains from Sorting, by Tax Progressivity

Notes: In this figure, we consider the gains from sorting on mean tax revenues. To do so, we randomly

re-assign firm effects across workers so that firm effects and worker effects are uncorrelated, then reconstruct log

gross income. Then, we use the estimated passthrough rates and the estimated tax-transfer system to collect

the implied changes in gross and net income, which in turn provide us the average tax revenue gains from

sorting. Finally, we change the parameter λ in order to investigate how the average tax revenue gains from

sorting depends on tax progressivity.

firm entry on both the extensive and intensive margin of EITC participation, though statistical

precision is somewhat limited. To put the estimates in context, we find that, if a firm employing

10 percent of employees in the commuting zone exits and lays off its workers, then workers

in existing employment relationships at other firms in the same commuting zone experience

approximately a 2.4 percent increase in EITC take-up and approximately a 3.1 percent increase

in the EITC deduction claimed. These results suggest that the EITC is an active channel

through which tax revenues adjust to insure against firm entry and exit shocks for workers

employed at other firms in the commuting zone.

Concluding remarks

In this report, we documented income volatility and examined its causes and consequences.

Our empirical findings raise questions such as: What do small firm effects, strong sorting and

significant pass-through of firm shocks tell us about the functioning of the labor market? How

would changes in tax policy affect earnings inequality, worker sorting, income volatility and tax

payments? To answer these questions, we have developed an equilibrium model of the labor

market that can match the empirical findings that we documented in this report. The model not

transformation of Davis et al. (1996), which is able to include any observation that experiences an extensive

margin change, and can be interpreted as an approximation to the log difference for small changes; see their

paper for further details.

only allows us to economically interpret the empirical findings reported here but also to improve

the analysis of income volatility and taxation. In particular, our model captures that changes in

tax policy may induce firms to change their hiring and wage setting, and such changes may affect

workers’ choice of firm, industry and region. Thus, we can perform model-based simulations

of tax reforms which relax the assumption made in Section 4.3 of no behavioral responses of

workers and firms to the changes in tax progressivity. See Appendix F for additional results

based on the equilibrium model of the labor market.

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Appendix: Sample Construction and Variable Definitions

All firm-level variables are constructed from annual business tax returns over the years 20012015: C-Corporations (Form 1120), S-Corporations (Form 1120-S), and Partnerships (Form

1065). Worker-level variables are constructed from annual tax returns over the years 2001-2015:

Direct employees (Form W-2), independent contractors (Form 1099), and household income and

taxation (Form 1040).

Variable Definitions:

• Earnings: Reported on W-2 box 1 for each Taxpayer Identification Number (TIN). Each

TIN is de-identified in our data.

• Gross Household Income: Using a definition similar to that of Piketty and Saez (2003),

we define gross household income as the sum of taxable wages and other income (line 22

on Form 1040) minus unemployment benefits (line 19 on Form 1040) minus taxable Social

Security benefits (line 20a on Form 1040) plus tax-exempt interest income (line 8b on Form

1040). We at times also consider this measure when subtracting off Schedule D capital

gains (line 13 on Form 1040).

• Federal Taxes on Household Income: This is given by the sum of two components.

The first component is the sum of FICA Social Security taxes (given by 0.0620 times

the minimum of the Social Security taxable earnings threshold, which varies by year, and

taxable FICA earnings, which are reported on Box 3 of Form W-2) and FICA Medicare

taxes (given by 0.0145 times Medicare earnings, which are reported on Box 5 of Form

W-2). The second component is the sum of the amount of taxes owed (the difference

between line 63 and line 74 on Form 1040, which is negative to indicate a refund) and the

taxes already paid or withheld (the sum of lines 64, 65, 70, and 71 on Form 1040).

• Net Household Income: We construct a measure of net household income as Gross

Household Income minus Federal Taxes on Household Income plus two types of benefits:

unemployment benefits (line 19 of Form 1040) and Social Security benefits (line 20a of

Form 1040).

• Employer: The Employer Identification Number (EIN) reported on W-2 for a given TIN.

Each EIN is de-identified in our data.

• Wage Bill: Sum of Earnings for a given EIN plus the sum of 1099-MISC, box 7 nonemployee compensation for a given EIN in year t.

• Size: Number of FTE workers matched to an EIN in year t.

• NAICS Code: The NAICS code is reported on line 21 on Schedule K of Form 1120

for C-corporations, line 2a Schedule B of Form 1120S for S-corporations, and Box A of

form 1065 for partnerships. We consider the first three digits to be the industry. We code

invalid industries as missing.

• Commuting Zone: This is formed by mapping the ZIP code from the business filing

address of the EIN on Form 1120, 1120S, or 1065 to its commuting zone.

• Value Added: Line 3 of Form 1120 for C-Corporations, Form 1120S for S-Corporations,

and Form 1065 for partnerships. Line 3 is the difference between Revenues, reported on

Line 1c, and the Cost of Goods Sold, reported on Line 2. We replace non-positive value

added with missing values.

– For manufacturers (NAICS Codes beginning 31, 32, or 33) and miners (NAICS Codes

beginning 212), Line 3 is equal to Value Added minus Production Wages, defined

as wage compensation for workers directly involved in the production process, per

Schedule A, Line 3 instructions. If we had access to data from Form 1125-A, Line 3,

we could directly add back in these production wages to recover value added. Without

1125-A, Line 3, we construct a measure of Production Wages as the difference between

the Wage Bill and the Firm-reported Taxable Labor Compensation, defined below, as

these differ conceptually only due to the inclusion of production wages in the Wage

Bill.

• Value Added Net of Depreciation: Value Added minus Depreciation, where Depreciation is reported on Line 20 on Form 1120 for C-corporations, Line 14 on Form 1120S for

S-corporations, and Line 16c on Form 1065 for partnerships.

• EBITD: We follow Kline et al. (2019) in defining Earnings Before Interest, Taxes, and

Depreciation (EBITD) as the difference between total income and total deductions other

than interest and depreciation. Total income is reported on Line 11 on Form 1120 for

C-corporations, Line 1c on Form 1120S for S-corporations, and Line 1c on Form 1065 for

Partnerships. Total deductions other than interest and depreciation are computed as Line

27 minus Lines 18 and 20 on Form 1120 for C-corporations, Line 20 minus Lines 13 and

14 on Firm 1120S for S-corporations, and Line 21 minus Lines 15 and 16c on Form 1065

for partnerships.

• Operating Profits: We follow Kline et al. (2019), who use a similar approach to Yagan

(2015), in defining Operating Profits as the sum of Lines 1c, 18, and 20, minus the sum of

Lines 2 and 27 on Form 1120 for C-corporations„ the sum of Lines 1c, 13, and 15, minus

the sum of Lines 2 and 20 on Form 1120S for S-corporations, and the sum of Lines 1c, 16,

and 16c, minus the sum of Lines 2 and 21 on Form 1065 for partnerships.

• Firm-reported Taxable Labor Compensation: This is the sum of compensation

of officers and salaries and wages, reported on Lines 12 and 13 on Form 1120 for Ccorporations, Lines 7 and 8 on Form 1120S for S-corporations, and Lines 9 and 10 on

Form 1065 for Partnerships.

• Firm-reported Non-taxable Labor Compensation: This is the sum of employer

pension and employee benefit program contributions, reported on Lines 17 and 18 on

Form 1120 for C-corporations, Lines 17 and 18 on form 1120S for S-corporations, and

Lines 18 and 19 on Form 1065 for Partnerships.

• Multinational Firm: We define an EIN as a multinational in year t if it reports a nonzero foreign tax credit on Schedule J, Part I, Line 5a of Form 1120 or Form 1118, Schedule

B, Part III, Line 6 of Form 1118 for a C-corporation in year t, or if it reports a positive

Total Foreign Taxes Amount on Schedule K, Line 16l of of Form 1065 for a partnership in

year t.

• Foreign Ownership: We define an EIN as foreign-owned in year t if it files Form 5472

in year t. The country of foreign ownership is also reported on Form 5472.

• Tenure: For a given TIN, we define tenure at the EIN as the number of prior years in

which the EIN was the highest-paying. A TIN has No Tenure if Tenure is zero years and

has High Tenure if tenure is at least five years.

• Age and Sex: Age at t is the difference between t and birth year reported on Data

Master-1 (DM-1) from the Social Security Administration, and sex is the gender reported

on DM-1 (see Chetty et al. (2011) for further details on the DM-1 link). We define Young

Age as Age less than or equal to 45 years, and Not Young Age as Age greater than 45

years.

• Gross State Lottery Winnings: This is the total reported in Box 1 of Form W-2G

when the form is identified as a state lottery payment in Box 3 of Form W-2G.

• Adjusted Gross Income: This is the tax-payer unit (TPU) adjusted gross income reported on Form 1040, divided by 2 in households of married filers.

• Observed Capital Income: This is the tax-payer unit (TPU) total observed capital

income (excluding capital gains), defined as the sum of dividends, interest income, pension income, rent and royalty income, and miscellaneous Schedule E rental income. All

components are reported on Form 1040. We divide by 2 in households of married filers.

• Marginal Tax Rate: This is the tax-payer unit (TPU) change in total taxes owed (state

+ federal) for a $1 change in TPU wage earnings. We calculate this using a tax calculator

written by Jon Bakija.

• Total Taxes Owed: This is the tax-payer unit (TPU) total taxes owed (state + federal).

We calculate this using a tax calculator written by Jon Bakija.

Sample Definitions:

• Analysis Sample: A TIN belongs to the Analysis Sample in year t if (a) her highestpaying EIN on form W-2 has positive Value Added in year t, (b) associated Earnings are

at least $15,000 in year t, (c) the commuting zone and 3-digit NAICS code of the EIN are

valid in year t, and (d) the TIN is matched to SSA records and the age associated with

the TIN at t is between 25 and 60.

• Stayers Sample: A worker belongs to the Stayers Sample in year t if (a) the worker

belongs to the Analysis Sample in years t, t-1, . . . , t-7, (b) her associated highest-paying

EIN is the same in years t, t-1, . . . , t-7, (c) the commuting zone and industry associated

with her highest-paying EIN are the same in years t, t-1, . . . , t-7, (d) there are at least 10

stayers per firm, and (e) there are at least 10 firms per commuting zone and industry.

• Movers Sample: A worker belongs to the Movers Sample if (a) the worker belongs to

the Analysis sample in years t and s, (b) her associated highest-paying EIN is different in

years t and s, and (c) there are at least two movers associated with the EIN.

• State Lottery Sample: A worker belongs to the State Lottery Sample in year t if (a) she

received a state lottery payment on Form W-2G between 2001 and 2016, (b) the worker

is not missing age or sex data from SSA records, (c) she was 21 to 64 years old at the

time of receiving the Form W-2G, and (d) her first recorded W-2G state lottery payment

between 2001 and 2016 was for $30,000 or more.

• Procurement Auctions Sample: A firm belongs to the Procurement Auctions Sample

if the matching algorithm detects a string match on name and address. The algorithm,

which uses a “fuzzy matching” approach with match quality measured using a sieve, is

validated using a subsample of 5 states which provided the firm’s EIN in the procurement

auction records and thus permit exact matching. Table A.4(a) shows that the algorithm

outperforms a simple text search (85% versus 79%).

Goods

Midwest

Northeast

Services

South

West

Panel A.

Midwest

All

Northeast

South

West

All

Full Sample

Observation Counts:

Number of FTE Worker-Years

Number of Unique FTE Workers

Number of Unique Firms with FTE Workers

Number of Unique Markets with FTE Workers

Group Counts:

Mean Number of FTE Workers per Firm

Mean Number of FTE Workers per Market

Mean Number of Firms per Market with FTE Workers

Outcome Variables in Log $:

Mean Log Wage for FTE Workers

Mean Value Added for FTE Workers

Firm Aggregates in $1,000:

Wage Bill per Worker

Value Added per Worker

42,910,324

9,319,084

294,907

1,514

26,701,886

6,088,816

232,740

270

40,332,913

10,218,947

439,823

1,780

31,598,149

7,714,829

329,721

916

69,049,669

17,315,144

1,051,608

4,108

62,399,969

15,168,284

1,055,084

761

103,263,800

26,530,182

1,908,800

4,926

71,385,819

17,953,911

1,314,677

2,509

447,642,529

89,579,704

6,479,326

16,164

22.1

2,007.0

91.0

17.8

6,778.8

380.6

16.1

1,581.7

98.0

16.3

2,524.2

155.2

10.4

1,217.4

117.0

9.7

5,623.1

577.9

9.5

1,488.4

156.2

9.6

2,084.0

216.3

11.4

1,906.6

166.9

10.76

17.36

10.81

16.80

10.70

16.67

10.81

16.64

10.61

16.18

10.74

16.04

10.62

15.94

10.70

16.07

10.69

16.31

43.6

91.2

50.7

107.5

42.2

85.1

52.9

91.6

34.3

90.5

44.2

111.1

35.8

94.2

40.3

92.3

40.9

95.2

17,458,234

4,125,425

188,405

1,463

11,545,098

2,830,268

144,294

266

18,078,675

4,822,238

265,504

1,753

15,521,491

3,877,827

215,212

878

31,647,628

7,724,643

571,413

3,915

28,398,961

6,663,264

549,162

755

50,074,776

11,909,494

1,019,393

4,783

35,344,937

8,324,587

700,921

2,359

208,069,800

32,077,850

3,560,534

15,609

13.5

862.4

64.0

11.9

2,964.1

248.9

11.2

730.3

65.3

11.6

1,310.7

112.8

8.2

597.7

72.6

7.9

2,617.4

332.3

7.9

759.3

96.1

8.2

1,116.4

136.8

8.9

936.7

105.0

10.76

17.36

10.81

16.80

10.70

16.67

10.81

16.64

10.61

16.18

10.74

16.04

10.62

15.94

10.70

16.07

10.69

16.31

2,588,628

798,575

13,884

197

1,777,928

532,507

10,896

111

1,237,821

416,549

9,409

216

1,150,115

354,518

9,767

104

2,315,238

740,091

18,083

335

2,527,212

764,699

19,475

213

2,609,997

865,629

19,626

438

2,207,552

724,155

16,185

219

16,506,865

5,217,960

117,698

1,826

10.95

18.04

10.99

17.56

10.97

17.46

10.99

16.56

10.90

17.45

11.01

17.23

10.96

17.89

11.05

17.93

10.97

17.61

Panel B.

Movers Sample

Observation Counts:

Number of FTE Mover-Years

Number of Unique FTE Movers

Number of Unique Firms with FTE Movers

Number of Unique Markets with FTE Movers

Group Counts:

Mean Number of FTE Movers per Firm with FTE Movers

Mean Number of Movers per Market with FTE Movers

Mean Number of Firms per Market with FTE Movers

Outcome Variables in Log $:

Mean Log Wage for FTE Movers

Mean Value Added for FTE Movers

Panel C.

Stayers Sample

Sample Counts:

Number of 8-year Worker-Firm Stayer Spells

Number of Unique FTE Stayers in Firms with 10 FTE Stayers

Number of Unique Firms with 10 FTE Stayers

Number of Unique Markets with 10 Firms with 10 FTE Stayers

Outcome Variables in Log $:

Mean Log Wage for FTE Stayers

Mean Log Value Added for FTE Stayers

Table A.1: Detailed sample characteristics

Notes: This table provides a detailed examination of the full sample, movers sample, and stayers sample.

Appendix: Earnings process, value added process and

pass-through

B.1

Explanation of the Empirical Approach

In this section, we use the panel data on workers and firms to describe key features of the U.S.

labor market. We begin by describing the statistical model of earnings that we will apply to this

data. Next, we present the empirical findings, and then discuss how they motivate and guide

our choices of how to model the labor market.

B.1.1

Statistical model of earnings

We assume that workers’ earnings can be described by the following equation:

log Wit = Xit0 ϑ + wit ,

(3)

where Wit denotes the earnings for individual i in year t, Xit is a vector of covariates which

includes a full set of indicators for calendar years and a cubic polynomial in age, and wit denotes

log earnings net of age effects and common aggregate time trends. As described below, we allow

wit to depend on both the workers’ own productivity and the firm in which she works. Our

measure of firm performance is value added, which is determined by the equation:

log Yjt = Zt0 ϕ + yjt ,

(4)

where Yjt denotes the value added for firm j in year t, Zt includes a full set of indicators

for calendar years, and yjt is log value added net of common aggregate time trends. The key

elements of equations (3) and (4) are the time series properties of wit and yjt , which we now

specify.

Specification of processes We assume that yjt evolve according to the following process:

+ ξjt + δ y ξjt−1

yjt = ζj + yjt

(5)

yjt

= yjt−1

+ ujt ,

ujt = ũjt + ūr(j),t

where r(j) denotes the market of firm j, ζj is a fixed effect for the firm, and the time-varying part

of yjt is decomposed into a permanent component, assumed to follow a unit root process with

innovation shock ujt , and a transitory component, which is assumed to follow a MA(1) process

with coefficients δ y and innovation variance σξ2 . The permanent innovation ujt consists of a

common innovation to all firms in a given market r, ūr(j),t ≡ E [ujt |r(j)=r], and an idiosyncratic

innovation specific to the firm, ũjt ≡ ujt −ūr(j),t .

We assume that wit evolve according to the following process:

wit = φij(i,t) + wit

+ νit + δ w νit−1

(6)

wit

= wit−1

+ γ ũj(i,t),t + Υ ūr(i,t),t + µit ,

where j(i, t) and r(i, t) denote the firm and market of worker i in year t, and φij is a fixed effect

for worker i if she works in firm j. The time-varying part of wit is decomposed into a permanent

component wit

and a transitory component, assumed to follow a MA(1) process with coefficients

δ w and innovation variance σv2 . The permanent earnings component evolves for three reasons:

worker-specific innovations µit , pass through of firm-specific value added shocks γ ũj(i),t,t , and

pass through of market level value added shocks Υ ūr(i,t),t .

Parameters of interest and assumptions Our interest is centered on two aspects of this

statistical model of earnings. The first is how changes in firm performance affect the earnings

of incumbent workers, as measured by the pass-through rates γ and Υ . The second is the

determinants of the cross-sectional distribution of earnings, which we measure by decomposing

φij into components that capture worker heterogeneity, firm-specific wage premiums, worker

sorting, and interactions between worker and firm effects.

For these purposes, it is necessary to invoke some restrictions on the statistical model of

earnings. Let J = {j(i, t)}i,t and U = {ũjt , ūr(j),t }j,t and Q = {ξjt }j,t . We make the following

assumptions:

Assumption 1. E [ξjt |r(j)=r, J, U ] = E [ξjt0 ξjt |r(j)=r, J, U ] = 0 for all j, r, t, t0 .

Assumption 2. E [µit , νit |J, U, Q] = 0 for all i, t.

Assumption 1 is the same restriction on the error structure of the value added process as in Guiso

et al. (2005). It implies that transitory shocks to value added are mean zero and uncorrelated

with past transitory shocks to value added. Assumption 2 is a condition on the relationship

between the worker-specific innovations to earnings, worker mobility, and innovations to firm

value added. The assumption embodies two types of economic restrictions. The first restriction,

from conditioning on j(i, t), implies that mobility is exogenous to the worker-specific innovations

to earnings (which are paid to the worker independent of the choice of firm). This is the

same restriction on worker mobility as invoked in the Abowd et al. (1999) model. The second

restriction, from the conditioning on the innovations to firm value added, implies that the

worker-specific innovations to earnings neither co-vary across coworkers nor with shocks to firm

value added. This is the same restriction as in Guiso et al. (2005).

It is important to observe what is not being restricted under Assumptions 1 and 2. First,

we do not restrict whether or how workers sort into firms according to the worker effects, the

firm effects, or the interactions between the worker and firm effects. Second, we do not restrict

whether or what type of workers move across firms in response to innovations to firm value

added. In fact, workers with different values of φij may have arbitrarily different mobility

patterns. Third, the statistical model of earnings does not specify why individuals choose the

firm that they do. However, it also does not preclude the possibility that individuals choose firms

to maximize earnings or utilities. For instance, Assumptions 1 and 2 are consistent with each

worker choosing the firm that offers his preferred combination of wages and non-wage attributes.

B.1.2

Pass through of firm shocks

In this section, we are interested in estimating the parameters γ and Υ , which we refer to as

the pass-through rates of firm-specific and market level value added shocks. Before presenting

estimates of the pass-through rates, we show how these parameters can be identified through a

difference-in-differences (DiD) strategy.

Identification, moment conditions and DiD representation

To compare with existing

work, we first consider a special case of the statistical model of earnings where γ = Υ . That is, we

assume the pass-through rate of an idiosyncratic value added shock to the current firm is of the

same size as the pass-through rate of a value added shock to all firms in the current market. We

focus on the sample of stayers as captured by the indicator variable Si = 1[j(i, 1)=...=j(i, T )].

Assumptions 1 and 2 give the following moment conditions:

E ∆yj(i)t wit+τ − wit−τ 0 − γ yj(i),t+τ − yj(i),t−τ 0 |Si =1 = 0

for τ ≥ 2, τ 0 ≥ 3

(7)

Solving for γ we identify the pass through of a firm-specific shock to the earnings of incumbent

workers:

E ∆yj(i)t (wit+τ − wit−τ 0 ) |Si =1

γ=

E ∆yj(i)t yj(i),t+τ − yj(i),t−τ 0 |Si =1

Thus, we can identify the pass through of a firm-specific shock from our panel data on firms

and workers.

DiD interpretation

To interpret this identification result and assess the underlying assumptions, note that the statistical model of earnings includes fixed effects for time and agents. By controlling for these fixed

effects we obtain a DiD strategy, looking within workers and firms while eliminating common

changes over time in the labor market or the economy more generally. To see the DiD representation, suppose for simplicity the workers can be assigned to two groups of firms: one half has

∆yj(i)t = +δ and the other half has ∆yj(i)t = −δ . We then get the following interpretation of

γ as the ratio of two DiDs.

γ=

E [wit+τ − wit−τ 0 |+δ, Si =1] − E [wit+τ − wit−τ 0 |−δ, Si =1]

E yj(i),t+τ − yj(i),t−τ 0 |+δ, Si =1 − E yj(i),t+τ − yj(i),t−τ 0 |−δ, Si =1

Under an assumption of common underlying trends between the two groups, the numerator

gives the treatment effect on log earnings; the denominator gives the treatment effect on log

value added; and the ratio gives the elasticity of earnings with respect to value added.

Graphical evidence

In Figure A.1, we empirically assess the DiD strategy. The figure is constructed in the following

way: In any given calendar year (denoted period t = 0), we i) order firms according to the

increase ∆yj(i)t ; ii) separate the firms at the median in the distribution of ∆yj(i)t , letting the

upper half constitute the treatment firms and the lower half the control firms; and iii) plot

the differences in yjt between these two groups in period t = 0 as well as in the years before

(periods t < 0) and after (periods t > 0). We perform these three steps separately for various

calendar years, always weighting each firm by the number of workers. The solid (dashed) black

line represents the difference in log value added (wages) for the treatment and control firms

where each firm is weighted by the number of workers.

By construction, the treatment and control groups differ in the value added growth from

period t−1 to period t. On average, firms in the treatment group experience about 30 percentage

points larger growth in value added as compared to firms in the control group. According to the

value added process (5), the growth in value added should be the sum of a permanent component

and a transitory, mean-reverting component. Due to the transitory component, ∆yj(i)t could

be correlated with ∆yj(i)τ at τ = t − 2, ..., t + 2. However, ∆yj(i)t should be orthogonal to

∆yj(i)τ in the periods before τ = t − 2 and after τ = t + 2. Consistent with this orthogonality

condition, the figure shows a very similar trend in log value added between the treatment and

control group at these periods. Reassuringly, firms that experienced large growth in value added

in period 0 are no more or less likely to experience large growth in value added in periods -6 to

-3 or in periods 3 to 6.

The dashed black line performs the same exercise, but this time for log wages of incumbent

workers who stay in the firm in all six years. On average, workers in treatment firms experience

an additional 5 percentage points increase in earnings in period 0 as compared to workers in

the control firms. Interpreted through the lens of the DiD design, this finding suggests a passthrough rate of firm shocks γ above .15. The growth in earnings is also the sum of a permanent

component and a transitory, mean-reverting component. Therefore, ∆wit could be correlated

with ∆wiτ at τ = t − 2, ..., t + 2, but it should be orthogonal to ∆wiτ in the periods before

τ = t − 2 and after τ = t + 2. Reassuringly, the dashed line shows a very similar trend in log

earnings between workers in the treatment and control group during these periods.

Firm versus market level shocks

We now shift attention to the general case where γ may differ from Υ , thereby allowing the

earnings of an incumbent worker to respond differently to an idiosyncratic value added shock

to the current firm than to a (same size) shock to all firms in a given market. To identify the

firm-level pass-through rate γ, we then need to demean the variables of interest using a within

market times year transformation, w̃it = wit − E [wit |r(i, t)=r] and ỹjt = yjt − E [yjt |r(j)=r].

Assumptions 1 and 2 then give the following moment conditions that we can use to identify the

pass-through rates of firm-specific value and market level added shocks by solving for γ and Υ :

E ∆ỹj(i),t w̃it+τ − w̃it−τ 0 − γ ỹj(i),t+τ − ỹj(i),t−τ 0 |Si =1 = 0

E ∆ȳj(i),t w̄it+τ − w̄it−τ 0 − Υ ȳj(i),t+τ − ȳj(i),t−τ 0 |Si =1 = 0

(8)

(9)

for τ ≥ 2, τ ≥ 3

where ȳr(j),t ≡ E [yjt |r(j)=r] and w̄r(j),t ≡ E [wjt |r(j)=r].

The red and blue lines in Figure A.1 represent the differences between the treatment and

control group in (w̃it , ỹjt ) and (w̄r(i,t),t , ȳr(j),t ) over time. These lines are constructed in the

same way as the black lines, except the red and blue lines use the demeaned variables w̃ and ỹ

and the market averages w̄ and ȳ, respectively. Comparing the red solid line to the red dashed

line reveals that conditioning on the full set of year times market fixed effects attenuates slightly

the treatment effect on log earnings relative to the treatment effect on log value added. Interpreted through the lens of the DiD design, this finding suggests the estimated pass-through rate

of a firm-specific shock will be slightly lower once we allow for Υ to differ from γ. By way of

comparison, the DiD applied to the market averages of wages and value added suggests a relatively large estimate of Υ . Thus, we expect the estimated pass-through rate of an idiosyncratic

value added shock to the current firm γ to be smaller than the pass-through rate of a same size

shock to all firms in the market Υ .

B.2

Tables and Figures

0.12

Log VA Difference (Solid)

0.08

0.2

0.04

0.1

0.0

0.00

−6

−3

Log Earnings Difference (Dashed)

0.3

Years from Event

Figure A.1: Differences-in-differences representation of the estimation strategy

Notes: This figure displays the mean differences in log value added (solid lines) and log earnings (dotted lines)

between firms that receive an above-median versus below-median log value added change at event time zero.

Results are presented for the unconditional measures of log value added and log earnings (black lines), for the

measures of log value added and log earnings net of market interacted with year effects (red lines), and for the

averages of log value added and log earnings by market and year (blue lines) The shaded area denotes the time

periods during which the orthogonality condition need not hold in the identification of the permanent

pass-through rate.

0.25

0.20

0.15

0.10

0.05

0.00

All

Older than 45

Some Tenure

Passthrough

Men

Firm Only

High Wage

High Wage Firm

All

Passthrough

Net of Market

(a) Heterogeneity across Workers

Oper. profits EBITD VA − deprec.VA < 10BNo multinat.

Workers < 100

Firm Only

Net of Market

(b) Heterogeneity across Firms and V.A. Measures

Figure A.2: Pass-through Heterogeneity

Notes: This figure displays heterogeneity in the GMM estimates of the pass-through, both firm only (imposing

Υ = γ) and removing market by year means (permitting Υ 6= γ).

GMM Estimates of Joint Process

Firm Only

Log Value Added

Panel A.

Accounting for Markets

Log Earnings

Log Value Added

Log Earnings

Process: MA(1)

Total Growth (Std. Dev.)

0.31

(0.01)

0.17

(0.00)

0.29

(0.01)

0.16

(0.00)

Permanent Shock (Std. Dev.)

0.20

(0.01)

0.10

(0.00)

0.17

(0.01)

0.10

(0.00)

Transitory Shock (Std. Dev.)

0.18

(0.01)

0.10

(0.00)

0.17

(0.01)

0.10

(0.00)

MA Coefficient, Lag 1

0.09

(0.01)

0.15

(0.00)

0.09

(0.01)

0.15

(0.00)

MA Coefficient, Lag 2

0.00

(0.00)

0.00

(0.00)

0.00

(0.00)

0.00

(0.00)

Permanent Passthrough Coefficient

0.14

(0.01)

0.13

(0.01)

Transitory Passthrough Coefficient

-0.01

(0.01)

0.00

(0.00)

Market Passthrough Coefficient

0.18

(0.02)

Panel B.

Process: MA(2)

Total Growth (Std. Dev.)

0.31

(0.01)

0.17

(0.00)

0.29

(0.01)

0.16

(0.00)

Permanent Shock (Std. Dev.)

0.20

(0.01)

0.10

(0.00)

0.17

(0.00)

0.10

(0.00)

Transitory Shock (Std. Dev.)

0.17

(0.01)

0.10

(0.00)

0.17

(0.01)

0.10

(0.00)

MA Coefficient, Lag 1

0.05

(0.05)

0.21

(0.01)

0.07

(0.04)

0.21

(0.01)

MA Coefficient, Lag 2

-0.03

(0.03)

0.04

(0.00)

-0.01

(0.02)

0.04

(0.00)

Permanent Passthrough Coefficient

0.15

(0.01)

0.13

(0.01)

Transitory Passthrough Coefficient

-0.02

(0.01)

0.00

(0.00)

Market Passthrough Coefficient

0.18

(0.03)

Table A.2: Estimated Process for Log Earnings and Pass-through

Notes: This table displays the parameter estimates of the log value added and log earnings growth processes as

well as the passthrough coefficients when using the GMM estimator. It presents these estimates for the firm

only model (which imposes Υ = γ) as well as the model in which firm and market pass-through coefficients are

allowed to differ (which permits Υ 6= γ).

Goods

Services

Midwest

Northeast

South

West

Midwest

Northeast

South

West

Log Earnings:

Unconditional

Net of Market

Market

Selection Coefficient

0.156

0.157

0.250

0.126

0.132

0.101

0.190

0.143

0.136

0.163

0.243

0.176

0.168

0.211

0.184

0.136

0.124

0.205

0.143

0.113

0.110

0.139

0.115

0.143

0.140

0.154

0.238

0.146

0.119

0.264

0.182

Log Size:

Unconditional

Net of Market

0.454

0.492

0.480

0.517

0.348

0.352

0.441

0.455

0.501

0.480

0.354

0.360

0.479

0.585

0.464

0.444

Other Moments:

Market Size (millions)

Labor Share

Profits per FTE Worker ($1,000)

Wagebill per FTE Worker ($1,000)

42.9

0.630

47.6

43.6

26.7

0.663

56.9

50.7

40.3

0.746

43.0

42.2

31.6

0.790

38.7

52.9

69.0

0.660

56.5

34.1

62.4

0.659

66.9

44.2

103.2

0.700

58.4

35.8

71.4

0.662

52.0

40.3

Table A.3: Detailed Passthrough Estimates and Aggregate Statistics across Regions and Sectors

Notes: In this table, we present passthrough estimates for various outcomes as well as other empirical moments

across broad regions and sectors.

100

Income

Earnings

Gross

Net

Pass−through Rate (%)

Income

Earnings

Gross

Net

Permanent Worker Shocks

Transitory Worker Shocks

Passed−through Firm Shocks

Pass−through

Permanent Worker Shocks

(a) Firm Only

Transitory Worker Shocks

Passed−through Firm Shocks

Pass−through

(b) Net of Market

Figure A.3: Growth and Pass-through Estimation for Alternate Income Concepts

0.30

0.25

0.20

Income

Earnings

0.15

Gross Income

Net Income

0.10

0.05

Pass−through Rate

Notes: In subfigure (a), we present the shares of (i) earnings, (ii) gross income, and (iii) net income growth

attributable to permanent and transitory shocks to workers and permanent shocks to firms, as well as the

passthrough rate from firms to workers, in the baseline specification (“Firm Only”). In subfigure (b), we repeat

this exercise when conditioning on a full set of market-year indicators (“Net of Market”).

0.20

Income

Earnings

0.15

Gross Income

Net Income

0.10

0.05

0.00

Midwest_Goods Midwest_Services Northeast_Goods Northeast_Services

South_Goods

South_Services

West_Goods

West_Services

Midwest_Goods Midwest_Services Northeast_Goods Northeast_Services

(a) Firm Only

South_Goods

South_Services

West_Goods

West_Services

(b) Net of Market

Figure A.4: Broad Market Heterogeneity in Passthrough Estimation by Income Measure

Notes: In this figure, we present broad market heterogeneity in the firm only and net passthrough rate of

permanent shocks from firms to workers.

Simple Search

Fuzzy Match

(1)

(2)

(3)

(4)

(5)

% Bidders Matched to Any Tax Record

% Bidders Matched to the True Tax Record

% Potential Matches Correctly Matched to Tax Records

80.2

65.3

78.6

99.9

63.0

75.8

97.6

62.5

75.1

99.9

71.0

85.4

95.8

70.3

84.5

Algorithm Parameters:

Match must be perfect (string score = 1.0)

Match must be high-quality (string score ≥ 0.6)

Prefer matches in same state as auction

(a) Algorithm Match Performance

DOT Auction Records

State

Data Source

Final Sample: Matched Auction-Tax Data

Includes EIN

State Website

FOIA Request

State Website

BidX Website

State Website

BidX Website

FOIA Request

BidX Website

FOIA Request

BidX Website

FOIA Request

BidX Website

BidX and State Websites

National

Bidders in 2010

Share of 2010 Construction Sector:

(Num. Firms)

Value Added

FTE Workers

196

149

1,041

241

126

344

137

256

112

213

130

167

141

391

262

179

122

135

320

140

551

241

200

194

103

15.7%

7.9%

8.3%

12.6%

9.4%

30.7%

4.3%

15.4%

17.2%

10.6%

13.7%

11.5%

13.7%

9.5%

13.5%

14.9%

15.0%

5.2%

43.7%

5.3%

4.9%

14.2%

7.5%

12.1%

13.7%

17.4%

12.8%

11.2%

14.7%

15.5%

10.6%

7.0%

20.7%

13.6%

16.6%

21.6%

10.8%

16.9%

16.3%

19.8%

13.3%

23.6%

9.8%

17.5%

11.5%

9.6%

12.0%

14.0%

14.6%

19.0%

6,792

10.7%

9.9%

(b) Shares by State of the Matched Firms in 2010

Number of Firms

Workers per Firm

Sales

EBITD

Intermediate Costs

Wage bill

Sample Size

Share of the

Construction Sector

7,876

0.9%

11.7%

Value Per Firm

($ millions)

Mean of the Log

Share of the

Construction Sector (%)

19.927

9.159

14.661

2.737

15.061

14.075

14.719

13.549

12.1%

9.6%

12.4%

13.4%

Table A.4: Characteristics of the Procurement Auctions Sample

Notes: These table characterizes the matched sample of firms that bid in procurement auctions. Table (a)

provides information on the performance of various matching algorithms. Table (b) provides information on the

representativeness of the matched sample in 2010, where states with more than zero but fewer than 100 matched

37 statistics (in 2010 unless stated otherwise).

firms are omitted (denoted by *). Table (c) displays sample

0.04

0.02

Event Time

0.00

Before

After

tio

−w

t−

tim

−0.02

(a) Log earnings per worker (numerator of θIV )

0.15

0.10

Event Time

0.05

Before

After

0.00

tio

−w

t−

lin

tim

−0.05

(b) Log number of employees (denominator of θIV )

Figure A.5: Pass-through of Observable Demand Shocks

Notes: This figure presents average treatment effect on the treated estimates using the difference-in-differences

specification defined in the text. All results include firm fixed effects. The control units are those firms that

place a bid in a procurement auction in the same year that the reference treatment cohort wins. The omitted

relative time is −2. 90% confidence intervals are displayed, clustering on firm.

tra

irs

t−

−w

tio

tim

tio

tim

lin

0.02

0.01

0.00

0.10

0.05

0.00

(a) Log number of employees

Non−

RTW

0.03

RTW

(b) Log number of employees

(a) Log earnings per stayer

0.03

Non−

RTW

Non−

0.04

Figure A.6: Reduced Form Estimates at Annual Frequency

0.15

(b) Log wage bill

Figure A.7: Reduced Form Estimates by Right-to-Work or Prevailing Wage States

Figure A.8: Labor Supply Elasticity: Main Estimates and Robustness Checks

(−1)

(−1,...,1)

(−2,...,2)

(−3,...,3)

Stayer Spell (Event Times)

Years of Tenure (Count)

(a) Robustness by Stayer Spell

(b) Robustness by Tenure Length

100

110

120

130

140

150

0.1

0.2

Share of FTE Wage (%)

0.3

0.4

0.5

Bandwidth

(d) Bandwidth Threshold

Figure A.9: Labor Supply Elasticity: Baseline Estimate and Alternative Specifications

Outcome Sample

First Stage

(Std. Error)

Reduced Form

(Std. Error)

Second Stage

(Std. Error)

Procurement auction shock at firm-level

8,677 unique auction bidders

0.143

(0.039)

0.020

(0.006)

0.142

(0.068)

Shift-share industry value added shock

667 unique commuting zones

0.708

(0.216)

0.134

(0.061)

0.189

(0.041)

Table A.5: Additional details regarding passthrough estimation

Notes: This table provides additional details on the passthrough estimation using procurement auctions and

shift-share instruments.

Appendix: Movers Analyses

C.1

Limited mobility bias

Even if the restrictions discussed in the text hold, it is challenging to draw inference about the

inequality contribution from firm effects and worker sorting. A key challenge is the incidental

parameter bias caused by the large number of firm-specific parameters that are solely identified

from workers who move across firms. The analysis of Andrews et al. (2008) suggests this limited

mobility bias can be substantial. With few movers per firm, the firm component is biased

upwards while the sorting component is biased downwards, with the size of the bias depending

inversely on the degree of worker mobility among firms.

To get a better sense of the scope for limited mobility bias in the U.S. data, we would ideally

apply the AKM estimator to alternative samples of workers and firms that are comparable except

for the number of movers per firm. Figure A.10 presents the results from such an analysis,

suggesting that the variance of firm effects declines monotonically as the number of movers

per firm increases. To construct this figure, we consider a subsample of firms with reasonably

many movers; that is, at least 15 movers per firm over the period 2001-2008. Applying AKM

to this subsample gives an estimate of the variance of firm effects of 6.7 percent. Next, we

remove movers randomly within firms (keeping the connected set of firms approximately the

same) before re-estimating the AKM model. The solid line displays the AKM estimates of

the variance of firm effects after randomly removing movers. Consistent with limited mobility

bias, the fewer the number of movers per firm, the larger the variance of firm effects. For

approximately the same set of firms, the estimated variance of firm effects is several times as

large (23 percent) if we only keep ten percent of the movers within each firm (on average, 7

movers per firm) as compared to what we obtained if we keep all the movers per firm (at a

minimum 15 and, on average, 62 movers per firm). By way of comparison, there are around

18 movers per firm in the full estimation sample (which roughly corresponds to the number of

movers per firm when randomly removing 40% of movers).

Until recently, the procedures for addressing limited mobility bias required strong and questionable assumptions about the covariance structure of the time-varying errors (see e.g. the

discussion in Card et al., 2018). To address this shortcoming, BLM and Kline et al. (2020)

propose approaches to address limited mobility bias that rely on a different or weaker set of

assumptions.1 The first approach reduces the dimension of firm heterogeneity to a finite number of types. BLM show how this approach can be used to alleviate the biases arising from

low mobility rates. The second approach uses a version of the Jackknife method. Kline et al.

(2020) show how this approach allows one to relax the homoskedasticity assumption in the bias

correction procedure proposed by Andrews et al. (2008). Since it is computationally infeasible

to apply Andrews et al. (2008) and Kline et al. (2020) to very large data sets (as one needs

to compute the trace of the inverse of the mobility matrix), our main analysis is based on the

approach of BLM. As a robustness check, however, we use a subset of the U.S. states to assess

1 Another possibility is to change the definition of a firm effect. See Borovickova and Shimer (2017) for such

an approach.

the sensitivity of the results to the choice of procedure for addressing limited mobility bias.

In Figure A.10, the dotted line shows estimates of the variance of firm effects based on the

procedure of BLM that addresses limited mobility bias. Firms are first classified into groups

based on the empirical earnings distribution using the k-means clustering algorithm. The kmeans classification groups together firms whose earnings distribution is most similar. Then,

in a second step, the worker effects and firm effects are estimated. While the specification of

BLM in Figure A.10 assumes there exists 10 firm types, Appendix Figure A.11 shows the BLM

estimates do not materially change if we instead allow for 20, 30, 40 or 50 firm types. Consistent

with limited mobility bias, the BLM estimates are noticeably smaller than the standard AKM

estimates in the samples with few movers. As expected, the AKM estimates become more

similar to the BLM estimates when there is a large number of movers per firm, and thus, limited

mobility bias should be small.

C.2

Extensions to the AKM Model

The assumptions that φij = xi + ψj and γ = Υ = 0 implies strong restrictions on the wage

structure. The absence of interactions between worker and firm effects rules out strong complementaries in production, as in Shimer and Smith (2000) and Eeckhout and Kircher (2011). The

assumption of no pass through of firm and market shocks is at odds with our data and a large

body of evidence from many other developed countries. Thus, investigating these assumptions

seems important to draw credible conclusions about the functioning of the U.S. labor market.

Non-additivity and complementarities

The assumption that φij = xi + ψj implies that all workers who move from firm j to j 0 will

experience an earnings change of ψj 0 - ψj , no matter their quality xi . An informal way to assess

this log additive structure is to perform an event study of the earnings changes experienced by

workers moving between different types of firms. Card et al. (2013b) and Card et al. (2018)

use matched employer-employee data from Germany and Portugal to perform such event-study

analyses of the earnings changes experienced by workers moving between different types of firms.

In Appendix Figure A.15, we perform the same exercise, but this time for our U.S. data. This

analysis uses the movers sample. As in Card et al. (2013b) and Card et al. (2018), we define

firm groups based on the average pay of coworkers.

The results from the event study mirror those reported in Card et al. (2013b) and Card

et al. (2018). Workers who move to firms with more highly-paid coworkers experience earnings

raises, while those who move in the opposite direction experience earnings decreases of similar

magnitude. Additionally, the gains and losses for movers in opposite directions between any

two groups of firms are relatively symmetric. By comparison, earnings do not change materially

when workers move between firms with similarly paid coworkers. Another relevant finding from

the event study is that the earnings profiles of the various groups are all relatively stable in

the years before and after a job move. This lends support to Assumption 2, as it suggests

that worker mobility does not seem to depend strongly on the trends in earnings beforehand or

afterwards. Lastly, it is interesting to observe that the gains and losses for movers seem to be

permanent. In contrast, in a large class of search models with job ladders, moves to firms that

currently pay less is rationalized by arguing that these firms will pay more in the future.

Although the event study results are consistent with the log additive functional form, we

cannot rule out interaction effects between worker and firm effects. Indeed, Bonhomme et al.

(2019) point out that even if the functional form is non-additive, the gains and losses may look

symmetric if workers making upward moves are of the same quality as those making downward

moves. More generally, the degree of asymmetry one observes in the event study depends both

on the magnitudes of any interaction effects and on the extent to which workers making upward

moves differ in quality from those making downward moves. Thus, the event study analysis

needs to be interpreted with caution.

To obtain an actual estimate of the importance of interactions between worker and firm

effects, we follow BLM in using the following model of earnings:

wit = θj(i,t) · xi +ψj(i,t) + it

| {z }

(10)

interaction

which reduces to AKM when θj is the same for all firms. Under Assumptions 1 and 2 , we

obtain:

E[wit+1 |j2 → j1 ] − E[wit |j1 → j2 ] = θj1 (E [xi |j2 → j1 ] − E [xi |j1 → j2 ])

E[wit+1 |j1 → j2 ] − E[wit |j2 → j1 ] = −θj2 (E [xi |j2 → j1 ] − E [xi |j1 → j2 ])

where j1 → j2 (j2 → j1 ) is an indicator for a worker moving from firm 1 to 2 (firm 2 to 1). As

long as the workers moving from 1 to 2 are not exactly the same as those moving from 1 to 2,

the right hand side of these equalities are non-zero and we can recover θj1 /θj2 from the moment

condition:

θj1

E[wit+1 |j2 → j1 ] − E[wit |j1 → j2 ]

E[wit |j2 → j1 ] − E[wit+1 |j1 → j2 ]

θj2

(11)

Thus, provided that the composition of movers differs across firms, it is possible to identify θj

(up to scale) for every firm. To take (10) to the data, however, it is useful to reduce the number

of parameters to estimate. As above, we follow BLM in classifying firms to ten types according

to the empirical earnings distribution within firms. Then we restrict θj to be the same for all

firms of a given type.

Figure A.12 displays the estimated nonlinearities. We plot the means of log earnings for each

firm type and at 10 deciles of worker heterogeneity. On the x-axis, firm types are ordered in

ascending order, where “lower” and “higher” types refer to low and high mean log earnings. The

results show clear evidence of worker heterogeneity: For the same type of firm, better workers

earn significantly more. For a given worker, there is also some variation in log earnings between

firm types, although to a lesser extent. As shown in equation (11), the parameters governing

nonlinearities are identified from comparing the gains from moving from a low to a high type of

firm for workers of different quality. As evident from Figure A.12, the gains from such a move are

considerably larger for better workers. For example, moving from the lowest to the highest type

of firm increases earnings by 22, 47 and 78 percentage points for individuals at the 20, 50 and

80 percentile in the worker quality distribution. As an alternative, we apply another estimator

suggested by BLM which partitions workers into 5 discrete types, then estimates an interaction

parameter for each firm-worker-type pair. The results are displayed in A.14, finding a similar

pattern in which there are stronger interactions among high-type workers and high-type firms.

The evidence of nonlinearities raises several questions. To what extent do interaction effects

bias the estimates from the log additive model? Are nonlinearities empirically important as a

source of earnings inequality? In Table A.8, we investigate these questions by extending the

AKM decomposition to incorporate the contribution from interactions between worker and firm

effects. Re-arranging equation (10), we get

wit = θ̄(xi − x̄) + ψj(i,t) + θj(i,t) x̄ + (θj(i,t) − θ̄)(xi − x̄) +it

| {z } |

} |

}

x̃i

(12)

%ij(i,t)

ψ̃j(i,t)

where θ̄ ≡ E θj(i,t) and x̄ ≡ E [xi ]. This equation decomposes the earnings of worker i in

period t into three distinct components: x̃i gives the direct effect of the quality of worker i

(evaluated at the average firm), ψ̃j(i,t) represents the direct effect of firm j (evaluated at the

average worker), and %ij(i,t) captures the interaction effect between firm j and worker i quality.

Using equation (12), we obtain a new variance decomposition of log earnings:

V ar(wit ) =V ar [x̃i ] + V ar ψ̃j(i,t) + 2Cov x̃i , ψ̃j(i,t)

+ V ar %ij(i,t) + 2Cov x̃i + ψ̃j(i,t) , %ij(i,t)

(13)

The first three components are informative about the inequality contribution from worker effects, firm effects and worker sorting, net of interaction effects. The last two components are

informative about the inequality contribution from interaction effects, as measured by the dispersion of %ij(i,t) across firms and the extent to %ij(i,t) is larger in firms with high wages. If

θj = θ̄ for every firm j, then these two components would be zero, and the decomposition in

(13) reduces to the standard AKM decomposition.

The results from the decomposition in (13) are presented in column (2) of Table A.8. Our

estimates suggest the dispersion of interaction effects across firms explains three percent of the

earnings inequality. However, the total contribution to earnings inequality from nonlinearities

is muted by the interaction effects being larger in firms with higher paid workers. We also find

that omitting interaction effects causes a downward bias in the firm effects and an upward bias

in the worker effects.

Pass through of shocks and time-varying types

The assumption that γ = Υ = 0 restricts firm effects to be constant over time. However, the

significant pass-through rates imply that firm effects actually evolve over time as employers

experience changes in the value added at the firm or market level. To capture this, we now let

γ differ from Υ and propose an adjustment to the AKM model which allows us to isolate the

time-invariant component of the firm effects.

Our approach proceeds in two steps. First, we construct an adjusted earnings measure by

removing the time-varying firm and market specific component of earnings. To do so, we use

the firm and market level value added multiplied by the estimated passthrough coefficients at

the firm and market level (see Table 2). Second, we recover the time-invariant firm and worker

effects by applying the methods of AKM or BLM to the adjusted measure of earnings. Consider

the following adjusted two-way specification for earnings of workers across firms:

E[wit − γ(yj(i,t),t − yj(i,t),1 ) − (Υ − γ) ȳr(i,t),t − ȳr(i,t),1 |j(i, 1), ..., j(i, T )] = xi + ψj .

The left-hand side removes the earnings dynamics due to passthrough of firm-specific shocks,

γ(yj(i,t),t − ȳr(i,t),t ), and market shocks, Υ ȳr(i,t),t . What remains is the worker effect xi and the

time-invariant firm effect ψj , which can be estimated by applying AKM or BLM to the adjusted

earnings measure.

In column (3) of Table A.8, we extend the BLM decomposition of the variance of log earnings

in (2) to incorporate the contribution from time-invariant and time-varying firm effects. We find

that time-varying firm effects explain little if any of the variation in log earnings, and that the

importance of firm effects and worker sorting do not change materially if we take the pass

through of firm shocks into account. Comparing the results in column (4) to those presented in

column (2) shows that time variation also has little to no explanatory power when accounting

for nonlinearities.

C.3

Additional robustness checks

In our main analysis, we follow the literature in looking at individuals aged 25-60 for whom

earnings exceed the full-time equivalence. This raises the question of how sensitive the results

are to changing these sample selection criteria. In Appendix Figure A.16, we re-estimate the

AKM model with alternative employment definitions, reporting the variance of log earnings and

the firm effects. This figure also examines how the results change if we include workers aged

20-25. As expected, the variance of log earnings and the estimated firm effects increase if we

include individuals earning less than the full-time equivalence. By comparison, the inclusion of

younger workers do not materially change the estimates. In Appendix Figure A.18, we examine

how the firm effects differ between men and women when using the AKM model. We find fairly

similar patterns, with men tending to sort more strong towards firms with higher firm effects.

We repeat many of the movers analyses for the “Broad Sample”. This sample is similar to the

Baseline Sample considered elsewhere, but with five differences. First, firms are not required

to have positive value added. Second, firms are not required to have at least two movers.

Third, locations are taken from worker rather than firm forms. Fourth, we consider shorter time

intervals of 2, 3, or 6 years rather than 8 years. Fifth, because the sample is smaller, we can

feasibly compare many alternate estimation strategies.

Characteristics of the Broad Sample are displayed in Table A.9(a). We see that, when using a

smaller numbers of years, there are fewer movers relative to the number of stayers, on average as

well as across the distribution of movers. This results in a much smaller share of firms belonging

to the connected set. Table A.9(a) also characterizes the leave-one-out set of Kline et al. (2020),

which requires that firms are connected by at least one mover even after dropping a mover from

the sample and is required to use the bias correction method of Kline et al. (2020).

The main national results for the Broad Sample are displayed in Appendix Tables A.9(b) for

the connected set and A.9(c) for the leave-one-out set. In the connected set, the AKM estimator

(FE) estimates a variance of firm effects of 12% to 16%, which are greater than the estimate

of 9% in the Baseline Sample, and a sorting share of -12% to 1%, which are less than 5% in

the Baseline Sample, which is consistent with greater bias if there are fewer movers per firm.

Imposing the leave-one-out set, the FE estimates become more similar to the Baseline Sample,

as the number of movers per firm rises. Applying three types of bias correction procedures

by Bonhomme et al. (2019) (CRE), Andrews et al. (2008) (FE-HO), and Kline et al. (2020)

(FE-HE), we find that the variance of firm effects ranges from 4% to 6%, which is similar to the

3% bias-corrected estimate in the Baseline Sample.

Using the Broad Sample, we repeat the various exercises presented above. Appendix Figure

A.15 compares the event study of earnings changes for workers who move across firms in the

Baseline Sample (subfigure a) and the Broad Sample (subfigure b), finding strong similarities.

Appendix Figure A.11 compares BLM and CRE estimates as the number of clusters increases

from 10 to 50 for the Baseline Sample (subfigure a) and the Broad Sample (subfigure b), finding

that the number of clusters does not affect the estimates. Using the Broad Sample to investigate

the full-time earnings threshold, we find in Appendix Figure A.19(a-b) a similar pattern as we

found in Appendix Figure A.16 for the Baseline Sample. In Appendix Figure A.19(c-d), we

examine the sensitivity of the estimates to the minimum number of workers per firm, finding

that much of the bias in the FE estimator dissipates if only considering larger firms. Using the

Broad Sample to investigate limited mobility bias by share of movers kept, we find in Appendix

Figure A.19(e-h) a similar pattern as we found in Appendix Figure A.10 for the Baseline Sample.

We consider several additional robustness checks that make use of the Broad Sample. Appendix Figure A.19(i-j) shows that the qualitative results for the Baseline Sample and the Broad

Sample are present even when considering very short 2-year panels. Appendix Figure A.19(k-l)

demonstrates that the bias in the AKM estimator would become even stronger if we used a strict

definition of movers in which we require workers to be employed for three consecutive years at

each firm. Appendix Figure A.19(m-n) considers the 20 smallest states, showing that the main

qualitative results hold at the state level, while Appendix Figure A.19(o-p) shows that these

results hold at the state level even when using the exact solution to the estimator rather than

the approximation method required for feasible estimation on large samples.

C.4

Tables and Figures

Sample:

Full Sample

≥ 2 Movers

Connected Set

245.0

(100.0%)

66.2

(100.0%)

227.8

(93.0%)

61.8

(93.3%)

227.4

(92.8%)

61.7

(93.2%)

232.9

(100.0%)

64.0

(100.0%)

212.4

(91.2%)

58.8

(91.9%)

211.9

(91.0%)

58.6

(91.7%)

Workers in 2001-2008:

Worker-Years (Millions)

Unique Workers (Millions)

Workers in 2008-2015:

Worker-Years (Millions)

Unique Workers (Millions)

Table A.6: Floor on Number of Movers and the Connected Set

Notes: This table demonstrates the fraction of workers lost from the sample in the AKM and BLM analysis

when imposing that a firm must have at least two movers and must belong to the connected set of firms.

Years:

2001-2008

Panel A.

2008-2015

Pooled

Levels

Total SD

Worker Effects SD

Firm Effects SD

Covariates SD

Correlation: xi and ψj(i)

Correlation: xi and Xi0 b

Correlation: Xi0 b and ψj(i)

0.67

0.57

0.20

0.11

0.09

0.00

0.02

Panel B.

0.68

0.58

0.20

0.12

0.11

0.00

0.03

0.67

0.57

0.20

0.11

0.10

0.00

0.03

Percentages

V ar(xi + Xi0 b)

V ar(xi )

V ar(Xi0 b)

2Cov(xi , Xi0 b)

V ar(ψj(i) )

2Cov(xi + Xi0 b, ψj(i) )

2Cov(xi , ψj(i) )

2Cov(Xi0 b, ψj(i) )

Residual

75.4%

72.9%

2.5%

0.0%

8.8%

4.9%

4.6%

0.2%

11.0%

75.5%

72.4%

3.1%

0.0%

9.0%

5.7%

5.4%

0.3%

9.9%

75.4%

72.6%

2.8%

0.0%

8.9%

5.3%

5.0%

0.3%

10.4%

Table A.7: Detailed AKM Decomposition

Notes: This table decomposes the variance of log earnings into components of worker effect variance, firm effect

variance, the variance of time-varying observables, and the covariances among these components. Results are

presented for the AKM estimator for the 2001-2008 and 2008-2015 samples, as well as their average (Pooled).

Variance of Firm Effects

●

0.10

●

Estimator

●

AKM

BLM

●

0.05

●

(7)

(11)

●

0.00

(21)

(32)

(46)

100

(62)

Share of Movers Kept (%)

(Mean Movers per Firm)

Figure A.10: Empirical Characterization of Limited Mobility Bias

Notes: In this figure, we consider the subset of firms with at least 15 movers. We randomly remove movers

within each firm and re-estimate the variance of firm effects using the AKM and BLM estimators. For each

estimator, we repeat this procedure several times, and then take averages of the variance estimates across these

repetitions. The procedure allows us to keep the connected set of firms approximately the same and examine

the bias that results from having fewer movers available in estimation.

●

CRE: Share of Variance (%)

Share of Variance Explained (%)

Firm Effects

Sorting

●

Firm Effects

Sorting

●

Number of Clusters in BLM

Clusters

(a) Baseline Sample

(b) Broad Sample

Figure A.11: BLM Decomposition by Number of Clusters

Notes: In this figure, we estimate the BLM decomposition for different numbers of firm clusters.

Predicted Log Earnings

1.0

Worker Quantile

0.5

0.0

−0.5

−1.0

Firm Type (ordered by mean log earnings)

Figure A.12: Assessing Identifying Assumptions: Evidence on Firm-Worker Interactions

Notes: In this figure, we present estimates of interactions between firm and worker effects using the BLM

estimator. We plot the means of log earnings for each firm type and deciles of worker heterogeneity. On the

x-axis, firm types are ordered in ascending order of mean log earnings.

Share of Workers (%)

100

Firm Type (ordered by mean log earnings)

Worker Effect Quintile

Figure A.13: Sorting of Firms and Workers

Notes: In this figure, we divide workers into 5 quintile bins and compute the share of workers in each quintile

bin by firm class. We plot the firm classes in increasing order of firm effects.

1.5

Predicted Log Earnings

1.0

0.5

0.0

−0.5

2.5

5.0

7.5

10.0

Firm Type

Share of Worker Type

0.1

0.2

0.3

Worker Type

Figure A.14: Robustness to BLM Estimator with Discrete Worker Types

Notes: This figure plots predicted log earnings when using the BLM estimator with 5 discrete worker types.

“Share of Worker Type” refers to the distribution of a given worker type across firm types.

0.50

0.4

4−4

4−2

2−4

0.00

●

−3

−2

−1

●

0.2

2−4

●

0.0

●

3−1

1−4

4−2

●

−0.25

Log Earnings

4−1

0.25

●

1−4

1−3

4−1

−0.2

2010

2011

2014

2015

Year

Time relative to Move

(a) Baseline Sample

(b) Broad Sample

Figure A.15: Assessing Identifying Assumptions: Evidence on Symmetric Changes around the

Move

Notes: In this figure, we classify firms into four equally sized groups based on the mean earnings of stayers in

the firm (with 1 and 4 being the group with the lowest and highest mean earnings, respectively). We then

compute mean log earnings for the workers that move between these groups of firms in the years before and

after the move. Note that the employer differs between event times -1 and 1, but we do not know exactly when

the change in employer occurred. Thus, to avoid concerns over workers exiting and entering employment during

these years, one might prefer to compare earnings in event years -2 and 2.

Model Specification

(1)

(2)

(3)

(4)

Share explained by:

i) Worker Quality

ii) Firm Effects

iii) Sorting

iv) Interactions

v) Time-varying Effects

Sorting Correlation:

Variance Explained:

V ar(xi )

V ar(ψj(i) )

2Cov(xi , ψj(i) )

V ar(%ij )

+2Cov(xi + ψj(i) , %ij )

V ar(ψj(i),t − ψj(i) )

+2Cov(xi , ψj(i),t − ψj(i) )

Cor(xi , ψj(i) )

Specification:

Firm-Worker Interactions

Time-varying Firm Effects

72.4%

3.2%

12.9%

70.4%

4.3%

13.1%

3.0%

-1.8%

73.5%

3.0%

12.8%

0.3%

71.6%

4.3%

13.1%

3.3%

-2.5%

0.3%

0.43

0.89

0.38

0.89

0.43

0.90

0.37

0.90

Table A.8: Comparison of BLM Specifications

Notes: This table presents the decomposition of log earnings variation into firm and worker effects using the

BLM estimator for four specifications: baseline, allowing for worker effects to interact with firm effects

(“Firm-Worker Interactions”), allowing for a time-varying component in the firm effects due to the pass through

of value added shocks (“Time-varying Firm Effects”), and allowing for both interactions between firm and

worker effects and time-varying firm effects. The analysis uses both workers who move between firms and

stayers.

Variance of Log Earnings (Solid)

●

0.8

●

0.6

●

0.4

0.2

0.0

% Variance from Firm Effects (Dashed)

1.0

Age Floor

●

100

Earnings Floor (% of Annualized Minimum Wage)

Figure A.16: Comparison of Log Earnings Variance by Earnings Floor

Notes: In this figure, we re-construct the full sample used to estimate the variance of log earnings (left y-axis)

and the variance of AKM firm effects (right y-axis) when imposing different earnings floors and different age

floors.

●

12.0

●

11.5

●

Log Net Income

●

11.0

Observed

Predicted

●

10.5

●

10.0

●

10.0

10.5

11.0

11.5

12.0

Log Gross Income Bin

Figure A.17: Fit of the Tax Function

Notes: In this figure, we display the log net income predicted by the tax function compared to the log net

income observed in the data.

Firm Effect

−0.1

−0.2

−0.3

−0.4

Log Surplus per Worker

Female

Male

Figure A.18: Comparison of Firm Effects by Gender

Notes: This figure plots AKM firm effects for females and males against log value added per worker. On

average, the difference in firm effects conditional on being male (female) is 0.0137 (0.0128) if using AKM and

0.0168 (0.0099) if using BLM-interacted. The difference in sorting conditional on being male (female) is 0.0291

(0.0300) if using AKM and 0.0276 (0.0345) if using BLM-interacted.

Set:

Baseline Years

Full Set

Connected Set

Leave-one-out Set

2001-2006

2010-2012

2010-2015

Sample Counts (1,000):

Unique Firms

(Share of Full Set)

6,717

(100%)

2,954

(44%)

2,009

(30%)

8,870

(100%)

1,241

(14%)

670

(8%)

7,565

(100%)

2,568

(34%)

1,689

(22%)

Unique Workers

(Share of Full Set)

63,146

(100%)

59,748

(95%)

57,027

(90%)

44,182

(100%)

36,826

(83%)

33,031

(75%)

59,621

(100%)

55,464

(93%)

52,484

(88%)

Distribution of Moves:

Moves per Firm

Worker-weighted quantiles:

10th Quantile

50th Quantile

90th Quantile

2.9

6.6

9.2

0.5

3.4

5.4

2.0

5.8

8.3

4.0

72.0

6,226.1

4.0

73.0

6,277.1

6.0

82.0

6,560.6

2.0

23.0

1,604.3

2.0

25.0

1,649.5

3.0

33.0

1,822.5

3.0

56.0

4,214.2

4.0

58.0

4,304.3

5.0

67.0

4,675.8

Log Earnings Distrib.:

Variance

Between-firm Share

0.397

34%

0.395

34%

0.395

33%

0.432

39%

0.436

38%

0.440

38%

0.413

40%

0.414

40%

0.416

39%

(a) Sample Characteristics

Panel A.

Share of Total Variation

Years:

2001-2006

Firm Effects

Sorting

Posterior Firm Effects

12.8%

-0.7%

FE-HO

6.5%

10.6%

2010-2015

CRE

6.4%

12.1%

7.1%

Panel B.

16.3%

-12.0%

FE-HO

4.1%

11.7%

2010-2015

CRE

5.2%

12.5%

12.2%

1.1%

FE-HO

5.5%

13.5%

CRE

6.2%

15.0%

6.7%

Share of Between Firm Variation

Years:

2001-2006

37.3%

-1.9%

64.6%

Firm Effects

Sorting

Segregation

FE-HO

19.1%

31.1%

49.7%

2010-2015

CRE

18.7%

35.2%

46.1%

42.8%

-31.3%

88.5%

FE-HO

10.7%

30.7%

58.6%

2010-2015

CRE

13.8%

32.7%

53.5%

30.9%

2.7%

66.3%

FE-HO

13.9%

34.1%

51.9%

CRE

15.8%

38.0%

46.3%

(b) Connected Set

Panel A.

Share of Total Variation

Years:

Firm Effects

Sorting

Posterior Firm Effects

2001-2006

10.2%

3.7%

FE-HO

6.4%

10.4%

FE-HE

6.7%

9.9%

2010-2012

CRE

6.2%

11.7%

6.8%

Panel B.

FE-HO

4.3%

11.0%

FE-HE

4.5%

10.6%

2010-2015

CRE

5.0%

12.1%

5.2%

9.5%

5.9%

FE-HO

5.5%

13.0%

24.3%

15.1%

60.6%

FE-HO

14.2%

33.5%

52.3%

FE-HE

5.8%

12.5%

CRE

5.9%

14.6%

6.4%

Share of Between Firm Variation

Years:

Firm Effects

Sorting

Segregation

10.4%

-0.8%

2001-2006

30.5%

11.2%

58.3%

FE-HO

19.3%

31.2%

49.5%

FE-HE

20.0%

29.8%

50.3%

2010-2012

CRE

18.6%

35.0%

46.4%

27.7%

-2.1%

74.4%

FE-HO

11.3%

29.3%

59.4%

FE-HE

11.9%

28.2%

59.9%

2010-2015

CRE

13.2%

32.2%

54.6%

Table A.9: Broad Sample - Total and Between Decompositions for Various Estimators

Notes: This table presents the decomposition of log earnings variation within and between firms using various

estimators for three time intervals in the Broad Sample. The analysis uses both workers who move between

firms and stayers.

FE-HE

14.9%

32.2%

52.9%

CRE

15.3%

37.6%

47.1%

4000

6000

8000

10000

12000

14000

4000

6000

Minimum Earnings

Estimator

CRE

8000

10000

12000

Sorting: Share of Variance (%)

Firm Effects: Share of Variance (%)

Sorting: Share of Variance (%)

Firm Effects: Share of Variance (%)

14000

Estimator

FE−HO

CRE

Minimum Earnings

Minimum Firm Size

Estimator

FE−HO

Minimum Firm Size

Estimator

CRE

FE−HO

CRE

−10

100

Share of Movers Kept (%)

FE−HO

−10

100

Share of Movers Kept (%)

Estimator

Sorting: Share of Variance (%)

Firm Effects: Share of Variance (%)

(a) Earnings Threshold: Firm(b) Earnings Threshold: Sorting(c) Firm Size Threshold: Firm(d) Firm Size Threshold: SortEffects

Effects

ing

Estimator

CRE

FE−HO

100

Share of Movers Kept (%)

FE−HE

Estimator

CRE

FE−HO

100

Share of Movers Kept (%)

Estimator

CRE

FE−HO

FE−HE

CRE

−10

Sorting: Share of Variance (%)

Firm Effects: Share of Variance (%)

(e) Limited Mobility Bias: Firm(f) Limited Mobility Bias: Firm(g) Limited Mobility Bias: Sort-(h) Limited Mobility Bias: SortEffects (connected)

Effects (leave-one-out)

ing (connected)

ing (leave-one-out)

−10

−20

−30

2011

2012

2013

2014

2015

2011

2012

2013

Year

2014

−20

Baseline

Strict Movers

Firm Effects Share (%)

2015

Year

FE−HO

CRE

FE−HO

Estimator:

CRE

Baseline

Strict Movers

Sorting Share (%)

Estimator:

FE−HO

(i) Short Panels: Firm Effects (j) Short Panels: Firm Effects (k) Strict Movers: Firm Effects

Firm Effects Share (%)

●

●●

●

● ●

● ●● ●

●●●●

●● ●

●●

Approximate Solution

Other Estimators

●

Approximate Solution

●

CRE

Estimator

CRE−P

FE−HO

●

Estimator

FE ● FE−HE

FE−HO

Estimator

CRE

●

●● ●

●

●●

●

●●

●

Exact Solution

CRE

FE ● FE−HE

−10

FE−HO

Sorting Share (%)

●

● ●●●

● ●

(l) Strict Movers: Sorting

CRE

●

Exact Solution

FE−HO

Estimator

CRE

FE−HO

●

FE−HE

(m) States: Firm Effects (leave-(n) States: Sorting (leave-one-(o) States:

Approximation(p) States:

Approximation

one-out)

out)

Methods (connected)

Methods (leave-one-out)

Figure A.19: Broad Sample - Various Robustness Checks

Notes: In this figure, we repeat several exercises shown previously, but now applied to the 2010-15 Broad

Sample instead of the Baseline Sample (unless otherwise noted). See the text for details on the robustness

exercises.

Appendix: Analyses based on Exogenous Income Shocks

D.1

Identifying lottery-induced income effects

We begin by laying out the individual comparisons that allow us to estimate the effect of lottery

income shocks by comparing lottery winners with earlier win years to those with later win years.

Throughout, when we refer to individuals who win the lottery in the same calendar year, we will

call them a cohort. To start, let Yit be an outcome (such as earnings) observed for individual i

in year t. Let Ei denote the year when individual i receives a lottery income shock. As a running

example, consider the simple case with two groups – a group of winners winning in the year

2003 (the Ei = 2003 cohort) and all later winners (the Ei > 2003 cohorts). Suppose that for

individuals in both groups, we have outcome data on year 2002 and 2003. In principle, we could

calculate the average difference over time for the Ei = 2003 cohort and deem the average yearon-year change (e.g., E [ Yi2003 − Yi2002 | Ei = 2003] ) as the on-impact effect of lottery income

shocks on the outcome. However, we may worry that events coinciding with the lottery or preexisting trends in the outcome would bias our estimate of the effect of lottery income on the

outcome with such a single difference. The existence of the later-winning group helps resolve

these issues to the extent that it experiences similar evolution in the outcome over time (i.e., a

parallel trend). Such a cohort is useful because its outcome is also observed in both 2002 and

2003, but it only receives a lottery shock in 2004 or later, meaning that any year-on-year change

in the outcome for the Ei > 2003 group in 2002 and 2003 will be due to the pre-existing factors

but not the (future) income shock.2 Together, these suggest a difference-in-differences strategy

to recover the effect of a lottery shock for the Ei = 2003 cohort in 2003:

E [ Yi2003 − Yi2002 | Ei = 2003] − E [ Yi2003 − Yi2002 | Ei > 2003]

(14)

With the availability of data on subsequent calendar years, we could recover a set of dynamic

effects for the Ei = 2003 in all calendar years for which there remains a not-yet-treated cohort

of individuals. Taking this logic further, for each Ei with any later-treated cohorts, we could

estimate a set of cohort-specific dynamic effects. In our subsequent event study estimates, we

use all winning cohorts with all available later winners, holding the baseline pre-treatment year

as two years pre-win. We produce these estimates using a sample that begins with the universe

of recipients of a Form W-2G with recorded state lottery income between 2001 and 2016. We

first restrict attention to winners who also have recorded age and sex data available from SSA

2 In the presence of possible anticipation of future lottery win, some of the year-on-year changes in the E >

2003 group’s outcome may be due to the anticipatory response in addition to pre-existing trends. We abstract

from this in our discussion, but note that one natural approach to acknowledge the potential for such anticipation

would be to allow for an anticipation window for later-winning cohorts and only use their observations in the

period prior to the onset of anticipation. We take this anticipation window approach when producing event study

estimates for the change in asset value and consumption expenditure, both of which include a first-difference

term and hence mechnically includes something akin to ”anticipation.”

records. We then focus on individuals who were 21 to 64 years of age (i.e., working age) at the

time of receiving the Form W-2G, and whose first recorded W-2G state lottery payment between

2001 and 2016 was for $30,000 or more. We use this first state lottery payment to define the

size of the shock that an individual experienced; however, all individuals in the sample receive

a lottery-induced income shock at some point between 2001 and 2016. See Table A.10 for an

overview of the descriptive characteristics, and Figure A.20 for a motivation of the research

design and main event study estimates.

D.2

Income shocks on earnings, employment, and related outcomes

We proceed to a discussion of our main findings on the effect of lottery income shocks on employment, earnings, and related outcomes. Starting with wage earnings of the winner, we find that

cohorts shocked with lottery income decrease their earnings by approximately $4000 one year

after winning, with relatively little change (increase or decrease) in this impact in the subsequent

4 years. The analogous employment response is a 4 percentage point reduction in employment,

with effects growing over time. Together with these responses in the labor market, individuals

shocked with lottery income appear to increase their asset holdings as reflected by their increase

in reported capital income (coming largely in the form of interest-bearing assets) and to increase

their total expenditure (as implied by their chainge in capital income, once capitalized).3 One of

the key behavioral response margins, however, is geographic mobility. In particular, individuals

do move in response to winning, but it is less clear what characterizes these moves (Figures

A.21-A.22). As individuals win lottery prizes of varying sizes, we normalize the above effects

by scaling them by the mean post-tax adult-equivalent lottery winnings, constructing effects

per-dollar won (post-tax) in Table A.11. In order to capture two potentially important sources

of heterogeneity, we explore these per-dollar effects accomodating variation in patterns over time

(short run of years 1 and 2, and long run of years 3 to 5) and well as across pre-win incomes

(quartiles of adjusted gross income).4 Starting, as before, from the labor market outcomes, we

see that wage earnings decline by approximately $0.02 per post-tax dollar won. However, this

masks heterogeneity in earnings responses across the income distribution – per-dollar effects

increase (in absolute value) from $0.01 per post-tax dollar won up to $0.03 per post-tax dollar

won as we move across income quartiles. This pattern of increasing (in absolute value) per

dollar effects is reversed for employment effects (which we scale by 100,000 for readability). Of

this total effect we report a non-negligible share is represented by extensive margin, whether

retiring or leaving the labor force (Table A.12) or moving into alternative work (Table A.13).

3 For capitalizing capital income into asset value, we use the mean rate of return over time of 0.054, as

calculated from the supplementary materials of Saez and Zucman (2016). We also explore alternative choices of

capitalization rate; namely 0.07 and 0.10.

4 As we do not observe precisely the date that an individual wins, we focus on effects starting from the first

complete calendar year after the win year.

D.3

Heterogeneity in response

Marital status. Given that winners vary in terms of their marital status at the time of win,

two natural questions to ask are: 1) do the earnings responses document above vary by marital

status, and 2) are there marital responses to winning in the form or new marriages or family

dissolutions? While married winners tend to have, if anything, smaller aggregate responses

to winnings, once we consider that household resources are shared, we find that per-dollar,

married winners are actually more responsive, decreasing their earnings by approximately $0.03

per post-tax dollar won while singles reduce their earnings by approximately $0.02 per post-tax

dollar won (Table A.14). Beyond larger earnings responses, we also observe that winning tends

induce new marriages (among single winners) and preserve existing marriages (among married

winners). In light of these findings, we ask: among married winners, who (within the household)

is the most responsive? In Table A.15, we find that the winner is nearly three times as responsive

as the spouse.

Gender. A large existing literature documents differential responses of men and women to

changes in wages and other determinants of labor supply and earnings. To explore if this

heterogeneity also arises in terms of responses to an exogenous income shock, we explore heterogeneity in responses by gender of the winner. We report our findings in Table A.15: male

winners are significantly more responsive (per dollar won) than female winners.

D.4

From per-dollar effects to per-period income effects

While lottery income shocks present a unique opportunity to study income effects, in order

to make them more comparable to the kind of income shocks in our modelling approach, we

need to translate the one-time wealth shock of a lottery prize into a change of per-period

income. To do so, we take two approaches. In the first, we suppose that individuals live to

the age of 80 and convert the one-time post-tax lottery win into a stream of fixed annuity

payments (with an internal rate of return of 2.5%, approximately matching inflation-adjusted

risk-free Treasury securities). In the second, we utilize observed sources of unearned income

(such as dividends, interest payments, and rental and royalty income, among others) and use

the capitalization approach (Saez and Zucman (2016)) to recover the winner’s chosen allocation

of unearned income over time. With both per-period income concepts, we form ratios as we did

in the prior section, recovering per-period income effects for the set of outcomes explored before.

We summarize the per-period income effects when we take the annuitization approach in Figure

A.23. In particular, we can highlight that for each dollar of income from the lottery annuity,

earnings fall by roughly $0.50, and expenditure increases by $0.60. As with the per-dollar effects,

per-period income effects on earnings increase with pre-win income, whereas per-period income

effects on expenditure decrease with pre-win income. When we instead use the second perperiod income approach (allocated unearned income), we find that across outcomes of interest,

per-period income effects are very similar. In the remaining Tables A.16-A.24, we demonstrate

that the pattern of responses across the additional margins and subgroups discussed above are

robust to modeling per-dollar effects as per-period income.

D.5

Tables and Figures

Table A.10: Descriptive statistics

(a) Winners Sample versus Broader Population

Winners (Age 21-64)

(1)

Tax Filers (Age 21-64)

(2)

$34,541

0.79

43.93

0.39

0.45

$33,005

0.80

41.78

0.51

0.58

0.49

Relative Q1 AGI Share

Relative Q2 AGI Share

Relative Q3 AGI Share

Relative Q4 AGI Share

0.28

0.21

0.24

0.27

0.25

90,731

154,372,671

Covariate

Wage Earnings

Employment

Age

Female

Married

Homeowner

Covariate

Wage Earnings

Employment

Age

Female

Married

Homeowner

Size of the Lottery Win

Statistic

Mean

Prop.

Mean

Prop.

Treatment Group (Current Winners)

(1)

Control Group (Not-Yet Winners)

(2)

$34,649

0.80

43.94

0.39

0.45

$182,902

$34,278

0.80

41.84

0.39

0.45

0.44

$184,184

Statistic

Mean

Prop.

Mean

Prop.

Mean

(b) Winners Sample versus Later Winners (Control Units)

Prize Range

Count

(1)

Mean Pre-Tax Winnings

(per winner)

(2)

Median Pre-Tax Winnings

(per winner)

(3)

< 50K

50K to 100K

100K to 200K

200K+

24,800

28,689

17,521

19,721

$36,512

$63,374

$126,020

$1,405,008

$34,700

$59,400

$119,100

$307,200

All Winners

90,731

$359,743

$67,800

Covariate

Wage Earnings

Employment

Age

Female

Primary Earner

Older Member

Same Age

Statistic

Mean

Prop.

Winner

(1)

Spouse

(2)

$42,465

0.80

47.07

0.36

0.62

0.50

0.11

$33,037

0.73

46.65

0.64

0.38

0.50

0.11

p < 0.001

(d) Winner versus Spouse

Notes: These tables presents a summary of the descriptive statistics in our sample of working-age winners. All monetary

values are reported in 2016 U.S. dollars, using the Consumer Price Index to adjust for inflation. The control gorup

consists of later winners. Medians rounded to nearest hundred.

Figure A.20: Motivation for Research Design and Responses

(a) First-Difference (Single Cohort)

(b)

First-Difference

Across Cohorts)

(Pooled

(d) Difference-in-Differences (Using Non-Winners as Controls)

(e) Comparison of Estimators

(f) Comparison of Approaches to

Control for Life-Cycle Effects

(g) Lottery-Induced Income Effect on Wage Earnings

(h) Lottery-Induced Income Effect on Per-Adult Wage Earnings

(i) Lottery-Induced Income Effect on Per-Adult Total Earnings (Wage + Self-Employment

Income)

(j) Lottery-Induced Income Effect

on Per-Adult Capital Income

(k) Lottery-Induced Income Effect on

Per-Adult Capital Income

(l) Lottery-Induced Income Effect

on Geographic Mobility

(m) Lottery-Induced Income Effect on Total Employment

(n) Lottery-Induced Income Effect on Winner Employment

(o) Lottery-Induced Income Effect

on Charitable Contributions

Notes: These figure provides a comparison of various estimators for the effect of winning the lottery on earnings. In

addition, we present event study estimates of the effect of lottery-induced shocks on wage earnings and

employment, as well as several outcomes which might have behavioral responses linked to earnings / employment

responses. 90% confidence intervals are displayed for event studies, clustering on individual winners.

Figure A.21: Geographic Mobility and Decompositions by Subgroups

(a) Homeowners and renters

(b) Young and old winners

(d) Parents with young kids

(e) Decomposition by Distance Moved

(f) Wealth Effects

(g) Wealth Effects by Subgroup

Notes: This figure presents estimates of the impact of winning on the propensity to move across Census tracts for several

subgroups, as well as decompositions of where they move. All outcomes are deteremined using Census tracts. 90 percent

confidence intervals are displayed for event studies, clustering on winner.

Figure A.22: Geographic Mobility and Decompositions by Subgroups

(a) Amenities and Disamenities

(b) Attributes of Neighbours

Winners by Labor Market Attachment

(d) Amenities and Disamenities by Age of

Winner

(e) Winner Characteristics

(f) Destination Characteristics: Local Labor Market

(g) Destination Characteristics: Neighborhood Quality

(h) Neighborhood Characteristics for Winners with Young Children

Notes: This figure presents estimates of the impact of winning on the propensity to move across Census tracts for several

subgroups, as well as decompositions of where they move. All outcomes are deteremined using Census tracts.

Table A.11: Wealth effects across outcomes

Sample

(1)

Quartile 1

Pre-Win Income

(2)

Winner Wage Earnings

(per $100)

-2.2856

(0.0571)

-1.4003

(0.0628)

-2.2948

(0.0861)

-2.6196

(0.0935)

-3.0596

(0.1541)

Per-Adult Wage Earnings

(per $100)

-2.0245

(0.0492)

-1.2514

(0.0589)

-2.0422

(0.0764)

-2.2590

(0.0813)

-2.7035

(0.1311)

Per-Adult Total Labor Earnings

(per $100)

-2.3394

(0.0657)

-1.3339

(0.1051)

-2.2720

(0.0867)

-2.6450

(0.0996)

-3.1298

(0.1820)

Per-Adult Capital Income

(per $100)

0.8738

(0.0406)

0.5784

(0.0540)

0.7626

(0.0784)

0.9658

(0.0709)

0.9265

(0.0974)

Winner Employment

(per $100,000)

-0.0368

(0.0008)

-0.0517

(0.0021)

-0.0444

(0.0019)

-0.0350

(0.0013)

-0.0231

(0.0010)

Total Employment

(per $100,000)

-0.0385

(0.0008)

-0.0639

(0.0025)

-0.0447

(0.0018)

-0.0322

(0.0012)

-0.0218

(0.0008)

Outcome

Full Sample

Quartile 2

Pre-Win Income

(3)

Quartile 3

Pre-Win Income

(4)

Quartile 4

Pre-Win Income

(5)

(a) Wealth effects across time and pre-win income (wage earnings and per-adult labor earnings)

(b) Wealth effects by prize size over time time and pre-win income (per-adult labor earnings

and total employment)

labor earnings)

Notes: These tables and figures presents estimates of the mean effect per dollar of lottery winnings (i.e., wealth effect) on

six earnings and employment outcomes. We use the delta method to calculate standard errors (reported in parenthesis),

clustering on winner. To ease interpretability, we scale earnings and capital income responses by $100. In the case of

employment responses, we scale each estimate by $100,000. In addition, in the figures, we highlight differences in estimates

over time, by income quartile, and by age of winner.

Table A.12: Extensive margin responses (level and share of earnings response)

Outcome

Full Sample

Value

(1)

Quartile 1

Pre-Win Income

(2)

Quartile 4

Pre-Win Income

(3)

Take-Up of Retirement Benefits

Claiming OASI Benefits

Estimate

Standard Error

Counterfactual Mean

%∆

0.0114

(0.0041)

0.77

1.5

0.0224

(0.0122)

0.74

3.0

0.0077

(0.0077)

0.73

1.1

One-Year Exit

Estimate

Standard Error

Counterfactual Mean

%∆

0.0489

(0.0053)

0.43

11.3

0.0361

(0.0095)

0.63

5.8

0.0392

(0.0103)

0.33

11.7

Two-Year Exit

Estimate

Standard Error

Counterfactual Mean

%∆

0.0536

(0.0058)

0.40

13.4

0.0477

(0.0106)

0.58

8.3

0.0457

(0.0111)

0.30

15.0

Five-Year Exit

Estimate

Standard Error

Counterfactual Mean

%∆

0.0490

(0.0098)

0.35

14.0

0.0599

(0.0265)

0.48

12.6

0.0195

(0.0170)

0.31

6.4

Labor Market Exit

(a) Extensive margin share - Full Sample

Sample

(1)

Quartile 1

Pre-Win Income

(2)

Winner Wage Earnings

0.60

0.65

0.50

0.52

0.50

Per-Adult Total Labor Earnings

0.54

0.59

0.44

0.41

Outcome

Full Sample

Quartile 2

Pre-Win Income

(3)

Quartile 3

Pre-Win Income

(4)

Quartile 4

Pre-Win Income

(5)

(b) Extensive margina share - Across Prize Size

Sample

(1)

Quartile 1

Pre-Win Income

(2)

Winner Wage Earnings

0.62

0.66

0.50

0.53

0.49

Per-Adult Total Labor Earnings

0.64

0.77

0.51

0.49

0.48

Outcome

Full Sample

Quartile 2

Pre-Win Income

(3)

Quartile 3

Pre-Win Income

(4)

Quartile 4

Pre-Win Income

(5)

(d) Labor market exit

Notes: Thess tables and figures present levels and share reponses along the extensive margin. On top, we report estimates

of the mean effect per dollar of lottery winnings (i.e., wealth effect) on take up of retirement benefits and labor market

exit for winners aged 62-64. The dependent variables are binary indicators for the receipt of OASI benefits and labor force

exit respectively. We use the delta method to calculate standard errors (reported in parenthesis), clustering on winner. To

ease interpretability, each estimate is scaled by $100,000. Then, the two bottom tables present the share of the response

due to extensive margin in aggregate and across prize sizes. 90 percent confidence intervals are displayed for event studies,

clustering on winner.

Table A.13: Effects of wealth on labor market transitions

(a) Wealth effects by labor market attachment

Sample

Outcome

Winner Wage Earnings

Per-Adult Wage Earnings

Per-Adult Total Labor Earnings

(1)

Quartile 1

Pre-Win Income

(2)

Quartile 2

Pre-Win Income

(3)

Quartile 3

Pre-Win Income

(4)

Quartile 4

Pre-Win Income

(5)

Baseline

-2.2856

(0.0571)

-1.4003

(0.0628)

-2.2948

(0.0861)

-2.6196

(0.0935)

-3.0596

(0.1541)

Employed Pre-Win

-2.6437

(0.0661)

-1.7358

(0.0968)

-2.6309

(0.0903)

-2.8243

(0.0995)

-3.3511

(0.1580)

FT Employed Pre-Win

-2.9566

(0.0792)

-2.6015

(0.3019)

-2.9885

(0.0987)

-2.9500

(0.1046)

-3.4603

(0.1621)

Baseline

-2.0245

(0.0492)

-1.2514

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