Labor Unions and Occupational Safety∗

Ling Li† Shawn Rohlin ‡ Perry Singleton §

January 12, 2019

Abstract

This study examines the causal effect of unionization on occupational safety. The em-pirical strategy exploits union election outcomes, using establishments in which elec-tions narrowly failed as a comparison group for establishments in which elections thatnarrowly passed. Data on elections come from the National Labor Relations Board,and data on occupational safety come from the Occupational Safety and Health Ad-ministration. Using accident case rates as a measure of occupational safety, the analysisfinds that unionization had no detectable effect on accident case rates at the mean, butincreased the percent of establishments with a case rate of zero by approximately 2.5percentage points. The extensive-margin effect is evident among both manufacturingand non-manufacturing establishments.

Keywords: unions, occupational safety, OSHAJEL Codes: J28, J51, J81

Corresponding Author: Perry Singleton; Syracuse University; 426 Eggers Hall;Syracuse, NY 13244; psinglet@syr.edu

∗For helpful comments and suggestions, the authors would like to thank Gary Engelhardt, BrighamFrandsen, Barry Hirsch, Hugo Jales, Jeffrey Kubik, and conference participants at the Annual Meetingof the Society of Labor Economists. The authors would also like to thank Jeanette Walters-Marquez forproviding data from the Federal Mediation and Conciliation Service.†University of Wisconsin - Parkside, Department of Economics‡Kent State University, Department of Economics, and the Center for Entrepreneurship and Business

Innovation§Syracuse University, Department of Economics, and the Center for Policy Research

1 Introduction

Workers form labor unions to bargain over wages, employment, and working condi-

tions. While most research focuses on the determination of wages and employment (Farber,

1986), less research focuses on working conditions. To address this limitation, this study

examines the effect of unions on occupational safety. As Morantz (2009) notes, unions en-

gage in numerous safety-enhancing activities, including pressuring employers to maintain

safe workplaces, educating workers about workplace hazards, and developing safety-related

innovations through economies of scale. The effect on occupational safety has direct im-

plications for worker welfare and the efficiency of labor unions. The effect is also relevant

to research on unions and wages (Branchflower and Bryson, 2004; DiNardo and Lee, 2004;

Frandsen, 2014; Freeman and Medoff, 1984), since occupational safety may affect wages

through compensating differentials (Kniesner and Leeth, 2014; Rosen, 1974).

This study attempts to identify the causal effect of unionization on occupational

safety. Following DiNardo and Lee (2004), Frandsen (2014) and others, the empirical strat-

egy exploits the timing and outcome of union elections. Specifically, using the regression

discontinuity model, establishments in which elections narrowly failed are used as a compar-

ison group for establishments in which elections narrowly passed. Data on union elections

come from the U.S. National Labor Relations Board (NLRB). The analysis is limited to elec-

tions in 1991 to 2010. The data on occupational safety come from the Occupational Safety

and Health Administration (OSHA), specifically the OSHA Data Initiative (ODI). These

data report the total case rate (TCR) at the establishment level per 100 full-time equivalent

annually. The TCR includes cases involving death, days away from work, job restrictions,

job transfers, and medical attention beyond first aid. To examine union activity following an

election, the data are matched to “notices of bargaining” filed with the Federal Mediation

and Conciliation Service (FMCS).

According to the empirical analysis, unionization had no detectable effect on the

TCR at the mean, but did increase the percent of establishments with a case rate of zero by

1

approximately 2.5 percentage points. The extensive-margin effect appears to be driven by es-

tablishments that would have been at the low-end of the case-rate distribution in the absence

of unionization. Additionally, the extensive-margin effect is evident immediately after the

union election, suggesting that the effect is due to within-firm changes in occupational safety,

rather than the impact of unionization on establishment survival differentially by occupa-

tional safety. By industry, the extensive-margin effect is evident among both manufacturing

and non-manufacturing establishments.

The study contributes to an existing literature on unionization and occupational

safety. Despite the numerous safety-enhancing activities of unions, most empirical studies

find that unionization is associated with greater accidents and injuries (Donado, 2015). One

possible explanation is selection, whereby more dangerous establishments are more likely

to unionize. A few studies find that unions improve occupational safety, but these findings

pertain to specific eras and industries (Boal, 2009; Fairris, 1995; Morantz, 2013).

This study differs from related studies on two important dimensions. First, this

study exploits union elections with narrow outcomes for identification. The advantage of

this strategy is that it potentially addresses selection into unionization. A disadvantage,

however, is that the findings pertain only to newly unionized establishments with narrow

election victories. For this reason, the results form this study are not generalizable to other

contexts or directly comparable to related studies. Second, the study is the first to utilize

ODI data to examine the effect of unionization on occupational safety. This allows for a

more contemporary analysis of multiple industries, with largest shares of establishments in

manufacturing and health services.

2 Background

Workers form labor unions to create or capture monopoly rents (Farber, 1986). A

single union represents workers across multiple firms and establishments, forming national

2

and increasingly international coalitions. At the establishment level, union officials represent

workers in contract negotiations. Labor contracts generally specify compensation, but may

also specify employment levels and working conditions.

In the US, workers typically form unions through elections.1 Elections are facilitated

by the National Labor Relations Board (NLRB), established in 1935 to enforce collective

bargaining laws. To hold an election, organizers must first demonstrate at least 30 percent

support for a union election among eligible workers. This is achieved by petitions or autho-

rization cards. If successful, the NLRB determines the size and scope of the bargaining unit

and the time and location of the election. The election is conducted by secret ballot, and

a successful election requires a simple majority. If an election is successful, employers must

bargain “in good faith” with the union during contract negotiations.

A framework of union bargaining power is developed by DiNardo and Lee (2004).

In their framework, bargaining power is a function of the share of workers who favor union-

ization. In a baseline case, where union elections are permitted, but none occur, bargaining

power increases monotonically with the vote share. If an election occurs, bargaining power

increases independent of the election outcome. This is referred to as the indirect effect of

unionization. If the election is successful, bargaining power increases further. This is re-

ferred to as the direct effect of unionization. As DiNardo and Lee (2004) note, because a

successful election requires a simple majority, bargaining power increases discontinuously at

the 50-percent vote share.

In an analysis of union behavior, Farber (1986) considers two types of bargaining

structures. In the first structure, unions bargain over wages only, leaving employers to

determine employment levels and other conditions of employment. In this case, unions

negotiate along the employer’s demand curve, increasing wages and decreasing employment,

constrained by a non-negative profit condition. However, the resulting labor contract is

generally inefficient, as one party can be made better off without negatively impacting the

1An employer may independently recognize a labor union, forgoing a union election.

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other. In the second structure, unions bargain over both wages and employment. In this

case, unions negotiate along the employer’s isoprofit curve, decreasing wages and increasing

employment relative to the demand curve. In this case, the resulting labor contract may be

efficient, but the net effect on wages and employment is ambiguous.

While most economic research on unionization has focused on wages and employ-

ment, unionization could impact other aspects of employment such as occupational safety.

Indeed, unions engage in numerous safety-enhancing activities, including pressuring employ-

ers to maintain safe workplaces, educating workers about workplace hazards, developing

safety-related innovations through economies of scale, and influencing the stringency of reg-

ulatory oversight (Morantz, 2009). A more recent study finds that unions increase OSHA

inspections, violations, and citations, which may be an important mechanism for safety

improvements (Sojourner and Yang, 2015).

Despite the safety-enhancing activities of unions, the causal effect of unions on

occupational safety is ambiguous. The conceptual framework is analogous to the framework

for wages and employment. If unions contract on wages only, employers may respond to

higher wages by decreasing investment in occupational safety. However, if unions contract

on both wages and occupational safety, occupational safety may improve. The ability to

contract on occupational safety depends, in part, on whether safety can be monitored.

The effect of unions on occupational safety is also affected by measurement and

reporting. For example, OSHA requires many employers to log workplace accidents that

require job restrictions, job transfers, or medical attention beyond first aid. One issue is

that, with unionization, employers may be more likely to accommodate workers following an

accident, thereby increasing the accident case rate. Another issue is that, with unionization,

employers may be more likely to report accidents, holding incidence constant. This may be

due to an employer’s tendency to underreport, a union’s tendency to overreport, or both.

To complicate matters further, the causal effect of unionization on occupational

safety is difficult to identify empirically. One issue is that other factors may affect both

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occupational safety and unionization. For example, management quality may improve oc-

cupational safety and establishment profitability, with the latter increasing the likelihood of

unionization. This would generate a positive correlation between unionization and safety.

Another issue is that poor working conditions may precipitate unionization. This would

generate a negative correlation between unionization and safety. Thus, in observational

data, the correlation between unionization and occupational safety is likely biased relative

to unionization’s true causal effect.

In the empirical literature, most studies find that unionization is associated with

greater accidents and injuries (Donado, 2015). A major concern is selection, whereby es-

tablishments with greater accidents and injuries are more likely to unionize (Hills, 1985). A

few studies find positive effects of unions on occupational safety, but these findings pertain

to specific eras and industries. For example, Boal (2009) examines turn-of-the-century coal

mining, Fairris (1995) examines company unions in the 1920s, and Morantz (2013) focuses

on mining-related injuries and fatalities in the 1970s and 1980s.

3 Empirical Strategy

For identification, this study pursues an empirical strategy of DiNardo and Lee

(2004) and Frandsen (2014) and others that focuses on close union elections. In the potential

outcomes framework (Rubin, 1974; Holland, 1986), each establishment has two potential

outcomes with respect to union status: an establishment is either unionized, indicated by

Wi = 1, or not unionized, indicated by Wi = 0. The outcome with respect to union status

is denoted Yi(Wi); the causal effect among an individual establishment is denoted Yi(1) −

Yi(0); and the causal effect of unionization among all establishments is denoted E[Y (1) −

Y (0)]. Using the regression discontinuity design model (Hahn et al., 2001; Imbens and

Lemieux, 2008; Lee and Lemieux, 2010), the empirical strategy identifies the causal effect of

unionization among establishments with a vote share in favor of unionization of 50 percent,

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the cutoff for a successful union election. This is denoted E[Y (1)−Y (0)|X = 0], where X is

the vote share relative to the 50-percent cutoff.2 The key identification assumption is that

the conditional expectation functions E[Y (1)|X] and E[Y (0)|X] are smooth at X = 0. If

so, the causal effect is given by the estimand from the sharp regression discontinuity model:

limx↓0

E[Y (1)|X]− limx↑0

E[Y (0)|X]. (1)

The left and right terms correspond to above and below the cutoff, respectively.

The causal effect can be examined both graphically and through local polynomial

regression. The regression model has the following form:

Yi = α + βWi + F (Xi) +WiG(Xi) + γZi + εi (2)

The variable Yi is a measure of occupational safety following the union election, Wi is an

indicator of union status, Xi is the vote share relative to the cutoff, and Zi is a vector of

establishment characteristics. F (.) and G(.) are polynomial functions of the vote share. By

interacting G(Xi) with Wi, the model allows for separate conditional expectation functions

above and below the cutoff. The coefficient of interest is β, which measures the discontinuity

of occupational safety at the cutoff and thus unionization’s causal effect. Because the effect

is identified locally, estimation utilizes observations only within a symmetric bandwidth

around the cutoff. The empirical analysis considers both first-order polynomials with a

narrow bandwidth and second-order polynomials with a wider bandwidth. The error term

εi is robust to heteroskedasticity.3

The effect of unionization on occupational safety may differ across the case-rate

2To impose symmetry in the vote share distribution regardless of the number of vote cast, an amountequal to 0.5 divided by the number of votes cast is subtracted from the vote share if the number of votescast is even (DiNardo and Lee, 2004).

3Discussed below, some establishments have multiple observations of occupational safety in different cal-endar years. In the empirical anlaysis, clustering the error term at the establishment level generally increasesthe standard errors, but this does not change the substantive conclusions or the statistical significance ofthe results.

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distribution. On one hand, unions may focus their safety-enhancing efforts on high case-rate

establishments, affecting only the right tail of the case-rate distribution. On the other hand,

the right tail of the case-rate distribution may reflect idiosyncratic shocks that are unaffected

by union efforts. To estimate distributional effects, the outcome variable is replaced with an

indicator function 1(Yi ≤ y), and βy measures the discontinuity of the conditional cumulative

density function evaluated at y (Frandsen et al., 2012).

A threat to identification is non-random sorting at the cutoff. This occurs when

the vote share is manipulated at the margin of victory to alter the election outcome. Non-

random sorting would generally create discontinuities in the density of the vote share X, the

conditional distribution of establishment characteristics Z, and ultimately the conditional

distribution of the outcome of interest Y . Thus, to provide empirical support for the identi-

fication assumptions, we test for discontinuities in the density of the vote share according to

McCrary (2008) and for discontinuities in establishment characteristics using equation (2),

with Y replaced with Z.

Because the conditional distribution of covariates Zi is assumed continuous at the

cutoff, including them in equation (2) does not affect the identification strategy. Their

inclusion, however, may reduce small sample bias and improve the precision of the estimates

(Imbens and Lemieux, 2008). Given the available data, covariates include calendar year fixed

effects, industy by calendar year fixed effects, state by year fixed effects, and the number of

valid votes cast.

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4 Data and Sample

4.1 Union Elections: National Labor Relations Board

The NLRB data on union elections come from two sources. The first is a database

compiled by the AFL-CIO, which contains elections held from 1965 to 1998.4 The second

is an online data repository, www.data.gov, which contains annual NLRB files from 1999 to

2010.5 Data from both sources include the establishment name, address, and industry, as

well as the number of eligible voters, valid votes cast, and votes for and against unionization.

Combined, the data contain 45,582 elections from 1991 to 2010.6 These years were

chosen to coincide with the years of data on occupational safety described below. The first

data source contains 21,917 elections from 1991 to 1998, and the second contains 23,665

elections from 1999 to 2010.7 The annual number of elections decreased over time, from

2,855 in 1991 to 1,644 in 2010.8 To ensure uncertainty in the election outcome, the data

are restricted to elections with at least 20 valid votes, leaving 24,758 elections from 1991 to

2010. This restriction is similarly imposed in related studies, including DiNardo and Lee

(2004), Lee and Mas (2012), Frandsen (2014), and Sojourner et al. (2015).

Table 1 provides summary statistics of the elections. The average number of votes

cast is 97.27, the average vote share in favor of unionization is 50.89 percent, and the share of

successful elections is 46.77 percent. The greatest share of the elections is in manufacturing

(28.94 percent), followed by health services (19.63 percent), transportation (16.86 percent),

4The AFL-CIO is the American Federation of Labor and the Congress of Industrial Organizations. Thedata are available to download from John-Paul Ferguson at https://github.com/jpfergongithub/nlrb oldrcases.

5The data files are labeled by calendar year, but the file name does not necessarily correspond with tallyyear of the elections within the file. After pooling the files, observations were deleted if they appeared to beduplicates or were petitions that were withdrawn or dismissed cases. For more details of the NLRB files, seethe Appendix.

6There were 455 elections that were omitted due to a missing or invalid vote share in favor of unionization.7From 1991 to 1998, the year is based on the date of the election; from 1999 to 2010, the year is bsed on

the date of the vote tally.8The number of elections is lower in 1999 compared to 1998 and 2000 - 1,686 compared to 2,761 and

2,867, respectively - suggesting some missing data in that year.

8

and construction (4.88 percent). A greater share of elections occurred in the Northeast and

Midwest, compared to the South and West.

4.2 Union Contracts: Federal Mediation and Conciliation Service

The empirical strategy assumes that bargaining power of workers increases discon-

tinuously at the 50-percent cutoff following the union election. To support this assumption,

the election data from 1999 to 2010 are matched to “notices of bargaining” data in years

1997 to 2016 from the Federal Mediation and Conciliation Service (FMCS).9 A notice is

required to initiate, terminate, or modify a labor contract and, as such, is an indicator of

union activity. The NLRB elections are matched to FMCS records by establishment name

and address.

4.3 Occupational Safety: OSHA Data Initiative

Data on occupational safety come from the ODI. The ODI was part of OSHA’s Site

Specific Targeting (SST) plan, designed to better target more dangerous establishments for

a workplace inspection. The ODI first collected a sample of accident case rates directly from

employers at the establishment level. The data were collected in annual cycles, spanning

calendar years 1996 to 2011. The sample was derived from a registry of US businesses

compiled by Dun & Bradstreet. While the sampling frame changed from cycle to cycle,

the ODI generally excluded the construction industry and smaller establishments.10 Once

collected, the data were used by the SST plan to target high case-rate establishments for an

inspection.11

The data on occupational safety come specifically from OSHA’s Form 300. This

9DiNardo and Lee (2004) similarly match union election data to the FMCS data.10In 1996, the ODI excluded establishments with fewer than 40 employees. From 1997, this threshold was

increased to 60 employees.11Using the ODI data, Li and Singleton (2018) exploit the SST plan to identify the effect of workplace

inspections on worker safety.

9

form is provided by OSHA to employers to log workplace accidents and injuries. In general,

employers with 10 or more full-time employees are required to complete the form. Cases are

logged separately involving death, days away from work, job restrictions or transfers, and

medical attention beyond first aid. Based on these logs, the ODI calculated accident case

rates per 100 full-time equivalent workers annually. The total case rate (TCR) includes all

four cases. A second rate includes only cases involving days away from work, job restrictions,

and job transfers (DART). The NLRB elections are matched to each year of the ODI based

on the establishment name and address.

Of the 24,758 union elections, 6,976 have at least one match to the ODI across all

the available years of data. Due to the years of the election and ODI data, elections closer to

1991 and 2010 were less likely to match to the ODI than elections in the intervening years.

Table 1 provides summary statistics of elections with and without a match. The number

of valid votes is greater among elections with a match, which is consistent with the ODI

excluding smaller establishments. Elections with a match are also less likely to have passed:

40.25 percent versus 49.37 percent. Regarding industry and geography, elections with a

match are more likely to be in manufacturing and health services, compared to construction

and transportation, and more likely to be in the Midwest, compared to the Northeast, South,

and West.

A single election may match to multiple ODI records in different years. Among

the 6,976 establishments with at least one match to the ODI, there are 19,318 matches from

five calendar years before the election to five calendar years after. During this period, 17.06

percent of elections have no matches, 24.68 percent have one match, 15.05 percent have two

matches, and 43.21 percent have three to eleven matches.

Figure 1 illustrates the ODI match rate each year relative to the year of the election.

The match rates are calculated using only calendar years for which ODI data are available.12

As shown, the match rate is highest in the year of the election, when the establishment is

12For example, elections tallied in 1999 were not used to calculate the ODI match rates in periods -4 and-5, which correspond to calendar years 1995 and 1994, respectively.

10

known to exist. In that year, the match rate is 11.73 percent. The match rate gradually

declines with years before and after the election, which is consistent with establishment

formation and dissolution, respectively. The match rate also reflects the ODI sampling size

and frame, which changed from cycle to cycle.13

5 Results

5.1 Vote Share

A potential threat to the identification strategy is non-random sorting at the cutoff

for a successful union election. Evidence of non-random sorting includes bunching of elections

just above or below the cutoff. To check for bunching graphically, Figure 2 plots the vote

share density relative to the cutoff, computed across 20 non-overlapping bins of 5 percentage

points each. The figure indeed suggests bunching: excluding the far-right bin, the density

increases from the right towards the cutoff, but increases only slightly in the bin just above

the cutoff, suggesting too few narrow election victories.14 The McCrary (2008) test is used

to test for bunching at the cutoff, where the null hypothesis is continuity. Using a uniform

kernel, the test fails to reject the null hypothesis at the 95 percent confidence level (p-

value=0.0696), though the test statistic is only marginally insignificant.

Manipulating the vote share may become increasingly more difficult as the number

of voters increases. While Figure 2 illustrates the vote share density among elections with at

least 20 votes, Figure 3 illustrates the vote share densities using greater vote thresholds. As

shown, the lower density just above the cutoff is no longer apparent among elections with

13Because the sampling frame changed from cycle to cycle, matched ODI observations are not directlycomparable across calendar years or analysis periods (Figure 1). This prevents event-study analysis, whichcompares changes in the mean case rate before and after the union election.

14Frandsen (2014) also finds evidence of bunching, suggesting too few narrow election victories. A keydifference is that his data include earlier years, from 1980 to 2009. In our data, evidence of bunching isstronger in earlier years (e.g. 1992 to 1999) than later years (e.g. 2000 to 2010).

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greater votes. Moreoever, the McCrary (2008) test consistently fails to reject continuity.15

Thus, a potential strategy to address non-random sorting at the cutoff is to focus on union

elections with greater votes cast.

5.2 Establishment Characteristics

Non-random sorting may also lead to discontinuities in the distribution of estab-

lishment and election characteristics. Regarding election characteristics, Figure 4 plots the

conditional mean of eligible employees and valid votes cast.16 As shown, both measures

increase and then decrease with the vote share, with no apparent discontinuity at the cutoff.

Table 2 presents discontinuity estimates using equation (2). The rows correspond to different

outcome variables: the first row is eligible employees; the second row is valid votes cast. Each

column corresponds to a discontinuity estimate from a single model: In the first column, the

model utilizes a polynomial of order one (linear) and a bandwidth of 15 percentage points; in

the second column, the model utilizes a polynomial of order is two (quadratic) and a band-

width of 25 percentage points. As shown, all the discontinuity estimates are small compared

to the mean near the cutoff, and none are statistically significant. In the first column, the

estimated discontinuity for eligible employees is 2.41, compared to a mean of 116.98, and the

estimated discontinuity for valid votes is 3.06, compared to a mean of 102.90.17

Figure 5 illustrates the percent of establishments in manufacturing and health ser-

vices. As shown, the share in manufacturing increases and then decreases with the vote

share, whereas the share in health services generally increases, except for a sharp decrease

at the highest bins. Graphically, neither measure of industry exhibits a discontinuity at the

cutoff. Additionally, the discontinuity estimates presented in the third and fourth rows of

15Using the uniform kernel, the p-values are 0.241, 0.664, 0.583, and 0.712 using a vote threshold of 30,50, 70, and 100, respectively.

16When examining discontinuities in the number of eligible employees and votes cast, one extreme outlieris omitted from the analysis. For this outlier, the number of eligible employees and votes case is 17,195 and15,471, respecitively. The next highest values are 7,000 and 4,589, respectively.

17The means are calculated among elections within plus or minus 10 percentage points from the cutoff.

12

Table 2 are small and statistically insignificant.

A final measure of establishment characteristics is whether an establishment matches

to the ODI. Stated above, a match to the ODI reflects, in part, the sampling size and frame,

which varied from cycle to cycle. Figure 6 illustrates the percent of firms that match to the

ODI. As shown, the match rate increases and then decreases with the vote share, with no

apparent discontinuity at the cutoff. Additionally, the discontinuity estimate presented in

the fifth row of Table 2 is small and statistically insignificant.

Taken together, the results suggest that establishments are comparable just above

and below the cutoff with respect to establishment and election characteristics. These find-

ings are consistent with the identification assumption that the conditional expectation func-

tions of occupational safety, as well as both observable and unobservable factors that affect

occupational safety, are smooth at the cutoff. If so, the estimated discontinuity of occupa-

tional safety at the cutoff may be interpreted as the causal effect of unionization.

5.3 Union Activity

The identification strategy assumes that bargaining power of workers increases dis-

continuously at the cutoff for a successful union election. Using the FMCS data on notices

of bargaining, Figure 7 plots the FMCS match percent by calendar year before and after

the union election, separately by the election outcome. Among establishments in which the

election passed, the match rate increases sharply in the calendar year of the election and

the year after, then returns to its pre-existing trend. Among establishments in which the

election failed, the match rate remains relatively unchanged compared to the pre-existing

trend. These results confirm that union activity increases following a successful election.

To examine union activity at the cutoff, Figure 8 plots the FMCS match percent

in periods 0 and 1 by vote share. These periods had the greatest increase in union activity

following a successful union election, according to Figure 7. As shown, union activity in-

creases discontinuously at the cutoff following a union election. The discontinuity estimates

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presented in the sixth row of Table 2 are 34.63 percentage points using the first model and

32.37 percentage points using the second model. Both estimates are statistically significant

at the one percent level.

5.4 Occupational Safety

5.4.1 After Election

The discontinuous increase in union activity at the cutoff is used to identify the

effect of unionization on occupational safety. Using NLRB-ODI matched observations, the

empirical analysis focuses intially on the TCR after the election. To increase the sample

size, the data are pooled across periods one through five, corresponding to the first through

fifth calendar years after the election. The pooled data contain 10,835 observations.

The left panel of Figure 9 illustrates the mean TCR by vote share. As shown, the

mean TCR generally increases with the vote share, except for a decrease at the highest bins.

The estimates appear noisier towards the extremes of the vote share, where the density of

the vote share is lower. Importantly, there is no apparent discontinuity in the mean TCR at

the cutoff. Table 3 reports the discontinuity estimates using equation (2). In the first row,

the outcome variable is the TCR, and each column corresponds to an estimate from a single

model. In the first column, the polynomial order is one, and the bandwidth is 15 percentage

points. In this case, the discontinuity estimate is -0.0770. Although the estimate is negative,

which suggests that unionization improved occupational safety, it is small and statistically

insignificant. The point estimate is similar if the model includes covariates, as reported in

the second column. In the third column, the polynomial order is two (quadratic), and the

bandwidth is 25 percentage points. In this specification, the discontinuity estimate is -0.394,

which is also negative, but statistically insignificant. Again, the point estimate is similar if

the model includes covariates, as reported in the fourth column. While the results suggest

that unionization does not affect occupational safety at the mean, the standard errors do not

14

rule out a wide range of effects. For example, in the first column, the 95 percent confidence

interval is -1.25 to 1.10, compared to a mean near the cutoff of approximately 14.

Stated above, unionization may affect occupational safety at different parts of the

case-rate distribution. To examine occupational safety on the extensive margin, the right

panel of Figure 9 illustrates the percent of establishments in which the TCR is zero. As

shown, the percent with zero cases decreases and then increases with the vote share, reach-

ing a minimum near the cutoff. Importantly, the percent with zero cases increases discon-

tinuously at the cutoff, suggesting that unionization improved occupational safety on the

extensive margin. The discontinuity estimates with 1(TCR = 0) as the outcome variable

are reported in the second row of Table 3. As shown, the estimates are similar across all

models, ranging from 2.521 percentage points to 2.852 percentage points. All the estimates

are statistically significant at the five percent level, and the estimate in the first column is

significant at the one percent level.

If unionization improved occupational safety on the extensive margin, but had

no detectable effect at the mean, then the extensive-margin effects likely occurred among

establishments that would have been at the low-end of the case-rate distribution in the

absence of unionization. If the effects occurred at the high-end, instead, the effect at the

mean would be larger. To confirm this point, Figure 10 illustrates discontinuity estimates of

the conditional cumulative density function at each integer of the TCR distribution, from 1

to 25.18 The models in the left panel have a first-order polynomial and a bandwidth of 15

percentage points, and the models in the right panel have a second-order polynomial and

a bandwidth of 25 percentage points. The models in both panels include covariates. As

shown, the discontinuity estimates are positive and statistically significant from 1 to 4, but

decrease and become statistically insignificant thereafter. From 5 to 25, most of the estimates

are small, and all of the estimates are statistically insignificant. These results confirm that

the shift in the case-rate distribution towards zero occurred at the bottom of the case-rate

18A TCR at 25 corresponds to the 90th percentile of the case-rate distribution.

15

distribution.

5.4.2 Before Election

To establish causality, it is important to consider whether there is a discontinuity

in occupational safety at the cutoff before the election. Figure 11 illustrates the TCR by

vote share before the election, using NLRB-ODI matched observations in periods negative

five through negative one. As shown, the estimates before the election appear somewhat

noisier than the those after the election. This is due, in part, to fewer NLRB-ODI matched

observations before the election: 6,445 versus 10,835.19 Graphically, there is no apparent

discontinuity at the mean in the left panel or at the extensive margin in the right panel.

The third row of Table 3 presents discontinuity estimates for the TCR at the mean. While

the estimates in the first and third columns suggest a negative discontinuity at the cutoff,

only the estimate in the first column is statistically significant at the five percent level, and

neither estimate is robust to the inclusion of covariates, as shown in the second and fourth

columns. Moreover, the discontinuity estimates are sensitive to outliers in the case-rate

distribution. For example, by winsorizing the case rate at the 99th percent, the estimate

in the first column decreases from -1.801 with a standard error of 0.897 to -1.337 with a

standard error of 0.827, which is statistically insignificant. By windsorizing at the 95th

percentile, the estimates decreases further to -0.727 with a standard error of 0.701. The

fourth row of Table 3 presents discontinuity estimates of the TCR on the extensive margin.

As shown, all the estimates are negative and statistically insignificant. The estimates are

also sensitive to the model specification, appearing smaller in the model with a second order

polynomial and the wider bandwidth (columns three and four).

To examine distributional effects before the election, Figure 12 illustrates disconti-

nuity estimates of the conditional cumulative density function of the TCR, similar to Fig-

ure 10. As shown, most estimates are relatively small and statistically insignificant. Impor-

19The difference in matched observations before and after the election partially reflects that the rate offirm formation before the election is higher than the rate of firm dissolution after the election (Figure 1).

16

tantly, the discontinuity estimates at one through four, where the estimates are positive and

statistically significant after the election, are small and statistically insignificant before the

election. This suggests that the extensive margin effects are causal, having arisen only after

a union election.

5.4.3 DART

The ODI data also report the DART rate, a subset of the TCR. Specifically, the

DART includes cases involving days away from work, job restrictions, job transfers, and

excludes cases involving death or medical attention beyond first aid. Table 4 reports discon-

tinuity estimates for the DART at the mean and on the extensive margin both before and

after the election. After the election, the results for the DART are qualitatively similar to

the results for the TCR. The mean effects are mostly negative, though statistically insignif-

icant, and the extensive margin effects are positive and statistically significant (Figure 13).

Before the election, the results for the DART differ slightly from the results for the TCR.

The mean effects are positive, but small and statistically insignificant, and the extensive

margin are sizeable, ranging from -2.054 to -2.724, but are statistically insignificant. By

examining the extensive margin effects graphically, they appear to reflect sampling noise,

rather than systemic differences between establishments just above and below the cutoff

(Figure 14). Because the results for the TCR and the DART are qualitatively similar, and

because the DART is a subset of the TCR, the effect of unionization on occupational safety

predominately stems from cases involving days away from work, job restrictions, and job

transfers.

5.4.4 Firm Size

When examining the vote share distribution, there was concern for non-random

sorting at the cutoff, specifically among establishments with fewer than 30 valid votes. To

address this issue, the empirical analysis is repeated using only establishments with 30 or

17

more valid votes. The results are qualitatively similar with the higher cutoff. For example,

with a cutoff of 20, the discontinuity estimate on the extensive margin, reported in column

two of Table 3, is 2.521 percentage points, which is statistically significant at the five percent

level. With a cutoff of 30, the discontinuity estimate is 2.404, which is also statistically

significant at the five percent level. Because non-random sorting is arguably less of a concern

among larger establishments, the discontinuity estimates using the higher cutoff are more

likely to reflect the causal effect of unionization.

5.4.5 Firm Survival

To properly interpret the results, it is important to consider whether unionization

affects firm survival. While DiNardo and Lee (2004) and Freeman and Kleiner (1999) find

no effects of unionization on firm survival, Brown and Heywood (2006) and Frandsen (2014)

suggest unionization decreases firm survival, evident three years after the union election. If

so, a particular issue is whether unionization affects firm survival differentially by occupa-

tional safety. For example, unionization may cause more dangerous firms to dissolve, which

would decrease the average case rate and increase the percent of establishments with a case

rate of zero, independent of within-establishment effects of unionization on occupational

safety.

To address this issue, the analysis is repeated using only observations shortly after

the election, before the effect of unionization on firm survival is evident. When using periods

1 through 5, with a sample size of 5,499, the discontinuity estimate on the extensive margin,

reported in column two of Table 3, is 2.521 percentage points and statistically significant

at the five percent level. When using periods 1 through 2, with a sample of 2,200, the

discontinuity estimate is 2.292, but statistically insignificant. When using periods 1 through

3, with a sample of 3,327, the discontinuity estimate is 2.804 and statistically significant.

Because the extensive-margin effects are evident in the short run, the effect of unionization on

occupational safety likely reflects within-establishment changes in ocupational safety, rather

18

than differential impacts on firm survival with respect to occupational safety.

5.4.6 Multiple Elections

A single establishment may have multiple elections. For example, among the 45,582

elections from 1991 to 2010, there are 35,643 unique establishments based on an establish-

ment name, state, and city. 89.61 percent of establishments had only one election, and

8.13 percent had two elections. One concern with the preceding analysis is that multiple

elections, as well as their individual matches to the ODI, were counted as multiple observa-

tions. Another concern is that an establishment in which an election barely fails may have a

subsequent election that is successful, which would contaminate the comparison group with

treatment several years after the election.

To address this issue, the analysis is restricted to elections with no other elections

five periods before or after. The results are qualitatively similar. When using all elections,

with a sample size of 5,499, the discontinuity estimate on the extensive margin, reported

in column two of Table 3, is 2.521 percentage points and statistically significant at the five

percent level. When using the added restirction, with a sample size of 3,929, the discontinuity

estimate is 3.106 percentage points and statistically significant.

5.4.7 Effects by Industry

To examine whether the extensive margin effects vary by industry, the analysis is

repeated separately for manufacturing and non-manufacturing, which approximately halves

the sample. Figure 15 illustrates the percent of establishments in which the TCR is zero. As

shown, the percent with zero cases appears to increase discontinuously at the cutoff for both

industry categories. When using all elections, with a sample size of 5,499, the discontinuity

estimate on the extensive margin, reported in column two of Table 3, is 2.521 percentage

points and statistically significant. When using all elections in manufacturing, with a sample

size of 2,987, the discontinuity estimate is 3.222 percentage points and statistically significant

19

at the five percent level. When using all elections not in manufacturing, with a sample size

of 2,512, the discontinuity estimate is 3.826 percentage points and statistically significant.

Thus, the extensive-margin effects of unionization on occupational safety are evident in both

manufacturing and non-manufacturing establishments.

6 Conclusion

Unions engage in numerous safety-enhancing activities. To identify the effect of

unionization on occupational safety, this study exploits union election outcomes, using es-

tablishments in which elections narrowly failed as a comparison group for establishments

in which elections narrowly passed. While unionization had no detectable effect on occu-

pational safety at the mean, unionization did improve occupational safety on the extensive

margin, increasing the share of establishments with an annual accident case rate of zero by

approximately 2.5 percentage points. According to auxiliary analysis, the extensive-margin

effect appears to have occurred among establishments that would have been at the low end

of the case-rate distribution in the absence of unionization.

The results have direct implications for research on unions and wages, since occu-

pational safety may affects wages through compensating differentials (Kniesner and Leeth,

2014; Rosen, 1974). According to the analysis, the extensive-margin effects occurred among

establishments that would have had an annual TCR of four or less in the absence of union-

ization. Thus, as an upper bound among these establishments, the case rate could have

decreased by as much as four per 100 full-time equivalent workers annually. The implicit

value of statistical injury ranges from $33 thousand to $182 thousand in 2010 dollars (Viscusi

and Aldy, 2003), so a reduction of four cases is valued at $132 thousand to $728 thousand.

This translates into an increase in the hourly wage between $0.66 and $3.64, based on a

full-time work schedule of 2,000 hours per year. The median hourly wage among unionized

workers in manufacturing was $20.70 (Bureau of Labor Statistics, 2011). Thus, as an upper

20

bound among affected establishments, wages could be as much as 17.6 percent higher after

accounting for improvements in occupational safety.

21

Appendix

The study uses data from multiple sources. Data on union elections come from

the National Labor Relations Board (NLRB) and the American Federation of Labor and

the Congress of Industrial Organizations; data on union activity come from the Federal

Mediation and Conciliation Service (FMCS); and data on occupational safety come from

the Occupational Safety and Health Administration (OSHA), specifically the OSHA Data

Initiative (ODI). These data are matched at the establishment level.

The NLRB reports the establishment name, address, and industry, as well as the

number of eligible voters, valid votes cast, and votes for and against unionization. The

NLRB data are first restricted to closed cases. To match the NLRB data to the other data,

the establishment name and address were standardized. For the establishment name, all

the special characters and common words, such as company, limited, and corporation, were

deleted. If the listed formal name and the case name differed, or if the establishment is

“doing business as (DBA) under a different name, both names are retained and used for

matching. For the street address, all special characters and numbers for floor, suite, and

room were deleted. Common words, such as street, avenue, and road, were replaced with

their respective abbreviations. To standardize and clean the city name, each name was best

matched to an exhaustive list of all city names in the US, compiled by the US Census Bureau.

City names without a perfect match were checked manually for typos.

The FMCS data indicate whether an establishment filed a ”notice of bargaining,”

an indicator of union activity. The ODI reports accident case rates, measured annually

per 100 full-time equivalent workers. To match the FMCS and the ODI to the NLRB, the

establishment name and address were standardized using the same method as the NLRB.

The matching procedure utilized the establishment name, street address, city, state, and

zip code. The NLRB was matched to the FMCS and ODI in several stages. In the first

stage and most restrictive stage, the data were matched on the establishment name, street,

city, and state. In the second stage, the data were matched on the establishment name, zip

22

code, city, and state. In the third stage, the data were matched based on the first six letters

of the establishment name and address. If an FMCS or ODI record successfully matched

in one stage, the matched record was removed from matching in subsequent stages. If a

record contained multiple establishment names, the matching procedure was repeated for

each name until a successful match, if any.

23

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26

Table 1: Summary Statistics by Match to ODI

ODIMatch

All Yes No

Eligible employees (number) 114.0 139.0 104.1(1.381) (2.696) (1.598)

Valid votes (number) 97.27 122.7 87.13(1.139) (2.252) (1.309)

Vote share 50.89 47.70 52.16(0.151) (0.261) (0.183)

Pass 46.77 40.25 49.37(0.319) (0.587) (0.378)

Construction 4.884 3.813 5.310(0.138) (0.229) (0.169)

Manufacturing 28.94 47.91 21.38(0.290) (0.598) (0.310)

Transportation 16.86 9.389 19.84(0.239) (0.349) (0.301)

Health services 19.63 21.44 18.91(0.254) (0.491) (0.296)

Other 29.68 17.45 34.56(0.292) (0.454) (0.359)

Northeast 27.08 25.73 27.61(0.284) (0.523) (0.338)

Midwest 29.77 37.28 26.78(0.292) (0.579) (0.335)

South 22.41 20.83 23.03(0.266) (0.486) (0.318)

West 20.74 16.16 22.57(0.259) (0.441) (0.316)

Elections 24,758 6,976 17,782

The table presents summary statistics of union elections. The sample is derived from union

elections contained in the NLRB, file years 1991 to 2010. The sample is restricted to elections

with at least 20 valid votes and a valid vote share in favor of unionization. The second and

third columns present summary statistics separately by whether the union election is matched

to any observations in the OSHA Data Initiative (ODI), file years 1996 to 2011. Standard

errors are in parentheses.

27

Table 2: Discontinuity Estimates of Establishment Characteristics

Outcome Variable (1) (2)Employees eligible (number) 2.412 -1.360

(6.733) (7.883)[11,149] [17,186]

Valid votes (number) 3.059 1.535(5.626) (6.600)[11,149] [17,186]

Manufacturing -0.802 -0.682(1.779) (2.100)[11,150] [17,187]

Health services 0.884 1.127(1.582) (1.865)[11,150] [17,187]

ODI match 0.507 0.0241(1.780) (2.085)[11,150] [17,187]

FMCS match in periods 0 and 1 34.63*** 32.37***(2.482) (2.940)[5,365] [8,282]

Polynomial 1 2Bandwidth 0.15 0.25

The table presents discontinuity estimates of establishment characteristics. The sample is

derived from union elections contained in the NLRB, file years 1991 to 2010. The sample

is restricted to elections with at least 20 valid votes and a valid vote share in favor of

unionization. One outlier is dropped when the outcome variable is employees eligible and

valid votes. Robust standard errors are in parentheses, and sample sizes are in brackets.

Estimates are in percentage points unless otherwise noted. ∗∗∗, ∗∗, and ∗ indicate significance

at the one, five, and ten percent levels, respectively.

28

Table 3: Discontinuity Estimates of TCR

Outcome Variable Periods (1) (2) (3) (4)TCR 1 through 5 -0.0770 -0.0939 -0.394 -0.344

(0.599) (0.608) (0.697) (0.689)[5,499] [5,499] [8,303] [8,303]

TCR=0 1 through 5 2.578*** 2.521** 2.587** 2.852**(0.991) (0.991) (1.196) (1.176)[5,499] [5,499] [8,303] [8,303]

TCR -5 through -1 -1.801** -1.215 -1.884* -1.018(0.897) (0.967) (1.067) (1.079)[3,025] [3,025] [4,617] [4,617]

TCR=0 -5 through -1 -1.915 -1.878 -0.906 -0.894(1.317) (1.516) (1.640) (1.758)[3,025] [3,025] [4,617] [4,617]

Polynomial 1 1 2 2Bandwidth 0.15 0.15 0.25 0.25Covariates No Yes No Yes

The table presents discontinuity estimates of the TCR. The sample is derived from union

elections contained in the NLRB, file years 1991 to 2010. The sample is restricted to elections

with at least 20 valid votes and a valid vote share in favor of unionization. The total case rate

(TCR) includes cases involving death, days away from work, job restrictions, job transfers,

and medical attention beyond first aid. The case rate is measured per 100 full-time equivalent

workers annually. Robust standard errors are in parentheses. The estimates for 1(TCR = 0)

are reported in percentage points. ∗∗∗, ∗∗, and ∗ indicate significance at the one, five, and

ten percent levels, respectively.

29

Table 4: Discontinuity Estimates of DART

Outcome Variable Periods (1) (2) (3) (4)DART 1 through 5 0.0668 -0.164 -0.131 -0.450

(0.395) (0.406) (0.461) (0.464)[5,499] [5,499] [8,303] [8,303]

DART=0 1 through 5 3.995*** 3.440*** 4.685*** 4.196***(1.318) (1.330) (1.580) (1.570)[5,499] [5,499] [8,303] [8,303]

DART -5 through -1 0.184 0.322 0.424 0.724(0.497) (0.542) (0.579) (0.590)[3,025] [3,025] [4,617] [4,617]

DART=0 -5 through -1 -2.724 -2.446 -2.419 -2.054(1.767) (1.974) (2.183) (2.339)[3,025] [3,025] [4,617] [4,617]

Polynomial 1 1 2 2Bandwidth 0.15 0.15 0.25 0.25Covariates No Yes No Yes

The table presents discontinuity estimates of the DART. The sample is derived from union

elections contained in the NLRB, file years 1991 to 2010. The sample is restricted to elections

with at least 20 valid votes and a valid vote share in favor of unionization. The DART

includes cases involving days away from work, job restrictions, and job transfers. The case

rate is measured per 100 full-time equivalent workers annually. Robust standard errors are

in parentheses. The estimates for 1(DART = 0) are reported in percentage points. ∗∗∗, ∗∗,

and ∗ indicate significance at the one, five, and ten percent levels, respectively.

30

Figure 1: ODI Match Rate by Period

05

1015

20M

atch

Per

cent

-5 -4 -3 -2 -1 0 1 2 3 4 5Period

The figure illustrates the match rate of union elections contained in the NRLB to occupa-

tional safety data contained in the ODI. The sample is derived from union elections contained

in the NLRB, file years 1991 to 2010. The sample is restricted to elections with at least 20

valid votes and a valid vote share in favor of unionization. The periods correspond to calen-

dar years relative to the calendar year of the election. The match rates are calculated using

only calendar years for which ODI data are available. For example, elections tallied in 1999

were not used to calculate the ODI match rates in periods -4 and -5, which correspond to

calendar years 1995 and 1994, respectively.

31

Figure 2: Distribution of Vote Share

0.5

11.

52

2.5

3D

ensi

ty

-.5 -.25 0 .25 .5Vote Share

Full Sample

The figure illustrates the vote share distribution in favor of unionization. The sample is

derived from union elections contained in the NLRB, file years 1991 to 2010. The sample

is restricted to elections with at least 20 valid votes and a valid vote share in favor of

unionization.

32

Figure 3: Distribution of Vote Share

0.5

11.

52

2.5

3D

ensi

ty

-.5 -.25 0 .25 .5Vote Share

Votes>=30

0.5

11.

52

2.5

3D

ensi

ty

-.5 -.25 0 .25 .5Vote Share

Votes>=50

0.5

11.

52

2.5

3D

ensi

ty

-.5 -.25 0 .25 .5Vote Share

Votes>=70

0.5

11.

52

2.5

3D

ensi

ty

-.5 -.25 0 .25 .5Vote Share

Votes>=100

The figure illustrates the vote share distribution in favor of unionization. The sample is

derived from union elections contained in the NLRB, file years 1991 to 2010. The sample

is restricted to elections with at least 20 valid votes and a valid vote share in favor of

unionization. In each panel, the sample is restricted to elections with a minimum number of

valid votes cast, as indicated.

33

Figure 4: Employees and Votes by Vote Share

050

100

150

200

250

Num

ber

-.5 0 .5Vote Share

Eligible Employees

050

100

150

200

250

Num

ber

-.5 0 .5Vote Share

Valid Votes

The figure illustrates the average number of eligible voters and valid votes cast for 20 non-

overlapping bins of 5 percentage points each. The sample is derived from union elections

contained in the NLRB, file years 1991 to 2010. The sample is restricted to elections with

at least 20 valid votes and a valid vote share in favor of unionization.

34

Figure 5: Industry by Vote Share

010

2030

4050

6070

8090

100

Perc

ent

-.5 0 .5Vote Share

Manufacturing

010

2030

4050

6070

8090

100

Perc

ent

-.5 0 .5Vote Share

Health Services

The figure illustrates the share of establishment in manufacturing and health services for 20

non-overlapping bins of 5 percentage points each. The sample is derived from union elections

contained in the NLRB, file years 1991 to 2010. The sample is restricted to elections with

at least 20 valid votes and a valid vote share in favor of unionization.

35

Figure 6: ODI Match by Vote Share

010

2030

4050

6070

8090

100

Perc

ent

-.5 0 .5Vote Share

ODI Match

The figure illustrates the match rate of union elections to the ODI for 20 non-overlapping bins

of 5 percentage points each. The ODI contains data on occupational safety and is compiled

by the Occupational Safety and Health Administration. The sample is derived from union

elections contained in the NLRB, file years 1991 to 2010. The sample is restricted to elections

with at least 20 valid votes and a valid vote share in favor of unionization.

36

Figure 7: FMCS Match by Period

010

2030

4050

Mat

ch P

erce

nt

-5 -4 -3 -2 -1 0 1 2 3 4 5Period

Pass Fail

The figure illustrates the match rate of union elections contained in the NRLB to notices of

bargaining filed with the FMCS. The sample is derived from union elections contained in the

NLRB, file years 1999 to 2010. The sample is restricted to elections with at least 20 valid

votes and a valid vote share in favor of unionization. The periods correspond to calendar

years relative to the calendar year of the election.

37

Figure 8: FMCS Match by Vote Share

010

2030

4050

6070

8090

100

Mat

ch P

erce

nt

-.5 0 .5Vote Share

The figure illustrates the match rate of union elections contained in the NRLB to notices of

bargining filed with the FMCS in periods zero or one across bins of five percentage points.

The sample is derived from union elections contained in the NLRB, file years 1999 to 2010.

The sample is restricted to elections with at least 20 valid votes and a valid vote share in

favor of unionization.

38

Figure 9: TCR by Vote Share, Periods 1 through 5

010

2030

TCR

/100

full-

time

empl

oyee

s an

nual

ly

-.5 0 .5Vote Share

TCR

010

2030

Perc

ent A

nnua

l TC

R=0

-.5 0 .5Vote Share

TCR=0

The figure illustrates the TCR in periods 1 to 5 for 20 non-overlapping bins of 5 percentage

points each. The sample is derived from union elections contained in the NLRB, file years

1991 to 2010. The sample is restricted to elections with at least 20 valid votes and a valid

vote share in favor of unionization.

39

Figure 10: Discontinuity Estimates of the Cumulative Density Function ofthe TCR, Periods 1 through 5

-30

-20

-10

010

2030

Dis

cont

inui

ty E

stim

ate

0 5 10 15 20 25Outcome: I(TCR

Figure 11: TCR by Vote Share, Periods -5 through -1

010

2030

TCR

/100

full-

time

empl

oyee

s an

nual

ly

-.5 0 .5Vote Share

TCR

010

2030

Perc

ent A

nnua

l TC

R=0

-.5 0 .5Vote Share

TCR=0

The figure illustrates the mean TCR in periods -5 to -1 for 20 non-overlapping bins of 5

percentage points each. The sample is derived from union elections contained in the NLRB,

file years 1991 to 2010. The sample is restricted to elections with at least 20 valid votes and

a valid vote share in favor of unionization.

41

Figure 12: Discontinuity Estimates of the Cumulative Density Function ofthe TCR, Periods -5 to -1

-30

-20

-10

010

2030

Dis

cont

inui

ty E

stim

ate

0 5 10 15 20 25Outcome: I(TCR

Figure 13: DART by Vote Share, Periods 1 through 5

010

2030

DAR

T/10

0 fu

ll-tim

e em

ploy

ees

annu

ally

-.5 0 .5Vote Share

DART

010

2030

Perc

ent A

nnua

l DAR

T=0

-.5 0 .5Vote Share

DART=0

The figure illustrates the DART in periods 1 to 5 for 20 non-overlapping bins of 5 percentage

points each. The sample is derived from union elections contained in the NLRB, file years

1991 to 2010. The sample is restricted to elections with at least 20 valid votes and a valid

vote share in favor of unionization.

43

Figure 14: DART by Vote Share, Periods -5 through -1

010

2030

DAR

T/10

0 fu

ll-tim

e em

ploy

ees

annu

ally

-.5 0 .5Vote Share

DART

010

2030

Perc

ent A

nnua

l DAR

T=0

-.5 0 .5Vote Share

DART=0

The figure illustrates the DART in periods -5 to -1 for 20 non-overlapping bins of 5 percentage

points each. The sample is derived from union elections contained in the NLRB, file years

1991 to 2010. The sample is restricted to elections with at least 20 valid votes and a valid

vote share in favor of unionization.

44

Figure 15: Discontinuity Estimates of the Cumulative Density Function ofthe TCR, Periods 1 to 5

010

2030

Perc

ent A

nnua

l TC

R=0

-.5 0 .5Vote Share

Manufacturing

010

2030

Perc

ent A

nnua

l TC

R=0

-.5 0 .5Vote Share

Not Manufacturing

The figure illustrates the TCR in periods 1 to 5 for 20 non-overlapping bins of 5 percentage

points each. The sample is derived from union elections contained in the NLRB, file years

1991 to 2010. The sample is restricted to elections with at least 20 valid votes and a valid

vote share in favor of unionization.

45