Safety Science 145 (2022) 105497

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Safety Science
journal homepage: www.elsevier.com/locate/safety

The effect of within-firm vertical pay disparity in occupational safety

Cristian Ramírez, Jorge Tarziján *, Marcos Singer
School of Management, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago, Chile

A R T I C L E I N F O A B S T R A C T

Keywords: Greater vertical pay disparity is associated with compensation schemes that reward relative performance.
Pay-disparity Considering tournament theory as a leading framework for those schemes, along with boosting productivity, they
Workplace injuries are likely to increase workers’ willingness to exert effort at the risk of injuries or occupational sickness. We find
Ownership type
evidence of such pervasive effect on a novel database that includes more than 110,000 Chileans firms. For
Gender
workers in the bottom half of the wage distribution, an increment of one standard deviation in within-firm
vertical pay disparity is associated with an increase of around 10% in the number of injuries and almost 19%
in the number of days lost. These results are negatively moderated by the proportion of female employees and
state ownership.

1. Introduction 2016; Viscusi and Aldy, 2003). According to the Occupational Safety
and Health Administration (2019), employers in the U.S. pay almost $1
Compensations schemes that reward relative performance through in­ billion per week for direct workers’ compensation costs alone for
centives has been shown to motivate employees to exert more effort to get workplace injuries and illnesses.
wage increments (Connelly et al., 2014). As documented by Bloom et al. Different drivers explain the frequency and magnitude of workplace
(2019), management practices associated with performance incentives are injuries; many of them are related to an exaggerated effort by workers.
correlated with (and may induce) greater within-firm vertical pay disper­ For example, Goh et al. (2016) find that employees’ health is affected by
sion.1 Such dispersion has positive effects on firm performance such as workplace stressors. Cioni and Savioli (2016) argue that poor working
promoting competition and providing incentives for the best to rise above conditions are an important determinant of injuries and illnesses
others (Fredrickson et al., 2010; Mueller et al., 2017). occurring at work, while Lombardi et al. (2010) find that less sleep time
In this work we focus on a rather unanticipated effect of within-firm at nights is associated with more workplace injuries. Though these
vertical pay dispersion: an increase of workplace injuries and sick­ studies have generated important insights, none of them have analyzed
nesses.2 Considering tournament theory as a leading example of relative how within-firm vertical pay dispersion affects working conditions and,
performance compensations schemes, we deduce that greater prizes hence, workplace injuries.
implicit in a wider pay gap may increase the willingness to take risks by We test our hypotheses using a database that covers more than
workers, at effort levels above their own limits (Bothner et al., 2007; 110,000 Chilean companies and more than six million workers. The
Hvide, 2002; Yu and Chen, 2013; Lim, 2019). This hidden cost may be database contains information regarding the monthly salaries of each
considerable and severely harm the sustainability of the firm. Workplace worker of those firms for the period between January 2011 and
injuries increase downtime, reduce employees’ morale, lower produc­ December 2017, as well as data on workplace injuries and illnesses
tivity, increase health insurance costs, make it harder to attract and suffered by each employee and the resulting number of days lost per
retain talent, and entail hiring and training substitute employees (e.g., event. We also have data on the workers’ gender and the industry in
Cohn and Wardlaw, 2017; Fernández-Muñiz et al., 2009; Goh et al., which each firm operates. Our database is fairly representative of the

* Corresponding author.
E-mail addresses: cristian.ramirez@uc.cl (C. Ramírez), jtarzija@uc.cl (J. Tarziján), msinger@uc.cl (M. Singer).
1
Research has differentiated between vertical and horizontal pay dispersion. The level of within-firm vertical pay dispersion is defined as the difference in pay
between job levels (e.g., Bloom, 1999), whereas the level of within-firm horizontal pay dispersion is associated with differences in pay within job levels (e.g., Gupta
et al., 2012; Siegel and Hambrick, 2005).
2
We use the word “injury” indistinctively throughout this paper to refer to occupational injuries and work-related diseases or illnesses. In particular, Dahl and
Pierce (2020) find a four to six percent increase in the usage of anti-depressant and anti-anxiety medication after firms adopt pay-for-performance.

https://doi.org/10.1016/j.ssci.2021.105497
Received 4 January 2020; Received in revised form 21 April 2021; Accepted 10 September 2021
Available online 14 October 2021
0925-7535/© 2021 Elsevier Ltd. All rights reserved.
C. Ramírez et al. Safety Science 145 (2022) 105497

Chilean economy. On average, for each month in our database, we have Lazear and Rosen’s (1981) formulation of tournament theory was
about 34% of the total labor force in Chile that had formal employment originally put forth to explain promotion tournaments at the top man­
during that time. agement team (TMT) level, in which the wage increases associated with
Using different econometric specifications, we find a positive rela­ promotion are the prizes that align executives’ incentives and organi­
tionship between increasing levels of within-firm vertical pay disparity zational goals (Henderson and Fredrickson, 2001; Lazear and Rosen,
and the number of injuries (and days lost) among those employees who 1981; Ridge et al., 2015). Lately, other studies have used tournament
earn below the median salary in the firm. Our results are robust to al­ theory to explain behavior from employees who do not belong to the
ternatives definitions of pay disparity (e.g., as a ratio of wages or as the TMT (e.g., Kacperczyk and Balachandran, 2018).
Gini coefficient) and even to different functional forms (Poisson and OLS Despite the potential positive effects of greater within-firm vertical
regression). In summary, an increase of one standard deviation in our pay differentials, higher levels of pay disparity may also have negative
measure of within-firm vertical pay disparity (relative to its mean value) effects on employees’ well-being and firm performance. For example,
is associated with an increment of around 10% in the number of injuries Bloom and Michel (2002) show that a larger pay gap is associated with
and almost 19% in the number of days lost. an increased likelihood of executive turnover. Shi et al. (2016) present
To better understand the effect of within-firm vertical pay disparity evidence that the pay gap between the CEO’s remuneration and the
on workplace injuries (and to rule out reverse causality, as explained average compensation of other top executives result in an increase in
later), we examine the effect of firm ownership, finding that it is securities class action lawsuits. DeVaro and Gürtler (2016) show that
significantly weaker in state-owned firms (SOF). A possible explanation strategic shirking (i.e., underperforming on tasks that are unimportant
is that SOFs’ employees may feel that their promotions depend more to promotion) increases when pay disparity is greater. Sanders and
heavily on variables such as political connections, years in the organi­ Hambrick (2007) state that, faced with the potential for a large payout,
zation, or the attainment of the goals of government actors interested in top managers are less attuned to the early signs of project failure and
ensuring long tenure (Chen et al., 2017; Inoue et al., 2013) and not on more reckless about mitigating risk. Lazear (1989) argues that agents
additional exertion of effort. We also study the moderating role of may respond to the stronger incentives implied in a compensation
gender. Two of the main gender differences relevant to labor markets structure with larger vertical pay gaps sabotaging their rivals (i.e., un­
behavior are that men seem to be more risk-prone and more willing to dertaking actions that adversely affect others’ output), while Becker and
compete than women (e.g., Byrnes et al., 1999; Croson and Gneezy, Huselid (1992) find that professional car racing drivers’ impetuousness
2009; Eckel and Grossman, 2008)—both of which imply that women is positively associated with the spread of race prizes.
might be less willing than men to take risks in order to earn greater Among the negative effects of relative performance compensation
monetary prizes. Under this premise, workplace injuries should be less schemes, risk taking is crucial (Eriksen and Kvaløy, 2014). Because of
affected by increases in the level of within-firm vertical pay disparity in the intense pressure for high performance, workers may be tempted to
companies where the proportion of women in the workforce is greater, face additional risks to improve their chances of being promoted (Hvide,
which is coherent with our empirical findings. 2002; Ridge, 2012). Bothner et al. (2007) show that athletes take more
We aim to make several contributions. First, by studying the rela­ risks when prizes are greater, whereas in a laboratory experiment Kilduff
tionship between within-firm vertical pay disparity and workplace in­ et al. (2018) demonstrate that competition raises risk-taking via
juries, we add –from a novel perspective– to the discussion of the hidden increased promotion focus and arousal. Additionally, there is evidence
costs of incentives. Though much has been said about compensation that indicates that workers might fail to understand the risks of actions
policies, there has not been a discussion of how changes in vertical pay that involve additional effort and, when faced with the potential for a
disparity within an organization might change employees’ attitude to large payout, they might be less attuned to the signs of safety issues and
assume risks and therefore increase the chances of hurting themselves. If be more reckless about mitigating risk (e.g., Sanders and Hambrick,
larger vertical pay gaps increase the number and/or severity of work­ 2007). In this context, we argue that a larger vertical pay gap could
place injuries, then compensation policies that involve a rise in the level trigger workers to rationalize that the heightened risk is worth the po­
of within-firm vertical pay disparity should be complemented with tential payoff of winning a higher salary increase, which can result in a
improved safety measures. Second, we intend to contribute to the nu­ higher number and severity of workplace injuries.3 This discussion leads
ances of the effects of pay disparity on performance by analyzing to the following hypothesis:
ownership and gender effects. With this, we respond to calls that more
Hypothesis 1. An increment in the level of within-firm vertical pay
research is necessary to explore whether gender differences affect the
disparity positively influences the number (and magnitude) of work­
relationship between wage dispersion and productivity in organizations
place injuries.
(Connelly et al., 2014). Third, contrary to the main focus of interest in
the pay dispersion literature—which has concentrated its efforts on Next, we analyze two moderators that can shed light on the mech­
CEOs and top management teams (e.g., Greckhamer, 2016; Mueller anisms behind our theorized relationship between within-firm pay
et al., 2017; Shi et al., 2016)– we seek to understand the effects of disparity and workplace injuries: state-ownership and gender.
changes in vertical pay disparity at the operative organization level.
Finally, we try to answer the calls for conducting empirical research on
2.1. The moderating effect of state ownership
pay disparity using a broad sample of organizations and employees
rather than conducting studies on specialized samples (Bloom and
The potential effects of institutional variables such as regulations,
Michel, 2002, Connelly et al., 2014).
capital market characteristics and firm governance features on firm
performance have been widely studied (e.g., Rajan and Zingales, 2004).
2. Theoretical framework We analyze an important institutional variable: whether the firm is state
or privately owned (Vanacker et al., 2017; Xia and Walker, 2015). Major
Tournament theory (Lazear and Rosen, 1981) has served as a differences between SOFs and privately-owned firms (POFs) appear to
cornerstone for research on relative performance compensation schemes
(e.g., Connelly et al., 2014). According to its assumptions, greater levels
of within-firm vertical pay dispersion motivate employees to exert more 3
Given that employees at different salary levels face different willingness to
effort to get the wage increments implied in wider pay gaps structures exert additional effort and take risks, we analyze our predictions for the full set
(Zhang et al., 2019). In fact, there is evidence that a worker’s effort of workers and for subsets of firm employees. This departs from most of the
increases more with compensation spread than with compensation literature in management, finance, and strategy, which focuses on TMTs
levels (Brown et al., 2003; Shaw et al., 2002). compensation (Larkin et al., 2012).

2
C. Ramírez et al. Safety Science 145 (2022) 105497

be driven by their different motivations and objectives. CEOs of SOFs are in economics (Eckel and Grossman, 2008) and psychology (Byrnes et al.,
generally focused on creating wealth in the economy and ensuring the 1999). For instance, in a study based on neural systems, Becker et al.
well-being and employment of citizens, whereas the managers of POFs (2012) posit that males are more likely than females to engage in risky
primarily focus on creating wealth for their shareholders (e.g., Musac­ behaviors and that these differences are due, at least in part, to gender
chio and Lazzarini, 2014). Other empirical studies have shown how differences in the organization of the neural systems responsible for
differences in the type of ownership of firms can affect performance and motivation.
the value captured by employees (e.g., Ramírez and Tarziján, 2018; Xia In a similar vein, it has been observed that women are less willing to
and Walker, 2015). exert additional effort to compete than men and that men’s perfor­
There are different approaches concerning the role of state owner­ mance, relative to women’s, improves under competition (e.g., Croson
ship (Sapienza, 2004) that are relevant when studying compensation and Gneezy, 2009; Gneezy and Rustichini, 2004). For instance, in a lab
policies in firms with different ownership structures. The social experiment, Gneezy et al. (2003) asked men and women to solve mazes
approach (Atkinson and Stiglitz, 1980) suggests that SOFs are created to on a computer for 15 min. Participants were paid either according to a
address market failures (with SOFs maximizing broader social objectives piece rate (a dollar amount per maze solved) or a winner-take-all tour­
and POF maximizing profits). The political approach (Shleifer and nament. In the piece rate, men performed similarly to women; however,
Vishny, 1997) argues that SOFs are utilized as a mechanism for pursuing when participants were paid on a competitive basis and only the best
the goals of politicians, such as boosting employment. Finally, the person in the group was to be rewarded, males’ performance was
agency approach shares with the social view the idea that SOFs are significantly higher than females’ performance. In a related study,
created to maximize social welfare but stresses that SOFs can also Niederle and Vesterlund (2007) used a controlled laboratory experiment
generate resources’ misallocation because of weak managerial in­ to examine individual choices between competitive and non-
centives and low employee effort (Banerjee, 1997). competitive compensation schemes in a nondiscriminatory environ­
The theories above suggest that state ownership may be an important ment, finding that women are less likely to choose to compete than men.
factor affecting the wage structure and the pay disparity of firms. More Other scholars find that men appear to be more motivated by prize
specifically, a general premise is that the effect of pay disparity on spreads than women (Lallemand et al., 2008) and that women may be
employees’ willingness to compete and take risk is different in SOFs than motivated by factors different from prize spreads (McCormick and
in POFs (Zhou et al., 2017). Employees of SOFs may feel that their Maloney, 2000). Women also appear to respond less strongly to bonus
promotions depend more heavily on variables such as political con­ payments, whereas such bonuses increase performance dispersion
nections, years in the firm, or the attainment of the political goals of among men (Frick, 2003).
governmental actors (Chen et al., 2017). Conversely, managers of SOFs In our baseline hypothesis (H1), we argue that increases in within-
have longer-term job stability and their contracts are less responsive to firm pay disparity can induce additional effort and competition that
performance (Musacchio and Lazzarini, 2014). The multiple and often can be beneficial to the firm’s prospects (e.g., Connelly et al., 2014) but
conflicting objectives pursued by SOFs’ employees suggest that the level at the cost of an additional number and severity of workplace injuries.
of effort they can devote to reach the higher prizes implied by increases However, the increase in the level of risk that workers are willing to
in within-firm pay disparity may be different from the efforts exerted by accept to compete for better prizes is bound by their level of risk toler­
POFs’ employees (Kato and Long, 2011). ance. Assuming that women are more risk-averse and less prone to exert
Thus, in a setting in which multiple goals exist and principals are additional effort to compete than men, we hypothesize that the effect of
looking for different outcomes, as it is the case in SOFs, monetary prizes an increase in the level of within-firm pay disparity on workplace in­
will tend to have a weaker effect on motivation and behavior than in juries is negatively moderated by the proportion of females in the firm’s
POFs, where there is usually one main goal, one principal, and pro­ workforce. From this discussion, we obtain the following hypothesis:
motions are more responsive to performance (Dixit, 2002). Given that
Hypothesis 3. The effect of an increment in the level of within-firm
workers of SOFs are less willing to exert more effort and take additional
vertical pay disparity on the number and magnitude of workplace in­
risks than their POFs counterparts, we expect a lower effect of in­
juries is negatively moderated by the proportion of women employed in
crements in within-firm vertical pay disparity on workplace injuries in
the firm.
SOFs. This discussion leads to the following hypothesis:
Hypothesis 2. The effect of an increment in the level of within-firm 3. Materials and methods
vertical pay disparity on the number and magnitude of workplace in­
juries is lower in state-owned firms than in privately-owned firms. 3.1. Data

Our data on injuries and wages come from the Chilean Safety Asso­
2.2. The moderating effect of gender
ciation (ACHS, for its acronym in Spanish). The ACHS is an association
of companies and workers in Chile whose main purpose is the preven­
Gender differences have been observed in several contexts, including
tion of occupational injuries and illnesses and the promotion of a culture
labor markets. It is often hypothesized that some of these differences are
that ensures the safety, health, and quality of life of workers. The Chil­
associated with preferences for competition and risk-taking (e.g., Blau
ean law requires all the companies to affiliate to one safety association,
and Kahn 2000; Goerke and Pannenberg, 2012). Croson and Gneezy
which are strictly regulated by a government agency. The ACHS is the
(2009) argue that women are more risk-averse than men owing to the
oldest and largest safety association in Chile, and according to Brahm
differences in emotional reactions to risky situations and the degree of
and Singer (2013), the companies it serves are fairly similar to the rest in
overconfidence. Women report greater anxiety and fear than men in
the country. As of December 2017, the figure of affiliated institutions to
anticipation of negative outcomes (Loewenstein et al. 2001), whereas
the ACHS is 65,854 and the number of affiliated workers exceeds 2.5
men tend to be more overconfident in their likelihood of success in
million (ACHS, 2021) at any point of time, although there is a natural
uncertain situations than women (e.g., Niederle and Vesterlund, 2007).
turnover of firms from one association to another.
In their review, Croson and Gneezy (2009) also find that men are more
Affiliated firms are required to send the information concerning
risk-prone than women, a result that is coherent with previous findings

3
C. Ramírez et al. Safety Science 145 (2022) 105497

occupational injuries and their payroll to the ACHS on a monthly basis. ACHS’ database. The range of the Gini coefficient goes from 0 to 1, with
ACHS as well as the other associations must submit such information to 0 representing complete equality of wages (i.e., all workers receive the
the government agency, as its accuracy is essential in case of severe same salary) and 1 being absolute inequality (i.e., one worker receives a
injuries. For this study, data related to affiliated companies are available positive salary while the others get nothing). Organizations with higher
for 84 months, corresponding to the period from January 2011 through Gini coefficients have more hierarchical pay dispersion. In broad terms,
December 2017. The ACHS records every workplace injury in its data­ the Gini coefficient measures half the relative mean difference of the pay
bases, including the number of days lost as a result of each injury and of any two employees selected at random from a firm’s compensation
disease and the number of days lost that has occurred in each affiliated distribution, (Carnahan et al., 2012). The Gini coefficient has been used
institution in each month. From January 2015 onwards, the ACHS’ in the literature as a measure of pay disparity (e.g., Bloom, 1999; Bloom
database also includes information on workplace prevention activities and Michel, 2002; Carnahan et al., 2012; Shaw et al., 2002) even as an
performed at each affiliated company. The database from the ACHS also alternative to other measures of compensation dispersion such as the
provides (i) the six-digit International Standard Industrial Classification coefficient of variation (e.g., Fredrickson et al., 2010).
(ISIC) code for each firm and (ii) information on whether the company is
state or privately owned. 3.4. Moderators
Regarding wages, the original number of monthly salary records in
our database is around 190 million, which means that, on average, for State ownership. The ACHS database includes information on
each month we have almost 2.2 million employee-month observations whether a firm is privately or state owned. We code this variable with a 1
(about 34% of the total labor force in Chile that had an employment if the firm is state owned and with a 0 in case it is privately owned.
contract during that time). Proportion of female workers. The ACHS’ records include the
gender of each worker. We compute the proportion of female workers
3.2. Dependent variables for each firm i in month t.

Given the observed positive correlation between occupational safety 3.5. Control variables
and firm value (Cohn and Wardlaw, 2017) and how the number of in­
juries at each firm is an accurate measure of how the company executes Median wage. We compute the median of the wages that each firm i
its day-to-day operations (Asfawa et al., 2013; Böckerman et al., 2012; paid its employees in month t. We only consider employees who
Pagell et al., 2015), we consider measures of both the number and received more than the minimum wage salary. We operationalize the
severity of work-related injuries and diseases as our dependent vari­ median wage variable as the natural logarithm of the median compen­
ables. In all our computations, we focus on occupational injuries and sation expressed in Chilean pesos of each month (i.e., nominal amounts).
diseases that implied the loss of at least one day of work. We include this variable (log transformed) in our regression models to
We first calculate the total number of reported occupational injuries and control for the different propensities to exert additional effort that might
diseases in firm i in month t. Since injuries and diseases vary in their result from dissimilar levels of earnings, for instance because lower
severity, with some of them requiring just ambulatory treatment while salaries attract poorer human capital (Siegel and Hambrick, 2005).
others implying serious consequences for the injured workers, we then focus Size. Firms of different sizes might face dissimilar situations and
on the quantification of the total number of days of work lost as a result of likelihoods of experimenting workplace injuries and diseases (besides
occupational injuries and diseases that occurred in each firm in a specific just the natural increment in the quantity of injuries and days lost that
month. This variable, which we call days lost, highlights the loss in re­ should occur as consequence of having a higher number of workers in
sources for a company as the outcome of occupational injuries and the organization). For example, as firms grow and professionalize their
diseases.4 activities, the chances they will set up a risk prevention program in­
crease and, with that, the likelihood of observing an injury is reduced.
3.3. Independent variables Consistent with the definition of other variables included in our ana­
lyses, we measure size as the natural logarithm of the number of workers
Pay disparity. We consider two variables to measure within-firm that earn a wage greater than or equal to the minimum wage in each
pay disparity: the ratio 90–10 and the Gini coefficient. month. Scholars have used a similar measure in other studies that
Ratio 90–10. For each company in each month, we calculate the involve pay dispersion (e.g., Shaw et al., 2002).
deciles of the distribution of wages. With these, we compute the ratio of Percentage of censored wage records. In Chile, employees’ social
the 9th decile to the 1st decile (r90–10)—a measure of pay disparity that security contributions are computed as a percentage of gross income.
has been used extensively in the literature (e.g., Greckhamer, 2016; However, there is a cap over which such contributions are calculated.
Ridge et al., 2015; Shin, 2014; Siegel and Hambrick, 2005). Other This cap—which during the time considered in our database is around
measures of economic inequality, such as variance, the Gini coefficient CLP 1.7 million (or approximately USD 3,000) per month—is deter­
(discussed below), and the coefficient of variation (Fredrickson et al., mined by a panel of authorities at the beginning of each calendar year
2010), are useful in describing the overall distribution, capturing both and is expressed in real terms (so it increases according to the inflation
vertical and horizontal differences in wages. Although r90–10 is not rate each month). The ACHS’ database includes workers’ wages in each
completely free of this problem, the degree to which a wage in the 90th month if they are less than or equal to the cap, otherwise the cap for that
percentile could reflect horizontal wage gaps instead of vertical ones is month is reported. This means that wages are right-censored. For the
greatly reduced in comparison to the measures mentioned above. To sample as a whole, the average percentage of censored records per firm
ease interpretation, we include this variable in all our regression models is about 5.1, which means that, on average, a small fraction of em­
log transformed, so its coefficient can be interpreted as an elasticity. ployees in each firm is affected by the censorship. As we can expect, this
Gini coefficient. For each firm in each month, we compute the Gini proportion is not constant across firms (standard deviation of 0.066).
coefficient using the firm’s payroll for that period as is presented in the The standard deviation of the proportion of censored outcomes remains
fairly stable over time, which reinforces our idea that the dispersion of
the proportion of employees with censored wages does not change
4
We do not consider fatal injuries or diseases in the computation of our significantly during the period covered by our database.
dependent variables. Fatal events represent less than 0.03% of the total number To correct for the bias towards 0 in our independent variables that
of injuries or diseases in our dataset. Additionally, there is not a clear number of measure pay disparity—as a consequence of the right-censorship that
days lost that we could associate to each fatal injury. affects our records of wages—we include a regressor that reflects the

4
C. Ramírez et al. Safety Science 145 (2022) 105497

percentage of workers in each firm i in month t that receives a wage coefficients of the other regressors included in our models is similar.7 As
greater than or equal to the cap. Although this does not solve our issue of mentioned in the previous section, firm-year and industry-month fixed
underestimating the full pay disparity in each firm, it helps us get a effects are included to control for yearly-invariant characteristics of
cleaner estimate of the relationship between injuries (or their severity) firms and industry-month specific shocks, respectively, that could affect
and pay disparity. In any case, despite the r90–10 index not being the number and severity of injuries.
completely free of the censoring issue, the bias is less pronounced than in
the case of the Gini index mainly because the salary received by a worker

∑5
ln (θit ) = β1 pay disparityit + β2 (pay disparityit × prop femit ) + β3 (pay disparityit × ownershipit ) + γ controlcit + ind monthjt + firm yeariy . (2)
c=1 c

in the 90th percentile is closer to the upper bound than the salary of a Eq. (2) expands our base model and includes the interaction terms
worker in the 99th percentile, which is still reported as being equal to between pay disparity with the proportion of female workers in the
the cap and considered in the computation of the Gini index. organization and the type of ownership.
Prevention activities. Starting from January 2015, we have infor­
mation on the number of monthly prevention activities performed at
3.7. Filters
each firm that are coordinated by the ACHS’ specialists. These activities
are jointly determined between each firm and the ACHS and ought to be
The original dataset contains information on more than 110,000
relevant to the firm’s context and safety risks faced by its employees. We
firms and more than six million different workers, which gives a total of
include the raw number of activities carried out at each firm i in each
almost 190 million worker-month observations. We apply the following
month t in some of our analyses.
filters to the raw database to get the final sample used in the analyses.
Since our final database is comprised of an unbalanced panel of firms
First, in order to focus our analyses on organizations with at least some
that we observe between January 2011 to December 2017, we include firm-
layers of workers, we excluded all firm-month observations with fewer
year fixed effects in all our specifications to control for yearly characteristics
than 20 employees (Kacperczyk and Balachandran, 2018). Second, we
of firms (such as year-specific compensation policies or bonuses, attributes
removed all observations for which we do not have information on the
of the working environment, and even the presence of an occupation risk
industry they operate. Third, we dropped all observations with a pro­
prevention program during the period) that might affect the propensity of
portion of censored wages greater than one third. Fourth, we computed
all employees in a firm to take risks or suffer an injury in that year.5
the number of injuries and days lost per employee per firm per month
Additionally, and to control for shocks that could influence the likelihood or
and, only considering the observations for which those measures were
severity of occupational injuries and diseases for firms operating in a spe­
greater than zero, we eliminated the top 1% of each since those obser­
cific industry in each month t, we add industry-month fixed effects to all our
vations seem to correspond to rare events. Fifth, we dropped the top and
specifications. Our main objective with these industry-month fixed effects is
bottom 1% of our main measures of pay disparity (r90–10 and Gini
to capture all variations in the injury rate or days lost that could be a
coefficient) to decrease the chances that extreme values could influence
consequence of industry-specific events that affected firms in a particular
our results.
month. For example, we could think of natural events such as floods or
earthquakes that might have affected the likelihood of observing workplace
injuries in companies operating in a similar industry. In a similar vein, these 4. Results
industry-month fixed effects might help us capture the effect of any changes
made to safety regulations at the industry level. In our setting, we define 4.1. Descriptive statistics
industries according to the first four digits of the corresponding ISIC codes.6
Tables 1 and 2 present descriptive statistics and correlation co­
efficients. Our final dataset includes 17,435 firms and 238 industries
3.6. Econometric model
(the latter defined using the first four digits of the ISIC codes). As we can
see in Table 1, the database has 561,892 firm-month observations. The
Eq. (1) presents our base model for the relationship between pay
average number of workplace injuries and diseases per firm-month is
disparity and number or severity of occupational injuries and diseases
around 0.69, while the average number of days lost per firm-month is
(θit ) in firm i in month t.
9.44. There is a relatively large variation in the data, with a great portion
∑5
ln(θit ) = β1 pay disparityit + γ controlcit + ind monthjt + firm yeariy .
c=1 c
(1) 7
Given that we are interested in injuries and days lost, which are by defi­
In Eq. (1), β1 represents the impact of pay disparity on our dependent nition count variables, a traditional OLS approach would not provide a good fit,
variable of interest. Since Eq. (1) involves exponentiation, the inter­ especially since injuries and days lost are heavily skewed to the right. Modeling
the conditional mean of our dependent variables using an exponential function
pretation of the β coefficients differs somehow from the ones obtained
solves this problem without the need to transform the dependent variable
from an OLS regression. For example, a one-unit change in our measure
(Wooldridge, 2010), with the interpretation of the parameters being akin to a
of pay disparity would imply a multiplicative effect on the expected log-linear regression. Besides, since our dependent variables are integers (in­
number of our dependent variable of exp(β1 ). The interpretation of the juries and days lost), a Poisson regression becomes the natural alternative to
test our hypotheses. In our setting, it will be more likely to observe a higher
number of injuries in firms with a higher number of employees, because there
5
Further, firm-year fixed effects control for factors that do not change easily are a greater number of chances of experiencing an injury. Therefore, the
from one year to another such as the technology used in production, the types natural exposure variable would be size or the number of employees in a firm.
of positions available to employees, workforce composition, etc. Instead of fixing the coefficient of this variable to one, we allow our model to
6
We included industry-month fixed effects considering the different levels of freely estimate it to capture any effect size could have on the number of injuries
aggregation (three and four digits), and our main results still hold. or magnitude.

5
C. Ramírez et al. Safety Science 145 (2022) 105497

Table 1 related to the scale of each index; while the Gini coefficient is defined in
Descriptive statistics. the range [0, 1], r90–10 can take on any positive value greater than or
Variable Observations Mean SD Min Max equal to 1.
The average number of employees is around 200, with a median
Injuries 561,892 0.69 2.70 0.00 215.00
Days lost 561,892 9.44 47.92 0.00 5,653.00 monthly wage of CLP 562,311 (roughly about USD 1,000 considering
Employees 561,892 198.90 636.51 20.00 22,229.00 the average exchange rate during the time covered by our dataset). The
r90–10 561,892 3.21 1.08 1.24 6.30 proportion of female workers is almost 0.32, which although low is in
Gini 561,892 0.24 0.06 0.07 0.37 line with the data reported by governmental agencies in Chile on the
Median wage (000 s) 561,892 562.31 220.69 187.83 1,849.00
Proportion of female 561,892 0.32 0.25 0.00 1.00
participation rate for women. SOFs comprised 4.3% of the sample
workers (24,197 observations from 596 different firms). The average number of
Ownership 561,632 0.04 0.20 0.00 1.00 prevention activities performed per firm per month is 0.62 between the
Prevention activities 238,765 0.62 3.82 0.00 358.00 years 2015 and 2017. Finally, the mean proportion of censored wages
Proportion of 561,892 0.05 0.07 0.00 0.33
per firm per month is about 5%, which is in line with the filters applied.
censored records
In the correlation coefficients presented in Table 2, we can see a

Table 2
Correlation Coefficients.a
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

(1) Injuries 1.00

(2) Days lost 0.68 1.00
(3) Employees 0.75 0.58 1.00
(4) r90–10 0.01 0.02 0.08 1.00
(5) Gini 0.02 0.02 0.06 0.86 1.00
(6) Median wage (000 s) − 0.03 0.02 0.07 0.30 0.09 1.00
(7) Proportion of female workers 0.04 0.03 0.11 0.14 0.17 − 0.04 1.00
(8) Ownership 0.08 0.10 0.20 0.18 0.12 0.11 0.14 1.00
(9) Prevention activities 0.51 0.35 0.64 0.02 0.02 0.04 0.04 0.08 1.00
(10) Proportion of censored wages − 0.01 0.02 0.08 0.45 0.33 0.64 − 0.04 0.03 0.03 1.00
a
All correlation coefficients are statistically significant at the 99% of confidence.

of observations not including any lost days in a given month (375,569). positive and strong correlation between the number of employees and
For those firm-month observations with a positive number of injuries, the number of injuries and days lost reported (0.75 and 0.58, respec­
the average number of events is 2.08 with a mean of 28.48 days lost per tively). An even stronger correlation (0.86) is observed for our measures
month. of pay disparity (r90–10 and Gini coefficient) which reinforces our idea
The left panel of Fig. 1 presents the evolution of the number of in­ that both measures capture relevant and similar dimensions of the pay
juries, days lost, and severity over the period covered by our dataset. As dispersion in firms. The correlation between the median wage and the
we can see, there is a decrease in the average number of injuries per firm proportion of censored records follows intuition since wages are right-
as time progresses, with a similar pattern observed for the average censored. The number of prevention activities is positively correlated
number of days lost. However, the severity of each injury (which can be with the occurrence of injuries, days lost, and number of employees in a
understood as the average number of days lost per injury) shows an firm, which suggests that larger companies that experience more
increase during the first five years and a decrease after that (ending in workplace injuries are more likely to coordinate the execution of pre­
around 12.7 days lost per injury). The right panel of Fig. 1 shows that the vention activities as either response or in anticipation of occupational
proportion of female workers remain stable over time, with around 32 injuries and diseases.
percent of workers in each firm being female. The proportion of state-
owned companies in the sample is also stable, although there is a rise 4.2. Econometric estimations
in the last months; around 5.5 percent of the firms in the sample are
owned by the Chilean state in December 2017. Table 3 presents the results of the model outlined in Eq. (1). Since all
In a Poisson process, there is the assumption that the mean is equal to our Poisson regressions include thousands of firm-year and industry-
the variance (Wooldridge, 2010). By looking at Table 1, we can observe month fixed effects, we estimate our models using the ppmlhdfe
that the standard deviation of the number of injuries (including dis­ routine developed by Correia et al. (2019) (which is based on the reghdfe
eases) and days lost is almost four and five times greater than their module (Correia, 2017) on Stata 15 (StataCorp, 2017)). All estimations
mean, respectively—something that would imply that our data is consider robust standard errors (clustered at the firm level).
affected by over-dispersion. Nevertheless, in the maximum likelihood Columns (1) and (3) present the results from our baseline model (Eq.
process that is used to estimate the parameters of a Poisson regression (1)) for the number of injuries and days lost. The coefficients for our
model, the assumption of equality between the mean and variance does r90–10 variables are both positive, although significant at the 99% of
not play a role; in other words, point estimates are not affected. In order confidence only for the number of days lost.8 Since r90–10 is log
to make correct statistical inference, we use robust standard errors transformed, its coefficient is interpreted as an elasticity. For example,
(clustered at the firm level) throughout all our regression models. an increase in r90–10 of one standard deviation (relative to its mean
The mean value for the r90–10 variable in our database is around value) is associated with a 0.67% rise in the number of monthly injuries
three, which means that the wage received by an employee in the 90th (although this result is not significant in statistical terms using the
percentile is, on average, three times the earnings of the employee on the tradition threshold levels) and a 5.05% increment in the quantity of days
10th percentile. The minimum value that the r90–10 index can take is 1, lost per month. In both models, the influence of the proportion of female
while the maximum does not have a ceiling, but in our database the
highest observed r90–10 is 6.3. For the Gini coefficient, the average
value observed is 0.25, while the maximum is 0.368. The observed 8
The p-value for the coefficient under column (1) is 0.25, while the p-value
difference in the average value for the r90–10 and the Gini coefficient is for the coefficient under column (3) is 0.01.

6
C. Ramírez et al. Safety Science 145 (2022) 105497

Fig. 1. Average values per firm of number of injuries, days lost, severity, proportion of female workers, and state ownership.

significance of the coefficient of the r90–10 variable increased (p-value

Table 3
of 0.11) when the number of injuries is the dependent variable.
Injuries and Days Lost (Full Sample). Poisson Regression.a
Regarding our interaction effects, none of them reach statistical signif­
(1) (2) (3) (4) icance at the usual threshold levels.
Variables Injuries Injuries Days lost Days lost
Although the results discussed above do not offer support for our
r90–10 (log) 0.02 0.05 0.15*** 0.10 hypotheses regarding the moderating effect of proportion of female
(0.02) (0.03) (0.05) (0.07)
workers and ownership on injuries and days lost, our estimates, at least
Proportion of female workers − 0.29*** − 0.20* − 0.52** − 0.70**
(0.09) (0.12) (0.21) (0.28)
for the number of days lost, endorse our main hypotheses. However, the
r90–10 × prop. female workers − 0.09 0.20 relationship between pay disparity and injuries (and days lost) might be
(0.08) (0.20) different depending on the type of workers we analyze. For example,
r90–10 × ownership 0.05 − 0.11 according to our computations, around two thirds of all injuries and days
(0.10) (0.23)
lost occur among the workers that earn less than or equal to the median
Employees (log) 1.31*** 1.31*** 1.42*** 1.42***
(0.02) (0.02) (0.05) (0.05) wage of the company they work for. Therefore, the effect of an increase
Medium wage (log) 0.09*** 0.10*** 0.17** 0.17** in pay disparity should be more pronounced among those employees.
(0.03) (0.03) (0.07) (0.07) To explore the relationship between injuries (and days lost) and the
Proportion of censored records − 0.69*** − 0.69*** − 0.62** − 0.63**
pay disparity present at different layers of the organization, we estimate
(0.12) (0.12) (0.29) (0.29)
Observations 561,892 561,578 561,892 561,578
an expanded version of our baseline model that includes four different
Deviance 411,694 411,440 8,232,046 8,223,789 measures of pay disparity—r100-75, r75-50, r50-25, and r25-0. The first
a number in the definition of the new ratios represents the percentile of
Robust standard errors in parentheses. Firm-year and industry-month fixed
the wage distribution used as the numerator, while the second is the
effects included in all specifications. Statistical analyses performed on Stata 15.
*
p < 0.10. denominator of the ratio (both numbers are computed monthly). For the
**
p < 0.05. 100th percentile, we use the maximum wage reported, whereas the 0th
***
p < 0.01. percentile corresponds to the lowest wage observed.9 All these ratios are
computed for each firm in each month. These ratios were log trans­
workers is negative, while there is a strong effect of the number of formed before estimating the models. Table 4 presents the results for
workers in a firm on both the quantity and overall number of days lost. injuries and days lost as dependent variables. As we can see in column
The median wage is positively associated with both a higher number of (1), the estimated coefficients for the variables r100–75 and r75–50 are
injuries and days lost, whereas the coefficient of the proportion of negative (close to zero) and not statistically significant, while the co­
censored records is negative. The interpretation of this last coefficient efficients for r50–25 and r25–0 are positive and highly significant in
implies that the higher the number of censored records, the lesser the both magnitude and statistical terms. A similar picture is observed under
expected number of injuries (days lost) in a firm. This last estimate column (2); the relationship between days lost and pay disparity is
suggests that the number of injuries and days lost might not be distrib­ concentrated in the bottom half of the wage distribution. To interpret
uted uniformly through the organization and that workers in higher- the coefficients, let’s take r25–0 as an example: for the average firm
paid positions might experience fewer occupational injuries and dis­
eases. We discuss this further in the next subsection.
Columns (2) and (4) present the estimates for the full model (Eq. (2)). 9
In Table 3, our measure of pay disparity (r90–10) included the 90th and
Although the main effect for the r90–10 variable remains positive, some 10th percentile, which is a common variable used in the literature to capture
statistical significance is lost for the case where lost days is the depen­ the vertical differences in wages for an organization as a whole (e.g., Ridge
dent variable (p-value of 0.16). On the other hand, the statistical et al., 2015; Siegel and Hambrick, 2005).

7
C. Ramírez et al. Safety Science 145 (2022) 105497

Table 4 proportion of female workers and pay disparity is negative (with a p-

Injuries and Days Lost: Pay Disparity per Quartile. Poisson Regression.a value of 0.06), which implies that the higher the relative number of
(1) (2) female employees in an organization, the lesser the association between
Variables Injuries Days lost pay gap and total number of injuries. In the case of the interaction term
r100–75 (log) − 0.01 0.06 of ownership and pay disparity, the estimated coefficient is also negative
(0.03) (0.09) and highly significant (p-value of 0.00), a finding that supports our
r75–50 (log) − 0.05 0.24** hypothesis regarding the lower incentive power of pay gaps in SOFs.
(0.05) (0.12) The estimated relationship between the number of days lost and pay
r50–25 (log) 0.26*** 0.52***
(0.04) (0.11)
disparity (columns 3 and 4) also supports our main hypotheses—a one
r25–0 (log) 0.30*** 0.52*** standard deviation increment in pay disparity (relative to its mean
(0.03) (0.06) value) is related to an increment of 19.08% in the expected number of
Proportion of female workers − 0.29*** − 0.52** days lost reported as a consequence of workplace injuries (column 3).
(0.09) (0.21)
Moderators of this relationship—the proportion of female workers and
Employees (log) 1.29*** 1.38***
(0.02) (0.05) type of ownership—have the hypothesized coefficients, although only
Medium wage (log) − 0.18*** − 0.21* the estimated coefficient for the ownership variable is statistically sig­
(0.05) (0.12) nificant at the usual thresholds (p-value of 0.00).
Proportion of censored records − 0.65*** − 0.68** Fig. 2 presents the marginal effect of pay disparity (and its 95%
(0.12) (0.30)
confidence interval) on our two main dependent variables (injuries and
Observations 561,892 561,892 days lost) for different combinations of the proportion of female workers
Deviance 411,544 8,226,341
and type of ownership. As we can appreciate, the estimated pay
a
Robust standard errors in parentheses. Firm-year and industry-month fixed disparity-injury and pay disparity-days lost elasticities are at their
effects included in all specifications. Statistical analyses performed on Stata 15. highest levels when the workforce is only comprised of male workers
*
p < 0.10. and the firm is privately owned. These marginal effects are reduced as
**
p < 0.05. the proportion of female employees increases, although they are still
***
p < 0.01. significantly different from 0 as long as the company is not state owned.
It is worth noting that the marginal effect of pay disparity, although
(with a mean value of r25–0 of 1.65), an increase in the measure of pay positive for most cases depicted in Fig. 2, loses its statistical significance
disparity of one standard deviation (0.47) for the lowest quartile of (at the 95% of confidence) when we consider SOFs.
workers is associated with an increment of 8.55% in the total number of According to our estimates, a one standard deviation increase in pay
injuries and an additional 14.81% of days lost. Although these results disparity (relative to its mean value) is associated with a 10.41% rise in
are just a rough estimation of the true relationship between pay disparity the number of injuries (column 1 in Table 5), while the increment in
and the quantity of injuries and days lost at different organizational days lost is around 19.08% (column 3). This implies that the total
layers, our estimates do reflect potentially heterogeneous effects of pay observed effect that pay disparity may have on days lost cannot only be a
disparity. function of a higher number of injuries and professional diseases; there
Overall, the results in Table 4 indicate that the pay disparity in the must be an increment in the severity of each of those events. To test this,
bottom layers of the organization are the ones most closely associated we run our two models (Eqs. (1) and (2)) considering the average
with the number of injuries and days lost reported. Since the number of severity of the injuries (defined as the sum of days lost over the total
injuries and days lost are concentrated in the bottom half of the wage number of injuries) suffered by employees in the bottom half of the wage
distribution, it is reasonable to expect that the pay disparity among distribution in each firm and month. The estimates under column (5)
workers in the bottom half of the distribution would be the main driver indicate that a one standard deviation increase in pay disparity has an
of the effects observed in Table 3. With this in mind, for the rest of the accompanying rise in the expected severity of each injury of 9.36%. This
paper, we focus on the injuries (and days lost) suffered by the workers in way, the total effect on days lost can be explained approximately as the
the bottom half of the wage distribution. sum of the impact of the rise in pay disparity on both the number of
Table 5 presents the results of the estimation of our models in Eqs. (1) injuries and the average severity of each injury. The interaction effect of
and (2) for the workers in each firm that earn equal to or less than the pay disparity and ownership seems to have a statistically significant
median wage in each firm. For our dependent variables, we compute the effect, with a sign that matches our hypothesis about the moderating
total number of injuries and days lost suffered by those workers in each effect that ownership should have on the relationship between pay
month. We can do this since our data allows us to identify, exactly, the disparity and severity. The coefficient on the interaction between the
employee that had an injury and the number of days lost associated with proportion of female workers and pay disparity is positive, although it
that event. The definition of the control variables is changed in a similar does not reach significance at the traditional levels (p-value of 0.12).
fashion as well; for example, the proportion of female workers considers
only the employees in the bottom half of the wage distribution. Simi­ 4.3. Robustness checks
larly, the number of employees only considers those that earn less than
or equal to the median wage. We control for the wage earned for the We perform several robustness checks to test the validity of our re­
worker in the 25th percentile. Since the maximum proportion of sults. Table 6 presents the results of these specifications. First, we esti­
censored wages was 33% (Table 2), there is no censorship in worker mate our full models (Eq. (2)) considering a linear model, where the
earnings when we consider workers in the bottom half of the wage dependent variables are log-transformed versions of the variables used
distribution. in the models estimated in Table 5. Given the high number of fixed ef­
The estimated coefficient for our measure of pay disparity (r50–0, fects involved in our estimations (firm-year and industry-month), we use
which is also log transformed) is positive with high significance (p-value the reghdfe (Correia, 2017) routine in Stata 15 to estimate the co­
of 0.00 in our models (columns 1–6)). For the number of injuries (col­ efficients of our variables of interest. The results under column (1)–(3)
umn 1), an increase of one standard deviation (0.77) in our measured of are similar in significance and magnitude to the ones in Table 5. The
pay disparity for the average firm in the sample (i.e., with a level of interaction of the proportion of female workers and our measure of pay
r50–0 equal to 2.22) is associated with a rise of 10.41% in the expected disparity are highly significant in statistical terms in the models that
number of injuries in a given month. In the case of our full model consider injuries and days lost as dependent variables (p-value of 0.01).
(column 2), the estimated coefficient of the interaction between the For the case of average severity as dependent variable, the effect of pay

8
C. Ramírez et al. Safety Science 145 (2022) 105497

Table 5
Injuries and Days Lost: Bottom Half of Wage Distribution. Poisson Regression.a
(1) (2) (3) (4) (5) (6)
Variables Injuries Injuries Days lost Days lost Severity Severity

r50-0 (log) 0.30*** 0.38*** 0.55*** 0.68*** 0.27*** 0.24***

(0.03) (0.03) (0.06) (0.07) (0.06) (0.08)
Proportion of female workers − 0.13** − 0.03 − 0.49*** − 0.39** − 0.24* − 0.44**
(0.0624) (0.08) (0.14) (0.19) (0.15) (0.19)
r50–0 × prop. female workers − 0.15* − 0.15 0.34
(0.08) (0.22) (0.22)
r50–0 × ownership − 0.28*** − 0.49*** − 0.39**
(0.06) (0.14) (0.18)
Employees (log) 1.27*** 1.27*** 1.34*** 1.34*** 0.03 0.02
(0.02) (0.02) (0.05) (0.05) (0.05) (0.05)
Medium wage (log) − 0.18*** − 0.16*** − 0.24*** − 0.21*** − 0.03 − 0.04
(0.03) (0.03) (0.08) (0.07) (0.08) (0.08)

Observations 496,027 495,694 496,027 495,694 122,927 122,782

Deviance 344,140 343,852 6,408,576 6,400,162 1,262,005 1,260,187
a
Robust standard errors in parentheses. Firm-year and industry-month fixed effects included in all specifications. Statistical analyses performed on Stata 15.
*
p < 0.10.
**
p < 0.05.
***
p < 0.01.

Fig. 2. Marginal effects of pay disparity.

disparity and its interaction effect with ownership are statistically sig­ (column (6)), only the coefficient of the Gini variable is significant at the
nificant at the usual threshold levels (p-values of 0.00 and 0.01). 10% of confidence. Although the estimated effect of the interaction
Under column (4), we test our full model (Eq. (2)) using the Gini between proportion of female workers and the Gini coefficient is now
coefficient (log transformed)—computed using the wages of only the positive, it does not reach statistical significance at the 10% of confi­
workers in the bottom of the wage distribution of each firm in each dence (p-value of 0.16). The interaction term of ownership and Gini has
month—for injuries as the dependent variable. The estimated coefficient a negative estimated coefficient, but its p-value of 0.34 does not allow us
of the Gini coefficient is negative and highly significant (p-value of to reject the null hypothesis of no effect.
0.00). Similar results are obtained for the interaction terms, with both To test whether our results are driven by firms with few workers,
coefficients statistically significant at the 95% of confidence. For the columns (9) and (11) present the results of our full model for companies
case of days lost (column (5)), the main effect of the Gini coefficient is with at least 50 employees. As can be seen, the estimates are similar in
also positive and significant in statistical terms (p-value of 0.00). both magnitude and statistical significance, although the coefficient for
Although some statistical confidence is lost for the coefficient of the the interaction term between the proportion of female workers and pay
interaction between the proportion of female workers and the Gini disparity is positive and significant at the 95% of confidence in the case
variable (p-value of 0.11), the sign of the estimated coefficient is still where severity is the dependent variable.
negative. The moderating role of ownership is significant in both
magnitude and statistical significance (p-value of 0.00), thus supporting
our hypothesis. When the average severity of each injury is considered

9
C. Ramírez et al. Safety Science 145 (2022) 105497

Table 6
Robustness Checks: Bottom Half of Wage Distribution.a
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)
OLS OLS OLS Gini Gini Gini Emp ≥ Emp ≥ 50 Emp ≥ 50 Prev. Prev. Act. Prev.
50 Act. Act.
Variables Injuries Days lost Severity Injuries Days lost Severity Injuries Days lost Severity Injuries Days lost Severity

r50-0 (log) 0.37*** 0.63*** 0.36*** 0.28*** 0.53*** 0.19* 0.42*** 0.73*** 0.15
(0.04) (0.05) (0.05) (0.04) (0.09) (0.10) (0.05) (0.11) (0.14)
Gini (log) 0.25*** 0.43*** 0.09*
(0.02) (0.05) (0.05)
Proportion of 0.02 0.01 − 0.12 − 0.39*** − 0.93*** 0.25 0.02 − 0.49** − 0.64*** 0.01 − 0.34 − 0.43
female workers
(0.08) (0.11) (0.11) (0.14) (0.33) (0.38) (0.10) (0.24) (0.23) (0.12) (0.30) (0.33)
r50–0 × prop. − 0.20** − 0.34*** 0.02 − 0.13 − 0.07 0.49** − 0.19 0.00 0.64*
female workers
(0.09) (0.12) (0.13) (0.10) (0.25) (0.25) (0.13) (0.31) (0.38)
Gini × prop. − 0.11** − 0.18 0.18
female workers
(0.05) (0.11) (0.13)
r50–0 × ownership − 0.25* − 0.41** − 0.29** − 0.25*** − 0.45*** − 0.41** − 0.28** − 0.28 − 0.38
(0.13) (0.18) (0.12) (0.07) (0.15) (0.19) (0.11) (0.20) (0.31)
Gini × ownership − 0.19*** − 0.39*** − 0.20
(0.06) (0.12) (0.21)
Employees (log) 1.29*** 1.75*** 0.07*** 1.27*** 1.35*** 0.03 1.33*** 1.33*** 0.01 1.27*** 1.30*** − 0.09
(0.03) (0.03) (0.03) (0.02) (0.05) (0.05) (0.03) (0.06) (0.06) (0.03) (0.08) (0.09)
Medium wage (log) − 0.15*** − 0.24*** − 0.08 − 0.07** 0.01 0.08 − 0.04 − 0.08 − 0.06 − 0.18*** − 0.28** − 0.09
(0.04) (0.05) (0.05) (0.03) (0.07) (0.08) (0.04) (0.09) (0.10) (0.06) (0.13) (0.15)
Prevention 0.01*** 0.03*** 0.02***
activities (log)
(0.00) (0.01) (0.01)

Observations 495,694 495,694 122,782 495,694 495,694 122,782 318,978 318,978 104,702 207,467 207,467 46,601
R-squared 0.3535 0.3446 0.3890 – – – – – – – – –
Deviance – – – 343,812 6,400,774 1,260,556 245,240 5,291,014 1,157,028 139,652 2,674,307 523,837
a
Robust standard errors in parentheses. Firm-year and industry-month fixed effects included in all specifications. Results under columns (1)–(3) are estimated using
OLS. Results under columns (4)–(12) are obtained from Poisson regressions. Statistical analyses performed on Stata 15.
*
p < 0.10.
**
p < 0.05.
***
p < 0.01.

4.4. Endogeneity risks would translate in a higher pay disparity compared with POFs.
Recalling that women are more risk averse than men, they would de­
One of the main concerns in our study is the lack of exogenous mand a higher compensation to assume a higher likelihood of injuries,
variation in the variables used to measure within-firm pay disparity. In so again the corresponding control variable would have a positive effect.
an ideal world, we would compute the effect on the magnitude of Finally, there is a chance that omitted regressors—correlated with
workplace injuries by randomly manipulating the firms’ pay disparity our pay disparity measures—are actually biasing our results. We
levels. Our database, however, only allows us to observe the reported included as many variables as possible in our regression models trying to
distribution of wages and number of days lost per worker per month. control for all relevant characteristics of firms and industries, although
Therefore, there is a risk that endogeneity—i.e., the correlation between there is always a chance that important variables are left out of the re­
our pay disparity variables and the error terms in our regressions—could gressions. For example, it is possible that changes in the magnitude of
be biasing our results. workplace injuries could be erroneously linked to a decrease in pay
Endogeneity has the following three main causes: measurement disparity.10 The ACHS database includes information relative to safety
error, reverse causality and omitted variables (Wooldridge, 2010). Since and prevention programs in affiliated companies, but only starting from
we have data on salaries received by all contracted workers and the January 2015. The data available are the number of prevention activ­
consequences of the injuries they suffered, the only source of measure­ ities performed in each firm and month. As a robustness check, we es­
ment error could come from the cap on salaries discussed in previous timate our full model (for the three different dependent variables
sections. Since we focus in the bottom half of the wage distribution, considered throughout this study) using a logarithmic transformation of
there is no censorship on earnings for workers in that portion of the the number of prevention activities performed (we added a constant
distribution. This alleviates our concerns about measurement error equal to 0.01 before applying the transformation to avoid getting
playing a notorious effect on our estimates. missing observations for the months in which firms did not perform any
Regarding reverse causality, one could pose the following explana­ prevention activity). The results are in columns (10)–(12) in Table 6.
tion for our results: when injuries increase, workers subject to greater Even though we lost around 60% of our sample, since we restricted our
risks demand to be better compensated. We discard any reward after an analyses to the period for which we have information on prevention
injury has occurred, as such a possibility is illicit in Chile since it would activities, the majority of our findings regarding the impact of pay
generate pervasive incentives to incur in (minor) injuries. A more likely disparity and the moderating effect of ownership are still similar in
possibility is that labor union or individual workers demand and ex ante magnitude, although some statistical significance is lost. To the extent
pay increase, which is referred as compensating wage differentials
(Viscusi and Aldy, 2003; Strawiński and Celińska-Kopczyńska, 2019). If
such was the case, both control variables, ownership and gender, would 10
Since we include firm-year effects, the only portion of safety programs we
have the opposite effect in our regressions. As explained above, workers are not capturing in our models is the one that changes during a year within
in SOFs exert a higher negotiation power so an increase on occupational each firm.

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C. Ramírez et al. Safety Science 145 (2022) 105497

Table 7 different levels of within-firm vertical pay dispersion has long been an
Values of δ that Make the Estimated Coefficient of Pay Disparity Equal to Zero.a important research topic in management and economics. This study
Dependent Observations 2
δ(R2MAX = δ(R2MAX = δ(R2MAX = analyzes the influence of within-firm pay disparity on the magnitude of
R
variable 1.3R )
2 2
2R )
2
3R ) workplace injuries, finding that the vertical pay gap is positively asso­
ciated with the extent of workplace injuries. We conclude that higher
Injuries 207,467 1.67% 7.01 2.19 1.11 levels of pay disparity impact the magnitude of workplace injuries
Days lost 207,467 1.61% 7.79 2.48 1.25
through the higher risk and willingness to compete that workers exert
Severity 56,966 0.43% 4.37 1.82 0.99
because of the larger prizes implicit in a broader pay gap. The moder­
a
Statistical analyses performed on Stata 15. ators we tested tend to confirm our results and the mechanisms behind
them.
that the number of prevention activities is informative about other The main novel contributions of our study are as follows. First,
potentially important omitted variables (Oster, 2019), the fact that our despite workplace injuries being a relevant outcome that affects the
coefficients of interest do not change substantially among our models in firm’s performance, the analysis of how changes in within-firm vertical
Table 5 and the ones in columns (10)–(12) in Table 6 is reassuring. pay disparity affect workplace injuries has received a small amount of
However, as Oster (2019) shows, it is necessary to consider both the attention, most likely because of data constraints. We believe that the
stability of the coefficient of interest (as controls are added to the reporting of potentially important operational costs of wider vertical pay
regression model) and the movement in R2 to evaluate the extent to gaps adds value to the extant theoretical analysis of wage structures
which omitted variable bias could be affecting the results. Oster’s within firms. Second, we observe that the effect of changes in pay
approach (which is also connected to the work of Altonji et al., 2005), is disparity on workplace injuries is lower in SOFs than in POFs. We think
based on a parameter δ that summarizes the degree of selection of un­ this result is explained by (i) possible distinct objectives functions in
observed variables relative to observables (Oster, 2019: 195), or each of those types of firms and (ii) different promotion policies. If effort
–alternatively– the share of variation of unobservable relative to and risk-taking are rewarded more in POFs than in SOFs, then we should
observable variables so that the estimated coefficient of interest be­ expect a larger effect of increasing levels of pay disparity on workplace
comes zero. For the computation of this parameter δ, we need to injuries in POFs. Third, we find that gender matters for the analysis of
determine the R-squared from the regression if both observed and un­ the effect of pay disparity in operational outcomes. Although gender has
observed variables were included in the model (we call this R-squared been considered a relevant issue when analyzing the incentive to
R2MAX ). Based on evidence from experimental studies published in top compete in tournaments (e.g., Kulich et al., 2011; Leslie et al., 2017;
economic journals, Oster suggests considering the following expression Niederle and Vesterlund, 2007), there has not been a detailed analysis of
2 2
for R2MAX = 1.3R , where R represents the R-squared obtained in the the gender effect on the cost of increasing pay disparity in operational
regression with just the observed controls. The command psacalc, outcomes, such as workplace injuries. Fourth, we detect that the effects
available as a user-written routine in Stata 15, allows for the estimation of increasing pay disparity are different at distinct wage levels of an
of δ after a panel data model is fitted, but only for a model with one organization; workplace injuries are less affected by changes in vertical
variable of interest. Therefore, we focus on our baseline specifications pay disparity at higher salary levels. Top earners care more about the
that include the number of prevention activities in each month. Ac­ risks they can take and the consequences of workplace injuries, for
cording to Oster and Altonji et al. (2005), a value of δ = 1 represents a instance, because of the higher costs of missing working days. Effort and
suitable threshold since it implies that observed and unobserved vari­ motivation are directly proportional to the magnitude of the gains that a
ables are equally relevant. We compute the δ coefficients for different worker expects to derive, which agrees with the view that firms with
2 greater pay dispersion offer more room for advancement to those at the
values of R2MAX , starting with the proposed R2MAX = 1.3R and then
bottom of the wage distribution (Sørensen and Sharkey, 2014). Our
2 2
moving up to R2MAX = 2R and R2MAX = 3R . Given the definition of our results are coherent with recent calls for research that looks at the de­
variables and the inclusion of firm-year fixed effects, we use the “within” terminants of pay dispersion at different organizational levels (Greck­
2
R-squared as the relevant R for each model. hamer, 2016; Kacperczyk and Balachandran, 2018; Shin, 2014).
As we can see in Table 7, the values of δ obtained from the analysis Our proposed mechanism for the relationship between changes in
2 within-firm pay disparity and workplace injuries is one that relates
where R2MAX = 1.3R are distant from 1 (around 7.0 for injuries, 7.8 for
increasing personal effort and risk-taking, and a higher chance of
days lost, and 4.4 for severity). Although we cannot rule out the possi­
suffering an occupational injury or disease as a consequence, with the
bility that our regression models lack some relevant determinants of the
presence of rewards as an employee climbs the organizational ladder.
number of injuries (and their severity), those variables need to be seven
According to Kacperczyk and Balachandran (2018), a higher vertical
to four times as important as the controls already included in the models
pay dispersion should decrease the movement of workers between firms
to make the coefficient of pay disparity equal to zero. The values for δ
2
because the benefits implicit in a longer vertical pay gap can only be
decrease as we increase R2MAX , but even at R2MAX = 3R all but one δ are obtained if one decides to keep working in that firm. These authors also
above the threshold proposed by Oster (2019). This way, even though argued that this effect should be more pronounced for workers at the
we cannot disregard omitted variable bias as an issue in our estimates, bottom of the wage distribution, since those are the ones who are the
we are able to say something about the relative importance those vari­ most likely to obtain the benefits of getting promoted and, therefore,
ables should have in order to explain away our main results: for the have more incentives to stay in their current firm. Our results show a
majority of cases in Table 7, unobservable regressors need to be at least positive and significant relationship between the level of initial pay
twice as important as included variables so the estimated effect of our disparity and the proportion of employees in the bottom half of the wage
pay disparity variable becomes zero. distribution that continue working for the firm at the end of the period,
reinforcing the confidence in our measure of pay disparity.11
5. Discussion By studying the effect of changes in within-firm pay dispersion on
workplace injuries we are not arguing that larger pay gaps are negative
Within-firm vertical pay differentials are important for management per se for firm performance. It could be that the additional effort from
research because they can have critical implications for employees’ at­
titudes and behaviors, strategy implementation, and organizations’
competitive position and performance (e.g., Shin, 2014; Lim, 2019). As 11
The results, which consider robust standard errors, are available from the
such, the development of a deeper understanding of the consequences of authors upon request.

11
C. Ramírez et al. Safety Science 145 (2022) 105497

workers –and their willingness to take risks– compensate the negative researchers and practitioners. Another important avenue for further
effects of a potential increase in workplace injuries. This is coherent with research is to deepen the analysis of the effects of compensation schemes
Larkin and Pierce (2016) who posit that compensation policies that in firms with different ownership structures. As our analyses show, there
promote a high level of productive effort usually display some coun­ is evidence that pay disparity is associated with different magnitudes of
terproductive behavior. Thus, although we are not arguing against workplace injuries in POFs and SOFs. This way, it will be interesting to
higher wage gaps because of its negative effects on injuries, we do argue analyze the effects of pay disparity in other organizational outcomes (e.
that this negative effect has to be considered when assessing the benefits g., motivation or turnover) in those types of firms. Devoting some efforts
of increasing pay gaps. For the firms in our dataset, there is a negative to understand how different regulations influence the effect of pay
and statistically significant correlation (at the 95 percent of confidence) disparity on the severity of workplace injuries (and other firm-level
between the number of injuries in each firm in January 2011 and the outcomes) might also be a potential way to expand our understanding
growth rate of its workforce between January 2011 and December 2017 about the relationship between pay dispersion and firm performance.
(the first and last months covered by our database). This negative cor­
relation suggests that the injury rate experimented by a company could 6. Conclusion
be related –negatively– to the growth rate in the number of employees, a
variable that has been used as a proxy of company size and performance In this paper, we theorize and document how changes in employees’
(e.g., Mueller et al. 2017). For managers, our results indicate that behavior in terms of propensity to experience workplace injuries can
companies that are increasing their vertical pay dispersion levels should limit the benefits of greater vertical pay disparity within firms. Though
establish policies (such as investments in workplace safety) to diminish the benefits of pay disparity have been widely analyzed in the literature,
the negative effect on injuries of such wider pay gap structures. its effects on dimensions such as the magnitude of workplace injuries are
less understood and evaluated, and hence less anticipated. Hence,
5.1. Limitations and ideas for future research managers should be cautious when thinking about the consequences of
different internal compensation structures. For instance, firms should
Our study is not devoid of limitations, which we hope can stimulate have indicators of their pay disparity to anticipate potential changes in
further research. An obvious set of limitations are those that stem from workers’ injury rates. In this regard, the provision of information about
the nature of our sample. We choose to work with a diverse sample of the relative compensation of the CEO and the median employee and
firms in terms of company size, internal organization, and industries in about the relative compensation of the median employee and the lowest-
which firms compete. Although this might be costly in terms of the paid employee could shed more light on the effect of pay disparity on
different types of organizations considered, which might affect our worker health and wellbeing. Our results also indicate that companies
chances of actually finding an effect, we prefer this in order to respond to with high levels of pay dispersion should be especially careful in
calls (e.g., Downes and Choi, 2014) that mention the use of specialized designing incentive plans and devote resources to avoid or decrease the
samples as a weakness of most of the existing empirical studies (an likelihood of workplace injuries.
exception is Mueller et al., 2017). Also, even though we use different
ratios of wages to measure vertical pay disparity, we cannot rule out Declaration of Competing Interest
completely the fact that we could be capturing some horizontal pay
dispersion as well. We believe that our theorizing and results are more The authors declare that they have no known competing financial
coherent with vertical pay disparity than with horizontal pay dispersion, interests or personal relationships that could have appeared to influence
but since we lack information on the job position held by each worker, the work reported in this paper.
we do not have the means to fully disentangle both types of pay
dispersion. However, we are confident that cases in which a ratio such as Acknowledgements
r50-0 reflect horizontal instead of vertical pay disparity should be rare
and require a rather extreme organizational structure. We thank the support of the Associate Editor and two anonymous
Another limitation is that we cannot make a strong claim about reviewers for their comments and suggestions, which helped improve
causality. However, we think that the robustness checks and the results the article significantly. We also thank participants at research seminars
of the effects of female participation and state-ownership are coherent at the Strategic Management Society, Academy of Management (Stra­
with the assertion that causality goes from pay disparity to injuries and tegic Management division), the Lutgert College of Business, Florida
not in the reverse direction. For instance, the results on the interaction Gulf Coast University, as well as Edgar Kausel and Bernie Quiroga for
term involving pay disparity and state ownership point to a perfectly their valuable insights. A previous version of this article was presented
plausible interpretation that pay disparity is less likely to affect injuries at the Chicago AoM conference.
in SOFs and is consistent with previous findings arguing for lower effects One of the authors acknowledges Fondecyt Research Grant 1170654.
of monetary rewards in SOFs (Chen et al., 2017; Kato and Long, 2011).
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