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Are Female CEOs Paid Less?
Bakhtear Talukdar Assistant Professor
University of Wisconsin-Whitewater
Department of Finance and Business Law
HH 3516, 800 W Main Street
Whitewater WI 53190
Telephone: (262) 472-7036
E-mail: [email protected]
Preliminary Draft: January 15, 2017(Do not quote without explicit consent of the author)
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Are Female CEOs Paid Less?
Abstract:
We show that there exists a significant gender pay gap in CEO compensation of the S&P 1500
firms. However, this pay gap is conducive to the society because this time female CEOs earn more
than their male counterparts. We use a large sample of 22,119 firm-year observations over the
period of 1998-2015. Our finding is robust under various specifications and estimation techniques.
We use pooled cross-sectional fixed effect regression as a base model. Thereafter, we use matched
sample using propensity score matching and instrumental variable regression under 2SLS and
GMM with robust weighting matrix. Our finding holds in every model: female CEO coefficient is
a positive and significant (at 1% level). We show that the reason behind female CEOs earning a
higher pay is attributable to their better capacity in handling firm risk than male CEOs.
Furthermore, using quantile regression model (QRM), we show that the CEO compensation is
asymmetric, i.e., gender pay gap exists at the lower quantiles, however, fades away at the median
and higher quantiles. Therefore, it is not surprising that earlier research concluded (depending on
mean-based models) that there is no gender pay gap in the CEO level.
Keywords: CEO Compensation; Gender Pay Gap; CEO Risk Management Ability; Delta; Vega;
Asymmetry in CEO Compensation
JEL Classification: G30, J16, J30
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Are Female CEOs Paid Less?
1. Introduction
Women are holding the role of the chief executive officer (CEO) in 22 (4.40%) companies
of S&P 500 companies. Companies like GM, Oracle Corp., Lockheed Martin, Yahoo! Inc.,
PepsiCo, IBM, and HP are headed by female CEOs1. National campaigns such as 2020 Women
on Boards published their 2015 honor roll companies that have more than 20% female members
on board for the last five consecutive years (2011-2015)2. The campaign’s vision is that by 2020
all the boards of US companies will have 20% or more female directors. Although 22 is a relatively
lower number in comparison with 500, the picture is much better than it was a decade ago (refer
to Figure 1, Panel A). More and more women are thriving to the highest position of corporate
America. With these structural changes that are beneficial to women CEOs, we wanted to
investigate whether there exists any gender pay gap in the CEO position.
There is an extensive amount of research on gender gap and the findings of this research
are mixed. Some research finds that there exists a significant pay gap across genders (see Bayard
et al. 2003; Bertrand and Hallock, 2001; Bell 2005; Munoz-Bullon, 2010; Vieito and Khan, 2012).
On the contrary, some research finds that there is no gender pay-gap (see Bugeja et al. 2012;
Bowlin, Renner and Rives, 2003). Jordan et al. (2007) and Elkinawy and Stater (2011) find no
gender gap exists at the CEO level, however, it exists at the lower level. A recent paper by Flabbi
et al. (2014) shows that female leadership has a positive effect on the top female executives’
compensation. Moreover, female CEOs for firms with at least 20% female employees can increase
1 Source: http://www.catalyst.org/knowledge/women-ceos-sp-500
2 Source: https://www.2020wob.com/companies/2013-honor-roll-companies
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the sales 6.70% per worker. A survey published in the Harvard Business Review shows that the
majority of the participants (69%) think that a female CEO can better turnaround a troubled
company than a male CEO.
The objective of this paper is to investigate whether these structural changes, such as more
female taking CEO positions in big known companies, more women on the board, and more
awareness in society regarding the “glass ceiling,” have changed the female CEO compensation.
The reason we expect female CEOs to earn more are manifold. First, female CEOs face a tougher
path to become CEOs than their male counterparts. They have to go through a tighter scrutiny than
the male candidates for the CEO. Second, in terms of certain attributes, women have shown that
they perform better than their male counterparts. For example, taking manageable risk, keeping
cool in the crisis situation, effective leadership style, communication skills and ability to encourage
others (Bruckmüller and Branscombe, 2011). Third, female CEOs may understand their
subordinates better than male counterparts. Flabbi et al. (2014) show that female CEOs can better
interpret productivity signals from female workers. Fourth, presence of females has increased
throughout the organization. In S&P 500 firms, 44.30% employees are female, 19.90% board
members are female and 9.50% top earners are female3.
We show that there exists a gender pay gap in the CEOs of S&P 1500 firms. However, this
time it is the female CEOs who earn more than their male counterparts. We find that a female CEO
on average earns a total compensation of $6,142,980 (median=$3,794,120) versus $5,822,050
(median=$3,504,350) for a male CEO, a statistically significant difference (t-statistic is 2.26).
Moreover, female CEOs earn on average a salary of $830,100 (median=$773,650) versus male
CEOs’ salary of $767,790 (median=$722,820), again a statistically significant difference (t-
3 Source: http://www.catalyst.org/knowledge/women-sp-500-companies
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statistic is 4.68). At the multivariate setting, variable “female CEO” remains positive and
statistically significant across various models. We find the reason behind the favorable pay gap
toward female CEOs is due to their ability to better handle firm risk than their male counterparts.
Their risk reduction is reflected on a firm’s stable stock price. However, female CEOs do this risk
reduction so effectively that they are not sacrificing a firm’s profitable investment opportunities
by becoming risk averse4. Furthermore, we find that female CEO compensation is asymmetric
(more specifically, U-shaped): with the positive and significant coefficient for “female CEO”
variable at quantiles below median, however, the significance goes away (or fades away) at median
and above-median quantiles.
In our study, we use CEO compensation data of S&P 1500 firms reported in Execucomp
database. We control for other economic, governance and CEO characteristic variables. After
matching with all other databases, we have 22,119 firm-year observations for the period of 1998-
2015. Because female CEO observations are relatively lower (553 firm-year observations) in
comparison to male firm-year observations, biases from selection can be an issue. In order to curb
selectivity biases, we use caliper-based propensity score matching in which each female CEO
observation is matched with a male CEO observation from a firm of similar characteristics.
Moreover, we also use instrumental variable regression5 techniques with two estimations: two
stage least square (2SLS) and generalized method of moments (GMM) with robust weighting
matrix. We control for unobserved firm or industry characteristics by using fixed-effect models.
To determine female CEOs risk taking behavior (and risk aversion), we use two pay-performance
4 Some earlier studies find female CEOs are more risk averse (meaning that they sometimes forgo positive NPV
projects). See Barber and Odeon (2001) and Graham, Harvey, and Puri (2009). However, we did not find any
support in favor of this argument.
5 We use two instruments: female to total executive ratio and female to male executive ratio.
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sensitivity matrixes: a) delta (change in CEO wealth due to 1% change in stock price) and b) vega
(change in CEO wealth due to 1% volatility in stock returns). Finally, to evaluate whether female
CEO pay is an asymmetric function, we run quantile regression that by construction can handle
any non-normal (or skewed) distribution.
We contribute to the existing gender gap literature in a few ways. First, we use a large data
set of 22,119 observations, with 553 female CEO firm-year over 18 years of data. The analysis
close to ours is Bugeja et al.’s (2012) paper, who use 210 female CEO firm-years. Thus, our
analysis is more robust, specifically our analysis will receive the benefit of “law of large number.”
Second, we show the reason why female CEOs earn more than their male counterparts. Figuring
out the reason was necessary because it may seem very unusual/unexpected of female CEOs
earning more. A recent statement about Yahoo! Inc.’s current CEO Ms. Marissa Mayer’s historical
and contingent compensation may provide an idea about top female executives’ payoff, “Yahoo’s
boss has already taken home $78m since she was installed as CEO, according to the stock analytics
firm MSCI6.” Third, we provide two choices for instruments by this analysis. Studies like ours
usually use matched sample for robustness. They avoid using instrumental regression because
identifying effective instrument(s) is always a challenge. We identify and successfully use two
instruments. Future researchers can use either of the identified instruments and test the strength of
their research on gender pay gap.
The remainder of the paper is organized as follows: section 2 discusses data and sample
selection, section 3 describes methodology used, section 4 sheds light on the empirical results,
section 5 discusses additional robustness check, section 6 focuses on CEO risk management
6 Source: https://www.theguardian.com/technology/2016/jul/25/yahoo-to-sell-core-web-business-to-verizon
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ability, section 7 analyzes asymmetry in CEO pay, and section 8 ends the paper with concluding
remarks.
2. Data and sample selection
We use Compustat’s Execucomp database. The database reports total compensation,
salary, bonus, and percent of shares owned by the top five executives of S&P 1500 firms. We
separate only chief executive officers from the database. Although Execucomp reports as far as
1992, other databases we use start reporting from 1998. Therefore, our data covers 1998-2015. In
addition to CEO compensation, we use major three categories of variables: a) economic, b)
governance, and c) other CEO characteristics. Economic variables come from Compustat and
CRSP. Governance and other CEO characteristics come from IIS (formerly RiskMetrics)7. Board
related data come both from IIS and BoardEx8. After merging with all databases, we end up with
22,119 firm-years observations, including 553 firm-year for female CEOs.
Pay-performance sensitivity data created by utilizing SAS program (customized based on
our needs) from Lalitha Naveen’s website9. We drop a firm-year observation for any missing value
for any of the variables used in the study. We use caliper-based propensity score matching, in
which a female CEO firm-year is matched with a corresponding male CEO firm-year. We use non
replacement descending matching and allow propensity score to vary 10% between control firms
(male CEO) and treatment firms (female CEO). We lost 15 firm-year observations because
propensity score match could not find a close match based on the set criteria. Thus, for matched
sample, we have 538 (=553-15) *2=1,076 firm-year observations. In order to mitigate the influence
7 The database was accessed at the author’s previous institution.
8 The database was accessed at the author’s previous institution.
9 https://sites.temple.edu/lnaveen/data/. This data span over the period of 1998-2014.
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of outliers on the results, we winsorize our data at 1 percentile and 99 percentiles. However, we
use the raw (non-winsorized) data in the case of matched samples to protect the integrity of the
(matched) sample.
The distribution of female CEOs is given in Table 1. Panel A shows that over the years the
number of female CEOs increases. In 1998, only 12 CEOs were female, whereas in 2015 there are
58 female CEOs, a 383.33% increase. Figure 1, Panel A shows the increasing trend of females
taking the highest echelon of corporate America. However, in comparison with the total firms, the
percent increase is only 3.34% (=4.36%-1.02%). Overall, there is only 2.50% female CEO firm-
year in the total CEO firm-years (=22,119). Panel B includes female CEO firm-year distribution
by the global industry classification standard (GICS). Information technology (GICS=45) consists
the highest firm-year observations and telecommunication services (GICS=50) consists the lowest
firm-year observation. In terms of female CEO firm-year, energy (GICS=10) has the lowest firm-
year and telecommunication services has the highest firm-year observations. From Panel B, it is
evident that female CEOs work in all industries, although the prevalence is more in consumer
discretionary (4.61%), consumer staples (5.11%) and telecommunication services (6.73%).
3. Methodology
3.1. Pooled cross-sectional regression
Our data are panel data, i.e., various firms in time series format. Furthermore, all firms can
be grouped based on the industry in which they operate. Not all firms have started in the same year
and therefore, the panel data would not be a squared matrix or “balanced” panel. We choose to use
pooled cross-sectional regression. Similar to Bugeja et al. (2012), we have the following model:
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𝐶𝐸𝑂𝑃𝑎𝑦𝑖 = 𝑓(𝛽0 + 𝛽1𝐹𝑒𝑚𝑎𝑙𝑒𝐶𝐸𝑂 + ∑ 𝛽𝑗𝐸𝑐𝑜𝑛𝑜𝑚𝑖𝑐𝐶ℎ𝑎𝑟𝑎𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐𝑠 +
∑ 𝛽𝑘𝐺𝑜𝑣𝑒𝑟𝑛𝑎𝑛𝑐𝑒𝐶ℎ𝑎𝑟𝑎𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐𝑠 + ∑ 𝛽𝑙𝐶𝐸𝑂𝐶ℎ𝑎𝑟𝑎𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐𝑠 + ∑ 𝛽𝑚𝐼𝑛𝑑𝑢𝑠𝑡𝑟𝑦𝐷𝑢𝑚𝑚𝑖𝑒𝑠 +
∑ 𝛽𝑛𝑌𝑒𝑎𝑟𝐷𝑢𝑚𝑚𝑖𝑒𝑠 + 𝜀𝑖) (1)
CEOPay is the dependent variable and takes any of the three compensation types: total
compensation, salary, and bonus. Total compensation (in thousand Dollars) is TDC1 in
Excecucomp database, which has been defined as “Total compensation for the individual year,
comprised of the following: Salary, Bonus, Other Annual, Total Value of Restricted Stock
Granted, Total Value of Stock Options Granted (using Black-Scholes), Long-Term Incentive
Payouts, and All Other Total.” We use the natural logarithm of TDC1 to make the compensation
distribution normal. Salary (in thousand Dollars) is defined in Execucomp as “The dollar value of
the base salary (cash and non-cash) earned by the named executive officer during the fiscal year.”
We use the natural log of salary. Finally, Bonus (in Thousand Dollars) is defined in Execucomp
database as “The dollar value of a bonus (cash and non-cash) earned by the named executive officer
during the fiscal year.” Please note that not all CEOs earn bonus, thus, we use the natural
log(1+Bonus) as third CEO compensation type10.
We use both firm-fixed effect and industry-fixed effect. However, we chose to report only
industry-fixed effect11. There are a few reasons for reporting industry fixed effect as opposed to
firm fixed effect. First, there are very few female CEO firm-years, in total 553; some industries
have as low as 12, 14, and so observations (see Table 1, Panel B). In this circumstance, per firm
female CEO observations would be either zero or close to zero. Thus, firm fixed effect would
10 For some CEOs, the value would be zero. If we take the natural log on zero, it will come out as a missing value.
However, that can be avoided if we add 1 before taking the log then the final value would be 0 and the observation
would be considered in the analysis.
11 The results under firm-fixed effect and industry-fixed effect are similar.
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produce so much disturbance in the error terms that the estimator would be biased. Second, CEO
compensation is more an industry-wide phenomenon than a firm-wide phenomenon, i.e., CEO
compensation of firms within an industry would vary more than per firm basis. Thus, industry
fixed effect would control more unobservable effects than firm fixed effect. Third, the benefit from
statistical properties such as “law of large number” can be achieved by grouping all firms into
smaller groups (thus having more observations per group) by industry than larger groups based on
firms. Fourth, later in the robustness section the matched data by propensity score matching
precludes us from using firm-fixed effect (or using firm dummies), however, we could use industry
dummies (similar to industry fixed effect) to control for industry unobservable variation. Thus, to
remain comparable, we chose to report industry-fixed effect.
3.1.1. Economic characteristics
Economic characteristics are firm related control variables that affect CEO pay. Consulting
extant literature, we use the natural logarithm of sales to control for firm size. Smith and Watts
(1992) show that larger firms pay more to their executives than smaller firms; Cole and Mehran
(2016) show that executive pay increases with firm size. Because executive compensation is a
function of firm performance (Core et al. 1999), we control for both accounting and market
measure for firm performance. We use one buy and hold return for market measure of performance
and return on assets, ROA, which is calculated as EBIT/average assets. Firm investment
opportunities and degree of leverage are controlled by book-to-market ratio (BMV) and debt-to-
equity ratio (DE). In order to control for firm risk on CEO compensation, we use the natural
logarithm of standard deviation of the last three years’ return and ROAs. In order to ensure a
normal distribution (with negative values) of these risk measures, we take the natural log of them.
Standard deviation is always positive. Bugeja et al. (2012) have used the same operation.
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3.1.2. Governance characteristics
Core et al. (1999) find that CEOs earn more when there is less effective governance
structure in a firm. Coles at el. (2008) show that for complex firms, the relationship between board
size and performance (Tobin’s Q) is positive. We use board size as governance control. Other two
board related governance controls are board-independence and presence of female directors on
board. There is a significant increase in female directors over the past 18 years (refer to Figure 1,
Panel B). In our sample, about 16% of the board members are female (refer to Figure 1 Panel B).
Board independence is defined as the fraction of independent directors to the board size. Core et
al. (1999) show that CEO compensation is higher when there are more outside directors. We also
use the variable, female directors, which is calculated as the fraction of directors who are female
to the board size. In regard to compensation committee, we use two variables: independent
compensation committee and female compensation committee. The former variable takes a value
of 1 if all the members of the compensation committee are independent directors, whereas, the
latter variable takes a value of 1 if at least one member in the compensation committee is female.
3.1.3. CEO characteristics
We control for CEO characteristics such as CEO tenure, CEO-chair, CEO stock ownership,
and CEO first year. We take the natural logarithm of CEO tenure (which is CEO experience in the
current firm). Core et al. (1999) find that CEO compensation is higher when the CEO is also the
chair of the board and that CEO compensation is a decreasing function of CEO ownership. We
define CEO duality as a state when the CEO is also the chair of the board. CEO duality is an
indicator variable; it takes a value of 1 if CEO is also a chair, 0 otherwise. CEO five % indicates
CEO ownership and it takes value of 1 if CEO owns at least 5% of company’s stock and 0 for less
than 5% (Bugeja et al., 2012 use the identical definition). Finally, we use CEO first-year which
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takes a value of 1 if the current year is CEO’s first year, 0 otherwise. Compensation package for a
newly hired CEO is current (marked to market) compared to the CEO who has been working for
a while. This indicator variable controls for compensation hike that is due to a new CEO hire from
the external labor market.
3.2. 2SLS and GMM
In the above specification, endogeneity can arise potentially from three sources: a) omitted
variable bias (i.e., one or more independent variables are correlated with error term, thus, violates
the condition for OLS), b) when an independent variable is a function of the dependent variable
and c) measurement error bias (i.e., when variables are measured incorrectly). In order to tackle
endogeneity, we use instrumental regression under two estimation techniques: two-stage least
squares (2SLS) and generalized method of moments (GMM) with robust standard errors.
The challenge in instrumental variable regression is to find the correct instrument (Balsam
et al. 2016). An instrument should be chosen in a way that is not correlated with the dependent
variable (in our case, CEO compensation), however, has a correlation with the independent
variable (in our case female CEO). We identify two potential candidates for being instruments:
female to total executive ratio and female to male executive ratio. Female to total executive ratio
(Fem_to_Total) is calculated as total female executive over total executive in the company and
female to male executive ratio (Fem_to_Male) is calculated as total female over total male
executives12. Here, we argue that the proportion of female executives has a bearing on hiring a
female CEO, however, does not directly affect the CEO compensation. Under 2SLS, the likelihood
of female CEO regresses on Fem_to_Total, then, the predicted value of female CEO is used as
independent variable in the second stage.
12 We use Compustat’s Execucomp database to calculate these ratios.
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3.3. CEO risk management ability
Smith and Watts (1992), Core et al. (1999) and Core (2000) show that firm risk is an
important determinant of CEO compensation. In order to test whether CEO gender has any bearing
on firm risk and hence compensation, we borrow two measures of pay-performance sensitivity
from Bizjak et al. (1993), Core and Guay (1999), Core and Guay (2002), Coles et al. (2006), and
that are delta and vega. Delta is defined as the change in CEO wealth due to 1% change in firm
stock price. Vega is defined as the change in CEO wealth due to 1% change in volatility of stock
returns. We use delta as a proxy for CEO risk handling capacity and vega as CEO risk aversion.
Higher delta means managers are exposed to more risk and lower delta means managers have a
grasp over the activities of the firm and can handle firm risk more effectively (see Coles et al.
2006). Delta and vega pinpoint CEO risk handling capacity and risk aversion, respectively. Coles
et al. (2006, p. 432) argue, “Option-based compensation, by providing convex payoffs, can
potentially reduce aversion to risky policies that arise from high delta.” We use the following fixed
effect regressions in measuring the relation between CEO gender and risk handling capacity
through option based compensation.
𝐷𝑒𝑙𝑡𝑎𝑖 = 𝛽0 + 𝛽1𝐹𝑒𝑚𝑎𝑙𝑒𝐶𝐸𝑂 + 𝛽2𝐶𝑎𝑠ℎ𝐶𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑖𝑜𝑛 + 𝛽3𝐵𝑜𝑎𝑟𝑑𝑆𝑖𝑧𝑒 +
𝛽4𝑁𝑢𝑚𝑏𝑒𝑟𝑜𝑓𝑆𝑒𝑔𝑚𝑒𝑛𝑡 + 𝛽5𝑅&𝐷 + ∑ 𝛽𝑗𝐸𝑐𝑜𝑛𝑜𝑚𝑖𝑐𝐶ℎ𝑎𝑟𝑎𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐𝑠 + 𝜀𝑖 (2)
𝑉𝑒𝑔𝑎𝑖 = 𝛽0 + 𝛽1𝐹𝑒𝑚𝑎𝑙𝑒𝐶𝐸𝑂 + 𝛽2𝐶𝑎𝑠ℎ𝐶𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑖𝑜𝑛 + 𝛽3𝐵𝑜𝑎𝑟𝑑𝑆𝑖𝑧𝑒 +
𝛽4𝑁𝑢𝑚𝑏𝑒𝑟𝑜𝑓𝑆𝑒𝑔𝑚𝑒𝑛𝑡 + 𝛽5𝑅&𝐷 + ∑ 𝛽𝑗𝐸𝑐𝑜𝑛𝑜𝑚𝑖𝑐𝐶ℎ𝑎𝑟𝑎𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐𝑠 + 𝜀𝑖 (3)
Delta is a proxy for the firm risk and vega is a proxy for CEO risk aversion. We added
cash compensation (salary plus bonus), number of segment as a measure of firm’s business focus
and research and development (R&D) as additional controls (Core and Guay 1999, Guay 1999,
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and Coles et al., 2006 show that these variables have a significant relation with delta and vega).
We excluded governance related characteristics (except board size) and other CEO
characteristics in this specification in order to estimate (only) CEO gender effect on delta or
vega.
3.4. Quantile regression model (QRM)
In order to test whether CEO pay is asymmetric, we use the quantile regression model13
(QRM) on the matched sample. The following discussion on QRM is heavily drawn upon a recent
work by Talukdar et al. (2016). Alike OLS, which minimizes the sum of squared residuals, QRM
minimizes the sum of the absolute residuals. However, while OLS solves for the mean, QRM
solves for the median. The median by definition divides the residuals into two halves: one half
positive residuals and another half negative residuals. In the similar fashion, for quantiles other
than the median, QRM assigns different weight to positive and negative residuals and then
minimizes the sum of the weighted absolute residuals. This sum which is asymmetrically weighted
is referred to as the quantile function and is given by:
min𝜑∈𝔑
∑ 𝜌𝜏(𝑦𝑖 − 𝜑) (4)
where 𝜌𝑞(. ) is the asymmetric absolute value function which generates the 𝑞th sample
quantile as solution and 𝜑 is a scalar. Relation (4) is the quantile function for the specific 𝑞th
quantile.
The methodology that underlies QRM could best be explained by analogy to OLS. For a
series of random variables, 𝑦 = {𝑦1, 𝑦2, ⋯ ⋯ 𝑦𝑛 }, OLS solves the following equation:
13 Koenker and Basset (1978) first introduced quantile regression model (QRM).
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min𝜑∈𝔑
∑ (𝑦𝑖 − 𝜇)2𝑛𝑖=1 (5)
where 𝜇 is the sample mean which is also an estimate for the unconditional true mean E[Y].
By replacing 𝜇 with its parametric function 𝜇(𝑥, 𝛽) and solving:
min𝜑∈𝔑
∑ (𝑦𝑖 − 𝜇(𝑥, 𝛽) )2𝑛𝑖=1 (6)
an estimate for the conditional expectation, 𝐸(𝑌|𝑥), is obtained. Analogous to OLS, we can obtain
conditional median by simply replacing the scalar 𝜑 by its parametric function 𝜑(𝑥𝑖, 𝛽) and set
𝑞 = 0.50. This yields:
min𝜑∈𝔑
∑ 𝜌𝑞(𝑦𝑖 − 𝜑(𝑥𝑖 , 𝛽)) (7)
Or equivalently,
min𝜑∈𝔑
[∑ 𝑞|𝑦𝑖 − 𝜑(𝑥𝑖, 𝛽)| + (1 − 𝑞)|𝑦𝑖 − 𝜑(𝑥𝑖, 𝛽)|𝑖:𝑦𝑖≥𝜑 ] (8)
The conditional function for all other quantiles are obtained while setting 𝑞 =
0.05, 0.10, … , 0.50, … , 0.90, 0.95. The optimization is done by linear programming (Koenker and
Hallock, 2001) and the standard errors of the coefficients are obtained by a bootstrapping method.
It should be noted that QRM uses all observations (=1076) in estimating each quantile.
4. Empirical results
Table 2 includes the Wilcoxon-Mann-Whitney two-sample statistic (Wilcoxon 1945;
Mann and Whitney 1947), which tells that whether there is a difference between two populations.
The test assumes that the two independent samples are drawn from the populations with the same
distribution. In all three compensation categories, such as total compensation (in ‘000), salary (in
‘000) and bonus (in ‘000), there is a significant difference between two groups of CEOs. Female
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CEOs earn higher average total compensation ($6,142.98 vs. $5,822.05) and salary ($830.10 vs.
$767.79) than their counterparts. However, they earn lower bonus than male CEOs, $511.58 vs.
$225.02. Under the economic characteristics of the firms, firms led by female CEOs do not differ
significantly from the firms that are led by male CEOs. For example, stock return, return on assets
(ROA), debt to equity ratio (DE), book to market ratio (BMV), 3-year standard deviation of return
and 3-year standard deviation of ROA for both group of firms are more or less similar. Neither of
these economic factors is statistically significant between the two groups of firms.
However, both group of firms differ from each other in terms of firm’s governance
characteristics and CEO characteristics. Firms that employ female CEOs have a smaller board,
more independent board members, and more females on the board than firms that have hired male
CEOs. For example, female CEO firms have on average 9 members whereas male CEO firms have
about 10 members. On the contrary, female CEO firms have 77% independent and 26% female
directors versus male CEO firms having 73% independent and 11% female directors. In terms of
CEO characteristics, male CEOs have worked about one more year as the CEO than the female
CEOs (4.84 years versus 3.75 years). More female CEOs are on their first year role than their male
counterparts (15% versus 11%). Moreover, male CEOs serve as a chair of the board more than the
female CEOs (29% versus 19%). If we combine the aforementioned CEO characteristics, it can be
argued more and more female CEOs are hired from the outside labor market with an updated
compensation package. Whereas, compensation for male CEOs who work for a longer time as an
insider and mostly for their own companies (as manifested by CEO duality—CEO also holding
the board chair position Core et al. 1999) is not updated frequently. The existence of the
independent compensation committee does not differ between the group of firms. Also, the
presence of a female member in the compensation committee does not differ between two groups.
17
Table 3 reports the output from logit regression that is run each year. We kept the same
variables used in Bugeja et al. (2012). We find size of the firm (denoted by sales) is not a significant
determinant of CEO compensation post financial crisis. In all 18 years, we find that the proportion
of female directors in the board positively affect the likelihood of appointing a female CEO. Earlier
studies also find this variable having significant positive impact on female CEO appointment (see
Bell 2005, Elkinawy and Stater 2011, and Bugeja et al. 2012). Contrary to Bugeja et al. (2012),
we do not find board size having a significant negative impact on the likelihood of female CEO
appointment.
Table 4 shows the Wilcoxon–Mann–Whitney test of difference in matched data. We loss
15 firm years due to propensity score matching not being able to identify a reasonable match. Like
Bugeja et al. (2012), we performed a caliper match and allowed the propensity score to vary by
10% between treatment (=female CEO firms) and control group (=male CEO firms)14. We use
propensity score to match a male CEO for every female CEO. Our objective to match the same
number of male CEO firms as female CEO firms. Out of 19 variables only four variables are
significant. Propensity score match using the likelihood ratio from Table 3 does an excellent job
in this regard. Using these matched samples in the multivariate setting, if we can find female CEO
variable is significant then we would be able to argue our main theme of the paper that female
CEOs earn more than their counterparts.
Female CEOs have significantly (t-stat is 5.70) lower tenure than male counterparts.
Moreover, 14.90% of the female CEOs are at their first year, whereas only 7.80% male CEOs are
at their first year, a significant difference as well (t-stat is 3.65). Combining these two pieces of
information, we can posit that more firms are hiring female CEOs at recent times than before. This
14 Caliper was set equal to 0.10 with non-replacement and descending.
18
phenomenon also affects female CEO compensation as they are hired with recent compensation
package or “marked to market” compensation package. The presence of at least one female
member in the compensation committee is also significantly different between two types of CEOs.
For female CEO firms, there are no compensation committees that have a female member,
however, about 2% of the male CEO firms have one female in the compensation committee. This
may not directly help female CEO compensation, but may indirectly reduce the compensation gap
between genders.
Table 5 reports pooled cross sectional regression using all data (N=22,119). We use similar
variables used in previous research (see Bugeja et al. 2012). Along with 16 independent variables,
we use 18 year dummies to control for time variation. To control for unobservable time-invariant
characteristics for firms, we use both firm fixed effect and industry fixed effect models. However,
to remain consistent throughout the paper (and the reason mentioned in the methodology section),
we report only industry fixed effect15. Our variable of interest, female CEO, is positively
significant under both total compensation and salary models. The economic meaning is a female
CEO earns about $1,060 more in total compensation16 per year than her male counterpart. In the
case of salary, the result is statistically stronger (significant at 1% level). The coefficient indicates
a female CEO earns about $1,043 more per year than her male counterpart. Because total
compensation includes the implied value of a CEO’s stock awards and options which can
negatively affect the growth in total compensation, the size of coefficient is smaller than under
salary.
15 In fact, for robustness, we did firm-fixed effect in our main model (refer to Table 3). The results remain similar. In
fact, in some cases, it becomes stronger. For example, under salary, the coefficient for female CEO is 0.046*** (t-
statistic=3.07).
16 Exp(0.058)*$1,000=$1,060.00
19
Sales, board size, board independence, CEO tenure, and CEO duality affect all three areas
of compensation positively. Higher sales and bigger board represent bigger companies. Thus,
salary is positively related with these variables. Bonus is positively affected by higher sales.
Independent members in the board make sure that they hire and retain smart CEOs and thus impact
their compensation positively. Core et al. (1999) show that CEO compensation is higher when
there are more outside directors on the board. It is conceivable that the longer the CEO serves a
company, the higher his/her compensation becomes (Bugeja et al. 2012). The natural logarithm of
CEO work experience in the current company (ln of CEO tenure) has positive coefficient under
all six models. For example, in the first two models, one year of experience increases CEO salary
by 4.80% and total compensation by 3.80%17 respectively. When the CEO is also the chair of the
board (or CEO duality), it has a positive effect on CEO compensation. The CEO who is also the
chair of the board may have greater influence on the board in determining his or her salary.
Two interesting variables that are important to discuss are the presence of female directors
and the existence of at least one female member in the compensation committee. As outlined in
Bugeja et al. (2012), we also find female directors positively impact CEO compensation. However,
a female member in the compensation committee reduces total compensation and bonuses.
Interestingly, in our sample only male CEO firms have female(s) in the compensation committee.
Thus, the negative effect of female compensation committee can be argued as a factor to reduce
gender pay gap in the CEOs. As it is shown in Figure 1 (Panel C), since 2010 there has been a
sharp increase of appointment of female members in the compensation committee.
17 Under these models, the dependent variable is in “Log” form. Whenever, we explain a coefficient of an
independent variable which is also in “Log” form we can express that coefficient in percent.
20
Table 6 reports the output using only matched sample by propensity score matching. As
mentioned earlier, we lost 15 firm-year observations in the process of propensity score caliper-
based matching. Thus, the total number of observation is 1,076 (=538*2). We use the same
specification as we have use for all-data. Our variable of interest-female CEO remains strongly
positively significant at 1%. This means that if a similar firm hires a female CEO it has to pay
$1,176 more salary than if it hires a male CEO (refer to Model 2). Total compensation of female
CEOs is $1,104 higher than the male counterparts (refer to Model 1). A point to be noted is that
we are not positing that CEOs are paid higher simply because they are female. There may be other
tenets such as risk aversion, management skill, proven track record, and leadership style that can
make a female CEO more marketable than her male counterpart. We will explore this issue in the
later section. In terms of bonuses, CEO gender does not play a role which makes intuitive sense
because bonuses are awarded based on superior performance of the CEO.
Results are similar as in the “full model” (Refer to Table 5), however, with few exceptions.
The strong significance of the board size dropped in the “matched data” which means that size of
the board does not have an influence on determining the compensation of CEOs. The finding is
consistent with Bugeja et al. (2012). Some CEO characteristics such as CEO tenure, CEO duality
and CEO first-year become less strong than the “full model.” Like the original model, board
independence remains a strong determinant of CEO compensation which makes sense because
independent directors usually have an impartial view of the CEO and try to make sure that they
hire and retain the smart and bright CEOs. In Bonus (Model 3 and 4), we could not include the
independent compensation committee variable because a very insignificant number of firms has
the committee available (i.e., all of the members in the compensation committee are independent
members). Like in the full model, when the CEO owns 5% or more of the company’s stock it
21
significantly reduces her/his salary and total compensation. For example, owning 5% or more share
reduces CEO salary by $2,138 on average (refer to Model 2).
Overall, the models are similar to models in “full data” with significant F-values (fixed-effect
regression models) and LR chi2 (for Tobit models).
5. Additional robustness check
In addition to using propensity based matched sample to eliminate selection-biases18, we
use instrumental variable regression using all firm-year observation. We use two instruments as
discussed in the methodology section: female to total executive ratio and female to male executive
ratio.
For reporting purpose, we only report the output using female to total executive ratio as
instrument. However, the output using either instrument remains the same. Furthermore, we use
two estimation techniques: 2SLS and Generalized Method of Moments (GMM, Hansen 1982) with
robust weighting matrix in instrumental variable regression. In 2SLS of Model 1, at the first stage
where only a female CEO is regressed on female to total ratio, the adjusted R2 is 14.89% with a
partial F-statistic of 1994.87*** which is much higher than the suggested value of 10.00 (Stock,
Wright, and Yogo 2002 suggest a minimum value of 10.00). Thus, we have found a strong
instrument to use in our models.
Table 7 reports the results of instrumental regression under two estimation techniques:
2SLS and GMM. Like in our previous models, female CEO is significant in Model 1, Model 2,
Model 4 and Model 6. The R2 has improved from 42% from the full model to 48% in the
instrumental regression estimation. A female CEO earns $1,262 more in total compensation,
18 Selection biases arise when the sample is chosen from a universe with some specific characteristics and the
sample is relatively smaller with the condition being met. In our case, only 553 firm-year out of 22,119 firm-year
observation have met our selection criterion, i.e., having a female CEO=1.
22
$1,274 in salary than her male counterpart. The coefficients for female CEO (0.233 and 0.242) are
strongly robust in GMM estimation.
Board size and board independence affect CEOs’ total compensation and salary
significantly positively. However, the presence of female directors does not affect CEO
compensation. The plausible explanation that the female directors do not have a stronger influence
of CEO compensation is female directors are about one-tenth for the majority of the companies.
Referring to Table-2, we see that for male CEO firms 11% of the directors are female and for
female CEO firms 26% of the directors are female. Although the presence of female directors is
higher in female CEO firms, there are only 553 firm-years in the whole sample which is relatively
a very small portion of the sample. We can conclude that female directors are still not in a position
to affect the CEO salary significantly; they may however affect the appointment of a female CEO
(refer to Table-3).
CEO related characteristics such as CEO tenure, CEO duality, CEO first year and CEO
five percent are significant under all models except CEO first year in Model 1 and Model 4. One
year of CEO experience in the current company increases CEO salary by 5%, total compensation
by 4% and bonuses by 6%. CEO five percent (i.e., CEO holds five percent or more of the
company’s stock by stock reward or stock option) negatively affects CEO cash compensation,
salary and total compensation. Core et al. (1999) find that CEO compensation is a deceasing
function of CEO ownership. However, CEO stock holding positively affects bonus which
comprises both cash and non-cash reward to CEOs. To align CEO incentives with that of
shareholders, CEO compensation is composed of non-cash pay such as stock awards and stock
options (see Murphy, 1985; Jensen and Murphy, 1990; Hall and Liebman, 1998; Core and Guay,
1999). Thus, this finding is not surprising.
23
6. CEO risk management ability
Up until this point, we show that female CEOs are paid higher. This finding is robust under
various models and estimation techniques. We control for firm characteristics, other CEO
characteristics (in addition to gender) and firm governance characteristics (specially board
characteristics).
In this section, we explore the reason why female CEOs earn more than male CEOs. Being
at the top echelon of a firm, the CEO cannot be expected to be paid higher just because she is a
female. The female CEOs must have more valuable tenets than their male counterparts. Tenets
such as better management style, better leadership or better risk management capacities might
contribute to this higher pay. These tenets are difficult to measure or to find proxy for them as they
are more psychological or behavioral. Nevertheless, we use two measures to evaluate the
behavioral aspect of the female CEOs: delta and vega. Delta is the dollar change in the CEO’s
wealth for a 1% change in stock price, whereas vega is the dollar change in CEO’s for 1% change
in volatility of stock return. We use delta as a proxy for firm risk that has a direct impact on CEO
wealth and vega as CEO’s risk aversion.
CEO compensation by using stocks and stock options is structured to give executives
appropriate risk taking incentives (Guay 1999). When managers are paid by stocks and/or stock
options, a dependence exists between his/her wealth and firm’s stock price movements (Jensen
and Meckling 1976 and Jensen and Murphy 1990). In the literature, this dependence is commonly
known as wealth-performance relation (Guay 1999). Delta or sensitivity of CEO’s wealth to stock
price change is viewed as an alignment of CEO’s risk taking behavior with the interest of the
shareholders (Coles et al. 2006). Higher delta means managers are exposed to more risk and lower
delta means managers have a grasp over the activities of the firm and can handle firm risk more
24
effectively. Coles et al. 2006 argue that allowing managers option-based compensation reduces
the tendency to ignore positive NPV or profitable project. Vega, the convexity or curvature of the
slope of CEO wealth-performance relation, is a measure of managers’ risk aversion. Coles et al.
(2006, p. 432) argue, “Option-based compensation, by providing convex payoffs, can potentially
reduce aversion to risky policies that arise from high delta.”
Table 8 reports the influence of the female CEO on the slope of wealth-performance
relation, delta or risk of a firm and convexity of the wealth-performance relation, vega with other
variables. Delta and vega are used both as dependent variable (see Bizjak et al. 1993 and Core and
Guay 1999) and independent variables (see Guay 1999, Cohen et al. 2000 and Coles et al. 2006).
In our case, delta and vega are used as dependent variables to identify the impact of the female
CEOs on them. We added three variables, such as cash compensation (salary and bonus) research
and development expenses, and number of business segments a firms operates; these variables are
found to have direct relation with CEO option based compensation (See Guay 1999 and Coles et
al. 2006).
The female CEO significantly reduces firm related risk or delta. They also have negative
impact on the convexity or risk aversion, however, it is not statistically significant. Therefore, we
can argue that the female CEOs have better tools to manage firm risk. Due to their risk handling
capacity firm stock price does not have much volatility as does stock price of firms headed by male
CEOs. Whether this risk mitigation is good or bad for the firm stockholders in the long run is
beyond the scope of this paper. Nonetheless, it is evident that female CEOs reduce both delta
(statistically significant at 1%) and vega (statistically not significant).
Cash compensation and research and development expenses (R&D) are positively
impacting both delta and vega. For example, the coefficient of R&D is 1.351 (t-statistic is 4.65)
25
under model 3 and 5.587 (t-statistic is 12.73) under Model 6. Focus of business or number of
business segment is negatively impacting delta; coefficient is -0.011 (t-statistic is -3.50). These
findings are consistent with the previous research, especially ones that focus on pay-performance
sensitivity, research and development, and focus (see Guay 1999; Coles et al. 2006). We argue
that female CEOs are better in handing firm risk than their male counterparts. Risk aversion
(denoted by vega) of female CEOs do have the correct sign, however, is not significant. Thus, we
cannot conclusively say that female CEOs are risk averse.
7. Asymmetry in CEO compensation
In this section, we ask whether the CEO compensation is asymmetric? The reason we asked
this question is even though the CEO is the chief executive of a firm and has homogenous
responsibilities across firms, some CEOs may be paid astronomically higher than the rest. This is
even more true currently because firms are paying more compensation in stocks and stock options.
Moreover, the mixed findings in the literature about the gender gap and compensation may be
explained by asymmetries, if any, in the CEO compensation. Using quantile regression, we show
that female CEO compensation is indeed asymmetric (more specifically U-shaped).
Table 9 reports the output from quantile regression using 19 quantiles19 and using matched
data (refer to Table 6). For quantiles below median, female CEO is significant and its coefficient
value decreases with the value of quantiles. Surrounding median, the significance completely goes
away. For this reason, earlier papers that did only mean-based statistical models did not find any
statistical significance. The significance comes back at the higher quantile. Panel D in Figure 1
depicts the coefficient with 95% confidence intervals. As we can see that the female CEO
19 For brevity, we report 11 quantiles: five below median, median and five above median. However, output from all
19 quantile regressions are available upon request.
26
coefficient takes a U-shaped in the quantile regression. Some other interesting phenomena are DE
(debt-equity ratio), independent board, CEO-Chair position, and CEO five percent are significant
at median and at the quantiles below median. They have different signs though. DE, CEO-Chair
and CEO five percent have negative effect on CEO total compensation at median and at the lower
quantiles, while independent board has a positive effect on CEO compensation.
CEO tenure has a strong positive effect on CEO compensation at the higher quantiles. This
makes intuitive sense because as CEOs become more and more experienced they earn more
money. Coefficients for sales are consistently positive and significant at every reported quantile.
However, coefficients for BMV (book to market value) ratio consistently negative and significant
at each quantile. Higher BMV means poor performance of the firms, therefore, the CEOs of those
firms generally earn less than the CEOs of similar profitable firms.
8. Conclusion
We show that although women are seriously underrepresented at the top position in
corporate America, female CEOs earn higher compensation than their male counterparts. They
earn this extra pay by their superior risk handling capabilities. Female representation in all aspects
of organization can benefit the organization and the society at a greater level. Flabbi et al (2014)
show that female CEOs can better interpret the productivity signal from female workers. For a
female concentration firm (at least 20% workforce are female), this better interpretation increases
worker productivity. Their paper is based on a European market. To the best of our knowledge,
our paper is the first to show that female CEOs earn higher than male CEOs for S&P 1500 firms.
This finding is robust under various specifications and estimation techniques.
Earlier research finds a significant gender pay gap really should have isolated CEOs from
the rest of the employees. As we have shown female CEOs are better handlers of risk and thus earn
27
more than their counterparts. Some other studies on CEOs find no gender pay gap exists. We have
shown that CEO pay is actually asymmetric in nature. At median (or surround median), the gender
pay gap fades away, however, the gap is very much present at the lower (or higher) level quantiles,
as we have shown. Thus, mean-based model may not be appropriate to identify the gender pay gap
among the CEOs.
“Glass Cliff,” a term first coined by two university professors in the UK in 2005 explains
that women are intentionally put into a dire situation and are bound to fail. A recent Harvard
Review article lists at least five female CEOs in the USA who lived out this so called glass cliff
including 2016 US presidential candidate and former HP CEO Ms. Carly Fiorina. This has proven
that female CEOs can actually turnaround and shatter the glass ceiling. Our research is just
showing up this recent trend that female CEOs are and will be better managers and hence earn
higher compensation. We expect more research on this matter because robust findings like ours
can encourage more young female executives to aspire to become the head of the organization
with a knowledge that they can be worth more than their male counterparts.
28
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Figure 1: Female as CEOs, members in the baord and compensation committee
Panel A: No. of Female CEOs Panel B: Fractions of Female Board Members
Panel C: No. of Compensation Com. that has
atleast one female member
0
10
20
30
40
50
60
70
19
98
20
00
20
02
20
04
20
06
20
08
20
10
20
12
20
14
20
16
Female CEOs
0.06
0.08
0.1
0.12
0.14
0.16
0.18
19
98
20
00
20
02
20
04
20
06
20
08
20
10
20
12
20
14
20
16
Fem. Directors (% of Board)
0
2
4
6
8
10
12
14
19
98
20
00
20
02
20
04
20
06
20
08
20
10
20
12
20
14
20
16
Fem. Comp. Com
Panel D: Female CEO coefficient
in QRM with 95% confidence
limits
32
Table 1: Distribution of CEOs by year and industry.
Panel A: Distribution of CEOs by year
Year Female CEOs Total Female CEOs (%)
1998 12 1,172 1.02
1999 11 1,185 0.93
2000 13 1,176 1.11
2001 15 1,198 1.25
2002 15 1,168 1.28
2003 19 1,200 1.58
2004 18 1,206 1.49
2005 20 1,196 1.67
2006 25 1,155 2.16
2007 31 1,031 3.01
2008 36 1,239 2.91
2009 39 1,270 3.07
2010 42 1,298 3.24
2011 44 1,290 3.41
2012 46 1,303 3.53
2013 52 1,293 4.02
2014 57 1,408 4.05
2015 58 1,331 4.36
Total 553 22,119 2.50
Panel B: Distribution of CEOs by industries
GICS No. of
firm-years
% of total
firm-years
Female
CEOs
% of firm-years
for industry
10= Energy 1,245 5.63 12 0.96
15= Materials 1,570 7.10 27 1.72
20= Industrials 3,314 14.98 45 1.36
25= Consumer Discretionary 3,777 17.08 174 4.61
30= Consumer Staples 1,115 5.04 57 5.11
35= Health Care 2,375 10.74 51 2.15
40= Financials 2,780 12.57 39 1.40
45= Information Technology 3,983 18.01 88 2.21
50= Telecommunication Services 208 0.94 14 6.73
55= Utilities 1,091 4.93 28 2.57
60= Real Estate 661 2.99 18 2.72
Total 22,119 100 553 2.50
33
Table 2: Wilcoxon–Mann–Whitney test of difference: All data
Male CEOs
(N=21,566)
Female CEOs
(N=553)
Wilcoxon–Mann–Whitney
test
Variable Mean Median Mean Median Z p>|Z|
Total Compensation 5822.05 3504.35 6142.98 3794.12 -2.26** 0.02
Salary 767.79 722.82 830.10 773.65 -4.68*** 0.00
Bonus 511.58 0.00 225.02 0.00 8.24*** 0.00
Sale 6723.37 1586.74 7664.24 1342.40 1.79* 0.07
Return (%) 8.02 3.70 5.34 4.80 0.32 0.75
ROA (%) 9.28 8.45 9.84 8.60 -1.18 0.24
DE 2.28 1.24 1.98 1.20 1.59 0.11
BMV 0.52 0.46 0.54 0.46 0.88 0.38
std3ret (%) 39.56 29.79 36.94 29.53 -0.12 0.91
std3roa (%) 2.91 1.64 2.73 1.69 0.63 0.53
Board Size 9.45 9.00 9.00 9.00 3.55*** 0.00
Ind. Board (%) 0.73 0.75 0.77 0.80 -7.03*** 0.00
Fem Directors (%) 0.11 0.11 0.26 0.25 -29.30*** 0.00
CEO Tenure 4.84 4.00 3.75 3.00 6.31*** 0.00
CEO First Year 0.11 0.00 0.15 0.00 -2.58** 0.01
CEO Duality 0.29 0.00 0.19 0.00 5.22*** 0.00
CEO Five % 0.05 0.00 0.04 0.00 1.36 0.18
Ind. Comp. Com. 0.00 0.00 0.00 0.00 0.88 0.38
Fem. Comp. Com. 0.00 0.00 0.00 0.00 1.39 0.16
This table reports Wilcoxon–Mann–Whitney test of difference using all data. Total compensation (in
thousand Dollars) is TDC1 in Execucomp database, which has been defined as “Total compensation for the
individual year, comprised of the following: Salary, Bonus, Other Annual, Total Value of Restricted Stock
Granted, Total Value of Stock Options Granted (using Black-Scholes), Long-Term Incentive Payouts, and
All Other Total.” Salary (in thousand Dollars) is defined in Execucomp as “The dollar value of the base
salary (cash and non-cash) earned by the named executive officer during the fiscal year.” Bonus (in
Thousand Dollars) is defined in Execucomp database as “The dollar value of a bonus (cash and non-cash)
earned by the named executive officer during the fiscal year.” Sale “represents gross sales (the amount of
actual billings to customers for regular sales completed during the period) reduced by cash discounts, trade
discounts, and returned sales and allowances for which credit is given to customers” (in million Dollars).
Return is one year buy-and-hold stock return. ROA is measured as EBIT over average total assets. DE
stands for debt equity ratio and calculated as average total liabilities over average total equity. BMV stands
for book-to-market value and is calculated as book value per stock over market value per stock. std3ret and
std3roa are standard deviation of the last 3 years of return and ROA, respectively. Board size is the total
number of directors on the board. Ind. Directors and Fem. Directors are the fraction of directors who are
independent and female, respectively. CEO Tenure is the number of years CEO is serving the current
company. CEO First Year is an indicator variable that takes a value of 1 if this is the first year of CEO
employment. CEO Duality is an indicator variable that takes a value of 1 if CEO also holds the chair position
of the board. CEO Five % is an indicator variable that takes a value of 1 if the CEO holds 5% or more share
of the firm, otherwise, 0. Ind. Comp. Com. is an indicator variable that takes a value of 1 if the compensation
is composed of all independent directors, otherwise, 0. Fem. Comp. Com. is an indicator variable that takes
a value of 1 if there sits at least one female on the compensation committee, otherwise, 0. ***, **, *
represent 10%, 5%, and 1% statistical significance, respectively.
34
Table 3: Year-wise logit regression (predicting π(Female CEO)=1)
This table reports the likelihood of appointing a female CEO. We use the same set of variables that are used
in Bugeja et al. (2012) in a logit regression framework and run separately at each year. Ln of Sale is the
natural log of sale. Sale “represents gross sales (the amount of actual billings to customers for regular sales
completed during the period) reduced by cash discounts, trade discounts, and returned sales and allowances
for which credit is given to customers” (in million Dollars). Board size is the total number of directors on
the board. Fem. Directors are the fraction of female directors on the board. Chi2 statistic is reported in the
parenthesis. ***, **, * represent 10%, 5%, and 1% statistical significance, respectively.
Year Intercept Fem. Directors Ln of Sale Board Size Pseudo R2
1998 -1.949 12.663*** -0.331 -0.196 0.198
(-1.34) (5.08) (-1.39) (-1.31)
1999 -2.308 14.589*** -0.608** -0.033 0.298
(1.43) (5.56) (2.31) (0.23)
2000 -2.020 13.090*** -0.474** -0.110 0.249
(1.41) (5.58) (2.14) (0.76)
2001 -0.570 14.160*** -0.577*** -0.236 0.320
(0.44) (6.34) (3.00) (1.49)
2002 -0.926 12.592*** -0.536** -0.181 0.227
(0.75) (5.61) (2.39) (1.18)
2003 -0.676 15.851*** -0.581** -0.241 0.333
(0.51) (6.75) (2.55) (1.51)
2004 -1.838 14.513*** -0.591*** -0.070 0.283
(-1.38) (6.51) (2.61) (-0.49)
2005 -2.021 14.708*** -0.638*** -0.001 0.287
(-1.47) (6.78) (-2.85) (-0.01)
2006 -2.820** 11.924*** -0.358** -0.033 0.199
(-2.28) (6.52) (-1.97) (-0.30)
2007 -1.872* 10.562*** -0.284* -0.133 0.173
(-1.81) (6.33) (-1.79) (-1.23)
2008 -2.281** 13.965*** -0.368** -0.105 0.249
(-2.28) (7.97) (-2.47) (-1.05)
2009 -3.374*** 14.744*** -0.308** -0.052 0.254
(-3.48) (8.35) (-2.20) (-0.57)
2010 -3.343*** 13.681*** -0.138 -0.163 0.236
(-3.56) (8.43) (-1.10) (-1.73)
2011 -3.259*** 13.297*** -0.077 -0.217 0.235
(-3.48) (8.54) (-0.60) (-2.27)
2012 -4.275*** 11.831*** -0.088 -0.060 0.179
(-4.64) (8.05) (-0.74) (-0.67)
2013 -4.532*** 11.914*** -0.057 -0.056 0.180
(-5.11) (8.32) (-0.50) (-0.65)
2014 -5.954*** 12.842*** 0.018 -0.007 0.206
(-6.77) (8.89) (0.17) (-0.09)
2015 -4.887*** 11.122*** -0.070 -0.008 0.183
(-5.78) (8.51) (-0.66) (-0.10)
35
Table 4: Wilcoxon–Mann–Whitney test of difference: Matched sample
Male CEOs
(N=538)
Female CEOs
(N=538)
Wilcoxon–Mann–
Whitney test
Variable Mean Median Mean Median Z p>|Z|
Total Compensation 6129.080 3699.319 6172.512 3793.663 -1.19 0.23
Salary 823.184 790.625 829.096 770.580 -0.81 0.42
Bonus 240.200 0.000 221.655 0.000 0.61 0.54
Sale 7795.744 1637.820 8547.326 1352.352 1.12 0.26
Return (%) 8.462 5.134 5.482 4.563 1.01 0.31
ROA (%) 8.186 8.364 9.826 8.547 -1.25 0.21
DE 2.290 1.290 1.971 1.205 1.38 0.17
BMV 0.551 0.454 0.536 0.465 0.43 0.67
std3ret (%) 39.635 29.454 36.751 29.368 -0.57 0.57
std3roa (%) 2.772 1.499 2.703 1.690 -0.91 0.36
Board Size 9.033 9.000 9.026 9.000 0.21 0.84
Ind. Board 0.765 0.800 0.772 0.800 -0.17 0.87
Fem directors 0.252 0.250 0.255 0.250 0.17 0.86
CEO Tenure 5.093 4.000 3.786 3.000 5.70*** 0.00
CEO First Year 0.078 0.000 0.149 0.000 -3.65*** 0.00
CEO Duality 0.216 0.000 0.186 0.000 1.22 0.22
CEO Five % 0.065 0.000 0.041 0.000 1.77* 0.08
Ind. Comp. Com. 0.006 0.000 0.002 0.000 1.00 0.32
Fem. Comp. Com. 0.017 0.000 0.000 0.000 3.01*** 0.00
This table reports Wilcoxon–Mann–Whitney test of difference using matched sample. We use caliper-based
(set caliper=0.10) propensity score matching. The matching process could not find a closed match for 15
firm years, therefore, we have 538 female CEO firm years. Total compensation (in thousand Dollars) is
TDC1 in Execucomp database, which has been defined as “Total compensation for the individual year,
comprised of the following: Salary, Bonus, Other Annual, Total Value of Restricted Stock Granted, Total
Value of Stock Options Granted (using Black-Scholes), Long-Term Incentive Payouts, and All Other
Total.” Salary (in thousand Dollars) is defined in Execucomp as “The dollar value of the base salary (cash
and non-cash) earned by the named executive officer during the fiscal year.” Bonus (in Thousand Dollars)
is defined in Execucomp database as “The dollar value of a bonus (cash and non-cash) earned by the named
executive officer during the fiscal year.” Sale “represents gross sales (the amount of actual billings to
customers for regular sales completed during the period) reduced by cash discounts, trade discounts, and
returned sales and allowances for which credit is given to customers” (in million Dollars). Return is one
year buy-and-hold stock return. ROA is measured as EBIT over average total assets. DE stands for debt
equity ratio and calculated as average total liabilities over average total equity. BMV stands for book-to-
market value and is calculated as book value per stock over market value per stock. std3ret and std3roa are
standard deviation of the last 3 years of return and ROA, respectively. Board size is the total number of
directors on the board. Ind. Directors and Fem. Directors are the fraction of directors who are independent
and female, respectively. CEO Tenure is number of years CEO is serving the current company. CEO First
Year is an indicator variable that takes a value of 1 if this is the first year of CEO employment. CEO Duality
is an indicator variable that takes a value of 1 if CEO also holds the chair position of the board. CEO Five
% is an indicator variable that takes a value of 1 if the CEO holds 5% or more share of the firm, otherwise,
0. Ind. Comp. Com. is an indicator variable that takes a value of 1 if the compensation is composed of all
independent directors, otherwise, 0. Fem. Comp. Com. is an indicator variable that takes a value of 1 if
there sits at least one female on the compensation committee, otherwise, 0. ***, **, * represent 10%, 5%,
and 1% statistical significance, respectively.
36
Table 5: Pooled cross-sectional regression: All data (N=22,119)
Parameter Mode-1
Total Comp.
Mode-2
Salary
Mode-3
Bonus
Mode-4
Total Comp.
Mode-5
Salary
Mode-6
Bonus
Female CEO 0.058* 0.042*** -0.132 0.061* 0.055*** -0.147
(1.78) (2.73) (-1.19) (1.91) (3.70) (-1.36)
Ln of Sale 0.395*** 0.164*** 0.158*** 0.396*** 0.165*** 0.158***
(93.18) (81.75) (11.03) (95.10) (84.08) (11.22)
Return -0.0002 0.0001 0.006*** -0.0002 0.0001 0.006***
(-1.13) (-1.58) (13.08) (-1.13) (-1.59) (13.09)
ROA 0.001 -0.002*** 0.036*** 0.001 -0.002*** 0.036***
(1.21) (-4.60) (15.17) (1.22) (-4.60) (15.18)
DE -0.005** 0.003*** -0.009 -0.005** 0.003*** -0.009
(-2.31) (2.92) (-1.35) (-2.33) (2.95) (-1.38)
BMV -0.438*** -0.026*** -0.210*** -0.438*** -0.026*** -0.207***
(-26.84) (-3.33) (-3.80) (-26.81) (-3.37) (-3.75)
lnstd3ret 0.073*** -0.005* 0.051** 0.074*** -0.005 0.052**
(10.53) (-1.65) (2.18) (10.56) (-1.64) (2.20)
lnstd3roa 0.008 -0.009*** -0.134*** 0.008 -0.010*** -0.134***
(1.48) (-3.84) (-7.60) (1.50) (-3.89) (-7.56)
Board Size 0.018*** 0.017*** 0.035*** 0.018*** 0.018*** 0.034***
(7.00) (14.18) (3.92) (7.08) (14.56) (3.89)
Ind. Board 0.645*** 0.207*** -0.106 0.648*** 0.217*** -0.115
(16.54) (11.24) (-0.81) (16.82) (11.95) (-0.88)
Fem. Directors 0.027 0.107*** -0.098
(0.45) (3.74) (-0.48)
Fem. Comp. Com. -0.228** -0.069 -0.740**
(-2.51) (-1.61) (-2.40)
Ln CEO Tenure 0.038*** 0.048*** 0.070** 0.038*** 0.047*** 0.070**
(4.04) (10.79) (2.19) (4.02) (10.69) (2.19)
CEO Duality 0.145*** 0.076*** 0.196*** 0.145*** 0.078*** 0.194***
(9.70) (10.87) (3.88) (9.72) (11.06) (3.86)
CEO First Year 0.029 -0.079*** 0.423*** 0.029 -0.079*** 0.425***
(1.33) (-7.60) (5.69) (1.34) (-7.64) (5.72)
CEO Five % -0.238*** -0.103*** 0.547*** -0.238*** -0.104*** 0.548***
(-10.32) (-9.45) (7.02) (-10.35) (-9.59) (7.04)
Ind. Comp. Com. -0.003 -0.045 -0.069 0.07 -0.024 0.169
(-0.04) (-1.25) (-0.27) (0.85) (-0.63) (0.61)
Intercept and Year Dummies Yes Yes Yes Yes Yes Yes
Fixed Effect/Industry
Dummies Industry Industry Yes Industry Industry Yes
Adjusted R2 0.472 0.455 0.472 0.455
F-value 600.23*** 557.94*** 600.58*** 557.30***
Pseudo R2 0.102 0.102
LR chi2 11649.51*** 11655.00*** This table reports the results from pooled cross-sectional regression (= Model 1, 2, 4 and 5) and Tobit regression
(=Model 3 and 6) using all data=22,119 observations. The variable definitions are the same as provided in Table 4.
We use the natural log of Total Compensation, Salary, and (1+Bonus). We winsorize the data at 1% and 99%. We use
industry-fixed effect in Model 1, 2, 4, and 5 and industry dummies in Model 3 and 6. We also use year dummies for
all models. T-statistics are reported in the parenthesis. ***, **, * represent 10%, 5%, and 1% statistical significance,
respectively.
37
Table 6: Pooled cross-sectional regression: Matched data (N=1,076)
Parameter Model-1
Total Comp
Model-2
Salary
Model-3
Bonus
Model-4
Total Comp
Model-5
Salary
Model-6
Bonus
Female CEO 0.099* 0.162*** -0.348 0.094* 0.160** -0.391
(1.85) (2.61) (-0.75) (1.74) (2.57) (-0.84)
Ln of sale 0.356*** 0.157*** -0.058 0.353*** 0.155*** -0.063
(15.68) (5.98) (-0.29) (15.88) (6.03) (-0.33)
return 0.0004 0.0001 0.006 0.0004 0.0001 0.006
(0.47) (0.12) (1.04) (0.49) (0.14) (1.03)
ROA -0.0001 -0.003 0.026 -0.0001 -0.003 0.027
(-0.04) (-1.00) (1.20) (-0.04) (-1.00) (1.23)
DE -0.008 0.001 -0.168*** -0.008 0.001 -0.169***
(-1.22) (0.16) (-3.10) (-1.19) (0.18) (-3.12)
BMV -0.325*** -0.006 -0.861* -0.323*** -0.005 -0.850*
(-6.38) (-0.10) (-1.86) (-6.34) (-0.09) (-1.84)
lnstd3ret 0.028 -0.017 0.289 0.027 -0.017 0.297
(0.75) (-0.40) (0.90) (0.75) (-0.40) (0.93)
lnstd3roa 0.066** 0.016 -0.191 0.068** 0.017 -0.195
(2.38) (0.52) (-0.80) (2.45) (0.54) (-0.82)
board 0.016 -0.006 -0.109 0.017 -0.005 -0.109
(0.98) (-0.31) (-0.76) (1.04) (-0.27) (-0.77)
Ind. Board 0.636*** 0.899*** -2.816 0.609*** 0.886*** -2.945
(2.70) (3.31) (-1.50) (2.60) (3.27) (-1.57)
Fem. Directors -0.148 -0.098 0.379
(-0.54) (-0.31) (0.16)
Fem. Comp. Com -0.364 -0.125 0.303
(-1.09) (-0.32) (0.67)
Ln of CEO tenure 0.072 0.140** 0.308 0.07 0.140** 1.380**
(1.41) (2.37) (0.68) (1.37) (2.36) (1.98)
CEO Duality 0.139 -0.010 1.384** 0.137 -0.012 3.323***
(1.55) (-0.09) (1.98) (1.52) (-0.11) (3.37)
CEO first year 0.058 -0.074 3.334*** 0.056 -0.074 0.275
(0.49) (-0.55) (3.38) (0.48) (-0.55) (0.25)
CEO five % -0.861*** -0.760*** 0.271 -0.854*** -0.757*** 0.303
(-6.83) (-5.23) (0.25) (-6.78) (-5.21) (0.67)
Ind. Comp. Com. -0.371 0.315 -0.111 0.402
(-0.86) (0.63) (-0.22) (0.70)
Intercept and Year Dummies Yes Yes Yes Yes Yes Yes
Fixed Effect/Industry Dummies Industry Industry Yes Industry Industry Yes
Adjusted R2 0.424 0.112 0.424 0.112
F-value 25.24*** 5.42*** 25.29*** 5.42***
Pseudo R2 0.130 0.131
LR chi2 389.89*** 391.33***
This table reports the results from pooled cross-sectional regression (= Model 1, 2, 4 and 5) and Tobit regression
(=Model 3 and 6) using matched sample of 1,076 (=538*2) observations. Propensity score matching was conducted
each year with a caliper of 10%. The propensity scores were created using logit models reported in Table 3. The
variable definitions are the same as provided in Table 4. We use the natural log of Total Compensation, Salary, and
(1+Bonus). We winsorize the data at 1% and 99%. We use industry-fixed effect in Model 1, 2, 4, and 5 and industry
dummies in Model 3 and 6. We also use year dummies for all models. T-statistics are reported in the parenthesis. ***,
**, * represent 10%, 5%, and 1% statistical significance, respectively. Similar to Beugeja et al. (2012) we use female
directors (%) and female compensation committee in separate models.
38
Table 7: Instrumental variable (instrument used: Female to total executive ratio) regression
This table reports output from 2nd Stage of 2SLS (Model 1-Model 3) and GMM with robust weighting matrix. Female
to total executive ratio is used as an instrument. The strength of the instrument is very high with a partial F-statistic of
1994.87*** which is much higher than the suggested value of 10.00 (Stock, Wright, and Yogo 2002 suggest a
minimum value of 10.00). In the first stage, the likelihood of a female CEO is determined, then predicted female CEO
is used at the second stage with other controls. The variable definitions are the same as provided in Table 4. T-
statistics are reported in the parenthesis. ***, **, * represent 10%, 5%, and 1% statistical significance, respectively.
2nd Stage of 2SLS GMM (Weight Matrix: Robust)
Parameter Mode-1
Total Comp
Mode-2
Salary
Mode-3
Bonus
Mode-4
Total Comp
Mode-5
Salary
Mode-6
Bonus
Female CEO 0.233** 0.242*** -0.590 0.233** 0.242*** -0.590
(2.04) (4.51) (-1.53) (2.09) (4.76) (-1.55)
Ln of Sale 0.397*** 0.166*** 0.155*** 0.397*** 0.166*** 0.155***
(91.61) (80.62) (10.55) (79.74) (64.08) (10.11)
Return -0.0002 -0.0001 0.006*** -0.0002 -0.0001 0.006***
(-1.07) (-1.42) (13.02) (-0.93) (-1.29) (12.98)
ROA 0.001 -0.002*** 0.036*** 0.001 -0.002*** 0.036***
(1.22) (-4.58) (15.17) (0.99) (-3.91) (14.51)
DE -0.005** 0.003*** -0.009 -0.005** 0.003** -0.009
(-2.33) (2.85) (-1.32) (-2.30) (2.55) (-1.27)
BMV -0.439*** -0.026*** -0.209*** -0.439*** -0.026*** -0.209***
(-26.86) (-3.35) (-3.77) (-24.31) (-3.06) (-3.54)
lnstd3ret 0.073*** -0.006* 0.052** 0.073*** -0.006* 0.052**
(10.48) (-1.76) (2.21) (10.06) (-1.76) (2.19)
lnstd3roa 0.008 -0.009*** -0.135*** 0.008 -0.009*** -0.135***
(1.51) (-3.77) (-7.62) (1.47) (-3.60) (-7.59)
Board Size 0.019*** 0.018*** 0.033*** 0.019*** 0.018*** 0.033***
(7.16) (14.55) (3.69) (6.63) (12.87) (3.52)
Ind. Board 0.647*** 0.209*** -0.113 0.647*** 0.209*** -0.113
(16.60) (11.36) (-0.85) (14.81) (10.40) (-0.82)
Fem. Directors -0.049 0.02 0.101 -0.049 0.02 0.101
(-0.63) (0.55) (0.39) (-0.63) (0.54) (0.39)
Ln CEO Tenure 0.040*** 0.050*** 0.064** 0.040*** 0.050*** 0.064**
(4.23) (11.20) (1.99) (4.25) (10.80) (2.03)
CEO Duality 0.146*** 0.077*** 0.194*** 0.146*** 0.077*** 0.194***
(9.74) (10.95) (3.85) (9.09) (10.56) (3.73)
CEO First Year 0.031 -0.076*** 0.418*** 0.031 -0.076*** 0.418***
(1.42) (-7.34) (5.61) (1.37) (-7.43) (5.50)
CEO Five % -0.236*** -0.101*** 0.543*** -0.236*** -0.101*** 0.543***
(-10.25) (-9.27) (6.97) (-8.34) (-5.59) (6.56)
Ind. Comp. Com. 0.00009 -0.041 -0.077 0.00009 -0.041 -0.077
(0.00) (-1.14) (-0.30) (0.00) (-1.17) (-0.25)
Intercept & Year Dummies Yes Yes Yes Yes Yes Yes
Industry Dummies Yes Yes Yes Yes Yes Yes
Adjusted R2 0.481 0.484 0.408 0.481 0.484 0.408
Wald Chi2 20625.58 20,866.00 15326.20 21138.98 21313.06 19046.06
39
Table 8: CEO risk management ability:
Delta Vega
Parameter Model-1 Model-2 Model-3 Model-1 Model-2 Model-3
Female CEO -0.423*** -0.363*** -0.295*** -0.166* -0.095 -0.003
(-5.87) (-5.38) (-4.88) (-1.68) (-1.01) (-0.04)
Ln of cash compensation 0.840*** 0.358*** 1.046*** 0.593***
(48.95) (18.94) (43.98) (20.95)
Ln of Sale 0.373*** 0.245***
(40.57) (17.73)
Return 0.001*** -0.002***
(3.38) (-4.57)
ROA 0.008*** -0.005**
(5.78) (-2.36)
DE -0.065*** 0.006
(-15.68) (1.01)
BMV -1.310*** -0.734***
(-36.01) (-13.50)
Lnstd3ret 0.005 -0.100***
(0.40) (-4.89)
Lnstd3roa -0.053*** -0.026*
(-5.13) (-1.68)
Board Size -0.055*** 0.086***
(-11.00) (11.43)
No. of Segment -0.014*** 0.003
(-4.41) (0.57)
R&D 1.125*** 5.219***
(3.91) (12.03)
Intercept and Year Dummies Yes Yes Yes Yes Yes Yes
Fixed Effect Industry Industry Industry Industry Industry Industry
Adjusted R2 0.037 0.157 0.326 0.078 0.172 0.228
F-value 41.96 186.06 303.84 92.53 210.7 189.31
No. of obs. 16856 16856 16856 17159 17159 17159
This table reports CEO risk management ability by their wealth change due to 1% change in firm stock price (=delta)
and 1% volatility of stock returns (=vega). The measure of delta and vega was generated by following Coles, Daniel,
and Naveen (2006) paper entitled, “Managerial incentives and risk-taking” in the Journal of Financial Economics,
and by using programs provided by Lalitha Naveen’s website (https://sites.temple.edu/lnaveen/data/). R&D is the
research and development expenses (in million Dollars) that the company spends during the year to develop new
products or services. No. of (business) segments measures the company’s business focus. The variable definitions are
the same as provided in Table 4. T-statistics are reported in the parenthesis. ***, **, * represent 10%, 5%, and 1%
statistical significance, respectively.
40
Table 9: Asymmetry in CEO compensation: Quantile regression
q Female
CEO Ln sale Return ROA DE BMV
LnSTD3
Ret
LnSTD3
ROA
Board
Size Ind. Board
% Fem.
Directors
Ln CEO
Tenure
CEO
Duality
CEO
First
Year
CEO Five
Percent
Ind.
Comp.
Comm.
R2
(%)
0.05 0.430*** 0.402*** 0.000 0.009 -0.023*** -0.455*** 0.022 -0.021 0.023 1.443*** 0.682 0.229* -0.144 0.338 -1.382 0.652 39
(3.39) (9.55) (-0.08) (1.36) (-3.52) (-2.67) (0.31) (-0.41) (0.63) (3.50) (1.34) (1.70) (-1.37) (1.16) (-1.52) (0.05)
0.10 0.261*** 0.397*** 0.002 0.001 -0.020*** -0.458*** 0.065 -0.017 0.033 1.238*** 0.760** 0.141* -0.234*** 0.063 -0.968** 0.273 42
(3.23) (15.54) (1.60) (0.20) (-4.73) (-3.11) (1.45) (-0.53) (1.55) (3.85) (2.32) (1.83) (-2.60) (0.39) (-2.24) (0.05)
0.15 0.211*** 0.403*** 0.001 0.002 -0.018*** -0.499*** 0.065* -0.027 0.023 1.356*** 0.398 0.115** -0.193** 0.039 -0.832*** 0.111 41
(3.56) (19.41) (1.38) (0.27) (-3.27) (-3.29) (1.73) (-1.09) (1.47) (5.92) (1.61) (2.05) (-2.29) (0.30) (-3.84) (0.02)
0.20 0.155*** 0.399*** 0.001 0.001 -0.014** -0.446*** 0.064* -0.007 0.009 1.643*** 0.265 0.064 -0.161** -0.049 -0.885*** -0.058 40
(2.94) (19.68) (0.57) (0.27) (-2.23) (-3.13) (1.73) (-0.31) (0.57) (6.92) (1.26) (1.37) (-2.29) (-0.42) (-6.89) (-0.02)
0.25 0.090* 0.397*** 0.000 0.001 -0.010* -0.406*** 0.041 0.010 0.017 1.293*** 0.227 0.057 -0.182*** -0.053 -0.879*** -0.265 40
(1.77) (20.79) (0.60) (0.34) (-1.92) (-3.49) (1.13) (0.42) (1.08) (4.93) (0.98) (1.37) (-2.86) (-0.50) (-7.83) (-0.09)
Med -0.020 0.392*** 0.000 -0.002 -0.008** -0.376*** 0.071** 0.013 0.004 1.036*** 0.086 0.106** -0.044 0.022 -0.880*** -0.462 39
(-0.48) (23.70) (0.11) (-0.60) (-2.50) (-4.51) (2.31) (0.56) (0.34) (5.42) (0.41) (2.37) (-0.67) (0.22) (-4.05) (-0.37)
0.75 0.026 0.386*** 0.000 -0.003 -0.008 -0.325*** 0.055** 0.029 -0.023* 0.580*** -0.125 0.107*** -0.045 0.051 -0.145 -0.694 39
(0.54) (23.12) (0.24) (-0.85) (-1.27) (-4.76) (2.08) (1.56) (-1.67) (4.01) (-0.55) (2.98) (-0.75) (0.57) (-0.61) (-0.30)
0.80 0.079 0.385*** 0.000 -0.006* -0.008 -0.361*** 0.066** 0.032* -0.025* 0.351* -0.158 0.105*** -0.043 0.034 -0.155 0.160 38
(1.47) (21.30) (0.45) (-1.87) (-0.98) (-5.75) (2.18) (1.74) (-1.73) (1.86) (-0.67) (2.59) (-0.57) (0.32) (-1.24) (0.05)
0.85 0.118** 0.376*** 0.000 -0.007*** -0.009 -0.356*** 0.057* 0.036* -0.026 -0.125 -0.124 0.111** -0.067 -0.028 -0.262** 0.020 39
(2.24) (19.77) (0.34) (-2.73) (-0.99) (-6.90) (1.81) (1.73) (-1.52) (-0.59) (-0.60) (2.43) (-1.07) (-0.23) (-2.41) (0.01)
0.90 0.126** 0.370*** 0.000 -0.005 -0.009 -0.332*** 0.094** 0.038 -0.023 -0.373 -0.300 0.177*** -0.048 0.091 -0.326* -0.041 39
(2.07) (13.81) (0.37) (-1.51) (-0.86) (-5.02) (2.52) (1.54) (-1.44) (-1.25) (-1.10) (3.18) (-0.57) (0.66) (-1.91) (-0.01)
0.95 0.155 0.389*** 0.003* -0.009 0.005 -0.238*** 0.091 0.124*** -0.033 -1.081** -0.803** 0.215** 0.003 0.144 -0.391 -0.102 32
(1.32) (9.09) (1.86) (-1.54) (0.46) (-3.15) (1.56) (3.51) (-1.14) (-2.28) (-1.97) (2.33) (0.02) (0.57) (-0.65) (-0.01)
Note: This table reports coefficient estimates of 16 covariates from quantile regression model (QRM). 19 quantile regressions (the 1st quantile is at 0.05 and the
19th quantile is at 0.95) are run, however, to preserve space, 11 quantiles (five below median, median, and five above median) are reported. Intercept was used in
all the quantiles. However, to fit the output in one page, we did not report them in the table. All the intercepts are positive and significant. The standard errors are
obtained using the bootstrap method. The variable definitions are the same as provided in Table 4. Robust t-statistics are reported in parentheses. ***, **, * represent
10%, 5%, and 1% statistical significance, respectively.