# Recent highlights from the LHCb experiment

Abhijit Mathad (on behalf of the LHCb collaboration)

###### Abstract

The Large Hadron Collider beauty (LHCb) detector is a single-arm forward
spectrometer at the LHC, designed for the study of heavy flavour physics. In
this proceedings, an overview of the detector performance and a few recent
results in the field of beauty and charm physics are presented. The LHCb
experiment has also undergone a major upgrade in preparation for Run 3 and Run
4 of LHC, the proceedings will briefly highlight the current activities
undertaken during this period. This proceedings is based on the plenary talk
presented at the XXV DAE-BRNS High Energy Physics Symposium held from 12-16
December 2022 at IISER Mohali, India.

##  1 Introduction

The Large Hadron Collider beauty (LHCb) detector, located near Ferney-
Voltaire, France, operates at the LHC interaction point 8 (IP8) at CERN.
Originally proposed in 1998 [1, 2], LHCb has evolved into a forward general
purpose detector, exploring beauty and charm hadron decays with exceptional
precision. It plays a crucial role in measuring flavor observables to probe
new physics beyond the Standard Model at multi-TeV energy scales [3, 4].

The proceedings are organised into sections that describe the LHCb detector
and its performance (section 2), recent highlights from the experiment
(section 3), and a brief overview of the LHCb upgrade (section 4).

##  2 Detector and performance

The LHCb detector is a single-arm forward spectrometer focused on studying
beauty and charm hadron decays in $pp$ collisions at the LHC [5]. It benefits
from the abundant production of $b\bar{b}$ and $c\bar{c}$ pairs, with cross-
sections $\sigma_{b\bar{b}}\approx 500,\mu$b and $\sigma_{c\bar{c}}\approx
20\times\sigma_{b\bar{b}}$ at $\sqrt{s}=13$ TeV. LHCb observes all species of
beauty and charm hadrons produced and boosted forward, distinguishing it from
B factories.

The detector includes a high-precision track and vertex reconstruction system,
a particle identification system, and an efficient trigger system. The
tracking and vertex information come from the VErtex LOcator (VELO), silicon-
strip and straw tube trackign detectors (TT and T1-T3), and multi-wire
proportional chambers in the muon system. The VELO reconstructs primary and
secondary vertices, while the tracking system achieves excellent momentum
resolution ($\sigma_{p_{T}}/p_{T}\approx 0.5\%$ for $p_{T}=10$ GeV/$c$) and
decay time resolution ($\sigma_{t}\approx 45$ fs for $\tau_{B^{0}_{s}}\approx
1.5$ ps) [6]. Particle identification relies on RICH detectors (RICH1 and
RICH2) and the calorimeter system (SPD, PS, ECAL, and HCAL) in conjunction
with the muon system. The PID system demonstrates efficient separation between
pions, kaons, and protons, with a kaon identification efficiency $>95\%$ and a
pion mis-identification rate $<5\%$. The LHCb trigger system consists of a
hardware trigger (Level-0) and a software trigger (HLT), reducing the event
rate from 40MHz to 1MHz and further to 12.5 kHz, respectively [7, 8].

Data collection at LHCb occurred at proton-proton center-of-mass energies of
7, 8, and 13 TeV during 2010-2011, 2012, and 2015-2018, with integrated
luminosities of $1.15,\rm{fb}^{-1}$, $2.08,\rm{fb}^{-1}$, and
$5.9,\rm{fb}^{-1}$, respectively.

##  3 Highlights of physics results

The LHCb collaboration has published over 600 papers spanning a broad range of
topics such as studies of Charge-Parity (CP) violation in beauty and charm
decays, semileptonic decays, spectroscopy, electroweak physics, and heavy-ion
physics. In this proceedings, we will discuss results concerning charm
physics, semileptonic decays, and CP violation in beauty decays.

###  3.1 CP violation and charm physics

The Cabibbo-Kobayashi-Maskawa (CKM) matrix within the Standard Model governs
quark flavor mixing and is represented by a unitary $3\times 3$ matrix,
satisfying one of the unitarity conditions
$V_{ud}V_{ub}^{*}+V_{cd}V_{cb}^{*}+V_{td}V_{tb}^{*}=0$. This unitarity
condition can be represented as a triangle in the complex plane, known as the
Unitarity Triangle (UT) [3]. Remarkable progress has been made since 1995
through measurements of angles and sides of the UT. A pivotal measurement is
the angle $\gamma$, denoting the phase of the CKM matrix element $V_{ub}$.
Obtained from tree-level $B$ meson decays, $\gamma$ can be compared with its
indirect estimate from the UT fit, utilising observables sensitive to loop-
level processes. This rigorous examination serves as a stringent test of the
SM and a probe for new physics (NP) effects.

In a recent paper by LHCb [9], the angle $\gamma$ was precisely measured via
$B^{\pm}\to DK^{\pm}$ decays, with $D$ being either $D^{0}$ or $\bar{D}^{0}$
mesons reconstructed from $D\to K^{\mp}\pi^{\pm}\pi^{\pm}\pi^{\mp}$ decays.
The model-independent extraction of $\gamma$ was performed in four phase space
bins of $D$ decay using Run 1 and Run 2 data. The analysis explored the ratio
of opposite-sign to like-sign decay channels to obtain $\gamma$. Charm decay
parameters were obtained from external input from CLEO-c and BESIII. Figure 1
shows the asymmetry between $B^{\pm}\to DK^{\pm}$ and its charge conjugate
decay, which is used in the extraction of angle $\gamma$. The precise
measurement resulted in
$\gamma=(54.8^{+6.0}_{-5.8}$${}^{+0.6}_{-0.6}$${}^{+6.7}_{-4.3})^{\circ}$,
with uncertainties attributed to statistical, systematic, and external input
sources. This measurement represents the most precise determination of
$\gamma$ to date using a single $D$ decay mode.

Figure 1:  (Top) Asymmetry between $B^{\pm}\to DK^{\pm}$ and its charge
conjugate decay used to extract $\gamma$. (Bottom-left) The time distribution
of $B_{s}$ mesons decaying to $D_{s}^{-}\pi^{+}$. (Bottom-right) The
measurement of charm mixing parameters $x$ and $y$.

Another essential observable utilised to test the unitarity of the CKM matrix
is the oscillation frequency ($\Delta m_{s}$) of $B_{s}$ mesons. A recent LHCb
measurement investigates $B_{s}$ meson oscillation to $\bar{B}_{s}$ mesons via
$B_{s}\to D_{s}^{-}\pi^{+}$ decays [9]. This measurement utilises Run 1 and
Run 2 data, reconstructing $D_{s}^{-}$ from $D_{s}^{-}\to K^{+}K^{-}\pi^{-}$
and $D_{s}^{-}\to\pi^{+}\pi^{-}\pi^{-}$ decays. The oscillation frequency
($\Delta m_{s}$) is extracted from the time distribution of $B_{s}$ mesons, as
shown in Figure 1 on the bottom-left. The measured value of $\Delta m_{s}$ is
$17.7683\pm 0.0051\pm 0.0032,\rm{ps}^{-1}$, where the first uncertainty is
statistical, and the second is systematic. This measurement represents the
most precise determination of $\Delta m_{s}$ to date.

Particle-antiparticle oscillation can occur in the charm sector with mixing
parameters: $x=\Delta m/\Gamma$ and $y=\Delta\Gamma/2\Gamma$. LHCb made the
first observation of $D^{0}$ oscillations in 2012 [10], and the first
observation of $x\neq 0$ was made in 2021 [11]. A novel study, utilising full
Run 2 data, analyses the time evolution of $D^{0}\to K_{S}\pi^{+}\pi^{-}$
phase space, requiring $D^{0}$ to originate from $B^{0}\to
D^{0}\mu^{-}\bar{\nu}_{\mu}X$ decays [12, 13]. This analysis extracts mixing
and CPV parameters by measuring yield ratios between different $D^{0}$ phase
space bins as a function of the $D^{0}$ decay time. The result of the
measurement is shown in Figure 1 on the bottom-right. Uncertainty on external
inputs from CLEO and BESIII are the limiting systematic for this measurement.

A new LHCb combination of observables yields
$\gamma=(63.8_{-3.7}^{+3.5})^{\circ}$ and charm mixing parameters from 173
measurements. This value is consistent with the indirect estimate
$\gamma=(65.5_{-2.7}^{+1.1})^{\circ}$ and extractions from UTfit and
CKMfitter. However, tensions between different B species for $\gamma$ persist
at around 2 sigma [14].

###  3.2 Semileptonic decays

The semileptonic decays of $b$-hadrons can proceed via two types of
transitions: charged current ($b\to c\ell\nu$) and neutral current ($b\to
s\ell^{+}\ell^{-}$). The charged current decays (CC) have relatively large
branching fractions of a few percent and yield significant signals, but they
pose experimental challenges due to the presence of undetectable neutrinos. As
a result, their measurements are dominated by systematic uncertainties. On the
other hand, the neutral current decays (NC) occur only through loop processes
and have branching fractions of approximately $O(10^{-7})$. These measurements
are typically limited by statistical uncertainties, but they offer
opportunities to explore the effects of new particles that might enhance
amplitudes suppressed in the Standard Model.

The LHCb experiment has undertaken various measurements related to both NC and
CC semileptonic decays. In the context of NC decays, LHCb has investigated
pure leptonic decays of $B$ mesons, which are theoretically and experimentally
cleaner processes. The most recent measurement reveals the branching fraction
for $B_{s}^{0}\to\mu^{+}\mu^{-}$ to be $(3.9_{-0.43-0.11}^{+0.46+0.15})\times
10^{-9}$ and constrains $BF(B^{0}\to\mu^{+}\mu^{-})$ to be less than
$2.6\times 10^{-10}$ [15]. Additionally, differential measurements of NC
decays, particularly $\frac{d\Gamma}{dq^{2}}$ (where
$q^{2}=m^{2}(l^{+}l^{-})$, excluding $c\bar{c}$ resonances), have been
conducted [16, 17, 18]. Notably, the recent measurement for
$B_{s}^{0}\to\phi\mu^{+}\mu^{-}$ shows a $3.6\sigma$ tension with respect to
the Standard Model, indicating potential hints of new physics, as depicted in
Figure 2 on the left [19]. Moreover, angular observables, including
$P_{5}\prime$ and $F_{L}$, have been measured, showing consistent trends
across different modes, hinting at the presence of a new physics vector
coupling with $Re(\Delta C_{9})\approx-1$ [20, 21, 22, 23].

LHCb has also conducted tests of lepton flavor universality (LFU) within the
Standard Model for both NC and CC decays. LFU implies that the ratio of
branching fractions for decays involving different species of leptons should
only depend on the masses of the leptons. For NC decays, the ratios $R_{K}$
and $R_{K^{*}}$, which involve muons and electrons, have been measured and
found to be consistent with the Standard Model [24] 111 Since the presentation
of this talk, a new measurement of $R_{K}$ and $R_{K^{*}}$ has been published
[25], superseding the previous reference [24]. . Similarly, for CC decays,
LHCb has carried out its first simultaneous measurement of the ratios $R(D)$
and $R(D^{*})$, which involves $\tau$ and $\mu$ leptons. The results from data
collected during the 2016 run period yield $R(D)=0.441\pm 0.060\pm 0.066$ and
$R(D^{*})=0.281\pm 0.018\pm 0.023$, with a correlation coefficient of $-0.43$
[26]. Figure 2 on the right compares these results with other measurements and
Standard Model predictions. Notably, the world average of $R(D)$ and
$R(D^{*})$ exhibits a $3.3\sigma$ tension with respect to the Standard Model
222 Since this talk, two new measurements of $R(D)$ and $R(D^{*})$ have been
presented. One by LHCb [27] and the other by Belle-II [28]. However, the
significance of the tension with respect to SM remains unchanged. .

Figure 2:  (Left) Different measurement of $B_{s}^{0}\to\phi\mu^{+}\mu^{-}$
branching fraction in neutral current decays. (Right) Measurement of lepton
flavour universality ratio $R(D)$-$R(D^{*})$ in charged current decays.

##  4 Future prospects and conclusion

The LHCb experiment is currently undergoing a significant upgrade to its
detector, in preparation for Run 3 of the LHC. This upgrade is tailored to
handle a luminosity that is five times higher than that of Run 2. The detector
enhancements include a cutting-edge pixel-based vertex locator, an improved
tracking system with higher granularity, upgraded RICH detectors equipped with
new photon detectors, and a state-of-the-art readout system. Moreover, the
LHCb trigger system is transitioning to a fully software-based approach,
enabling more flexibility and efficiency in triggering processes. With these
improvements, LHCb aims to amass an impressive data sample of 50 fb-1 by the
conclusion of LHC Run 4, and an astounding 300 fb-1 during the operation of
the High Luminosity LHC (HL-LHC). In the HL-LHC era, the instantaneous
luminosity will surge by a factor of 50, and ongoing research and development
are actively exploring the implementation of new detector components with
timing information. The expanded data set will empower LHCb to achieve more
precise measurements of rare decays and CP violation phenomena, while also
providing the capability to thoroughly search for new physics across a wide
array of channels. The LHCb upgrade heralds an exciting era of particle
physics exploration, unlocking deeper insights into the fundamental properties
of the universe.

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#  Discrimination and Constraints: Evidence from The Voice

Anuar Assamidanov  Department of Economics, Claremont Graduate University, 150
E 10th St, Claremont, CA 91711<EMAIL_ADDRESS>
I am grateful for valuable comments and discussions from Gregory DeAngelo,
Fernando Lozano, Mark Hoekstra, CarlyWill Sloan, Bryan McCannon, Benjamin
Blemings, Aruna Ranganathan and numerous seminar participants. Any errors are
my own.

( November 2022
)

###### Abstract

Gender discrimination in the hiring process is one significant factor
contributing to labor market disparities. However, there is little evidence on
the extent to which gender bias by hiring managers is responsible for these
disparities. In this paper, I exploit a unique dataset of blind auditions of
_The Voice_ television show as an experiment to identify own gender bias in
the selection process. The first televised stage audition, in which four
noteworthy recording artists are coaches, listens to the contestants “blindly”
(chairs facing away from the stage) to avoid seeing the contestant. Using a
difference-in-differences estimation strategy, a coach (hiring person) is
demonstrably exogenous with respect to the artist’s gender, I find that
artists are 4.5 percentage points (11 percent) more likely to be selected when
they are the recipients of an opposite-gender coach. I also utilize the
machine-learning approach in Athey et al. (2018) to include heterogeneity from
team gender composition, order of performance, and failure rates of the
coaches. The findings offer a new perspective to enrich past research on
gender discrimination, shedding light on the instances of gender bias
variation by the gender of the decision maker and team gender composition.

Gender discrimination in the hiring process is one significant factor
contributing to the poor labor market (Blau and Kahn, 2007). Gender
differences in hiring are challenging to measure, making it difficult to
distinguish its effect on employment from confounding variables, such as
differences in human capital and relevant skills. However, Baert (2018) have
cataloged studies on evidence of gender discrimination in hiring using
experimental methods where confounding factors were disentangled to estimate
the true effect on the labor market outcomes.

Studies have found hiring discrimination practices against women in the labor
market, but most of this research has utilized experimental methods(Bertrand
and Duflo, 2017; Baert, 2018; Neumark, 2018) . Within these experiments, pairs
of fictitious job applications, only differing by the gender of the candidate,
are sent to actual job openings. Discrimination is identified with the
subsequent call-back from the employer and the gender of the candidate. The
correspondence testing methodology is the gold standard for estimating hiring
discrimination in the labor market (Baert, 2015). However, in this hiring
literature, the gender of hiring decision-makers is unobservable, or decisions
are made collectively. Furthermore, these experiments only capture call-back
rates and do not go beyond the initial stage of the hiring process. In
addition, assuming employers’ hiring decisions are based on a cut-off rule,
there could be unobserved variable differences in the productivity between the
two groups, which can cause biased discrimination measures (Neumark, 2012).

Another part of the literature on gender discrimination is own gender bias
(i.e., favoritism toward people of one’s own gender) in hiring decisions.
Laboratory experiments often find that women show own gender bias when
information is processed automatically, but these results are not found for
men (Rudman and Goodwin, 2004). However, it is unclear whether these results
hold in real-world hiring decisions, which are likely to be characterized by a
reflective (non-automatic) process. The existing studies on real-world hiring
decisions typically consider particular segments of the labor market and find
mixed evidence for own gender bias (Booth and Leigh, 2010; Bagues and Esteve-
Volart, 2010; Bagues et al., 2017). Because of the data limitations in these
settings, it is hard to distinguish if there is favoritism of the gender of
the employer over the gender of the candidate (i.e., own-gender bias). This
paper’s primary purpose is to test whether own-gender bias exists in the
hiring process. Potential findings could inform our understanding of the
current labor market at the individual level and the subsequent large-scale
implications.

The main difficulty in testing gender bias in the hiring process is that
hiring decision-makers and applicants are not the outcome of a random
selection process to claim a causal factor in generating own gender bias.
Also, the fundamental identification challenge is that researchers only
observe real-world data on already hired workers—if the applicant is not
employed, it is never recorded. Due to these limitations, there is an open
question in this literature if the gender of the hiring decision-maker
determines the gender of applicants being hired. In this paper, I exploit a
unique dataset of blind auditions of the Voice TV show as a natural experiment
to identify the own-gender bias in the selection process.

I assess own-gender bias in The Voice show, a setting in which a coach (hiring
person) is demonstrably exogenous with respect to the artist’s gender. The
first televised stage in the Voice TV show is the blind auditions. The four
coaches, all noteworthy recording artists, listen to the contestants in chairs
facing away from the stage to avoid seeing the contestants. If a coach likes
the contestant’s voice, they press a button to rotate their chairs to signal
that they are interested in working with that contestant. The advantage of
these estimations is that the coaches only observe the voice of the
contestants and conclude from the voice the probable gender of the contestant.
So, due to the ”blind” decision process, other characteristics related to the
artist and coach will be eliminated in this setting. I believe this is a
plausible environment to use a generalized difference-in-difference
identification strategy with random assignment of coaches to participants.
Like Price and Wolfers (2010) study on racial bias by NBA referees, I compare
differences in the probability of female and male contestants being chosen by
female and male coaches.

By drawing several types of inferences, the analysis shows systematic evidence
of an opposite-gender bias (favoritism toward the opposite gender). Coaches
that are men predominantly prefer contestants that are women, while female
coaches prefer male contestants. Contestants are 4.5 percentage points (11
percent) more likely to be selected by a coach that is the opposite gender. To
examine heterogeneity more systematically, I adapt the machine-learning
approach of Athey and Wager (2019). I have extended the analysis by including
heterogeneity in the gender composition of each coach’s team, the coaches’
failure rates, and the performance order. The results provide intriguing
insights into gender bias that varies widely across team composition during
the selection of new contestants.

This paper offers one of the first explorations of hiring practices using
random variation in gender to examine the effects on the selection process.
The random variation in gender enables me to overcome potential concerns that
observed disparities could be due to unobserved differences across contestant
gender. Second, this paper applies the Athey and Wager (2019) method of causal
forest machine learning inference on heterogeneous treatment effects to a
quasi-experimental difference-in-difference identification strategy.

This paper is closely related to work by Carlsson and Eriksson (2019). Their
work provides related evidence suggesting a role for in-group gender
preferences has been documented in many other contexts. They investigated in-
group and own-gender bias in real-world hiring decisions by combining data on
the gender of the recruiter and the share of women employees in many firms
with data from a large-scale field experiment on hiring. The results suggested
that women (female recruiters or firms with a high share of female employees)
favor women in the recruitment process. Nevertheless, this study provides only
a tiny fraction of the participating firms’ information regarding recruiters’
gender, which might result in a considerable measurement error.

Similar to this work, Goldin and Rouse (2000) studied blindness in the
orchestra context to examine sex-biased orchestra member selection as a policy
intervention. This paper differs from their work in that I can observe the
gender of the hiring and contestant, and coaches can observe the gender of the
performer based on their voice. The coaches’ decisions will also be made
individually, whereas, in the blind audition in the orchestra, there was a
collective decision. Finally, the other uniqueness of this setting is that I
could analyze the market structure where each coach could be assumed as a
firm. I was able to illustrate the market power of the coaches by leveraging
the order of the performance and the genre of the song they performed.
Controlling for all these factors gives a new dimension to gender
discrimination in the competitive market.

The rest of the paper is organized as follows. Section 1 provides a brief
background on The Voice, summarizes the blind audition stage of the show, and
gives a preview of our estimation strategy. Section 2 describes the data.
Section 4 describes the empirical strategy in detail. Section 5 presents
results, and Section 5 concludes.

##  1 Background

An international television singing competition franchise initially created by
Dutch television producer John de Mol and singer Roel van Velzen. One hundred
forty-five countries have adopted the format and begun airing their versions
since 2010. The show’s format features five stages of competition: producers’
auditions, blind auditions, battle rounds, knockouts (since 2012), and live
performance shows.

Each season employs a panel of four coaches who critique the artists’
performances and guide their teams of selected artists through the remainder
of the season. They also compete to ensure that their act wins the
competition, thus making them the winning coach. While these constraints mean
that the assignment of coaches to the season is not literally random, the more
relevant claim for this research design is an entirely arbitrary assignment of
coaches to the artists.

Each season begins with the ”Blind Auditions,” where coaches form their team
of artists they mentor through the remainder of the season. The coaches’
chairs are faced toward the audience during artists’ performances; those
interested in an artist press their button, which turns their chair towards
the artist and illuminates the bottom of the chair to read ”I want you.” Each
coach has the length of the auditioner’s performance (about one minute) to
decide if he or she wants that singer on his or her team; if two or more
coaches want the same singer (as happens frequently), the singer has the final
choice of coach. After the performance, an artist either defaults to the only
coach who turned around or selects the coach if more than one coach expresses
interest. The coaches not seeing the artists is a setting in which coaches’
encounters are demonstrably exogenous with respect to artists’ performances
(White, 2022).

##  2 Data

I used the blind audition part of the show as a natural experiment in this
work. The data on a blind audition was compiled from historical Voice TV shows
on Wikipedia. I web-scraped the results of the blind audition for four
countries: the UK, France, Germany, and Australia. Each country held
approximately ten seasons each year, starting from the year 2012. Each
country’s Voice Wiki page is divided by season, each season is divided by the
episodes, and the order of the performance splits each episode. The page
includes the singer and coach’s information, the singer’s age, the order of
performance, and the song.

From the Wiki page, I constructed the outcome variable based on the coaches
who pressed the button if the coach chose the specific artist. Thus, I can
build the result of the four coaches for each artist. Similarly, the page
provides the actual order of the performance. Since the primary goal of the
analysis is to identify gender-specific preferences, I needed to determine the
gender of the artist.

I infer the gender of the artists based on their first names. I used an online
application programming interface (API) called Genderize.io. The application
has pre-trained machine learning algorithms that are used to predict gender.
The API gives a confidence level in probabilistic terms and the exact name
count in their already used datasets. Utilizing a threshold of 90%
probability, I am able to attach a gender to approximately 97% of the whole
dataset. For the remaining 3% of the first names, I hardcoded by checking the
performance on the YouTube webpage. The gender of the coaches can easily be
identified as all of them are well-established artists.

I also used the genre of the song the artist performs. Using song information
from the Wikipedia page, I extracted the genre of the music from the Spotify
API. The API gives multiple genres that correspond to the given song. By doing
frequency distribution, I determined the most frequent genres and came up with
the eleven unique genres.

Summary statistics are shown at the coach level in Table 1. Column (1)
includes all coaches in the sample, while Columns (2) and (3) disaggregate to
coaches who are female or male, respectively. The data has 11,972
observations, 58 unique coaches, and 3,009 unique artists. 31.6 percent of the
coaches were female, though there is considerable heterogeneity across the
team gender composition and failure rates for female and male artists.
Similarly, about 46.3 percent of artists are men, providing decent statistical
power for an own-gender bias analysis.

My primary analysis includes all the coaches’ choices, with approximately 40
percent of the artists being chosen in the blind audition round. Female
artists are chosen about 21.6 percent of the time. The difference between
female coaches and male coaches choosing female artists is a 1 percent
difference. This pattern of having a 1% difference continues to hold for the
male artists who are chosen 18 percent of the time. Thus, a naive comparison
of the raw data for female and male gender would yield a conclusion of no
gender bias. Since the preference of female and male artists across female and
male coaches is similar, the selection difference lies at about one percent.
To justify this premise, I examine the order of each performance at the artist
level and how TV show-related specification affects decision-making.

Table 1 also provides summary statistics for TV show-related specifications,
considering them heterogeneous in the analysis. Each coach and artist has a
unique specification, such as the order of their performance, their preference
towards a specific coach, and the genre of the song. Ultimately, 16.8 percent
of the artists ended up on a team. From that team configuration, we can
determine the gender composition of the team, which is the number of women and
men on the team during the blind audition stage. The average difference
between the number of males and females for each order on the team is -0.533,
meaning that the number of female artists is 0.5 people higher on average
compared with the male artists. Additional information is obtained when two or
more coaches pursue the same artist, providing the artist with the final
choice. I estimated the failure rate for these cases, and each coach has about
a 0.27 failure rate for female artists and 0.24 for male artists. This is the
rate at which a coach wanted an artist of a particular gender on their team,
and the artist did not choose the coach. Both of these variables have
considerable differences across the gender of the coach, which enriches our
study to identify own-gender bias in the selection process.

Table 1: Summary statistics for coaches

| All coaches | Male coaches | Female coaches
---|---|---|---
| (N = 58) | (N = 36) | (N = 22)
| (1) | (2) | (3)
Female Coaches | 0.684 | 1 | 0
Male Artist Auditioned | 0.463 | 0.465 | 0.458
Coaches’ Choice in the Audition | 0.398 | 0.399 | 0.394
Female Artist Choice of Coach | 0.216 | 0.219 | 0.209
Artist’s choice of coach | 0.168 | 0.168 | 0.169
Male relative to female | -0.533 | -0.514 | -0.574
in the team | (2.57) | (2.55) | (2.60)
The failure rate | 0.273 | 0.238 | 0.289
for Female Artists | (0.148) | (0.151) | (0.134)
The failure rate | 0.24 | 0.234 | 0.242
for Male Artists | (0.141) | (0.145) | (0.134)
Number of Observations | 11,972 | 8,189 | 3,783

Notes: This table presents summary statistics for the estimation sample. The
unit of observation is performance in the blind audition stage. The table
shows statistics of all performances for which artists and drivers are men and
women. The sample includes four countries, and each country has ten seasons.
Standard deviations in parentheses. All values reported in this table are
unconditional average rates of the variables indicated in rows.

As discussed and shown in the Section 1, the institutional setting provides
for the exogenous assignment of gender encounters between coach and artist.
Table 2 examines this exogeneity assumption by estimating differences in the
observed characteristics of male and female artists. The first column shows
mean characteristics for all artists, while the second and third columns
present average outcomes for male and female artists. The fourth column
reports the difference between the two means. Comparing overall raw means is
consistent with the assignment procedure described above. There is no
significant difference between male and female artists in any show-related
specifications, such as being chosen by coaches, selecting a team, being
chosen by a male coach, and the order of their performance. This supports our
identification strategy: in a given show setting, there is little evidence to
suggest that male artists’ performances systematically differ from those
performed by female ones. However, I also find some statistically significant
differences. For example, male artists are 5.2 percent more likely to perform
pop genre songs. Similarly, the share of classic style and the share of rock
style is lower, while the share of country style is higher among male artists.
All these significant observables will be estimated in the setting as
confounding factors.

Table 2: Balancing tests for the performance of artists

| All Artists | Male Artist | Female Artist | Difference in Means
---|---|---|---|---
|  |  |  | Male vs. Female Artist
| (1) | (2) | (3) | (4)
Coaches’ Choice | 0.398 | 0.402 | 0.393 | 0.009
in the Audition |  |  |  | [.009]
Artist’s choice of coach | 0.168 | 0.17 | 0.167 | 0.003
|  |  |  | [0.007]
Auditioned by Male Coach | 0.684 | 0.681 | 0.687 | -.005
|  |  |  | [0.009]
Performance Order | 42.19 | 42.34 | 42.02 | 0.328
| (25.49) | (25.61) | (25.39) | [0.468]
Pop | 0.557 | 0.581 | 0.529 | 0.052***
|  |  |  | [0.009]
Hip-hop | 0.121 | 0.122 | 0.119 | 0.004
|  |  |  | [0.006]
Rock | 0.27 | 0.233 | 0.314 | -0.082***
|  |  |  | [0.008]
Country | 0.046 | 0.050 | 0.042 | 0.009**
|  |  |  | [0.004]
R&b | 0.0695 | 0.075 | .062 | 0.013
|  |  |  | [0.005]
Funk | 0.0736 | 0.07 | 0.0776 | -0.007
|  |  |  | [0.005]
Jazz | 0.0312 | 0.0331 | 0.029 | 0.004
|  |  |  | [0.003]
Number of Observations | 11,972 | 6,432 | 5,540 | 11,972

Notes: Standard deviations in parentheses in columns 1,2 and 3. Each entry in
column 4 is derived from a separate OLS regression where explanatory variable
is indicator for male artist. * $p<0.1$, ** $p<0.05$, *** $p<0.01$

##  3 Methodology

The identification strategy used in this study is Difference in Differences
with Dummy Outcomes (Price and Wolfers, 2010), which focuses on coach and
artist gender interaction. Specifically, we estimate the following linear
probability model:

$\begin{array}[]{c}Y_{it}=\alpha_{i}+\beta_{1}MaleCoach_{c}+\beta_{2}MaleArtist_{i}+\beta_{3}(MaleArtist\
{\&}\ MaleCoach)_{i,c}\\\ +\ Coach_{c}+X_{i,c}+\epsilon_{it}\end{array}$ (1)

where the outcome of interest, $Choice_{i,c}$ is the binary variable equal to
one when the coach chooses the artist in performance, where $i$ denotes an
artist selected by the coach $c$ . Similarly, $MaleCoach_{c}$ is one when the
Coach is male and zero otherwise. $MaleArtist_{c}$ is one when the artist is
male and 0 otherwise. The primary variable of interest is the interaction
between male coaches and male contestants. $\beta_{2}$ captures the difference
between male artists chosen by female coaches relative to female artists
chosen by female coaches, allowing for artists to differ in their overall
propensities to be selected. $\beta_{1}$ coefficient captures differences in
selection rates of female artists by male coaches relative to female artists
by female coaches, allowing coaches to differ in their overall propensities to
select the artist. $\beta_{3}$ is the difference in differences coefficient of
interest and indicates the degree of own-gender bias. Notably, the difference
in differences estimator provides only a symmetric and relative measure of
gender bias. So the coefficient captures the comparison of the difference in
selection rates of female artists by male coaches relative to female artists
by female coaches to the difference in selection rates of male artists by male
coaches relative to male artists by female coaches. If there is no gender
bias, then $\beta_{3}$ = 0. A positive sign indicates same-gender leniency (or
other-gender harshness) in blind audition selection.

The richness of the data allows for extending this analysis to control for the
various confounding factors such as contestant-specific characteristics and
coach fixed effect, genre, and order of the performance. In the model, I
include $Coach_{c}$ coach-specific fixed effect, which captures time-invariant
coach characteristics. $X_{i,c}$ is the set of control variables at the
performance level, including the genre of song, performance order, the number
of male relative to female artists in the coach’s team, the coach’s failure
rate for male and female artists during the audition as well as fixed effect
for the country of the TV show. I also cluster standard errors for all
estimations at the coach level, as this seems ex-ante to be the appropriate
cluster for most autocorrelation concerns.

The regression model in the difference-in-differences framework does not
capture potential heterogeneous effects across covariates. There could be a
positive effect on some groups in the covariates but a negative or no effect
on other groups. For example, the coaches in the initial stage of the blind
audition could elicit own-gender bias, but in the later stage, opposite-gender
bias. The standard regression model will provide a weighted average of effect
size, even if an effect varies across a population represented by different
groups. One plausible solution is to estimate heterogeneous treatment effects.
Instead of just estimating one effect, I estimate a distribution of effect
size for a given unit with a given set of attributes and what their impact
might be. To analyze this heterogeneous effect of own-gender bias, I
incorporated the first difference approach into the causal forest approach. I
will discuss the performance of the proposed causal forest approach and how to
apply it to my empirical example.

The causal forest approach is consistent and asymptotically Gaussian and
provides an estimator for their asymptotic variance that allows us to
construct valid confidence intervals (Athey and Wager, 2019). Causal forest
utilizes a forest-based approach to calculate a similarity weight and then
applies the local generalized method of moments to estimate based on a
weighted set of neighbors. The authors also show that using the centered
instead of the original outcome and treatment allows a forest to focus its
splits on the features that affect the treatment effect instead of the primary
outcome. Intuitively, a causal forest consists of regression trees (Athey and
Imbens, 2016; Breiman et al., 1984), which estimate conditional average
treatment effects (CATE) at the leaves of the trees instead of predicting the
outcome variables.

I utilize a two-step approach by incorporating the first-difference approach
into the causal forest approach, the similar two-step approach in the standard
difference-in-difference method. In the first step, I estimate the first
difference, which is the change in the selection of individual contestants
from a male coach to a female coach. This step teases out the systematic
differences between coaches in female and male coach groups. In the second
step, I use the outcome variables obtained from the first step and apply the
causal forest approach for heterogeneous treatment-effect analysis. This step
teases out the effect of contestant gender trends that exist in both women and
men.

My methods rely heavily on the causal forest approach, a machine learning
method that can estimate heterogeneous causal effect functions under the above
assumptions. The main strength associated with the causal forest is that it
provides a strategy for learning patterns of heterogeneity from the data. This
method requires little researcher discretion compared to traditional subgroup
analyses. For instance, one does not have to decide which cutoffs to use to
analyze heterogeneity in effects along continuous covariates, nor do we
require to define the functional condition of the heterogeneity; the causal
forest algorithm is designed to automate this search and find the most
appropriate model that best characterizes the heterogeneous effect in the data
(Bonander and Svensson, 2021).

##  4 Results

My identification strategy is to leverage the exogenous assignment of coaches
to the artist and use a difference-in-differences estimator across these
coach-artist interactions to estimate the degree of gender bias in selection.
The baseline difference in differences results shows that female coaches are
more likely to choose male artists, and male coaches are more likely to select
female artists, opposite gender bias (Figure 1). A simple calculation suggests
an opposite gender bias of 4.2 percentage points.

Figure 1: Baseline Own-Gender Bias

Notes: This figure reports the share of selected male and female artists
assigned to male and female coaches. There is a statistical difference in the
selection of female artists assigned to female or male coaches. The same is
true for male artists.

###  4.1 Effect of Own-Gender Coaches on Selection

Table 3 reports results from estimating Equation 1 using four separate
specifications. The ”same gender coach” difference in differences coefficient
shows how much more or less likely an artist is to be chosen by a coach of a
different gender relative to one of the same genders as the artist, adjusted
for overall gender propensities of artists to get selected and coaches to
choose. According to Table 3, the results represent the regression outcome of
the chosen dependent variable artist. Overall, it can be seen that the primary
independent variable interaction between the gender of the coach and artist is
showing consistent output with controlling various confounders. The outcome
gives ranges of - 4.4 and - 5 percentage points, indicating that magnitude
increases with covariates. Standard errors also decreased and showed a range
of 15% and 9% for the margin of error or alpha level.

Column (1) of Table 3, includes coach and country effects and no other
controls. The estimated degree of gender bias for selection in the male/female
comparison is -4.4 percentage points. That is, after adjusting for gender-
specific differences in propensities for contestants to perform and adjusting
for gender-specific differences in coaches’ propensities to select, a male
contestant who is exogenously assigned a male coach is 4.4 percentage points
less likely to be chosen relative to a male contestant who is exogenously
assigned a female coach (and vice versa). Given a mean of 39.75 percent, the
pooled result indicates that gender bias causes a contestant assigned an
other-gender coach to be nearly 11 percent more likely to be selected for any
performance.

Table 3: Estimates of own-gender Bias for Artist Selection

| (1) | (2) | (3) | (4)
---|---|---|---|---
Outcome: Choice |
Male Coach*Male Artist | -0.0441∗ | -0.0453∗∗ | -0.0485∗∗ | -0.0498∗∗
| (0.0237) | (0.0221) | (0.0216) | (0.0216)
Male Coach | 0.0226 | -0.212∗∗∗ | -0.277∗∗∗ | -0.274∗∗∗
| (0.0185) | (0.0170) | (0.0166) | (0.0166)
Male Artist | 0.0144 | 0.0199 | 0.0206 | 0.0190
| (0.0185) | (0.0170) | (0.0166) | (0.0166)
Mean | 0.398 | 0.398 | 0.398 | 0.398
$N$ | 11,195 | 11,195 | 11,195 | 11,135
Coach FE | Y | Y | Y | Y
Country FE | Y | Y | Y | Y
Performance Order FE | - | Y | Y | Y
Genre FE | - | - | Y | Y
Constraints | - | - | - | Y

Notes: Table 3 presents a difference in differences estimate of gender bias
using regression of Equation 1. This table reports the coefficient on the
interaction of Male Artist and Male Coach from the regression of Choice on
indicators for coach gender, artist gender, and the interaction term. Each
specification includes coach and country fixed effects. Column 2 adds the
order of the performance fixed effects. Column 3 includes the same controls as
column 3, with the exception of adding genre-fixed effects. Column 4 adds
controls for the number of males relative to females in the team, the failure
rate of the coach for female artists, and the failure rate of the coach for
male artists. Standard errors are clustered by coach. * $p<0.1$, ** $p<0.05$,
*** $p<0.01$

The additional columns of Table 3, address potential confounders to this
gender bias estimate. Column (2) adds the order of the performance fixed
effect to the coach fixed effect to account for order trends; results in these
columns slightly increase in magnitude compared with those in Column (1). I
have also included genre covariates in Column (3), which means coaches of a
particular gender disproportionately favor certain genre styles. Suppose
contestants of a different gender from these coaches are disproportionately
likely to choose genre style. In that case, failure to control for genre
covariates could result in a spurious gender bias estimate. In Column (4), I
have incorporated the show-related specification, which I specify as
constraints to the coaches. It comes from the coaches having a limited slot in
their team, which will be a confounding factor in getting selected. For
example, if a coach has a majority of women on the team, it might push the
coach to change the strategy of choosing the contestant. Similarly, the coach
has been rejected by a particular gender disproportionally more, which might
lead to reluctance in selecting the next same-gender contestant. By including
these covariates as confounding factors, I can control for constraints imposed
by this contested environment. Across these five columns, the female/male
estimates range from 4.4 to 5 percentage points. These four estimates are
statistically significant at $p<0.05$.

To sum up, the primary result of this study is that there is meaningful
opposite-gender bias by coaches in a context in which the performance of
contestants is exogenously assigned to the coaches. This finding contrasts
significantly with the previous work of Carlsson and Eriksson (2019). They
found that women (female recruiters or firms with a high share of female
employees) favor women in the recruitment process. However, they did not see
much evidence that men (male recruiters or firms with a high share of male
employees) favor men. Results could differ due to differences in the sample
studied. As the author analyzes low- and medium-skilled occupations in Sweden,
there could be differences between the countries I use and Sweden. To make the
comparison, I split my sample into separate countries and compared the results
with Table 3. The reported coefficients for the UK, France, and Australia in
Table A1 provide a similar magnitude to my initial analysis but with less
precision. The standard errors are high due to the decreased sample size.
Regardless, Germany has a null coefficient. Thus, there could be differences
in the results due to the context of the country. Again, I account for this
discrepancy in my initial analysis by controlling for country-fixed effects.
The remainder of this manuscript examines heterogeneity in these effects to
better characterize the nature of this gender bias and shed light on the
likely mechanisms.

###  4.2 Effect of Own and Opposite Gender Coaches by Constraints

Given the findings discussed above, it is natural to ask whether the
differences by gender are due to only a handful of coaches or if they are more
systemic. To address this question, the remainder of the empirical results
examines heterogeneity in the estimated gender bias by confounding factors -
team gender composition, order of performance, and failure rates of the
coaches. We also discuss the extent to which difference-in-difference
estimates are sensitive to these confounding factors. To do so, I use the
causal forest approach described in Section 4 to estimate the heterogeneous
effects of gender bias.

Because the difference in differences estimator can only identify relative
gender bias across coaches, it does not show gender bias separately for male
and female coaches. There could be a case when the likelihood of male coaches
preferring female artists is more than female coaches to female artists. If we
decompose this into separate female and male coaches, male coaches prefer
female artists more than male artists, and female coaches prefer female
artists more than male artists. In this case, difference-in-differences
estimation shows an opposite gender bias, but opposite gender bias occurs for
male coaches and own-gender bias for female coaches. To observe the source of
the bias, I estimate gender bias separately for men and women for a more
straightforward interpretation.

To examine heterogeneity at the coach level, I fixed coach characteristics
such as coach gender. Firstly, I evaluate heterogeneity in gender bias by the
gender composition of the team. To do so, I take the difference between the
number of men and women in the team when the coaches hear the performance. The
results of this exercise are shown in Figure 2, where the estimated effect
translates into the percentage point of selecting a male artist. We can see
specific local average treatment effect coefficients for gender bias when we
vary team gender composition. If the majority gender group in the team is
women, male coaches tend to select more female artists.

In contrast, when a majority of the team is men, male coaches tend to choose
male artists, unlike female coaches, who have the opposite tendency to select
opposite-gender artists when a particular gender is in the minority. The
exciting aspect of this analysis is that the estimated effect on the
likelihood of choosing male artists is essentially centered to zero when the
number of men and women in the team is equal.

I have also done the same heterogeneity analysis of gender team composition by
standard ordinary least squares by grouping my dataset into males relative to
the female difference in each coach’s team during the audition. According to
Table A2, the estimate shows a statistically significant result when the teams
are female-dominant, and the magnitude is around 8.5 percentage points of the
opposite gender bias. The weight for this estimate comes from the male coach
being more likely to select female artists. The analysis provides a consistent
result with a causal forest estimation but has little statistical power
because of the data subsets by certain cutoffs.

Figure 2: Estimate of gender bias by gender composition in the team

(a) Conditional on Male Coach

(b) Conditional on Female Coach

Notes: This figure summarizes the results from the causal forest by approach
in Athey and Wager (2019), where each estimate shown represents the effect of
own-gender and opposite-gender interactions on selecting the artists in the
case controlling for the gender of the coach and coach fixed effects. From
left to right, the outcome of interest is a set of indicators for the
differences in the number of male artists to the number of female artists in
the team during the audition. This result effectively yields the estimates of
own and opposite gender bias in selections that are specific to each team’s
gender composition. Standard errors clustered by coach.

This exercise yields additional compelling evidence that gender bias, I
estimate, is a systematic effect not attributable to just a handful of coaches
or types of situations. Similarly, I ask whether estimates are driven by
failure rates of coaches for male and female artists and the order of the
artists’ performance. It is thus unsurprising to see in Figures A1, A2, and A3
that other variable-specific estimates of gender bias are uncorrelated with
the failure rate of coaches for male and female artists and the order of the
performance.

##  5 Discussion and Conclusion

In this paper, we examine whether the gender of the coach and artist matters
when it comes to selecting the performance in the blind audition stage in the
Voice TV show. Results provide strong evidence that gender matters and I show
that coaches choose other gender artists 12 percent more when they hear
similar performances in the audition. The results are robust with many
variations, such as coach and artist-specific covariates. Under the
interpretation of opposite-gender bias, the results would be due to male
and/or female coaches being either too lenient to opposite-gender artists,
being too tough on own-gender artists, or both.

Relatedly, a potential mechanism through which opposite-gender interaction
cause statistically significant gender bias could be employers hiring for
female-dominated occupations showing a preference for male applicants
(Weichselbaumer, 2004; Protsch, 2021). However, Weichselbaumer (2004) and
Protsch (2021)’s research also found that employers preferred male applicants
in male-dominated occupations. Still, because of data limitations, they do not
observe the gender of the recruiter. Others who do not observe what I observe
in my work found that employers prefer male applicants in male-dominated
occupations and female applicants in female-dominated occupations (Campero and
Fernandez, 2018; Benard and Correll, 2010; Glick et al., 1988; Ridgeway and
Correll, 2004). These works provide robust evidence of gender bias in hiring.
Still, we cannot distinguish whether it is an opposite-gender or own-gender
bias hiring since the gender of the decision-makers is unobservable or
decisions are made collectively. In my setting, I observe the gender of the
coach and the coach’s individual choice in selecting the artists. Therefore I
incorporate this gender composition feature into my setting to address whether
the coach changes their behavior based on the gender composition in the team.
For example, If one coach’s team is dominated by one gender, would the coach
shift behavior during the audition and select an artist from another gender, a
minority gender?

I conduct a heterogeneity analysis assessing the effect of different gender
compositions in the team on the likelihood of being selected. To do so, I took
advantage of the fact that the sample I used includes both selection of male
and female coaches in the blind audition stages and if the artist ended up
being in the team of the selected coach. Additionally, the other advantage of
the sample is substantial variations in gender composition in each team,
including both male-dominated and female-dominated settings. Typically, we
observe only one type of setting, where the firm is female-dominated or male-
dominated. Leveraging this variation in the gender composition, I estimate the
heterogeneous effect of gender bias for male and female coaches. I found that
male artists have an advantage over female artists in a male-dominated team
when the coach is male. Likewise, women have an advantage over men in a
female-dominated team. When the coach is female, we can see opposite
scenarios. Female coaches tend to choose women over men in male-dominated
teams and men over women in the female-dominated team. This difference is
partially statistically significant, but the magnitude remains consistent.

The literature provides robust support for a hypothesis on group formation
dynamics, which is different for male and female leaders. One study of bias in
other contexts suggests that men might not respond favorably to the presence
of gender diversity, particularly in domains that men have historically
dominated. Also, gender-related issues were most likely to be raised in groups
where women are a minority or where the female is a leader (Crocker and
McGraw, 1984). In addition, there is substantial evidence that women in team
formation care about equality, men care about efficiency, and men consider
male or female dominance in the team as more efficient. More directly, Kuhn
and Villeval (2014) found that women respond differently to alternative rules
for team formation in a manner consistent with advantageous inequity aversion.
In contrast, men show greater responsiveness to efficiency gains associated
with team production, meaning that when forming a team, men make their
selections based on who will be the most efficient rather than on the grounds
of gender equality. Overall, our findings indicate that gender composition and
the gender of the decision-maker are important determinants in the hiring
process. While it is difficult to know if these findings extend to other
industries, these results corroborate the debate over gender discrimination in
the hiring process.

In conclusion, the results add evidence to a growing literature testing own or
opposite gender bias in decision-making. This finding provides insights into
the extent to which situational factors work to mitigate or exacerbate gender
disparities in the hiring process. I show strong evidence of the heterogeneity
in gender bias from gender composition in the team. This evidence suggests
that the selection process is primarily rooted in the female and male
recruiters’ behavioral preferences of inequality or efficiency. In addition,
the findings offer a new perspective to enrich past research on gender
discrimination, shedding light on the instances of gender bias variation by
the gender of the decision maker and team gender composition.

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##  Appendix A Appendix Tables and Figures

Appendix Table A1: Estimates of own-gender bias in artist selection by country

| (1) | (2) | (3) | (4)
---|---|---|---|---
|  | Germany
---
| Australia
---
| UK
---
| France
---
Outcome: Choice |
Male Coach*Male Artist | 0.0168 | -0.0473 | -0.0687 | -0.0531
| (0.0455) | (0.0366) | (0.0425) | (0.0386)
Male Coach | -0.0614∗∗ | -0.0990∗∗∗ | 0.0617 | -0.124∗∗∗
| (-0.0247) | (-0.0326) | (-0.0408) | (-0.0189)
Male Artist | -0.00171 | 0.0559∗ | -1.60E-05 | 0.0397
| (0.0413) | (0.0281) | (0.0388) | (0.0255)
Mean | 0.411 | 0.422 | 0.301 | 0.446
$N$ | 2,688 | 2,964 | 2,860 | 3,396
Coach FE | Y | Y | Y | Y
Performance Order FE | Y | Y | Y | Y
Genre FE | Y | Y | Y | Y
Constraints | Y | Y | Y | Y

Notes: Table A1 presents a difference in differences estimate of gender bias
using regression of Equation 1. This table reports the coefficient on the
interaction of Male Artist and Male Coach from the regression of Choice on
indicators for coach gender, artist gender, and the interaction term. The
reported coefficients are for ”own-gender coach” using data subsets by country
indicated in columns. Each specification includes coach and country fixed
effects, the order of the performance fixed effects, genre-fixed effects, the
number of males relative to females in the team, the failure rate of the coach
for female artists, and the failure rate of the coach for male artists.
Standard errors are clustered by coach. ∗ $p<0.1$, ∗∗ $p<0.05$, ∗∗∗ $p<0.01$

Appendix Table A2: Estimates of own gender-race bias in artist selection by
team gender composition

| (1) | (2) | (3) | (4) |
---|---|---|---|---|---
|  | Male relative to Female in the Team |  |
| $X<-2$ | -$3<X$$<0$ | -$1<X$$<3$ | $X>3$ |
Outcome: Choice |  |
Male Coach*Male Artist | -0.0863∗∗ | -0.0852∗∗ | -0.0403 | 0.0519 |
| (0.0417) | (0.0366) | (0.0293) | (0.0661) |
Male Coach | -0.0109 | -0.226∗∗∗ | -0.228∗∗∗ | 0.633∗∗∗ |
| (0.0377) | (0.0289) | (0.0343) | (0.136) |
Male Artist | -0.108∗∗∗ | -0.0253 | 0.107∗∗∗ | 0.0336 |
| (0.0352) | (0.0272) | (0.0222) | (0.0571) |
Mean | 0.389 | 0.401 | 0.408 | 0.345 |
$N$ | 2,174 | 3,304 | 4,469 | 1,188 |
Coach FE | Y | Y | Y | Y |
Country FE | Y | Y | Y | Y |
Performance Order FE | Y | Y | Y | Y |
Genre FE | Y | Y | Y | Y |
Constraints | Y | Y | Y | Y |

Notes: Table A2 presents a difference in differences estimate of gender bias
using regression of Equation 1. This table reports the coefficient on the
interaction of Male Artist and Male Coach from the regression of Choice on
indicators for coach gender, artist gender, and the interaction term. The
reported coefficients are for ”own-gender coach” using data subsets by gender
composition in the team indicated in columns. $X<-2$ means that difference in
the number of women and men in the team is 3 or higher. Similarly, $X>3$ means
that difference in the number of men and women is 4 or higher. Each
specification includes coach and country fixed effects, the order of the
performance fixed effects, genre-fixed effects, the failure rate of the coach
for female artists, and the failure rate of the coach for male artists.
Standard errors are clustered by coach. ∗ $p<0.1$, ∗∗ $p<0.05$, ∗∗∗ $p<0.01$

Appendix Figure A1: Estimate of gender bias by failure rate for male artists

(a) Conditional on Male Coach

(b) Conditional on Female Coach

This figure summarizes the results from the causal forest by approach in Athey
and Wager (2019), where each estimate shown represents the effect of own-
gender and opposite-gender interactions on selecting the artists in the case
controlling for the gender of the coach and coach fixed effects. From left to
right, the outcome of interest is a set of indicators for the failure rate of
coaches for male artists. This is the rate at which a coach wanted an artist
of a particular gender on their team, and the artist did not choose the coach.
This result effectively yields the estimates of own and opposite gender bias
in selections that are specific to variation by the failure rate of coaches
for male artists. Standard errors clustered by coach.

Appendix Figure A2: Estimate of gender bias by failure rate for female artists

(a) Conditional on Male Coach

(b) Conditional on Female Coach

This figure summarizes the results from the causal forest by approach in Athey
and Wager (2019), where each estimate shown represents the effect of own-
gender and opposite-gender interactions on selecting the artists in the case
controlling for the gender of the coach and coach fixed effects. From left to
right, the outcome of interest is a set of indicators for the failure rate of
coaches for female artists. This is the rate at which a coach wanted an artist
of a particular gender on their team, and the artist did not choose the coach.
This result effectively yields the estimates of own and opposite gender bias
in selections that are specific to variation by the failure rate of coaches
for female artists. Standard errors clustered by coach.

Appendix Figure A3: Estimate of gender bias by the performance order

(a) Conditional on Male Coach

(b) Conditional on Female Coach

This figure summarizes the results from the causal forest by approach in Athey
and Wager (2019), where each estimate shown represents the effect of own-
gender and opposite-gender interactions on selecting the artists in the case
controlling for the gender of the coach and coach fixed effects. From left to
right, the outcome of interest is a set of indicators for each audition
episode. Each 10th order of ten performances aggregates into the episodes in
the same order. This result effectively yields the estimates of own and
opposite gender bias in selections that are specific to variation by the
grouped order of performance. Standard errors clustered by coach.