This paper contributes to the empirical literature on the connection between productivity and gender by using experimental methods in order to produce the relevant data that is missing. This experiment is based on a principal agent game in which principals offer payments and agents choose a costly level of effort, unobservable to the principal. The experimental findings confirm that, an uncertain outcome activity, females are less productive than males.Experiment, Gender, Productivity, Principal-agent game

Ahmed Ennasri

English

Research Papers in Economics

     
 
 
  
  
Volume 31, Issue 4 
  
An experimental analysis of the existing differences of productivity across 
genders 
  
 
 
Ahmed Ennasri  
LAMETA 
Abstract 
This paper contributes to the empirical literature on the connection between productivity and gender by using 
experimental methods in order to produce the relevant data that is missing. This experiment is based on a principal 
agent game in which principals offer payments and agents choose a costly level of effort, unobservable to the 
principal. The experimental findings confirm that, an uncertain outcome activity, females are less productive than 
males.
Acknowledgements: I'm grateful to Dimitri Dubois who developed the software for the experiment. I thank Jérémy Celse and Stéphane 
Mussard for their comments on an earlier version of the manuscript. Funds for the experiments were provided by the Laboratoire d'Economie 
Expérimental de Montpellier (LEEM).  
Citation: Ahmed Ennasri, (2011) ''An experimental analysis of the existing differences of productivity across genders'', Economics Bulletin, 
Vol. 31 No. 4 pp. 3304-3310. 
Contact: Ahmed Ennasri - ennasri@lameta.univ-montp1.fr. 
Submitted: September 19, 2011.   Published: December 09, 2011. 
 
     Economics Bulletin, 2011, Vol. 31 No. 4 pp. 3304-3310
1.  Introduction 
Gender wage gap cannot be explained only by the difference in characteristics between 
men  and  women  (education,  work  experience,  occupation  …).  After  isolation  of  these 
individual characteristics, this gap persists (e.g. Altonji and Blank, 1999). Can the gender 
wage gap be explained by productivity differences between males and females? I examine this 
question in a  laboratory experiment using a principal-agent game, in which a  player (the 
principal thereafter) must decide how much to pay another player (the agent thereafter) who 
may choose an effort level (productivity).  
There  are  several  papers  studying  the  relationship  between  wages,  productivity  and 
gender.  Hellerstein  and  Neumark  (1999)  find  that  the  gender  wage  gap  corresponds  to  a 
gender productivity gap of approximately the same size. Therefore, the wage discrimination is 
not a justification for wage disparities between male and female workers. The women’s lower 
pay  may  be  explained  by  their  lower  productivity  levels.  In  contrast  to  these  findings, 
Hellerstein et al. (1999) report that gender wage differentials are larger than the corresponding 
productivity  differentials,  indicating  that  women  are  victims  of  wage  discrimination. 
Hægeland and Klette (1999) analyze the wage differences and differences in productivity 
between  males  and  females  in  Norway,  Crepon  et  al.  (2002)  in  France,  Ilmakunnas  and 
Maliranta (2005) in Finland, and McDevitt et al. (2009) in Canada. These studies conclude 
that women are less productive than male workers and that wages reflect these differentials. 
All quoted studies focus on wage equations that are estimated as a function of individual 
level  data.  It  is  difficult  to  measure  the  productivity  level  of  the  workers  and  to  isolate 
individual characteristics. This paper contributes to the empirical literature on the connection 
between  productivity  and  gender  by  using  experimental  methods  in  order  to  produce  the 
relevant data that is missing. The results show that women are less productive than men when 
production/performance concerns an uncertain outcome activity.  
2.  Experimental Design 
The experiment consists in an adaptation of the principal agent game. In each session, 
20 subjects are randomly assigned either to the role of principal or agent. In total 120 students 
participated in the experiment (6 sessions × 20 subjects). Participants are privately informed 
about their assignment which was kept constant over the whole session. Note that our data are 
drawn  from a  much larger study of  the principal-agent game, one that had several goals 
beyond the study of gender effects. 
At  the  beginning  of  each  round  (10  rounds),  5  groups  made  up  of  4  subjects  are 
randomly formed. Each group so formed, contains randomly two principals and two agents. 
At the end of each round, new groups are randomly formed. Costs, payoffs, and outcomes are 
measured in Experimental Currency Units (ECU). At the end of the experiment, each subject 
is paid in cash according to his cumulative payoff. 
In each round, the principal can either be in a “Good State” or in a “Bad State”. Each 
round is divided into five stages: 
In  stage  1,  each  of  the  two  principals  in  each  group  proposes  a  payment,     
                   , which will be paid to the agent if the “Good State” comes true for the 
principal.  
3305Economics Bulletin, 2011, Vol. 31 No. 4 pp. 3304-3310
In  stage  2,  both  agents  of  the  group  receive  both  proposed  payments  and  can  then 
realize mouse clicks on their computer during 30 seconds. 
In stage 3, the agent who makes the highest number of clicks (let say Agent 1) decides 
first. He must choose between accepting one of the two payments made by principals and 
rejecting both payments. If he accepts one payment, the second agent (let say Agent 2) must 
decide between accepting the remaining payment and refusing it. If Agent 1 refuses both 
payments, Agent 2 faces the same choice that Agent 1 in the first step: accepting one of the 
two payments made by principals or rejecting both. 
In  stage  4,  if  an  agent  accepts  a  payment,  he  then  has  to  choose  an  effort,     
                 ,  unobservable  by  the  principal.  This  effort  corresponds  to  the 
probability of realization of the “Good State”. After the choice of p by the agent, the central 
computer randomly draws a number between 0 and 100. If the number drawn is less than or 
equal to the value of p the good state is realized. If the number drawn is greater than the value 
of p the bad state is realized. To each possible effort corresponds a cost for the agent,     , 
which is given in table 1.  
In stage 5 of the game, players are informed about the realized state and the individual 
payoff. Furthermore, at the end of each round, subjects receive the following summary data: 
the principal’s contract offer, the order of the agents’ choice, the agent’s acceptance decision, 
the realized state and the realized payoffs. 
Table 1: Costs associated with each value of p 
p (%)  9  18  27  36  45  54  63  72  81  90  99 
C(p)  0.2  1  2.2  3.9  6.1  8.7  11.9  15.6  19.7  24.3  29.4 
 
The  agent  earns  zero  if  he  rejects  the  payment(s).  If  he  accepts  one  payment,  he 
earns          in the “Good State” and loses -     in the “Bad state”. The principal earns 
        in the “Good State” and 36 in the “Bad state”. Table 2 summarizes the various 
possible cases. The optimum payment offered by the principal is       , and the optimum 
effort chosen by the agent is        
1. Each subject participated in one of the six organized 
sessions, and was paid a participation fee plus all earnings from games played. The average 
gain has been 27€. 
Table 2: Payoffs 
State  Agent’s payoff in 
case of refusal 
Agent’s payoff in 
case of acceptance 
Payoff of the 
principal 
Good   0  w - C(p)  144 - w 
Bad   0  - C(p)  36 
 
3.  Experimental Results 
All of our statistical tests require a 5% rejection threshold of the null hypothesis. The 
first part of this section analyses the principals’ payment offers. Afterwards, I analyze the 
agents’ decisions in terms of acceptance and effort level. 
                                                       
1 For more information on the theoretical predictions of the game, see Ennasri, A. and Willinger, M. (2011). 
3306Economics Bulletin, 2011, Vol. 31 No. 4 pp. 3304-3310
3.1.   Payment Offers 
Table 3: Avearage contract offer according to gender 
Gender  Men  Women 
Prediction  54 
G1  48.2  50.8 
G2  55.5  60.0 
G3  62.3  66.8 
G4  58.5  45.6 
G5  51.8  53.0 
G6  66.8  54.0 
Total  57.1  55.0 
 
Table 3 shows the average of contract offers by gender for each of the six groups. The 
average payment offered by men is 57.1 and 55 by women, a non-significant difference (p-
value = 0.916, Wilcoxon two-sided) and which doesn’t differ from the theoretical prediction 
(t-test, p-value = 0.308 for male and p-value = 0.748 for female).  
Figure 1: Evolution of the average payment over time according to the gender 
 
Figure 1 shows the evolution of the average payment over time by gender. The figure 
also shows that over time the average payment offered by the male is not significantly larger 
than the one offered by the female (p-value = 0.114, Wilcoxon one-sided). Therefore, there is 
no evidence for a difference in payment offers between male and female. 
Table 4: Agent’s Expected Surplus Share 
Gender  Men  Women 
Prediction  33% 
G1  31.9%  33.1% 
G2  36.7%  41.8% 
G3  43.8%  49.7% 
G4  40.5%  27.6% 
G5  32.4%  35.4% 
G6  49.2%  34.2% 
Total  39.1%  37.0% 
 
Table 4 shows the agent’s expected surplus share (ESS), i.e. the agent’s expected net 
payment divided by the total expected surplus assuming that he chooses optimally the level of 
effort. The agent’s ESS is 39.1% for men and 37.0% for women, an insignificant difference 
45 
50 
55 
60 
65 
1  2  3  4  5  6  7  8  9  10 
A
v
e
r
a
g
e
 
p
a
y
m
e
n
t
 
Periods 
Men 
Women 
3307Economics Bulletin, 2011, Vol. 31 No. 4 pp. 3304-3310
(p-value  =  0.916,  Wilcoxon  one-sided).  However,  the  ESS  is  significantly  larger  than 
theoretical  prediction,  i.e.  33.3%,  for  men  (t-test,  p-value=0.039)  but  not  significantly 
different for women (t-test, p-value=0.246). Therefore, we conclude that men and women 
offer similar payments that allow them to share the expected surplus in their favor. 
3.2.   Agent’s Decision 
Table 5: Acceptance rate according to gender 
Gender  Men  Women 
Prediction  100%  100% 
G1  87%  80% 
G2  94%  88% 
G3  92%  100% 
G4  100%  96% 
G5  93%  95% 
G6  90%  83% 
Total  93%  90% 
 
Table 5 shows the acceptance rates. From a theoretical point of view, all payments 
should be accepted
2. The acceptance rate is 93% for males and 90% for females, which are 
not different (p-value = 0.463, Wilcoxon two-sided). Approximately 10% of the payments are 
rejected whatever the gender, in accordance with earlier findings about payment offers (Keser 
and Willinger, 2000). 
I  use  a  Logit  panel regression in order to estimate the acceptance probability of a 
payment. The acceptance probability of subject i in period t is given by:  
            
   
     , where                                     (1) 
    is the payment of subject i in period t,   is a dichotomous variables indicating the 
gender  (1  for  female  and  0  for  male).      is  a  normally  distributed  random  variable  that 
captures the individual random effect and     is a standard random error term. Results from 
the random effects panel regression are summarized in table 6.  The Wald test shows that the 
models are globally significant.  
Table 6: Logistic regression of the acceptance probability 
Acceptance 
probability  Coef.  Std. Err.  Z  P>|z|  [95% Conf. Interval] 
Payment offers  0.179  0.023  7.60  0.000  0.133          0.225 
Female  0.261  0.733  -0.36  0.721  -1.699          1.175 
Constant  -4.128  0.969  -4.26  0.000  -6.029          2.227 
Wald χ²(2) = 57.78, Log likelihood = -95.943, Prob > χ² = 0.0000 
 
An increase of the payment has a significant and positive impact on the acceptance 
probability. The estimated female coefficient is insignificant, indicating that men and women 
react similarly to payments in acceptance choice. Therefore, the acceptance probability is not 
affected by gender. 
 
                                                       
2 Participation constraint is always satisfied. 
3308Economics Bulletin, 2011, Vol. 31 No. 4 pp. 3304-3310
Table 7: Average effort level for accepted contracts 
Gender  Men  Women 
Prediction  90% 
G1  85.4%  55.9% 
G2  66.4%  64.0% 
G3  82.2%  66.8% 
G4  76.1%  56.8% 
G5  79.5%  63.2% 
G6  80.3%  76.0% 
Total  78.3%  63.8% 
 
Table 7 shows the average effort level chosen by male and female after accepting a 
payment. Males choose an average effort of 78.3% whereas women choose an average effort 
of 63.8%. Indeed, males choose an average effort significantly higher than females do (p-
value = 0.027, Wilcoxon one-sided). Nevertheless, effort levels are significantly lower than 
the optimal effort for both genders (t-test, p-value = 0.003 for men and p-value <0.001 for 
women).  
Table 8 shows the results of a random-effects panel regression, with effort level as the 
dependent variable.  
Table 8: Determinants of the choice of effort level 
Effort level  Coef.  Std. Err.  Z  P>|z|  [95% Conf. Interval] 
Payment received  0.481  0.031  15.35  0.000  0.420           0.543 
Female  -12.811  1.697  -7.55  0.000  -16.137         -9.484 
Constant  51.996  2.195  23.68  0.000  47.693        56.299 
Wald χ²(2) = 288.16, Prob > χ² = 0.0000, Log likelihood = -2292.105 
 
Results show that the effort level is strongly correlated to the payment received. The 
estimate indicates a positive relationship between payment and effort. The estimate shows 
also that the gender dummy is significantly and negatively correlated with effort: for the same 
payment, females choose significantly lower effort than males. Therefore, there is evidence 
for a gender effect concerning the choice of the effort level. 
4.  Discussion 
In this article, I examine a repeated principal-agent game in which women and men 
were randomly assigned to the roles of principal and agent. Subjects could not identify their 
playing partners. My results therefore show that gender does appear to be connected to the 
effort level. In the experiment, for a given payment, women choose on average an effort level 
18% lower than men. Therefore, in uncertain outcome activity, there are some evidences of a 
gender productivity gap: males are more productive than females. One possible explanation is 
that women are more risk averse than men (Eckel and Grossman, 2002, 2008). Also, my 
results  indicate  that,  under  these  experimental  conditions,  gender  does  not  influence  the 
payment offers and acceptance rates. Hence, men and women differ neither in the payment 
offers nor in acceptance decision. For that purpose, it would be interesting to realize some 
experiment that disentangles the effort and risk aversion and inform the participants about the 
partner gender. 
 
3309Economics Bulletin, 2011, Vol. 31 No. 4 pp. 3304-3310
Acknowledgements 
I’m grateful to Dimitri Dubois who developed the software for the experiment. I thank 
Jérémy  Celse  and  Stéphane  Mussard  for  their  comments  on  an  earlier  version  of  the 
manuscript.  Funds  for  the  experiments  were  provided  by  the  Laboratoire  d’Economie 
Expérimental de Montpellier (LEEM). 
References 
  Altonji, J.G. and Blank, R.M. (1999) “Race and gender in the labor market, Handbook 
of  Labor  Economics”  in:  O.  Ashenfelter  &  D.  Card  (ed.),  Handbook  of  Labor 
Economics, edition 1, volume 3, chapter 48, pages 3143-3259 Elsevier. 
  Crepon, B., Deniau, N. and Pérez-Duarte, S. (2002) “Wages, productivity, and worker 
characteristics:  A  French  Perspective”  Mimeo.  Paris,  France:  National  Institute  for 
Statistics and Economic Studies (INSEE). 
  Eckel, C.C. and Grossman, P.J. (2002) “Sex differences and statistical stereotyping in 
attitudes toward financial risk” Evolution and Human Behavior 23, 281–295. 
  Eckel, C.C.  and Grossman, P.J.  (2008) “Forecasting risk attitudes: An  experimental 
study using actual and forecast gamble choices” Journal of Economic Behavior and 
Organization 68, 1-17. 
  Ennasri,  A.  and  Willinger,  M.  (2011)  “Managerial  incentives  under  competitive 
pressure: Experimental investigation” ASFEE Research Paper number 2011-03.  
  Haegeland, T. and Klette, T.J. (1999) “Do higher wages reflect higher productivity? 
Education, gender, and experience premiums in a matched plant-worker data set” in: 
Haltiwanger, J.C., Lane, J.I., Spletzer, J.R., Theeuwes, J.J., Troske, K.R. (Eds), The 
Creation  and  Analysis  of  Employer-Employee  Matched  Data,  North  Holland, 
Amsterdam, pp. 231-259. 
  Hellerstein, J.K. and Neumark, D. (1999) “Sex, wages, and productivity: an analysis of 
Israeli firm-level data” International Economic Review 40, 95-123. 
  Hellerstein,  J.K.,  Neumark,  D.  and  Troske,  K.R.  (1999)  “Wages,  productivity,  and 
worker  characteristics:  evidence  from  plant-level  production  functions  and  wage 
equations” Journal of Labor Economics 17, 409-446. 
  Ilmakunnas,  P.  and  Maliranta,  M.  (2005)  “Technology,  labour  characteristics,  and 
wage-productivity gaps” Oxford Bulletin of Economics and Statistics 67, 623-645. 
  Keser, C. and Willinger, M. (2000) “Principals’ Principles when Agents’ Actions are 
Hidden” International Journal of Industrial Organization 18, 163–185. 
  McDevitt, C.L., Irwin, J.R. and Inwood, K. (2009) “Gender pay gap, productivity gap, 
and  discrimination  in  Canadian  clothing  manufacturing  in  1870”  Eastern  Economic 
Journal 35, 24-36. 
 
3310

Do higher wages reflect higher productivity? Education, gender, and experience premiums in a matched plant-worker data set” in:

Forecasting risk attitudes: An experimental study using actual and forecast gamble choices”

Gender pay gap, productivity gap, and discrimination in Canadian clothing manufacturing in 1870”

Managerial incentives under competitive pressure:

Race and gender in the labor market, Handbook of Labor Economics”

Sex differences and statistical stereotyping in attitudes toward financial risk”

Sex, wages, and productivity: an analysis of Israeli firm-level data”

Technology, labour characteristics, and wage-productivity gaps”

Wages, productivity, and worker characteristics: A French Perspective” Mimeo.

Wages, productivity, and worker characteristics: evidence from plant-level production functions and wage equations”

An experimental analysis of the existing differences of productivity across genders

http://www.accessecon.com/Pubs/EB/2011/Volume31/EB-11-V31-I4-P301.pdf

An experimental analysis of the existing differences of productivity across genders

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics