Performance Pay and Multidimensional Sorting: Productivity, Preferences, and Gender

TL;DR: In this article, the authors studied the impact of incentives on worker self-selection in a controlled laboratory experiment and found that output is higher in the variable pay schemes (piece rate, tournament, and revenue sharing) compared to the fixed payment scheme.

Abstract: This paper studies the impact of incentives on worker self-selection in a controlled laboratory experiment. Subjects face the choice between a fixed and a variable payment scheme. Depending on the treatment, the variable payment is a piece rate, a tournament or a revenue-sharing scheme. We find that output is higher in the variable pay schemes (piece rate, tournament, and revenue sharing) compared to the fixed payment scheme. This difference is largely driven by productivity sorting. In addition personal attitudes such as willingness to take risks and relative self-assessment as well as gender affect the sorting decision in a systematic way. Moreover, self-reported effort is significantly higher in all variable pay conditions than in the fixed wage condition. Our lab findings are supported by an additional analysis using data from a large and representative sample. In sum, our findings underline the importance of multi-dimensional sorting, i.e., the tendency for different incentive schemes to systematically attract people with different individual characteristics.

Summary

Introduction

• Performance pay and multi-dimensional sorting : productivity, preferences and gender Citation for published version (APA): Dohmen, T. J., & Falk, A. (2010).
• When facing the alternative between variable and fixed payments, more productive workers systematically prefer the variable pay.
• In an additional analysis the authors show that the extent to which personal 3 characteristics affect the sorting decision depends on whether a subject is a “marginal” type, i.e., someone whose decision is on the fence.
• When comparing output under performance pay schemes to output when remuneration is independent of effort, it is often hard to determine whether higher output under the former is due to incentives or sorting.

I. An Experimental Approach to the Study of Incentives and Multi-Dimensional Sorting

• The ideal data set for studying how individual characteristics affect the sorting decision into different incentive schemes combines knowledge of individual productivity and personal characteristics along with direct observation of the selection decision in a well defined environment.
• Such data are difficult to obtain in the field.
• Likewise, workers without explicit performance pay contracts might face work incentives stemming from implicit contracts and repeated game effects (MacLeod and James M. Malcomson, 1989, 1998).
• Waiting too long, however, increases the likelihood that other factors besides the change in the incentive scheme will affect the sorting process.
• It is further possible to elicit measures of individual productivity with little measurement error as well as individual characteristics and preferences.

A. The Work Task

• The work task implemented in their experiment consists of multiplying one-digit numbers by two-digit numbers.
• This “real effort” task implies that subjects have to actually work4 and are to some extent uncertain about their productivity and the productivity of others.
• Moreover, this task is a relatively good proxy for general cognitive ability, and in light of recent neuroscience evidence, learning effects during the experiment are expected to be small (Gerhard Roth, 2001).
• As the authors will see below, solving more difficult problems is more time-consuming.
• If the answer was wrong, subjects had to tackle the same problem again until the correct solution was entered.

B. Design and Treatments of the Experiment

• In order to study how individual characteristics affect the sorting decision into different incentive schemes, the authors implemented an experiment that includes 12 steps .
• The authors third measure of an individual’s productivity (Productivity Indicator 3) is the number of problems that a subject solved when working for five minutes for a piece rate of 10 points per correct answer.
• It was made clear to subjects that they would receive 400 points independent of whether they solved a few, many, or no problems at all.
• Step 11 elicits subjects’ risk preferences using simple lottery choices, similar to Charles A. Holt and Susan K. Laury (2002).
• After a subject had made a decision for each row, it was randomly determined which row became relevant for payment.

C. Procedural Details

• The experiment was computerized using the software z-Tree (Urs Fischbacher, 1999).
• The German-language version of the 16 PF was developed by Klaus A. Schneewind, Gundo Schröder and Raymond B. Cattell (1983) and contains 192 items that compass sixteen primary scales of personality.
• Subjects were told that no aid was allowed for answering the problems (calculator, paper and pencil etc.) and that the authors would check this throughout the experiment.
• The authors ran eighteen sessions, six sessions in each of the three treatments.

II. Results

• In this section the authors present the main results.
• In Section A, the authors start by investigating whether subjects who opt for a variable pay contract produce more than subjects who prefer to work for a fixed payment.

A. Output

• The authors first result concerns output differences between variable and fixed payment schemes.
• The authors expect a positive output effect of variable pay schemes for two reasons.
• The horizontal bars in the figure represent how much time (in seconds) subjects with a particular remuneration contract need on average to enter the correct solution to a problem with a certain degree of difficulty.
• The first 20 subjects who showed up at the lab participated in the experiment.
• The difference in output variances among tournament participants and participants in the revenue-sharing scheme is marginally statistically significant (p-value < 0.0714), and the variance of output among workers who opted for the variable pay in the revenue-sharing treatment is significantly higher than the output variance of variable-pay workers in the piece-rate treatment (p-value < 0.0337).

Productivity

• If subjects choose between the fixed-payment contract wF (equation (1)) and the piecerate contract wPR (equation (2)), it is straightforward to show that subjects whose productivity exceeds a certain threshold value optimally opt for the piece-rate contract, while subjects with lower productivity prefer the fixed-payment contract.
• Thus the sorting decision does not only depend on own productivity but also on the expected productivity of the other player who has sorted into the tournament.
• Abstracting from effort costs, the corresponding critical output is 80 correct answers during the 10-minute working time.
• Figure 3 contains three charts, each of which compares the cumulative distributions of productivity (measured by Productivity Indicator 3) of subjects who sorted into the fixed payment scheme and of subjects who sorted into the variable payment scheme in a particular treatment.
• When the fixed payment is 50, all workers prefer the piece rate, while 60.8 percent prefer the piece rate when the fixed payment is 400 points, the level actually implemented in the experiment.

Risk Attitudes, Relative Self-Assessment, Social Preferences and Gender

• In the previous section the authors have shown that productivity systematically affects selfselection into different incentive schemes.
• Risk averse workers are less likely to self-select into piece rates (Column (1)) and tournaments (Column (2)), while no such effect is observed for the revenue-sharing treatment.
• Finally the authors study whether gender affects the sorting decision into variable pay.
• Risk attitudes might be such an important factor through which gender differences manifest: for one thing, their findings show that risk attitudes affect the sorting decision.
• Columns (2) and (3) show the results for the piece-rate treatment.

C. Effort Provision and Output Changes

• In this section the authors therefore discuss how output and effort provision vary across different incentive schemes.
• Intuitively, subjects in the variable pay schemes should provide at least as much effort as subjects who are paid according to a fixed-payment contract, simply because all variable payment schemes add an explicit reward for providing effort.
• These expectations are all borne out by the data.
• 26 A comparison of Columns (1) and (4) reveals that self-reported effort for the 10-minute work task is higher in all treatments.
• To test, for example, whether tournament incentives trigger larger changes in output than piece-rate or revenue-sharing incentives – as suggested by the self-reported measures – the authors compare output in the 5-minute work period with output in the first 5 minutes of the 10-minute work period for participants in these three different variable incentive schemes.

III. Discussion

• In this paper the authors have provided controlled laboratory evidence on the importance of multi-dimensional sorting.
• Productive workers are more likely to self-select into variable payment schemes when offered a fixed payment scheme as an alternative.
• While productivity is a strong and significant determinant of sorting into all variable pay schemes, the importance of preferences and attitudes on the sorting decision depends on the type of variable incentives.
• This does not necessarily imply, however, that subjects who ended up with less than 400 points did not make a sorting decision that was revenuemaximizing in expectations because their decision had to be based on expected output of all participants who opted for revenue-sharing.
• Respondents in the 2004 wave also answered a survey question on their willingness to take risks that subjects in the experiment answered and that has been experimentally validated in Dohmen et al. (2009) (See section B).

Figures

Figure 2. Performance and Task Difficulty

Figure 3. Productivity of Subjects before Self-Selection Into Incentive Contract

Table 4—Proportions of Men and Women Sorting Into Variable Pay Schemes

Table 5—Effort, Stress, and Exhaustion

Figure 4. Fraction of Subjects Opting for Variable Pay and Average Productivity of Sorted Subjects

Table 6—Survey Evidence on Sorting into Performance Pay

Table 2—Determinants of Sorting

Figure 5. Gender and Sorting

Figure 1. Output of Self-Selected Subjects in Different Compensation Schemes

Full text

Performance pay and multi-dimensional sorting :
productivity, preferences and gender
Citation for published version (APA):
Dohmen, T. J., & Falk, A. (2010). Performance pay and multi-dimensional sorting : productivity,
preferences and gender. Researchcentrum voor Onderwijs en Arbeidsmarkt, Faculteit der Economische
Wetenschappen. ROA Research Memoranda No. 3 https://doi.org/10.26481/umaror.2010003
Document status and date:
Published: 01/01/2010
DOI:
10.26481/umaror.2010003
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Performance Pay and Multi-dimensional Sorting -
Productivity, Preferences and Gender
Thomas Dohmen
Armin Falk
Research Centre for Education and the Labour Market
|
ROA
Research Centre for Education and the Labour Market
Maastricht University
P.O. Box 616, 6200 MD Maastricht, The Netherlands
T +31 43 3883647 F +31 43 3884914
secretary-roa-sbe@maastrichtuniversity.nl
www.roa.nl
ROA-RM-2010/3
ROA Research Memorandum

Performance Pay and Multi-dimensional
Sorting - Productivity, Preferences and
Gender
Thomas Dohmen
Armin Falk
ROA-RM-2010/3
*
February 2010
* The ROA Research Memorandum Series was created in order to make research results available for discussion,
before those results are submitted for publication in journals.
Research Centre for Education and the Labour Market
Maastricht University
P.O. Box 616, 6200 MD Maastricht, The Netherlands
T +31 43 3883647 F +31 43 3884914
secretary-roa-sbe@maastrichtuniversity.nl
www.roa.nl

Abstract
Performance Pay and Multi-dimensional Sorting - Productivity, Preferences and
Gender**
This paper studies the impact of incentives on worker self-selection in a controlled
laboratory experiment. Subjects face the choice between a xed and a variable payment
scheme. Depending on the treatment, the variable payment is a piece rate, a tournament
or a revenue-sharing scheme. We nd that output is higher in the variable pay schemes
(piece rate, tournament, and revenue sharing) compared to the xed payment scheme.
This difference is largely driven by productivity sorting. In addition personal attitudes
such as willingness to take risks and relative self-assessment as well as gender affect
the sorting decision in a systematic way. Moreover, self-reported effort is signicantly
higher in all variable pay conditions than in the xed wage condition. Our lab ndings
are supported by an additional analysis using data from a large and representative
sample. In sum, our ndings underline the importance of multi-dimensional sorting,
i.e., the tendency for different incentive schemes to systematically attract people with
different individual characteristics.
JEL classication: J3, M52, C91, D81, J16
Keywords: Sorting, Incentives, Piece Rates, Tournament, Revenue-Sharing, Risk
Preferences, Social Preferences, Gender, Experiment, Field Evidence
Thomas Dohmen
ROA, IZA, DIW
Maastricht University
P.O. Box 616
6200 MD Maastricht
The Netherlands
t.dohmen@maastrichtuniversity.nl
Armin Falk
University of Bonn
Department of Economics,
Adenauerallee 24-42,
D-53113 Bonn
Germany
emp@uni-bonn.de
** We thank Vincent Crawford, Simon Gächter, James Heckman, David Huffman and Uwe Sunde for helpful
discussions. Valuable comments were also received from Mike Bognanno, Edward Lazear, W. Bentley MacLeod,
Markus Nöth and numerous seminar and conference participants. Felix Marklein, Philippe Raab, and Frédéric
Schneider provided excellent research assistance. Financial support from the Deutsche Forschungsgemeinschaft
through SFB/TR 15 and from the European Research Council (ERC) Starting Grant is gratefully acknowledged.

2
Introduction
Typically the rationale for providing incentive schemes is to align the interests of prin-
cipals and agents in the presence of a contract enforcement problem. This view under-
estimates the importance of worker self-selection, i.e., the possibility that agents with
different individual characteristics feel attracted by different pay schemes and therefore
systematically self-select into particular firms and organizations. In the presence of self-
selection performance is likely to depend not only on the the incentive effect per se, but
also on the sorting effect, which affects the composition of the workforce. A few studies
(e.g., Edward P. Lazear, 2000) indicate that productivity sorting contributes to output
differences between different incentive systems. Little is known empirically, however,
about the nature of this selection process along other dimensions that are crucial to an
organization’s success such as workers’ preferences and attitudes.
Field data often lack important information on workers’ preferences and motives, and
confounding factors impede causal inference. This paper therefore explores the driving
forces of self-selection in a controlled laboratory environment. We address the follow-
ing questions: Which personal characteristics beyond individual productivity differences
provoke workers to self-select into variable instead of fixed pay contracts? In particular,
how do relevant characteristics like risk aversion, relative self-assessment, social prefer-
ences, gender or personality shape the selection process? How does the composition of
the workforce differ when firms offer either fixed wages or variable payments in the form
of piece rates, tournaments, or revenue sharing?
The idea of the experiment is to first elicit subjects’ individual productivity levels.
Subjects then face the choice between a variable and a fixed payment scheme. We ob-
serve which payment mo de they prefer and how much they work. We then elicit further
individual characteristics that may be relevant for the sorting decision. Finally, we obtain
self-reported measures of work effort, stress and exhaustion. The work task consists of
multiplying one-digit numbers by two-digit numbers and is characterized by a substan-
tial degree of heterogeneity in productivity. We study three treatment conditions, which
are characterized by different variable pay schemes. This allows us to study the sorting
patterns when the choice is between a fixed payment on the one hand and either a piece
rate, a tournament, or a revenue-sharing scheme on the other hand. These three forms
of variable pay constitute the most important forms of explicit performance incentives.
Since the treatments are exactly identical except for the alternative variable pay scheme,
our design allows us to study different sorting patterns as a response to these different
pay schemes in a uniform and comprehensive framework.
Our results reveal the importance of multi-dimensional sorting. We first establish that
output in all variable payment schemes is higher than output under the fixed wage regime.
This output difference is mainly attributable to productivity sorting, which is strong and
present in all three treatments. When facing the alternative between variable and fixed
payments, more productive workers systematically prefer the variable pay. This holds re-
gardless of whether the latter is offered as a piece rate, a tournament or a revenue-sharing
scheme. Our results further show that relative self-assessment plays an important role
for sorting into tournaments, which makes sense as payments in tournament schemes
depend on relative performance. Another important driver of self-selection is a subject’s
attitude towards risk: the likelihood that subjects prefer the piece rate or the tournament
is higher the less risk averse they are. This finding reflects the fact that the fixed pay-
ment yields a safe payoff whereas earnings variation renders the variable pay alternative
risky. We also show that women are less likely to select into variable pay schemes than
men. This is mostly explained by differences in risk attitudes and productivity between
men and women. In an additional analysis we show that the extent to which personal

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Performance pay and multi-dimensional sorting - productivity, preferences and gender" ?

Performance Pay and Multi-dimensional Sorting Productivity, Preferences, and Productivity this paper, and Preferences. 

Q2. What are the Spearman rank correlations and corresponding p-values of Ab?

The Spearman rank correlations and corresponding p-values of math grades and Productivity Indicators 1 to 3 are respectively: -0.296 (p-value < 0.001), -0.198 (p-value < 0.002), and 0.286 (p-value < 0.001). 

Q3. How much more likely is a subject to opt for a piece rate contract?

In the piece-rate treatment, a one point higher indication of willingness to take risks on the eleven-point scale makes a subject 5.3 percent more likely to opt for the piece-rate contract for a given level of productivity. 

Q4. What other real effort experiments have subjects solve mazes?

Other real effort experiments include, e.g., René Fahr and Bernd Irlenbusch (2000) who have subjects crack walnuts, van Dijk, Sonnemans and van Winden (2001) who asked subjects to perform cognitively demanding tasks on the computer, Gneezy, Niederle, and Rustichini (2003) who had subjects solve mazes at the computer and Falk and Andrea Ichino (2006) who asked subjects to stuff letters into envelopes. 

Q5. What is the percentage of subjects who self-select into the variable pay scheme?

The fractions of subjects who self-select into the variable pay scheme are 60.83 percent in the piece-rate treatment, 50.0 percent in the tournament and 63.33 percent in the revenue-sharing treatment.