This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Optimal Compensation Schemes
Lecture 8, March 6, 2012 Announcements
• Term Paper -- Remaining deadlines:
– Peer Assessments, Tuesday March 13th, 11:00 am
– Final Submission, Tuesday March 20th, 11:00 am
• On peerScholar and turnitin. • Final Exam:
– A-LI TUE 17 APR AM 9-11 SEEL
– LL-Z TUE 17 APR AM 9-11 SHER • And don’t forget to work on the problems.
• Tutorials continue this Friday
– Alfia will be taking up selected problem set questions
– Every Friday for the remainder of the semester • ELL010H1F: Intensive Academic English 1 Outline
• Motivation: Internal labour markets
• Piece Rates versus Time Rates
• Principal-Agent Problems:
– Application: Executive Compensation • Tournaments
• Economics of Superstars
• Deferred Compensation
– Why do wages rise with seniority? • Efficiency Wages & Implicit Contracts
– Discuss in the context of unemployment 2 So far: Spot Labour Markets
• To this point, we have focused on the “supply and demand” model of
employment and wage determination.
– Strictly speaking, the model implies that W = VMP continuously. • It is especially useful for studying long term trends in the labour market.
– Even when studying unemployment, this approach is still insightful. • But do employment patterns suggest that a dynamic labour market is
continuously adjusting employment to keep wages equal to marginal
• Many institutions or practices exist that suggest that INTERNAL labour
markets are also important.
• Consider the distribution of job tenure – defined as years spent with the
– Measured in labour force surveys.
3 Long-term employment Table 2.1 Average employment tenure (years) and distribution of class of tenure
(% of labour force), 1992–2000
Country Average tenure (years) Tenure under 1 year
(% of labour force) Tenure 10 years and over
(% of labour force) 1992 2000 1992 2000 % change
1992–2000 1992 2000 Belgium 11.0 11.5 4.5 10.4 13.6 30.8 45.3 46.2 2.0 Denmark
0.6 10.2 10.4 2.1 14.9 16.8 12.5 40.7 41.1 0.8 United Kingdom
Average % change
1992–2000 % change
1992–2000 a Change from 1995 to 2000. b Average tenure data refer to 1991 instead of 1992. For US and Japan, data refer to 1998
instead of 2000. c Without Austria. n.a. not available.
Source: Authors’ calculations, based on Eurostat and national sources. Source: ILO, 2003 “Employment Stability in an Age of Flexibility” 4 Canadian Evidence: Job Tenure over Time Source: LFS (Statistics Canada), calculations by Stephen Gordon
(Blog, Worthwhile Canadian Initiative, January 2011) 5 Long Term Attachment
between Workers and Firms
• There is much less mobility in the labour market than one might guess:
• Do Human Resource departments just set W = VMP and make continuous
• We already saw one example where there was a divergence between VMP
and the wage:
– Specific Human Capital • Expand the set of mechanisms available to firms for paying workers in
ways (or with contract structures) that go beyond a straight wage.
– “Contracts” will allow for more dimensions and contingencies.
– Imperfect information will play a key role in models that try to explain these
compensation schemes. 6 Piece Rates versus Time Rates
• A piece rate system compensates workers according to some measure of
the worker’s output (e.g., clothing home-workers, trees planted, sales);
• A time rate system pays workers on the basis of hours allocated to the job,
and at least in the short run, may not be directly related to productivity.
• Why not pay everyone on the basis of piece rates?
– Output may not be observable. • Assume that individual’s differ in their productivity, but this is private
– If the firm knows worker output, with a piece rate, can set wage equal to VMP;
– If output cannot be directly observed, the employer will have to spend M as a
monitoring cost. • Time rates are therefore cheaper to administer, as they require no (or at
least less) supervision.
7 A simple model comparing
Piece versus time rates
• If the market is competitive, then W = VMP in the long run, and this
implies that workers will have to pay their own monitoring costs.
– Monitoring costs will be a major determinant of whether piece rates are used.
– Also expect that piece rate workers will be more productive, in order for them
to be willing to pay for the monitoring. • Workers will sort themselves across firms with different compensation
• To illustrate, assume that each unit produced is worth r.
• Assume that q* units of output can be easily monitored, but that it is costly
to measure output/effort effort after that.
• No worker will have incentive to work harder than what it takes to produce
q*, and the equilibrium time wage will be rq*.
• On the other hand, more productive workers can earn a higher wage if their
output can be monitored. 8 Illustrating Worker Sorting By Ability
Pay Piece Rate Pay rq* Time Wage A X* B Ability
9 Workers sort across schemes
• In this simple setting, the piece rate induces extra effort by more able
• For more able workers (like B), piece rate schemes are preferred.
• If workers sort themselves across firms by ability – expect that piece rate
workers will earn more than time-rate workers.
– Evidence suggest that this is the case. • This makes it difficult to know whether piece rates actually improve work
• Why don’t we see more piece-rate schemes? 10 Disadvantages of Piece Rates
• Team versus Individual Effort
– e.g., assembly lines
If compensation is offered to the team, there is a problem of free-riding
The “1/N problem”
Designing team compensation is a general problem. • Quality versus Quantity
• Fluctuations of income
– Especially if some amount of output is outside worker control (e.g., the
weather), piece-rates will be more risky.
– Risk-averse workers will then require compensation for the higher risk. • Ratchet Effect
– Firms may “game” or adjust the piece rates in response to past output.
– Workers may also be reluctant to put forward maximum effort
11 How to pay doctors?
• These issues all arise in the design of compensation schemes for doctors –
an important matter of public policy.
– Especially in public health care systems • One model – Fee for Service – is a form of piece rate.
– Pay doctors by the visit, prescription, operation, etc. • At the other extreme, pay doctors a fixed salary.
– Independent of how much work is performed? • Capitation: Pay doctors on the basis of the number of patients (or potential
patients) on their roster.
• Compensation within group practices.
• Various blended models
• In Canada, also the need to address regional shortages. 12 Principal Agent Theory
• A principal hires an agent to perform a specific task, and must design a
contract so that it provides incentives for the agent to perform the task.
Want to design contracts to be self-reinforcing (no needs for courts, etc.).
– Courts may not be able to solve the problem anyway. • The most important challenge in designing these contracts is imperfect (or
– Heterogeneity of underlying worker quality (VMP), and the difficulty of
observing quality before and after signing the contract.
• Adverse Selection – Variation of effort / motivation, and the difficulty of observing effort.
• Moral Hazard 13 Principal Agent Theory
• Principal-Agent problems with imperfect information are frequently
– Group considerations;
– Other exogenous variation in productivity • Various mechanisms may be employed by the principal and agent:
– Supervision and monitoring;
– Pay for performance • But specific circumstances may make these tools difficult to use. 14 Sketch of Principal Agent Model
• Assume that output, y, is given by: y= a+ε
• Where a is the action taken by the agent, and ε is a random (exogenous)
• Generally, assume that y is observable (and can be the basis of a contract),
but that neither a nor ε are observable.
• The agent is paid according to: w = s + by
• Where s is a fixed part of compensation, and b ( 0 < b < 1) depends on
output. 15 Solving for the contract
• It would not be interesting unless it was also costly for the agent to provide
a. The agent’s compensation, x, is given by:
x = w − c( a )
• The payoff to the principal is given by:
π = y−w
• The objective is to solve for an efficient contract:
– Maximize principal’s payoff subject to an agent’s participation constraint: u( x ) ≥ u – Or, maximize agent’s utility subject to principal’s participation constraint π ≥π
• The resulting contract structure depends on the parameters of the specific
problem, including the information sets of each party. 16 Example: Land Contracts in Agriculture
• The more that the agent’s compensation depends on observed output y, the
greater amount of risk is borne by the agent.
– Many contracts are set to optimally share risk between the principal and agent. • A classic example is the design of land-labour contracts in agriculture:
Contract type Value of b Risk sharing Wage Labour b=0 Landlord bears all risk Fixed Rent b=1 Farmer (worker) bears all risk 0<b<1 Landlord and farmer share risk Share-cropping • Studies suggest that the choice of contract depends on local risk conditions.
– May also be inter-linkages with other markets (especially credit). • More generally:
– What is output?
– What if there are many potential actions? 17 Application: Executive Compensation
• Executive compensation is frequently in the news, as incomes are
– Why is Mr. X paid so much? • High salary alone is not enough to establish that someone is overpaid.
– But is W = VMP? • One can imagine that executive pay is determined according to a PrincipalAgent model:
– Principal is the “shareholders” • A possible model for executive (managerial) pay could then be: w = s + bV
• Pay then depends on the “value” of the firm. 18 Evidence
• Two questions have dominated empirical research on this topic:
– How sensitive is manager pay to firm value?
– Does this pay structure lead managers to do the right things?
• Acting in shareholders’ best interests • It turns out to be difficult to answer these questions:
– There difficult measurement issues concerning the valuation of stock options;
– Estimates of b are quite low – this implies that managers may not have
sufficient incentives to maximize firm value;
• One set of estimates: $3.25 per $1000 of firm value. – On the other hand, stock options are risky, and CEO’s may thus hold suboptimal portfolios;
– Why compensate CEO’s for aggregate market performance? • It does appear that managers react to compensation incentives (sometimes
in unintended, adverse ways). 19 Tournaments
• In internal labour markets, after a promotion, an individual often makes
much more money than the alternative candidates within a firm, even
though the winner may only be marginally better.
• Rewards sometimes appear to be based on relative performance/
productivity, rather than absolute productivity.
– And the relative rewards exceed the relative productivity differences. • In effect, firms hold a tournament to rank workers (especially executives)
according to their productivity. The rewards are then distributed according
to rank, with the winner receiving a disproportionate share.
– 2011 Superbowl – Players on the winning team (Packers) won $83,000 versus
$42,000 for the losing team (Steelers).
– Tennis, golf, boxing prize money
– CEOs get 150% raise after promotion from VP 20 Why tournaments?
• Why might firms offer such payoff structures instead of just paying
W = VMP?
• As usual, it depends on imperfect information.
– Sometimes it may be easier to rank workers than to measure their actual
contribution. • Given the information structure, tournaments may be the best way to elicit
• In a simple game where winner gets W1 and loser gets W2:
– The marginal return to effort equals the increase probability of winning, times
the additional prize money, which clearly depends on the spread, W1 – W2.
– It must also be the case that the probability of winning is increasing in effort.
Cannot be “hopeless” or players will not be motivated.
– Relative ability of players will affect the size of necessary prizes: If ability
levels are similar, will need bigger prizes.
21 Evidence from Sports
• The world of sports serves as a fascinating laboratory for the study of
tournament design, and responses of players to incentives.
– “Sports Economics” • Golf, especially, has been carefully studied:
– Individual-level sport;
– Well-defined scoring, and easy to measure performance • Consider the prize structure of the 2011 Masters Tournament
– Common structure applies to ALL PGA championships.
– Purses vary to attract players to tournaments, especially less prestigious ones. • Studies show:
– Higher prize money is associated with lower scores. Golfers perform better
when there is more money at stake.
– In the final round, those players closest to the leader (controlling for previous
round play) have lowest scores on average (they had the greatest incentives). 22 Prize Structure:
2011 Master’s Golf Tournament
Purse Ratio to Next
60.1% 23 Consolation Prizes
• What about the losers?
– Not all the diligent workers get the prize
– May not be an incentive to continue with effort.
• Dog fighting, etc.
• “Up or out” • Who would want to work for such a firm?
• Firms known for firing older mid-level managers may not be able to attract
– Firms may find it optimal to guarantee the losers desirable jobs somewhere else
in the organization.
– It may even be the case that W > VMP for such employees (otherwise no risk
of firing in the first place).
– Tournaments may help explain the existence of “deadwood” in a firm, though it
also raises the issue of mandatory retirement.
24 Disadvantages of Tournaments
• Collusion among participants
• Cheating or “playing dirty” (including sabotage)
• May destroy teamwork and cooperation 25 Economics of Superstars
• Not specifically related to compensation or incentive issues, but rather the
• Superstar Phenomenon: A few individuals in certain professions earn
astronomical salaries. These individuals earn many times more than their
colleagues, even though they may only be marginally better.
– Why? • This is really nothing more than “supply” and “demand”.
• Scarce supply combined with specific demand conditions:
– Homogeneity of consumer preferences (i.e., agreement) regarding the ranking
(ordering) of quality (i.e., who is best);
– Technology – low cost of reaching a mass audience.
– If many people are willing to pay a small amount for the “best”, then this can
aggregate to a huge sum. • In firms, there may also be small spillovers from the “best” worker to the
others’ productivity. 26 Returns to Seniority tion Systems, Deferred Compensation, and Mandatory Retirement 401 • Why do age-experience profiles slope upwards?
• In the most obvious case, W = VMP, and productivity rises with age:
productivity W = VMP Seniority Seniority
ing off at a
ow the individ- (b) Spot market
Wages are equal to productivity at each and every level of seniority;
that is, workers are always paid the value of their marginal product. 27 Seniority
contract market Seniority General Human Capital
(b) Spot market arginal productivity, is
y, though tapering off at a
es start off below the individcating underpayment relative
more rapidly than productivity,
ven point, and then are above
els of seniority (indicating
uctivity). Wages are equal to productivity at each and every level of seniority;
that is, workers are always paid the value of their marginal product. • Or perhaps there is general human capital acquired by the worker on the
• This makes the profile steeper: W, wage Wage,
productivity VMPt = Wt
productivity SB Seniority with company- VMP0 = W0
(no training) St Seniority (d) General training
28 ual’s productivity during the initial period
ompany-specific training. The sponsoring
ining (since it is usable only in that com- Wages are considerably below productivity in the initial period up to St,
not only because of the deferred wage but also because the trainee
is “paying” for the general training by accepting a lower wage during Seniority SB
(a) Deferred wages contract market (b) Spot market Firm Specific Human Capital • Productivity, or the value of marginal productivity, is
assumed to rise with seniority, though tapering off at a
higher level of seniority. Wages start off below the individual’s productivity profile (indicating underpayment relative
to productivity) but they rise more rapidly than productivity,
eventually reaching a breakeven point, and then are above
The worker productivity at the higher levels of seniority (indicating
may acquire firm-specific human capital,
o encourage retention:
W > VMP to verpayment relative to productivity). Wage,
productivity Wages are equal to productivit
that is, workers are always paid where eventually W, wage Wage,
productivity ST SB Seniority St (c) Deferred wages with companyspecific training (d) General training Wages are above the individual’s productivity during the initial period
up to St while they receive company-specific training. The sponsoring
company benefits by that training (since it is usable only in that company) and hence it “pays” for the training, by accepting the fact that 29
Wages are considerably below p
not only because of the deferre
is “paying” for the general trainin
the training period. Trainees pay Deferred Compensation
• Alternatively, a rising wage profile may serve as a disincentive to shirking,
where it is difficult to constantly monitor workers. (Lazear)
• If a relatively flat profile (VMP) is offered, there is no cost to shirking and
– Can just get a job elsewhere, being paid VMP. • Delayed compensation keeps worker incentives aligned over the duration
of the employment relationship.
• Essentially, the worker posts a bond with the firm.
– Upward sloping profile elicits more effort and reduces shirking. • May need mandatory retirement or some other mechanism to clear out the
W > VMP workers at some point.
• Model relies on imperfect information, and firms staying in business. 30 CHAPTER 13: Optimal Compensation Systems, Deferred Compensation, a F eferred Compensation Profile
DIGURE 13.1 Wage Productivity Profiles
productivity SB Seniority (a) Deferred wages contract market
Productivity, or the value of marginal productivity, is
assumed to rise with seniority, though tapering off at a
higher level of seniority. Wages start off below the individual’s productivity profile (indicating underpayment relative
to productivity) but they rise more rapidly than productivity, (b) Spot m Wages are eq
that is, worke 31 Next Week
• Unions (the following two weeks)
– Background (Chapter 14)
– Models of employment and wage determination (Chapter 15)
– Impact of unions on wages, etc. (Chapter 16) • Recommended Problems from Chapter 13
– Problems #3, #4, and #6 32 ...
View Full Document
This note was uploaded on 03/30/2012 for the course ECO 339 taught by Professor Mbaker during the Spring '11 term at University of Toronto- Toronto.
- Spring '11