Personnel Economics Lecture 4

Personnel Economics Lecture 4 

Deferred Compensation 

Definitions and examples 

DEFINITION- Wages increase with tenure at a faster rate than productivity. Young workers are paid less than productivity, older workers are paid more. 

• Applies only to tenure at the firm- not outside experience. 
• Overpayment at end of career acts as a performance bond, "golden handcuffs"
• Deferred compensation - like efficiency wage in that future earnings at the firm are greater than the market wage. Unlike efficiency wage worker may pay for this by earning less at the start of career. 

Examples: 

• Seniority based pay increase. Seniority used as criteria for promotion. Pensions (productivity =0, wages still positive)

The existence of a relationship between tenure and pay does not necessarily imply deferred compensation. 

Why deferred compensation? 

Handle the problem of imperfect information and moral hazard- assume monitoring of workers is imperfect and costly. 

Acts like efficiency wage without the cost - worker: future wages are greater than outside option. Firm: lifetime wages are at the market rate. 

Provides workers with an incentive - not to quit, not to do anything for dismissal. Future wages are greater than outside opportunity. 

Thus the firm will offer deferred compensation if turnover or low effort is costly and monitoring is difficult (problem of detection of shirking). 

Reward long term performance - lower turnover than short-term pay

Maybe a good way to incentivise "honest but talented" workers - occurs automatically, low implementation cost, only basic competence. 

A model of deferred compensation 

2 players- worker and firm 

3 periods - young, old, retired

Firm chooses W1, W2, W3 

W1 and W2 are wages 

W3 pension 

The worker must choose effort level - e=0 or e=1 

High effort has a cost of C 

A model of deferred compensation 

If the worker chooses e=0 then there is a probability of (1-p) that they will not be caught and thus not be fired and probability p that they will get caught and fired. 

p = monitoring technology- assume it is fixed and is not a choice variable. 

If the worker is fired after period 1, they receive W1 in period 1 and 0 in periods 2 and 3. 

If the worker is fired after period 2 they receive W1 in period 1, W2 in period 2 and 0 in period 3. 

Assume that productivity with high effort is Z 

Assume productivity with low effort is 0 

Also, assume Z>C  high effort is socially optimal. 

The workers problem 

• Choose e=1 is expected payoff > than e=0 
• Firm'sproblem choose (W1, W2, W3) such that the worker chooses e=1 
• Solve backwards - in period 2 choose e=1 if:

(W2 – C) + W3> W2 + (1 – p)W3

Solving this gives W3>C/p

p is the probability that the game does not continue to round 3 if the worker shirks in round 2. 

A high p implies shirker is more likely to be caught. 

As with efficiency wage, a low detection probability leads to a high wage. 

The Worker's problem continued 

• Assume that this holds, Then in period 1 choose e=1 if:
• (W1 – C) + (W2 – C) + W3> W1 + (1-p)(W2 – C + W3) solving gives: W2> C
• W1 has no incentive effect, it is a gift 
• Worker does not consider past wages in their optimisation decision because these can not be taken away or increased. 
• In equilibrium: (W1, W2, W3) = (0, C, C/p)
• Output = Z,Z,0
• Wages are (0,C,C/P)
• Social optimal - if effort is high then in periods 1 and 2 output+ utlitiy= (Z-C)>0. If effort is low in periods 1 and 2 output + utlitiy = 0 

The worker's effort choice in period 1

 Image graph 

Intuition of the model 

• In period 1 worker produces Z and earns 0, thus productivity is greater than wages
• In period 3 worker produces 0 and earns C/P thus wages are greater than productivity 
• This gives the worker optimal incentives not to shirk because they risk losing out on high future wages. 
• This is profitable for the firm because high effort leads to higher output. 

The commitment problem in the model 

In the first version of the model the firm made the wage offer W1, W2, and W3 at the start of the contract and was legally bound by that offer. 

Suppose instead the firm is not legally bound by that offer, and instead makes a wage offer at the start of each period. They are committed to the offer for one period only. 

• Before stage 1 they offer W1, W21, W31, where W21 is the offer for period 2 made in period 1. 
• In full commitment case, W21 is binding, In other words, W21=W22 
• In the no commitment case the firm can change their offer at the start of each period so W21 is not necessarily =W22. 

Equilibrium in the no-commitment model 

• In period 3 the firm offers a wage of 0 
• In period 2 the workers knows that the firm will offer them 0 in period 3 and doesn't supply effort. 
• In period 2 the firms knows that the worker won't supply effort and thus offers a wage of 0. 
• In period 1 the worker knows that the firm will give them a wage of 0 in the future and doesn't supply effort 
• In period 1 the firm knows that the worker won't supply effort and thus offers a wage of 0 
• The game unravels backwards and there is zero wages and no effort. 

The commitment and no-commitment equilibria 

No commitment:

• Wages (0,0,0) 
• Productivity (0,0,0) 
• Effort (0,0) 

This is pareto inferiod to the full-commitment deferred compensation equilibirum 

• Wages (0,C,C/P)
• Productivity (Z,Z,0)
• Effort (1,1) 

Diagram of a deferred compensation contract in continuous time 

graph 

Commitment problem in the contract 

Firm wants to renege and dismiss workers after T* 

• Need a legally binding contract 
• Alternatively enforcement through reputation - need to hire workers in the future 

Worker wants to stay on after T** because they are overpaid 

• Initially, the worker was happy with a deferred compensation where they retire at T** because lifetime pay equals lifetime productivity. 
• Solution is mandatory retirement

Policy implications 

• Anti-age discrimination legislation 
• Compulsory vesting of pension 

Deferred compensation and worker selection 

As with all contracts, deferred compensation is more attractive to some workers than others. The following will be attracted to deferred compensation:

• Workers who are future-minded - low discount rate implies higher value of future earnings, those with greater preference for stability 
• Workers with low effort cost 
• Honest workers - those who would not engage in extreme forms of shirking even if they could get away with it. 

Union generally like deferred compensation 

• Attaching pay to tenure is transparent, not subject to manipulation 
• Rewards the average worker, who may be the median union member. 
• Promotes long-term employer-employee relationship, which in turn facilitates unionisation. 

Empirical testing for deferred compensation 

Problem - can't observe productivity, so need indirect tests 

Regress slope of the wage profile on job characteristics such as: 

• Difficulty of monitoring 
• Hiring, training and turnover costs 
• Loss from moral hazard 

Testing for deferred compensation continued 

Regress slope of wage profile on workers and firm characteristics 

Regress wages on characteristics, including age/tenure. Regress performance evaluations on the same characteristics. 

Experimental tests - In the lab it is possible to “measure” effort. •Does effort increase if W2 + W3 > (C + C/P) ? •Is effort lower if the firm can not commit to a wage schedule in advance? •Are the actual wages (W22 and W33) lower if the firm can not commit to a wage schedule in advance? •Answer is generally yes, but there is typically less effort that in equilibrium in the full commitment case and higher wages and more effort in the no-commitment case

General observation: deferred compensation seems to be declining over time. Why? 

Computers, etc. make it easier to continually monitor workers - Higher detection probabilities mean that future wages can be closer to the market rates Trend toward general skills (higher education) - lower fixed cost of training and thus lower turnover costs Higher female participation rates mean that labour markets are “thicker” - easier and less costly to replace workers Higher firm failure rates - promise not to dismiss workers after T** is less credible Structural change - decline of certain manufacturing jobs Better access to financial markets - A personal pension has become a close substitute for a company pension Legislation has made it more difficult to offer deferred compensation - Mandatory retirement is prohibited in most cases (age discrimination) - Pensions are increasingly transferrable (compulsory vesting laws)

Summary 

Deferred compensation acts in a similar way to efficiency wages, incentivising high effort when monitoring is imperfect For the worker, future wages are greater than outside opportunities For the firm high future wages have been “paid for” with low past wages Deferred compensation is only effective if the firm can effectively commit to a future wage schedule and to ensuring the future employment of non-shirking workers