Recruitment and effort of teachers The principal-agent problem

Kjell G. Salvanes

Background

Background

Description of the results so far: More resources in general does not seem to be the

answer Teacher quality appears to be an import factor for

improvement Alternatives:

Setting standards for teachers Incentives to attract better teachers

Incentives in general in order to utilize given resources better

Incentives

Incentives

Incentives

Outline

The structure of incentives

A simple principle agent model for wage contract

Main results of how incentives works in school and between schools.

Aims of an incentive contract

What problems can an incentive wage contract solve? The moral hazard problem (hidden action)

Motivation: To give incentives to high effort (or to balance incentives for owner and employee)

Adverse selection (hidden information) Sorting of workers: Provide incentives to attract the

right workers for a job Risk sharing

A simple prinicpal agent model Assumptions:

Asymmetric information The manager does not know how good the worker is Nor whether he will work hard

No risk aversion

The wage contract that the principal (the firm) offers to the agent (worker) are constructed to obtain efficienct along two dimensions: Solve the adverse selection problem Solve the moral hazard problem.

The main principle is that the agent reveal how good they are themselves, they act on incentives given to them.

Moral hazard or hidden action

Definition: Hidden action as a problem is defined as the

problem that an economic agent’s actions are hidden and the action influence the results

Example: A manager of a firm takes action that are in his

self interest and which is hidden from the owner A worker shirks Crop sharing

A simple prinicpal agent model

The problem to be solved can be stated as :

1) For a given compensation structure we can derive the worker’s effort

2) Given the workers supply respons, the firm must decide the compensation structure to maximise profits

The worker’s problem: Decide effort given wage contract Wage contract:

are compensation parameters decided by the firm, and q is output.

The production is a function of effort, e, or luck or measusrement error, v. Effort is normalised so that one unit of effort produces one unit of production : q=e+v.

The worker loves income but not to work: C(e), der C’(e)>0 og C’’(e)>0

A simple prinicpal agent model

qqw )(

og

A simple prinicpal agent model

The workers optimasation problem is: (1) ;

FOC: (2) C’(e)=

Equation (2) is the worker’s supply function. The workers marginal costs of effort equals the

marginal revenue of effort. Note: The supply function is increasing in the wage

since C’(e)>0 (og C’’(e)>0).

)()( eCveEeMax

The problem of the firm The firm takes the workers effort function (2) as

given when they do their choice of wage parameters: Maximise net income of capital and other

expenditures minus labour income: Net income (gross over capital expenditures) is

defined as : q=e+v. I.e. the firm maximises:

Note that q=e+v, but v er stokastisk E(v)=0, and then E(q)=e.

given a) participation condition b) C’(e)= Incentive compatability

)(,

eeMax

)(eCe

A simple prinicpal agent model Substitute a) into the maximisation problem :

Foc 1: Foc 2 is :

So that it does not bind. Foc 1 says that the worker must set the marginal

cost of effort (C’(e)) equal to the (social) value of effort ( ) which in this case is 1.

)(,

eCeMax

0)('1

e

eC

0/ e

e

qE

A simple prinicpal agent model By combining the optimal choice for the worker and

for the firm, this result tells us that should be set equal to 1 to obtain efficiency in effort to work :

In other words the firm shall offer a contract that

sets the marginal value of effort equal to the marginal (social) value of effort.

)('1 eC

Interpretation The interpretation is that 100 percent of net profits

(over capital costs etc) are going to the worker. Make the worker “full residual claimant” All exstra income of extra effort should go to the

worker. In addition the firm rents the job to the worker for: - . and - must be set equal to the rental price or user

cost of capital. This means that the rental price a worker pays is

higher the more capital he works with.

How does the model fit? Usually one do not get 100 percent of net profits,

but smaller share of gross income. Costs may be manipulted.

This model does not solve the problem that the capital equipment is not carefully taken care of.

Usually one does not pay for a job. But it is quite usual to have a fixed pay first and the the incentive pay starts. In this case the incentive pay part will dominate

since one will be sacked if on eis producing below a certain level of output.

Risk aversion

The most important reason for not using the optimal wage contract: The worker is risk avers: Since the production both depends on the worker’s

effort and a stochastic element which is outside the control of the worker, the worker does not want that his income completely depens on his effort : q=e+v

He therefor wants higher And less , if he is risk averse.

Other important reason for not using the optimal model

If the worker cannot influence the production one cannot use this type of wage policy.

Dynamic aspects: The worker may be afraid to reveal how efficient he

is if thinks that the manager may reduse the pay in the next period.

Multitasking

Use incentive wage contracts when

Input is difficult to measure Monitoring of output must be possible Workers can influence output Risk aversion is low The quality of out put is measurable Multi tasking is not so important

Important results

The optimal incentive wage contract both solves the problem of Incentives for effort Sorting or recruiting the best workers

This is an important result for hiring better or more able teachers

Given wages the most able teachers will self select into this type of jobs

Recent UK policies

Incentives in schools

Incentives in schools

Incentives in schools

Uk experience

Incentives for schools

Incentives for schools

Incentives for schools

UK policy Publication of leage tables Formula funding

Conclusions