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
A simple prinicpal agent model



The worker’s problem: Decide effort given wage
contract
w( q )     q
 Wage contract:
 og 
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

The workers optimasation problem is:
 (1)
;
Max
 E    ( e  v )  C ( e)
e

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).


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:

Max
  e  (  e)
, 
 Note
that q=e+v, but v er stokastisk E(v)=0, and then
E(q)=e.



given
a)   e  C (e) participation condition
b) C’(e)= 
Incentive compatability
A simple prinicpal agent model

Substitute a) into the maximisation problem :
Max
 e  C ( e)
, 
1:   1  C ' (e) e  0
 Foc 2 is : e /   0
So that it does not bind.
 Foc

Foc 1 says that the worker must set the marginal
cost of effort (C’(e)) equal to the (social) value of
effort ( Eqe ) which in this case is 1.
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 :
1  C ' ( e)  


In other words the firm shall offer a contract that
sets the marginal value of effort equal to the
marginal (social) value of effort.
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