Recruitment and effort of teachers The principal-agent problem Kjell G. Salvanes

Background

n Description of the results so far: u More resources in general does not seem to be the answer n Teacher quality appears to be an import factor for improvement n Alternatives: u Setting standards for teachers u Incentives to attract better teachers n Incentives in general in order to utilize given resources better

Incentives

Outline n The structure of incentives A simple principle agent model for wage contract n Main results of how incentives works in school and between schools.

Aims of an incentive contract n What problems can an incentive wage contract solve? u The moral hazard problem (hidden action) F Motivation: To give incentives to high effort (or to balance incentives for owner and employee) u Adverse selection (hidden information) F Sorting of workers: Provide incentives to attract the right workers for a job u Risk sharing

A simple prinicpal agent model n Assumptions: u Asymmetric information F The manager does not know how good the worker is F Nor whether he will work hard u No risk aversion u The wage contract that the principal (the firm) offers to the agent (worker) are constructed to obtain efficienct along two dimensions: F Solve the adverse selection problem F Solve the moral hazard problem. u 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 n Definition: n Hidden action as a problem is defined as the problem that an economic agent’s actions are hidden and the action influence the results n Example: u A manager of a firm takes action that are in his self interest and which is hidden from the owner u A worker shirks u Crop sharing

A simple prinicpal agent model n The problem to be solved can be stated as : n 1) For a given compensation structure we can derive the worker’s effort n 2) Given the workers supply respons, the firm must decide the compensation structure to maximise profits

n The worker’s problem: Decide effort given wage contract u Wage contract: n are compensation parameters decided by the firm, and q is output. n 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 : u q=e+v. n The worker loves income but not to work: u C(e), der C’(e)>0 og C’’(e)>0 A simple prinicpal agent model

n The workers optimasation problem is: u (1) ; n FOC: n (2) C’(e)=  n Equation (2) is the worker’s supply function. F The workers marginal costs of effort equals the marginal revenue of effort. n Note: The supply function is increasing in the wage since C’(e)>0 (og C’’(e)>0).

n The problem of the firm n The firm takes the workers effort function (2) as given when they do their choice of wage parameters: u Maximise net income of capital and other expenditures minus labour income: u Net income (gross over capital expenditures) is defined as : q=e+v. n I.e. the firm maximises: u F Note that q=e+v, but v er stokastisk E(v)=0, and then E(q)=e. n given n a)participation condition n b) C’(e)=Incentive compatability

A simple prinicpal agent model n Substitute a) into the maximisation problem : u Foc 1: u Foc 2 is : So that it does not bind. n 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.

A simple prinicpal agent model n 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 : n n 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 n The interpretation is that 100 percent of net profits (over capital costs etc) are going to the worker. n Make the worker “full residual claimant” n All exstra income of extra effort should go to the worker. n In addition the firm rents the job to the worker for: n -. n and - must be set equal to the rental price or user cost of capital. F This means that the rental price a worker pays is higher the more capital he works with.

n How does the model fit? n Usually one do not get 100 percent of net profits, but smaller share of gross income. Costs may be manipulted. n This model does not solve the problem that the capital equipment is not carefully taken care of. n 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. u 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 n The most important reason for not using the optimal wage contract: u The worker is risk avers: u 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 n He therefor wants higher n And less, if he is risk averse.

Other important reason for not using the optimal model n If the worker cannot influence the production one cannot use this type of wage policy. n Dynamic aspects: u The worker may be afraid to reveal how efficient he is if thinks that the manager may reduse the pay in the next period. n Multitasking

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

Important results n The optimal incentive wage contract both solves the problem of u Incentives for effort u Sorting or recruiting the best workers F This is an important result for hiring better or more able teachers F Given wages the most able teachers will self select into this type of jobs

Recent UK policies

Incentives in schools

Uk experience

Incentives for schools

n UK policy u Publication of leage tables u Formula funding

Conclusions