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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:
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Recruitment and effort of teachers The principal-agent problem Kjell G. Salvanes
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
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 • 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 • 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).
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
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.
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.
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
Incentives for schools • UK policy • Publication of leage tables • Formula funding