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Holmstrom (1999) - Managerial Incentive Problems (view source)
Revision as of 18:54, 7 April 2010
, 18:54, 7 April 2010no edit summary
Wages are paid in advance so in the second period the agent exerts no effort. In equilbrium <math>a_{1}^{*}\,</math> is correctly anticipated.
The market observes <math>z_{1}\equiv \eta +\varepsilon _{1}=y_{1}-a_{1}^{*}\,</math> and uses this to form its conditional expectation <math>\mathbb{E}[\eta|z_{1}]\,</math>. Given the assumption of normality we can use the [[Conditional Normal Distribution | conditional normal equation]] to give:
:<math>[\eta |z_{1}]\sim N(m_{2},\frac{1}{h_{2}})\,</math>
where
:<math>m_{2}(z_{1})=\frac{h_{1}}{h_{1}+h_{\varepsilon }}\cdot m_{1}+\frac{h_{\varepsilon }}{h_{1}+h_{\varepsilon }}\cdot z_{1}\,</math>
:<math>h_{2}=h_{1}+h_{\varepsilon }\,</math>
