Kamali Shahdadi, Behrang

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  • Publication
    Essays on Matching With Endogenous Effort
    (2016-01-01) Kamali Shahdadi, Behrang
    This thesis extends the two-sided matching literature by including an endogenous effort choice after the matching stage. We examine how different matching rules affect incentives to exert effort and the costs paid to induce various effort levels in three settings: a legal system, an education system, and a labor market. In an indigent defense program, the government provides counsel for indigent defendants. After the assignment of an attorney to a defendant, the attorney exerts a costly effort; however, the government only observes a noisy signal of the effort. We model the problem as a one-to-one matching problem with moral hazard. We show that holding the total expenditure for counsel fixed and changing the matching procedure to accommodate defendants' and attorneys' preferences, i.e., switch from random matching to stable matching, defendants become worse off because a stable matching exacerbates the moral hazard problem on the part of counsel. In in the second case we consider a teacher who chooses a costly effort after observing the distribution of students assigned to his/her class. We model the problem as a many-to-one matching with a costly non-contractible effort choice. We show that the effect of policies that affect the student assignment to classes, such as tracking, implementing school choice, and voucher programs, depends on the curvature of teachers' marginal utility of effort. We find conditions under which the argmax of a maximization problem is strictly supermodular or strictly submodular. Subsequently, we characterize conditions under which sorting students based on their academic performances increases (decreases) the total effort of teachers and the average performance of students. In the third setting, we consider a labor market in which each worker chooses an effort after assignment to a firm. The effort choice, labor in this setting, is observable and contractible. We show that the profit maximizing labor maximizes the total surplus of the match. Moreover, the unique matching in any equilibrium maximizes the total surplus; however, this matching may have a lower total output compared with any other matching. Stated differently, eliminating labor market frictions increases the efficiency; however, it may increase or decrease the total output.