Dichotomous decisions based on dichotomously scored items: a case study

In a course in elementary statistics for psychology students using criterion-referenced achievement tests, the total test score, based on dichotomously scored items, was used for classifying students into those who passed and those who failed. The score on a test is considered as depending on a latent variable; it is assumed that the students can be dichotomized into the categories “mastery” (with scores on the latent variable above a cutting score), and “no mastery” (with scores below the cutting score on the latent variable). Two problems are considered: (a) How many students are classified incorrectly? Using the binomial error model a procedure is described for computing the classification proportions: p(mastery, passed), p(mastery, failed), p(no mastery, passed), and p(no mastery, failed), (b) What is the optimal cutting score on a test? Using a loss function a procedure for computing the optimal curring score is described.     

Optimal Redistributive Taxation in a Search Equilibrium Model

This paper characterizes optimal non-linear income taxation in an economy with a continuum of unobservable productivity levels and endogenous involuntary unemployment due to frictions in the labour markets. Redistributive taxation distorts labour demand and wages. Compared to their efficient values, gross wages, unemployment, and participation are lower. Average tax rates are increasing. Marginal tax rates are positive, even at the top. Finally, numerical simulations suggest that redistribution is much more important in our setting than in a comparable Mirrlees-type setting.     

On the Optimality of Search Matching Equilibrium When Workers Are Risk Averse

This paper revisits the normative properties of search‐matching economies when homogeneous workers have concave utility functions and wages are bargained over. The optimal allocation of resources is characterized first when information is perfect and second when search effort is not observable. In the former case, employees should be unable to extract a rent. The optimal marginal tax rate is then 100%. As search effort becomes unobservable, an appropriate positive rent is needed and the optimal marginal tax rate is lower. Moreover, the pretax wage is lower in order to boost labor demand. Finally, in both cases, nonlinear income taxation is a key complement to unemployment insurance.