Regression-Based Methods for Using Control and Antithetic Variates in Monte Carlo Experiments

Methods based on linear regression provide a very easy way to use the information in control and antithetic variates to improve the efficiency with which certain features of the distributions of estimators and test statistics are estimated in Monte Carlo experiments. We propose a new technique that allows these methods to be used when the quantities of interest are quantiles. Ways to obtain approximately optimal control variates in many cases of interest are also proposed. These methods seem to work well in practice, and can greatly reduce the number of replications required to obtain a given level of accuracy.

An Empirical Test of the Reder Hypothesis

A firm that faces insufficient supply of labor can either increase the wage offer to attract more applicants, or reduce the hiring standard to enlarge the pool of potential employees, or do both. This simultaneous adjustment of wages and hiring standards in response to changes in market conditions has been emphasized in a classical contribution by Reder and leads to the effect that wage reactions to employment changes can be expected to be more pronounced for low wage workers than for high wage workers. This is the `Reder Hypothesis'. The present contribution sets out to test this hypothesis using German employment register data and a censored panel quantile regression approach. Our findings support the Reder Hypothesis, suggesting that market clearing in labor markets is achieved by a combination of wage adjustments and changes in hiring standards

An Empirical Test of the Reder Hypothesis

A firm that faces insufficient supply of labor can either increase the wage offer to attract more applicants, or reduce the hiring standard to enlarge the pool of potential employees, or do both. This simultaneous adjustment of wages and hiring standards in response to changes in market conditions has been emphasized in a classical contribution by Reder and leads to the effect that wage reactions to employment changes can be expected to be more pronounced for low wage workers than for high wage workers. This is the `Reder Hypothesis'. The present contribution sets out to test this hypothesis using German employment register data and a censored panel quantile regression approach. Our findings support the Reder Hypothesis, suggesting that market clearing in labor markets is achieved by a combination of wage adjustments and changes in hiring standards.standards; overqualification; wage structure; panel quantile regression; censoring

Quantile estimation with adaptive importance sampling

We introduce new quantile estimators with adaptive importance sampling. The adaptive estimators are based on weighted samples that are neither independent nor identically distributed. Using a new law of iterated logarithm for martingales, we prove the convergence of the adaptive quantile estimators for general distributions with nonunique quantiles thereby extending the work of Feldman and Tucker [Ann. Math. Statist. 37 (1996) 451--457]. We illustrate the algorithm with an example from credit portfolio risk analysis.Comment: Published in at http://dx.doi.org/10.1214/09-AOS745 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org