A large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables. If the denominator variable is positive, then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random...

This paper shows how in Medicare Part D insurers' gaming of the subsidy paid to low-income enrollees distorts premiums and raises the program cost. Using plan-level data from the first five years of the program, I find multiple instances of pricing strategy distortions for the largest insurers....

This paper studies simultaneous equations models for two or more discrete outcomes. These models may be incoherent, delivering no values of the outcomes at certain values of the latent variables and covariates, and they may be incomplete, delivering more than one value of the outcomes at certain...