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...

We analyze the effect of education on wages using German Socio-Economic Panel data and regional variation in mandatory years of schooling and the supply of schools. This allows us to estimate more than one local average treatment effect and heterogeneous effects for different groups of...