Date of Award

Spring 1-1-2016

Document Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Carlos Martins-Filho

Second Advisor

Xiaodong Liu

Third Advisor

Donald Waldman

Fourth Advisor

Scott Savage

Fifth Advisor

Vanja Dukic


In this thesis, I focus on the nonparametric estimation of the profit frontier, a topic which has been rarely addressed but with many potential applications in economics. I introduce the concept of a profit frontier of continuous order alpha and provide an easy to implement nonparametric estimator for such profit frontiers. From a statistical perspective the estimator of frontier I propose is, in essence, the estimator for a conditional quantile with a suitably defined conditioning set.

First, inspired by Aragon et al. (2005) in a production function setting, instead of studying a traditional profit frontier, whose estimation might be very sensitive to outliers and extreme values, I define a class of functions of order alpha, which are useful in measuring profit efficiency based on conditional quantiles of an appropriate distribution of profit, input and output prices.

Second, I propose a nonparametric conditional quantile estimator for the profit function of order alpha based on a recently proposed class of nonparametric kernel estimators introduced by Mynbaev and Martins-Filho (2010). I establish consistency and asymptotic normality of this smooth quantile estimator. The measure of profit efficiency is more robust to outliers since the estimated profit frontier of order alpha do not envelope the data. Under some smoothness assumption on the distribution function, the bias of proposed estimator converges to zero faster than that of the estimator which uses traditional kernels. A Monte-Carlo simulation seems to support the theoretical results and show a better performance of this estimator compared to its competitors in most scenarios.

Finally, I implement the quantile estimation method on a data set from Swedish paper industry, and show that profit frontiers as well as firm level profit efficiency indexes can be estimated accordingly.