A production function satisfying the Regular Ultra Passum (RUP) law is characterized by increasing returns to scale followed by decreasing returns to scale along any expansion path, which is referred to as S-shape function. Although there are existing nonparametric estimators imposing the RUP law, they impose additional strong assumptions such as: deterministic model, homotheticity or constant elasticity of scale. This paper proposes an iterative algorithm to estimate adaptively a function that satisfies the RUP law while relaxing these other assumptions.

This project seeks to analyze the potential for U.S.-Cuban sugar trade with a particular focus on Cuban sugar production. Cuba has historically been an important global sugar producer and U.S. sugar producers are sensitive to foreign competition. Furthermore, the potential for Cuban liberalization and subsequent possible inflow of foreign investment makes analysis of this industry important. The project’s implications are significant for U.S. sugar producers, U.S. national agricultural policy, and for agricultural development in developing countries generally.

Organizations like census bureaus rely on non-exhaustive surveys to estimate industry population-level production functions. In this paper we propose selecting an estimator based on a weighting of its in-sample and predictive performance on actual application datasets. We compare Cobb-Douglas functional assumptions to existing nonparametric shape constrained estimators and a newly proposed estimated presented in this paper. For actual data, specifically the 2010 Chilean Annual National Industrial Survey, a Cobb-Douglas specification describes at least 90% as much variance as the best alternative estimators in practically all cases considered.

We use U.S. hospital data from 2004 to 2011 to estimate a cost function using a Bayesisan semi-nonparametric method that allows for a heteroskedastic inefficiency. Moreover, we evaluate what is the impact of variables, such as region and hospital size, on cost estimating both the size and robustness of the variables in terms of reducing cost for hospitals.

This research overcomes both the decreased accuracy of Convex Adaptive Partitioning on real production survey datasets and the cross-validation performance challenges of CNLS to create a robust and scalable adaptive partitioning-based convex regression method.

We discover that real production datasets often contain local monotonicity violations, which affect CAP’s ability to propose feasible basis region splits. Moreover, we note that CNLS’s error minimization strategy within the observed dataset results in poor estimations on unobserved firms due to over-fitting. We create a hybrid of both methods that preserves their most favorable properties at a small computational time expense. The paper summarizing this research is available on Arxiv.

SCKLS (shape constrained kernel-weighted least squares) estimator integrates kernel-weighting to convex nonparametric least squares.

Kernel regression is one of the powerful nonparametric estimation methods. By imposing more weight to some closer points, kernel regression helps to avoid over-fitting although it requires the tuning parameter, bandwidth. By imposing some shape constraints such as monotonicity and concavity, we propose SCKLS estimator and apply it to estimate production function with simulated and real data. We also investigate the relationship with Convex Nonparametric Least Squares (CNLS) and we found that CNLS is minimum bias estimator in the class of SCKLS estimator. This is on-going research with Daisuke Yagi. This is the first chapter of his dissertation.

We propose a shape-constrained production function estimator starting from the method described in Kumbhakar, Park, Simar, Tsionas 2006 (KPST).

We maximize the loglikelihood of a local linear estimator at each observation. We estimate the parameters for the noise and inefficiency distributions that are potentially heteroscedasticity.

The challenge to imposing shape constraints, such as monotonicity and concavity, is we need to jointly esitmate the maximum likelihood function for all observations while imposing the constraints. This is on-going research with Kevin Layer.

This research builds on Nonparametric Multi-variate Bayesian Convex Regression to develop a method to estimate shape constrained production frontiers with heteroskedastic inefficiency distributions that scales up to thousands of observations.

We propose a Bayesian method which allows the estimation of a semiparametric production frontiers with a flexible inefficiency distribution, to use panel data and to measure the impact of environmental variables. A Metropolis-Hastings framework is considered to compute smoothed and non-smooth estimates of the production frontier.

Working Paper available at Arxiv.