Multi-variate Bayesian Convex Regression with Inefficiency


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.

Shape Restricted Estimation of the Power Curve for a Wind Turbine

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The estimation of the power curve provides an application for methods to estimate production functions consistent with the regular ultra passum law.

It is well known based on fluid dynamics and kinetic energy that the power generated by a wind turbine follows power curve that appears to be S-shaped. In production economics we also believe the production function has a similar S-shaped when the regular ultra-passim law proposed by Ranger Frisch is satisfied. In this research project executed with Hoon Hwangbo and Yu Ding, we are developing a method to estimate a production function that satisfies the regular ultra passum law, is homothetic, has a single output, and allows for noise in the model. Our goal is to improve estimation in small samples through imposing the shape constraints and to develop methods competitive with kernel regression based methods that are currently widely used in the power curve estimation literature.

Working Paper available at SSRN.

Orthogonality Conditions for Identification of Joint Production Technologies: Axiomatic Nonparametric Approach to the Estimation of Stochastic Distance Functions


The selection of the direction in the directional distance function provides a way to address some endogeneity issues in the estimation of production functions.

In the summer of 2013, Timo Kuosmanen, Christopher Parmeter, and I taught a week long Ph.D. course before the EWEPA conference at Aalto University. Out of this activity we have had a variety of discussion on various research topics. One of which is the issue of endogeneity in production function models. Olley and Pakes (1996) is widely accepted as the way to estimate production functions in main stream economics. In this paper we propose an alternative that does not require proxies or instruments, but rather uses the flexibility to select the direction in the directional distance function to reduce the endogeneity problems.

The classic econometric approach treats productivity as a residual term of the standard microeconomic production model. Critics of this approach argue that productivity shocks correlate with the input factors that are used as explanatory variables of the regression model, causing simultaneity bias. This paper uses production theory and the known properties of the stochastic distance and directional distance functions to address the simultaneity bias. We first examine the standard cost minimization problem subject to a production function with a multiplicative error term to demonstrate that even if the observed inputs and outputs are endogenous, consistent estimation of the input distance function is possible under certain conditions. This result reveals that the orthogonality conditions required for econometric identification critically depend on the specification of the distance metric, which suggests the directional distance function as one possible solution to the simultaneity problem. We then introduce a general stochastic data generating process of joint production where all inputs and outputs correlate with inefficiency and noise. We show that an appropriately specified direction vector provides the orthogonality conditions required for identification of the directional distance functions. A consistent nonparametric estimator of the directional distance function is developed, which satisfies the essential axioms of the production theory. We examine the specification of the direction vector for the two different purposes of econometric estimation versus efficiency evaluation in an application to electricity distribution firms.

A nonparametric method to estimate a technical change effect on marginal abatement costs of U.S. coal power plants, published in Energy Economics

     Emission at coal fired power plants

This paper develops a method to investigate the effects of technical change on marginal abatement costs (MAC). This was the second chapter of Maethee Mekaroonreung Ph.D. dissertation. The research was motivated by a paper by Erin Baker that suggested that technical change does not always reduce MAC. In their analysis they made parametric assumptions to investigate a variety of models relating technical change and MAC. In this paper we used nonparametric methods to investigate this question for boilers in coal fired power plants. We find that while technical change reduces MAC, non-technical change related to changes in abatement input costs, production input levels, and pollutant level change is a larger effect. So the investment and installation pollution abatement equipment has lead to larger MACs.

The literature usually assumes that technical change reduces marginal abatement cost; however, recent results suggest that precisely the opposite occurs. This paper proposes a nonparametric method to determine the effect of technical change on marginal abatement cost. The method decomposes NOx marginal abatement cost changes in 2000–2004 and in 2004–2008 for 325 boilers operating in 134 U.S. bituminous coal power plant into technical and non-technical change effects. We find that technical change reduces the NOx marginal cost about 28.3% in 2000–2004 and 26.5% in 2004–2008. However, more stringent regulations enacted the NOx budget program results in lower NOx emission levels as plant operators install more advanced NOx abatement equipment which in turn causes an overall increase in marginal abatement cost.

Nonparametric measurement of productivity and efficiency in education, published in Annals of Operations Research


This paper was written in 2010 and appeared on-line in 2011. It has taken Annals of Operations Research more than 3 years to publish the paper. This paper combines a deterministic contextual variables model with a Malmquist productivity analysis. The methods are applied to Ohio school data. See the abstract below for more details.

This paper was written with John Ruggiero one of the most widely cited researchers in the area of DEA. John and I have written several papers over the years and he has acted as a mention to me. He is generally considered to be the life of the conference as most academic conferences he attends.

Nondiscretionary environmental inputs are critical in explaining relative efficiency differences and productivity changes in public sector applications. For example, the literature on education production shows that school districts perform better when student poverty is lower. In this paper, we extend the nonparametric approach to decompose the Malmquist Productivity Index suggested by Färe et al. (American Economic Rewiew 84:66–83, 1994) into efficiency, technological and environmental changes. The approach is applied to analyze educational production of Ohio school districts. Applying the extended approach in an analysis of the educational production of 604 school districts in Ohio, we find changes in environmental harshness are the primary drivers in productivity changes of underperforming school districts, while technical progress drives the performance of top performing school districts.

September 25: The 6th Helsinki Workshop on Efficiency and Productivity Analysis, Helsinki Finland


Bayesian StoNED or Multi-variate Bayesian Convex Regression with inefficiency: Two sides of the same coin.

Bayesian methods allow researchers to simulate regression models to investigate the effects of prior distributional assumptions and modeling restrictions on posterior estimates of model parameters. Here we try to develop a Bayesian version of Stochastic Nonparametric Envelopment of Data (StoNED). There are strong similarities between StoNED and Multi-variate Bayesian Convex Regression (MBCR) proposed by Hannah and Dunson (2013). This talk describes some of these similarities along with some computational results regarding problem size and accuracy of the estimated parameters. We propose an MBCR model with an inefficiency term as a Bayesian StoNED equivalent.

June 23-27 International Material Handling Research Colloquium – Cincinnati, OH

Intelligrated HQ

The International Material Handling Research Colloquium (IMHRC) purpose is to share world-class research accomplishments, projects and trends in the field of material handling, facility logistics and intralogistics.

It aims to facilitate dialog and collaborative research by teams of university researchers on leading edge topics of interest to end users as well as technology and solutions providers. The Colloquium operates on an immersion philosophy of complete participation by all participants in all the Colloquium events. The Colloquium program includes a mix of invited presentations, facilitated discussions, poster sessions, facility tours and social events.

The first Research Colloquium took place June 1990 on the corporate campus of Litton Industrial Automated Systems in Hebron, Kentucky, USA. The success of this Colloquium prompted the conduct of other Colloquia: in 1992 in Milwaukee, Wisconsin, USA at the corporate headquarters of Rockwell Automation/Allen-Bradley; in 1994 in Grand Rapids, Michigan, USA at the corporate headquarters of Rapistan Demag Corporation; in 1996 in ‘s-Hertogenbosch, the Netherlands, at the corporate headquarters of Vanderlande Industries; in 1998 in Chandler, Arizona, USA at the headquarters of Motorola Corporation; in 2000 in York, Pennsylvania, USA at the headquarters of St. Onge Company; in 2002 in Portland, Maine, USA at the headquarters Southworth International; in 2004 in Graz, Austria on the campus of Technical University of Graz with additional financial support provided by Knapp, Salomon, SSI Schaefer Peem, and TGW; in 2006 in Salt Lake City, Utah, USA at the headquarters of Daifuku America; in 2008 in Dortmund, Germany hosted by the Fraunhofer Institute for Material Flow and Logistics (IML) at the University of Dortmund with support provided by Beumer and Savoye; in 2010 in Milwaukee, USA, financially supported by RedPrairie and HK Systems, with the Center for Supply Chain Management at Marquette University serving as academic host; and in 2012 in Gardanne, France, hosted and financially supported by École Nationale Supérieure des Mines de SaintÉtienne (EMSE) who served as academic host. The 2014 industrial host is Intelligrated.

Andrew Johnson’s research lab presented “Order batching with time constraints in a parallel-aisle warehouse: a multiple-policy approach”. This paper investigate the potential gains in terms of reduced blocking and delays in order picking systems when multiple routing strategies and order gather strategies are considered. The paper will appear as part of the conference proceedings.

June 17: University of Science and Technology of China – Hefei


Stochastic nonparametric approach to efficiency analysis: A Unified Framework

Efficiency analysis is an essential and extensive research area that provides answers to such important questions as: Who are the best performing firms and can we learn something from their behavior? What are the sources of efficiency differences across firms? Can efficiency be improved by government policy or better managerial practices? Are there benefits to increasing the scale of operations? These are examples of important questions we hope to resolve with efficiency analyses.

Efficiency analysis is an interdisciplinary field that spans such disciplines as economics, econometrics, operations research and management science, and engineering, among others. The methods of efficiency analysis are utilized in several fields of application including agriculture, banking, education, environment, health care, energy, manufacturing, transportation, and utilities, among many others. Efficiency analysis is performed at various different scales. Micro level applications range from individual persons, teams, production plants and facilities to company level and industry level efficiency assessments. Macro level applications range from comparative efficiency assessments of production systems or industries across countries to efficiency assessment of national economies. Indeed, efficiency improvement is one of the key components of productivity growth (e.g., Färe et al., 1994), which in turn is the primary driver of economic welfare.

Unfortunately, there currently is no commonly accepted methodology of efficiency analysis, but the field is divided between two competing approaches: Data envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA). Bridging the gap between axiomatic DEA and stochastic SFA was for a long time one of the most vexing problems in the field of efficiency analysis. The recent works on convex nonparametric least squares (CNLS) by Kuosmanen (2008), Kuosmanen and Johnson (2010), and Kuosmanen and Kortelainen (2012) have led to the full integration of DEA and SFA into a unified framework of productivity analysis, which we refer to as stochastic nonparametric envelopment of data (StoNED).

We see the development of StoNED as a paradigm shift for efficiency analysis. It is no longer necessary to decide if modeling noise is more important than imposing axioms of production theory: we can do both using StoNED. The unified framework of StoNED offers deeper insights to the foundations of DEA and SFA, but it also provides a more general and flexible platform for efficiency analysis and related themes such as frontier estimation and production analysis. Further, a number of extensions to the original DEA and SFA methods have been developed over the past decades. The unified StoNED framework allows us to combine the existing tools of efficiency analysis in novel ways across the DEA-SFA spectrum, facilitating new opportunities for further methodological development.

This presentation’s main objective is to describe CNLS and StoNED methods.

June 4th: North American Productivity Workshop


The North American Productivity Workshop (NAPW) is a biennial conference held in North America in even years and its sister conference European Workshop on Efficiency and Productivity Analysis (EWEPA) is held in odd years. It brings together researchers in economics, operations research, management science, engineering and a wide variety of application areas to discuss the latest innovations in efficiency and productivity research.

The 9th NAPW was held in Ottawa Canada from June 4th to the 7th. Keynote speakers included Ariel Pakes, Thomas Professor of Economics (Harvard University), Erwin Diewert, Professor in the Vancouver School of Economics (University of British Columbia)(University of British Columbia), William Greene, Robert Stansky Professor of Economics and Toyota Motor Corp. Professor of Economics (New York University), John C. Haltiwanger, Dudley and Louisa Dillard Professor of Economics and Distinguished University Professor (University of Maryland), Dale Jorgenson, Samuel W. Morris University Professor of Economics (Harvard University), and Robin C. Sickles,Reginald Henry Hargrove Professor of Economics, Professor of Statistics (Rice University and Visiting Professor of Production Econometrics University of Loughborough).

Andrew Johnson’s research team made two presentations (links below). Both will be chapters in José Luis Preciado Arreola Ph.D. dissertation, the first of which has been accepted for publication in the American Journal of Agricultural Economics.

A Birth-Death Markov Chain Monte Carlo method to estimate the number of states in a state- contingent production frontier model”, José Luis Preciado Arreola (Texas A&M University), Andrew (Andy) Johnson (Texas A&M University).

“A Semi-parametric Bayesian Concave Regression Method to Estimate Production Frontiers”, José Luis Preciado Arreola (Texas A&M University), Andrew (Andy) Johnson (Texas A&M University).

Johnson named Department Editor at IIE Transactions


Affective September 1st 2014, Andrew Johnson is the department editor for facilities and production logistics at the IIE Transactions. As the flagship journal of the Institute of Industrial Engineers, IIE Transactions publishes original high-quality papers on a wide range of topics of interest to industrial engineers who want to remain current with the state-of-the-art technologies. The refereed journal aims to foster the engineering community by publishing papers with a strong methodological focus motivated by real problems that impact engineering practice and research. Published monthly, the journal is composed of four focus issues: Design and Manufacturing, Operations Engineering and Analytics, Quality and Reliability Engineering, and Scheduling and Logistics.

IIE Transactions encourages research motivated by critical and complex engineering problems that arise in a wide variety of domains including service, public policy, health care, security, biotechnology, transportation, and others. The journal publishes papers that integrate industrial engineering with other disciplines including statistics, other engineering disciplines, computer science, biological science, and operations research. Articles covering new methodologies and state-of-the-art surveys are included in the journal.