Trevor C. Collier

Technical efficiency estimation with multiple inputs and multiple outputs using regression analysis

Regression and linear programming provide the basis for popular techniques for estimating technical efficiency. Regression-based approaches are typically parametric and can be both deterministic or stochastic where the later allows for measurement error. In contrast, linear programming models are nonparametric and allow multiple inputs and outputs. The purported disadvantage of the regression-based models is the inability to allow multiple outputs without additional data on input prices. In this paper, deterministic cross-sectional and stochastic panel data regression models that allow multiple inputs and outputs are developed. Notably, technical efficiency can be estimated using regression models characterized by multiple input, multiple output environments without input price data. We provide multiple examples including a Monte Carlo analysis.

Measuring Technical Efficiency in Sports

Standard economic production theory is the basis for measuring technical efficiency in sports. Using programming or regression models, efficiency is defined as the distance of a given team observation from the technology. In this article, the authors show that the standard measures of efficiency using deterministic models are biased downward due to serial correlation with respect to the efficiency measure. In particular, if the number of observed wins for a given team is affected by the team’s inefficiency, it is necessarily true that another team is able to produce outside of the technology. As a result, the observed frontier is not feasible if all inefficiency is eliminated. In this article, the authors propose a correction to this problem and apply new models to estimate efficiency in professional football.

Aggression in Mixed Martial Arts: An Analysis of the Likelihood of Winning a Decision

Within the last decade, mixed martial arts has become one of the most popular sports worldwide. The Ultimate Fighting Championship (UFC) is the largest and most successful organization within the industry. In the USA, however, the sport is not sanctioned in all states because some politicians view the sport as too violent. The sport consists of many fighting forms and, unlike boxing, winning a decision requires judging in multiple facets including wrestling, boxing, kick boxing, and jiu-jitsu. In this study, we estimate the likelihood of winning a decision in the UFC. Using data on individual fights, we estimate the probability of winning based on fighter characteristics. We emphasize power strikes as it relates to aggression to determine the likelihood of winning. Our results indicate that knockdowns and damage inflicted are all statistically significant determinants of winning a fight and have the largest marginal effect of influencing judge’s decisions.

Nonparametric Estimation of Production Functions

While the primary use of data envelopment analysis is the estimation of production frontiers and the subsequent measurement of efficiency, a more recent literature has been concerned with the estimation of production functions that allow observed points beyond the frontier. This could arise with noisy data for example. Banker and Maindiratta (1992) provided a foundation by extending DEA to estimate efficiency in the presence of statistical noise. The programming model estimates the frontier via maximum likelihood while constraining the production set to be convex by imposing the celebrated Afriat conditions. Since then, there have been several alternative models that have been developed. In this paper we apply several competing methodologies to estimate production functions using data from the English Premier League from 2009 to 2010.

Scouts versus Stats: the impact of Moneyball on the Major League Baseball draft

Michael Lewis’ influential book Moneyball (2003) discusses several sources of inefficiency in the Major League Baseball (MLB) labour market; one of these being the failure of baseball scouts to place a draft premium on college players. We test this implication of the Moneyball thesis – the superiority of college players – by measuring the productivity of players who were drafted in the first round of five MLB drafts covering the years 1995–1999. Employing a variety of specifications, we find that the performance of college draft choices is no better than those of high school picks and argue that this is consistent with Hayeks (1944) work on the economics of information and his emphasis on the importance of localized knowledge. Additionally, we utilize data on the first three rounds of the MLB draft from 1965 to 2010 to test whether Lewis’ book had any impact on teams’ draft strategies. We find no significant structural change in the draft following the publication of Moneyball.

The Impact of Institutional Arrangements on Educational Efficiency

Per pupil expenditures on education in the United States have grown immensely in recent decades, yet student achievement has been stagnant. An abundance of research has sought to solve this enigma, much of it centered on the incentive structure facing administrators. Some recent papers use TIMSS data to analyze the relationship between institutional arrangements—that typically do not vary within a single country—and student achievement. Similarly, we utilize TIMSS 1999 to determine if there is an indirect relationship between institutional arrangements and student achievement, via a relationship with school efficiency. Our results show that the specified link between institutional arrangements and student achievement (direct or indirect) is important in certain instances and confirm evidence found in previous research that certain arrangements are beneficial or detrimental to student achievement, regardless of the specification chosen.