Christopher F. Parmeter

This textbook provides an up-to-date treatment of the two-tier stochastic frontier model and its applications across the social sciences. It is a cohesive treatise on both the classical methods of estimation and inference and various machinations of the two-tier stochastic frontier model, as well as more recently developed tools that can shed new insight into why these opposing latent forces which affect economic, sociopolitical, and even psychological outcomes, exist, and to what extent. The text is intended to be a self-contained reference for practitioners to rely on when using these methods in their research, regardless of field. It includes sixteen empirical applications on diverse topics (labor market, housing market, consumer goods, production economics, sociology, international relations, psychology, public education, healthcare management, environmental policy). The book is accompanied by a dedicated website where 2TSF software code in the R and gretl open-source platforms is provided.

Quantile Methods for Stochastic Frontier Analysis seeks to merge two seemingly disparate econometric fields, quantile estimation and stochastic frontier analysis (SFA). Why might these two fields be viewed as disparate? Quantiles exist on a continuum of the distribution; the frontier is a fixed object of it. As will be seen, these two approaches can, when used properly, be merged to provide a unified approach to studying a stochastic boundary. Sections 1 to 5 present the current state of affairs. Section 1 details the very close link between the regression function and the conditional quantile function, in order to show that the quantile relation is not some disconnected statistical aspect that lives independently of our regression specification. This section also shows what the quantile approach and the Q-estimator actually do, and we contrast this with what SFA models want to do, using also a simulated example. Section 2 presents the main characteristics and properties of the linear Q-estimator when the error term is independent of the regressors, as a necessary preparation to move to Section 3, where the authors show how some of these properties are fundamentally incompatible with the goals and purposes of SFA. Section 4 discusses recent advances that properly construct the deterministic frontier. Section 5 moves away from quantile regression and presents likelihood-based approaches that use density functions that include as one of their parameters the probability of the zero-quantile of their distributions. Sections 6 to 9 present a new estimator, but also metrics and insights that allow to fruitfully use the quantile approach in SFA. Section 6 shows how one can use the Qestimator together with additional assumptions in order to provide conceptually valid and useful estimation and inference results in SFMs. Section 7 presents quantile-dependent measures of efficiency both at the sample level, and at the individual level, but also how the conditional quantiles of the distribution of inefficiency can be used to offer a picture of how individual efficiency scores are distributed around a chosen quantile of the efficiency distribution. Section 8 proves a fundamental result: that positive and high values of the composite error term of production SFA models, are expected to co-exist with low inefficiency, in a concrete probabilistic sense. Section 9 examines the case of dependence between the error term and the regressors or other covariates. Section 10 provides an empirical illustration that showcases the approach of the four previous Sections, and functions as a guide for detailed applied studies. Section 11 includes a list of the various open issues as well as ideas and directions for future research, while Section 12 offers a short summary and conclusions.

The majority of empirical research in economics ignores the potential benefits of nonparametric methods, while the majority of advances in nonparametric theory ignore the problems faced in applied econometrics. This book helps bridge this gap between applied economists and theoretical nonparametric econometricians. It discusses in depth, and in terms that someone with only one year of graduate econometrics can understand, basic to advanced nonparametric methods. The analysis starts with density estimation and motivates the procedures through methods that should be familiar to the reader. It then moves on to kernel regression, estimation with discrete data, and advanced methods such as estimation with panel data and instrumental variables models. The book pays close attention to the issues that arise with programming, computing speed, and application. In each chapter, the methods discussed are applied to actual data, paying attention to presentation of results and potential pitfalls.

The majority of empirical research in economics ignores the potential benefits of nonparametric methods, while the majority of advances in nonparametric theory ignore the problems faced in applied econometrics. This book helps bridge this gap between applied economists and theoretical nonparametric econometricians. It discusses in depth, and in terms that someone with only one year of graduate econometrics can understand, basic to advanced nonparametric methods. The analysis starts with density estimation and motivates the procedures through methods that should be familiar to the reader. It then moves on to kernel regression, estimation with discrete data, and advanced methods such as estimation with panel data and instrumental variables models. The book pays close attention to the issues that arise with programming, computing speed, and application. In each chapter, the methods discussed are applied to actual data, paying attention to presentation of results and potential pitfalls.

Efficiency Analysis details the important econometric area of efficiency estimation, both past approaches as well as new methodology. There are two main camps in efficiency analysis: that which estimates maximal output and attributes all departures from this as inefficiency, known as Data Envelopment Analysis (DEA), and that which allows for both unobserved variation in output due to shocks and Measurement error as well as inefficiency, known as Stochastic Frontier Analysis (SFA). This volume focuses exclusively on SFA. The econometric study of efficiency analysis typically begins by constructing a convoluted error term that is composed on noise, shocks, Measurement error, and a one-sided shock called inefficiency. Early in the development of these methods, attention focused on the proposal of distributional assumptions which yielded a likelihood function whereby the parameters of the distributional components of the convoluted error could be recovered. The field evolved to the study of individual specific efficiency scores and the extension of these methods to panel data. Recently, attention has focused on relaxing the stringent distributional assumptions that are commonly imposed, relaxing the functional form assumptions commonly placed on the underlying technology, or some combination of both. All told exciting and seminal breakthroughs have occurred in this literature, and reviews of these methods are needed to effectively detail the state of the art. The generality of SFA is such that the study of efficiency has gone beyond simple application of frontier methods to study firms and appears across a diverse Set of applied milieus. This review should appeal to those outside of the efficiency literature seeking to learn about new methods which might assist them in uncovering phenomena in their applied area of interest.