Undesirable outputs and a primal Divisia productivity index based on the directional output distance function

Despite their great popularity, all the conventional Divisia productivity indexes ignore undesirable outputs. The purpose of this study is to fill in this gap by proposing a primal Divisia-type productivity index that is valid in the presence of undesirable outputs. The new productivity index is derived by total differentiation of the directional output distance function with respect to a time trend and referred to as the Divisia–Luenberger productivity index. We also empirically compare the Divisia–Luenberger productivity index and a representative of the conventional Divisia productivity indexes–the radial-output-distance-function-based Feng and Serletis (2010) productivity index–using aggregate data on 15 OECD countries over the period 1981–2000. Our empirical results show that failure to take into account undesirable outputs not only leads to misleading rankings of countries both in terms of productivity growth and in terms of technological change, but also results in wrong conclusions concerning efficiency change.     

Efficiency measurement with multiple outputs and multiple inputs

This paper discusses modeling technical and allocative inefficiencies in both cost minimizing and profit maximizing frameworks with special emphasis on multiple inputs and multiple outputs. Both primal and dual models are considered for this purpose. In the primal approach we use a separable output and input function (the constant elasticity of transformation output function and Cobb-Douglas input function). The dual models assume translog cost or profit functions. Technical inefficiency is assumed to be random in the cross-sectional models, and fixed firm-specific parameter in the panel data models. Allocative inefficiencies are always treated as input-specific parameters. We derive exact relations linking technical inefficiency and allocative inefficiencies to cost and profit when the underlying technology is represented by a flexible functional form such as the translog. It is shown that appending a one-sided homoscedastic error term to model technical inefficiency, or neglecting technical inefficiency altogether in a translog profit tunciton results in model misspecification and inconsistent parameter estimates.     

Hicks-Moorsteen versus Malmquist: a connection by means of a radial productivity index

A primal index of productivity change is introduced which decomposes exactly into three components: technical change, technical efficiency change and average scale economies (radial scale change). The productivity index is defined using variations of the distance function along pre-assigned input–output rays and, for this reason, it is deemed a radial productivity index (RPI). It is proven that: first, the RPI index collapses to the Malmquist productivity index when the technology is constant returns to scale (CRS); second the RPI index equals the Hicks-Moorsteen productivity index under homotheticity of technology (and non-CRS). The key to these results is a new definition and measure of the contribution of scale economies to productivity change.     

Econometric estimation of distance functions and associated measures of productivity and efficiency change

Multi-input multi-output production technologies can be represented using distance functions. Econometric estimation of these functions typically involves factoring out one of the outputs or inputs and estimating the resulting equation using maximum likelihood methods. A problem with this approach is that the outputs or inputs that are not factored out may be correlated with the composite error term. Fernandez et al. (J Econ 98:47–79, 2000) show how to solve this so-called ‘endogeneity problem’ using Bayesian methods. In this paper I use the approach to estimate an output distance function and an associated index of total factor productivity (TFP) change. The TFP index is a new index that satisfies most, if not all, economically-relevant axioms from index number theory. It can also be exhaustively decomposed into a measure of technical change and various measures of efficiency change. I illustrate the methodology using state-level data on U.S. agricultural input and output quantities (no prices are needed). Results are summarized in terms of the characteristics (e.g., means) of estimated probability density functions for measures of TFP change, technical change and efficiency change.     

Oligopsony/oligopoly power and factor market performance

This paper is concerned with the economic performance of factor markets in an oligopsony/ oligopoly setting. Firm arid industry indexes are developed to measure factor market price distortions caused by exerted oligopsony/oligopoly power. These measures indicate that the elasticity of output demand, the elasticity of input supply, and the input and output conjectural elasticities determine the degree of non-competitive performance in factor markets. It is also shown that under special conditions the firm index equals the Lerner index and the industry index equals the Herfindahl-Hirschman index.     

Theory and Application of Directional Distance Functions

In 1957 Farrell demonstrated how cost inefficiency could be decomposed into two mutually exclusive and exhaustive components: technical and allocative inefficiency. This result is consequence of the fact that—as shown by Shephard—the cost function and the input distance function (the reciprocal of Farrell's technical efficiency measure) are dual to each other. Similarly, the revenue function and the output distance function are dual providing the basis for the decomposition of revenue inefficiency into technical and allocative components (see for example, Färe, Grosskopf and Lovell (1994)). Here we extend those results to include the directional distance function and its dual, the profit function. This provides the basis for defining and decomposing profit efficiency. As we show, the output and input distance functions (reciprocals of Farrell efficiency measures) are special cases of the directional distance function. We also show how to use the directional distance function as a tool for measuring capacity utilization using DEA type techniques.     

Imperfect Competition and Total Factor Productivity Growth

This article examines the role of imperfect competition in determining total factor productivity growth (TFPG) by bringing together a New Empirical Industrial Organization (NEIO) model and the TFPG model of Good, Nadiri and Sickles (1999). Application of the integrated model to 1973–1992 data from 29 food processing industries revealed that, overall, changes in markups, economies of scale, and demand growth contributed positively to TFPG while the disembodied technical change was a negative contributor. Furthermore, the factors underlying the TFPG estimates are interactive and their net effects are starkly different from the conventional Solow (1957) residual TFPG measures, underscoring the need to account for imperfect competition, returns to scale, and demand growth in analyses of this type.     

Production Risk and Productivity Growth: Some Findings for Norwegian Salmon Aquaculture

This paper deals with estimation of primal panel data models of production risk, focusing on measurement of risk properties of inputs and productivity growth. Under production risk one should estimate technical change separately for the deterministic part and risk part of the technology, since risk averse producers will take into account both the mean and variance of output when they rank alternative technologies. For a panel of Norwegian salmon farms fish feed and fish input are found to increase output risk, while labor has a risk-decreasing effect on output. In the analysis of technical change by the first order stochastic dominance criterion the increase in mean output dominates the increase in output risk.     

Input Hedging,Output Hedging,and Market Power

We argue that commodity input hedging is different from commodity output hedging. Output hedging can be detrimental to “sector play.” Furthermore, firms with market power that hedge outputs have incentives to over‐produce and distort market prices. In rational markets, such hedging will be expensive and we expect to see a negative relationship between hedging and market power in “output industries” but not in “input industries.” We test these predictions on a sample of S&P500 firms from 2001 to 2005. Our results support both hypotheses. Placebo tests show that the same empirical regularities do not apply to currency hedging. Finally, our empirical framework, which differentiates between hedging inputs and hedging outputs, can also help in reconciling conflicting results in prior studies.     

From market shares to consumer types: Duality in differentiated product demand estimation

A widely applied method for differentiated product demand estimation, introduced by Berry, Levinsohn and Pakes in 1995, is founded on matching observed and theoretical market shares of products. In this paper, we allow for discrete consumer tastes and derive an equivalent matching occurring in the consumer type space. The equivalence between the two formulations expresses a duality between market shares and consumer types. In applications where a large number of products and a small number of consumer types is natural, the dual formulation introduced in this paper is computationally more efficient than the primal. Indeed, simulation exercises show that the dual method can be significantly faster. Copyright © 2010 John Wiley & Sons, Ltd.     

Revisiting the decomposition of cost efficiency for non-homothetic technologies: a directional distance function approach

In the early 1980’s Kopp and Diewert proposed a popular method to decompose cost efficiency into allocative and technical efficiency for parametric functional forms based on the radial approach initiated by Farrell. We show that, relying on recently proposed homogeneity and duality results, their approach is unnecessary for self-dual homothetic production functions, while it is inconsistent in the non-homothetic case. By stressing that for homothetic technologies the radial distance function can be correctly interpreted as a technical efficiency measure, since allocative efficiency is independent of the output level and radial input reductions leave it unchanged, we contend that for non-homothetic technologies this is not the case because optimal input demands depend on the output targeted by the firm, as does the inequality between marginal rates of substitution and market prices—allocative inefficiency. We demonstrate that a correct definition of technical efficiency corresponds to the directional distance function because its flexibility ensures that allocative efficiency is kept unchanged through movements in the input production possibility set when solving technical inefficiency, and therefore the associated cost reductions can be solely—and rightly—ascribed to technical-engineering-improvements. The new methodology allowing for a consistent decomposition of cost inefficiency is illustrated resorting to simple examples of non-homothetic production functions.     

Estimation of commodity-by-commodity input–output matrices

In this paper we derive a method for the estimation of symmetric input–output tables (SIOTs), which makes it possible to use the commodity technology assumption even when use- and make tables are rectangular. The method also solves the problem of negative coefficients. In the empirical part we derive annual SIOTs in order to evaluate the differences between SIOTs calculated with different methods and the change in technical coefficients over time. Our results, based on data for Sweden, show that the impact of using different technology assumptions is rather large. However, in a factor content of trade application the impact of different technology assumptions does not seem to be very important. Also the size of the changes in the technical coefficients over time is found to be quite large, indicating the importance of calculating SIOTs annually.     

Stochastic error specification in primal and dual production systems

In this paper we derive both primal and dual‐cost systems in which the stochastic specifications arise from the model (random environment or measurement errors and optimization errors)—not tacked on at the end after the deterministic system is worked out. Derivation of the error structures is based on cost‐minimizing behavior on the firms. The primal systems constitute the production function and the first‐order conditions of cost minimization. We consider two dual‐cost systems. The first dual system is based on the cost function and cost share equations. The second dual system is based on a multiplicative general error production model that is an alternative to McElroy's additive general error production model. Our multiplicative general error model gives a clear and intuitive economic meaning to the error components. The resulting cost system is easy to estimate compared to the alternative cost systems. The error components in the multiplicative general error model can capture heterogeneity in the technology parameters even in a cross‐sectional model. Panel data are not necessary to estimate either the primal or dual systems. The models are estimated using data on 72 fossil fuel‐fired steam electric power generation plants (observed for the period 1986–1999) in the USA. Copyright © 2009 John Wiley & Sons, Ltd.     

Estimating demand with distance functions: Parameterization in the primal and dual

Our purpose is to investigate the ability of different parametric forms to ‘correctly’ estimate consumer demands based on distance functions using Monte Carlo methods. Our approach combines economic theory, econometrics and quadratic approximation. We begin by deriving parameterizations for transformed quadratic functions which are linear in parameters and characterized by either homogeneity or which satisfy the translation property. Homogeneity is typical of Shephard distance functions and expenditure functions, whereas translation is characteristic of benefit/shortage or directional distance functions. The functional forms which satisfy these conditions and include both first- and second-order terms are the translog and quadratic forms, respectively. We then derive a primal characterization which is homogeneous and parameterized as translog and a dual model which satisfies the translation property and is specified as quadratic. We assess functional form performance by focusing on empirical violations of the regularity conditions. Our analysis corroborates results from earlier Monte Carlo studies on the production side suggesting that the quadratic form more closely approximates the ‘true’ technology or in our context consumer preferences than the translog.     

Assessing Aggregate Structural Change

The aim of this paper is to investigate the evolution of Italian aggregate structural change over the years 1965–85. We use annual input–output (IO) tables in current and constant prices to derive an aggregate index of structural change. We adopt several techniques for such an explorative analysis. First, we borrow from qualitative matrix analysis and graph theory some basic concepts to assess direct and indirect links among sectors, and interrelatedness measures are derived in a straightforward way. However, qualitative analysis of indirect links may be flawed, since it can establish a path that is quantitatively negligible. Then, we turn our attention to a non-standard quantitative index derived from structural path analysis, expressed by a simple function of the input matrix determinant. Since empirical findings indicate a structural break in 1975, we derive another measure of technical change: the dominant eigenvalue. Such an index has several interesting properties but no clear relationship to the circularity process implicit in the Leontief model. Results for constant- and actual-price IO tables are discussed and compared with main macro-economic variables over the sample. Empirical findings indicate a relationship between investment, variability in final demand and aggregate structural change.     

Competition in long-distance and telecommunications equipment markets: Effects of the MFJ

The Modification of Final Judgement (MJF) is now 10 years old. The MFJ was a historic change in US antitrust policy and in telecommunications policy. Pre-divestiture AT&T was divided into a single company, AT&T, which was allowed to compete in long-distance markets, telecommunications equipment markets and (with some delay) information service markets. Seven regional Bell Operating Companies (RBOCs) were permitted to provide local service and nearby long-distance service. However, the BOCs were not permitted to enter the three markets reserved for AT&T. In 1991 the Information Services restriction was eliminated for the BOCs. However, the ban on provision of (interLATA) long distance and equipment remains. The policy experiment was quite interesting since no other nation has followed the USA, despite numerous other countries ending the formerly monopoly status of their telecommunications provider. In this paper I evaluate how competitive the remaining markets reserved for AT&T, and from which the BOCS are banned, have become. I conclude that (interLATA) long-distance market for residential and small business users, by far the largest fraction of users of long distance is currently uncompetitive. AT&Ts prices are constrained by FCC regulation, not by competition. AT&T has market power and is exercising market power. For equipment markets, I find a good deal more competition. However, I conclude that the BOCs could not impede competition in long distance and that removal of the MFJ restrictions would be pro-competitive. Thus, I conclude that removal of the MFJ estrictions on the BOCs would be pro-competitive, would increase economic efficiency, and would improve consumer welfare.     

Generalized quadratic revenue functions

In this paper we focus on the specification of revenue functions in their dual price space. We consider two distance functions–the Shephard output distance function and the directional output distance function–and define both in price space. The former is multiplicative in nature and satisfies homogeneity, whereas the latter is additive and satisfies the translation property. Functional equation methods yield the translog specification in the case of the Shephard distance function and a quadratic specification in the case of the directional distance function. Monte Carlo evidence suggests that the quadratic specification outperforms the translog in large samples and in true models with plenty of curvature.     

Has agricultural labor restructuring improved agricultural labor productivity in China? A decomposition approach

This paper presents a framework for analyzing the changes in agricultural labor productivity with regards to the structural, land intensity, and land productivity effects. This approach allows for the residual-free decomposition of data from different levels of aggregation. The logarithmic mean Divisia index was applied for the analysis and a data envelopment analysis model was constructed to identify potential gains in agricultural labor productivity due to the optimization of input use and output production. The proposed approach was applied to the case of China over the period of 1997–2017. Province-level data were used to identify the major driving factors behind agricultural labor productivity change. Land productivity change appeared to be the major source of agricultural labor productivity gains in China. The structural change was rather negligible, suggesting that the reallocation of the agricultural labor force did not add to the agricultural labor productivity growth in China. A frontier analysis indicated that agricultural labor productivity could increase by some 45% on average in case full technical efficiency is achieved.     

Scale Efficiency and Productivity Change

Thefirst objective of this paper is to develop a generic measureof scale efficiency for a multiple-input multiple-output firm,using basic principles of modern production theory. The secondobjective is to combine measures of technological change, technicalefficiency change, and scale efficiency change into an encompassing(primal) measure of productivity change. This measure and itsdecomposition is compared to a number of recent proposals inorder to shed light on what seems to have become a controversialissue. The paper proceeds by developing an encompassing dualmeasure of productivity change. This dual measure is then appliedto panel data of a set of Dutch firms, continuing the empiricalwork of Balk (1998). It turns out that extending the Malmquistproductivity index with factors measuring scale efficiency changeand input mix change leads to appreciably different outcomes.     

Estimation of technical and allocative inefficiency: A primal system approach

The estimation of technical and allocative inefficiencies using a flexible (translog) cost system is found to be quite difficult, especially when both the inefficiencies are random. In this paper we use the alternative primal system consisting of the production function (translog) and the first-order conditions of cost minimization. The estimation of the primal system is more straightforward and it enables us to estimate observation-specific technical and allocative inefficiencies, and their impact on input demand and cost. We use data on steam-electric generating plants from the U.S. to estimate the model using both Cobb–Douglas and translog production functions.