Estimating farmers’ productive and marketing inefficiency: an application to vegetable producers in Benin

This paper estimates the technical and marketing inefficiency of a sample of urban vegetable producers in Benin. Marketing inefficiency is defined as the failure of farmers to achieve better marketing output and is reflected in lower output price indices. The study proposes a Russell-type measure of inefficiency using a directional distance function that accounts simultaneously for the expansion of outputs and price indices and the contraction of variable inputs. A truncated bootstrap regression is used in the second stage to consistently analyze factors that underlie differences in inefficiency. The first-stage results suggest that vegetable producers are more inefficient with respect to marketing than production. The second-stage results indicate that technical inefficiency is affected by the production environment and private extension services. Marketing inefficiency is affected by the type of marketing arrangements.     

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.     

Identifying bank outputs and inputs with a directional technology distance function

The bank efficiency literature lacks an agreed definition of bank outputs and inputs. This is problematic given the long-standing controversy concerning the status of deposits, but also because bank efficiency estimates are known to be affected by the inclusion of additional outputs such as non-traditional (fee-based) activities or risk measures. This paper proposes a data-driven identification of bank outputs and inputs using the directional technology distance function. While previous applications of this tool used symmetric expansion or contraction directions, we focus on a set of orthogonal directions, each corresponding to an assumption on the input/output status of an individual variable. These directions correspond to a set of different specifications, whose estimated coefficients can be used to determine the input or output status of all variables except the regressand. Our empirical analysis revealed a very consistent pattern across the alternative specifications estimated. There is strong evidence that customer deposits are an input, and that non-performing loans are an important undesirable output. Finally, the orthogonal expansions/contractions we consider avoid the simultaneity problem raised by the “convenient normalization” commonly used to impose linear homogeneity in stochastic frontier estimation.     

Probabilistic characterization of directional distances and their robust versions

In this work, we analyze the performance of production units using the directional distance function which allows to measure the distance to the frontier of the production set along any direction in the inputs/outputs space. We show that this distance can be expressed as a simple transformation of radial or hyperbolic distance. This formulation allows to define robust directional distances in the lines of α-quantile or order-m partial frontiers and also conditional directional distance functions, conditional to environmental factors. We propose simple methods of estimation and derive the asymptotic properties of our estimators.     

On Lipschitz continuity of the iterated function system in a stochastic optimal growth model

This paper provides qualitative properties of the iterated function system (IFS) generated by the optimal policy function for a class of stochastic one-sector optimal growth models. We obtain, explicitly in terms of the primitives of the model (i) a compact interval (not including the zero stock) in which the support of the invariant distribution of output must lie, and (ii) a Lipschitz property of the iterated function system on this interval. As applications, we are able to present parameter configurations under which (a) the support of the invariant distribution of the IFS is a generalized Cantor set, and (b) the invariant distribution is singular.     

Efficiency and technological change at US research universities

This article investigates the determinants of efficiency and technological progress at US research universities. It relies on a unique panel data set of multiple outputs and inputs from 92 universities covering the period 1981–1998. Over that time span, US universities experienced large increases in industry funding and in academic patenting activity. In this context, the directional distance function and a nonparametric representation of the underlying production technology are combined to obtain estimates of productivity growth and technical efficiency. An econometric analysis is then presented to examine the determinants of technical efficiency and the rate of technological progress. The results show how changes in funding sources for US research universities affects research performance.     

Analyzing Potentials for Reducing the Energy Requirement of Households in The Netherlands

The energy requirement of households represents a useful concept in studying energy use in relation to production structures and consumption patterns. Reduction potentials of the energy requirement for households provide insight on the possibilities for reducing energy use in the whole economy. We determine reduction potentials by means of implementing energy conservation options in an input–output model for calculating the household energy requirement. The implementation of a set of technical energy conservation options results in a reduction in the energy requirement of Dutch households by 55%. The reduction potential based on a set of demand-side options is 9%. The combination of both sets of conservation options results in a reduction potential of 59%. Therefore, by combining (sets of) options, some effects are cancelled out.     

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.     

Duality theory and pitfalls in the specification of technologies

Principles of duality enable the investigator to model the technology of a multiple-input-single- output firm either by means of a production function or a cost function. For empirical implementation, both alternatives employ the assumption of competitive market behaviour. Recently, functional forms have been developed which are sufficiently flexible to describe the substitution possibilities among factors when the technology consists of more than two factors. However, contrary to the strongly separable multi-factor Cobb-Douglas and CES forms, these functional forms are not self-dual. This poses the problem of choosing between two different maintained hypotheses. In this paper, we compare the inferences with respect to substitution possibilities obtained by imposing the two alternative specifications of a production function and a cost function on the same set of data. We find that they give very different inferences with respect to substitution possibilities between factors. Furthermore, these inferences continue to differ even when we explicitly adopt the position that both the production and cost functions are each approximations of the true technology.     

A Cost System Approach to the Stochastic Directional Technology Distance Function with Undesirable Outputs: The Case of us Banks in 2001–2010

This paper offers a methodology to address the endogeneity of inputs in the directional technology distance function (DTDF)‐based formulation of banking technology which explicitly accommodates the presence of undesirable nonperforming loans—an inherent characteristic of the bank's production due to its exposure to credit risk. Specifically, we model nonperforming loans as an undesirable output in the bank's production process. Since the stochastic DTDF describing banking technology is likely to suffer from the endogeneity of inputs, we propose addressing this problem by considering a system consisting of the DTDF and the first‐order conditions from the bank's cost minimization problem. The first‐order conditions also allow us to identify the ‘cost‐optimal’ directional vector for the banking DTDF, thus eliminating the uncertainty associated with an ad hoc choice of the direction. We apply our cost system approach to the data on large US commercial banks for the 2001–2010 period, which we estimate via Bayesian Markov chain Monte Carlo methods subject to theoretical regularity conditions. We document dramatic distortions in banks' efficiency, productivity growth and scale elasticity estimates when the endogeneity of inputs is assumed away and/or the DTDF is fitted in an arbitrary direction. Copyright © 2015 John Wiley & Sons, Ltd.     

The role of environmental factors in growth accounting

This paper explores a relatively new methodology, the directional distance function method, to analyse productivity growth. The method allows us to explicitly evaluate the role that undesirable outputs of the economy, such as carbon dioxide and other greenhouse gases, have on the frontier production process which we specify as a piecewise linear and convex boundary function. We decompose productivity growth into efficiency change (catching up) and technology change (innovation). We test the statistical significance of the estimates using recently developed bootstrap methods. We also explore implications for growth of total factor productivity in the OECD and Asian economies. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Deregulation and dairy production systems: a Bayesian distance function approach

Milk quota trading rules differ across EU member countries. In Denmark a biannual milk quota exchange was set up in 1997 to promote a more efficient reallocation of milk quotas as well as to reduce transaction costs related to the searching and matching of sellers and buyers. Using two comprehensive unbalanced panel data sets on organic and conventional milk farms this study attempts to disentangle the effects of the introduction of quota transferability on the production structure of those farms as well as the probability of market entry/exit. Bayesian estimation techniques are used to estimate an input oriented generalized Leontief distance function as well as a curvature constrained specification. The results suggest that the deregulation in the quota allocation mechanism led to an increased allocative efficiency of organic as well as conventional milk production as well as a relative shift of the PPF in favor of the production of organic milk.     

Grade inflation or productivity growth? An analysis of changing grade distributions at a regional university

We examine departmental grade distributions for the school years 1985?C1986, 1995?C1996, and 2004?C2005 at Southeast Missouri State University. Mean undergraduate grade point averages (GPAs) increased from 2.6 in 1985?C1986 to 3.1 in 2004?C2005. Although higher student GPAs might be evidence of grade inflation, university departments might have experienced productivity improvements that enhanced student learning, given inputs. We represent the technology by the directional distance function. Departments produce two outputs-grade points earned by students and the information content of those grades-using faculty and student inputs. The entropy index is used to proxy the information content of grade distributions. The estimates indicate; no systematic changes in inefficiency over time; a movement along the production frontier toward a mix of outputs with relative more grade points and less entropy; a shift toward non-tenure track faculty that increases the shadow price of entropy relative to grade points.     

Hyperbolic Efficiency and Parametric Distance Functions: With Application to Spanish Savings Banks

Distance functions are gaining relevance as alternative representations of production technologies, with growing numbers of empirical applications being made in the productivity and efficiency field. Distance functions were initially defined on the input or output production possibility sets by Shephard (1953, 1970) and extended to a graph representation of the technology by Färe, Grosskopf and Lovell (1985) through their graph hyperbolic distance function. Since then, different techniques such as non parametric-DEA and parametric-SFA have been used to calculate these distance functions. However, in the latter case we know of no study in which the restriction to input or output orientation has been relaxed. What we propose is to overcome such restrictiveness on dimensionality by defining and estimating a parametric hyperbolic distance function which simultaneously allows for the maximum equiproportionate expansion of outputs and reduction of inputs. In particular, we introduce a translog hyperbolic specification that complies with the conventional properties that the hyperbolic distance function satisfies. Finally, to illustrate its applicability in efficiency analysis we implement it using a data set of Spanish savings banks.     

A directional slacks-based measure of technical inefficiency

Radial measures of efficiency estimated using linear programming (LP) methods can be biased since slack in the constraints defining the technology suggests that at least one input can be reduced, or one output can be expanded, even though a firm is deemed to be “technically efficient.” In this paper, we propose a directional slacks-based measure of technical inefficiency to account for the potential of slack in technological constraints. When no such slacks exist, directional slacks-based inefficiency collapses to the directional technology distance function. Our proposed measure helps to generalize some of the existing slacks-based measures of inefficiency. We examine the financial services provided by Japanese cooperative Shinkin banks, and estimate their inefficiency during the period 2002–2005. This inefficiency declined slightly during the period. We thus propose that slack is an important source of inefficiency which is often not captured by the directional technology distance function.     

The directional profit efficiency measure: on why profit inefficiency is either technical or allocative

The directional distance function encompasses Shephard’s input and output distance functions and also allows nonradial projections of the assessed firm onto the frontier of the technology in a preassigned direction. However, the criteria underlying the choice of its associated directional vector are numerous. When market prices are observed and firms have a profit maximizing behavior, it seems natural to choose as the directional vector that projecting inefficient firms towards profit maximizing benchmarks. Based on that choice of directional vector, we introduce the directional profit efficiency measure and show that, in this general setting, profit inefficiency can be categorized as either technical, for firms situated within the interior of the technology, or allocative, for firms lying on the frontier. We implement and illustrate the analytical model by way of Data Envelopment Analysis techniques, and introduce the necessary optimization programs for profit inefficiency measurement.     

On the Consistency of Maximum Likelihood Estimation of Monotone and Concave Production Frontiers

Banker and Maindiratta (1992) provides a method for the estimation of a stochastic production frontier from the class of all monotone and concave functions. A key aspect of their procedure is that the arguments in the log-likelihood function are the fitted frontier outputs themselves rather than the parameters of some assumed parametric functional form. Estimation from the desired class of functions is ensured by constraining the fitted points to lie on some monotone and concave surface via a set of inequality restrictions. In this paper, we establish that this procedure yields consistent estimates of the fitted outputs and the composed error density function parameters.     

Is infrastructure capital productive? A dynamic heterogeneous approach

This paper offers an evaluation of the output contribution of infrastructure. Using a panel time series approach and a large cross‐country dataset, the paper estimates a long‐run aggregate production function relating gross domestic product to human capital, physical capital, and a synthetic measure of infrastructure comprising transport, power and telecommunications. Tests of the cointegration rank allowing it to vary across countries reveal a common rank with a single cointegrating vector, which we interpret as the long‐run production function. Estimation of its parameters is performed using the pooled mean group (PMG) estimator, which allows for unrestricted short‐run parameter heterogeneity across countries while imposing the (testable) restriction of long‐run parameter homogeneity. The long‐run elasticity of output with respect to the synthetic infrastructure index ranges between 0.07 and 0.10. The estimates are highly significant, both statistically and economically, and robust to alternative dynamic specifications and infrastructure measures. Tests of parameter homogeneity fail to yield evidence that the long‐run parameters differ across countries. Copyright © 2014 John Wiley & Sons, Ltd.     

Do we estimate an input or an output distance function? An application of the mixture approach to European railways

In this paper, we estimate parametric input and output distance functions and discuss how to estimate a mixture/latent class model (LCM) involving the output and input distance functions in the context of multi-input and multi-output production technology. The proposed technique is applied to a panel data on European Railways (1971–1994). This model allows us to identify determinants of the efficiency orientation, thereby providing useful information that can help researchers to choose between the input and the output-oriented approaches. In addition, we develop cross-indices that can be used to compute input (output) technical inefficiency from the estimates of output (input) distance function.