A primal-dual approach to nonparametric productivity analysis: The case of U.S. agriculture

Nonparametric methods for measuring productivity indexes based on bounds for the underlying production technology are presented. Following Banker and Maindiratta, the lower bound is obtained from a primal approach while the upper bound corresponds to a dual approach to nonparametric production analysis. These nonparametric bounds are then used to estimate input-based and output-based distance functions. These radial measures provide the basis for measuring productivity indexes. Application to times series data on U.S. agriculture indicates a large gap between the primal lower bound and the dual upper bound. This generates striking differences between the primal and dual nonparametric productivity indexes.Respectively, professor and associate professor of Agricultural Economics, University of Wisconsin-Madison. Seniority of authorship is equally shared. We would like to thank Rolf Färe and an anonymous reviewer for useful comments on an earlier draft of the paper. This research was supported in part by a Hatch grant from the College of Agriculture and Life Sciences, University of Wisconsin-Madison.     

A Quasi-Malmquist Productivity Index

The Malmquist productivity index is based on distance functions, which are reciprocals of radial Debreu-Farrell efficiency measures, and which have a number of desirable properties. Linear programming techniques are frequently employed to calculate the efficiency measures. However these techniques can leave slacks, which constitute a non-radial form of inefficiency which is not incorporated into the analysis. Thus a radial efficiency measure overstates true efficiency, the reciprocal distance function understates the distance to the relevant efficient subset, and the Malmquist productivity index is adversely affected, although in an analytically indeterminate direction. This has led us to consider a new definition of one-sided efficiency, and to develop a new nonradial efficiency measure which incorporates all slacks on the selected side. Replacing conventional radial efficiency measures with our new non-radial efficiency measures generates what we call a quasi-Malmquist productivity index. We illustrate our quasi-Malmquist productivity index with an application to productivity change in Spanish banking.     

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.     

Malmquist Indexes Using a Geometric Distance Function (GDF). Application to a Sample of Portuguese Bank Branches

Traditional approaches to calculate total factor productivity (TFP) change through Malmquist indexes rely on distance functions. In this paper we show that the use of distance functions as a means to calculate TFP change may introduce some bias in the analysis, and therefore we propose a procedure that calculates TFP change through observed values only. Our total TFP change is then decomposed into efficiency change, technological change, and a residual effect. This decomposition makes use of a non-oriented measure in order to avoid problems associated with the traditional use of radial oriented measures, especially when variable returns to scale technologies are to be compared. The proposed approach is applied in this paper to a sample of Portuguese bank branches.     

Measuring input-specific productivity change based on the principle of least action

In for-profit organizations, efficiency and productivity measurement with reference to the potential for input-specific reductions is particularly important and has been the focus of interest in the recent literature. Different approaches can be formulated to measure and decompose input-specific productivity change over time. In this paper, we highlight some problems within existing approaches and propose a new methodology based on the Principle of Least Action. In particular, this model is operationalized in the form of a non-radial Luenberger productivity indicator based on the determination of the least distance to the strongly efficient frontier of the considered production possibility sets, which are estimated by non-parametric techniques based upon Data Envelopment Analysis. In our approach, overall productivity change is the sum of input-specific productivity changes. Overall productivity change and input-specific changes are broken up into indicators of efficiency change and technical change. This decomposition enables the researcher to quantify the contributions of each production factor to productivity change and its components. In this way, the drivers of productivity development are revealed. For illustration purposes the new approach is applied to a recent dataset of Polish dairy processing firms.     

Evaluating food retailing efficiency: the role of information technology

Information and internet-based technologies have fostered new supply chain initiatives in food retailing but little research has evaluated performance and efficiency impacts. A distance function based on three key performance measures for food retailers is used to evaluate store performance and efficiency. The effects of store format, membership in a chain, unionization, and the adoption of a variety of information technologies. Supply chain technologies are groups into three general categories including data sharing technologies, decision sharing technologies, and technologies that support product assortment, pricing, and merchandising decisions.      

Parametric Decomposition of a Generalized Malmquist Productivity Index

This paper provides a parametric decomposition of a generalized Malmquist productivity index which takes into account scale economies. Unlike Balk (2001), the contribution of scale economies to productivity change is evaluated without recourse to scale efficiency measures, which are neither bounded for globally increasing, decreasing, or constant returns to scale technologies nor for ray-homogeneous technologies. An empirical application using panel data from Spanish savings banks is included. This application shows the advantages of the suggested method compared to Balk's approach. The results show an increase of total factor productivity which can be mainly attributed to technical progress and the positive effect of returns to scale.     

A profit function approach to measuring productivity growth: The case of U.S. manufacturing

This article proposes a method of estimating productivity growth using an estimated profit function. The approach has the advantage of incorporating endogenous changes in profit-maximizing output levels that would result from productivity changes. As with the cost function, it can be easily adapted to accomodate the presence of quasi-fixed factors. The article first develops the methodology and shows the equivalence between the proposed measure and other measures of productivity based on cost or production functions. An empirical application to the measurement of productivity changes in the U.S. manufacturing industry is presented next. The profit-function measure is compared to a nonparametric measure based on the same data and to the results of other studies of U.S. manufacturing.The refereeing process of this paper was handled through J. deMelo.     

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.     

An econometric approach to estimating support prices and measures of productivity change in public hospitals

In industry sectors where market prices for goods and services are unavailable, it is common to use estimated output and input distance functions to estimate rates of productivity change. It is also possible, but less common, to use estimated distance functions to estimate the normalised support (or efficient) prices of individual inputs and outputs. A problem that arises in the econometric estimation of these functions is that more than one variable in the estimating equation may be endogenous. In such cases, maximum likelihood estimation can lead to biased and inconsistent parameter estimates. To solve the problem, we use linear programming to construct a quantity index. The distance function is then written in the form of a conventional stochastic frontier model where the explanatory variables are unambiguously exogenous. We use this approach to estimate productivity indexes, measures of environmental change, levels of efficiency, and support prices for a sample of Australian public hospitals.     

Exponential environmental productivity index and indicators

The major contributions of this paper are twofold. First, it introduces an exponential environmental productivity indicator and its ratio-based counterpart constructed through an exponential distance function. These innovative exponential environmental productivity index and indicator inherit the basic structure of both Malmquist-Luenberger productivity index and environmental Luenberger productivity indicator. Thereafter, an exponential version of the environmental Luenberger-Hicks-Moorsteen productivity indicator is proposed. Such a specification allows to overcome the special issue of infeasabilities. Second, looking from a dynamical viewpoint, we propose an exponential generalized dynamical distance function. This new efficiency measure shows the degree of efficiency of an observation, taking into consideration its technical efficiency and/or technological variation adjustment path. A sample of 11 representative French airports is considered over the period 2008–2011, in order to implement these new exponential environmental productivity index and indicators.     

PRODUCTIVITY IN PUBLIC SERVICES

Abstract.  This paper discusses issues arising in the measurement of productivity in public services. Compared to measuring productivity in the private sector difficulties arise because the output of public services is often unpriced and because some public services are consumed collectively. A key problem is measuring the full range of outputs and quality improvements delivered by public sector organizations that are valued by society. Without comprehensive measures of output, productivity statistics may be misleading. I outline methods used in the measurement of both private and public sector productivity and discuss the measurement of public sector productivity in practice. Finally I discuss studies that examine factors underlying productivity differences and productivity growth in public and private sector organizations. Public sector reforms and the use of pilot schemes in public sector organizations present opportunities for research to identify causal effects on productivity.     

Spatial dependence,agglomeration externalities and the convergence of carbon productivity

By combining the extended slack based measurement (SBM) model directed distance function and the meta-constrained production function to measure China's carbon productivity, this paper studies the spatial spillover effects and convergence characteristics of carbon productivity. According to the results, carbon productivity showed obvious viscosity and spatial dependence in adjacent regions. China's carbon productivity had spatial conditional β-convergence and club convergence effects. Specifically, agglomeration externalities constituted an important mechanism for increasing carbon productivity and realizing the convergence thereof. Different agglomeration forms under different agglomeration degrees corresponded to different carbon productivity levels; with an increase in the degree of agglomeration, the emission reduction effect of specialized agglomeration diminished, while that of diversified agglomeration increased. Furthermore, depending on suitable agglomeration degrees, the emission reduction effect of specialized agglomeration could coexist with that of diversified agglomeration. In terms of regional distribution, in East China, both specialized agglomeration and diversified agglomeration presented relatively significant emission reduction effects. In contrast, in Central China and West China, only specialized agglomeration showed a weak emission reduction effect.     

Capital use intensity and productivity biases

Measures of productivity growth are often pro-cyclical. This paper focuses on measurement errors in capital inputs, associated with unobserved variations in capital utilization rates, as an explanation for the existence of pro-cyclical patterns in measures of productivity. Recently constructed national and state-specific indexes of inputs, outputs, and productivity in U.S. agriculture for 1949–2002 are used to estimate production functions that include proxy variables for changes in the utilization of durable inputs. The proxy variables include an index of farmers’ terms of trade and an index of local seasonal growing conditions. We find that utilization responses by farmers are significant and bias measures of productivity growth in a pro-cyclical pattern. We quantify the bias, adjust the measures of productivity for the estimated utilization responses, and compare the adjusted and conventional measures.     

Productivity gaps and capacity utilization in the manufacturing sectors of five OECD-countries, 1963–1982

The purpose of this paper is to apply some novel features in the theory of productivity indexes to the measurement of productivity gaps. It advances the proposition that one reason for the persistence of productivity gaps might be that the methodology of measuring gaps does not separate shifts of the production function due to intercountry efficiency from shifts due to intercountry differences in capacity utilization.In this paper we calculate productivity gaps for four OECD countries relative to the U.S., adjusted for cyclical variations in capacity utilization for the period 1963–1982. The theoretical foundation of our measurement is based on a variable cost function approach with short-run fixity of capital. Without adjusting for differences in capacity utilization within the countries, productivity gaps are a mixture of differences in productivity and in capacity utilization.The refereeing process of this paper was handled through C. Morrison.     

Spatial externalities and agglomeration in a competitive industry

We introduce spatial spillovers as an externality in the production function of competitive firms operating within a finite spatial domain under adjustment costs. Spillovers may attenuate with distance and the overall externality could contain positive and negative components with the overall effect being positive. We show that when the spatial externality is not internalized by firms, spatial agglomerations may emerge endogenously in a competitive equilibrium. The result does not require increasing returns at the private or the social level, increasing marginal productivity of private capital with respect to the externality, or location advantages. In fact agglomerations may emerge with decreasing returns to scale, declining marginal productivity of private capital with respect to the externality, and no location advantage. The result depends on the interactions between the structures of production technology and spatial effects as shown in the paper. No agglomerations emerge at the social optimum when spillovers are internalized and diminishing returns both from the private and the social point of view prevail. Numerical experiments with Cobb–Douglas and CES technologies and an isoelastic demand confirm our theoretical predictions.     

浅谈隧道监控量测技术

对隧道监控量测技术进行探讨,介绍了隧道监控量测方法、周边水平位移量测、拱顶下沉量测、地表下沉量测、量测数据分析和信息反馈等技术,为类似工程提供参考。     

Errors of measurement and the recent acceleration in manufacturing productivity growth

Using detailed (4-digit SIC) industry data for the years 1958–1989, I examine whether the recent acceleration in manufacturing productivity can be attributed to the effects of mismeasurement of the prices of inputs and output, by testing a model linking a set of proxy variables for measurement error to a series of measures of acceleration in total factor productivity (TFP). Alternative TFP estimates are presented in order to determine if the findings are sensitive to the method of TFP calculation. The results are inconsistent with the measurement error hypothesis and invariant to the specification of the TFP equation.     

Estimating Capital Inputs for Productivity Measurement: An Overview of U.S. Concepts and Methods

The U.S. Bureau of Labor Statistics (BLS) publishes measures of multifactor productivity, which are patterned after the Solow residual. Inputs of capital must be aggregated with inputs of labor. The theory requires a measure of the capital service flow, a rather abstract notion which is rarely observable. The BLS procedures for capital measurement are summarized, and the rationale for these procedures is explored. Implicit measures of capital services are derived from data on property income and data on historical investments which are detailed as to type of asset.     

A comparative assessment of the productivity of Australia's public rail systems 1971/72–1991/92

There is a growing interest in the establishment of suitable measures of the overall performance of government business enterprises, particularly railways, which are a major recipient of government subsidy. They must improve their performance and become more cost efficient. Any policy designed to reduce costs must consider the implications of resultant actions on the overall productivity of a business. We propose the use of the total factor productivity index as an appropriate reference benchmark, to enable each railway to evaluate the productivity implications of any change to the operating and managerial environment. Using the Institute of Transport Studies' rail database, total factor productivity indices are derived annually from 1971/72 to 1991/92 for the 5 major public rail systems in Australia and sources of variation are identified.The paper recognizes the need to identify sources of variation in productivity which translate into operational guidelines for management in assisting them to improve performance over time. A contribution is the recognition of the importance of including both demand side (final output) and supply, side measures of output (intermediate output). Final output may be more important for monitoring the performance of an enterprise from a cost-effectiveness perspective, but a supply side measure is often more useful to operators because it is the dimension of output over which they have more control.The research reported in this paper was partially funded by an Australian Research Council grant (No. A78930595).