Productivity Measurement from a Reference Technology: A Distance Function Approach

An approach to productivity measurement based on distance function measurement is developed in this paper. A series of reference technologies are constructed by augmenting observed inputs and outputs such that the resulting effective netputs are consistent with the weak axiom of profit maximization. Geometric means of year-ahead and year-back distance function values serve as measures of multifactor productivity changes. Both primal measures from the inner bound and dual measures from the outer bound of the reference technologies are calculated. Resulting productivity measures are similar to those derived using index number approaches, but potentially provide greater information regarding the reference technologies.     

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.     

Shadow Price Approach to Total Factor Productivity Measurement: With an Application to Finnish Grass-Silage Production

This paper explores an intermediate route between the Fisher and the Malmquist productivity indexes so as to minimize data requirements and assumptions about economic behavior of production units and their production technology. Assuming quantity data of inputs and outputs and the behavioral hypothesis of allocative efficiency, we calculate the exact value of the Fisher ideal productivity index using implicit shadow prices revealed by the choice of input–output mix. The approach is operationalized by means of a nonparametric data envelopment analysis (DEA) model. Empirical application to Finnish grass silage farms suggests that the Malmquist and the Fisher productivity indices yield similar results when averaged over firms, but there can be major differences in the results of the two approaches at the level of individual firms.     

Effective sub-simulation-free upper bounds for the Monte Carlo pricing of callable derivatives and various improvements to existing methodologies

We present a new non-nested approach for computing additive upper bounds for callable derivatives using Monte Carlo simulation. It relies on the regression of Greeks computed using adjoint methods. We also show that it is possible to early terminate paths once points of optimal exercise have been reached. A natural control variate for the multiplicative upper bound is introduced which renders it competitive to the additive one. In addition, a new bi-iterative family of upper bounds is introduced which takes a stopping time, an upper bound, and a martingale as inputs.     

How Common is Housing Discrimination? Improving on Traditional Measures

Fair housing audits are an important tool for measuring the incidence of racial and ethnic discrimination in housing markets. Traditional measures of incidence calculate the proportion of cases in which the white auditor is favored (gross adverse treatment) or the difference between the proportion of white-favored and minority-favored audits (net adverse treatment). The gross measure may overstate discrimination because treatment differences sometimes arise from differences in circumstances across auditor visits. On the other hand, the net measure understates discrimination because audits in which the minority auditor is favored for systematic reasons are incorrectly subtracted. This paper presents a model of agent behavior that more fully accounts for the audit design and employs the estimated parameters to calculate bounds on the incidence of discrimination. This approach leads to a lower bound for the incidence of discrimination that is often substantially higher than the simple net measure and to an upper bound that is close to and sometimes above the simple gross measure.     

Primal (quantity), dual (price) linear optimal control problems and the weak duality theorem

In the continuation primal and dual optimal control problems are formulated. The disticntion between state and control variables, state equations and control variable constraints are discarded. A general treatment is achieved by the introduction of a matrix F. The derivation of the dual from the primal follows approximately the approach by J.B. Rosen. The corresponding weak duality theorem is deduced. It is then indicated how typical optimal control formulations may be obtained by the specialisation of the matrices and vectors and their substitution.The authors gratefully acknowledge friendly advice and assistance given by Professor G.B. Dantzig, Stanford University, USA.     

Efficiency and Technical Change in Intertemporal Intersectoral DEA

A new procedure for the measurement of efficiency and technical change is presented, using DEA with three-dimension data (box data), pooling over sectors, regions and time. Until now, when pooling the data in panel applications it has been assumed that technology remained unchanged, so productivity change was entirely attributed to technical efficiency change. However, patterns of technology change and the decomposition into efficiency and technical change elements can be accomplished by means of restrictions on the general structure of the technology indexes. Under the assumption of non-regressive technical change, upper and lower bounds for efficiency and technical change are obtained. The new methodology is illustrated in an analysis of productivity growth in 13 manufacturing sectors in the Spanish regions from 1980 to 1992.     

Productivity indexes under Hicks neutral technical change

The Malmquist and Hicks–Moorsteen productivity indexes are the two most widely used theoretical indexes for measuring productivity growth of firms, industries and countries. We indicate that these two indexes coincide under constant returns to scale technology and Hicks neutral technical change. While the conditions on production technology under which two indexes coincide have been examined before, this is the first study on the types of technical change under which they coincide. We shed new insight on the relationship between these popular indexes.     

A Biased Valuation: The Treatment of a Professional Degree in Divorce Actions

A bstract Over the past two decades, courts have unsuccessfully attempted to develop a consistent approach to the treatments of a professional degree in divorce actions. After reviewing the conceptual issues involved, a measurement method is suggested which would provide the fact finder with both an upper and a lower bound for the value of a degree. Hypothetical future income streams for average lawyers and physicians, and their spouses, are used to examine the impact of basing property settlements upon each of these bounds. It is argued that both equityand conceptual considerations support the conclusion that past decisions have very often inappropriately failed to consider the upper bound in valuing a degree in divorce settlements.     

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.     

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.     

The effects of geographic expansion on the productivity of Spanish savings banks

This article analyzes the effects of geographic expansion on the productivity of Spanish savings banks. The study uses data from 1992 to 2004, the period when most savings banks expanded geographically. We consider an alternative approach to most multi-stage studies, which uses nonparametric methods both to measure productivity growth and to analyze its relationship with branch office expansion. Specifically, we use nonparametric regression techniques and their natural complement, conditional density estimation. Results indicate that savings banks that expand geographically outside their natural markets achieve greater productivity gains. However, there are some firms for which this result is more moderate. In contrast, lower increases in productivity are found in savings banks that expand on a nationwide basis, or that confine their territorial expansions to their traditional markets.     

A primal Divisia technical change index based on the output distance function

We derive a primal Divisia technical change index based on the output distance function and further show the validity of this index from both economic and axiomatic points of view. In particular, we derive the primal Divisia technical change index by total differentiation of the output distance function with respect to a time trend. We then show that this index is dual to the Jorgenson and Griliches (1967) dual Divisia total factor productivity growth (TFPG) index when both the output and input markets are competitive; dual to the Diewert and Fox (2008) markup-adjusted revenue-share-based dual Divisia technical change index when market power is limited to output markets; dual to the Denny et al. (1981) and Fuss (1994) cost-elasticity-share-based dual Divisia TFPG index when market power is limited to output markets and constant returns to scale is present; and also dual to a markup-and-markdown-adjusted Divisia technical change index when market power is present in both output and input markets. Finally, we show that the primal Divisia technical change index satisfies the properties of identity, commensurability, monotonicity, and time reversal. It also satisfies the property of proportionality in the presence of path independence, which in turn requires separability between inputs and outputs and homogeneity of subaggregator functions.     

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.     

Projection pursuit regression and disaggregate productivity effects: the case of the Indian blast furnaces

Productivity of blast furnaces in India is studied by disaggregating the production process and the utilization process. A dimension‐reducing nonparametric approach—projection pursuit regression—is used. We find that productivity can be increased significantly by improving the quality of coal. There is no evidence that executives have a positive marginal product. The production workers have a negative marginal product for the production process and a positive one for the utilization process. But the training of executives has a positive effect whereas that of the production workers has a negative effect on productivity. Copyright © 2004 John Wiley & Sons, Ltd.     

Bounds for the variance of an inverse binomial estimator

Summary  B est [1] found the variance of the minimum variance unbiased estimator of the parameter p of the negative binomial distribution. M ikulski and Sm [2] gave an upper bound to it, easier to calculate than B est's expression and a good approximation for small values of p and large values of r (the number of successes). In this paper both lower bounds and closer upper bounds are derived.     

Evaluation and monitoring of community youth prevention programs using a robust productivity index

Evidence-based prevention and intervention programs for youth behavioral and mental problems have been implemented by many local community program providers. Due to the differences among communities in resource availability and the demand for services, however, policymakers and program practitioners require ways of measuring organizational efficiency in terms of resource commitment and improvement in individual outcomes. In this paper, we propose a robust productivity index for monitoring managerial performance and detecting exceptions in dynamic environments. Robust productivity bounds are constructed to identify innovators who make a technical shift. The approach is illustrated with panel data on youth outcomes from a selected multi-site community prevention program between the fiscal years 2010 and 2015. The results suggest that our approach not only permits classification of the innovators, but also recognizes patterns of change in productivity.     

Estimation of firm-level productivity in the presence of exports: Evidence from China's manufacturing

Motivated by the long-standing interest of economists in understanding the nexus between firm productivity and export behavior, this paper develops a novel structural framework for control-function-based nonparametric identification of the gross production function and latent firm productivity in the presence of endogenous export opportunities that is robust to recent unidentification critiques of proxy estimators. We provide a workable identification strategy, whereby the firm's degree of export orientation provides the needed (excluded) relevant independent exogenous variation in endogenous freely varying inputs, thus allowing us to identify the production function. We estimate our fully nonparametric instrumental variable model using the Landweber–Fridman regularization with the unknown functions approximated via artificial neural network sieves with a sigmoid activation function, which are known for their superior performance relative to other popular sieve approximators, including the polynomial series favored in the literature. Using our methodology, we obtain robust productivity estimates for manufacturing firms from 28 industries in China during the 1999–2006 period to take a close look at China's exporter productivity puzzle, whereby exporters are found to exhibit lower productivity levels than nonexports.     

Measuring regional efficiency: A method tested on the fabricated metal products industry in Sweden, 1973–1975

This paper presents a method of measuring the efficiency of regions as production environments of manufacturing industries. The approach is a rather general view of the firm in a market economy. The functions which the firms must perform are discussed. From that, hypotheses are made regarding the elements of the environment which should constitute the regional production milieu and thus influence the efficiency of the firms. By way of factor analysis the original variables are reduced to seven regional factors, which are put into productivity functions where their parameters are estimated. From those parameters indexes of regional efficiency are calculated.     

Testing neoclassical production theory

In this paper we propose and carry out some tests that help us evaluate the neoclassical theory of production. First, we use the implied relationship between cost (production) and (inverse) derived demand equations to provide a test which can be interpreted as a test for the validity of the theory. Then, using the same relationships we provide a test for the internal consistency of the theory. Finally, we examine the extent to which the primal and dual models yield the same implications. We find that except for one case the theory does not pass the proposed tests and furthermore, the primal and dual do not yield the same implications.