The global properties of the two minflex Laurent flexible functional forms

The minflex Laurent flexible functional form is a special case of a second-order Laurent series expansion. The minflex Laurent, when constructed in square roots, is called the minflex Laurent (ML) generalized Leontief. The minflex Laurent (ML) translog model is the minflex Laurent in logarithms. We find that the regular region of the ML translog is most often even larger than that of the ML generalized Leontief model, except when substitutability is very low. We previously have shown that the regular region of the ML generalized Leontief is substantially larger than that of the usual translog and generalized Leontief models.     

Productivity trends in U.S. manufacturing: Evidence from the NQ and AIM cost functions

In this paper, we take the econometric approach to productivity measurement in United States manufacturing, using KLEM data over the period from 1953 to 2001. We are also interested in technical change bias, price elasticities, and elasticities of substitution in the U.S. manufacturing industry. We present an empirical comparison and evaluation of the effectiveness of four well-known flexible cost functions—the locally flexible generalized Leontief (see Diewert [1971. An application of the Shephard duality theorem: a generalized Leontief production function. Journal of Political Economy 79, 481–507]), translog (see Christensen et al. [1975. Transendendal logarithmic utility functions. American Economic Review 65, 367–364]), and normalized quadratic (see Diewert and Wales [1987. Flexible functional forms and global curvature conditions. Econometrica 55, 43–68])—and the globally flexible asymptotically ideal model (see Barnett et al. [1991. Semi-nonparametric Bayesian estimation of the asymptotically ideal production model. Journal of Econometrics 49, 5–50]), the latter modified to introduce technical change by means of Thomsen's [2000. Short cuts to dynamic factor demand modelling. Journal of Econometrics 97, 1–23] factor-augmenting efficiency index approach.     

Incorporating monotonicity and concavity conditions in flexible functional forms

Empirical economists using flexible functional forms often face the disturbing choice of drawing inferences from an approximation violating properties dictated by theory or imposing global restrictions that greatly restrict the flexibility of the functional form. Focusing on the cost function, this paper presents an alternative approach which imposes monotonicity and concavity properties only over the set of prices where inferences will be drawn. An application investigating elasticities for Berndt-Wood data set using the translog, generalized Leontief, and symmetric generalized McFadden flexible functional forms illustrates the technique. © 1996 John Wiley & Sons, Ltd.     

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.     

The impact of office machinery,and computer capital on the demand for heterogeneous labour

We study the impact of office and computing machinery (OCM) on the labour demand for workers with different educational levels. The empirical analysis relies on a system of demand equations that nests the translog, the generalised Leontief and the normalised quadratic specifications. Using panel data on 35 German industries, we find little evidence for a robust substitutability relationship between unskilled workers and OCM capital in manufacturing industries. In the non-manufacturing sector, however, we find some evidence for substitutability between OCM capital and unskilled workers.     

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.     

Estimating substitution elasticities with the Fourier cost function: Some Monte Carlo results

The Fourier flexible form possesses desirable asymptotic properties that are not shared by other flexible forms such as the translog, generalized Leontief, and generalized Box-Cox. One of them is that an elasticity of substitution can be estimated with negligible bias in sufficiently large samples regardless of what the true form actually is, save that it be smooth enough. This article reports the results of an experiment designed to determine whether or not this property obtains in samples of the sizes customarily encountered in practice. A three-input, homothetic version of the generalized Box-Cox cost function was used to generate technologies that were oriented in a two-dimensional design space according to a central composite rotatable design; the two factors of the design were the Box-Cox parameter and a measure of the dispersion of the substitution matrix. The Fourier cost function was used to estimate the substitution elasticities at each design point, and the bias at each point was estimated using the Monte Carlo method. A response surface over the entire design space was fitted to these estimates. An examination of the surface reveals that the bias is small over the entire design space. Roughly speaking, the estimates of elasticities of substitution are unbiased to three significant digits using the Fourier flexible form no matter what the true technology. Our conclusion is that the small bias property of the Fourier form does obtain in samples of reasonable size; this claim must be tampered by the usual caveats associated with inductive inference.     

Technical efficiency during economic reform in Nicaragua: evidence from farm household survey data

This paper employs a translog stochastic frontier model to examine technical efficiency of maize and bean farmers in two selected regions of Nicaragua using farm-level survey data for the 1994–1995 crop year. The average technical efficiency levels are 69.8 and 74.2% for maize and beans, respectively. The results from the maize and beans translog frontier functions show that farmers’ human capital represented by the level of schooling, access to formal credit and farming experience represented by age contribute positively to production efficiency, while farmers’ participation in non-farm employment tends to reduce production efficiency.     

Separating Technical Change from Time-Varying Technical Inefficiency in the Absence of Distributional Assumptions

This paper proposes an alternative model for separating technical change from time-varying technical inefficiency. The proposed formulation uses the general index, developed by Baltagi and Griffin (1988), to model technical change in the production frontier function and a quadratic function of time, as in Cornwell, Schmidt and Sickles (1990), to capture the temporal pattern of technical inefficiency. In such a setting, all parameters associated with the rate of technical change and the temporal pattern of technical inefficiency are identified separately. Moreover, the proposed formulation is independent of any distributional assumption concerning the one-sided error term associated with technical inefficiency, and it can be estimated in a single stage with non-linear FGLS. Empirical results based on a translog production frontier, and estimates of technical inefficiency and technical change are presented for the UK dairy sector over the period 1982–1992.     

A Parametric Distance Function Approach for Malmquist Productivity Index Estimation

Malmquistindexes of productivity are generally estimated using index numbertechniques or non-parametric frontier approaches. The aim ofthis paper is to show that Malmquist indexes can be estimatedin a similar way using parametric-deterministic or parametric-stochasticfrontier approaches. To allow a multi-output multi-input technologyand for technical change in production, we adopt an output distancefunction which is specified in a translog form. We then showthat using the estimated parameters, several radial distancefunctions can be calculated and combined in order to estimateand decompose the productivity index. Finally, this approachis applied to a panel of Spanish insurance companies. The mainresults confirm those generally obtained for financial services:very low rates of growth and technical change in spite of a rapidderegulation process and expansion of activity.     

Total Factor Productivity Growth and Technical Change in a Profit Function Framework

This paper develops a framework for measuring and decomposing TFP changes, within the parametric approach, by using directly the estimated parameters of a profit function. Two alternative relationships are derived for measuring and decomposing TFP changes via a profit function based on two alternative definitions of the rate of technical change, i.e., input- and output-based. Initially a long-run equilibrium framework is assumed and then the analysis is extended to the case of temporary equilibrium. The latter framework is applied to US agriculture by estimating a translog profit function and analyzing TFP changes during the period 1948–1994.     

DISAGGREGATING INPUT–OUTPUT MODELS WITH INCOMPLETE INFORMATION

Disaggregating a sector within the Leontief input–output (IO) framework is not a straightforward task since there is more than one possibility for the unknown technical coefficients of the disaggregated IO table, and more information than what is embodied in the aggregated IO table is thus required. This paper presents a methodology for disaggregating sectors into an arbitrary number of new sectors when the only available information about the newly formed sectors is their output weights. A random walk algorithm is used to explore the polytope containing the admissible combinations for the unknown technical coefficients of the disaggregated IO table. These combinations are then used to construct the probability distribution of the coefficients of the inverse Leontief matrix. The methodology is illustrated by disaggregating the electricity production sector of China's 2007 IO table and by looking at the probability distribution of the CO₂ emission intensity factors of the sectors of the economy.     

Australia’s mining productivity decline: implications for MFP measurement

This paper investigates the mining sector’s poor productivity performance as measured by the growth accounting formula for multifactor productivity (MFP) index during the recent mining boom in Australia. We provide an alternative measure of productivity growth by estimating a translog variable cost function, with parameters that separate productivity growth due to technical change from that due to the effects of returns to scale, capacity utilisation and natural resource inputs. The results show that the average MFP growth in Australian mining based on the dual cost-function measure of technical change is 2 % over the sample period 1974–1975 to 2007–2008, rather than ?0.2 % from the published index. The difference arises because declining natural resource inputs, the effects of capacity utilisation and returns to scale have all reduced the ‘true’ MFP growth.     

Production cost structure of us hospital pharmacies: Time-series,cross-sectional bed size evidence

There are current concerns about potential factor substitutions and their implications for factor employments and cost containment in US hospital pharmacies. A translog production cost model is estimated for these pharmacies, using 1981–9 times-series data consisting of seven cross-sectional bed size classes per year. Zellner's joint GLS estimation of three-factor cost share equations and the parent translog cost function reveals that pairwise factor substitutions are severely limited; production is non-homothetic, occurring in the range of scale diseconomies; biased and pure technical change effects dominate the scale-augmenting component. Implications of findings are rationalized in the context of the emerging biopharmaceutical technologies.     

On the cost-reducing effects of embodied technical progress: a panel study of the steel industry in Japan

To explicitly explain the cost-reducing effects of technical progress experienced by each firm, we assume that technical progress, namely, the prevalence of particular equipment, can be expressed by a function of logarithmic physical capital. Regarding the technology cost structure, we propose a modified dynamic cost function model that consists of the above equation, the translog variable cost equation containing technical progress as one of the factors, and Euler equations with respect to physical and research and development capital stocks. Using data on eight firms in the Japanese electric-furnace steel industry for the period 1970–1998, the model was empirically validated using the generalized method of moments. An elasticity of production cost with respect to technical progress showed a cost-reducing effect. This fact was influenced by the type of product and the extent of each firm’s R&D. Also derived from this model is one reasonable phenomenon of business-cyclically changing the use of endogenous capacity. This economic information supports the appropriateness of the above model, including the assumption of transforming technical progress into an endogenous variable, and the methods of analysis.     

A STRUCTURAL DECOMPOSITION APPROACH TO COMPARING MRIO DATABASES

The construction of multi-regional input–output tables is complex, and databases produced using different approaches lead to different analytical outcomes. We outline a decomposition methodology for investigating the variations that exist when using different multiregional input–output (MRIO) systems to calculate a region's consumption-based account. Structural decomposition analysis attributes the change in emissions to a set of dependent determinants, such as technical coefficients, the Leontief inverse and final demands. We apply our methodology to three MRIO databases – Eora, GTAP and WIOD. Findings reveal that the variation between Eora and GTAP can be attributed to differences in the Leontief inverse and emissions’ data, whereas the variation between Eora and WIOD is due to differences in final demand and the Leontief inverse. For the majority of regions, GTAP and WIOD produce similar results. The approach in this study could help move MRIO databases from the academic arena to a useful policy instrument.     

Productivity and efficiency at bank holding companies in the U.S.: a time-varying heterogeneity approach

This paper investigates the productivity and efficiency of large bank holding companies (BHCs) in the United States over the period 2004–2013, by estimating a translog stochastic distance frontier (SDF) model with time-varying heterogeneity. The main feature of this model is that a multi-factor structure is used to disentangle time-varying unobserved heterogeneity from inefficiency. Our empirical results strongly suggest that unobserved heterogeneity is not only present in the U.S. banking industry, but also varies over time. Our results from the translog SDF model with time-varying heterogeneity show that the majority of large BHCs in the U.S. exhibit increasing returns to scale, a small percentage exhibit constant returns to scale, and an even smaller percentage exhibit decreasing returns to scale. Our results also show that on average the BHCs have experienced small positive or even negative technical change and productivity growth.     

Measuring technical and allocative inefficiency in the translog cost system: a Bayesian approach

In this paper, we propose simulation-based Bayesian inference procedures in a cost system that includes the cost function and the cost share equations augmented to accommodate technical and allocative inefficiency. Markov chain Monte Carlo techniques are proposed and implemented for Bayesian inferences on costs of technical and allocative inefficiency, input price distortions and over- (under-) use of inputs. We show how to estimate a well-specified translog system (in which the error terms in the cost and cost share equations are internally consistent) in a random effects framework. The new methods are illustrated using panel data on U.S. commercial banks.     

Functional Forms of Stochastic Frontier Production Functions and Models for Technical Inefficiency Effects: A Comparative Study for Wheat Farmers in Pakistan

This paper considers translog and Cobb-Douglas stochastic frontiers in which the technical inefficiency effects are defined by three different models. The models involved are the time-varying inefficiency model, proposed by Battese and Coelli (1992), the inefficiency effects model for panel data, proposed by Battese and Coelli (1995), and the non-neutral frontier model, proposed by Huang and Liu (1994). Technical change is also accounted for in the frontier models. Predicted technical efficiencies of the wheat farmers and estimates of the elasticities of wheat production with respect to the different inputs and the returns-to-scale parameter are compared under the different model specifications.