Translog Specification Research Articles

Measurement of a cost function for US airlines: restricted and unrestricted translog models

This paper continues and expands several themes from previous studies of commercial airline cost functions. A well specified industrial cost function reveals characteristics about the market players, such as economies of scale and the cost elasticities with respect to operational styles. Using a translog specification, and its restricted first-order form, this paper updates previous parameter estimates, reworks the experimental design, and gives new analysis to describe the spectrum of choices facing airline firms in recent years. The translog model in this paper allows the energy cost share to interact with other variables and illuminate what factors may exacerbate cost sensitivity to energy prices, an advance in this specific area of interpretation. The result shows that fuel cost shares tend to be higher with older equipment, smaller fleet sizes, and to be increasing in aircraft size and seating density. The restricted first-order model indicates that older aircraft designs are more costly to operate, even accounting for operational style. This may imply that airlines with poorer access to capital suffer a cost disadvantage, particularly during a fuel spike - also a new contribution of the paper. Finally, the first-order model does not reject constant returns to scale (CRS) for fleet expansion, or increasing returns to scale (IRS) in aircraft size, which are the expected results.

Heterogeneous Farm Output and Technical Efficiency Estimates

Farmers in most OECD countries are engaged in different activities which go beyond agriculture. When assessing farm performance, it is appropriate to model these heterogeneous farm outputs separately. In this study, we use the distance function approach, which allows the consideration of technology with multiple outputs and multiple inputs. We compare estimates from single-output technology with estimates from multiple- output technology. Our empirical analysis is based on an unbalanced panel of dairy farms in the plain region of Switzerland for the period from 2003 to 2009. We choose the parametric estimation method and employ a translog specification of the production technology. The test of output separability favours a model that separately considers three different outputs: agricultural output; para-agricultural output; and direct payments. The separate modelling of direct payments has considerable influence on the estimated technology parameters as well as the technical efficiency scores. The consideration of direct payments as a separate output increases the elasticity of land by a factor greater than two and, accordingly, reduces the distance function elasticities of other inputs. The average technical efficiency estimates do not differ substantially when specifications differ. However, we reveal serious differences in the estimates of technical efficiency for individual farms. The estimated rank correlation coefficients show that the ranking of farms in terms of technical efficiency differs considerably when direct payments are modelled as a separate output.

On Price and Income Effects in Discrete Choice Models

We consider the classical micro-economic foundation of discrete choice, additive random utility models, with conditional utilities depending on expenditure on the numéraire. We show that signs of own- and cross-price effects are identified on the basis of the primal problem only, and Giffen behaviour is ruled out. For the translog specification, we prove that the alternative with highest price behaves as normal good, and the alternative with lowest price behaves as inferior good. We establish conditions for equivalence between the primal and the dual problem. We provide a discrete choice version of the Slutsky equation which, similarly to divisible goods, decomposes the own-price effect into a substitution and an income effect.

Integration of choice probabilities in logit

We find for logit with income effects a function that generates choice probabilities via Roy’s identity. We show that it possesses all the properties to qualify as an indirect utility, it has a closed-form expression for the practically interesting translog specification of the systematic utilities, it reduces in the case without income effects to the expectation of the maximum utility. We discuss the use of the findings in welfare measurement and the extension to observed heterogeneity and mixed logit.

Estimation and decomposition of inefficiency when producers maximize return to the outlay: an application to Norwegian fishing trawlers

This paper deals with estimation of a production technology where endogeneous choice of input and output variables is explicitly recognized. In particular, we assume that producers maximize return to the outlay (RO). For simplicity and tractability we start with a Cobb–Douglas transformation function with multiple inputs and outputs and show how the first-order conditions of RO maximization can be used to derive an estimating equation which is nothing but a partial input productivity equation. This equation does not suffer from the econometric endogeneity problem although the output and input variables are endogenous. First, we consider the case where producers are fully efficient allocatively but technically inefficient. The model is estimated using a single equation stochastic frontier approach. The model is then extended to allow allocative inefficiency and it is estimated as a system using generalized method of moment. Algebraic expressions are derived to decompose the effect of technical and allocative inefficiencies on RO. We also consider translog specifications that are estimated as (1) a single equation frontier model as well as (2) a system. We use a panel of Norwegian fishing trawlers data to estimate the model. Outputs are different species caught while inputs are labor and vessel size. We also control for number of days of operation, age of the vessel and year effects. Empirical results show that the average rate of RO is reduced by about 20 to 30 % due to technical inefficiency. On the other hand, average allocative efficiency is found to be about 78 %. The average overall efficiency is found to be around 60 %.

Functional form and aggregate energy demand elasticities: A nonparametric panel approach for 17 OECD countries

This paper studies whether the commonly used linear parametric model for estimating aggregate energy demand is the correct functional specification for the data generating process. Parametric and nonparametric econometric approaches to analyzing aggregate energy demand data for 17 OECD countries are used. The results from the nonparametric correct model specification test for the parametric model rejects the linear, log-linear and translog specifications. The nonparametric results indicate that the effect of the income variable is nonlinear, while that of the price variable is linear but not constant. The nonparametric estimates for the price variable is relatively low, approximately −0.2.

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.

Productivity Growth in German Dairy Farming using a Flexible Modelling Approach

AbstractA random‐coefficients specification of an output distance function is used to measure and decompose productivity growth in German dairy farming. This specification can accommodate heterogeneity with respect to the technology employed by dairy farms, allowing for specialised and non‐specialised farms to be included in the analysis. The proposed modelling approach is favoured by the data when compared with the conventional translog specification of distance functions. The average total factor productivity growth rate for German dairy farms is estimated at 1.1%, with the technical progress component contributing most of this growth.

International Airports: Economies of Scale and Marginal Costs

Regarding some regulation fields, such as optimal investments and pricing policies, marginal cost estimations for infrastructure-intensive transport services is always a challenging task. The lack of comparable data among airports is one of the causes which could explain the relative scarcity of this literature in the past. In this paper, the returns to scale and marginal costs are estimated using single-and multi-product translog specifications of a long-run cost function. A pooled database of financial data on 41 airports across Europe, North America, Asia, and Australia for the period 1991-2005 was used. Significant economies of scale and little degree of technological progress are found using Work Load Units (WLU) and Air Traffic Movements (ATM) as output measures. Additionally, individual long-run marginal cost estimates are provided for each output measure, and for every airport under study.

A Look Inside the Forge: Developer Productivity and Spillovers in Open Source Projects

This paper presents an empirical study on the production of open source software, based on a panel of 10,553 projects registered on SourceForge over a period of 28 months (February 2005 until May 2007). We use a flexible Translog specification to estimate a production function relating the number of program updates with the number of corporate and voluntary contributors, taking into account the spillovers flowing from other projects. We find that corporate developers are the more productive ones, but that associating them with other developers in a project entails inefficiencies. We also find evidence of non-decreasing returns to scale in open source projects, thus suggesting substantial efficiency gains of division of labor in large open source projects. Our empirical analysis finally highlights a substantial impact of spillovers on productivity. Spillovers mainly benefit mature projects. They especially flow between projects with the same topic and/or programming language, and have a stronger impact in projects involving corporate developers.

Generalized Quadratic Revenue Functions

In this paper we focus on specification of revenue functions in their dual price space. We consider two distance functions, both dual to the revenue function: Shephard output distance function and the directional output distance function, both in price space. The former is multiplicative, satisfying homogeneity, the latter is additive satisfying transitivity. Functional equation methods yield translog specification for the Shephard case and quadratic for the directional case. Monte Carlo evidence suggests that the quadratic specification more precisely represents technology.

R&D efficiency and economic performance: A cross-country analysis using the stochastic frontier approach

This paper constructs a cross-country production model for evaluating the relative efficiency of aggregate R&D activities. Stochastic frontier methods incorporating translog specification are applied to data of 30 countries in recent years. R&D capital stock and manpower are considered as inputs; patents and academic publications are regarded as outputs. Environmental factors that influence R&D performance are also taken into account. The means of efficiency scores without taking the environmental effects into account are about 0.65 in the cross-country study. After controlling for the operating environment, the means increase to about 0.85. R&D performance indices show a positive correlation with income level. Policy implications on resources allocation and R&D strategies are discussed.

Trip-Level Analysis of Efficiency Changes in Oregon's Deepwater Trawl Fishery

In 2003, an industry-financed, government-administered buyback of trawl fishing permits and vessels took place on the US West Coast, resulting in the retirement of about one-third of the limited-entry trawl fleet. The lack of cost data in this fishery precludes an analysis of how the buyback has affected profitability, but changes in technical efficiency can provide some insight into the program's effects. This paper, the first of a planned series of analyses of the buyback's effect on technical efficiency in the trawl fleet, applies stochastic frontier analysis to assess whether technical efficiency changed perceptibly after 2003. We adopt a hierarchical modeling approach estimated with Markov Chain Monte Carlo methods, and present results from both Cobb-Douglas and translog specifications. The analysis is limited to 13 boats active in Oregon's deepwater 'DTS' fishery, which targets dover sole, thornyheads, and sablefish. The results suggest that the buyback has had little impact on trip-level technical efficiency in the study fishery. However, departures from the frontier are markedly bi-modal, indicating that a mixed-density approach to estimation may be more appropriate.

Economic Theory and Econometric Practice: Parametric Efficiency Analysis

Parametric efficiency analysis is one of the most investigated areas in applied production economics. Nevertheless, the vast majority of empirical studies are not accompanied by a thorough theoretical interpretation of the underlying functional form and the obtained estimates. The robustness of policy suggestions based on inferences from efficiency measures nevertheless crucially depends on theoretically well-founded estimates. This research contribution adresses parametric efficiency measurement by critically reviewing the theoretical consistency of recently published technical efficiency estimates. The theoretical concerns are verified by empirical applications confirming the need for a posteriori checking the regularity of the estimated frontier by the researcher and, if necessary, the a priori imposition of the theoretical requirements. Bootstrapping based stochastic simulations of a simple parametric efficiency model by using different flexible functional forms confirmed the severeness of the theoretical concerns especially with respect to the merely locally restrictable translog specification.

Estimating Indirect Production Functions with a More General Specification: An Application of the Lewbel Model

Whereas consumer theory employs several different empirical specifications for estimating indirect utility functions, producer theory has relied on the Translog specification to estimate the indirect production function. In this paper, we apply Lewbel's more general functional specification and investigate its implications for the estimation of indirect production functions in productivity analysis. An attractive feature of the Lewbel model is that it nests both the Translog and the almost ideal supply system, offering a method to assess the empirical validity of all three specifications. Aggregate U.S. production data are used to examine the performance of the three models in an empirical application.

Regional Variation and Cereal Production in India

This paper analyzes the agricultural scenario in India by estimating a system of production functions for five major cereal crops (such as wheat, rice, maize, bajra and jowar), using a Translog specification instead of the more commonly used Cobb-Douglas (CD) specification. Our estimation methodology employs a Seemingly Unrelated Regressions in a panel data set up, which allows for cross equation correlation. We use district level data for 13 major states from 1966-1967 to 1994-1995. We examine the inter-regional heterogeneity using four kinds of dummy variables, viz. District dummy, state dummy, production function dummy and agro-ecological dummy. The result indicates presence of non-linear effects of various inputs on the yields. Our results show the significance of regional differences in terms of production system and agro-ecological climates.

Returns to scale in a matching model: evidence from disaggregated panel data

The returns to scale in the matching function play an important role in models with endogenous search effort. Due to positive externalities, increasing returns to scale in matching can support high or low activity equilibrium in the labour market. In this study, we examine this issue using panel data from Finnish employment offices. The study finds that the results from the Cobb–Douglas and translog specification are qualitatively different. The CD specification of the matching function exhibits constant returns to scale. The translog specification, in turn, exhibits increasing returns to scale. The elasticity estimate for returns, using the preferred specification and minimum and maximum sample values for job seekers and vacancies, fall in the range of 1.1 to 1.6.

Nonparametric analysis of returns to scale in the US hospital industry

AbstractThis paper presents new estimates of scale economies for US hospitals. We show that the common translog specification of hospital costs is a misspecification, and employ nonparametric, local linear estimation with both continuous and discrete covariates. A bootstrap method is used to provide inferences regarding ray scale economies and expansion path scale economies for a large sample of hospitals covering 1984–1996. We find evidence of changes in the structure of hospital costs over the sample period, as well as evidence of locally optimal hospital sizes. Copyright © 2004 John Wiley & Sons, Ltd.

Non-uniformity of job-matching in a transition economy – A nonparametric analysis for the Czech Republic

This study explores the properties and development of the matching technology in the Czech Republic during the transition to a market economy. Nonparametric additive modelling allows us to assess flexible functional forms, which comprise for instance CES and trans-log specifications. This enables us to evaluate the matching process locally for each combination of unemployment and vacancies rather than being restricted to global coefficients. Special interest is devoted to analysis and economic determinants of regional variation in the returns to scale of the matching function. Non-linearities are found in the partial adjustment process of unemployment outflows, and a negative coefficient on vacancies in some years. Moreover, increasing returns to scale in job-matching are found locally. Returns to scale are found to be negatively correlated to the share in employment in services and to outmigration, positively correlated to the employment share in industry, the unemployment rate and various measures of active labour market policies.

Malmquist productivity index estimation with zero-value variables: The case of Greek prefectural training councils

The paper suggests a technique for the parametric estimation of the Malmquist productivity growth index when the dataset to be analyzed contains a considerable number of observations with zero values. A dummy variable technique suggested by Battese (J. Agric. Econom. 48 (1997) 250) is extended to a translog specification of the input distance function. Moreover, technical changes (TCs) are decomposed into neutral and biased components and the sources of total productivity growth are computed via formulae explicitly accounting for the discrete nature of the data. Our approach has been applied to the Greek prefectural training councils—a state extension system for the general public. Findings indicate a considerably negative productivity growth primarily attributable to regressive TC.