Pdf problems involved with translog cost function and some. Subfleet translog style total cost regression, 20002007 27 table 10. Imposing curvature restrictions on a translog cost function. Deriving a production function from cost function using sheppards lemma. Recently there has been considerable progress in estimation techniques which take into account the fact that pro t maximizing rms. Chapter 9 flexible functional forms vancouver school of. Remarkably, in most applications, these inputs are not used beyond subtracting them from the grossoutput number to get value added, so the approach comes at no additional cost in data or computation. In the dynamic tran slog specification, differencing the. The function takes w and y as its inputs and returns minimum cost, where w is a vector of prices for the inputs to production and y is a single output. The stability of these results is assessed and illustrated for a number of different output aggregations. Longrun cost function cost function let w be the cost per unit of labor and r be the cost per unit of capital. Abstract this study measures cost efficiencies of 18 chinese commercial banks, divided into the stateowned banks and the jointstock banks, by the translog cost function based on stochastic frontier analysis sfa, and proves that translog cost function is more suitable in this study than cobbdouglas cost function.
In the present unit, we will discuss different approaches to examination of production and cost functions, analysis of some empirical estimates of thesefunctions, and managerial uses of the estimated functions. The name translog stands for transcendental logarithmic. A cost function allows us to view the cost effects of aircraft size, average length of haul, and seating capacity as matters of general principle. The next obvious step is to generate a function which allows. Cost functions are derived from a cost minimization process any decline in costs from an increase in one of the function s arguments would. Transcendental logarithmic cost function1 the purpose of the translog cost function is to identify a specific functional form for a cost function that embodies all of the assumptions and results of our cost minimization model. The translog function can be used not only in preferences but also in production and cost functions.
Pdf in a translog production function, the number of parameters practically explodes as the number of considered production factors increases find, read. This function has both linear and quadratic terms with the ability of using more than two factor inputs. C the cost function allows estimation when output prices are unavailable or are not determined in a competitive market. The translog production function is an approximation of the ces function by a secondorder taylor polynomial about, i. Imposing curvature restrictions on a translog cost.
Translog preferences and trade costs this section outlines the general equilibrium translog model and derives the theoretical gravity equation based on an endowment economy framework. As an alternative to panel data methods based on production function estimation, one can use duality theory to derive the cost function as well as the. Working paper series federal reserve bank of richmond. The estimation of a cost function cw, y requires observations on costs, outputs y and input prices w of. Substitute the values of these parameters into the translog cost function, and estimate its remaining three parameters, c, cq, and dqq, using linear multiple regression. Special production functions cobbdouglas, ces, ves. The translog cost function is commonly estimated with its cost minimizing input share equations in a seemingly unrelated equations sure regression zellner, 1962 and using maximum likelihood estimators. It also suggests how the main results extend to any functional form with certain properties. C the cost function allows a relatively straightforward calculation of.
Caves, christensen, and swanson 1981 develop and estimate multiproduct variable or short run cost functions on a pooled cross section of railroad firms in the united states for 1955. The normalized quadratic functional form is our preferred functional form, because convexity or concavity restrictions can. Dec 30, 2018 in this video i introduce the translog production function,discuss its properties and estimation. Production function estimation in stata using inputs to. Treating crops and livestock as two distinct outputs, this study utilizes standard results of neoclassical duality theory to obtain measures of pairwise elasticities of substitution between inputs, price elasticities of factor. In addition, we estimate partial elasticity of substitution, and own and cross price elasticities of factor inputs. These assumptions are relaxed at the end of section 2. Due to its properties, the translog production function can be used for the second order approximation of a linearhomogenous production, the. The use of frontier cost functions for the banking industry has gained acceptance in recent years following reports of good fit to data. The transcendental logarithmic translog christensen et al. Frontier cost functions and bank efficiency sciencedirect.
A translog cost function of the integrated air freight. The translog cost function will be used as an approximation to the multiple output cost function that we wish to estimate. In economics and econometrics, the cobbdouglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs particularly physical capital and labor and the amount of output that can be produced by those inputs. Pdf the paper attempts to find out some specific problems in connection with the specification, estimation and evaluation of the translog cost.
The translog cost function is frequently used in the banking literature, providing an estimation for the marginal cost of production for banks. Time invariant cost efficiency estimation method ml. Special production functions cobbdouglas, ces, ves, translog and their properties bse. The translog cost function the translog function with two inputs input shares easy to compute. The translog cost function can be estimated in a number of ways. The translog function is an attractive flexible function. In the general form, the translog function is given by. A note on allenuzawa partial elasticities of substitution. Technological innovation in tobacco industry in the united. For a much more extensive discussion of various types of production functions and their properties, their relationships and origin, see chambers 1988 and sickles and zelenyuk 2019, chapter 6. In this video i introduce the translog production function,discuss its properties and estimation.
Special production functions cobb douglas, ces, ves, translog and their properties duration. A translog cost estimation of capitallabour substitubility. Previous studies using translog cost function used ad hoc specifications to model allocative inefficiency in the cost function and the cost share equations. I am not very familiar with its implications in consumer theory, but from the production point of view, ive seen it widely used. We compare the results of estimation when using a seemingly unrelated regression sur model of the cost function plus the cost share equations, versus estimating the cost function alone. Estimating a derived demand system from a translog cost function. Modeling allocative inefficiency in a translog cost function. Recent criticism of the incorrect specification of homogeneity restrictions on the translog cost functions.
The case of the translog cost function this note provides a useful property of the allenuzawa partials for the translog cost function. The transcendental logarithmic cost function looks like. The analytical method used is descriptive method and analysis of translog production functions with scenarios. Purdue university, north carolina state university 14 march 2009 online at mpra paper no. Working with data from weill 20, we estimate a translog for european banking covering twenty countries and nine years. The cobbdouglas cost function can be used to expose the parameters of the technology of the production process, and then be used with the cobbdouglas production function to model how a firm combines inputs to produce outputs.
A functional form has to be postulated in the speci. In particular, we want a cost function that allows for ushaped. The cost function is based on quarterly timeseries data from 1990 to 2010 for fedex and ups. The translog cost function provides a convenient framework for analyzing u. We next estimate the translog cost function without curvature restrictions imposed. The translog function doesnt impose additivity and homogeneity, and hence constant elasticity of substitution.
Cost and production functions princeton new jersey. Thus the general form for the translog cost function with n inputs is as follows. An alternativetothecobbdouglasproduction function is the translog production function. This paper uses a translog cost function and establishes an exact relationship between allocative inefficiency in the cost share equations and in the cost function. Abstract the translog cost function approach is employed to characterize the production structure and to estimate the rate of technical change and technical bias in the saw and.
The threeinput translog production function can be written in terms of logarithms as. Input shares s i are obtained by applying shephards lemma 2. However, subsequent studies, including the present paper, nd that the translog function is a misspeci cation of bank cost relationships and therefore can lead. This fact, and the additional fact that the estimating equations that result from applying the translog functional form are linear in. Cobbdouglas cost function system cost function is a function of output and input prices.
Abstract the translog cost function approach is employed to characterize the production structure and to estimate the rate of technical change and technical bias in the saw and planing mills industry spm in the new brunswick province. This paper can be considered as a first attempt to estimate the threeinput translog production function for four digits seventy seven jordanian manufacturing industries in 2002. A translog cost function analysis with implications for economic development patrick mccarthy school of economics georgia institute of technology final report submitted to georgia department of transportation georgia transportation instituteuniversity transportation center december 2011. Estimating a derived demand system from a translog cost function overview the transcendental logarithmic translog functional form can capture many of the attributes of a cost function that are implied by economic theory. In particular, we want a cost function that allows for ushaped average cost.
Estimation of the model maximum likelihood estimation ml. This paper analyzes the cost structure of the integrated air freight business by means of a translog cost function. Pdf some aspects of the translog production function estimation. The only parameter of the cost function that is not captured by the derived demand system is the intercept term which is not used in calculating price or substitution elasticities. This is a generalization of cobbdouglas cost function. This allows to extend knowledge on the supply side and to examine if strategies of integrators are consistent with cost structure. The empirical estimation of production and cost functions is a standard exercise in econometrics. The remaining of the paper is organised as follows. Production functions are a key part of modelling national output and national income. The frontier production function or production frontier is an extension of the familiar regression model based on the theoretical premise that a production function, or its dual, the cost function, or the convex conjugate of the two, the profit. Cost efficiency, translog cost function, chinese commercial banks. However, pavelescu 2011 suggested that the translog production function can be used in a variety of alternatives, such as translog function linear, nonlinear translog functions, quadratic. The translog cost function is estimated as a system of equations.
Estimating a derived demand system from a translog cost. Subfleet translog total cost regression vs restricted model 34 table 11. The estimated coefficients of the translog production and cost functions will vary with the parameters sigma, nu, alpha, beta and gamma of the ces production function. With the input labor l and capital k, the production cost is w. In addition, the contributions of fixed cost and cost complementarities to scope economies are shown for the composite form.
When derived demand systems are obtained from a cost function, it is possible to estimate several elasticities of substitution along with price elasticities. The ces was a natural extension of the cobbdouglas in that it permitted the elasticity of substitution to be something other than unity. Moreover, only the cost shares in the system were estimated, that is, the total cost function was not included. The multioutput translog production cost function scholar commons. Pdf some aspects of the translog production function. In this study we use the translog cost function, which is a flexible.
Treating crops and livestock as two distinct outputs, this study utilizes standard results of neoclassical duality theory to obtain measures of pairwise elasticities of substitution between inputs, price elasticities of factor demands, and the rate of hicks. C the cost function more easily handles a multiproduct firm than the alternative of directly estimating the technology via a production function. Multiproduct cost functions and scale economies in banking multiproduct cost functions and scale economies in banking cebenoyan, a. Linear homogeneity of the cost function, symmetry of the secondorder derivatives, and. Extension of the traditional translog functional forms by the addition of trigonometric terms is reported to be especially. Production and cost functions allan collardwexler january 2, 2012 1 introduction production functions are indispensable tools for empirical i. A cost function cq is a function of q, which tells us what the minimum cost.
Munich personal repec archive the almost ideal and translog demand systems holt, matthew t. The aspects of the firms behavior that we observe are total cost, the allocation of total cost across. View translog cost function research papers on academia. A translog cost function for urban bus transit jstor. A translog cost function analysis of us agriculture. The transcendental logarithmic cost function looks like the. This function can be approximated by second order taylor series christensen, et al. Pdf a translog cost function analysis of us agriculture. This is a list of production functions that have been used in the economics literature. Letting w denote the price of input i and y denote the output j. Econometric estimation of the constant elasticity of.
Calculating elasticities from a translog cost function overview elasticities of substitution are an important measure of production relationships. If the production function is cobbdouglas and constant returns to scale. The translog specification of the dual cost function was initially justified as a second order taylorseries approximation to an unknown dual cost function berndt and christensen, 1973. Dec 17, 2015 special production functions cobbdouglas, ces, ves, translog and their properties bse. Some aspects of the translog production function estimation. Translog cost function translog flexible transcendental logarithmic function provides a secondorder numerical approximation to almost any underlying cost function at a given point multiple outputs.