Confidence Intervals for Elasticity Estimators in Translog Models

This paper examines the distribution fu nctions of elasticity estimators in translog demand models. The authors consider the normaland ratio-of-normals distributions and present confidence intervals for the elasticity estimators. The results suggest that only elasticity estimato rs based on the means of the actual cost shares are likely to follow either the normal or ratio-of-normals distribution function. Examination of three published empirical studies demonstrates that inferences regarding the values of elasticities cannot be made from point estimates alone and suggests a trade- off between the level of aggregation and the width of confidence intervals for the elasticit y estimators. Copyright 1986 by MIT Press.

[1]  H. White Using Least Squares to Approximate Unknown Regression Functions , 1980 .

[2]  Robin C. Sickles,et al.  A COMPARISON OF THE PERFORMANCE OF THREE FLEXIBLE FUNCTIONAL FORMS , 1983 .

[3]  E. Berndt,et al.  Technology, Prices, and the Derived Demand for Energy , 1975 .

[4]  C. Craig On the Frequency Function of $xy$ , 1936 .

[5]  C. A. Knox Lovell,et al.  On the Flexibility of the Translog Approximation , 1980 .

[6]  R. Byron,et al.  Least Squares Approximations to Unknown Regression Functions: A Comment , 1983 .

[7]  A. Gallant,et al.  Estimating substitution elasticities with the Fourier cost function : Some Monte Carlo results , 1985 .

[8]  D. Hinkley On the ratio of two correlated normal random variables , 1969 .

[9]  Franklin A. Graybill,et al.  Introduction to the Theory of Statistics, 3rd ed. , 1974 .

[10]  Laurits R. Christensen,et al.  The translog function and the substitution of equipment, structures, and labor in U.S. manufacturing 1929-68 , 1973 .

[11]  Daniel McFadden,et al.  A Survey of Functional Forms in the Economic Analysis of Production , 1978 .

[12]  E. C. Fieller THE DISTRIBUTION OF THE INDEX IN A NORMAL BIVARIATE POPULATION , 1932 .

[13]  Shelemyahu Zacks,et al.  The Theory of Statistical Inference. , 1972 .

[14]  J. Wolfowitz,et al.  Introduction to the Theory of Statistics. , 1951 .

[15]  G. Hanoch,et al.  CRESH Production Functions , 1971 .

[16]  T. D. Wallace,et al.  A Test of the Mean Square Error Criterion for Restrictions in Linear Regression , 1968 .

[17]  Leo A. Aroian,et al.  The probability function of the product of two normally distributed variables. , 1947 .

[18]  J. M. Griffin,et al.  An Intercountry Translog Model of Energy Substitution Responses , 1976 .

[19]  G. Marsaglia Ratios of Normal Variables and Ratios of Sums of Uniform Variables , 1965 .