The Capabilities Approximation of Translog, Generalized Leontief and Quadratic Models

We investigate the behaviour of three flexible forms of the cost Function: the Translog, which is the most used in empirical analyses, Generalized Leontief and Symmetric Generalized McFadden, which both have also become popular. Their performances are evaluated by their abilities (i) to respect basic theoretical properties, (ii) to provide plausible estimates of economic and technological characteristics such us values, signs and derivatives of price and Allen elasticities of substitution, technical change, as well as (iii) the precision by which they fit input shares, input-outputs coefficients and unit cost. This framework is then used to describe the substitution possibilities between capital labour and energy in the three industrial branches of French manufacturing industry. The most noteworthy result is that the Translog form fails to fit the unit cost and furthermore the input-output coefficients while the other two forms give satisfactory results under the same maintained hypothesis and for all three sets of data. We show that the origin of those shortcomings is due in part to the sensitivity of the Translog model to restrictions on parameters allowing for non-neutral technical change and non-homothetic technologies. As a consequence, this form is not suitable when one wants to measure the pure effect of biased technical change on the demand of energy or productivity indicators, for example. Our results suggest that the Translog model is less flexible then the two others. So, care should be attached to several previous studies