Estimating CES production functions in MAKRO

04-06-2021
MAKRO

Abstract

In this working paper, we estimate the elasticities of substitution between the different pro-duction factors in MAKRO. We use annual data for the period 1967-2017, primarily based on the national accounts. As the technological development is unobservable and potentially non-linear, a trend process is specified for the relative factor efficiency that is time-varying. We use the Kalman filter to estimate the CES elasticities and the technological development simultaneously. It is assumed that the latter develops sluggishly and expresses long-term trends.


The elasticity between capital and labor in the two primary private industries in MAKRO, manufacturing and services, are estimated at 0.51 and 0.42, respectively, and are both signifi-cantly different from 1. The elasticities towards buildings are most often estimated at 0, meaning that buildings are a Leontief input factor. This also applies to some extent to materials, but in the construction and manufacturing industries, where materials make up a large part of the total input in production, these elasticities are estimated at around 0.5.


In the long run, the technological development is labor-augmenting but there are significant periods of shift in the direction of capital-augmenting technology, e.g. in the service industry from the 1990s onwards, highlighting the importance of a flexible specification of technological development. The approach in the analysis provides well-specified models with parameter estimates similar to other analyzes on similar data for Denmark. However, point estimates are obtained with some uncertainty, which is probably a combination of uncertainty behind the trend specification and volatile prices, especially in the user cost terms.