Estimating CES production functions in MAKRO


In this working paper, we estimate the elasticities of substitution between the different production factors in MAKRO.


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.