Imposing curvature conditions on flexible functional forms for GNP functions

Abstract

This paper empirically investigates the implications of the choice of dates when imposing local restrictions to maintain convexity in output prices and concavity in factor endowments in the the estimation of a GNP function approximated by a translog (TL) function. Using macroeconomic data for Switzerland, we compare the TL to a symmetric normalized quadratic (SNQ) function on which global curvature restrictions can be imposed. When both functions are unrestricted for curvature, convexity in prices is violated more often than concavity in factor endowments. The number of points for which both curvature conditions hold is sensitive to the date at which local restrictions are imposed on the TL, but estimated TL elasticities are robust. Through searching for an appropriate date, the TL matched the SNQ’s ability to impose curvature conditions at all points. However, many TL and SNQ elasticities differ in sign and magnitude. The likelihood dominance criterion and in-sample forecasts comparisons favored the TL. Thus, choosing a functional form solely based on the possibility of imposing global curvature conditions is not advised.