Imposing Curvature Conditions on Flexible Functional Forms for GNP Functions

CREATE Working Paper 2012-5

39 Pages Posted: 8 May 2012

See all articles by Guy Chapda Nana

Guy Chapda Nana

Ministry of Finance, Quebec

Bruno Larue

Université Laval

Date Written: May 8, 2012


This paper empirically investigates the implications of the imposition of convexity in output prices and concavity in factor endowments on flexible functional forms for the GNP function. Using macroeconomic data for Switzerland, we estimate the Translog and the Symmetric Normalized Quadratic forms to investigate the manner with which curvature restrictions are imposed, the extend of curvature violations and the robustness of estimated elasticities. We also compare the predictive accuracy of the aforementioned flexible functional forms. Our result show that concavity in factor endowments is violated much more often than convexity in output prices. For the Translog, the date at which local restrictions are imposed matters a great deal in terms of remaining curvature violations in the sample, but far less for estimated elasticities. In contrast, we found that the size and sign of elasticities vary across functional forms. In-sample forecasting analysis demonstrates that the Translog model significantly dominates the Symmetric Normalized Quadratic.

Keywords: GNP function, flexible functional forms, curvature violations, elasticities

JEL Classification: D24, C30

Suggested Citation

Chapda Nana, Guy and Larue, Bruno, Imposing Curvature Conditions on Flexible Functional Forms for GNP Functions (May 8, 2012). CREATE Working Paper 2012-5, Available at SSRN: or

Guy Chapda Nana

Ministry of Finance, Quebec

12 St-Louis Quebec
Quebec, Quebec G1R 5L3

Bruno Larue (Contact Author)

Université Laval ( email )

2425 rue de l'Agriculture
local 4417
Quebec, Quebec G1V 0A6
418 656 2131 x5098 (Phone)
418 656 7821 (Fax)

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