Abstract
It is well-known that econometric productivity estimation using flexible functional forms often encounters violations of curvature conditions. However, the productivity literature does not provide any guidance on the selection of appropriate functional forms once they satisfy the theoretical regularity conditions. In this paper, we provide an empirical evidence that imposing local curvature conditions on the flexible functional forms affect total factor productivity (TFP) estimates in addition to the elasticity estimates. Moreover, we use this as a criterion for evaluating the performances of three widely used locally flexible cost functional forms—the translog (TL), the Generalized Leontief (GL), and the Normalized Quadratic (NQ)—in providing TFP estimates. Results suggest that the NQ model performs better than the other two functional forms in providing TFP estimates.
We gratefully acknowledge the financial assistance provided by the Social Sciences and Humanities Research Council of Canada (SSHRC). We thank Yazid Dissou for sharing the Canadian KLEMS data set obtained from Statistics Canada. We would like to thank Samuel Gamtessa, Lynda Khalaf, Yazid Dissou, Pierre Brochu and an anonymous referee for valuable comments and suggestions. We would also like to thank the participants at North American Productivity Workshop IX, June 2016, Quebec City, and 49th Annual Conference of Canadian Economics Association, May 2015, Toronto, for helpful comments and discussions.
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Notes
- 1.
Slade (1989) criticizes the traditional method of modelling the state of technology by including time trend in the production or cost function and, instead, suggests the use of state-space approach through the Kalman filter in estimating technical change. More recently, Jin and Jorgenson (2010) replaces the constant time trend by latent variables and use the Kalman filter to estimate the latent variables in the translog (TL) model.
- 2.
Fisher et al. (2001) provide an empirical evaluation of the performances of eight flexible functional forms in the context of consumer demand.
- 3.
See Hulten (2001) for a discussion on the historical development of quantitative analysis of productivity. For a brief discussion on various approaches to productivity measurement see Feng and Serletis (2008). Using simulation Van Biesebroeck (2007) provides a discussion on the robustness of productivity estimates obtained by different measurement approaches.
- 4.
- 5.
For notational simplicity we suppress the time subscripts.
- 6.
TFP estimates obtained from the smoothed Tornqvist index are almost identical to that obtained from the smoothed Fisher ideal index, and are not reported for brevity.
- 7.
Dissou and Ghazal (2010) utilize this dataset to examine energy substitutability in the primary metal and cement industries.
- 8.
The industries are at the L-level of aggregation in the North American Industry Classification System 2012.
- 9.
Young (2013), for example, uses this dataset to provide U.S. industry level estimates of the elasticity of substitution between labour and capital.
- 10.
Tables with estimated coefficients and their standard errors are not reported here for brevity. However, they are available upon request to the corresponding author.
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Hussain, J., Bernard, JT. (2018). Flexible Functional Forms and Curvature Conditions: Parametric Productivity Estimation in Canadian and U.S. Manufacturing Industries. In: Greene, W., Khalaf, L., Makdissi, P., Sickles, R., Veall, M., Voia, MC. (eds) Productivity and Inequality. NAPW 2016. Springer Proceedings in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-68678-3_10
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