Imposing Curvature and Monotonicity on Flexible Functional Forms: An Efficient Regional Approach
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In many areas of economic analysis, economic theory restricts the shape of functions. Examples are the monotonicity and curvature conditions that apply to utility, profit, and cost functions. Here we extend upon a currently available estimation method (Terrell, J Appl Econometr 11:179–194, 1996) for imposing regularity regionally on a connected subset of the regressor space. Our method offers important advantages by imposing theoretical consistency not only locally, at a given evaluation point but also within the whole empirically relevant region of the domain associated with the function being estimated. The method also provides benefits through higher flexibility, which generally leads to a better model fit to the sample data. Specific contributions of this paper are (a) to increase the computational speed, (b) to provide regularity preserving point estimates, and (c) to illustrate the benefits of this revised regional approach via numerical simulation results.
KeywordsNonlinear inequality constraints Flexible functional forms Metropolis-Hastings Accept–Reject algorithm Cost function Regularity conditions
JEL ClassificationC51 D21 C11
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- Adkins, L. C., Rickman, D. S., & Hameed, A. (2002). Bayesian estimation of regional production for CGE modeling. Paper presented at the fourteenth international conference on input–output techniques October 10–15, 2002, Montréal, Canada.Google Scholar
- Barnett, W. A., Kirova, M., & Pasupathy, M. (1995). Estimating policy-invariant deep parameters in the financial sector when risk and growth matter. Journal of Money, Credit Bank, 27(4), part 2, 1402–1430.Google Scholar
- Chen M. H., Shao Q. M., Ibrahim J. G. (2000) Monte Carlo methods in bayesian computation. Springer, New YorkGoogle Scholar
- Cuesta, R. A., O’Donnell, C. J., Coelli, T. J., & Singh, S. (2001). Imposing curvature conditions on a production frontier: With applications to Indian dairy processing plants. CEPA Working Papers, No. 2/2001, ISBN 1 86389 749 6. Armidale: School of Economics, University of New England.Google Scholar
- Diewert, W. E., & Wales, T. J. (1991). Multiproduct cost functions and subadditivity tests: A critique of the Evans and Heckman research on the U.S. Bell Systems. Discussions Paper 91-21 at the Department of Economics, University of British Columbia, Vancouver. http://faculty.arts.ubc.ca/ediewert/9121.pdf.
- Evans D. S., Heckman J. J. (1984) A Test for Subadditivity of the Cost Function with an Application to the Bell System. American Economic Review 74: 615–623Google Scholar
- Griffiths W. E. (2003) Bayesian inference in the seemingly unrelated regressions model. In: Giles D. E. A. (eds) Computer-aided econometrics. Marcel Dekker, New York, pp 263–290Google Scholar
- Griffiths W. E., Skeels C. L., Chotikapanich D. (2002) Sample size requirements for estimation in SUR Models. In: Ullah A., Chaturvedi A., Wan A. (eds) Handbook of Applied Econometrics and Statistical Inference. Marcel Dekker, New York, pp 575–590Google Scholar
- Lau L. J. (1978) Testing and imposing monotonicity, convexity, and quasi-convexity constraints. In: Fuss M., McFadden D. (eds) Production economics: A dual approach to theory and applications (volume 1). North-Holland, Amsterdam, pp 409–453Google Scholar
- Lau L. J. (1986) Functional forms in econometric model building. In: Griliches Z., Intriligator M. D. (eds) Chapter 26 in handbook of econometrics. Elsevier Science, Amsterdam, North Holland, pp 1515–1566Google Scholar
- Mas-Colell A., Whinston M. D., Green J. R. (1995) Microeconomic theory. Oxford University Press, USAGoogle Scholar
- Matzkin R. L. (1994) Restrictions of economic theory in nonparametric methods. In: Engle R. F., McFadden D. L. (eds) Handbook of Econometrics. North-Holland Pub Co, Amsterdam, pp 2524–2558Google Scholar
- O’Donnell, C. J., & Coelli, T. (2003). A bayesian approach to imposing curvature on distance functions. Paper presented at the Australasian Meeting of the Econometric Society, Sydney 2003.Google Scholar
- Racine, J. S., & Parmeter, C. F. (2008). Constrained nonparametric kernel regression estimation and inference. Working paper available at http://www1.maxwell.syr.edu/uploadedFiles/econ/kernel_cons.pdf?n=6322.
- Simon C. P., Blume L. (1994) Mathematics for economists. W.W. Norton, New YorkGoogle Scholar
- Terrell, D., & Dashti, I. (1997). Imposing monotonocity and concavity restrictions on stochastic frontiers. Working Paper, Department of Economics, Louisiana State University, E. J. Ourso College of Business Administration.Google Scholar
- Zellner A. (1971) An introduction to bayesian inference in econometrics. John Wiley and Sons, New York.Google Scholar