The estimation of Cobb-Douglas production function parameter through a robust partial least squares

Enaami, Maryouma

The estimation of Cobb-Douglas production function parameter through a robust partial least squares

AVAILABLE Article 278 Views

Back to search

Scan QR Code to share or view item link:

Digital Assets & Download Files

General Information Cached

Title

The estimation of Cobb-Douglas production function parameter through a robust partial least squares

Type

Article

Main Author

Enaami, Maryouma

Additional Authors

Sazelli Abdul Ghani
Zulkifley Mohamed

Subject

Q Science

ISSN

1985-7918

Language Code

eng

Bibliographic Details

Place of Production

Tanjong Malim

Publisher

Fakulti Sains dan Matematik

Year of publication

2011

Notes

Vol. 3 No. 1 (2011): Journal of Science and Mathematics

Degree Type

Others

Corporate Name

Perpustakaan Tuanku Bainun

Abstract

The Cobb-Douglas production function (Cobb and Douglas, 1928) is still today the most ubiquitous form in theoretical and empirical analyses of growth and productivity. The estimation of the parameters of aggregate production functions is central to much of today_s work on growth, technological change, productivity, and labour. Empirical estimates of aggregate production functions are a tool of analysis essential in macroeconomics, and important theoretical constructs, such as potential output, technical change, or the demand for labour, are based on them. It is usually fitted by first linearizing the models through logarithmic transformation and then applying method of least squares (Prajneshu, 2008), but the ordinary least squares (OLS) is not the best estimation method (Kahane , 2001). In statistics and econometrics, more and more attention is paid to techniques that can deal with data containing atypical observations, which can arise from outliers, miscoding, or heterogeneity and not captured or presumed in a model. This is of very high importance especially in (non) linear regression models and time series as the least squares (LS) and maximum likelihood estimators (MLE) are heavily influenced by data contamination (Pavel, 2007). In addition, multicollinearity often exists between the economic factors and could greatly affect parameter estimation. The seriousness of multicollinearity will affect the results mostly negatively. Partial least squares (PLS) are especially good in dealing with small sample data, plenty of variables and multicollinearity. It can greatly improve reliability and precision of model (Zhang & Shang, 2009). While Robust Partial Least Squares (RPLS) is used to solve the problems of multicollinearity and outliers. This can be done through Minimum Covariance Determinant (MCD) and the reweighted MCD (RMCD) estimator. This method is called RSIMPLS (Branden & Hubert, 2003). The purpose of this article is to suggest the best method in overcoming the outliers and multicollinearity problems of Cobb-Douglas production function. This is done by using the robust partial least squares (RPLS) method. This developed methodology will be illustrated in the contacts of its theoretical background. Keywords Cobb-Douglas production function, Minimum Covariance Determinant (MCD), Partial Least Squares (PLS), Robust Partial Least Squares (RPLS).

References

Abdi, H. (2003). Partial least squares regression (PLS regression), In M. Lewis-Beck, A. Bryman and T.

Futing (eds): Encyclopedia for research methods for the social sciences. Thousand Oaks, CA: Sage.

Aguirregabiria, V. (2009). Econometric issues and methods in the estimation of production functions.

MPRA. Department of Economics. University of Toronto.

Atkinson, A.C. (1993). Stalactite plots and robust estimation for the detection of multivariate outliers.

In S. Morgenthaler, E. Ronchetti, and W. A. Stahel (eds.). New directions in statistical data analysis

and robustness. Basel: Birkhäuser.

Atkinson, A.C. (1994). Fast robust methods for the detection of multiple outliers. Journal of the American

Statistical Association, 89: 1329 - 1339.

Baltagi, B.H. (2008). Econometrics. Fourth Edition. New York: Springer.

Bhanumurthy, K.V. (2002). Arguing a case for the Cobb-Douglas production function. Review of

Commerce Studie, 1(20 – 21).

Branden K. V., & Hubert, M. (2003). Robust methods for partial least squares regression. Journal of

Chemometrics, 17: 537 – 549.

Camminatiello, I. (2006). Robust methods for Partial Least Squares Regression: methodological

contributions and applications in environmental field. FedOA. Universita Degli Studi Di Napoli

Federico II.

Cobb, C.W., & Douglas, P.H. (1928). A Theory of Production. American Economic Review 18(1): 139

– 165.

Field, A. (2000). Discovering statistics using SPSS for windows. London: Sage

Kahane, L. H. (2001). Regression basics. Thousand Oaks, CA: Sage.

Mahalanobis, P.C. (1936). On the generalised distance in statistics. Proceedings of the National Institute

of Sciences of India 2(1): 49-55.

McIntosh, A.R., Bookstein, F., Haxby, J. & Grady, C. (1996). Spatial pattern analysis of functional brain

images using partial least squares. Neuroimage, 3: 143–157.

McIntosh, A.R. & Lobaugh, N.J., 2004. Partial least squares analysis of neuroimaging data: Applications

and advances. Neuroimage, 23: 250-263.

Pavel, C. (2007). Efficient robust estimation of regression models. CentER Discussion Paper. Department

of Econometrics & Operational Rsearch. Faculty of Economics and Business Administration,

Tilburg University, Tilburg: Netherlands.

Prajneshu. (2008). Fitting of Cobb-Douglas production functions: Revisited. Agricultural Economics

Research Review. 21:289 – 292.

Rousseeuw, P.J. (1984). Least median of squares regression, Journal of the American Statistical

Association 76: 871-880.

Rousseeuw, P.J., & Van Driessen, V. (1999). A fast algorithm for the minimum covariance determinant

estimator. Technometrics 41: 212 – 223.

Webster, T.J. (2003). Managerial economics, theory and practice. Amsterdam: Academic Press.

Wold, H. (1966). Estimation of Principal Components and Related Models by Iterative Least Squares. In

P. R. Krishnaiah, (eds.). Multivariate analysis. New York, NY: Academic Press.

Wold, H.(1982). Soft modeling-The basic design and some extensions. In K. Jöreskog & H. Wold, (eds.).

Systems under indirect observation II. Amsterdam: North-Holland Press.

Zhang, Y. & Shang, W. (2009). The relationship between rural infrastructure and economic growth

based on partial least-squares regression. 2009 International Conference on Networking and Digital

Society.