Dual Generalized Maximum Entropy Estimation for Panel Data Regression Models

- Journal title : Communications for Statistical Applications and Methods
- Volume 21, Issue 5, 2014, pp.395-409
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CSAM.2014.21.5.395

Title & Authors

Dual Generalized Maximum Entropy Estimation for Panel Data Regression Models

Lee, Jaejun; Cheon, Sooyoung;

Lee, Jaejun; Cheon, Sooyoung;

Abstract

Data limited, partial, or incomplete are known as an ill-posed problem. If the data with ill-posed problems are analyzed by traditional statistical methods, the results obviously are not reliable and lead to erroneous interpretations. To overcome these problems, we propose a dual generalized maximum entropy (dual GME) estimator for panel data regression models based on an unconstrained dual Lagrange multiplier method. Monte Carlo simulations for panel data regression models with exogeneity, endogeneity, or/and collinearity show that the dual GME estimator outperforms several other estimators such as using least squares and instruments even in small samples. We believe that our dual GME procedure developed for the panel data regression framework will be useful to analyze ill-posed and endogenous data sets.

Keywords

Collinearity;endogeneity;exogeneity;generalized maximum entropy;ill-posed problems;panel data;

Language

English

Cited by

1.

불균형 패널회귀모형에서의 이중 일반화 최대엔트로피 추정,이재준;전수영;

Journal of the Korean Data Analysis Society, 2015. vol.17. 3B, pp.1285-1295

References

1.

Ahn, S. C. and Schmidt, P. (1999). Estimation of linear panel data models using GMM, in Generalized method of Moments Estimation, L. Matyas (Eds.), Cambridge University Press, Cambridge.

2.

Amemiya, T. (1971). The estimation of the variances in a variance-components models, International Economic Review, 12, 1-13.

3.

Arora, S. (1973). Error components regression models and their applications, Annals of Economic and Social Measurement, 2, 451-462.

4.

Baltagi, B. H. (1981). Pooling: An experimental study of alternative testing and estimation procedures in a two-way error component model, Journal of Econometrics, 17, 21-49.

5.

Baltagi, B. H. (2001). Econometric Analysis of Panel Data, John Wiley, New York.

6.

Belsley, D. A. (1991). Conditioning Diagnostics: Collinearity and Weak Data in Regression, John Wiley & Sons, New York.

7.

Dennis, J. E. and Schnabel, R. B. (1983). Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs, New Jersey.

8.

Everaert, G. and Pozzi, L. (2014). The predictability of aggregate consumption growth in OECD countries: A panel data analysis, Journal of Applied Econometrics, 29, 431-453.

9.

Golan, A. and Judge, G. (1996). Recovering information in the case of underdetermined problems and incomplete data, Journal of Statistical Planning and Inference, 49, 127-136.

10.

Golan, A., Judge, G. and Miller, D. (1996a). Maximum Entropy Econometrics: Robust Estimation with Limited Data, John Wiley & Sons, Chichester.

11.

Golan, A., Judge, G. and Perloff, J. (1996b). A maximum entropy approach to recovering information from multinomial response data, Journal of the American Statistical Association, 91, 841-853.

12.

Golan, A., Judge, G. and Perloff, J. (1997). Estimation and inference with censored and ordered multinomial response data, Journal of Econometrics, 79, 23-51.

13.

Golan, A., Judge, G. and Robinson, S. (1994). Recovering information in the case of partial multisectorial economic data, Review of Economics and Statistics, 76, 541-549.

14.

Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators, Econometrica, 50, 1029-1054.

15.

Heckman, J. J. (1981). The incidental parameters problem and the problem of initial conditions in estimation a discrete time-discrete data stochastic process, in: C. Manski and D. McFadden, eds., Structural Analysis of Discrete Data with Econometric Application, MIT Press, Cambridge, Massachusetts.

16.

Hsiao, C. (1986). Analysis of Panel Data, Cambridge University Press, Cambridge.

17.

Im, K. S., Ahn, S. C., Schmidt, P. and Wooldridge, M. J. (1999). Efficient estimation of panel data models with strictly exogenous explanatory variables, Journal of Econometrics, 93, 177-201.

18.

Jaynes, E. T. (1957a). Information theory and statistical mechanics I, Physics Review, 106, 620-630.

19.

Jaynes, E. T. (1957b). Information theory and statistical mechanics II, Physics Review, 108, 171-190.

20.

Jaynes, E. T. (1984). Prior information and ambiguity in inverse problems, In McLaughlin D.W. (Ed.) Inverse Problems, 151-166, SIAM Proceedings, American Mathematical Society, Providence, Rhode Island.

21.

Judge, G. and Golan, A. (1992). Recovering information in the case of ill-posed inverse problems with noise, University of California at Berkeley, Unpublished Paper.

22.

Kullback, J. (1959). Information Theory and Statistics, John Wiley, New York.

23.

Levine, R. D. (1980). An Information theoretical approach to inverse problems, Journal of Physics A, 13, 91-108.

24.

Levine, R. D. and Tribus, M. (1979). The Maximum Entropy Formalism, MIT Press, Cambridge, MA.

25.

Nerlove, M. (1971). Further evidence on the estimation of dynamic economic relations from a time series of cross sections, Econometrica, 39, 359-382.

26.

Schnabel, R. B., Koontz, J. E. and Weiss, B. E. (1985). A modular system of algorithms for uncon-strained minimization, ACM Transactions on Mathematical Software, 11, 419-440.

27.

Shannon, C. E. (1948). A mathematical theory of communication, Bell System Technical Journal, 27, 379-423.

28.

Song, S. H. and Cheon, S. Y. (2006). A study of generalized maximum entropy estimator for the panel regression model, The Korean Journal of Applied Statistics, 19, 521-534.

29.

Swamy, P. A. V. B. and Arora, S. S. (1972). The exact finite sample properties of the estimators of coefficients in the error components regression models, Econometrica, 40, 261-275.

30.

Wansbeek, T. and Kapteyn, A. (1989). Estimation of the error-components model with incomplete panels, Journal of Econometrics, 41, 341-361.

31.

Wooldridge, J. M. (2003). Econometric Analysis of Cross Section and Panel Data, The MIT Press, Cambridge.