Modeling Panel Data: Comparison of GLS Estimation and Robust Covariance Matrix Estimation

Victor Muthama Musau; Anthony Gichuhi Waititu; Anthony Kibira Wanjoya

doi:doi:10.11648/j.ajtas.20150403.25

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Modeling Panel Data: Comparison of GLS Estimation and Robust Covariance Matrix Estimation

Victor Muthama Musau, Anthony Gichuhi Waititu, Anthony Kibira Wanjoya

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 3)

Received: 8 May 2015 Accepted: 17 May 2015 Published: 28 May 2015

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Abstract

The proliferation of panel studies which has been greatly motivated by the availability of data and greater capacity for modeling the complexity of human behavior than a single cross-section or time series data has led to the rise of challenging methodologies for estimating the data sets. Much controversy on these methodologies is the under-estimation of the standard errors leading to wrong conclusions of the involved hypothesis test as well as making inappropriate inference to the underlying model parameters. This is due to the heteroscedasticity and autocorrelation nature of the disturbance term in the classical linear regression model. This study sought to estimate linear-panel model parameters using conventional regression techniques which have the capacity to address the correlation and heteroscedasticity problem. By relaxing the homogeneity and non-correlation properties of the disturbance term in the classical linear regression model, we employed the generalized least squares method to estimate the model parameters. Using the available White Heteroscedasticity Consistent estimators i.e. HC0, HC1, HC2, HC3 and HC4, we also obtained estimates for the generalized ordinary least squares covariance matrix.

Published in	American Journal of Theoretical and Applied Statistics (Volume 4, Issue 3)
DOI	10.11648/j.ajtas.20150403.25
Page(s)	185-191
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Panel, Heteroscedasticity, Autocorrelation, Homogeneity

References

[1]	Cribari Neto, F. (2004), “Asymptotic panel inference under heteroscedasticity of unknown form,” Computational Statistics and Data Analysis, vol. 45, pp. 215–233., April 1955. (references)
[2]	Ferrari and Cordeiro (2000), ‘Improved heteroscedasticity consistent covariance matrix estimators’, Biometrika, vol. 87, pp 907-918
[3]	Grizzle, J. E. and D. M. Allen (1969), ‘Analysis of growth and dose response curves’, Biometrics Vol. 25, pp 357-381
[4]	Grunfeld, Y (1958), The Determinants of Corporate Investment, PhD thesis, University of Chicago.
[5]	Hausman, J. (1978), “Specification Tests in Econometrics”, Econometrica Vol. 46, pp 1251-1271
[6]	Kleiber and Zeileis (2010), ‘The Grunfeld data at 50’, German Economic Review.
[7]	Laird, Nan M. and James H. Ware (1982), ‘Random-effects models for longitudinal data’, Biometrics vol. 38, pp 963-974.
[8]	Lazarsfeld, Paul F. and Marjorie Fiske (1938), ‘The panel as a new tool for measuring opinion’, Public Opinion Quarterly 2 pp. 596–612
[9]	Long, J. S and L. Ervin (2000), ‘Using heteroscedasticity-consistent standard errors in the linear regression model’, The American Statistician Vol. 54, pp 217–224.
[10]	Marschak, J. (1939), “On combining market and budget data in demand studies”, Econometrica, Vol. 7, pp 332-335
[11]	Pesaran, M. (2004), ‘General diagnostic ttest for cross section dependence in panels’, CESinfo Working Papers Series p. 1229
[12]	Potthoff, R. F. and S. N. (1964) Roy (1964), ‘A generalized multivariate analysis of variance model useful especially for growth curve problems.’, Biometrika Vol. 51, 313–326
[13]	Rao, C. R. (1965), ‘The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves.’ Biometrika Vol. 52, 447–458.
[14]	Tobin, J. (1950), “A statistical demand function for food in the U.S.A”, Journal of the Royal Statistical Society, Series A, pp 113-141 Vol. 52, 447–458.
[15]	Wishart, J. (1938), ‘Growth-rate determinations in nutrition studies with the bacon pig, and their analysis.’ Biometrika Vol. 30, 16–28.
[16]	Wooldridge, J. (2002), ‘Econometric analysis of crosssection and panel data’, MIT press.
[17]	Zivot, E. and J. Wang (2003), Modeling Financial Time Series with S-plus, Springer-Verlag, New York.

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APA Style

Victor Muthama Musau, Anthony Gichuhi Waititu, Anthony Kibira Wanjoya. (2015). Modeling Panel Data: Comparison of GLS Estimation and Robust Covariance Matrix Estimation. American Journal of Theoretical and Applied Statistics, 4(3), 185-191. https://doi.org/10.11648/j.ajtas.20150403.25

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ACS Style

Victor Muthama Musau; Anthony Gichuhi Waititu; Anthony Kibira Wanjoya. Modeling Panel Data: Comparison of GLS Estimation and Robust Covariance Matrix Estimation. Am. J. Theor. Appl. Stat. 2015, 4(3), 185-191. doi: 10.11648/j.ajtas.20150403.25

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AMA Style

Victor Muthama Musau, Anthony Gichuhi Waititu, Anthony Kibira Wanjoya. Modeling Panel Data: Comparison of GLS Estimation and Robust Covariance Matrix Estimation. Am J Theor Appl Stat. 2015;4(3):185-191. doi: 10.11648/j.ajtas.20150403.25

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@article{10.11648/j.ajtas.20150403.25,
  author = {Victor Muthama Musau and Anthony Gichuhi Waititu and Anthony Kibira Wanjoya},
  title = {Modeling Panel Data: Comparison of GLS Estimation and Robust Covariance Matrix Estimation},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {3},
  pages = {185-191},
  doi = {10.11648/j.ajtas.20150403.25},
  url = {https://doi.org/10.11648/j.ajtas.20150403.25},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150403.25},
  abstract = {The proliferation of panel studies which has been greatly motivated by the availability of data and greater capacity for modeling the complexity of human behavior than a single cross-section or time series data has led to the rise of challenging methodologies for estimating the data sets. Much controversy on these methodologies is the under-estimation of the standard errors leading to wrong conclusions of the involved hypothesis test as well as making inappropriate inference to the underlying model parameters. This is due to the heteroscedasticity and autocorrelation nature of the disturbance term in the classical linear regression model. This study sought to estimate linear-panel model parameters using conventional regression techniques which have the capacity to address the correlation and heteroscedasticity problem. By relaxing the homogeneity and non-correlation properties of the disturbance term in the classical linear regression model, we employed the generalized least squares method to estimate the model parameters. Using the available White Heteroscedasticity Consistent estimators i.e. HC0, HC1, HC2, HC3 and HC4, we also obtained estimates for the generalized ordinary least squares covariance matrix.},
 year = {2015}
}

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TY  - JOUR
T1  - Modeling Panel Data: Comparison of GLS Estimation and Robust Covariance Matrix Estimation
AU  - Victor Muthama Musau
AU  - Anthony Gichuhi Waititu
AU  - Anthony Kibira Wanjoya
Y1  - 2015/05/28
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150403.25
DO  - 10.11648/j.ajtas.20150403.25
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 185
EP  - 191
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150403.25
AB  - The proliferation of panel studies which has been greatly motivated by the availability of data and greater capacity for modeling the complexity of human behavior than a single cross-section or time series data has led to the rise of challenging methodologies for estimating the data sets. Much controversy on these methodologies is the under-estimation of the standard errors leading to wrong conclusions of the involved hypothesis test as well as making inappropriate inference to the underlying model parameters. This is due to the heteroscedasticity and autocorrelation nature of the disturbance term in the classical linear regression model. This study sought to estimate linear-panel model parameters using conventional regression techniques which have the capacity to address the correlation and heteroscedasticity problem. By relaxing the homogeneity and non-correlation properties of the disturbance term in the classical linear regression model, we employed the generalized least squares method to estimate the model parameters. Using the available White Heteroscedasticity Consistent estimators i.e. HC0, HC1, HC2, HC3 and HC4, we also obtained estimates for the generalized ordinary least squares covariance matrix.
VL  - 4
IS  - 3
ER  -

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Author Information

Victor Muthama Musau

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi, Kenya
Anthony Gichuhi Waititu

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi, Kenya
Anthony Kibira Wanjoya

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

Victor Muthama Musau, Anthony Gichuhi Waititu, Anthony Kibira Wanjoya. (2015). Modeling Panel Data: Comparison of GLS Estimation and Robust Covariance Matrix Estimation. American Journal of Theoretical and Applied Statistics, 4(3), 185-191. https://doi.org/10.11648/j.ajtas.20150403.25

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ACS Style

Victor Muthama Musau; Anthony Gichuhi Waititu; Anthony Kibira Wanjoya. Modeling Panel Data: Comparison of GLS Estimation and Robust Covariance Matrix Estimation. Am. J. Theor. Appl. Stat. 2015, 4(3), 185-191. doi: 10.11648/j.ajtas.20150403.25

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AMA Style

Victor Muthama Musau, Anthony Gichuhi Waititu, Anthony Kibira Wanjoya. Modeling Panel Data: Comparison of GLS Estimation and Robust Covariance Matrix Estimation. Am J Theor Appl Stat. 2015;4(3):185-191. doi: 10.11648/j.ajtas.20150403.25

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@article{10.11648/j.ajtas.20150403.25,
  author = {Victor Muthama Musau and Anthony Gichuhi Waititu and Anthony Kibira Wanjoya},
  title = {Modeling Panel Data: Comparison of GLS Estimation and Robust Covariance Matrix Estimation},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {3},
  pages = {185-191},
  doi = {10.11648/j.ajtas.20150403.25},
  url = {https://doi.org/10.11648/j.ajtas.20150403.25},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150403.25},
  abstract = {The proliferation of panel studies which has been greatly motivated by the availability of data and greater capacity for modeling the complexity of human behavior than a single cross-section or time series data has led to the rise of challenging methodologies for estimating the data sets. Much controversy on these methodologies is the under-estimation of the standard errors leading to wrong conclusions of the involved hypothesis test as well as making inappropriate inference to the underlying model parameters. This is due to the heteroscedasticity and autocorrelation nature of the disturbance term in the classical linear regression model. This study sought to estimate linear-panel model parameters using conventional regression techniques which have the capacity to address the correlation and heteroscedasticity problem. By relaxing the homogeneity and non-correlation properties of the disturbance term in the classical linear regression model, we employed the generalized least squares method to estimate the model parameters. Using the available White Heteroscedasticity Consistent estimators i.e. HC0, HC1, HC2, HC3 and HC4, we also obtained estimates for the generalized ordinary least squares covariance matrix.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Modeling Panel Data: Comparison of GLS Estimation and Robust Covariance Matrix Estimation
AU  - Victor Muthama Musau
AU  - Anthony Gichuhi Waititu
AU  - Anthony Kibira Wanjoya
Y1  - 2015/05/28
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150403.25
DO  - 10.11648/j.ajtas.20150403.25
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 185
EP  - 191
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150403.25
AB  - The proliferation of panel studies which has been greatly motivated by the availability of data and greater capacity for modeling the complexity of human behavior than a single cross-section or time series data has led to the rise of challenging methodologies for estimating the data sets. Much controversy on these methodologies is the under-estimation of the standard errors leading to wrong conclusions of the involved hypothesis test as well as making inappropriate inference to the underlying model parameters. This is due to the heteroscedasticity and autocorrelation nature of the disturbance term in the classical linear regression model. This study sought to estimate linear-panel model parameters using conventional regression techniques which have the capacity to address the correlation and heteroscedasticity problem. By relaxing the homogeneity and non-correlation properties of the disturbance term in the classical linear regression model, we employed the generalized least squares method to estimate the model parameters. Using the available White Heteroscedasticity Consistent estimators i.e. HC0, HC1, HC2, HC3 and HC4, we also obtained estimates for the generalized ordinary least squares covariance matrix.
VL  - 4
IS  - 3
ER  -

Copy | Download