Abstract
We develop the panel-limited information maximum likelihood approach for estimating dynamic panel structural equation models. When there are dynamic effects and endogenous variables with individual effects at the same time, the LIML method for the filtered data does give not only a consistent estimator and asymptotic normality, but also attains the asymptotic bound when the number of orthogonal conditions is large. Our formulation includes Alvarez and Arellano (Econometrica 71:1121–1159, 2003), Blundell and Bond (Econ Rev 19-3:321–340, 2000) and other linear dynamic panel models as special cases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
We have used Example 1 in Akashi and Kunitomo (2012) to investigate Case (a) in more details. Example 1 can be regarded as a special case of Example 2.
References
Akashi, K. (2008). \(t\)-test in dynamic panel structural equations (unpublished manuscript).
Akashi, K., Kunitomo, N. (2012). Some properties of the LIML estimator in a dynamic panel structural equation. Journal of Econometrics, 166, 167–183.
Alonso-Borrego, C., Arellano, M. (1999). Symmetrically normalized instrumental-variable estimation using panel data. Journal of Business and Economic Statistics, 17, 36–49.
Alvarez, J., Arellano, M. (2003). The time series and cross section asymptotics of dynamic panel data estimators. Econometrica, 71, 1121–1159.
Anderson, T. W., Hsiao, C. (1981). Estimation of dynamic models with error components. Journal of the American Statistical Association, 76, 598–606.
Anderson, T. W., Hsiao, C. (1982). Formulation and estimation of dynamic models with panel data. Journal of Econometrics, 18, 47–82.
Anderson, T. W., Rubin, H. (1949). Estimation of the parameters of a single equation in a complete system of stochastic equations. Annals of Mathematical Statistics, 20, 46–63.
Anderson, T. W., Rubin, H. (1950). The asymptotic properties of estimates of the parameters of a single equation in a complete system of stochastic equation. Annals of Mathematical Statistics, 21, 570–582.
Anderson T.W., et al. (2005). A new light from old wisdoms: alternative estimation methods of simultaneous equations with possibly many instruments, Discussion Paper CIRJE-F-321. Tokyo: Graduate School of Economics, University of Tokyo.
Anderson, T.W., et al. (2010). On the asymptotic optimality of the LIML estimator with possibly many instruments. Journal of Econometrics, 157, 191–204.
Anderson, T.W., et al. (2011). On finite sample properties of alternative estimators of coefficients in a structural equation with many instruments. Journal of Econometrics, 165, 58–69.
Arellano, M. (2003). Panel Data Econometrics. New York: Oxford University Press.
Arellano, M., Bover, O. (1995). Another look at the instrumental variable estimation of error-components models. Journal of Econometrics, 68, 29–51.
Baltagi, B.H. (2005). Econometric Analysis of Panel Data (3rd ed.). New York: Wiley, Hoboken.
Blundell, R., Bond, S. (2000). GMM estimation with persistent panel data : an application to production function. Econometric Review, 19–3, 321–340.
Hahn, J., Kuersteiner, G. (2002). Asymptotically unbiased inference for a dynamic panel model with fixed effects when both n and T are large. Econometrica, 70, 1639–1657.
Hayakawa, K. (2006). Efficient GMM estimation of dynamic panel data models where large heterogeneity may be present. Tokyo: Hi-Stat Discussion Paper No.130, Hitotsubashi University.
Hayakawa, K. (2009). A simple efficient instrumental variable estimator in panel AR(p) models. Econometric Theory, 25, 873–890.
Holtz-Eakin, D., et al. (1988). Estimating vector autoregressions with panel data. Econometrica, 56, 1371–1395.
Hsiao, C. (2003). Analysis of Panel Data (2nd ed.). Cambridge: Cambridge University Press.
Kunitomo, N. (1980). Asymptotic expansions of distributions of estimators in a linear functional relationship and simultaneous equations. Journal of the American Statistical Association, 75, 693–700.
Kunitomo, N. (2012). An optimal modification of the LIML estimation for many instruments and persistent heteroscedasiticity. Annals of Institute of Statistical Mathematics, 64, 881–910.
Kunitomo, N., Akashi, K. (2010). An asymptotically optimal modification of the panel LIML estimation for individual heteroscedasticity. Tokyo: Discussion paper CIRJE-F-780, Graduate School of Economics, University of Tokyo. http://www.cirje.e.u-tokyo.ac.jp/research/dp
Acknowledgments
We thank the editor and two referees of this journal for helpful comments to the previous version. The earlier versions of this paper were presented at the 2006 Japan Statistical Society (JSS) meeting, the 62nd European Meeting of the Econometric Society, and the 2010 Econometric Society World Congress (2010, Shanghai) under the title “The Conditional Limited Information Maximum Likelihood Approach to Panel Dynamic Structural Equations”. We also thank T.W. Anderson, Y. Matsushita, K. Hayakawa, R. Okui, K. Hitomi and Y. Nishiyama for comments to the earlier versions.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
About this article
Cite this article
Akashi, K., Kunitomo, N. The limited information maximum likelihood approach to dynamic panel structural equation models. Ann Inst Stat Math 67, 39–73 (2015). https://doi.org/10.1007/s10463-013-0438-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10463-013-0438-5