Quasi Maximum Likelihood for MESS Varying Coefficient Panel Data Models with Fixed Effects

Yan Liu (College of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi, 541006, China)

Article ID: 3331

DOI: https://doi.org/10.30564/jesr.v4i3.3331


The study of spatial econometrics has developed rapidly and has found wide applications in many different scientific fields, such as demography, epidemiology, regional economics, and psychology. With the deepening of research, some scholars find that there are some model specifications in spatial econometrics, such as spatial autoregressive (SAR) model and matrix exponential spatial specification (MESS), which cannot be nested within each other. Compared with the common SAR models, the MESS models have computational advantages because it eliminates the need for logarithmic determinant calculation in maximum likelihood estimation and Bayesian estimation. Meanwhile, MESS models have theoretical advantages. However, the theoretical research and application of MESS models have not been promoted vigorously. Therefore, the study of MESS model theory has practical significance. This paper studies the quasi maximum likelihood estimation for matrix exponential spatial specification (MESS) varying coefficient panel data models with fixed effects. It is shown that the estimators of model parameters and function coefficients satisfy the consistency and asymptotic normality to make a further supplement for the theoretical study of MESS model.


Fixed effects; MESS panel data; Varying coefficient models; Quasi maximum likelihood

Full Text:



[1] LeSage, J.P., Pace, R.K. A matrix exponential spatial specification. J. Econometrics, 2007,140: 190-214.

[2] Debarsy, N., Jin, F., Lee, L.F. Large sample properties of the matrix exponential spatial specification with an application to FDI. J. Econometrics, 2015, 188: 1-21.

[3] Figueiredo, C., Silva, A.R.D. A matrix exponential spatial specification approach to panel data models. Empir Econ. , 2015, 49: 115-129.

[4] Zhang, Y., Feng, S., Jin, F. QML estimation of the matrix exponential spatial specification panel data model with fixed effects and heteroskedasticity. Economics Letters, 2019, 180: 1-5.

[5] Su, L., Jin, S. Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models. J. Econometrics, 2010, 157: 18-33.

[6] Su, L. Semiparametric GMM estimation of spatial autoregressive models. J. Econometrics 2012, 167: 543-560.

[7] Zhang, Z. A pairwise difference estimator for partially linear spatial autoregressive models. Spatial Economic Analysis, 2013, 8: 176-194.

[8] Sun, Y. Functional-coefficient spatial autoregressive models with nonparametric spatial weights. J. Econometrics, 2016, 195: 134-153.

[9] Koroglu, M., Sun, Y. Functional-coefficient spatial Durbin models with nonparametric spatial weights: An application to economic growth. Econometrics, 2016, 4: 1-16.

[10] Hastie, T., Tibshirani, R. Varying-coefficient models. Journal of the Royal Statistical Society: Series B (Methodological), 1993, 55: 757-779.

[11] Fan, J.Q., Zhang, W. Statistical estimation in varying coefficient models. The Annals of Statistics, 1999, 5: 1491-1518.

[12] Cai, Z., Fan, J.Q., Li, R. Efficient estimation and inferences for varying coefficient models. Journal of the American Statistical Association, 2000, 95: 888- 902.

[13] Xia, Y., Zhang, W., Tong, H. Efficient estimation for semivarying-coefficient models. Biometrika, 2004, 91:661-681.

[14] Cai, Z., Li, Q. Nonparametric estimation of varying coefficient dynamic panel data models. Econometric Theory, 2008, 24: 1321-1342.

[15] Chen, J., Li, K., Sun, L. Profile quasi maximum likelihood dummy variables estimation for spatial lag varying coefficient panel data model with fixed effects. Journal of Biomathematics, 2019, 34: 217-238. (in Chinese).

[16] Chiu, T.Y.M., Leonard, T. and Tsui, K.-W. The matrix-logarithmic covariance model. J. Amer. Statist. Assoc., 1996, 91: 198-210.

[17] Fan, J.Q., Huang, T. Profile likelihood inferences on semiparametric varying-coefficient partially linear models, Bernoulli, 2005, 11: 1031-1057.

[18] Lee, L.F. Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica, 2004, 72: 1899-1925.


  • There are currently no refbacks.
Copyright © 2021 Author(s)

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.