Quasi-maximum likelihood estimations and applications for spatial dynamic autoregressive panel model with fixed effects

ZHOU Shaofu, ZHANG Jiajun

Systems Engineering - Theory & Practice ›› 2021, Vol. 41 ›› Issue (1) : 45-57.

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Systems Engineering - Theory & Practice ›› 2021, Vol. 41 ›› Issue (1) : 45-57. DOI: 10.12011/SETP2019-0631

Quasi-maximum likelihood estimations and applications for spatial dynamic autoregressive panel model with fixed effects

  • ZHOU Shaofu, ZHANG Jiajun
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Abstract

The paper investigates the asymptotic properties of quasi-maximum likelihood estimators of the DSAC panel model with fixed effects when the space system is stable and both n and T are large. The paper shows that when using the transformation approach, the quasi-maximum likelihood estimators yield a bias of O(1/T) order in the general case. When (n-1)/T→0, the estimators converge consistently to the true value with the rate of √(n-1)T. When (n-1)/T→∞, the estimators converge to a degenerate distribution at the rate of T. The estimators obtained by the direct approach yield a bias of max(O(1/T),O(1/n)) order in the general case. When n/T→0 and n/T→∞, the estimators are converge to different degenerate distributions at the rate of n and T respectively. The bias corrected estimators have better finite sample properties than the quasi-maximum likelihood estimators. When n/T3→0, the bias corrected estimators obtained by the transformation approach are √(n-1)T consistently converge to the true value. When n/T3 and n3/T both tend to 0, the bias corrected estimators obtained by the direct approach converge to the true value consistently with the rate of √nT. The direct approach can consistently estimate the individual effects and time effects while transformation approach cannot. The finite sample property of the DASC panel model with fixed effects is better than that of DSAR panel model when the error term has the spatial correlation structure. Finally, an empirical research example shows the application value of the DSAC model.

Key words

dynamic spatial autoregressive confused (DSAC) panel model / two components fixed effects / quasi-maximum likelihood estimation / bias correction / population growth rate

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ZHOU Shaofu , ZHANG Jiajun. Quasi-maximum likelihood estimations and applications for spatial dynamic autoregressive panel model with fixed effects. Systems Engineering - Theory & Practice, 2021, 41(1): 45-57 https://doi.org/10.12011/SETP2019-0631

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Funding

Fundamental Research Funds for the Central Universities (2019WKYXZX020)
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