Purdue University Graduate School
Dissertation070721.pdf (1.62 MB)


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posted on 2021-07-22, 17:53 authored by Xiaotian LiuXiaotian Liu

First Chapter: The ordinary least squares (OLS) estimator for spatial autoregressions may be consistent as pointed out by Lee (2002), provided that each spatial unit is influenced aggregately by a significant portion of the total units. This paper presents a unified asymptotic distribution result of the properly recentered OLS estimator and proposes a new estimator that is based on the indirect inference (II) procedure. The resulting estimator can always be used regardless of the degree of aggregate influence on each spatial unit from other units and is consistent and asymptotically normal. The new estimator does not rely on distributional assumptions and is robust to unknown heteroscedasticity. Its good finite-sample performance, in comparison with existing estimators that are also robust to heteroscedasticity, is demonstrated by a Monte Carlo study.

Second Chapter: This paper proposes a new estimation procedure for the first-order spatial autoregressive (SAR) model, where the disturbance term also follows a first-order autoregression and its innovations may be heteroscedastic. The estimation procedure is based on the principle of indirect inference that matches the ordinary least squares estimator of the two SAR coefficients (one in the outcome equation and the other in the disturbance equation) with its approximate analytical expectation. The resulting estimator is shown to be consistent, asymptotically normal and robust to unknown heteroscedasticity. Monte Carlo experiments are provided to show its finite-sample performance in comparison with existing estimators that are based on the generalized method of moments. The new estimation procedure is applied to empirical studies on teenage pregnancy rates and Airbnb accommodation prices.

Third Chapter: This paper presents a sample selection model with spatial autoregressive interactions and studies the maximum likelihood (ML) approach to estimating this model. Consistency and asymptotic normality of the ML estimator are established by the spatial near-epoch dependent (NED) properties of the selection and outcome variables. Monte Carlo simulations, based on the characteristics of female labor supply example, show that the proposed estimator has good finite-sample performance. The new model is applied to empirical study on examining the impact of climate change on agriculture in Southeast Asia.


Degree Type

  • Doctor of Philosophy


  • Economics

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Yong Bao

Additional Committee Member 2

Mohitosh Kejriwal

Additional Committee Member 3

Justin Tobias

Additional Committee Member 4

Joshua Chan

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