Indirect Inference Estimation of Spatial Autoregressions

Abstract

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.

Continuously Updated Indirect Inference in Heteroskedastic Spatial Models

“…In particular, the simulations show that the new CUII estimator offers a substantial improvement over standard 2SLS and robust GMM as it does not rely on the construction of optimal instruments and, even more importantly, on the joint relevance of such instruments. In independent recent work that appeared after our paper was completed, Bao, Liu, and Yang (2020) extended results in KPR to SARX models with heteroskedastic error terms, and suggested an II-type transformation that produces results comparable to our findings reported in Sections 3 and 4. Bao et al (2020) adopted a different parameterization of the (nonconstant) variancecovariance matrix of the disturbances, resulting in a different asymptotic variance for their estimator.…”

“…In independent recent work that appeared after our paper was completed, Bao, Liu, and Yang (2020) extended results in KPR to SARX models with heteroskedastic error terms, and suggested an II-type transformation that produces results comparable to our findings reported in Sections 3 and 4. Bao et al (2020) adopted a different parameterization of the (nonconstant) variancecovariance matrix of the disturbances, resulting in a different asymptotic variance for their estimator.…”

“…We outline that our definition of the binding function is different fromBao et al (2020), as both numerator…”

“…We outline that our definition of the binding function is different fromBao et al (2020), as both numerator and denominator are parameterized as a function of λ.…”

Raising the bar (18)

“…Initially, Kyriacou et al (2017) started to consider this estimator for the spatial autoregressive (SAR) model. Then, Kyriacou et al (2019) and Bao et al (2020) extended this spatial econometric model with exogenous regressors and heteroskedastic errors. The paper by Bao and Liu (2021, this issue) further extends the latter model by also considering a spatial lag in the error term specification.…”