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Adjusted QMLE for the spatial autoregressive parameter

Federico Martellosio, Grant Hillier

arXiv 17 Sep 2019 · Econometrics · publishedJournal of Econometrics (2020) · 1 citations (OpenAlex)

arXiv:1909.08141 · PDF · DOI · OpenAlex · Extracted main text

Abstract

One simple, and often very effective, way to attenuate the impact of nuisance parameters on maximum likelihood estimation of a parameter of interest is to recenter the profile score for that parameter. We apply this general principle to the quasi-maximum likelihood estimator (QMLE) of the autoregressive parameter $\lambda$ in a spatial autoregression. The resulting estimator for $\lambda$ has better finite sample properties compared to the QMLE for $\lambda$, especially in the presence of a large number of covariates. It can also solve the incidental parameter problem that arises, for example, in social interaction models with network fixed effects, or in spatial panel models with individual or time fixed effects. However, spatial autoregressions present specific challenges for this type of adjustment, because recentering the profile score may cause the adjusted estimate to be outside the usual parameter space for $\lambda$. Conditions for this to happen are given, and implications are discussed. For inference, we propose confidence intervals based on a Lugannani--Rice approximation to the distribution of the adjusted QMLE of $\lambda$. Based on our simulations, the coverage properties of these intervals are excellent even in models with a large number of covariates.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Lee, L.-F., Liu, X., Lin, X (2010) Specification and estimation of social interaction models with network structures1.000133100%
2McCullagh, P., Tibshirani, R (1990) A simple method for the adjustment of profile likelihoods0.92843100%
3Hillier, G., Martellosio, F (2018) a self0.87412567%
4Lee, L.-F (2007) b0.81142100%
5Yu, D., Bai, P., Ding, C (2015) Adjusted quasi-maximum likelihood estimator for mixed regressive, spatial autoregressive model and its small sample bias0.81142100%
6Meyer, C. D. (Ed (2000) Matrix Analysis and Applied Linear Algebra0.7374275%
7Lee, L.-F., Yu, J (2010) Estimation of spatial autoregressive panel data models with fixed effects0.73732100%
8Lugannani, R., Rice, S (1980) Saddle point approximation for the distribution of the sum of independent random variables0.73732100%
9Paige, R. L., Trindade, A. A., Fernando, H. P (2009) Saddlepoint‐based bootstrap inference for quadratic estimating equations0.69351100%
10Bramoullé, Y., Djebbari, H., Fortin, B (2009) Identification of peer effects through social networks0.64422100%

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1The modified conditional sum-of-squares estimator for fractionally integrated models0.73732