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Adjusted QMLE for the spatial autoregressive parameter

Adjusted QMLE for the spatial autoregressive parameter
Adjusted QMLE for the spatial autoregressive parameter
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.
Adjusted maximum likelihood estimation, fixed effects, group interaction, networks, spatial autoregression.
0304-4076
Martellosio, Federico
30407632-7b34-4b01-b46c-b5870c9a4dd3
Hillier, Grant
3423bd61-c35f-497e-87a3-6a5fca73a2a1
Martellosio, Federico
30407632-7b34-4b01-b46c-b5870c9a4dd3
Hillier, Grant
3423bd61-c35f-497e-87a3-6a5fca73a2a1

Martellosio, Federico and Hillier, Grant (2019) Adjusted QMLE for the spatial autoregressive parameter. Journal of Econometrics. (In Press)

Record type: Article

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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More information

Accepted/In Press date: 7 March 2019
Keywords: Adjusted maximum likelihood estimation, fixed effects, group interaction, networks, spatial autoregression.

Identifiers

Local EPrints ID: 429203
URI: https://eprints.soton.ac.uk/id/eprint/429203
ISSN: 0304-4076
PURE UUID: 154b8757-e233-44d1-aa67-732c696775cd
ORCID for Grant Hillier: ORCID iD orcid.org/0000-0003-3261-5766

Catalogue record

Date deposited: 22 Mar 2019 17:30
Last modified: 27 Jul 2019 00:38

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Contributors

Author: Federico Martellosio
Author: Grant Hillier ORCID iD

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