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 λ in a spatial autoregression. The resulting estimator for λ has better finite sample properties compared to the QMLE for λ, 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. 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 λ. 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 λ. 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.
488-506
Martellosio, Federico
30407632-7b34-4b01-b46c-b5870c9a4dd3
Hillier, Grant
3423bd61-c35f-497e-87a3-6a5fca73a2a1
December 2020
Martellosio, Federico
30407632-7b34-4b01-b46c-b5870c9a4dd3
Hillier, Grant
3423bd61-c35f-497e-87a3-6a5fca73a2a1
Martellosio, Federico and Hillier, Grant
(2020)
Adjusted QMLE for the spatial autoregressive parameter.
Journal of Econometrics, 219 (2), .
(doi:10.1016/j.jeconom.2020.03.013).
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 λ in a spatial autoregression. The resulting estimator for λ has better finite sample properties compared to the QMLE for λ, 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. 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 λ. 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 λ. Based on our simulations, the coverage properties of these intervals are excellent even in models with a large number of covariates.
Text
adj_lik_3
- Accepted Manuscript
More information
Accepted/In Press date: 7 March 2019
e-pub ahead of print date: 4 June 2020
Published date: December 2020
Keywords:
Adjusted maximum likelihood estimation, fixed effects, group interaction, networks, spatial autoregression.
Identifiers
Local EPrints ID: 429203
URI: http://eprints.soton.ac.uk/id/eprint/429203
ISSN: 0304-4076
PURE UUID: 154b8757-e233-44d1-aa67-732c696775cd
Catalogue record
Date deposited: 22 Mar 2019 17:30
Last modified: 16 Mar 2024 07:40
Export record
Altmetrics
Contributors
Author:
Federico Martellosio
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
