Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T23:48:21.916Z Has data issue: false hasContentIssue false
  • English
  • Français

ESTIMATION OF SPATIAL AUTOREGRESSIONS WITH STOCHASTIC WEIGHT MATRICES

Published online by Cambridge University Press:  03 May 2018

Abhimanyu Gupta
Abhimanyu Gupta*
Affiliation:
University of Essex
*
*Address correspondence to Abhimanyu Gupta, Department of Economics, University of Essex; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

We examine a higher-order spatial autoregressive model with stochastic, but exogenous, spatial weight matrices. Allowing a general spatial linear process form for the disturbances that permits many common types of error specifications as well as potential ‘long memory’, we provide sufficient conditions for consistency and asymptotic normality of instrumental variables, ordinary least squares, and pseudo maximum likelihood estimates. The implications of popular weight matrix normalizations and structures for our theoretical conditions are discussed. A set of Monte Carlo simulations examines the behaviour of the estimates in a variety of situations. Our results are especially pertinent in situations where spatial weights are functions of stochastic economic variables, and this type of setting is also studied in our simulations.

Type
ARTICLES
Information
Econometric Theory , Volume 35 , Issue 2 , April 2019 , pp. 417 - 463
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

I am grateful to co-editor Guido Kuersteiner and three anonymous referees for excellent comments that improved the article substantially. I thank Peter Robinson for several comments and am also grateful to Nicolas Debarsy, Javier Hidalgo, Ingmar Prucha, and Renata Rabovic for useful suggestions and discussions.

References

REFERENCES

Baltagi, B.H., Fingleton, B., & Pirotte, A. (2014) Spatial lag models with nested random effects: An instrumental variable procedure with an application to English house prices. Journal of Urban Economics 80, 76–86.CrossRefGoogle Scholar
Bell, K.P. & Bockstael, N.E. (2000) Applying the generalized-moments estimation approach to spatial problems involving micro-level data. Review of Economics and Statistics 82, 72–82.CrossRefGoogle Scholar
Boucher, V. & Fortin, B. (2016) Some challenges in the empirics of the effects of networks. In Bramoullé, Y., Galeotti, A., & Rogers, B. (eds.), The Oxford Handbook of the Economics of Networks, chapter 12. Oxford University Press.Google Scholar
Case, A.C. (1991) Spatial patterns in household demand. Econometrica 59, 953–965.CrossRefGoogle Scholar
Cliff, A.D. & Ord, J.K. (1973) Spatial Autocorrelation. Pion.Google Scholar
Conley, T.G. & Dupor, B. (2003) A spatial analysis of sectoral complementarity. Journal of Political Economy 111, 311–352.CrossRefGoogle Scholar
Conley, T.G. & Ligon, E. (2002) Economic distance and cross-country spillovers. Journal of Economic Growth 7, 157–187.CrossRefGoogle Scholar
Das, D., Kelejian, H.H., & Prucha, I.R. (2003) Finite sample properties of estimators of spatial autoregressive models with autoregressive disturbances. Papers in Regional Science 82, 1–26.CrossRefGoogle Scholar
Davis, P.J. (1979) Circulant Matrices. Wiley Interscience.Google Scholar
Delgado, M. & Robinson, P.M. (2015) Non-nested testing of spatial correlation. Journal of Econometrics 187, 385–401.CrossRefGoogle Scholar
Gupta, A. & Robinson, P.M. (2015) Inference on higher-order spatial autoregressive models with increasingly many parameters. Journal of Econometrics 186, 19–31.CrossRefGoogle Scholar
Gupta, A. & Robinson, P.M. (2018) Pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension. Journal of Econometrics 202, 92–107.CrossRefGoogle Scholar
Hillier, G. & Martellosio, F. (2013) Properties of the Maximum Likelihood Estimator in Spatial Autoregressive Models. Mimeo.CrossRefGoogle Scholar
Hillier, G. & Martellosio, F. (2018) Exact likelihood inference in group interaction network models. Econometric Theory 34, 383–415.CrossRefGoogle Scholar
Jenish, N. & Prucha, I.R. (2012) On spatial processes and asymptotic inference under near-epoch dependence. Journal of Econometrics 170, 178–190.CrossRefGoogle ScholarPubMed
Kelejian, H.H. & Piras, G. (2014) Estimation of spatial models with endogenous weighting matrices, and an application to a demand model for cigarettes. Regional Science and Urban Economics 46, 140–149.CrossRefGoogle Scholar
Kelejian, H.H. & Prucha, I.R. (1998). A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. The Journal of Real Estate Finance and Economics 17, 99–121.CrossRefGoogle Scholar
Kelejian, H.H. & Prucha, I.R. (1999) A generalized moments estimator for the autoregressive parameter in a spatial model. International Economic Review 40, 509–533.CrossRefGoogle Scholar
Kelejian, H.H. & Prucha, I.R. (2001) On the asymptotic distribution of the Moran I test statistic with applications. Journal of Econometrics 104, 219–257.CrossRefGoogle Scholar
Kelejian, H.H. & Prucha, I.R. (2007) HAC estimation in a spatial framework. Journal of Econometrics 140, 131–154.CrossRefGoogle Scholar
Kelejian, H.H. & Prucha, I.R. (2010) Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. Journal of Econometrics 157, 53–67.CrossRefGoogle ScholarPubMed
Kuersteiner, G.M. & Prucha, I.R. (2013) Limit theory for panel data models with cross sectional dependence and sequential exogeneity. Journal of Econometrics 174, 107–126.CrossRefGoogle ScholarPubMed
Kuersteiner, G.M. & Prucha, I.R. (2015) Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity. CESifo Working paper 5445.Google Scholar
Lee, L.F. (2002) Consistency and efficiency of least squares estimation for mixed regressive, spatial autoregressive models. Econometric Theory 18, 252–277.CrossRefGoogle Scholar
Lee, L.F. (2003) Best spatial two-stage least squares estimators for a spatial autoregressive model with autoregressive disturbances. Econometric Reviews 22, 307–335.CrossRefGoogle Scholar
Lee, L.F. (2004) Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica 72, 1899–1925.CrossRefGoogle Scholar
Lee, L.F. & Liu, X. (2010) Efficient GMM estimation of high order spatial autoregressive models with autoregressive disturbances. Econometric Theory 26, 187–230.CrossRefGoogle Scholar
Lee, L.F. & Yu, J. (2013) Near unit root in the spatial autoregressive model. Spatial Economic Analysis 8, 314–351.CrossRefGoogle Scholar
Lee, L.F. & Yu, J. (2014) Efficient GMM estimation of spatial dynamic panel data models with fixed effects. Journal of Econometrics 180, 174–197.CrossRefGoogle Scholar
Qu, X. & Lee, L.F. (2015) Estimating a spatial autoregressive model with an endogenous spatial weight matrix. Journal of Econometrics 184, 209–232.CrossRefGoogle Scholar
Robinson, P.M. (2008) Correlation testing in time series, spatial and cross-sectional data. Journal of Econometrics 147, 5–16.CrossRefGoogle Scholar
Robinson, P.M. (2010) Efficient estimation of the semiparametric spatial autoregressive model. Journal of Econometrics 157, 6–17.CrossRefGoogle Scholar
Robinson, P.M. & Hidalgo, F.J. (1997) Time series regression with long-range dependence. The Annals of Statistics 25, 77–104.Google Scholar
Robinson, P.M. & Thawornkaiwong, S. (2012) Statistical inference on regression with spatial dependence. Journal of Econometrics 167, 521–542.CrossRefGoogle Scholar
Scott, D.J. (1973) Central limit theorems for martingales and for processes with stationary increments using a Skorokhod representation approach. Advances in Applied Probability 5, 119–137.CrossRefGoogle Scholar
Souza, P.C.L. (2015) Estimating Network Effects without Network Data. Mimeo.Google Scholar
Su, L. & Jin, S. (2010) Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models. Journal of Econometrics 157, 18–33.CrossRefGoogle Scholar
Xu, X. & Lee, L.F. (2015) A spatial autoregressive model with a nonlinear transformation of the dependent variable. Journal of Econometrics 186, 1–18.CrossRefGoogle Scholar
Yuzefovich, Y.A. (2003) Two Essays on Spatial Econometrics. Ph.D. thesis, University of Maryland.Google Scholar
Supplementary material: File

Gupta supplementary material 1

Gupta supplementary material

Download Gupta supplementary material 1(File)
File 24.7 KB
Supplementary material: PDF

Gupta supplementary material 2

Gupta supplementary material

Download Gupta supplementary material 2(PDF)
PDF 55.3 KB