Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-22T05:26:19.009Z Has data issue: false hasContentIssue false
  • English
  • Français

SEMIPARAMETRIC ESTIMATION OF CENSORED SPATIAL AUTOREGRESSIVE MODELS

Published online by Cambridge University Press:  28 February 2019

Tadao Hoshino
Tadao Hoshino*
Affiliation:
Waseda University
*
*Address correspondence to Tadao Hoshino, School of Political Science and Economics, Waseda University, 1-6-1 Nishi-waseda, Shinjuku-ku, Tokyo 169-8050, Japan; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

This study considers the estimation of spatial autoregressive models with censored dependent variables, where the spatial autocorrelation exists within the uncensored latent dependent variables. The estimator proposed in this paper is semiparametric, in the sense that the error distribution is not parametrically specified and can be heteroskedastic. Under a median restriction, we show that the proposed estimator is consistent and asymptotically normally distributed. As an empirical illustration, we investigate the determinants of the risk of assault and other violent crimes including injury in the Tokyo metropolitan area.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 1 , February 2020 , pp. 48 - 85
Copyright
Copyright © Cambridge University Press 2019 

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 thank Mamoru Amemiya for allowing me to use his data set, and the participants of the ESEM 2016 and the CUHK econometrics seminar 2017 for valuable suggestions. This work was supported financially by JSPS Grant-in-Aid for Young Scientists B-15K17039.

References

REFERENCES

Amemiya, T. (1973) Regression analysis when the dependent variable is truncated normal. Econometrica 41, 997–1016.CrossRefGoogle Scholar
Amemiya, M. & Iwakura, N. (2012) Development of district-level time-series crime database and its applicability to spatiotemporal analyses of crime. Proceedings, Geographic Information Systems Association of Japan, 21, CD-ROM. (in Japanese).Google Scholar
Amemiya, M. & Shimada, T. (2013) Identifying changing patterns in the geographical distribution of residential burglaries in Tokyo. Journal of the City Planning Institute of Japan 48, 60–66. (in Japanese).Google Scholar
Andrews, D.W. (1992) Generic uniform convergence. Econometric Theory 8, 241–257.CrossRefGoogle Scholar
Anselin, L., Cohen, J., Cook, D., Gorr, W., & Tita, G. (2000) Spatial analyses of crime. In Duffee, D. (ed.), Criminal Justice 2000, vol. 4, pp 213–262. Measurement and Analysis of Crime and Justice. National Institute of Justice.Google Scholar
Autant-Bernard, C. & LeSage, J.P. (2011) Quantifying knowledge spillovers using spatial econometric models. Journal of Regional Science 51, 471–496.CrossRefGoogle Scholar
Bernasco, W. & Elffers, H. (2010) Statistical analysis of spatial crime data. In Piquero, A.R. and Weisburd, D. (eds.), Handbook of Quantitative Criminology, pp 699–724. Springer.CrossRefGoogle Scholar
Buchinsky, M. & Hahn, J. (1998) An alternative estimator for the censored quantile regression model. Econometrica 66, 653–671.CrossRefGoogle Scholar
Chernozhukov, V. & Hong, H. (2002) Three-step censored quantile regression and extramarital affairs. Journal of the American Statistical Association 97, 872–882.CrossRefGoogle Scholar
Chernozhukov, V., Fernandez-Val, I., & Kowalski, A.E. (2015) Quantile regression with censoring and endogeneity. Journal of Econometrics 186, 201–221.CrossRefGoogle Scholar
Chen, S. (2000) Efficient estimation of binary choice models under symmetry. Journal of Econometrics 96, 183–199.CrossRefGoogle Scholar
Chen, S. & Khan, S. (2008) Semiparametric estimation of nonstationary censored panel data models with time varying factor loads. Econometric Theory 24, 1149–1173.CrossRefGoogle Scholar
Chen, S. & Zhou, Y. (2010) Semiparametric and nonparametric estimation of sample selection models under symmetry. Journal of Econometrics 157, 143–150.CrossRefGoogle Scholar
Chen, S., Zhou, Y., & Ji, Y. (2018) Nonparametric identification and estimation of sample selection models under symmetry. Journal of Econometrics 202, 148–160.CrossRefGoogle Scholar
Chen, T. & Tripathi, G. (2017) A simple consistent test of conditional symmetry in symmetrically trimmed tobit models. Journal of Econometrics 198, 29–40.CrossRefGoogle Scholar
Cracolici, M.F. & Uberti, T.E. (2009) Geographical distribution of crime in Italian provinces: A spatial econometric analysis. Jahrbuch für Regionalwissenschaft 29, 1–28.CrossRefGoogle Scholar
Davidson, J. (1994) Stochastic Limit Theory. Oxford University Press.CrossRefGoogle Scholar
Di Porto, E. & Revelli, F. (2013) Tax-limited reaction functions. Journal of Applied Econometrics 28, 823–839.CrossRefGoogle Scholar
Drukker, D.M., Egger, P., & Prucha, I.R. (2013) On two-step estimation of a spatial autoregressive model with autoregressive disturbances and endogenous regressors. Econometric Reviews 32, 686–733.CrossRefGoogle Scholar
He, X. & Shao, Q.M. (2000) On parameters of increasing dimensions. Journal of Multivariate Analysis 73, 120–135.CrossRefGoogle Scholar
Honoré, B.E. & Hu, L. (2004) On the performance of some robust instrumental variables estimators. Journal of Business and Economic Statistics 22, 30–39.CrossRefGoogle Scholar
Horowitz, J. (1992) A smoothed maximum score estimator for the binary response model. Econometrica 60, 505–531.CrossRefGoogle Scholar
Hoshino, T. (2018) Semiparametric spatial autoregressive models with endogenous regressors: With an application to crime data. Journal of Business and Economic Statistics 36, 160–172.CrossRefGoogle Scholar
Jenish, N. (2016) Spatial semiparametric model with endogenous regressors. Econometric Theory 32, 714–739.CrossRefGoogle Scholar
Jenish, N. & Prucha, I.R. (2009) Central limit theorems and uniform laws of large numbers for arrays of random fields. Journal of Econometrics 150, 86–98.CrossRefGoogle ScholarPubMed
Jenish, N. & Prucha, I.R. (2011) On spatial processes and asymptotic inference under near-epoch dependence. Working paper.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. & Prucha, I.R. (1998) A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. Journal of Real Estate Finance and Economics 17, 99–121.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
Khan, S. & Powell, J.L. (2001) Two-step estimation of semiparametric censored regression models. Journal of Econometrics 103, 73–110.CrossRefGoogle Scholar
Khan, S. & Tamer, E. (2009) Inference on endogenously censored regression models using conditional moment inequalities. Journal of Econometrics 152, 104–119.CrossRefGoogle Scholar
Knight, K. (1998) Limiting distributions for L 1 regression estimators under general conditions. Annals of Statistics 26, 755–770.Google Scholar
Lahiri, S.N. & Zhu, J. (2006) Resampling methods for spatial regression models under a class of stochastic designs. Annals of Statistics 34, 1774–1813.CrossRefGoogle Scholar
Lei, J. (2014) Smoothed spatial maximum score estimation of spatial autoregressive binary choice panel models. Working paper, Tilburg University.CrossRefGoogle Scholar
LeSage, J. & Pace, R.K. (2009) Introduction to Spatial Econometrics. CRC Press.CrossRefGoogle Scholar
Liu, X. & Lee, L.F. (2013) Two-stage least squares estimation of spatial autoregressive models with endogenous regressors and many instruments. Econometric Reviews 32, 734–753.CrossRefGoogle Scholar
Magnac, T. & Maurin, E. (2007) Identification and information in monotone binary models. Journal of Econometrics 139, 76–104.CrossRefGoogle Scholar
Manski, C.F. (1975) Maximum score estimation of the stochastic utility model of choice. Journal of Econometrics 3, 205–228.CrossRefGoogle Scholar
Messner, S.F. & Anselin, L. (2004) Spatial analyses of homicide with areal data. In Goodchild, M. and Janelle, D. (eds.), Spatially Integrated Social Science, pp. 127–144. Oxford University Press.Google Scholar
Newey, W.K. (1987) Specification tests for distributional assumptions in the Tobit model. Journal of Econometrics 34, 125–145.CrossRefGoogle Scholar
Oberhofer, W. & Haupt, H. (2016) Asymptotic theory for nonlinear quantile regression under weak dependence. Econometric Theory 32, 686–713.CrossRefGoogle Scholar
Pakes, A. & Pollard, D. (1989) Simulation and the asymptotics of optimization estimators. Econometrica 57, 1027–1057.CrossRefGoogle Scholar
Powell, J.L. (1984) Least absolute deviations estimation for the censored regression model. Journal of Econometrics 25, 303–325.CrossRefGoogle Scholar
Powell, J.L. (1986) Symmetrically trimmed least squares estimation for Tobit models. Econometrica 54, 1435–1460.CrossRefGoogle Scholar
Qu, X. & Lee, L.F. (2012) LM tests for spatial correlation in spatial models with limited dependent variables. Regional Science and Urban Economics 42, 430–445.CrossRefGoogle Scholar
Sauquet, A., Marchand, S., & Féres, J.G. (2014) Protected areas, local governments, and strategic interactions: The case of the ICMS-Ecológico in the Brazilian state of Paraná. Ecological Economics 107, 249–258.CrossRefGoogle Scholar
Su, L. & Yang, Z. (2011) Instrumental variable quantile estimation of spatial autoregressive models. Working paper, Singapore Management University.Google Scholar
Tita, G.E. & Radil, S.M. (2010) Spatial regression models in criminology: Modeling social processes in the spatial weights matrix. In Piquero, A.R. and Weisburd, D. (eds.), Handbook of Quantitative Criminology, pp 101–121. Springer.CrossRefGoogle Scholar
Wilhelm, S. & de Matos, M.G. (2013) Estimating spatial probit models in R. The R Journal 5, 130–143.CrossRefGoogle Scholar
Xu, X. & Lee, L.F. (2015) Maximum likelihood estimation of a spatial autoregressive Tobit model. Journal of Econometrics 188, 264–280.CrossRefGoogle Scholar
Xu, X. & Lee, L.F. (2018) Sieve maximum likelihood estimation of the spatial autoregressive Tobit model. Journal of Econometrics 203, 96–112.CrossRefGoogle Scholar