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  • Tadao Hoshino (a1)

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.

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*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:
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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.

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Amemiya, T. (1973) Regression analysis when the dependent variable is truncated normal. Econometrica 41, 9971016.
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).
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, 6066. (in Japanese).
Andrews, D.W. (1992) Generic uniform convergence. Econometric Theory 8, 241257.
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 213262. Measurement and Analysis of Crime and Justice. National Institute of Justice.
Autant-Bernard, C. & LeSage, J.P. (2011) Quantifying knowledge spillovers using spatial econometric models. Journal of Regional Science 51, 471496.
Bernasco, W. & Elffers, H. (2010) Statistical analysis of spatial crime data. In Piquero, A.R. and Weisburd, D. (eds.), Handbook of Quantitative Criminology, pp 699724. Springer.
Buchinsky, M. & Hahn, J. (1998) An alternative estimator for the censored quantile regression model. Econometrica 66, 653671.
Chernozhukov, V. & Hong, H. (2002) Three-step censored quantile regression and extramarital affairs. Journal of the American Statistical Association 97, 872882.
Chernozhukov, V., Fernandez-Val, I., & Kowalski, A.E. (2015) Quantile regression with censoring and endogeneity. Journal of Econometrics 186, 201221.
Chen, S. (2000) Efficient estimation of binary choice models under symmetry. Journal of Econometrics 96, 183199.
Chen, S. & Khan, S. (2008) Semiparametric estimation of nonstationary censored panel data models with time varying factor loads. Econometric Theory 24, 11491173.
Chen, S. & Zhou, Y. (2010) Semiparametric and nonparametric estimation of sample selection models under symmetry. Journal of Econometrics 157, 143150.
Chen, S., Zhou, Y., & Ji, Y. (2018) Nonparametric identification and estimation of sample selection models under symmetry. Journal of Econometrics 202, 148160.
Chen, T. & Tripathi, G. (2017) A simple consistent test of conditional symmetry in symmetrically trimmed tobit models. Journal of Econometrics 198, 2940.
Cracolici, M.F. & Uberti, T.E. (2009) Geographical distribution of crime in Italian provinces: A spatial econometric analysis. Jahrbuch für Regionalwissenschaft 29, 128.
Davidson, J. (1994) Stochastic Limit Theory. Oxford University Press.
Di Porto, E. & Revelli, F. (2013) Tax-limited reaction functions. Journal of Applied Econometrics 28, 823839.
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, 686733.
He, X. & Shao, Q.M. (2000) On parameters of increasing dimensions. Journal of Multivariate Analysis 73, 120135.
Honoré, B.E. & Hu, L. (2004) On the performance of some robust instrumental variables estimators. Journal of Business and Economic Statistics 22, 3039.
Horowitz, J. (1992) A smoothed maximum score estimator for the binary response model. Econometrica 60, 505531.
Hoshino, T. (2018) Semiparametric spatial autoregressive models with endogenous regressors: With an application to crime data. Journal of Business and Economic Statistics 36, 160172.
Jenish, N. (2016) Spatial semiparametric model with endogenous regressors. Econometric Theory 32, 714739.
Jenish, N. & Prucha, I.R. (2009) Central limit theorems and uniform laws of large numbers for arrays of random fields. Journal of Econometrics 150, 8698.
Jenish, N. & Prucha, I.R. (2011) On spatial processes and asymptotic inference under near-epoch dependence. Working paper.
Jenish, N. & Prucha, I.R. (2012) On spatial processes and asymptotic inference under near-epoch dependence. Journal of Econometrics 170, 178190.
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, 99121.
Kelejian, H.H. & Prucha, I.R. (2010) Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. Journal of Econometrics 157, 5367.
Khan, S. & Powell, J.L. (2001) Two-step estimation of semiparametric censored regression models. Journal of Econometrics 103, 73110.
Khan, S. & Tamer, E. (2009) Inference on endogenously censored regression models using conditional moment inequalities. Journal of Econometrics 152, 104119.
Knight, K. (1998) Limiting distributions for L 1 regression estimators under general conditions. Annals of Statistics 26, 755770.
Lahiri, S.N. & Zhu, J. (2006) Resampling methods for spatial regression models under a class of stochastic designs. Annals of Statistics 34, 17741813.
Lei, J. (2014) Smoothed spatial maximum score estimation of spatial autoregressive binary choice panel models. Working paper, Tilburg University.
LeSage, J. & Pace, R.K. (2009) Introduction to Spatial Econometrics. CRC Press.
Liu, X. & Lee, L.F. (2013) Two-stage least squares estimation of spatial autoregressive models with endogenous regressors and many instruments. Econometric Reviews 32, 734753.
Magnac, T. & Maurin, E. (2007) Identification and information in monotone binary models. Journal of Econometrics 139, 76104.
Manski, C.F. (1975) Maximum score estimation of the stochastic utility model of choice. Journal of Econometrics 3, 205228.
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. 127144. Oxford University Press.
Newey, W.K. (1987) Specification tests for distributional assumptions in the Tobit model. Journal of Econometrics 34, 125145.
Oberhofer, W. & Haupt, H. (2016) Asymptotic theory for nonlinear quantile regression under weak dependence. Econometric Theory 32, 686713.
Pakes, A. & Pollard, D. (1989) Simulation and the asymptotics of optimization estimators. Econometrica 57, 10271057.
Powell, J.L. (1984) Least absolute deviations estimation for the censored regression model. Journal of Econometrics 25, 303325.
Powell, J.L. (1986) Symmetrically trimmed least squares estimation for Tobit models. Econometrica 54, 14351460.
Qu, X. & Lee, L.F. (2012) LM tests for spatial correlation in spatial models with limited dependent variables. Regional Science and Urban Economics 42, 430445.
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, 249258.
Su, L. & Yang, Z. (2011) Instrumental variable quantile estimation of spatial autoregressive models. Working paper, Singapore Management University.
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 101121. Springer.
Wilhelm, S. & de Matos, M.G. (2013) Estimating spatial probit models in R. The R Journal 5, 130143.
Xu, X. & Lee, L.F. (2015) Maximum likelihood estimation of a spatial autoregressive Tobit model. Journal of Econometrics 188, 264280.
Xu, X. & Lee, L.F. (2018) Sieve maximum likelihood estimation of the spatial autoregressive Tobit model. Journal of Econometrics 203, 96112.
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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
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