Abstract
Private policing is generally used to curb crime in certain neighbourhoods. The impact of an increase in these services on the city as a whole is unclear, as crime could shift from protected to unprotected targets, causing greater social harm. In practice, estimating this effect at the city level encounters at least two problems. First, the simultaneity between the demand for private policing and criminal activity requires appropriate instrumental variables to mitigate endogeneity biases. Second, the dependent and endogenous variables can have an excessive number of zeros at the same time, requiring the use of more specialized econometric models. In this paper, I combine Clotfelter’s theoretical model for private policing and crime with Amemiya’s econometric model for simultaneously censored outcomes, linking structural and reduced forms and discussing identification issues. Then, a regular Bitobit is modified to estimate reduced forms with many zeros outcomes in a set of copulas to improve censoring specifications with endogeneity. Finally, I conduct an empirical study examining an exclusive database from Brazil to discuss the copula approach, and the hypothesis that more private policing reduces crime at the city level is not rejected.
Similar content being viewed by others
Data availability
The data and computer codes supporting the results of this study are available from the corresponding author upon request.
References
Amemiya T (1974) Multivariate regression and simultaneous equation models when the dependent variables are truncated normal. Econom J Econom Soc, 999–1012. https://www.jstor.org/stable/1914214
Amemiya T (1979) The estimation of a simultaneous-equation tobit model. Int Econ Rev 201:169–181. https://doi.org/10.2307/25264233
Anderson TW, Rubin H (1949) Estimation of the parameters of a single equation in a complete system of stochastic equations. Ann Math Stat 201:46–63. https://doi.org/10.1214/aoms/1177730090
Angrist JD, Krueger AB (2001) Instrumental variables and the search for identification: from supply and demand to natural experiments. J Econ Perspect 154:69–85. https://doi.org/10.1257/jep.15.4.69
Brent DA, Bridge J (2003) Firearms availability and suicide: evidence, interventions, and future directions. Am Behav Sci 469:1192–1210. https://doi.org/10.1177/0002764202250662
Chen S, Zhou X (2011) Semiparametric estimation of a bivariate tobit model. J Econom 1652:266–274. https://doi.org/10.1016/j.jeconom.2011.07.005
Clotfelter CT (1978) Private security and the public safety. J Urban Econ 53:388–402. https://doi.org/10.1016/0094-1190(78)90018-9
Cooray K (2010) Generalized gumbel distribution. J Appl Stat 371:171–179. https://doi.org/10.1080/02664760802698995
Deb P, Trivedi PK, Zimmer DM (2014) Cost-offsets of prescription drug expenditures: data analysis via a copula-based bivariate dynamic hurdle model. Health Econ 2310:1242–1259. https://doi.org/10.1002/hec.2982
Duggan M (2001) More guns, more crime. J Polit Econ 1095:1086–1114. https://doi.org/10.1086/322833
Finlay K, Magnusson LM (2009) Implementing weak-instrument robust tests for a general class of instrumental-variables models. Stand Genomic Sci 93:398–421. https://doi.org/10.1177/1536867X0900900304
Friehe T, Mungan MC (2022) Private protection against crime and public policing: political economy considerations. Econ Lett 220:110858. https://doi.org/10.1016/j.econlet.2022.110858
Greene WH (2012) Econometric analysis. 7th International Edition, ISBN-13: 978-0273753568. Pearson Education, London. https://isbnsearch.org/isbn/9780273753568
Han S, Vytlacil EJ (2017) Identification in a generalization of bivariate probit models with dummy endogenous regressors. J Econom 1991:63–73. https://doi.org/10.1016/j.jeconom.2017.04.001
Hickey R, Mongrain S, Van Roberts J, Ypersele T (2021) Private protection and public policing. J Public Econ Theory 231:5–28. https://doi.org/10.1111/jpet.12473
Johnston L (1999) Private policing in context. Eur J Crim Policy Res 72:175–196. https://doi.org/10.1023/A:1008753326991
Kempa M, Carrier R, Wood J, Shearing C (1999) Reflections of the evolving concept of ‘private policing’. Eur J Crim Policy Res 72:197–223. https://doi.org/10.1023/A:1008705411061
Krahmann E (2008) Security: Collective good or commodity? Eur J Int Rel 143:379–404. https://doi.org/10.1177/1354066108092304
Lee L-F (1993) Multivariate tobit models in econometrics. Handbook Statist 11:145–173. https://doi.org/10.1016/S0169-7161(05)80041-0
Louzada F, Ferreira P (2016) Modified inference function for margins for the bivariate clayton copula-based sun tobit model. J Appl Stat 4316:2956–2976. https://doi.org/10.1080/02664763.2016.1155204
Maddala GS (1983) Limited-dependent and qualitative variables in econometrics. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511810176
Meehan B, Benson BL (2017) Does private security affect crime?: A test using state regulations as instruments. Appl Econ 4948:4911–4924. https://doi.org/10.1080/00036846.2017.1296551
Nalla MK, Gurinskaya A (2020) Private police and security governance: mapping emerging trends and future directions. J Contemp Crim Justice 361:101–109. https://doi.org/10.1177/1043986219890208
Nelsen RB (2007) An introduction to copulas. Springer Sci Busi Media. https://doi.org/10.1007/0-387-28678-0
Oakes D (2005) On the preservation of copula structure under truncation. Can J Stat/La revue canadienne de statistique, 465–468. https://www.jstor.org/stable/25046191
Oliveira CA (2018) The impact of private precautions on home burglary and robbery in brazil. J Quant Criminol 34:111–137. https://doi.org/10.1007/s10940-016-9325-6
Siegel M, Rothman EF (2016) Firearm ownership and suicide rates among us men and women, 1981–2013. Am J Public Health 1067:1316–1322. https://doi.org/10.2105/AJPH.2016.303182
Smith RJ, Blundell RW (1986) An exogeneity test for a simultaneous equation Tobit model with an application to labor supply. J Econom Soc Econom. https://doi.org/10.2307/1911314
Stenning PC (2000) Powers and accountability of private police. Eur J Crim Policy Res 83:325–352. https://doi.org/10.1023/A:1008729129953
Stock JH, Yogo M (2005) Testing for weak instruments in linear iv regression. In: Andrews DWK, Stock JH (eds) Identification and inference for econometric models: essays in honor of Rothenberg TJ. Cambridge University Press, Cambridge. https://www.cambridge.org/us/universitypress/subjects/economics/econometrics-statistics-and-mathematical-economics
Trivedi PK, Zimmer DM (2007) Copula modeling: an introduction for practitioners. Now Publishers Inc, Hanover. https://doi.org/10.1561/0800000005
UNOC (2019) Global study on homicide. The United Nations Office on Drugs and Crime. https://www.unodc.org/documents/data-and-analysis/gsh/Booklet1.pdf
Wang A (2007) The analysis of bivariate truncated data using the clayton copula model. Int J Biostat. https://doi.org/10.2202/1557-4679.1050
Wang A, Chandra K, Jia X (2018) The analysis of left truncated bivariate data using frailty models. Scand J Stat 454:847–860. https://doi.org/10.1111/sjos.12324
Wooldridge JM (2010) Econometric analysis of cross section and panel data. MIT press. https://mitpress.mit.edu/9780262232586/econometric-analysis-of-cross-section-and-panel-data/
Zimmerman PR (2014) The deterrence of crime through private security efforts: theory and evidence. Int Rev Law Econ 37:66–75. https://doi.org/10.1016/j.irle.2013.06.003
Funding
National Council for Scientific and Technological Development (CNPq), grant number 308582/2021-7.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author has no conflicts of interest to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Petterini, F.C. Modelling simultaneously censored outcomes of private policing and crime. Empir Econ 66, 1311–1331 (2024). https://doi.org/10.1007/s00181-023-02488-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00181-023-02488-6