A cointegration analysis of crime, economic activity, and police performance in São Paulo city

Abstract

The main objective of this paper is to investigate possible causes for the significant reduction observed in crime rates in São Paulo city. By applying a cointegration analysis, we observed long-run relationships between crime, economic activity, and police performance. The results indicate that the lethal crime rate is positively related to unemployment and negatively related to real wages and to the results of law-enforcement activities, specifically arrests and seizure of firearms. Moreover, the hypothesis that the Disarmament Statute led to a reduction in the lethal crime rate is not rejected.

Keywords:

• crime
• time series
• cointegration analysis
• criminality
• lethal crime

Acknowledgements

We thank two anonymous referees, Mirian Rumenos Piedade Bacchi, Tulio Kahn, Humberto Francisco Spolador, Geraldo Sant‘Ana de Camargo Barros, Luiz Guilherme Scorzafave, and Pery Francisco Assis Shikida for their useful comments and suggestions. Any remaining errors and omissions are our own responsibility. We also thank CNPq for its financial support.

Notes

Federal Law 10,826 of December 2003, known as the DS, which was regulated in July 2004, disciplined the possession and carrying of firearms in Brazil, provided for stricter penalties for illegal possession and carrying of firearms, and made it possible for disarmament campaigns to be carried out. Its full text is available at: http://www.planalto.gov.br/ccivil_03/Leis/2003/L10.826.htm.

2004Q1 denotes the first quarter of 2004.

For a complete explanation of the econometric methodology that was applied, see 23 35 46, among others.

Actually, the lethal crime rate and the number of firearms seized by one hundred thousand population followed very similar long-run paths in the sampling period under analysis. The Pearson correlation coefficient estimated between them was 0.96 (t=24.42).

Crimes that include many behaviors related to the sale or distribution of substances that can cause physical or psychological addiction.

Data available at http://www.ssp.sp.gov.br/esttistica/trimestrais.aspx. Unfortunately, these data are published separately by quarter in pdf file. We would like to acknowledge that the data for the number of searches and identification of persons in periods preceding the first quarter of 2005 were kindly provided by Dr Tulio Kahn, former coordinator of the Coordinating Office for Planning and Analyses of the Public Security Department of the State of São Paulo. For details on the process of collecting and interpreting the data, see 11.

Saridakis 78 uses the unemployment rate among men. Besides this measure, we considered the possibility of using the unemployment rate only among family heads. However, no significant difference was observed in the time path of these three series.

Data available at http://www.seade.gov.br/produtos/ped/.

The minimum wage is deflated by the cost-of-living index in São Paulo, which is calculated by DIEESE. Other details can be found at http://www.dieese.org.br/esp/metodsm.xml.

We also applied the statistical criterion suggested by McLeod 62 to monitor the variance behavior in successive differences in the series. Simulations by the author suggest that an excessive number of differences result in a negative first-order autocorrelation value in the differentiated series tending to −0.5; when, however, the series is correctly differentiated, variance in the transformed series decreases; on the other hand, excessive differences increase variance.

The concomitant use of both tests is justified by the fact that, by reversing the null hypothesis, the first test reduces the low-power problem of the second, particularly as the autoregressive coefficient is closest to one.

To our knowledge, in Brazilian literature only Pereira and Carrera-Fernadez 66 had made a similar attempt, but using the methodology proposed by Engle and Granger 25. The authors reached the conclusion that there is a cointegrating relationship between crime (total crime and vehicle theft or vehicle robbery) and income inequality.

Note that the constant outside the cointegrating vectors represents a linear trend at the level of y _t . For details on five possible Johansen's specifications, see Johansen 44 46 and Harris 39, among others. Johansen 45 discusses the role of the deterministic regressors in a cointegration relantionship.

It should be observed that it is not different from the maximal eigenvalue test.

See Johansen et al. 48 for technical details as to how the two models are defined.

It is noteworthy that in the other two specifications, I and III, the diagnostic test results do not differ from the results obtained for the specifications II.

A multivariate version of this test can be computed by using the residuals that are standardized by a Choleski decomposition of the variance–covariance matrix for the centered residuals. In this case the test result is dependent upon the ordering of the variables. We used the ordering reported in the next section. To check the result, this test was redone with different sorts of model variables. There was no difference between the test results regarding the conclusion.

For details about restriction tests on α and β see Johansen and Juselius 47 and Johansen 46, among others.

Statistics with reduction of four degrees of freedom derived from order p+q of the model.

See Stligler 84 for an overview of threshold cointegration.

The variable definitions are provided in Table 1.

It should be noted that the value of the threshold, (τ), is unknown in these tests. It is estimated along with other parameters of the TAR model. In others worlds, these are ‘endogenous nonlinearity’ tests, in the sense that the transition variable is a function of the system variables. Following Hansen 37, we used τ=0.1 for the minimal percentage of observations in each assumed regime and, based on the linear model specification used in the previous linearity test, we used two lags in the specification, i.e. p=2.

According to the Ministry of Justice, national campaigns have, since 2004, removed around 570,000 firearms from circulation. In its 2011 edition, nearly 34,000 firearms were withdrawn from circulation, approximately 29.3% of which were in the state of São Paulo. Information available at http://portal.mj.gov.br; accessed on 01/13/2012.

McDowall 59 brings together and discusses the main points of this controversial discussion.