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Crime in India: specification and estimation of violent crime index

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Abstract

This paper addresses several important issues related to crime. First, we construct a violent crime index taking into account seven different types of crimes. We use an aggregator function to define a crime index that attaches crime-specific weights which can be interpreted as severity of each crime. These weights are estimated econometrically along with other parameters in the model thereby avoiding the problems associated with equally or arbitrary weighted aggregate crime index. Second, we utilize the aggregate crime index function to determine the impact of socio-economic variables on the overall (aggregated) crime, and further decompose them into crime-specific components. Third, in specifying the crime index we allow the possibility that crimes may be underreported and estimate crime underreporting using the stochastic frontier modeling approach. We use district level data from India for the census years 1981, 1991 and 2001. Our results fail to support the equally weighted crime index model and provide evidence of substantial underreporting.

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Notes

  1. Kelly (2000) demonstrates that for violent crimes the impact of inequality is large, even after controlling for the effects of poverty, race, and family composition. Ackerman and Murray (2004) emphasize on the role of poverty reduction in reducing crime. Lochner (2004) provides the evidence that property and violent crime increases with age during adolescence, reach a peak during teenage years, then decline thereafter. See Knack and Keefer (1997), Fajnzylber et al. (2002), and Freeman (1991, 1996, 1999) for reviews of the literature.

  2. Sellin and Wolfgang (1964) propose a seriousness scoring scale that uses the effects of the crimes rather than specific legal labels to index the gravity of criminal behavior. However the scoring scale requires detailed information on arrests and therefore the information is unknown for crimes for which no arrests take place. To circumvent this problem, Sickles and Williams (2008) generate the seriousness scores by taking random draws from the distribution of seriousness scores for arrests in the corresponding crime category.

  3. In fact, we can construct the crime index using data on individual crimes trivially without linking it to a crime regression function with the socio-economic variables.

  4. We have models with large N and small T. If we allow for district-specific fixed effects, we would end up estimating 320 parameters in a maximum-likelihood framework with 918 observations. Further, the Index 3 model is non-linear in parameters. Because of this we decided not to include fixed district-effects in our models.

  5. It is possible to consider a model to allow the case of some socio-economic variables affecting some kinds of crime and not others. However, it is difficult to argue a priori which socio-economic variables affect which crime. One can run a separate regression for each crime [as in Levitt (1997)]. But this will miss the possible substitutability among crimes. Also, it is possible that a socio-economic variable affect one crime positively but another crime negatively. This is difficult to justify and might arise because of the fact that substitutability among different crimes are not allowed when separate regression is used for separate crime. The other two models, Models B and C (shown below), differ in terms of the crime index \(\eta\) but the \(\Psi (.)\) function is exactly the same in all three specifications.

  6. Delhi, the capital city of India, has witnessed brutal gang rape and murder of a student on December 16, 2012. The attack provoked outrage and grief in India, with protests across the country leading to an unprecedented national debate and calls for widespread changes in cultural attitudes as well as policing and legal reform. The Delhi police records show a rise in reported rape cases in 2012 of nearly a quarter, taking the total to 702.

  7. Another way to interpret under-reporting in our framework is in terms of efficiency in policing. We are thankful to one anonymous referee for this alternative interpretation. We use the ‘word’ under-reporting.

  8. This has changed after the gang rape and death of a young student in New Delhi, the capital of India on December 16, 2012. Same happens with a 22-year-old photo journalist more recently in Mumbai on September 6, 2013. The attack provoked outrage and grief in India, with protests across the country leading to an unprecedented national debate and calls for widespread changes in cultural attitudes as well as policing and legal reform. The Delhi police records show a rise in reported rape cases in 2012 of nearly a quarter, taking the total to 702.

  9. Here we are modeling reporting error in the crime index and not for individual crime types which cannot be separately identified.

  10. Alternatively, one can estimate the ratio \(\eta _{it}/\eta ^0_{it} = \exp (-u_{it}) \le 1\) where \(\eta ^0_{it}\) is the overall crime without underreporting. Higher value of this ratio will indicate lower underreporting.

  11. We do not include crime variables such as riots and dowry deaths. As explained earlier, we do not include riots in our analysis as the determinants of riots could differ significantly from other categories of crime. We however note that share of riots is around 28% of the total violent crime in 2006.

  12. We could not include wage as it is only available for the organized sector. However in India a large proportion of labor works in the informal sector.

  13. Increase in inequality although does not always translates to a larger difference between legal and illegal activities as other factors may be responsible.

  14. We admit that age distribution of males in the population could be an important determinant of violent crime. Given the absence of consistent data on age distribution of males in the population at the district level, we have not used this information. However, we hope that the unobserved heterogeneity at the state level would capture this to some extent.

  15. We use Census-1981 as the reference year. Therefore, the districts of Census-1991 and Census-2001 has been mapped to Census-1981 by weighted average method, where weights are respective population shares of district units.

  16. We use land inequality instead of income inequality because of two reasons. Empirically, cross-country studies which examine the relationship between initial inequality and subsequent growth have found a stronger effect of land and human capital inequality than of income inequality. On the other hand, recall bias will be much less in questions relating to land holdings than recalling consumption expenditure over the past month for each expenditure item.

  17. The basic statistical unit for data collection in Agriculture Census is ‘Operational Holding’ rather than ‘Ownership Holding’, as the farm level decisions are taken by persons who operate land and not by those who own it.

  18. We thank Rohini Somanathan for the data which has been used in Banerjee and Somanathan (2007).

  19. The states are Andhra Pradesh, Bihar, Gujarat, Haryana, Karnataka, Kerala, Madhya Pradesh, Maharashtra, Orissa, Rajasthan, Tamil Nadu, Uttar Pradesh and West Bengal. The state of Punjab is not included in the study due to unavailability of the required data for 1981 Census.

  20. The descriptive statistics results are not reported at the district level but can be made available on request.

  21. The \(\eta\) function can be viewed as a production possibility frontier in which \(y_m\) are outputs. Thus, in Model A an increase in \(y_1\), for example, has to be followed by a decrease in \(y_2\) by the exact same amount, ceteris paribus. In Model B, this substitution is constant and are different for different output pairs. Finally, in Model C substitutability between any pairs of \(y\) depends on the values of \(y\) and therefore varies across \(i\) and \(t\).

  22. Dreze and Khera have estimated five specifications. Inclusion of sex ratio or the ratio of male to female child mortality below age five makes the urbanization variable enters with negative and insignificant coefficient. Excluding these two variables, urbanization enters with positive and significant coefficient. Their analysis uses 319 districts for 1981 Census only and is limited to murder rates.

  23. The one-sided error might be correlated with the socioeconomic variables. However, we believe that this correlation, if any, is weak and some of it is captured by the fixed state effects. We state this as a weakness of our approach and agree that the estimates in this case could be biased depending on the nature of the correlation.

  24. Note that Model A is rejected against Models B and C.

  25. Note that Crime-Index 1 is not estimated from an econometric model. It is simply the average of all crime types. We take the average (which makes the weight for each crime type the same (i.e., \(1/M\)) so that Crime-Index 1 is comparable to the other two indices in which sum of the weights is constrained to unity.

  26. We use the Indian district administrative map obtained from http://www.gadm.org. With our mapping from 1981 Census to 2001 Census, we end up with 459 districts out of a total of 594 districts, thus representing around 77 % of total districts.

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Authors and Affiliations

  1. University of Leeds, Leeds, UK

    Kausik Chaudhuri

  2. Department of Economics, University of California, Irvine, Irvine, CA, USA

    Payel Chowdhury

  3. Department of Economics, State University of New York, Binghamton, Binghamton, NY, USA

    Subal C. Kumbhakar

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  1. Kausik Chaudhuri
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  2. Payel Chowdhury
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  3. Subal C. Kumbhakar
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Correspondence to Subal C. Kumbhakar.

Additional information

We are grateful to the Editor (Robin Sickles) and two anonymous referees for their helpful comments.

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Chaudhuri, K., Chowdhury, P. & Kumbhakar, S.C. Crime in India: specification and estimation of violent crime index. J Prod Anal 43, 13–28 (2015). https://doi.org/10.1007/s11123-014-0398-7

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