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The Impact of Police Strength and Arrest Productivity on Fear of Crime and Subjective Assessments of the Police

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Abstract

We explore the effect of police strength and arrest productivity on citizens’ fear of crime and perceived risk of victimization, as well as their subjective perceptions of the police including their confidence in the police and ratings of police response time. Police strength is measured as the rate of officers per 1,000 and productivity is calculated as the average number of arrests per officer; we also controlled for the crime rate using crimes reported to the police. We use nationally representative survey data (n = 1,005) and conduct a supplemental analysis of data drawn from a representative sample of urban counties (n = 1,500). Police force size and productivity have limited and inconsistent effects on fear of crime, perceived risk, and ratings of response time and no apparent effects on confidence in the police. We also find a modest yet statistically significant negative effect of police confidence on fear of crime. Our findings indicate that it is questionable whether adding more police will reduce fear or perceived risk of victimization to any measurable degree. Consequently, we suggest that rather than hiring binges and increased arrests, the focus should be instead on making positive contacts with citizens.

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Notes

  1. But see Bennett, 1994 who found no effect of confidence on perceived probability of victimization, worry about victimization, and fear of crime when out in the neighborhood at night or during the day.

  2. We included municipal police, county police and sheriffs, Texas constables, tribal police, campus police, and officers assigned to local criminal investigations in each county’s total number of law enforcement officers.

  3. The ICPSR ordinarily assigns an imputed value for counties with less than 3 months of data. This value is taken from an agency that reports 12 months of data, is located in the same state, and matches on the population stratum. Florida, Illinois, Kansas, Kentucky, and Montana reported little or no data statewide and therefore presented a problem because the imputation procedure used by the ICPRSR matches agencies within states. Ultimately, since we elected to impute the data, we coded as missing all county data previously imputed by the ICPSR. This is a conservative approach because unlike the ICPSR’s imputation, our multiple imputation acknowledges the inherent uncertainty of the resulting estimates.

  4. Survey level questions related to perceived neighborhood incivilities such as broken windows and graffiti and to beliefs that the police were friendly and did not use excessive force. We also included UCR arrest and crimes reported data reported for years outside those used for the analysis. This was done because several counties and entire states that were missing data for one  year had more complete data another year and thus the inclusion of these data points in the imputation substantially improved the precision of the resulting estimates. We also included a dummy variable indicating the state where R resided; 48 states were represented, and no respondents were from Alaska or South Dakota. The state dummy variables were used only for models predicting missing UCR data. The 48 dummies created perfect prediction problems for the imputation of survey-level variables even though we used the data augmentation procedure intended to combat this problem (White, Daniel, & Royston, 2010).

  5. The fraction of missing information is also referred to as the rate of missing information and is not simply the proportion of the sample missing data on the variable in question. See Barnard & Rubin (1999) and Schafer (2001) for additional information on the calculation and use of the statistic.

  6. Monte Carlo error estimates are calculated using a jackknife procedure where each statistic of interest is computed repeatedly while omitting a single imputation each time. The resulting standard deviation is a measure of the variability of the statistic of interest across imputations (White, 2010)

  7. There is no definitive rule for determining when the Markov chain has converged. Instead, visual diagnostics are recommended – specifically, the chain should exhibit no trends and should traverse the distribution quickly (i.e. “good mixing”). We also used a generous 100 iterations for each imputation to ensure the Markov chain was stationary when the imputed values were drawn.

  8. We considered an alternative specification of this measure where the arrests per officer was calculated separately for each of 5 crime types, standardized, and then averaged. Standardization was essential because the average arrests for common crimes such as burglary was not, essentially, on the same scale as arrests for rare crimes such as murder. Alpha for this measure was a respectable .75. We ultimately abandoned this measure because its interpretation was less clear and it was correlated with the simple average number of arrests per officer at .9. Results were not substantively different with either measure.

  9. Not all departments reported data to the UCR each month. The UCR imputed missing data based on the monthly data that had been reported for that jurisdiction. Coverage reflects the proportion of the county’s data that is not imputed. Some jurisdictions had better coverage in 1994 and others in 1995. In general we felt the data were more trustworthy when averaged over 2 years.

  10. There was one such place in the present data – Montgomery County, GA with a population of 7,804 and no murders, rapes, robberies, burglaries, or aggravated assaults reported in 1994 or 1995. UCR crimes reported coverage for this county was 100 percent in 1994 and 41.7 percent in 1995.

  11. Alpha was calculated using the non-imputed values.

  12. Alpha was calculated using the non-imputed values.

  13. There were 77 Hispanics and 27 respondents who indicated belonging to some other racial group. The “other” group presented problems both in the imputation phase and the analysis phase because they were so few in number. Thus, the unfortunate but necessary solution was to consolidate the “others” with another racial/ethnic group – we chose Hispanics for this purpose.

  14. We could fix the other covariates at the mean which would provide the predicted score on the outcome for the “average observation.” However, because R’s generally are not, for example, 48 percent female, 8 percent black, and 54 percent married, the predicted outcome for an “average individual” is of questionable substantive value.

  15. This metric is a semi-elasticity – the proportional or percentage change in the outcome given a unit change in the number of arrests per officer.

  16. In the ordered logit model we also examined the predictive margins to evaluate the interaction between arrests per officer and the officer rate. This is the method proposed by Ai & Norton (2003) for non-linear models (see also Norton, Wang, & Ai, 2004). Results from this analysis also provided no evidence in support of an interactive effect.

  17. Full collinearity diagnostics including VIFs/tolerance statistics and the condition index were not possible with the imputed data.

  18. As a reminder, these measures are distinguished by more than simply the denominator in the calculation. The arrests per officer is based on UCR arrests while the crime rate is based on UCR crimes reported to the police.

  19. Do not confuse the change in the probability in additive terms with the proportional change in the probability. For example, in additive terms a .10 increase in probability would mean that the outcome is 10 percent more likely to occur for each unit increase in the predictor. In the proportional or semi-elastic metric, suppose the outcome had a 5 percent likelihood of occurring, in this case a .10 increase would be a 300 percent proportional change. We report additive changes in probability in decimal form and proportional changes in percentage form.

  20. The resulting graphs are omitted here to save space but are available from the lead author by request.

  21. At the median of arrests per officer the effect of officer rate was significant at p < =.1, two tailed.

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  1. School of Criminology and Criminal Justice, Florida Atlantic University, 777 Glades Road, SO bldg. Rm. 208, Boca Raton, FL, 33431, USA

    Will Hauser

  2. College of Criminology and Criminal Justice, Florida State University, 112 S. Copeland St, Tallahassee, FL, 32306-1273, USA

    Gary Kleck

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Correspondence to Will Hauser.

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Hauser, W., Kleck, G. The Impact of Police Strength and Arrest Productivity on Fear of Crime and Subjective Assessments of the Police. Am J Crim Just 42, 86–111 (2017). https://doi.org/10.1007/s12103-016-9334-x

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