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Aggregation Bias in Deterrence Research - An Empirical Analysis

NCJ Number
D F Greenberg, R C Kessler, C H Logan
Date Published
January 1981
10 pages
This study, based on urban arrest and crime data, shows that bias could be expected in deterrence research at the State level when estimation is carried out with spatially aggregated data.
In deterrence research, the theoretical framework of utility maximization deals with the expected behavior of individuals in the presence of possible lawful and illegal gains and costs. The bulk or research has been carried out using spatially aggregated data for cities, counties, States, and nations. However, when the parameters of a structural equation pertaining to a given level of aggregation are estimated with data aggregated at a higher level, the estimates may be biased. The mutual influence of crime rates and sanction levels is felt at the city rather than at the State level, since public pressure on police and judges can more easily be brought to bear at the city level. A parallel analysis for the mutual effect of Index crime rates and arrest clearance rates has been carried out to establish when aggregation bias will occur and to indicate how large a bias is introduced by aggregation. Data for a stratified random sample of 98 cities for the period between 1964 and 1970 and for 50 States for the years from 1964 to 1968 were used. Estimates of identical models for the reciprocal effects of per capita arrest rates and arrest clearance rates obtained from city and State data differ substantively. Both sets of models are consistent with the proposition that marginal changes in the probability of arrest have no effect on Index crime rates. However, the two sets of models differed regarding the effect of crime rates on arrest probabilities. Only in the State data was there evidence that crime rates influenced arrest probabilities. The estimates derived from city data are more credible than those derived from State data, and the findings should be attributed to aggregation bias. The bias can be avoided through a priori considerations involving empirical knowledge or plausible reasoning about modeled processes. The choice of an appropriate level of aggregation is in reality an element of proper specification. Statistical sources of aggregation bias are discussed. Statistical data, footnotes, and 12 references are included. (Author abstract modified)

Date Published: January 1, 1981