Partial Identification of the Dark Figure of Crime with Survey Data Under Misreporting Errors

Abstract Objective This article studies how misreporting errors in crime surveys affect our understanding of the Dark Figure of Crime (DFC). Methods The paper adopts a Partial Identification framework which relies on assumptions that are weaker (and thus more credible) than those required by parametric models. Unlike common parametric models, Partial Identification handles both under-reporting and over-reporting of crimes (due to, say, stigma, memory errors or misunderstanding of upsetting events). We apply this framework to the Crime Survey for England and Wales to characterise the uncertainty surrounding crimes by severity and geographic region. Results Depending on the assumptions considered, the partial identification regions for the DFC vary from [0.000, 0.774] to [0.351, 0.411]. A credible estimate places the true DFC in [0.31, 0.51]. This range was obtained while allowing for a substantive amount of reporting error (25%) and assuming that people do not over-report crimes in surveys (saying they are a victim of crime erroneously or falsely). Across regions, uncertainty is larger in the north of England. Conclusion Accounting for misreporting introduces uncertainty about the actual magnitude of the DFC. This uncertainty is contingent on the unknown proportion of misreported crimes in the survey. When this proportion is modest (10% or below), raw survey estimates offer valuable insights, albeit with lingering uncertainty. However, researchers may want to opt for Partial Identification regions based on larger misreported proportions when examining relatively infrequent crimes that carry substantial stigma, such as sexual crimes or domestic violence. The width of the partial identification regions in this paper fluctuates among different regions of England and Wales, indicating varying levels of uncertainty surrounding the DFC in distinct localities. Consequently, previous research relying on parametric assumptions and resulting in singular point estimates necessitates re-evaluation in light of the findings presented herein.