Reciprocal relationships, reverse causality, and temporal ordering: testing theories with cross-lagged panel models

• In Event: Theory-testing and relevant methodologies in criminological research

Abstract

Reciprocal causal relationships are a common feature of criminological theories. For example, police forces tend to use force more often in areas where crime concentrates, while at the same time legal cynicism theory suggests that cumulative exposures to police use-of-force can foster criminal activity. When multiple observations over time are available, cross-lagged panel models are commonly used to estimate these reciprocal effects. This is often done without careful attention to the assumptions that must be satisfied to produce valid estimates, such as correctly specified temporal lags, sufficient inter-temporal variation, and proper accounting for unobserved heterogeneity. Failure to satisfy these assumptions can produce severe issues including spurious associations and parameter estimates that are biased or even reversed in direction. In addition, reciprocal relationships violate causal assumptions based on graphical tools; criminological theories that suggest reciprocal causal relationships usually have an underlying macro-micro mechanism often not accounted for in empirical models. We provide guidance on how to align theory, model specification, and choice of estimator and illustrate this using an empirical example. We use data from Chicago at the census tract level and model the potential reciprocal relationship between police use-of-force and violent crime between 2004 and 2016. We finalise highlighting the importance of criminological theory and careful attention to empirical implications of theoretical premises when investigating reciprocal relationships.

Authors

• Thiago Oliveira, University of Manchester

• Charles C Lanfear, University of Cambridge