63: Interactive Fixed Effects for Longitudinal Instrumental Variables: Application to Traffic Safety

Music City Center 

In longitudinal data, unobserved confounders often vary by unit and time period. A common approach for adjusting for these confounders is to use instrumental variables in combination with two-way fixed effects. However, this approach requires that any unobserved confounders
correlated with the instrument vary solely by unit or time period, with no interactions between the two. In this paper, we relax this assumption by proposing a novel method in which instrumental variable regression is estimated with interactive fixed effects. Our method leverages nuclear norm penalization to adjust for confounders that vary across both unit and time period, assuming the variation is low-rank. We first demonstrate that under this assumption, the proposed estimator yields a consistent estimator of the average treatment effect. We then apply our method to investigate the relationship of traffic ticket issuance and car accident rates. The results of our analysis indicate that traffic tickets issued by police officers in New York City effectively reduce traffic collisions. Finally, we validate the efficacy and robustness of our approach by comparing it with competing methods.

Instrumental Variable

Interactive Fixed Effects

Factor Model

Longitudinal Data

Nuclear Norm

Causal Inference 

Transportation Statistics Interest Group