Identifying delayed human response to external risks: an econometric analysis of mobility change during a pandemic

Human behavioral responses to changes in risks are often delayed. Methods for estimating these delayed responses either rely on rigid assumptions about the delay distribution (e.g., Erlang distribution), producing a poor fit, or yield period-specific estimates (e.g., estimates from the Autoregressive Distributed Lag (ARDL) model) that are difficult to integrate into simulation models. We propose a hybrid ARDL-Erlang approach that yields an interpretable summary of behavioral responses suitable for incorporation into simulation models.

We apply the ARDL-Erlang approach to estimate the effect of COVID-19 deaths on mobility across US counties from October 2020 to July 2021. A standard panel autoregressive distributed lag (ARDL) model first estimates the effect of past deaths and past mobility on current mobility. The ARDL model is then transformed into an Infinite Distributed Lag (IDL) model consisting of only past deaths. The coefficients of the past deaths are aggregated into an overall effect and fit to an Erlang distribution, summarized by average delay length and shape parameter.

Our results show that on the national level, a one-standard-deviation permanent increase in weekly deaths per 100,000 population (log-transformed) is associated with a 0.46-standard-deviation decrease in human mobility in the long run, where the delay distribution follows a first-order Erlang distribution, and the average delay length is about 3.2 weeks. However, there is much heterogeneity across states, with first- to third-order Erlang delays and 2 to 18 weeks of average delay providing a theoretically cogent summary of how mobility followed changes in deaths during the first year and a half of the pandemic.

This study provides a novel approach to estimating delayed human responses to health risks using a hybrid ARDL-Erlang model. Our findings highlight significant variability in the impact and timing of responses across states, underscoring the need for tailored public health policies. This study can also serve as guidelines and an example for identifying delayed human behavior in other settings.