Ignoring Spatial and Spatiotemporal Dependence in the Disturbances Can Make Black Swans Appear Grey.

Automated valuation models (AVMs) are widely used by financial institutions to estimate the property value for a residential mortgage. The distribution of pricing errors obtained from AVMs generally show fat tails (Pender 2016; Demiroglu and James Management Science, 64(4), 1747-1760 2018). The extreme events on the tails are usually known as "black swans" (Taleb 2010) in finance and their existence complicates financial risk management, assessment, and regulation. We show via theory, Monte Carlo experiments, and an empirical example that a direct relation exists between non-normality of the pricing errors and goodness-of-fit of the house pricing models. Specifically, we provide an empirical example using US housing prices where we demonstrate an almost perfect linear relation between the estimated degrees-of-freedom for a Student's t distribution and the goodness-of-fit of sophisticated evaluation models with spatial and spatialtemporal dependence.

Demographic, jurisdictional, and spatial effects on social distancing in the United States during the COVID-19 pandemic.

Social distancing, a non-pharmaceutical tactic aimed at reducing the spread of COVID-19, can arise because individuals voluntarily distance from others to avoid contracting the disease. Alternatively, it can arise because of jurisdictional restrictions imposed by local authorities. We run reduced form models of social distancing as a function of county-level exogenous demographic variables and jurisdictional fixed effects for 49 states to assess the relative contributions of demographic and jurisdictional effects in explaining social distancing behavior. To allow for possible spatial aspects of a contagious disease, we also model the spillovers associated with demographic variables in surrounding counties as well as allow for disturbances that depend upon those in surrounding counties. We run our models weekly and examine the evolution of the estimated coefficients over time since the onset of the COVID-19 pandemic in the United States. These estimated coefficients express the revealed preferences of individuals who were able to and chose to stay at home to avoid the disease. Stay-at-home behavior measured using cell phone tracking data exhibits considerable cross-sectional variation, increasing over nine-fold from the end of January 2020 to the end of March 2020, and then decreasing by about 50% through mid-June 2020. Our estimation results show that demographic exogenous variables explain substantially more of this variation than predictions from jurisdictional fixed effects. Moreover, the explanations from demographic exogenous variables and jurisdictional fixed effects show an evolving correlation over the sample period, initially partially offsetting, and eventually reinforcing each other. Furthermore, the predicted social distance from demographic exogenous variables shows substantial spatial autoregressive dependence, indicating clustering in social distancing behavior. The increased variance of stay-at-home behavior coupled with the high level of spatial dependence can result in relatively intense hotspots and coldspots of social distance, which has implications for disease spread and mitigation.