Estimating the propagation of the COVID-19 virus with a stochastic frontier approximation of epidemiological models: a panel data econometric model with an application to Spain

The literature examining the propagation of COVID-19 has mainly used pure epidemiological models focused on estimating reproductive numbers, mortality and other epidemiological features. In this paper we use a stochastic frontier analysis (SFA) approach to model the propagation of the epidemic across geographical areas, which complements existing epidemiological models. Our work bridges the SFA and epidemiological literatures and shows that the translation from epidemiological models to SFA implies strong assumptions and introduces measurement errors. We propose two different specifications of the stochastic frontier model: first, a stochastic frontier based on an epidemiological SIR model specification; and second, an approximation to this SIR-based frontier based on functions of the length of time since the outbreak of the virus began. These models permit reported and undocumented cases to be estimated. The appeal of these models lies in the fact that they can be estimated using only epidemic-type data and yet are flexible enough to permit these reporting rates to vary across geographical cross-section units of observation and to allow other covariates affecting reported and undocumented rates to be incorporated. We provide an empirical application of our models to Spanish data corresponding to the initial months of the original outbreak of the virus in early 2019 where we introduce a series of series of extensions to base model and specification robustness checks.