Identification and estimation of the SEIRD epidemic model for COVID-19

Abstract

This paper studies the SEIRD epidemic model for COVID-19. First, I show that the model is poorly identified from the observed number of deaths and confirmed cases. There are many sets of parameters that are observationally equivalent in the short run but lead to markedly different long run forecasts. Second, I show that the basic reproduction number R0 can be identified from the data, conditional on epidemiologic parameters, and propose several nonlinear SUR approaches to estimate R0. I examine the performance of these methods using Monte Carlo studies and demonstrate that they yield fairly accurate estimates of R0. Next, I apply these methods to estimate R0 for the US, California, and Japan, and document heterogeneity in the value of R0 across regions. My estimation approach accounts for possible underreporting of the number of cases. I demonstrate that if one fails to take underreporting into account and estimates R0 from the reported cases data, the resulting estimate of R0 may be biased downward and the resulting forecasts may exaggerate the long run number of deaths. Finally, I discuss how auxiliary information from random tests can be used to calibrate the initial parameters of the model and narrow down the range of possible forecasts of the future number of deaths.