Optimal Lockdown in an Epidemiological-Macroeconomic Model

This paper sets out a coherent framework for studying the economic effects of the Covid-19 pandemic, and policies aimed at controlling both the health and economic trade-offs that it poses. It does this by combining two key epidemiological and macroeconomic models: the SIR model and the RBC model. We argue that much of the present literature can be understood using this framework. The SIR-type epidemiology model in the paper has the novel feature of both no-disease and endemic steady states, two possible outcomes of Covid-19. The stability properties of these equilibria are examined and are shown to depend on the reproduction number and also, possibly, on the complex dynamics introduced by `predator-prey' behaviour of the virus. In addition, we show how endogenous social interaction fits within the model. Lockdown - reducing the size of the susceptible population - is then introduced into the RBC model as a social planner's problem. By linking this epidemiolgy model with a simple RBC model, we provide an integrated framework for examining the economic effects of Covid-related policies and the economic cost of lockdown policies of particular scope and duration. In principle an empirical implementation of this framework can be used to deduce the price of a life implied by a particular lockdown policy. Looking forward, extensions of our framework offer the chance to study economic challenges in areas such as debt financing, human capital shocks, or vaccine production and roll-out, all of which are inevitably emerging.