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First Quarter 2022, 
Vol. 104, No. 1
Posted 2022-01-14

Economic Activity during the COVID-19 Pandemic: A Model with “Acquired Immunity”

by Juan Esteban Carranza, Juan David Martin, and Álvaro José Riascos


We calibrate a macroeconomic model with epidemiological restrictions using Colombian data. The key feature of our model is that a portion of the population is immune and cannot transmit the virus, which improves substantially the fit of the model to the observed contagion and economic activity data. The model implies that during 2020, government restrictions and the endogenous changes in individual behavior saved around 15,000 lives and decreased consumption by about 4.7 percent. The results suggest that most of this effect was the result of government policies.

Juan Esteban Carranza is the Director of Economic Studies at the Banco de la República; Juan David Martin is a researcher at the Banco de la República; and Álvaro José Riascos is a professor at the University of los Andes and Director of Quantil.


In this article we formulate and calibrate a dynamic macroeconomic model in which optimizing agents respond to the risk of contagion and restrictions imposed by the government during the recent public health crisis. Our model is similar to the model by Eichenbaum, Rebelo, and Trabandt (2020; henceforth ERT), except for the inclusion of a modified epidemiological model that incorporates the possibility of exogenous immunity to contagion. We calibrate the model with Colombian data and use it to simulate counterfactual policies.

The original ERT model was the first of a wave of new articles using variations of a simple susceptible-infected-recovered (SIR) epidemiological model to account for the endogenous risk of contagion faced by economic agents. Other articles with similar approaches include Atkeson (2020); Alvarez, Argente, and Lippi (2020); Acemoglu et al. (2020); and Berger, Herkenhoff, and Mongey (2020). In these models, both contagion and economic activity are the results of a dynamic programming problem in which agents maximize their intertemporal utility, accounting for the risk of contagion over the course of an epidemic.

In the SIR model and its variations (based on seminal work by Kermack and McKendrick, 1927), an epidemic runs its course as it infects individuals who then become immune. The epidemic ends when the population reaches "herd immunity," which occurs when enough people are immune and the virus cannot spread anymore. The main drawback of these models is the difficulty they have in fitting the observed COVID-19 contagion data. In particular, the standard model predicts very high numbers of both infections and deaths compared with the relatively low numbers observed in the data.

Our main contribution to understanding the pandemic is the modification of the SIR model to allow for the presence of individuals who are unaffected by the virus and who become immune over time at an exogenous rate. As our results show, the presence of this "immune" population helps to fit the model to the observed data. In particular, the model replicates well the rapid decline of observed deaths after the infection of a relatively low portion of the population during the first wave of the pandemic.

In contrast to ERT, we calibrate the model to match measures of both the pandemic and economic activity. We follow ERT in modeling government restrictions as a consumption tax, which induces consumers to cut back in their consumption activities, but we actually calibrate the parameterization of this tax.

The calibrated model predicts that almost all infections in Colombia will have already occurred by December 2020 and that the economy will be back on its long-term path by mid-2021. Our simulations suggest that government restrictions decreased yearly 2020 consumption by around 3 percent and saved around 10,000 lives. Without government restrictions, the economy would have still faced a 1 percent contraction, generated by consumers cutting back on consumption and labor to avoid contagion.

The model can be easily extended to accommodate successive contagion waves by allowing agents who become immune to become susceptible again. In the model, new waves can be triggered by making immunity disappear after an exogenous number of weeks or by letting immune agents become susceptible every period at an exogenous rate. This type of modeling would capture the possibility that, for example, either variations of the original virus appear or antibodies acquired from a mild infection disappear. Because the reasons individuals may or may not be immune are not well understood, we focus on the modeling of one wave of the pandemic and leave extensions for further research.

Read the full article.