Macro-Epidemic Modelling: A Deep Learning Approach

• Název práce v češtině: Makro-epidemické modelování: Metoda hlubokého učení
• Název v anglickém jazyce: Macro-Epidemic Modelling: A Deep Learning Approach
• Klíčová slova: Makro-epidemický model, rekurzivní equilibrium, agregátní riziko, projekce, hluboké učení
• Klíčová slova anglicky: Macro-Epidemic Model, Recursive Equilibrium, Aggregate Risk, Projection, Deep Learning
• Akademický rok vypsání: 2020/2021
• Typ práce: diplomová práce
• Jazyk práce: angličtina
• Ústav: CERGE (23-CERGE)
• Vedoucí / školitel: PhDr. Mgr. Ctirad Slavík, Ph.D.
• Řešitel: skrytý - zadáno a potvrzeno stud. odd.
• Datum přihlášení: 01.10.2020
• Datum zadání: 01.10.2020
• Datum potvrzení stud. oddělením: 01.10.2020
• Datum a čas obhajoby: 20.09.2021 14:00
• Místo konání obhajoby: CERGE-EI, JCERGE006, 006, učebna číslo 6
• Datum odevzdání elektronické podoby: 27.07.2021
• Datum proběhlé obhajoby: 20.09.2021
• Oponenti: doc. Mgr. Marek Kapička, Ph.D.

Seznam odborné literatury

Duarte, V. (2018). Gradient-Based Structural Estimation. Social Science Research Network

Eichenbaum, M. S., Rebelo, S., & Trabandt, M. (2020). The macroeconomics of epidemics (No. w26882). National Bureau of Economic Research.

Glover, A., Heathcote, J., Krueger, D., & Ríos-Rull, J. V. (2020). Health versus wealth: On the distributional effects of controlling a pandemic (No. w27046). National Bureau of Economic Research.

Kaplan, G., Moll, B., & Violante, G. L. (2020). The Great Lockdown and the Big Stimulus: Tracing the Pandemic Possibility Frontier for the US (No. w27794). National Bureau of Economic Research.

Judd, K. L., & Judd, K. L. (1998). Numerical methods in economics. MIT press.

Maliar, L., Maliar, S., & Winant, P. (2019). Will artificial intelligence replace computational economists any time soon?. Center for Economic Policy Research

Garibaldi, P., Moen, E. R., & Pissarides, C. A. (2020). Static and dynamic inefficiencies in an optimizing model of epidemics. Institute of Labor Economics

Gonzalez-Eiras, M., & Niepelt, D. (2020). Optimally Controlling an Epidemic. Center for Economic Policy Research

Předběžná náplň práce v anglickém jazyce

Motivation and Literature Review
Conventional solution methods for macroeconomic models aren't able to tackle the challenge presented by macro-epidemic models: strong nonlinearity of epidemic process coupled with rich heterogeneity of economic agents. Due to this fact, macro-epidemic modeling is restricted to rather simplistic environments abstracting either from heterogeneity among households and firms (e.g., Gonzalez-Eiras and Niepelt, 2020) or/and an uncertainty about aggregate dynamics (e.g., Eichenbaum et. al., 2020; Kaplan et. al., 2020). Because of these limitations of macro-epidemic models, policymakers are forced to rely on "mechanistic" SIRD models. Those models preclude analysis how people react to changing macro-epidemic variables and expectations about future government policies.

This thesis aims to contribute to macro-epidemic literature in two main directions. Firstly, it aims to provide an accurate and scalable solution method for general recursive formulation of macro-epidemic models that would allow to analyze macro-epidemic dynamics in realistic environments featuring complex economic system together with aggregate uncertainty. Secondly, it aims to facilitate optimal policy computation by leveraging the “manifold-learning” approach of Duarte (2018) for simultaneously solving the model for all relevant combination of government policy parameters and hence reducing the optimal policy computation into a simple optimization problem. To the best of my knowledge, this thesis would be the first paper, which applies deep learning based projection method for solving for competitive equilibria, and optimal policies in macro-epidemic models.


Research Question and Contribution
My thesis would contribute to the macro-epidemic literature in two directions. Firstly, I will develop an efficient deep learning solution method for recursive macro-epidemic models. Relative to the existing literature (e.g., Gonzalez-Eiras and Niepelt, 2020; Garibaldi and Pissarides, 2020) which rely on closed-form solutions or linear projection methods in a spirit of Judd (1998), my method would allow to analyze richer economies featuring more complex epidemic processes and economic structure. Secondly, I will utilize deep learning to accelerate computation of optimal government policies. Instead of re-solving the model many times for different parameterizations of government policies, I will use deep learning to approximate a whole equilibrium manifold indexed by policy parameters. This pre-computation in a spirit of Duarte (2018) should reduce the run-time of optimal policy computations by transforming the search for optimal policy parameters into a standard numerical optimization of readily-available function.

Methodology
I will extend the deep learning solution method of Maliar et. al. (2019) to accommodate peculiarities of macro-epidemic model, specifically absence of non-degenerate stationary distribution of state variables, which precludes usage of the ergodic grid method of Maliar et. al. (2019). Besides that, I will show how the deep learning method could be used to speed-up optimal policy computations by treating policy parameters as additional “pseudo-states” included in the network.

To provide an use case of my method, I will extend the benchmark macro-epidemic model of Eichenbaum, Rebelo, and Trabandt (2020) by providing its recursive formulation. Besides solving the basic model, I will demonstrate broad applicability of my method by solving a stochastic version of the model featuring stochastic changes in the epidemic characteristics (mutations) and solving for the optimal containment policy using the manifold learning approach. Because of data availability, I will focus the empirical part of my thesis on the case of the Czech Republic. For calibration of model parameters I will use data provided by the Czech Ministry of Health, the Czech National Bank, and the Czech Statistical Office.

Outline
1. Introduction
2. Literature
3. Stylized Facts
4. Model
a. Private Sector
b. Epidemic Dynamics
c. Government
d. Recursive Equilibrium
e. Policy Problem
5. Calibration
6. Numerical Solution
7. Results
8. Conclusion