IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2008.07335.html
   My bibliography  Save this paper

Verification Results for Age-Structured Models of Economic-Epidemics Dynamics

Author

Listed:
  • Giorgio Fabbri
  • Fausto Gozzi
  • Giovanni Zanco

Abstract

In this paper we propose a macro-dynamic age-structured set-up for the analysis of epidemics/economic dynamics in continuous time. The resulting optimal control problem is reformulated in an infinite dimensional Hilbert space framework where we perform the basic steps of dynamic programming approach. Our main result is a verification theorem which allows to guess the feedback form of optimal strategies. This will be a departure point to discuss the behavior of the models of the family we introduce and their policy implications.

Suggested Citation

  • Giorgio Fabbri & Fausto Gozzi & Giovanni Zanco, 2020. "Verification Results for Age-Structured Models of Economic-Epidemics Dynamics," Papers 2008.07335, arXiv.org.
    • Handle: RePEc:arx:papers:2008.07335
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2008.07335
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dirk Krueger & Harald Uhlig & Taojun Xie, 2022. "Macroeconomic dynamics and reallocation in an epidemic: evaluating the ‘Swedish solution’," Economic Policy, CEPR, CESifo, Sciences Po;CES;MSH, vol. 37(110), pages 341-398.
    2. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Capital accumulation under technological progress and learning: A vintage capital approach," European Journal of Operational Research, Elsevier, vol. 172(1), pages 293-310, July.
    3. Fernando Alvarez & David Argente, 2020. "A Simple Planning Problem for COVID-19 Lockdown," Working Papers 2020-34, Becker Friedman Institute for Research In Economics.
    4. Christian Gollier, 2020. "Cost–benefit analysis of age‐specific deconfinement strategies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(6), pages 1746-1771, December.
    5. Fabbri, Giorgio & Gozzi, Fausto & Swiech, Andrzej, 2007. "Verification theorem and construction of epsilon-optimal controls for control of abstract evolution equations," MPRA Paper 3547, University Library of Munich, Germany.
    6. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "Growth and agglomeration in the heterogeneous space: a generalized AK approach," Journal of Economic Geography, Oxford University Press, vol. 19(6), pages 1287-1318.
    7. Facundo Piguillem & Liyan Shi, 2022. "Optimal Covid-19 Quarantine and Testing Policies," The Economic Journal, Royal Economic Society, vol. 132(647), pages 2534-2562.
    8. Faggian, Silvia & Gozzi, Fausto, 2010. "Optimal investment models with vintage capital: Dynamic programming approach," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 416-437, July.
    9. Dirk Kruger & Harald Uhlig & Taojun Xie, 2020. "Macroeconomic Dynamics and Reallocation in an Epidemic," Working Papers 2020-43, Becker Friedman Institute for Research In Economics.
    10. Martin S Eichenbaum & Sergio Rebelo & Mathias Trabandt, 2021. "The Macroeconomics of Epidemics [Economic activity and the spread of viral diseases: Evidence from high frequency data]," The Review of Financial Studies, Society for Financial Studies, vol. 34(11), pages 5149-5187.
    11. Daron Acemoglu & Victor Chernozhukov & Iván Werning & Michael D. Whinston, 2021. "Optimal Targeted Lockdowns in a Multigroup SIR Model," American Economic Review: Insights, American Economic Association, vol. 3(4), pages 487-502, December.
    12. B. Skritek & V. M. Veliov, 2015. "On the Infinite-Horizon Optimal Control of Age-Structured Systems," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 243-271, October.
    13. Palivos, Theodore & Yip, Chong K., 1993. "Optimal population size and endogenous growth," Economics Letters, Elsevier, vol. 41(1), pages 107-110.
    14. Ichino, Andrea & Favero, Carlo A. & Rustichini, Aldo, 2020. "Restarting the economy while saving lives under Covid-19," CEPR Discussion Papers 14664, C.E.P.R. Discussion Papers.
    15. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Anticipation effects of technological progress on capital accumulation: a vintage capital approach," Journal of Economic Theory, Elsevier, vol. 126(1), pages 143-164, January.
    16. Emilio Barucci & Fausto Gozzi, 2001. "Technology adoption and accumulation in a vintage-capital model," Journal of Economics, Springer, vol. 74(1), pages 1-38, February.
    17. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
    18. Callum Jones & Thomas Philippon & Venky Venkateswaran, 2021. "Optimal Mitigation Policies in a Pandemic: Social Distancing and Working from Home [A simple planning problem for covid-19 lockdown]," The Review of Financial Studies, Society for Financial Studies, vol. 34(11), pages 5188-5223.
    19. Barucci, Emilio & Gozzi, Fausto, 1998. "Investment in a vintage capital model," Research in Economics, Elsevier, vol. 52(2), pages 159-188, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Augeraud-Véron, Emmanuelle & Fabbri, Giorgio & Schubert, Katheline, 2021. "Prevention and mitigation of epidemics: Biodiversity conservation and confinement policies," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    2. Raouf Boucekkine & Shankha Chakraborty & Aditya Goenka & Lin Liu, 2024. "A Brief Tour of Economic Epidemiology Modelling," LIDAM Discussion Papers IRES 2024002, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    3. Andy Dobson & Cristiano Ricci & Raouf Boucekkine & Giorgio Fabbri & Ted Loch-Temzelides & Mercedes Pascual, 2023. "Balancing economic and epidemiological interventions in the early stages of pathogen emergence," Post-Print hal-04150117, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yasushi Iwamoto, 2021. "Welfare economics of managing an epidemic: an exposition," The Japanese Economic Review, Springer, vol. 72(4), pages 537-579, October.
    2. Dizioli, Allan & Pinheiro, Roberto, 2021. "Information and inequality in the time of a pandemic," Journal of Economic Dynamics and Control, Elsevier, vol. 130(C).
    3. Farboodi, Maryam & Jarosch, Gregor & Shimer, Robert, 2021. "Internal and external effects of social distancing in a pandemic," Journal of Economic Theory, Elsevier, vol. 196(C).
    4. Garriga, Carlos & Manuelli, Rody & Sanghi, Siddhartha, 2022. "Optimal management of an epidemic: Lockdown, vaccine and value of life," Journal of Economic Dynamics and Control, Elsevier, vol. 140(C).
    5. Aspri, Andrea & Beretta, Elena & Gandolfi, Alberto & Wasmer, Etienne, 2021. "Mortality containment vs. Economics Opening: Optimal policies in a SEIARD model," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    6. Marina Azzimonti-Renzo & Alessandra Fogli & Fabrizio Perri & Mark Ponder, 2020. "Pandemic Control in ECON-EPI Networks," Staff Report 609, Federal Reserve Bank of Minneapolis.
    7. Timo Boppart & Karl Harmenberg & John Hassler & Per Krusell & Jonna Olsson, 2020. "Integrated Epi-Econ Assessment," NBER Working Papers 28282, National Bureau of Economic Research, Inc.
    8. Getachew, Yoseph, 2020. "Optimal social distancing in SIR based macroeconomic models," MERIT Working Papers 2020-034, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    9. Eichenbaum, Martin S. & Rebelo, Sergio & Trabandt, Mathias, 2022. "The macroeconomics of testing and quarantining," Journal of Economic Dynamics and Control, Elsevier, vol. 138(C).
    10. Yinon Bar-On & Tatiana Baron & Ofer Cornfeld & Eran Yashiv, 2023. "When to Lock, Not Whom: Managing Epidemics Using Time-Based Restrictions," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 51, pages 292-321, December.
    11. Çakmaklı, Cem & Demiralp, Selva & Özcan, Şebnem Kalemli & Yeşiltaş, Sevcan & Yıldırım, Muhammed A., 2023. "COVID-19 and emerging markets: A SIR model, demand shocks and capital flows," Journal of International Economics, Elsevier, vol. 145(C).
    12. Bianchi, Francesco & Bianchi, Giada & Song, Dongho, 2023. "The long-term impact of the COVID-19 unemployment shock on life expectancy and mortality rates," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    13. David Baqaee & Emmanuel Farhi, 2022. "Supply and Demand in Disaggregated Keynesian Economies with an Application to the COVID-19 Crisis," American Economic Review, American Economic Association, vol. 112(5), pages 1397-1436, May.
    14. Eichenbaum, Martin S. & Rebelo, Sergio & Trabandt, Mathias, 2022. "Epidemics in the New Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 140(C).
    15. Faggian, Silvia & Gozzi, Fausto & Kort, Peter M., 2021. "Optimal investment with vintage capital: Equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    16. Sewon Hur, 2023. "The Distributional Effects Of Covid‐19 And Optimal Mitigation Policies," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(1), pages 261-294, February.
    17. Christopher Cotton & Bahman Kashi & Huw Lloyd‐Ellis & Frederic Tremblay & Brett Crowley, 2022. "Quantifying the economic impacts of COVID‐19 policy responses on Canada's provinces in (almost) real time," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 55(S1), pages 406-445, February.
    18. Greg Kaplan & Benjamin Moll & Giovanni L. Violante, 2020. "The Great Lockdown and the Big Stimulus: Tracing the Pandemic Possibility Frontier for the U.S," NBER Working Papers 27794, National Bureau of Economic Research, Inc.
    19. Guimarães, Luís, 2021. "Antibody tests: They are more important than we thought," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    20. David Baqaee & Emmanuel Farhi, 2020. "Nonlinear Production Networks with an Application to the Covid-19 Crisis," NBER Working Papers 27281, National Bureau of Economic Research, Inc.

    More about this item

    JEL classification:

    • E60 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - General
    • I10 - Health, Education, and Welfare - - Health - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2008.07335. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.