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Exploiting MIT shocks in heterogeneous-agent economies: the impulse response as a numerical derivative

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  • Boppart, Timo
  • Krusell, Per
  • Mitman, Kurt

Abstract

We propose a new method for computing equilibria in heterogeneous-agent models with aggregate uncertainty. The idea relies on an assumption that linearization offers a good approximation; we share this assumption with existing linearization methods. However, unlike those methods, the approach here does not rely on direct derivation of first-order Taylor terms. It also does not use recursive methods, whereby aggregates and prices would be expressed as linear functions of the state, usually a very high-dimensional object (such as the wealth distribution). Rather, we rely merely on solving nonlinearly for a deterministic transition path: we study the equilibrium response to a single, small “MIT shock” carefully. We then regard this impulse response path as a numerical derivative in sequence space and hence provide our linearized solution directly using this path. The method can easily be extended to the case of many shocks and computation time rises linearly in the number of shocks. We also propose a set of checks on whether linearization is a good approximation. We assert that our method is the simplest and most transparent linearization technique among currently known methods. The key numerical tool required to implement it is value-function iteration, using a very limited set of state variables.

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  • Boppart, Timo & Krusell, Per & Mitman, Kurt, 2018. "Exploiting MIT shocks in heterogeneous-agent economies: the impulse response as a numerical derivative," Journal of Economic Dynamics and Control, Elsevier, vol. 89(C), pages 68-92.
  • Handle: RePEc:eee:dyncon:v:89:y:2018:i:c:p:68-92
    DOI: 10.1016/j.jedc.2018.01.002
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    1. Alberto Alesina & Dani Rodrik, 1994. "Distributive Politics and Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 109(2), pages 465-490.
    2. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
    3. Greenwood, Jeremy & Hercowitz, Zvi & Krusell, Per, 2000. "The role of investment-specific technological change in the business cycle," European Economic Review, Elsevier, vol. 44(1), pages 91-115, January.
    4. Krusell, Per & Smith, Anthony A., 1997. "Income And Wealth Heterogeneity, Portfolio Choice, And Equilibrium Asset Returns," Macroeconomic Dynamics, Cambridge University Press, vol. 1(2), pages 387-422, June.
    5. Kurt Mitman & Iourii Manovskii & Marcus Hagedorn, 2017. "The Fiscal Multiplier," 2017 Meeting Papers 1383, Society for Economic Dynamics.
    6. SeHyoun Ahn & Greg Kaplan & Benjamin Moll & Thomas Winberry & Christian Wolf, 2018. "When Inequality Matters for Macro and Macro Matters for Inequality," NBER Macroeconomics Annual, University of Chicago Press, vol. 32(1), pages 1-75.
    7. Karen Kopecky & Richard Suen, 2010. "Finite State Markov-chain Approximations to Highly Persistent Processes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(3), pages 701-714, July.
    8. Per Krusell & Toshihiko Mukoyama & Richard Rogerson & Ayşegül Şahin, 2017. "Gross Worker Flows over the Business Cycle," American Economic Review, American Economic Association, vol. 107(11), pages 3447-3476, November.
    9. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    10. Matthew Rognlie & Adrien Auclert, 2016. "Inequality and Aggregate Demand," 2016 Meeting Papers 1353, Society for Economic Dynamics.
    11. Judd, Kenneth L. & Guu, Sy-Ming, 1997. "Asymptotic methods for aggregate growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 1025-1042, June.
    12. Den Haan, Wouter J., 1997. "Solving Dynamic Models With Aggregate Shocks And Heterogeneous Agents," Macroeconomic Dynamics, Cambridge University Press, vol. 1(2), pages 355-386, June.
    13. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : II. New directions," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 309-341.
    14. Per Krusell & Toshihiko Mukoyama & Ayşegül Şahin, 2010. "Labour-Market Matching with Precautionary Savings and Aggregate Fluctuations," Review of Economic Studies, Oxford University Press, vol. 77(4), pages 1477-1507.
    15. Aubhik Khan & Julia K. Thomas, 2008. "Idiosyncratic Shocks and the Role of Nonconvexities in Plant and Aggregate Investment Dynamics," Econometrica, Econometric Society, vol. 76(2), pages 395-436, March.
    16. Reiter, Michael, 2009. "Solving heterogeneous-agent models by projection and perturbation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 649-665, March.
    17. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    18. Persson, Torsten & Tabellini, Guido, 1994. "Is Inequality Harmful for Growth?," American Economic Review, American Economic Association, vol. 84(3), pages 600-621, June.
    19. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, Oxford University Press, vol. 109(3), pages 659-684.
    20. Carroll, Christopher D., 2006. "The method of endogenous gridpoints for solving dynamic stochastic optimization problems," Economics Letters, Elsevier, vol. 91(3), pages 312-320, June.
    21. Krueger, D. & Mitman, K. & Perri, F., 2016. "Macroeconomics and Household Heterogeneity," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 843-921, Elsevier.
    22. King, Robert G & Plosser, Charles I & Rebelo, Sergio T, 2002. "Production, Growth and Business Cycles: Technical Appendix," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 87-116, October.
    23. Den Haan, Wouter J. & Judd, Kenneth L. & Juillard, Michel, 2010. "Computational suite of models with heterogeneous agents: Incomplete markets and aggregate uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 1-3, January.
    24. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    25. Per Krusell & Toshihiko Mukoyama & Aysegul Sahin & Anthony A. Smith, Jr., 2009. "Revisiting the Welfare Effects of Eliminating Business Cycles," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(3), pages 393-402, July.
    26. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    27. Meltzer, Allan H & Richard, Scott F, 1981. "A Rational Theory of the Size of Government," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 914-927, October.
    28. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135-135.
    29. Kanishka Misra & Paolo Surico, 2014. "Consumption, Income Changes, and Heterogeneity: Evidence from Two Fiscal Stimulus Programs," American Economic Journal: Macroeconomics, American Economic Association, vol. 6(4), pages 84-106, October.
    30. Pissarides, Christopher A, 1985. "Short-run Equilibrium Dynamics of Unemployment Vacancies, and Real Wages," American Economic Review, American Economic Association, vol. 75(4), pages 676-690, September.
    31. Den Haan, Wouter J. & Judd, Kenneth L. & Juillard, Michel, 2011. "Computational suite of models with heterogeneous agents II: Multi-country real business cycle models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 175-177, February.
    32. Jose-Victor Rios-Rull & Per Krusell, 1999. "On the Size of U.S. Government: Political Economy in the Neoclassical Growth Model," American Economic Review, American Economic Association, vol. 89(5), pages 1156-1181, December.
    33. Frank Smets & Raf Wouters, 2003. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, September.
    34. Imrohoruglu, Ayse, 1989. "Cost of Business Cycles with Indivisibilities and Liquidity Constraints," Journal of Political Economy, University of Chicago Press, vol. 97(6), pages 1364-1383, December.
    35. Reiter, Michael, 2010. "Approximate and Almost-Exact Aggregation in Dynamic Stochastic Heterogeneous-Agent Models," Economics Series 258, Institute for Advanced Studies.
    36. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
    37. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : I. The basic neoclassical model," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 195-232.
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    2. Christopher D. Carroll & Edmund Crawley & Jiri Slacalek & Kiichi Tokuoka & Matthew N. White, 2020. "Sticky Expectations and Consumption Dynamics," American Economic Journal: Macroeconomics, American Economic Association, vol. 12(3), pages 40-76, July.
    3. Adrien Auclert & Ludwig Straub & Matthew Rognlie, 2019. "Micro Jumps, Macro Humps: monetary policy and business cycles in an estimated HANK model," 2019 Meeting Papers 1449, Society for Economic Dynamics.
    4. Papp, Tamás K. & Reiter, Michael, 2020. "Estimating linearized heterogeneous agent models using panel data," Journal of Economic Dynamics and Control, Elsevier, vol. 115(C).
    5. Timo Boppart & Karl Harmenberg & John Hassler & Per Krusell & Jonna Olsson, 2020. "Integrated epi-econ assessment," Edinburgh School of Economics Discussion Paper Series 297, Edinburgh School of Economics, University of Edinburgh.
    6. de Ferra, Sergio & Mitman, Kurt & Romei, Federica, 2020. "Household heterogeneity and the transmission of foreign shocks," Journal of International Economics, Elsevier, vol. 124(C).
    7. Jonathan Chiu & Miguel Molico, . "Short-Run Dynamics in a Search-Theoretic Model of Monetary Exchange," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics.
    8. Per Krusell & Toshihiko Mukoyama & Richard Rogerson & Aysegul Sahin, 2020. "Gross Worker Flows and Fluctuations in the Aggregate Labor Market," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 37, pages 205-226, August.
    9. Mukoyama, Toshihiko, 2021. "MIT shocks imply market incompleteness," Economics Letters, Elsevier, vol. 198(C).
    10. Per Krusell & Toshihiko Mukoyama & Richard Rogerson & Ayşegül Şahin, 2017. "Gross Worker Flows over the Business Cycle," American Economic Review, American Economic Association, vol. 107(11), pages 3447-3476, November.
    11. Angelos Angelopoulos & Konstantinos Angelopoulos & Spyridon Lazarakis & Apostolis Philippopoulos, 2019. "The Distributional Consequences of Rent Seeking," CESifo Working Paper Series 7835, CESifo.
    12. Michael Reiter, 2019. "Solving Heterogeneous Agent Models with Non-convex Optimization Problems: Linearization and Beyond %," 2019 Meeting Papers 1048, Society for Economic Dynamics.
    13. Yi Zhang & Zhe Li & Yongchao Zhang, 2020. "Validation and Calibration of an Agent-Based Model: A Surrogate Approach," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-9, January.
    14. Toshihiko Mukoyama, 2020. "MIT Shocks Imply Market Incompleteness," Working Papers gueconwpa~20-20-04, Georgetown University, Department of Economics.
    15. Mitman, Kurt & Rabinovich, Stanislav, 2021. "Whether, When and How to Extend Unemployment Benefits: Theory and Application to COVID-19," CEPR Discussion Papers 15748, C.E.P.R. Discussion Papers.
    16. Auclert, Adrien & Bardoczy, Bence & Rognlie, Matthew & Straub, Ludwig, 2019. "Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models," CEPR Discussion Papers 13890, C.E.P.R. Discussion Papers.
    17. Mitman, Kurt & Rabinovich, Stanislav, 2020. "Optimal Unemployment Benefits in the Pandemic," CEPR Discussion Papers 14915, C.E.P.R. Discussion Papers.
    18. Angelopoulos, Konstantinos & Lazarakis, Spyridon & Malley, James, 2020. "The distributional implications of asymmetric income dynamics," European Economic Review, Elsevier, vol. 128(C).
    19. xavier Ragot, 2019. "Managing Inequality over the Business Cycles: Optimal Policies with Heterogeneous Agents and Aggregate Shocks," 2019 Meeting Papers 1090, Society for Economic Dynamics.
    20. Nobuhide Okahata, 2019. "An Alternative Solution Method for Continuous-Time Heterogeneous Agent Models with Aggregate Shocks," 2019 Meeting Papers 1470, Society for Economic Dynamics.
    21. Jonathan Chiu & Miguel Molico, . "Short-Run Dynamics in a Search-Theoretic Model of Monetary Exchange," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics.

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    More about this item

    Keywords

    Heterogeneous agents; Computation; Linearization; MIT Shock;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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