IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/26123.html
   My bibliography  Save this paper

Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models

Author

Listed:
  • Adrien Auclert
  • Bence Bardóczy
  • Matthew Rognlie
  • Ludwig Straub

Abstract

We propose a general and highly efficient method for solving and estimating general equilibrium heterogeneous-agent models with aggregate shocks in discrete time. Our approach relies on the rapid computation of sequence-space Jacobians—the derivatives of perfect-foresight equilibrium mappings between aggregate sequences around the steady state. Our main contribution is a fast algorithm for calculating Jacobians for a large class of heterogeneous-agent problems. We combine this algorithm with a systematic approach to composing and inverting Jacobians to solve for general equilibrium impulse responses. We obtain a rapid procedure for likelihood-based estimation and computation of nonlinear perfect-foresight transitions. We apply our methods to three canonical heterogeneous-agent models: a neoclassical model, a New Keynesian model with one asset, and a New Keynesian model with two assets.

Suggested Citation

  • Adrien Auclert & Bence Bardóczy & Matthew Rognlie & Ludwig Straub, 2019. "Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models," NBER Working Papers 26123, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:26123
    Note: EFG ME
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w26123.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Krueger, Dirk & Ludwig, Alexander, 2007. "On the consequences of demographic change for rates of returns to capital, and the distribution of wealth and welfare," Journal of Monetary Economics, Elsevier, vol. 54(1), pages 49-87, January.
    3. Alejandro Justiniano & Giorgio Primiceri & Andrea Tambalotti, 2011. "Investment Shocks and the Relative Price of Investment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 14(1), pages 101-121, January.
    4. Greg Kaplan & Giovanni L. Violante, 2018. "Microeconomic Heterogeneity and Macroeconomic Shocks," Journal of Economic Perspectives, American Economic Association, vol. 32(3), pages 167-194, Summer.
    5. Miguel Molico, 2006. "The Distribution Of Money And Prices In Search Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(3), pages 701-722, August.
    6. Fabien Postel-Vinay & Jean-Marc Robin, 2002. "Equilibrium Wage Dispersion with Worker and Employer Heterogeneity," Econometrica, Econometric Society, vol. 70(6), pages 2295-2350, November.
    7. Mansur, Ahsan & Whalley, John, 1982. "A Decomposition Algorithm for General Equilibrium Computation with Application to International Trade Models," Econometrica, Econometric Society, vol. 50(6), pages 1547-1557, November.
    8. Jean-Pierre Laffargue, 1990. "Résolution d'un modèle macroéconomique avec anticipations rationnelles," Annals of Economics and Statistics, GENES, issue 17, pages 97-119.
    9. Greg Kaplan & Benjamin Moll & Giovanni L. Violante, 2018. "Monetary Policy According to HANK," American Economic Review, American Economic Association, vol. 108(3), pages 697-743, March.
    10. Lubik, Thomas A. & Schorfheide, Frank, 2003. "Computing sunspot equilibria in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 273-285, November.
    11. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2010. "The Macroeconomic Implications of Rising Wage Inequality in the United States," Journal of Political Economy, University of Chicago Press, vol. 118(4), pages 681-722, August.
    12. 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.
    13. Sushant Acharya & Keshav Dogra, 2020. "Understanding HANK: Insights From a PRANK," Econometrica, Econometric Society, vol. 88(3), pages 1113-1158, May.
    14. Thomas Winberry, 2018. "A method for solving and estimating heterogeneous agent macro models," Quantitative Economics, Econometric Society, vol. 9(3), pages 1123-1151, November.
    15. Mikhail Golosov & Robert E. Lucas Jr., 2007. "Menu Costs and Phillips Curves," Journal of Political Economy, University of Chicago Press, vol. 115, pages 171-199.
    16. Lan, Hong & Meyer-Gohde, Alexander, 2013. "Solving DSGE models with a nonlinear moving average," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2643-2667.
    17. 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.
    18. 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.
    19. David Berger & Veronica Guerrieri & Guido Lorenzoni & Joseph Vavra, 2018. "House Prices and Consumer Spending," Review of Economic Studies, Oxford University Press, vol. 85(3), pages 1502-1542.
    20. Fernández-Villaverde, Jesús & Hurtado, Samuel & Nuño, Galo, 2019. "Financial Frictions and the Wealth Distribution," CEPR Discussion Papers 14002, C.E.P.R. Discussion Papers.
    21. 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.
    22. repec:adr:anecst:y:1990:i:17:p:04 is not listed on IDEAS
    23. Christian Bayer & Ralph Luetticke & Lien Pham‐Dao & Volker Tjaden, 2019. "Precautionary Savings, Illiquid Assets, and the Aggregate Consequences of Shocks to Household Income Risk," Econometrica, Econometric Society, vol. 87(1), pages 255-290, January.
    24. Mariacristina De Nardi, 2004. "Wealth Inequality and Intergenerational Links," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 743-768.
    25. Johannes Brumm & Simon Scheidegger, 2017. "Using Adaptive Sparse Grids to Solve High‐Dimensional Dynamic Models," Econometrica, Econometric Society, vol. 85, pages 1575-1612, September.
    26. Nils Gornemann & Keith Kuester & Makoto Nakajima, 2016. "Doves for the Rich, Hawks for the Poor? Distributional Consequences of Monetary Policy," International Finance Discussion Papers 1167, Board of Governors of the Federal Reserve System (U.S.).
    27. Yongsung Chang & Sun-Bin Kim, 2007. "Heterogeneity and Aggregation: Implications for Labor-Market Fluctuations," American Economic Review, American Economic Association, vol. 97(5), pages 1939-1956, December.
    28. Burdett, Kenneth & Mortensen, Dale T, 1998. "Wage Differentials, Employer Size, and Unemployment," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(2), pages 257-273, May.
    29. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
    30. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    31. Juillard, Michel, 1996. "Dynare : a program for the resolution and simulation of dynamic models with forward variables through the use of a relaxation algorithm," CEPREMAP Working Papers (Couverture Orange) 9602, CEPREMAP.
    32. 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.
    33. repec:adr:anecst:y:1990:i:17 is not listed on IDEAS
    34. Boucekkine, Raouf, 1995. "An alternative methodology for solving nonlinear forward-looking models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 711-734, May.
    35. Meyer-Gohde, Alexander, 2010. "Linear rational-expectations models with lagged expectations: A synthetic method," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 984-1002, May.
    36. Edward P. Herbst & Frank Schorfheide, 2016. "Bayesian Estimation of DSGE Models," Economics Books, Princeton University Press, edition 1, number 10612.
    37. 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.
    38. Bayer, Christian & Luetticke, Ralph, 2018. "Solving heterogeneous agent models in discrete time with many idiosyncratic states by perturbation methods," CEPR Discussion Papers 13071, C.E.P.R. Discussion Papers.
    39. Young, Eric R., 2010. "Solving the incomplete markets model with aggregate uncertainty using the Krusell-Smith algorithm and non-stochastic simulations," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 36-41, January.
    40. Hopenhayn, Hugo A, 1992. "Entry, Exit, and Firm Dynamics in Long Run Equilibrium," Econometrica, Econometric Society, vol. 60(5), pages 1127-1150, September.
    41. Reiter, Michael, 2010. "Approximate and Almost-Exact Aggregation in Dynamic Stochastic Heterogeneous-Agent Models," Economics Series 258, Institute for Advanced Studies.
    42. Mertens, Thomas M. & Judd, Kenneth L., 2018. "Solving an incomplete markets model with a large cross-section of agents," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 349-368.
    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. François Le Grand & Xavier Ragot, 2022. "Managing Inequality Over Business Cycles: Optimal Policies With Heterogeneous Agents And Aggregate Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 511-540, February.
    2. Papp, Tamás K. & Reiter, Michael, 2020. "Estimating linearized heterogeneous agent models using panel data," Journal of Economic Dynamics and Control, Elsevier, vol. 115(C).
    3. Christian Bayer & Ralph Luetticke, 2019. "Shocks, Frictions, and Inequality in US Business Cycles," 2019 Meeting Papers 256, Society for Economic Dynamics.
    4. Alisdair McKay & Johannes F. Wieland, 2019. "Lumpy Durable Consumption Demand and the Limited Ammunition of Monetary Policy," NBER Working Papers 26175, National Bureau of Economic Research, Inc.
    5. Jesús Fernández-Villaverde & Samuel Hurtado & Galo Nuño, 2019. "Financial Frictions and the Wealth Distribution," NBER Working Papers 26302, National Bureau of Economic Research, Inc.
    6. Felipe Alves, 2022. "Job Ladder and Business Cycles," Staff Working Papers 22-14, Bank of Canada.
    7. Cameron Fen, 2022. "Fast Simulation-Based Bayesian Estimation of Heterogeneous and Representative Agent Models using Normalizing Flow Neural Networks," Papers 2203.06537, arXiv.org.
    8. Darracq Pariès, Matthieu & Notarpietro, Alessandro & Kilponen, Juha & Papadopoulou, Niki & Zimic, Srečko & Aldama, Pierre & Langenus, Geert & Alvarez, Luis Julian & Lemoine, Matthieu & Angelini, Elena, 2021. "Review of macroeconomic modelling in the Eurosystem: current practices and scope for improvement," Occasional Paper Series 267, European Central Bank.
    9. Achdou, Yves & Han, Jiequn & Lasry, Jean Michel & Lions, Pierre Louis & Moll, Ben, 2022. "Income and wealth distribution in macroeconomics: a continuous-time approach," LSE Research Online Documents on Economics 107422, London School of Economics and Political Science, LSE Library.
    10. Ester Faia & Marianna Kudlyak & Ekaterina Shabalina, 2021. "Dynamic Labor Reallocation with Heterogeneous Skills and Uninsured Idiosyncratic Risk," Working Paper Series 2021-16, Federal Reserve Bank of San Francisco.
    11. Jiequn Han & Yucheng Yang & Weinan E, 2021. "DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks," Papers 2112.14377, arXiv.org, revised Feb 2022.
    12. Matthew D. Cocci & Mikkel Plagborg-Møller, 2021. "Standard Errors for Calibrated Parameters," Working Papers 2021-20, Princeton University. Economics Department..
    13. Alisdair McKay & Johannes F. Wieland, 2021. "Lumpy Durable Consumption Demand and the Limited Ammunition of Monetary Policy," Econometrica, Econometric Society, vol. 89(6), pages 2717-2749, November.
    14. Ben Moll, 2020. "The Research Agenda: Ben Moll on the Rich Interactions between Inequality and the Macroeconomy," EconomicDynamics Newsletter, Review of Economic Dynamics, vol. 21(2), November.
    15. Felipe Alves & Christian Bustamante & Xing Guo & Katya Kartashova & Soyoung Lee & Thomas Michael Pugh & Kurt See & Yaz Terajima & Alexander Ueberfeldt, 2022. "Heterogeneity and Monetary Policy: A Thematic Review," Discussion Papers 2022-2, Bank of Canada.

    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. Papp, Tamás K. & Reiter, Michael, 2020. "Estimating linearized heterogeneous agent models using panel data," Journal of Economic Dynamics and Control, Elsevier, vol. 115(C).
    2. Takeki Sunakawa, 2020. "Applying the Explicit Aggregation Algorithm to Heterogeneous Macro Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 845-874, March.
    3. Michael Reiter, 2019. "Solving Heterogeneous Agent Models with Non-convex Optimization Problems: Linearization and Beyond %," 2019 Meeting Papers 1048, Society for Economic Dynamics.
    4. Ralph Luetticke, 2021. "Transmission of Monetary Policy with Heterogeneity in Household Portfolios," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(2), pages 1-25, April.
    5. Jesús Fernández-Villaverde & Samuel Hurtado & Galo Nuño, 2019. "Financial Frictions and the Wealth Distribution," NBER Working Papers 26302, National Bureau of Economic Research, Inc.
    6. 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.
    7. Christian Bayer & Ralph Luetticke, 2019. "Shocks, Frictions, and Inequality in US Business Cycles," 2019 Meeting Papers 256, Society for Economic Dynamics.
    8. Emoto, Masakazu & Sunakawa, Takeki, 2021. "Applying the explicit aggregation algorithm to heterogeneous agent models in continuous time," Economics Letters, Elsevier, vol. 206(C).
    9. 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.
    10. François Le Grand & Xavier Ragot, 2022. "Managing Inequality Over Business Cycles: Optimal Policies With Heterogeneous Agents And Aggregate Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 511-540, February.
    11. 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.
    12. Chipeniuk, Karsten O. & Katz, Nets Hawk & Walker, Todd B., 2022. "Households, auctioneers, and aggregation," European Economic Review, Elsevier, vol. 141(C).
    13. Felipe Alves & Christian Bustamante & Xing Guo & Katya Kartashova & Soyoung Lee & Thomas Michael Pugh & Kurt See & Yaz Terajima & Alexander Ueberfeldt, 2022. "Heterogeneity and Monetary Policy: A Thematic Review," Discussion Papers 2022-2, Bank of Canada.
    14. Maliar, Lilia & Maliar, Serguei, 2022. "Deep learning classification: Modeling discrete labor choice," Journal of Economic Dynamics and Control, Elsevier, vol. 135(C).
    15. Maliar, Lilia & Maliar, Serguei & Winant, Pablo, 2021. "Deep learning for solving dynamic economic models," Journal of Monetary Economics, Elsevier, vol. 122(C), pages 76-101.
    16. Christian Bayer & Ralph Luetticke, 2020. "Solving discrete time heterogeneous agent models with aggregate risk and many idiosyncratic states by perturbation," Quantitative Economics, Econometric Society, vol. 11(4), pages 1253-1288, November.
    17. Stephen J. Terry, 2017. "Alternative Methods for Solving Heterogeneous Firm Models," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(6), pages 1081-1111, September.
    18. Heejeong Kim, 2022. "Inequality, Disaster risk, and the Great Recession," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 43, pages 217-240, January.
    19. Jiequn Han & Yucheng Yang & Weinan E, 2021. "DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks," Papers 2112.14377, arXiv.org, revised Feb 2022.
    20. Martin Kuncl & Alexander Ueberfeldt, 2021. "Monetary Policy and the Persistent Aggregate Effects of Wealth Redistribution," Staff Working Papers 21-38, Bank of Canada.

    More about this item

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:nbr:nberwo:26123. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    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: (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.