Post-Crisis Macrofinancial Modeling: Continuous Time Approaches

  • Jukka Isohätälä
  • Nataliya Klimenko
  • Alistair Milne


Prior to the crisis the dominant paradigm in macroeconomic modeling was the micro-founded “New-Keynesian” DSGE model (described in many textbooks including the influential exposition of Woodford (2003)). In its most basic form this combines price-stickiness with forward looking decision making by both households and firms. This provides a tractable framework for capturing the response of output and inflation to both demand and supply shocks and explaining intuitively the transmission of monetary policy (with monetary policy characterized as a choice over rules for current and future interest rates).


Monetary Policy Asset Price Stochastic Differential Equation Balance Sheet Real Interest Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Tobias Adrian and Nina Boyarchenko. Interdiary Leverage Cycles and Financial Stability. 2013. URL reports/sr567.pdf.
  2. Philippe Aghion and Peter Howitt. A Model of Growth Through Creative Destruction. Econometrica, 60(2):323–351, March 1992. ISSN 0012-9682. doi: 10.2307/2951599. URL Scholar
  3. Philippe Aghion and Peter Howitt. The Economics of Growth. MIT Press, Boston, 2009.Google Scholar
  4. S Rao Aiyagari. Uninsured idiosyncratic risk and aggregate saving. The Quarterly Journal of Economics, 109(3):659–684, 1994. ISSN 0033-5533.CrossRefGoogle Scholar
  5. Yann Algan, Olivier Allais, Wouter J Den Haan, and Pontus Rendahl. Solving and simulating models with heterogeneous agents and aggregate uncertainty. Handbook of Computational Economics, 2010.Google Scholar
  6. Bo Becker and Victoria Ivashina. Cyclicality of credit supply: Firm level evidence. Journal of Monetary Economics, 62:76–93, March 2014. ISSN 0304-3932. doi: 10.1016/j.jmoneco.2013.10.002.CrossRefGoogle Scholar
  7. Ben Bernanke, Mark Gertler, and Simon Gilchrist. The Financial Accelerator in a Quantitative Business Cycle Framework. In John B Taylor and Michael Woodford, editors, Handbook of Macroeconomics, Volume 1C, pages 1341–1393. Elsevier Science, North-Holland, 1999.Google Scholar
  8. Fischer Black and Myron Scholes. The pricing of options and corporate liabilities. The Journal of Political Economy, pages 637–654, 1973. ISSN 0022-3808.Google Scholar
  9. Patrick Bolton, Hui Chen, and Neng Wang. A Unified Theory of Tobin’s q, Corporate Investment, Financing, and Risk Management. The Journal of Finance, 66(5): 1545–1578, October 2011. ISSN 0022-1082. doi: 10.1111/j.1540–6261.2011.01681.x. URL Scholar
  10. Markus K Brunnermeier and Yuliy Sannikov. Macro, Money and Finance: A Continuous-Time Approach. In John Taylor and Harald Uhlig, editors, Handbook of Macroeconomics Vol 2 2016 forthcoming.Google Scholar
  11. Markus K. Brunnermeier and Yuliy Sannikov. International Credit Flows and Pecuniary Externalities. American Economic Journal: Macroeconimics, 7(1): 297–338, 2015Google Scholar
  12. Markus K. Brunnermeier and Yuliy Sannikov. A Macroeconomic Model with a Financial Sector. American Economic Review, 104(2):379–421, February 2014a. ISSN 0002-8282. doi: 10.1257/aer.104.2.379. URL Scholar
  13. Markus K Brunnermeier and Yuliy Sannikov. A Macroeconomic Model with a Financial Sector: online appendix. American Economic Review, (2), February 2014b. ISSN 0002-8282. doi: 10.1257/aer.104.2.379. URL Scholar
  14. Markus K Brunnermeier and Yuliy Sannikov. The I Theory of Money: version of April 2014. 2014c.Google Scholar
  15. Markus K Brunnermeier and Yuliy Sannikov. The I Theory of Money: version of November 2014. 2014d.Google Scholar
  16. Markus K Brunnermeier, Thomas M Eisenbach, and Yuliy Sannikov. Macroeconomics with financial frictions: A survey. Technical report, 2012.CrossRefGoogle Scholar
  17. Guillermo A. Calvo. Capital Market Crises. Journal of Applied Economics, 1(1):35–54, 1998.Google Scholar
  18. George M Constantinides. Intertemporal asset pricing with heterogeneous consumers and without demand aggregation. Journal of Business, pages 253–267, 1982. ISSN 0021-9398.Google Scholar
  19. Michael G Crandall, Ishii Hitoshi, and P.-L. Lions. User’s guide to viscosity solutions of second order partial differential equations. Bulletin of the American Mathematical Society. 27:1–67, 1992.CrossRefGoogle Scholar
  20. Harry DeAngelo and René M Stulz. Why high leverage is optimal for banks. Technical report, 2013.CrossRefGoogle Scholar
  21. Wouter J. Den Haan. Comparison of solutions to the incomplete markets model with aggregate uncertainty. Journal of Economic Dynamics and Control, 34(1):4–27, January 2010. ISSN 0165-1889. doi: 10.1016/j.jedc.2008.12.010. URL Scholar
  22. Douglas Diamond and Phillip Dybvig. Bank runs, deposit insurance and liquidity. Journal of Political Economy, 91:401–419, 1983.CrossRefGoogle Scholar
  23. Douglas W. Diamond. Financial Intermediation and Delegated Monitoring. The Review of Economic Studies, 51(3):393, July 1984. ISSN 0034-6527. doi: 10.2307/2297430. URL Scholar
  24. William Feller. An Introduction to Probability Theory and its Applications, volume II. Wiley, New York, 2nd edition, 1971.Google Scholar
  25. Zhigang Feng, Jianjun Miao, Adrian Peralta-Alva, and Manuel S Santos. Numerical simulation of nonoptimal dynamic equilibrium models. International Economic Review, 55(1):83–110, February 2014. ISSN 1468-2354. doi: 10.1111/iere.12042. URL Scholar
  26. Wendell Fleming and Halil Mete Soner. Controlled {Markov} Processes and Viscosity Solutions. Stochastic Modelling and Applied Probability. Springer, New York, 2nd edition, 2006.Google Scholar
  27. Marvin Frankel. The production function in allocation and growth: a synthesis. The American Economic Review, pages 996–1022, 1962. ISSN 0002-8282.Google Scholar
  28. Crispin Gardiner. Stochastic Methods: A Handbook for the Natural and Social Sciences. Springer Series in Synergetics. Springer, Berlin, 4th edition, 2009.Google Scholar
  29. William M Gorman. Separable utility and aggregation. Econometrica: Journal of the Econometric Society, pages 469–481, 1959. ISSN 0012-9682.Google Scholar
  30. Luca Guerrieri and Matteo Iacoviello. OccBin: A toolkit for solving dynamic models with occasionally binding constraints easily. Journal of Monetary Economics, 70: 22–38, March 2015. ISSN 0304-3932. doi: 10.1016/j.jmoneco.2014.08.005. URL Scholar
  31. Fatih Guvenen. Macroeconomics with hetereogeneity: a practical guide. Economic Quarterly, (3Q):255–326, 2011.Google Scholar
  32. Ernst Hairer, Gerhard Wanner, and Syvert P Nø rsett. Solving Ordinary Differential Equations I: Nonstiff Problems. Springer Series in Computational Mathematics. Springer, Berlin, 1993.Google Scholar
  33. Andrew G Haldane. On microscopes and telescopes, 2015. URL Scholar
  34. Zhigu He and Arvind Krishnamurthy. A model of capital and crises. The Review of Economic Studies, 79(2):735–777, 2012. ISSN 0034-6527.CrossRefGoogle Scholar
  35. Zhiguo He and Arvind Krishnamurthy. Intermediary asset pricing. American Economic Review, 103(2):732–770, 2013. ISSN 0002-8282.CrossRefGoogle Scholar
  36. Zhiguo He and Arvind Krishnamurthy. A macroeconomic framework for quantifying systemic risk. 2014, NBER Working Paper No. 19885, February.CrossRefGoogle Scholar
  37. B Holmstrom and J Tirole. Financial intermediation, loanable funds, and the real sector. Quarterly Journal of Economics, 112(3):663–691, 1997.CrossRefGoogle Scholar
  38. Mark Huggett. The risk-free rate in heterogeneous-agent incomplete-insurance economies. Journal of Economic Dynamics and Control, 17(5):953–969, 1993. ISSN 0165-1889.CrossRefGoogle Scholar
  39. Jukka Isohätälä, Feodor Kusmartsev, Alistair Milne, and Donald Robertson. Leverage constraints and real interest rates. The Manchester School 2015. URL id=2526790.Google Scholar
  40. Jukka Isohätälä, Alistair Milne, and Donald Robertson. The Net Worth Trap: Investment and Output Dynamics in the Presence of Financing Constraints. 2014. URL 26.aspx.Google Scholar
  41. Nobuhiro Kiyotaki and John Moore. Credit cycles. Journal of Political Economy, 105(2): 211–248, 1997.CrossRefGoogle Scholar
  42. Fima C Klebaner. Introduction to Stochastic Calculus with Applications. Imperial College Press, 2nd edition, 2005, Working Paper, University of Zurich.CrossRefGoogle Scholar
  43. Nataliya Klimenko, Sebastian Pfeil, and Jean-Charles Rochet. Bank Capital and Aggregate Credit. 2015.Google Scholar
  44. Dirk Krueger and Felix Kubler. Markov equilibria in macroeconomics. In The New Palgrave Dictionary of Economics’, Palgrave Macmillan, Basingstoke. 2008.Google Scholar
  45. Per Krusell and Anthony A Smith. Income and wealth heterogeneity, portfolio choice, and equilibrium asset returns. Macroeconomic dynamics, 1(02):387–422, 1997. ISSN 1469-8056.CrossRefGoogle Scholar
  46. Per Krusell and Anthony A Jr Smith. Income and wealth heterogeneity in the macroeconomy. Journal of Political Economy, 106(5):867–896, 1998. ISSN 0022-3808.CrossRefGoogle Scholar
  47. Ricardo Lagos and Randall Wright. A Unified Framework for Monetary Theory and Policy Analysis. Journal of Political Economy, 113(3):463–484, 2005.CrossRefGoogle Scholar
  48. P L Lions and A S Sznitman. Stochastic differential equations with reflecting boundary conditions. Communications on Pure and Applied Mathematics, 37(4):511–537, 1984. ISSN 1097-0312. doi: 10.1002/cpa.3160370408.CrossRefGoogle Scholar
  49. Lars Ljungqvist and Thomas J Sargent. Recursive Macroeconomic Theory. MIT Press, 2nd edition, 2000.Google Scholar
  50. Robert E Lucas and Nancy L Stokey. Money and Interest in a Cash-in-Advance Economy. Econometrica, 55(3):491–513, 1987.CrossRefGoogle Scholar
  51. Robert E Lucas Jr. Asset prices in an exchange economy. Econometrica, 46(6): 1429–1445, November 1978. ISSN 0012-9682. doi: 10.2307/1913837. URL Scholar
  52. N Gregory Mankiw. The equity premium and the concentration of aggregate shocks. Journal of Financial Economics, 17(1):211–219, 1986. ISSN 0304-405X.CrossRefGoogle Scholar
  53. Césaire A Meh and Kevin Moran. The Role of Bank Capital in the Propagation of Shocks. Journal of Economic Dynamics and Control, 34(3):555–576, 2010.CrossRefGoogle Scholar
  54. Robert C Merton. Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case. Review of Economics and Statistics., 51(3):247–257, 1969. doi: 10.2307/1926560.CrossRefGoogle Scholar
  55. Robert C. Merton. Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3(4):373–413, 1971. URL Scholar
  56. Bernt Øksendal. Stochastic Differential Equations: An Introduction with Applications. Universitext. Springer, Berlin, 6th edition, 2003.CrossRefGoogle Scholar
  57. Gregory Phelan. Financial intermediation, leverage, and macroeconomic instability. American Economic Journal: Macroeconomics, forthcoming, 2015.Google Scholar
  58. Adriano A Rampini and S Viswanathan. Financial intermediary capital. Available at SSRN 1785877, 2012.Google Scholar
  59. Carmen Reinhart and Kenneth Rogoff. This Time Is Different: Eight Centuries of Financial Folly. Princeton University Press, 2009. URL 1 1?ie=UTF8&qid=1404847123&sr=8-1&keywords=this+time+is+different+rogoff.Google Scholar
  60. Hannes Risken. The {Fokker-Planck} Equation: Methods of Solution and Applications. Springer Series in Synergetics. Springer, Berlin, 1996.CrossRefGoogle Scholar
  61. Paul M Romer. Growth Based on Increasing Returns Due to Specialization. American Economic Review, 77(2):56–62, 1987. ISSN 0002-8282.Google Scholar
  62. Paul M Romer. Endogenous Technological Change. Journal of Political Economy, 98(5): S71–102, 1990. ISSN 0022-3808.CrossRefGoogle Scholar
  63. Mark Rubinstein. An aggregation theorem for securities markets. Journal of Financial Economics, 1(3):225–244, 1974. ISSN 0304-405X.CrossRefGoogle Scholar
  64. Paul A Samuelson. An exact consumption-loan model of interest with or without the social contrivance of money. The Journal of Political Economy, pages 467–482, 1958. ISSN 0022-3808.Google Scholar
  65. F Smets and R Wouters. Comparing Shocks and Frictions in {US} and Euro Area Business Cycles: A {B}ayesian {DSGE} Approach. Journal of Applied Econometrics, 20:161–183, 2005.Google Scholar
  66. M Woodford. Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton University Press, 2003.Google Scholar

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© Jukka Isohätälä, Nataliya Klimenko and Alistair Milne 2016

Authors and Affiliations

  • Jukka Isohätälä
  • Nataliya Klimenko
  • Alistair Milne

There are no affiliations available

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