Topics in Macroeconomics: An Introduction to Stochastic Calculus
Rody Manuelli
March-April 2006
  1. Syllabus (pdf)
  2. Problem Set 1 (pdf)
  3. Problem Set 2 (pdf)
  4. Problem Set 3 (pdf)
  5. Readings:
  6. 0. Basic Material on Stochastic Processes

    IUU (chapter 3-4)

    Stokey ( chapter 1) (pdf), (chapter 2) (pdf), chapter 3 (pdf)

    Chang (chapters 1-4) (pdf)

    Note on Stochastic Processes and Brownian Motion (pdf)

    Note on Stochastic Integration and Ito's Lemma (pdf)

    Note on Optimal Stopping and Smooth Pasting (pdf)

    Note on Stochastic Differential Equations and the Feynman-Kac Theorem (pdf)

    Note on Fokker-Planck (pdf) (old)


    1. Options: Real and Financial.

        IUU (chapters, 5, 6, and 7).

        Stokey (chapters 4) (pdf), (chapter 5) (pdf)

       McDonald, R. and Siegel, (1986), "The Value of Waiting to Invest," The Quarterly Journal of Economics, Vol. 101, No. 4. (Nov., 1986), pp.    707-728. (ps)
       S. Agarwal, J. Driscoll and D. Laibson, (2002), "When Should Borrowers Refinance Their Mortgages?" working paper, Brown University. (pdf)
        Kort, P., P. Murto and G. Pawlina, (2004),"The Value of Flexibility in Sequencing Irreversible Investment," working paper. (pdf)

    2. Options: Strategic Exercise.

     Grenadier, S, (1996), "The Strategic Exercise of Options: Development Cascades and Overbuilding in Real Estate Markets," The Journal of Finance, Vol. 51, No. 5, pp: 1653-1679. (ps)
     Mella-Barral, P. and W. Perraudin, (1997), "Strategic Debt Service," The Journal of Finance, Vol. 52, No. 2, pp: 531-556. (pdf)
     Grenadier, S, (1999), "Information revelation Through Option Exercise," Review of Financial Studies, Vol. 12, No. 1, pp: 95-129. (ps)
     Mason, R and H. Weeds, "Can Greater Uncertainty Hasten Investment?" working paper. (pdf)

    Lambrecht, B. and S. Myers, 2005, "A Theory of Takeovers and Disinvestment," working paper (pdf)

    3. Optimal Consumption and Saving.

       Merton, R, (1973), "An Intertemporal Asset Pricing Model," Econometrica, Vol. 41, No. 5. (Sep., 1973), pp. 867-887. (ps)
       Cox, J, J. Ingersoll, and S. Ross, (1985a), "A Theory of the Term Structure of Interest Rates," Econometrica, Vol. 53, pp: 363-384. (ps)
       Cox, J, J. Ingersoll, and S. Ross, (1985a), "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Vol. 53, pp: 385-408. (ps)

       Wang, Neng, (2006), "Generalizing the Permanent Income Hypothesis: Revisiting Friedman's Conjecture on Consumption," Journal of Monetary Economics (forthcoming) (pdf)
       Duffie, D., (2002), "Intertemporal Asset Pricing Theory," working paper, Stanford University. (pdf)
       Cochrane, J, F Longstaff and P. Santa-Clara, (2003), "Two Trees: Asset Pricing Dynamics Induced by Market Clearing," working paper. (pdf)
       Pavlova, A. and R. Rigobon, (2003), "Asset Prices and Exchange Rates," working paper (pdf)

    4. Equilibrium Asset Prices

    D. Duffie, (1988), Security Markets, ch 24 and 25 (pdf)

    P. Veronesi (2005), Teaching Notes. [Used to be available (here)]

    5. Stochastic Growth Models.

       Manuelli, R and L. Jones, (2004), "Some Notes on Stochastic Growth Models," working paper. (pdf)

    6. .Investment.

       Abel, A,, (1983), "Optimal Investment Under Uncertainty," The American Economic Review, Vol. 73, No. 1. (Mar., 1983), pp. 228-233. (ps)
       Abel, A. and J. Eberly, (1994), "A Unified Model of Investment Under Uncertainty," The American Economic Review, Vol. 84, No. 5. (Dec., 1994), pp. 1369-1384. (ps)
       Stokey (chapter 11) (pdf)
       IUU (chapter 11).

    7. Durable Goods

       Grossman, S and G. Laroque, (1990), "Asset Pricing and Optimal Portfolio Choice in the Presence of Illiquid Durable Consumption Goods," Econometrica, Vol. 58, No. 1. (Jan., 1990), pp. 25-51. (ps)
       Stokey (chapter 9) (pdf).

    8. Industry Equilibrium

        Caballero, R. J. and R. Pindyck, (1996), "Uncertainty, Investment and Industry Evolution," International Economic Review, Vol. 37, No.3 (August), pp: 641-662. (pdf)

        IUU (chapter 8)

    9. Size Distribution of Cities

        Gabaix, X., (1999), "Zipf's Law for Cities: An Explanation," Quarterly Journal of Economics, 114 (3), pp: 739-767. (pdf)

        Cordoba, J.C., (2004), "A Generalized Gibrat's Law for Cities," working paper. (pdf)

        Cordoba, J.C., (2004), "On the Distribution of City Sizes," working paper. (pdf)

    9. Strategic Experimentation.

       Bolton, P. and C. Harris, (1999), "Strategic Experimentation," Econometrica, Vol. 67, N0. 2, pp: 349-374. (ps)
       Cripps, M., G. Keller and S. Rady, (2001), "Strategic Experimentation: The Case of Poisson Bandits," working paper. (pdf)

    10. Other Topics

    G. Bertola, L. Guiso and L. Pistaferri, "Uncertainty and Consumer Durables Adjustment," working paper (pdf)

    A. Wiggers, "Default-risky Sovereign Debt," working paper (pdf)

    P. Murto, "Valuing Options to Learn: Optimal Timing of Information Acquisition," working paper (pdf)