Advanced Topics: Theory of money ∗ Francesco Lippi University of Sassari and EIEF flippi‘at’uniss.it
November 20, 2013 The class has two parts. The first part describes models where money has value in equilibrium because of explicitly specified frictions. We use these models to discuss optimal monetary policy. Second, we study the propagation of monetary shocks in an economy with sticky prices. We will use continuous-time stochastic processes and optimal-control methods to model infrequent price adjustment by firms. Emphasis will be placed on the solution methods, mostly analytical, and on quantitative applications. We will solve the firm decision problem under different frictions, discuss aggregation of the individual firm decisions within a GE model, and study the propagation of shocks in an economy populated by “inactive” firms.
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1. Pure currency economies • Samuelson-Lucas OLG (Lucas (1996)) Competitive equilibrium • Lump-sum, proportional • Planner’s problem and welfare analysis • Money in the Utility function, CIA, Sidrausky and Goodfriend-MacCallun type of models, Lucas (2000). • Cost of Inflation with Heterogeneous agents. Money as a buffer stock: Lucas (1980), chapter 13.5 of Stokey and Lucas (1989), Imrohoroglu (1992), Lippi, Ragni, and Trachter (2013) 2. Money in a search and matching environment • Lagos and Wright (2005) model • Individual rationality and implementability of FR (Andolfatto (2013)) • Competing media of exchange Nosal and Rocheteau (2011) Ch. 10 3. Continuous time diffusions, controlled BM and Hamilton-Jacobi-Bellman equations • Chapters 1-4 from Dixit (1993) and Chapters 3 (1, 2 optional) Stokey (2009) • Discrete time - discrete state derivation of BM • Derivation of the Hamilton-Jacobi-Bellman equation • Controlled BM: expected time to hit barrier • Invariant distribution of a controlled diffusion: Kolmogorov equation • The smooth pasting principle 4. Applications I : money demand models (PE) • deterministic expenditures and free adjustments: Alvarez and Lippi (2009) • stochastic expenditures: Miller and Orr (1966) • structural estimation of money demand models • misc: model with jumps (lumpy purchases), cash credit 5. Applications II : price setting with menu cost (PE & GE) • Classics: sS without aggregate shocks, Dixit (1991) Sheshinski and Weiss (1977), Benabou and Konieczny (1994) 1
• The empirical evidence and the menu cost problem • The microeconomic foundations of the firm’s problem: Alvarez and Lippi (2012) • Analytics of decision rules and aggregation: Alvarez and Lippi (2012) 6. Applications III: price setting with observation cost • Classics Caballero (1989), Reis (2006) • Extensions: random observation costs Alvarez, Lippi, and Paciello (2012) • Problem with menu cost and observation costs Alvarez, Lippi, and Paciello (2011).
MORE READINGS More technical readings on cts time processes – theory: Karatzas and Shreve (1991), Karlin and Taylor (1999), Øksendal (2000) – Numerical methods: Kushner and Dupuis (2001), More reading and applications – Money Neutrality (aggregate shock only): “elevator coming up” aggregation Caplin and Spulber (1987) – Phillips Curve: “elevator in a shaft”: Caplin and Leahy (1991, 1997) also Chap 12 Stokey (2009) – Phillips Curve with constant prob. changes price: Danziger (1999) – Quantitative Examples: Golosov and Lucas (2007), Midrigan (2009).
References Alvarez, Fernando E. and Francesco Lippi. 2009. “Financial Innovation and the Transactions Demand for Cash.” Econometrica 77 (2):363–402. ———. 2012. “Price setting with menu cost for multi-product firms.” NBER Working Papers 17923, National Bureau of Economic Research, Inc. Alvarez, Fernando E., Francesco Lippi, and Luigi Paciello. 2011. “Optimal price setting with observation and menu costs.” The Quarterly Journal of Economics 126 (4):1909–1960. 2
———. 2012. “Monetary shocks in a Model with Inattentive Producers.” in preparation, EIEF. Andolfatto, David. 2013. “Incentive-feasible deflation.” Journal of Monetary Economics 60 (4):383–390. Benabou, R. and J.D. Konieczny. 1994. “On inflation and output with costly price changes: A simple unifying result.” The American Economic Review :290–297. Caballero, Ricardo J. 1989. “Time Dependent Rules, Aggregate Stickiness And Information Externalities.” Discussion Papers 198911, Columbia University. Caplin, Andrew and John Leahy. 1991. “State-Dependent Pricing and the Dynamics of Money and Output.” The Quarterly Journal of Economics 106 (3):683–708. ———. 1997. “Aggregation and Optimization with State-Dependent Pricing.” Econometrica 65 (3):601–626. Caplin, Andrew S and Daniel F Spulber. 1987. “Menu Costs and the Neutrality of Money.” The Quarterly Journal of Economics 102 (4):703–25. Danziger, Leif. 1999. “A Dynamic Economy with Costly Price Adjustments.” American Economic Review 89 (4):878–901. Dixit, Avinash. 1991. “Analytical Approximations in Models of Hysteresis.” Review of Economic Studies 58 (1):141–51. ———. 1993. The Art of Smooth Pasting. Harwood Academic Publishers. Golosov, Mikhail and Robert E. Jr. Lucas. 2007. “Menu Costs and Phillips Curves.” Journal of Political Economy 115:171–199. Imrohoroglu, Ayse. 1992. “The welfare cost of inflation under imperfect insurance.” Journal of Economic Dynamics and Control 16 (1):79–91. Karatzas, I. and S.E. Shreve. 1991. Brownian motion and stochastic calculus. Springer-Verlag. Karlin, S. and H.M. Taylor. 1999. A second course in stochastic processes. Academic press. Kushner, H.J. and P. Dupuis. 2001. Numerical methods for stochastic control problems in continuous time, vol. 24. Springer Verlag. Lagos, Ricardo and Randall Wright. 2005. “A Unified Framework for Monetary Theory and Policy Analysis.” Journal of Political Economy 113 (3):463–484. 3
Lippi, Francesco, Stefania Ragni, and Nicholas Trachter. 2013. “State dependent monetary policy.” Wp 13-17, Richmond Fed. Lucas, Jr, Robert E. 1980. “Equilibrium in a Pure Currency Economy.” Economic Inquiry 18 (2):203–20. ———. 1996. “Nobel Lecture: Monetary Neutrality.” 104 (4):661–82.
Journal of Political Economy
Lucas, Robert E. Jr. 2000. “Inflation and Welfare.” Econometrica 68 (2):247–274. Midrigan, Virgiliu. 2009. “Menu Costs, Multi-Product Firms, and Aggregate Fluctuations.” Working paper, NYU. Miller, Merton and Daniel Orr. 1966. “A model of the demand for money by firms.” Quarterly Journal of Economics 80 (3):413–435. Nosal, Ed and Guillaume Rocheteau. 2011. Money, Payments, and Liquidity. MIT Press. Øksendal, Bernt K. 2000. Stochastic differential equations: an introduction with applications. Sixth Edition, Springer Verlag. Reis, Ricardo. 2006. “Inattentive consumers.” Journal of Monetary Economics 53 (8):1761– 1800. Sheshinski, Eytan and Yoram Weiss. 1977. “Inflation and Costs of Price Adjustment.” Review of Economic Studies 44 (2):287–303. Stokey, Nancy. 2009. The Economics of Inaction: Stochastic Control Models with Fixed Costs. New Jersey, NJ: Princeton University Press. Stokey, Nancy L. and Robert E. Lucas. 1989. Recursive Methods in Economic Dynamics. Harvard University Press.
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