good macro leture book-----

good macro leture book----- - Advanced Macroeconomics...

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Advanced Macroeconomics * Lecturers: Debortoli & Rondina UC San Diego Fall 2009 Abstract The object of this course is to introduce students to a variety of tools used in advanced dynamic macroeconomic models. The focus will be on the theoretical aspects of these models, rather than on the specic economic implications or on the numerical solution methods (the objective of ECON 216). Indeed, the goal is to provide examples of how some specic problems are addressed and how the tools can be used in a variety of contexts. In the first part (taught by Davide Debortoli), we introduce techniques to analyze policy problems in dynamic models and discuss some applications to optimal policy problems. By way of contrast with some of the complete markets models you saw in Econ210C, we will discuss the implications of some sources of inefficiencies like market incompleteness, lack of commitment and imperfect information. In the second part of the course (taught by Giacomo Rondina) we will begin by studying a general global game framework that has proved to be particularly effective in modeling coordination problems in macroeconomics (such as financial crisis or bank runs). We then study how such framework can be embedded into dynamic settings by analyzing incomplete information models of the business cycle. If time permits, we will introduce some concepts and methods in the robust design of macroeconomic policies. Contents 1 Recursive Representation 3 1.1 A Typical Dynamic Macro Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Risk-Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Competitive Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.1 Household Problem in a Time-Zero Trade . . . . . . . . . . . . . . . . . . . . . 5 1.3.2 Example 1: CRRA Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.3 Example 2: Constant Aggregate Endowment . . . . . . . . . . . . . . . . . . . 6 1.3.4 Example 3: Periodic Endowment Process . . . . . . . . . . . . . . . . . . . . . 7 1.3.5 Solution Method: The Negishi Algorithm . . . . . . . . . . . . . . . . . . . . . 7 1.4 Pareto Optimum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4.1 Social Planner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4.2 Example 1: Lump-Sum Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4.3 Example 2: Taxes on Total Income . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4.4 Example 3: Taxes on Consumption . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4.5 Example 4: Introducing Labor . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Recursive Pareto Optimum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Ramsey Taxation 10 2.1 A Nonstochastic Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.1 Primal Approach Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 * Notes compiled in Economics PhD course 211 at UCSD by Steve Morris, Fall 2009; [email protected] 1
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2 Advanced Macroeconomics 2.1.2 Primal Approach Simplified Form . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.3 Property 1: Capital Taxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.4 Property 2: The Time-Inconsistency Problem . . . . . . . . . . . . . . . . . . . 14 2.1.5 Property 3: The Long-Run Behavior of Capital Taxation . . . . . . . . . . . . 14 2.1.6 Zero Capital Taxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 The Stochastic Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.1 Possibility of Time Inconsistency . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.2 Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3 Recursive Lagrangean 17 3.1 Ramsey Problem Without Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.1.1 Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.1.2 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2 Recursive Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2.1 Enforceability and Commitment . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2.2 Fiscal Policy with Incomplete Markets . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 Recursive Lagrangean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3.1 Planner Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3.2 Saddle Point Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.3.3 SPP obeys a Saddle Point Functional Equation . . . . . . . . . . . . . . . . . . 20 3.3.4 Risk Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3.5 SPP for Household . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4 Promised Utility 22 4.1 Utility Maximization Subject to Future Control Values . . . . . . . . . . . . . . . . . . 22 4.2 Promised Utility Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.3 Applications of Promised Utility Approach . . . . . . . . . . . . . . . . . . . . . . . . 23 4.4 Asymmetric Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.5 Abreu, Pearce, Stacchetti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.5.1 Definitions and Propositions .
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This note was uploaded on 01/29/2012 for the course ECONOMICS 101 taught by Professor Tikk during the Spring '11 term at University of Toronto.

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