Consumption and Asset Pricing

Size: px
Start display at page:

Download "Consumption and Asset Pricing"

Transcription

1 Consumption and Asset Pricing Yin-Chi Wang The Chinese University of Hong Kong November, 2012

2 References: Williamson s lecture notes (2006) ch5 and ch 6 Further references: Stochastic dynamic programming: Acemoglu (2010) ch16, Stokey-Lucas-Prescott (1989) ch9 Asset pricing: Cochrane (2005)

3 Background Knowledge Expected Utility Theory Risk aversion Stochastic dynamic programming Brock and Mirman (1972) Real business cycle models: Prescott (1986) and Cooley (1995)

4 Expected Utility Theory 1 Consumer s preferences Deterministic world: ranking in consumption bundles Uncertainty: ranking in lotteries Example: A world with a single consumption good c Lottery 1: Lottery 2: { c 1 1, with prob. p 1 { c 2, with prob. 1 p 1 c 1, with prob. p 2 c2 2, with prob. 1 p 2 Expected utility from lottery i, i = 1, 2, is ( ) ( ) p i u ci 1 + (1 p i ) u ci 2 The consumer ranks lottery 1 and 2 according to ( ) ( ) p i u c1 1 + (1 p i ) u c1 2 p i u ( c 1 2 ) + (1 p i ) u ( ) c2 2

5 Risk aversion Expected Utility Theory 2 Many aspects of observed behavior toward risk is consistent with risk aversion If the utility function is strictly concave, then the consumer is risk averse Jensen s inequality E [u (c)] u (E [c])

6 Expected Utility Theory 3

7 Expected Utility Theory 4 Anomalies in observed behavior towards risk The Allais Paradox Two measures of risk aversion Absolute risk aversion ARA(c) = u (c) u (c) Example: u (c) = e αc. Relative risk aversion RRA(c) = u (c) c u (c) Example: u (c) = c 1 σ 1 1 σ

8 Stochastic Optimal Growth Model Brock and Mirman (1972): stochastic optimal growth model The representative consumer s preferences E 0 β t u (c t ), t=0 where 0 < β < 1 and u ( ) strictly increasing, strictly concave and twice differentiable. E 0 : expectation operator conditional on information at t = 0. Production technology y t = z t F (k t, n t ) z t : random technology disturbance {z t } t=0 : a sequence of i.i.d. random variables drawn from G (z) Law of motion for capital k t+1 = i t + (1 δ) k t, 0 < δ < 1 Resource constraint: c t + i t = y t

9 Arrow-Debreu Eqm vs Rational Expectation Eqm 1 Competitive equilibrium: Two approaches 1. Arrow and Debreu (Arrow (1983) and Debreu (1983)) At t = 0, market for contingent claims is opened and the representative consumer and the representative firm trade State-contingent-commodities/claims: a promise to deliver a specified number of units of a particular object (labor or capital services) at a particular date T conditional on {z 0, z 1, z 2,..., z T } All markets clear

10 Arrow-Debreu Eqm vs Rational Expectation Eqm 2 2. Spot market trading with rational expectations (Muth (1960)) 1. At each date the consumer rents capital and sells labor at market price The consumer makes optimal saving decision based on his/her beliefs about the prob. distribution of future prices The markets clear at every date t for every possible realization of the random shock {z 0, z 1, z 2,..., z t } All expectations are rational: beliefs of the prob. distribution=actual prob. distribution Both equilibria are Pareto Optimal (but not true in models with heterogenous agents)

11 Social planner s problem Social Planner s Problem max E 0 {c t,k t+1 β t u (c t ) } t=0 s.t. c t + k t+1 = z t f (k t ) + (1 δ) k t where f (k) F (K, 1) The Bellman equation: v (k t, z t ) = max [u (c t ) + βe t v (k t+1, z t+1 )] s.t. c t + k t+1 = z t f (k t ) + (1 δ) k t Note that c t is know but c t+i, i = 1, 2, 3,..., is unknown (uncertain) Goal: solve for v (k, z) and the optimal decision rule k t+1 = g (k t, z t ) and c t = z t f (k t ) + (1 δ) k t k t+1

12 Example u (c t ) = ln c t, f (k t ) = k α t n 1 α t, 0 < α < 1, y t = z t F (k t, n t ), δ = 1 and E [ln z t ] = µ Guess and verify Guess that the value function takes the form It can be solved that v (k t, z t ) = A + B ln k t + D ln z t k t+1 = αβz t k α t c t = (1 αβ) z t k α t The economy will NOT converge to a steady state Technolgy disturbances will cause persistent fluctuations in output, consumption and investment Stochastic steady state Problems with the model Var (ln k t+1 ) = Var (ln y t ) = Var (ln c t ) : not the case in the data

13 Asset Pricing Model Lucas (1978) Treat consumption and output as exogenous and asset prices as endogenous Also called as the ICAPM (intertemporal capital asset pricing model) or consumption-based capital asset pricing model

14 Representative agent The Economy 1 E 0 t=0 β t u (c t ) Output 0 < β < 1, u ( ) strictly increasing, strictly concave, twice differentiable Exists n productive units (fruit trees), denote the productive unit by i, i = 1,..., n y it : quantity of output produced/yielded by production unit i at time t, a random variable Equilibrium: c t = n y it i=1

15 Asset holding The Economy 2 p it : price of tree i at time t z it : shares of tree held at time tgoal: determine the prices of the trees Shares are traded in competitive market Endowment: z i0 = 1, i =,..., n The fruits/output on each tree is proportionally distributed to their share holders according to their share holding After the distributing of fruits, the shares are traded again Budget constraint for t = 0, 1, 2,... n n p it z i,t+1 + c t = z it (p it + y it ) (1) i=1 i=1

16 The Bellman equation Optimization 1 v (z t, p t, y t ) = max c t,z t+1 [u (c t ) + βe t v (z t+1, p t+1, y t+1 )] s.t. c t = n i=1 z it (p it + y it ) Rewrite the Bellman equation as v (z t, p t, y t ) = max c t,z t+1 FOC and envelope theorem p it u ( n i=1 n i=1 p it z i,t+1 [ u ( n i=1 z it (p it + y it ) n i=1 p it z i,t+1 ) +βe t v (z t+1, p t+1, y t+1 ) z it (p it + y it ) v z i,t+1 = (p it + y it ) u for i = 1,..., n. ( n n i=1 i=1 p it z i,t+1 ) z it (p it + y it ) + βe t v z i,t+1 = 0 n i=1 p it z i,t+1 ) ]

17 Optimization 2 The basic formula for asset pricing p }{{} it = E t curret price of tree i (p i,t+1 + y i,t+1 ) }{{} future payoff of the share βu (c t+1 ) u (c t ) (2) }{{} the IMRS

18 Let Optimization 3 π it = p i,t+1 + y i,t+1 p i,t m t = βu (c t+1 ) u (c t ) (gross return) Equation (2) can be rewritten as E t (π it m t ) = 1 Use cov(x, Y ) = E (XY ) E (X )E (Y ) What is a good asset? cov (π it, m t ) + E t (π it ) E t (m t ) = 1 A good asset is one that pays you well when your consumption is low.

19 Optimization 4 Apply the law of iterated expectations E t [E t+s x t+s ] = E t x t+s, s 0, s 0 The price of tree i at time t can be rewritten as [ ] p it = E t (p i,t+1 + y i,t+1 ) βu (c t+1 ) u (c t ) βu (c t+1 ) u (c t y ) i,t+1 + β2 u (c t+2 ) = E t = E t [ s=t+1 u (c t ) + β3 u (c t+3 ) u (c t y ) i,t ] β s t u (c s ) u y is (c t ) y i,t+2 That is, the current price of any asset is the expected discounted value of future dividends, where the discount factor is the IMRS

20 Example 1 Assume that y it is i.i.d., and hence p it is i.i.d. ( )] n E t [(p i,t+1 + y i,t+1 ) u y i,t+1 = A i i=1 for i = 1,..., n, A i > 0 is a constant. From the basic asset-pricing formula p it = βa ( i ) n u y i,t i=1 n If y i,t low u high p it low i =1 n If y i,t high u low p it high i =1

21 Example 2: Risk Neutral Agent Assume that u (c) = c From the basic asset-pricing formula p it = βe t [p i,t+1 + y i,t+1 ] = E t [ pi,t+1 + y i,t+1 p it p it ] = 1 β 1 Familiar formula in finance: only hold when people are risk neutral p it can be rewritten as p it = E t β s t y is s=t+1

22 Example 3 Assume { that u (c) = ln (c), n = 1 and y1 w.p. π y t = y 2 w.p. 1 π, y 1 > y 2, y t is i.i.d. Let p i denote the price of a share when y t = y i for i = 1, 2. [ p 1 = β π y 1 (p 1 + y 1 ) + (1 π) y ] 1 (p 2 + y 2 ) y 1 y 2 [ p 1t = β π y 2 (p 1 + y 1 ) + (1 π) y ] 2 (p 2 + y 2 ) y 1 y 2 Can solve for p 1 = βy 1 1 β p 2 = βy 2 1 β since y 1 > y 2, it follows that p 1 > p 2.

23 The Equity Premium Puzzle 1 The average rate of return on equity is approximately 6% higher than the average rate of return on risk-free debt Mehra and Prescott (1985) showed that to generate such a big equity premium in Lucas asset pricing model, the implied IES of consumption must be very large, lying outside of the range of estimates for IES in empirical work 2 assets: a risk-free asset and a risky asset Risky-asset Pr [ y t+1 = y j y t = y i ] = πij where π ii = ρ, 0 < ρ < 1 Derive p i, q i, i = 1, 2 when y t = y i for i = 1, 2 and derive R 1, R 2, r 1, r 2 The average equity premium e (β, σ, ρ, y 1, y 2 ) = 1 2 (R 1 r 1 ) (R 2 r 2 ) 0.06

24 The Equity Premium Puzzle 2 Two explanations (u (c) = c 1 σ /(1 σ)) 1. The higher the σ is, the lower the IES is, and the greater is the tendency of the representative consumer to smooth consumption over time. Or, the higher the σ is, the less willing the agents are to save for future consumption. Hence, to induce the agent to save more, have to give more compensation (r t ) 2. σ also measures for risk aversion. The higher is σ the larger is the expected return on equity, as agents must be compensated more for bearing risk Fitting the model into data: not enough variability in aggregate consumption to produce a large enough risk premium, given plausible levels of risk aversion

Feb. 20th, Recursive, Stochastic Growth Model

Feb. 20th, Recursive, Stochastic Growth Model Feb 20th, 2007 1 Recursive, Stochastic Growth Model In previous sections, we discussed random shocks, stochastic processes and histories Now we will introduce those concepts into the growth model and analyze

More information

Homework 3: Asset Pricing

Homework 3: Asset Pricing Homework 3: Asset Pricing Mohammad Hossein Rahmati November 1, 2018 1. Consider an economy with a single representative consumer who maximize E β t u(c t ) 0 < β < 1, u(c t ) = ln(c t + α) t= The sole

More information

Notes on Macroeconomic Theory II

Notes on Macroeconomic Theory II Notes on Macroeconomic Theory II Chao Wei Department of Economics George Washington University Washington, DC 20052 January 2007 1 1 Deterministic Dynamic Programming Below I describe a typical dynamic

More information

Tries to understand the prices or values of claims to uncertain payments.

Tries to understand the prices or values of claims to uncertain payments. Asset pricing Tries to understand the prices or values of claims to uncertain payments. If stocks have an average real return of about 8%, then 2% may be due to interest rates and the remaining 6% is a

More information

Question 1 Consider an economy populated by a continuum of measure one of consumers whose preferences are defined by the utility function:

Question 1 Consider an economy populated by a continuum of measure one of consumers whose preferences are defined by the utility function: Question 1 Consider an economy populated by a continuum of measure one of consumers whose preferences are defined by the utility function: β t log(c t ), where C t is consumption and the parameter β satisfies

More information

Asset Prices in Consumption and Production Models. 1 Introduction. Levent Akdeniz and W. Davis Dechert. February 15, 2007

Asset Prices in Consumption and Production Models. 1 Introduction. Levent Akdeniz and W. Davis Dechert. February 15, 2007 Asset Prices in Consumption and Production Models Levent Akdeniz and W. Davis Dechert February 15, 2007 Abstract In this paper we use a simple model with a single Cobb Douglas firm and a consumer with

More information

1 Dynamic programming

1 Dynamic programming 1 Dynamic programming A country has just discovered a natural resource which yields an income per period R measured in terms of traded goods. The cost of exploitation is negligible. The government wants

More information

Problem Set 3. Thomas Philippon. April 19, Human Wealth, Financial Wealth and Consumption

Problem Set 3. Thomas Philippon. April 19, Human Wealth, Financial Wealth and Consumption Problem Set 3 Thomas Philippon April 19, 2002 1 Human Wealth, Financial Wealth and Consumption The goal of the question is to derive the formulas on p13 of Topic 2. This is a partial equilibrium analysis

More information

1 Consumption and saving under uncertainty

1 Consumption and saving under uncertainty 1 Consumption and saving under uncertainty 1.1 Modelling uncertainty As in the deterministic case, we keep assuming that agents live for two periods. The novelty here is that their earnings in the second

More information

MACROECONOMICS. Prelim Exam

MACROECONOMICS. Prelim Exam MACROECONOMICS Prelim Exam Austin, June 1, 2012 Instructions This is a closed book exam. If you get stuck in one section move to the next one. Do not waste time on sections that you find hard to solve.

More information

Macroeconomics Sequence, Block I. Introduction to Consumption Asset Pricing

Macroeconomics Sequence, Block I. Introduction to Consumption Asset Pricing Macroeconomics Sequence, Block I Introduction to Consumption Asset Pricing Nicola Pavoni October 21, 2016 The Lucas Tree Model This is a general equilibrium model where instead of deriving properties of

More information

Economics 8106 Macroeconomic Theory Recitation 2

Economics 8106 Macroeconomic Theory Recitation 2 Economics 8106 Macroeconomic Theory Recitation 2 Conor Ryan November 8st, 2016 Outline: Sequential Trading with Arrow Securities Lucas Tree Asset Pricing Model The Equity Premium Puzzle 1 Sequential Trading

More information

Topic 7: Asset Pricing and the Macroeconomy

Topic 7: Asset Pricing and the Macroeconomy Topic 7: Asset Pricing and the Macroeconomy Yulei Luo SEF of HKU November 15, 2013 Luo, Y. (SEF of HKU) Macro Theory November 15, 2013 1 / 56 Consumption-based Asset Pricing Even if we cannot easily solve

More information

ECOM 009 Macroeconomics B. Lecture 7

ECOM 009 Macroeconomics B. Lecture 7 ECOM 009 Macroeconomics B Lecture 7 Giulio Fella c Giulio Fella, 2014 ECOM 009 Macroeconomics B - Lecture 7 187/231 Plan for the rest of this lecture Introducing the general asset pricing equation Consumption-based

More information

Problem set 5. Asset pricing. Markus Roth. Chair for Macroeconomics Johannes Gutenberg Universität Mainz. Juli 5, 2010

Problem set 5. Asset pricing. Markus Roth. Chair for Macroeconomics Johannes Gutenberg Universität Mainz. Juli 5, 2010 Problem set 5 Asset pricing Markus Roth Chair for Macroeconomics Johannes Gutenberg Universität Mainz Juli 5, 200 Markus Roth (Macroeconomics 2) Problem set 5 Juli 5, 200 / 40 Contents Problem 5 of problem

More information

INTERTEMPORAL ASSET ALLOCATION: THEORY

INTERTEMPORAL ASSET ALLOCATION: THEORY INTERTEMPORAL ASSET ALLOCATION: THEORY Multi-Period Model The agent acts as a price-taker in asset markets and then chooses today s consumption and asset shares to maximise lifetime utility. This multi-period

More information

Lecture 12. Asset pricing model. Randall Romero Aguilar, PhD I Semestre 2017 Last updated: June 15, 2017

Lecture 12. Asset pricing model. Randall Romero Aguilar, PhD I Semestre 2017 Last updated: June 15, 2017 Lecture 12 Asset pricing model Randall Romero Aguilar, PhD I Semestre 2017 Last updated: June 15, 2017 Universidad de Costa Rica EC3201 - Teoría Macroeconómica 2 Table of contents 1. Introduction 2. The

More information

LECTURE NOTES 10 ARIEL M. VIALE

LECTURE NOTES 10 ARIEL M. VIALE LECTURE NOTES 10 ARIEL M VIALE 1 Behavioral Asset Pricing 11 Prospect theory based asset pricing model Barberis, Huang, and Santos (2001) assume a Lucas pure-exchange economy with three types of assets:

More information

ECON FINANCIAL ECONOMICS

ECON FINANCIAL ECONOMICS ECON 337901 FINANCIAL ECONOMICS Peter Ireland Boston College Spring 2018 These lecture notes by Peter Ireland are licensed under a Creative Commons Attribution-NonCommerical-ShareAlike 4.0 International

More information

STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics. Ph. D. Comprehensive Examination: Macroeconomics Spring, 2016

STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics. Ph. D. Comprehensive Examination: Macroeconomics Spring, 2016 STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics Ph. D. Comprehensive Examination: Macroeconomics Spring, 2016 Section 1. Suggested Time: 45 Minutes) For 3 of the following 6 statements,

More information

Asset Pricing and Equity Premium Puzzle. E. Young Lecture Notes Chapter 13

Asset Pricing and Equity Premium Puzzle. E. Young Lecture Notes Chapter 13 Asset Pricing and Equity Premium Puzzle 1 E. Young Lecture Notes Chapter 13 1 A Lucas Tree Model Consider a pure exchange, representative household economy. Suppose there exists an asset called a tree.

More information

ADVANCED MACROECONOMIC TECHNIQUES NOTE 6a

ADVANCED MACROECONOMIC TECHNIQUES NOTE 6a 316-406 ADVANCED MACROECONOMIC TECHNIQUES NOTE 6a Chris Edmond hcpedmond@unimelb.edu.aui Introduction to consumption-based asset pricing We will begin our brief look at asset pricing with a review of the

More information

Assets with possibly negative dividends

Assets with possibly negative dividends Assets with possibly negative dividends (Preliminary and incomplete. Comments welcome.) Ngoc-Sang PHAM Montpellier Business School March 12, 2017 Abstract The paper introduces assets whose dividends can

More information

Lecture 2 General Equilibrium Models: Finite Period Economies

Lecture 2 General Equilibrium Models: Finite Period Economies Lecture 2 General Equilibrium Models: Finite Period Economies Introduction In macroeconomics, we study the behavior of economy-wide aggregates e.g. GDP, savings, investment, employment and so on - and

More information

CHOICE THEORY, UTILITY FUNCTIONS AND RISK AVERSION

CHOICE THEORY, UTILITY FUNCTIONS AND RISK AVERSION CHOICE THEORY, UTILITY FUNCTIONS AND RISK AVERSION Szabolcs Sebestyén szabolcs.sebestyen@iscte.pt Master in Finance INVESTMENTS Sebestyén (ISCTE-IUL) Choice Theory Investments 1 / 65 Outline 1 An Introduction

More information

Advanced Modern Macroeconomics

Advanced Modern Macroeconomics Advanced Modern Macroeconomics Asset Prices and Finance Max Gillman Cardi Business School 0 December 200 Gillman (Cardi Business School) Chapter 7 0 December 200 / 38 Chapter 7: Asset Prices and Finance

More information

STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics. Ph. D. Comprehensive Examination: Macroeconomics Spring, 2009

STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics. Ph. D. Comprehensive Examination: Macroeconomics Spring, 2009 STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics Ph. D. Comprehensive Examination: Macroeconomics Spring, 2009 Section 1. (Suggested Time: 45 Minutes) For 3 of the following 6 statements,

More information

Macroeconomics I Chapter 3. Consumption

Macroeconomics I Chapter 3. Consumption Toulouse School of Economics Notes written by Ernesto Pasten (epasten@cict.fr) Slightly re-edited by Frank Portier (fportier@cict.fr) M-TSE. Macro I. 200-20. Chapter 3: Consumption Macroeconomics I Chapter

More information

ECON 815. Uncertainty and Asset Prices

ECON 815. Uncertainty and Asset Prices ECON 815 Uncertainty and Asset Prices Winter 2015 Queen s University ECON 815 1 Adding Uncertainty Endowments are now stochastic. endowment in period 1 is known at y t two states s {1, 2} in period 2 with

More information

Slides III - Complete Markets

Slides III - Complete Markets Slides III - Complete Markets Julio Garín University of Georgia Macroeconomic Theory II (Ph.D.) Spring 2017 Macroeconomic Theory II Slides III - Complete Markets Spring 2017 1 / 33 Outline 1. Risk, Uncertainty,

More information

Portfolio Investment

Portfolio Investment Portfolio Investment Robert A. Miller Tepper School of Business CMU 45-871 Lecture 5 Miller (Tepper School of Business CMU) Portfolio Investment 45-871 Lecture 5 1 / 22 Simplifying the framework for analysis

More information

X ln( +1 ) +1 [0 ] Γ( )

X ln( +1 ) +1 [0 ] Γ( ) Problem Set #1 Due: 11 September 2014 Instructor: David Laibson Economics 2010c Problem 1 (Growth Model): Recall the growth model that we discussed in class. We expressed the sequence problem as ( 0 )=

More information

Macroeconomics. Lecture 5: Consumption. Hernán D. Seoane. Spring, 2016 MEDEG, UC3M UC3M

Macroeconomics. Lecture 5: Consumption. Hernán D. Seoane. Spring, 2016 MEDEG, UC3M UC3M Macroeconomics MEDEG, UC3M Lecture 5: Consumption Hernán D. Seoane UC3M Spring, 2016 Introduction A key component in NIPA accounts and the households budget constraint is the consumption It represents

More information

Notes on Macroeconomic Theory. Steve Williamson Dept. of Economics Washington University in St. Louis St. Louis, MO 63130

Notes on Macroeconomic Theory. Steve Williamson Dept. of Economics Washington University in St. Louis St. Louis, MO 63130 Notes on Macroeconomic Theory Steve Williamson Dept. of Economics Washington University in St. Louis St. Louis, MO 63130 September 2006 Chapter 2 Growth With Overlapping Generations This chapter will serve

More information

Microeconomics II. CIDE, MsC Economics. List of Problems

Microeconomics II. CIDE, MsC Economics. List of Problems Microeconomics II CIDE, MsC Economics List of Problems 1. There are three people, Amy (A), Bart (B) and Chris (C): A and B have hats. These three people are arranged in a room so that B can see everything

More information

1 Precautionary Savings: Prudence and Borrowing Constraints

1 Precautionary Savings: Prudence and Borrowing Constraints 1 Precautionary Savings: Prudence and Borrowing Constraints In this section we study conditions under which savings react to changes in income uncertainty. Recall that in the PIH, when you abstract from

More information

STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics. Ph. D. Preliminary Examination: Macroeconomics Spring, 2007

STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics. Ph. D. Preliminary Examination: Macroeconomics Spring, 2007 STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics Ph. D. Preliminary Examination: Macroeconomics Spring, 2007 Instructions: Read the questions carefully and make sure to show your work. You

More information

General Examination in Macroeconomic Theory SPRING 2016

General Examination in Macroeconomic Theory SPRING 2016 HARVARD UNIVERSITY DEPARTMENT OF ECONOMICS General Examination in Macroeconomic Theory SPRING 2016 You have FOUR hours. Answer all questions Part A (Prof. Laibson): 60 minutes Part B (Prof. Barro): 60

More information

Microeconomics of Banking: Lecture 2

Microeconomics of Banking: Lecture 2 Microeconomics of Banking: Lecture 2 Prof. Ronaldo CARPIO September 25, 2015 A Brief Look at General Equilibrium Asset Pricing Last week, we saw a general equilibrium model in which banks were irrelevant.

More information

Asset Pricing under Information-processing Constraints

Asset Pricing under Information-processing Constraints The University of Hong Kong From the SelectedWorks of Yulei Luo 00 Asset Pricing under Information-processing Constraints Yulei Luo, The University of Hong Kong Eric Young, University of Virginia Available

More information

Arrow-Debreu Equilibrium

Arrow-Debreu Equilibrium Arrow-Debreu Equilibrium Econ 2100 Fall 2017 Lecture 23, November 21 Outline 1 Arrow-Debreu Equilibrium Recap 2 Arrow-Debreu Equilibrium With Only One Good 1 Pareto Effi ciency and Equilibrium 2 Properties

More information

Birkbeck MSc/Phd Economics. Advanced Macroeconomics, Spring Lecture 2: The Consumption CAPM and the Equity Premium Puzzle

Birkbeck MSc/Phd Economics. Advanced Macroeconomics, Spring Lecture 2: The Consumption CAPM and the Equity Premium Puzzle Birkbeck MSc/Phd Economics Advanced Macroeconomics, Spring 2006 Lecture 2: The Consumption CAPM and the Equity Premium Puzzle 1 Overview This lecture derives the consumption-based capital asset pricing

More information

STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics. Ph. D. Preliminary Examination: Macroeconomics Fall, 2009

STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics. Ph. D. Preliminary Examination: Macroeconomics Fall, 2009 STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics Ph. D. Preliminary Examination: Macroeconomics Fall, 2009 Instructions: Read the questions carefully and make sure to show your work. You

More information

Chapter 9 Dynamic Models of Investment

Chapter 9 Dynamic Models of Investment George Alogoskoufis, Dynamic Macroeconomic Theory, 2015 Chapter 9 Dynamic Models of Investment In this chapter we present the main neoclassical model of investment, under convex adjustment costs. This

More information

ECON 4325 Monetary Policy and Business Fluctuations

ECON 4325 Monetary Policy and Business Fluctuations ECON 4325 Monetary Policy and Business Fluctuations Tommy Sveen Norges Bank January 28, 2009 TS (NB) ECON 4325 January 28, 2009 / 35 Introduction A simple model of a classical monetary economy. Perfect

More information

Topic 6. Introducing money

Topic 6. Introducing money 14.452. Topic 6. Introducing money Olivier Blanchard April 2007 Nr. 1 1. Motivation No role for money in the models we have looked at. Implicitly, centralized markets, with an auctioneer: Possibly open

More information

Asymmetric Information: Walrasian Equilibria, and Rational Expectations Equilibria

Asymmetric Information: Walrasian Equilibria, and Rational Expectations Equilibria Asymmetric Information: Walrasian Equilibria and Rational Expectations Equilibria 1 Basic Setup Two periods: 0 and 1 One riskless asset with interest rate r One risky asset which pays a normally distributed

More information

1 Asset Pricing: Bonds vs Stocks

1 Asset Pricing: Bonds vs Stocks Asset Pricing: Bonds vs Stocks The historical data on financial asset returns show that one dollar invested in the Dow- Jones yields 6 times more than one dollar invested in U.S. Treasury bonds. The return

More information

Lecture 1: Lucas Model and Asset Pricing

Lecture 1: Lucas Model and Asset Pricing Lecture 1: Lucas Model and Asset Pricing Economics 714, Spring 2018 1 Asset Pricing 1.1 Lucas (1978) Asset Pricing Model We assume that there are a large number of identical agents, modeled as a representative

More information

1 Mar Review. Consumer s problem is. V (z, K, a; G, q z ) = max. subject to. c+ X q z. w(z, K) = zf 2 (K, H(K)) (4) K 0 = G(z, K) (5)

1 Mar Review. Consumer s problem is. V (z, K, a; G, q z ) = max. subject to. c+ X q z. w(z, K) = zf 2 (K, H(K)) (4) K 0 = G(z, K) (5) 1 Mar 4 1.1 Review ² Stochastic RCE with and without state-contingent asset Consider the economy with shock to production. People are allowed to purchase statecontingent asset for next period. Consumer

More information

GMM Estimation. 1 Introduction. 2 Consumption-CAPM

GMM Estimation. 1 Introduction. 2 Consumption-CAPM GMM Estimation 1 Introduction Modern macroeconomic models are typically based on the intertemporal optimization and rational expectations. The Generalized Method of Moments (GMM) is an econometric framework

More information

CONSUMPTION-BASED MACROECONOMIC MODELS OF ASSET PRICING THEORY

CONSUMPTION-BASED MACROECONOMIC MODELS OF ASSET PRICING THEORY ECONOMIC ANNALS, Volume LXI, No. 211 / October December 2016 UDC: 3.33 ISSN: 0013-3264 DOI:10.2298/EKA1611007D Marija Đorđević* CONSUMPTION-BASED MACROECONOMIC MODELS OF ASSET PRICING THEORY ABSTRACT:

More information

Lecture 2 Dynamic Equilibrium Models: Three and More (Finite) Periods

Lecture 2 Dynamic Equilibrium Models: Three and More (Finite) Periods Lecture 2 Dynamic Equilibrium Models: Three and More (Finite) Periods. Introduction In ECON 50, we discussed the structure of two-period dynamic general equilibrium models, some solution methods, and their

More information

From Discrete Time to Continuous Time Modeling

From Discrete Time to Continuous Time Modeling From Discrete Time to Continuous Time Modeling Prof. S. Jaimungal, Department of Statistics, University of Toronto 2004 Arrow-Debreu Securities 2004 Prof. S. Jaimungal 2 Consider a simple one-period economy

More information

Return to Capital in a Real Business Cycle Model

Return to Capital in a Real Business Cycle Model Return to Capital in a Real Business Cycle Model Paul Gomme, B. Ravikumar, and Peter Rupert Can the neoclassical growth model generate fluctuations in the return to capital similar to those observed in

More information

STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics. Ph. D. Comprehensive Examination: Macroeconomics Fall, 2010

STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics. Ph. D. Comprehensive Examination: Macroeconomics Fall, 2010 STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics Ph. D. Comprehensive Examination: Macroeconomics Fall, 2010 Section 1. (Suggested Time: 45 Minutes) For 3 of the following 6 statements, state

More information

Uncertainty in Equilibrium

Uncertainty in Equilibrium Uncertainty in Equilibrium Larry Blume May 1, 2007 1 Introduction The state-preference approach to uncertainty of Kenneth J. Arrow (1953) and Gérard Debreu (1959) lends itself rather easily to Walrasian

More information

Chapter 5 Macroeconomics and Finance

Chapter 5 Macroeconomics and Finance Macro II Chapter 5 Macro and Finance 1 Chapter 5 Macroeconomics and Finance Main references : - L. Ljundqvist and T. Sargent, Chapter 7 - Mehra and Prescott 1985 JME paper - Jerman 1998 JME paper - J.

More information

Course Handouts - Introduction ECON 8704 FINANCIAL ECONOMICS. Jan Werner. University of Minnesota

Course Handouts - Introduction ECON 8704 FINANCIAL ECONOMICS. Jan Werner. University of Minnesota Course Handouts - Introduction ECON 8704 FINANCIAL ECONOMICS Jan Werner University of Minnesota SPRING 2019 1 I.1 Equilibrium Prices in Security Markets Assume throughout this section that utility functions

More information

Part A: Questions on ECN 200D (Rendahl)

Part A: Questions on ECN 200D (Rendahl) University of California, Davis Date: September 1, 2011 Department of Economics Time: 5 hours Macroeconomics Reading Time: 20 minutes PRELIMINARY EXAMINATION FOR THE Ph.D. DEGREE Directions: Answer all

More information

In the Name of God. Macroeconomics. Sharif University of Technology Problem Bank

In the Name of God. Macroeconomics. Sharif University of Technology Problem Bank In the Name of God Macroeconomics Sharif University of Technology Problem Bank 1 Microeconomics 1.1 Short Questions: Write True/False/Ambiguous. then write your argument for it: 1. The elasticity of demand

More information

Interest Rates and Currency Prices in a Two-Country World. Robert E. Lucas, Jr. 1982

Interest Rates and Currency Prices in a Two-Country World. Robert E. Lucas, Jr. 1982 Interest Rates and Currency Prices in a Two-Country World Robert E. Lucas, Jr. 1982 Contribution Integrates domestic and international monetary theory with financial economics to provide a complete theory

More information

Copyright (C) 2001 David K. Levine This document is an open textbook; you can redistribute it and/or modify it under the terms of version 1 of the

Copyright (C) 2001 David K. Levine This document is an open textbook; you can redistribute it and/or modify it under the terms of version 1 of the Copyright (C) 2001 David K. Levine This document is an open textbook; you can redistribute it and/or modify it under the terms of version 1 of the open text license amendment to version 2 of the GNU General

More information

The Real Business Cycle Model

The Real Business Cycle Model The Real Business Cycle Model Economics 3307 - Intermediate Macroeconomics Aaron Hedlund Baylor University Fall 2013 Econ 3307 (Baylor University) The Real Business Cycle Model Fall 2013 1 / 23 Business

More information

UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS

UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Postponed exam: ECON4310 Macroeconomic Theory Date of exam: Monday, December 14, 2015 Time for exam: 09:00 a.m. 12:00 noon The problem set covers 13 pages (incl.

More information

ECON FINANCIAL ECONOMICS

ECON FINANCIAL ECONOMICS ECON 337901 FINANCIAL ECONOMICS Peter Ireland Boston College Spring 2018 These lecture notes by Peter Ireland are licensed under a Creative Commons Attribution-NonCommerical-ShareAlike 4.0 International

More information

The Basic New Keynesian Model

The Basic New Keynesian Model Jordi Gali Monetary Policy, inflation, and the business cycle Lian Allub 15/12/2009 In The Classical Monetary economy we have perfect competition and fully flexible prices in all markets. Here there is

More information

STOCHASTIC CONSUMPTION-SAVINGS MODEL: CANONICAL APPLICATIONS FEBRUARY 19, 2013

STOCHASTIC CONSUMPTION-SAVINGS MODEL: CANONICAL APPLICATIONS FEBRUARY 19, 2013 STOCHASTIC CONSUMPTION-SAVINGS MODEL: CANONICAL APPLICATIONS FEBRUARY 19, 2013 Model Structure EXPECTED UTILITY Preferences v(c 1, c 2 ) with all the usual properties Lifetime expected utility function

More information

1 No-arbitrage pricing

1 No-arbitrage pricing BURNABY SIMON FRASER UNIVERSITY BRITISH COLUMBIA Paul Klein Office: WMC 3635 Phone: TBA Email: paul klein 2@sfu.ca URL: http://paulklein.ca/newsite/teaching/809.php Economics 809 Advanced macroeconomic

More information

Chapter 6. Endogenous Growth I: AK, H, and G

Chapter 6. Endogenous Growth I: AK, H, and G Chapter 6 Endogenous Growth I: AK, H, and G 195 6.1 The Simple AK Model Economic Growth: Lecture Notes 6.1.1 Pareto Allocations Total output in the economy is given by Y t = F (K t, L t ) = AK t, where

More information

The Equity Premium in. Brock s Asset Pricing Model

The Equity Premium in. Brock s Asset Pricing Model The Equity Premium in Brock s Asset Pricing Model by Levent Akdeniz and W. Davis Dechert April 25, 2006 Preliminary Version Please Do Not Quote We thank W. A. Brock for many helpful comments and encouragement.

More information

Part A: Questions on ECN 200D (Rendahl)

Part A: Questions on ECN 200D (Rendahl) University of California, Davis Date: June 27, 2011 Department of Economics Time: 5 hours Macroeconomics Reading Time: 20 minutes PRELIMINARY EXAMINATION FOR THE Ph.D. DEGREE Directions: Answer all questions.

More information

Exercises on the New-Keynesian Model

Exercises on the New-Keynesian Model Advanced Macroeconomics II Professor Lorenza Rossi/Jordi Gali T.A. Daniël van Schoot, daniel.vanschoot@upf.edu Exercises on the New-Keynesian Model Schedule: 28th of May (seminar 4): Exercises 1, 2 and

More information

Expected Utility And Risk Aversion

Expected Utility And Risk Aversion Expected Utility And Risk Aversion Econ 2100 Fall 2017 Lecture 12, October 4 Outline 1 Risk Aversion 2 Certainty Equivalent 3 Risk Premium 4 Relative Risk Aversion 5 Stochastic Dominance Notation From

More information

Lecture 8: Asset pricing

Lecture 8: Asset pricing BURNABY SIMON FRASER UNIVERSITY BRITISH COLUMBIA Paul Klein Office: WMC 3635 Phone: (778) 782-9391 Email: paul klein 2@sfu.ca URL: http://paulklein.ca/newsite/teaching/483.php Economics 483 Advanced Topics

More information

Suggested Solutions to Homework #5 Econ 511b (Part I), Spring 2004

Suggested Solutions to Homework #5 Econ 511b (Part I), Spring 2004 Suggested Solutions to Homework #5 Econ 5b (Part I), Spring 004. Consider the planning problem for a neoclassical growth model with logarithmic utility, full depreciation of the capital stock in one period,

More information

Consumption- Savings, Portfolio Choice, and Asset Pricing

Consumption- Savings, Portfolio Choice, and Asset Pricing Finance 400 A. Penati - G. Pennacchi Consumption- Savings, Portfolio Choice, and Asset Pricing I. The Consumption - Portfolio Choice Problem We have studied the portfolio choice problem of an individual

More information

Lecture 8: Introduction to asset pricing

Lecture 8: Introduction to asset pricing THE UNIVERSITY OF SOUTHAMPTON Paul Klein Office: Murray Building, 3005 Email: p.klein@soton.ac.uk URL: http://paulklein.se Economics 3010 Topics in Macroeconomics 3 Autumn 2010 Lecture 8: Introduction

More information

Basics of Asset Pricing. Ali Nejadmalayeri

Basics of Asset Pricing. Ali Nejadmalayeri Basics of Asset Pricing Ali Nejadmalayeri January 2009 No-Arbitrage and Equilibrium Pricing in Complete Markets: Imagine a finite state space with s {1,..., S} where there exist n traded assets with a

More information

Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth

Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth Suresh M. Sundaresan Columbia University In this article we construct a model in which a consumer s utility depends on

More information

Linear Capital Taxation and Tax Smoothing

Linear Capital Taxation and Tax Smoothing Florian Scheuer 5/1/2014 Linear Capital Taxation and Tax Smoothing 1 Finite Horizon 1.1 Setup 2 periods t = 0, 1 preferences U i c 0, c 1, l 0 sequential budget constraints in t = 0, 1 c i 0 + pbi 1 +

More information

1 Answers to the Sept 08 macro prelim - Long Questions

1 Answers to the Sept 08 macro prelim - Long Questions Answers to the Sept 08 macro prelim - Long Questions. Suppose that a representative consumer receives an endowment of a non-storable consumption good. The endowment evolves exogenously according to ln

More information

Homework 2: Dynamic Moral Hazard

Homework 2: Dynamic Moral Hazard Homework 2: Dynamic Moral Hazard Question 0 (Normal learning model) Suppose that z t = θ + ɛ t, where θ N(m 0, 1/h 0 ) and ɛ t N(0, 1/h ɛ ) are IID. Show that θ z 1 N ( hɛ z 1 h 0 + h ɛ + h 0m 0 h 0 +

More information

Topic 3: International Risk Sharing and Portfolio Diversification

Topic 3: International Risk Sharing and Portfolio Diversification Topic 3: International Risk Sharing and Portfolio Diversification Part 1) Working through a complete markets case - In the previous lecture, I claimed that assuming complete asset markets produced a perfect-pooling

More information

Optimal Capital Accumulation in a Stochastic Growth Model under Loss Aversion

Optimal Capital Accumulation in a Stochastic Growth Model under Loss Aversion Working Paper Series National Centre of Competence in Research Financial Valuation and Risk Management Working Paper No. 222 Optimal Capital Accumulation in a Stochastic Growth Model under Loss Aversion

More information

Asset Pricing under Information-processing Constraints

Asset Pricing under Information-processing Constraints Asset Pricing under Information-processing Constraints YuleiLuo University of Hong Kong Eric.Young University of Virginia November 2007 Abstract This paper studies the implications of limited information-processing

More information

Fluctuations. Shocks, Uncertainty, and the Consumption/Saving Choice

Fluctuations. Shocks, Uncertainty, and the Consumption/Saving Choice Fluctuations. Shocks, Uncertainty, and the Consumption/Saving Choice Olivier Blanchard April 2005 14.452. Spring 2005. Topic2. 1 Want to start with a model with two ingredients: Shocks, so uncertainty.

More information

1 Two Period Exchange Economy

1 Two Period Exchange Economy University of British Columbia Department of Economics, Macroeconomics (Econ 502) Prof. Amartya Lahiri Handout # 2 1 Two Period Exchange Economy We shall start our exploration of dynamic economies with

More information

1. Introduction of another instrument of savings, namely, capital

1. Introduction of another instrument of savings, namely, capital Chapter 7 Capital Main Aims: 1. Introduction of another instrument of savings, namely, capital 2. Study conditions for the co-existence of money and capital as instruments of savings 3. Studies the effects

More information

CONSUMPTION-SAVINGS MODEL JANUARY 19, 2018

CONSUMPTION-SAVINGS MODEL JANUARY 19, 2018 CONSUMPTION-SAVINGS MODEL JANUARY 19, 018 Stochastic Consumption-Savings Model APPLICATIONS Use (solution to) stochastic two-period model to illustrate some basic results and ideas in Consumption research

More information

Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017

Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017 Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.

More information

Lecture Notes: November 29, 2012 TIME AND UNCERTAINTY: FUTURES MARKETS

Lecture Notes: November 29, 2012 TIME AND UNCERTAINTY: FUTURES MARKETS Lecture Notes: November 29, 2012 TIME AND UNCERTAINTY: FUTURES MARKETS Gerard says: theory's in the math. The rest is interpretation. (See Debreu quote in textbook, p. 204) make the markets for goods over

More information

STOCHASTIC CONSUMPTION-SAVINGS MODEL: CANONICAL APPLICATIONS SEPTEMBER 13, 2010 BASICS. Introduction

STOCHASTIC CONSUMPTION-SAVINGS MODEL: CANONICAL APPLICATIONS SEPTEMBER 13, 2010 BASICS. Introduction STOCASTIC CONSUMPTION-SAVINGS MODE: CANONICA APPICATIONS SEPTEMBER 3, 00 Introduction BASICS Consumption-Savings Framework So far only a deterministic analysis now introduce uncertainty Still an application

More information

Comprehensive Exam. August 19, 2013

Comprehensive Exam. August 19, 2013 Comprehensive Exam August 19, 2013 You have a total of 180 minutes to complete the exam. If a question seems ambiguous, state why, sharpen it up and answer the sharpened-up question. Good luck! 1 1 Menu

More information

Real Business Cycles (Solution)

Real Business Cycles (Solution) Real Business Cycles (Solution) Exercise: A two-period real business cycle model Consider a representative household of a closed economy. The household has a planning horizon of two periods and is endowed

More information

Lecture 2. (1) Permanent Income Hypothesis. (2) Precautionary Savings. Erick Sager. September 21, 2015

Lecture 2. (1) Permanent Income Hypothesis. (2) Precautionary Savings. Erick Sager. September 21, 2015 Lecture 2 (1) Permanent Income Hypothesis (2) Precautionary Savings Erick Sager September 21, 2015 Econ 605: Adv. Topics in Macroeconomics Johns Hopkins University, Fall 2015 Erick Sager Lecture 2 (9/21/15)

More information

STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics. Ph. D. Comprehensive Examination: Macroeconomics Spring, 2013

STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics. Ph. D. Comprehensive Examination: Macroeconomics Spring, 2013 STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics Ph. D. Comprehensive Examination: Macroeconomics Spring, 2013 Section 1. (Suggested Time: 45 Minutes) For 3 of the following 6 statements,

More information

Money in a Neoclassical Framework

Money in a Neoclassical Framework Money in a Neoclassical Framework Noah Williams University of Wisconsin-Madison Noah Williams (UW Madison) Macroeconomic Theory 1 / 21 Money Two basic questions: 1 Modern economies use money. Why? 2 How/why

More information

Problem Set 2. Theory of Banking - Academic Year Maria Bachelet March 2, 2017

Problem Set 2. Theory of Banking - Academic Year Maria Bachelet March 2, 2017 Problem Set Theory of Banking - Academic Year 06-7 Maria Bachelet maria.jua.bachelet@gmai.com March, 07 Exercise Consider an agency relationship in which the principal contracts the agent, whose effort

More information

Topic 4. Introducing investment (and saving) decisions

Topic 4. Introducing investment (and saving) decisions 14.452. Topic 4. Introducing investment (and saving) decisions Olivier Blanchard April 27 Nr. 1 1. Motivation In the benchmark model (and the RBC extension), there was a clear consump tion/saving decision.

More information