10.
Intertemporal model under uncertainty: prudence
Highlights
consumption & saving, prudence, precautionary saving
10.1
Marginal propensity to consume (no uncertainty yet)
consider two-period, no income model again: the FOC is
u0 (c1 ) u0 (z0 c1 ) = 0
Economics of Uncertainty and Information
2. Risk aversion
Sung Hyun Kim
Ewha Womans University
Fall 2016
1 / 17
Certainty equivalent, risk premium I
C = cfw_A, B, C, if p = 0.5 then the graph of u() is linear:
0.5u(A) + 0.5u(C) = u(B) u(A) u(B) = u(B) u(
7.
Another look at portfolio choice
Highlights
diversification
comparative statics of optimal portfolio with respect to risks (cf wealth, risk aversion)
7.1
Comparative statics
Consider the model of portfolio choice from 4.2 again:
a risk averse invest
1
Economics of Uncertainty and Information
Sung Hyun Kim
Ewha Womans University
Fall 2016
Economics of Uncertainty and Information
2
Contents (tentative)
Part I Uncertainty and decision theory
1. Introduction to expected utility theory
2. Risk aversion
3.
Handout 1: Review of probability
Yichong Zhang1
1 School of Economics
Singapore Management University
Fall 2016
Econ 107 Handout 1 (SMU)
Introduction to Econometrics
Fall 2016
1 / 114
Outline
1
Discussion of syllabus
2
Introduction
3
Review of probability
Handout 1: Review of probability
Yichong Zhang1
1 School of Economics
Singapore Management University
Fall 2016
Econ 107 Handout 1 (SMU)
Introduction to Econometrics
Fall 2016
1 / 111
Outline
1
Discussion of syllabus
2
Introduction
3
Review of probability
Suggested Answers to Problem Set 1
Yubo Tao
August 27, 2016
Problem 1
e = E(X) E(X).
e Then by definition of X,
e we have
Proof. a. E(W ) = E(X X)
E(W ) = E(X) E(E(X|Z),
and by law of iterated expectations, we know E(E(X|Z) = E(X), and thus
E(W ) = E(X) E
ii? X and Z are two jointly distributed random varitiirie Suppose you kn "
the 1value. of Z,'b_ut not the 1Jalue of X. Let X :1 cfw_it a i Z) denote a gall
of the value of X using the information on Z? and iei ii?" I X - X denote
the error associated with
Economics of Uncertainty and Information
1. Introduction to expected utility
Sung Hyun Kim
Ewha Womans University
Fall 2016
1 / 16
Overview of the Course
1
decision theory: rational choice under uncertainty (8 weeks)
2
expected utility theory
risk aversio
8.
Comparative statics exercises
Highlights
comparative statics exercises using DARA and stochastic dominance
8.1
Portfolio choice
key formulas from the basic portfolio choice model (one risky asset)
e )] =
( x; u) E[u(w
0 ( x ; u) =
Z r
r
Z r
r
u(w + x
9.
Intertemporal model under certainty
Highlights
introduce time, ignore uncertainty
9.1
Modelling issues in intertemporal models
9.1.1
Time separability
agent lives from t = 0 to t = n, with consumption ct at date t
lifetime utility U (c0 , c1 , . . .
Money
Money is any asset that can be used in making
purchases
Examples include coins and currency, checking
account balances, and traveler's checks
Shares of stock are not money
Money has three principal uses
Medium of exchange
2. Unit of account
3. Store
East Asia Forum
Economics, Politics and Public Policy in East Asia
and the Pacific
http:/www.eastasiaforum.org
China's demographic bombshell
10th September, 2012
Author: Peter Drysdale, Editor, East Asia Forum
Asias high growth rates over the past few dec
East Asia Forum
Economics, Politics and Public Policy in East Asia
and the Pacific
http:/www.eastasiaforum.org
Population and the challenge of Chinese growth
9th September, 2012
Author: Cai Fang, CASS
In 1980, when the one-child policy was officially intr
6.
Measuring risk: stochastic dominance
Highlights
preference ranking of risks (cf risk aversion), also applicable to income inequality
for some class of utility functions, without specific functional forms
the classic mean-variance framework is a usef
4.
Wealth and risk aversion
Highlights
risk aversion as a function of wealth (for a given agent)
comparative statics of a simple portfolio choice model
constant risk aversion utility functions
4.1
Comparison of risk aversion across wealth levels
Arrow
3.
Measuring risk aversion
Highlights
comparison of risk attitudes between agents
what does it mean to say that an agent is more risk averse than another agent?
measures of risk aversion: Arrow-Pratt, Ross
behavioral characterizations of risk aversion
5.
A primer in probability theory
Highlights
an elementary introduction to probability theory
random variable, probability distribution, expected value, variance
computing CE, RP for constant risk aversion utility functions
5.1
Random variable
we mode
2.
Risk aversion
Highlights
introduction to key notions related to risk attitudes (at the undergraduate level)1
risk neutrality, risk aversion, insurance, diversification of risky investments
2.1
Certainty equivalent, risk premium
In the C = cfw_ A, B,
Suggested Answers to Problem Set 2
Yubo Tao
September 1, 2016
Problem 2
iid
iid
Proof. a. Define Xi := Yi /, then by Yi N (0, 2 ) for i = 1, 2, , n, we know Xi N (0, 1).
Thus,
E Yi2 / 2 = E Xi2 = Var(Xi ) + E (Xi )2 = 1.
P
P
iid
b. Note W = 1/ 2 ni=1 Yi2
Problem Set 2
ECON 107
Due Tuesday, Sept 6
1. Stock and Watson, Empirical exercise E2.1, p.109.
Instructions: The dataset that you will need for this exercise is available on the
companion website of Stock and Watson. Aside from your written answers to th
ECO2009
Q1.
EXERCISE 1
Prof. AHN
A random variable X has the following pdf:
x
f(x)
0
b
1
2b
2
3b
3
4b
4
5b
1) What is the value of b? Why?
2) Find Pr(X 3).
3) Find E(x).
Q2.
The joint probability distribution of X and Y is given by the following table: (F