Fixed, float or flaky
why should we care?
Does it matter?
Denmark has a peg
Sweden has changed several times, now floating
Finland changed several times, joined euro in 2002
Hill of beans?
Much more important for countries with
fiscal or monetary volati
ECON 401: Matrices
Siyang Xiong
Rice University
August 23, 2011
Xiong (Rice University)
ECON 401
August 23, 2011
1 / 24
Matrice
n equations of m variable
a11 x1 C a12 x2 C . C a1m xm D b1
(1)
a21 x1 C a22 x2 C . C a2m xm D b2
.
an 1 x1 C an 2 x2 C . C anm
Deriving the
DD Schedule
1
Shifting
exogenous DD
parameters:
G, T, I
2
ShortRun Equilibrium in Asset Markets
We consider the same two sets of asset markets:
1. Foreign exchange markets
interest parity represents equilibrium:
R = R* + (Ee E)/E
1. Money ma
Modeling Y
D = C + I + G + CA
C = C(YD,r)
1
2
Modeling Y
D = C + I + G + CA
C = C(YD,r)
I = I(r) = investment, with a negative coefficient on
r
G = government spending will be assumed
exogenous
CA = CA(q, YD,r) = current account balance
CA EX IM;
Monetary Approach to FX
Real Exchange Rate
Approach to FX
1
Real Exchange Rate
The real exchange rate is the rate of exchange for goods and services
across countries.
As opposed to the nominal exchange rate, which includes financial
flows.
It describes th
Monetary Approach to FX
Real Exchange Rate
Approach to FX
1
Exchange Rate Models: SR vs.
LR
Models predict how exchange rates behave.
SR model: Keynesian story about
money
money > interest rates > exchange rate
LR model: Classical story about money
money
Testing PPP with Big Macs
The Law of One Price and PPP say a Big
Mac should cost the same anywhere,
once converted to a common currency
Why doesnt this work in practice?
Testing PPP with Big Macs
The Law of One Price and PPP say a Big
Mac should cost t
Permanent increase in
US money supply
A permanent shift in the US money supply
changes exchange rate expectations, so
there are 2 changes in the short run to
consider.
With longrun money neutrality, people will
expect prices, including exchange rates t
Money supply and money
demand
Determination of the Equilibrium Interest Rate
Ms/P = L(R,Y)
2
Model for the FX market equilibrium:
Uncovered interest parity
R$ = R + (Ee$/ E$/)/E$/
Linking the money market and
exchange rate market
Federal
Federal
Reserve
R
Covered Interest Parity
Same as UIP, but with forward rates instead of expected
exchange rates
R$ = R + (F$/ E$/)/E$/
where F$/ is the forward exchange rate.
(F$/ E$/)/E$/ is the forward premium: In practice it should be
close to the difference in inter
Huge growth in FX market turnover
Only 13% of the market are nonfinancial entities (corporate, govt
and retail)
80% of trading within about 10
banks.
USD dominance, AUD
ascendence, CNY and HKD stories
later
London is the major FX market.
Spot Rates and Fo
Labor Mobility in Action
MA share of US
employment
MA
unemployment
rate
US
unemployment
rate
1986
2.7
4
7
1991
2.48
8.8
6.8
1996
2.43
4.6
5.4
Source: Krugman blog, June 24, 2012
Divergent Real Interest Rates in the Euro Zone
Source:Datastream.
3 Optimal N
Econ 421 Lecture 20, Nov 13, 2012
Is Europe an OCA?
What are the key features you want to consider to determine an OCA from the
theory we learned last class?
o Integration of goods and services trade and factor mkts: K and L
o Notice the theory doesnt me
Inflation Convergence for Six Original EMS
Members, 19782009
Source:CPIinflationratesfromInternationalMonetaryFund, InternationalFinancialStatistics.
Members of the Euro Zone
ECON 401: Determinant and Inverse of a Matrice
Siyang Xiong
Rice University
August 25, 2011
Xiong (Rice University)
ECON 401
August 25, 2011
1 / 20
Matrice
n equations of n variable
a11 x1 C a12 x2 C . C a1n xn D b1
(1)
a21 x1 C a22 x2 C . C a2n xn D b2
.
ECON 401: Utility function
Siyang Xiong
Rice University
August 29, 2011
Xiong (Rice University)
ECON 401
August 29, 2011
1 / 12
A classic optimization problem in Economics
There are n goods;
income: I 2 RC ;
consumption: x D .x1 , x2 , ., xn / 2 Rn ;
C
ut
ECON 401 Optimization problems
Siyang Xiong
Rice University
August 31, 2011
Xiong (Rice University)
ECON 401
August 31, 2011
1 / 22
Maxima, Minima, Suprema, Inma
Given a nonempty A
R,
max A D fa 2 A : a
b for any b 2 Ag ;
min A D fa 2 A : a
b for any b 2
1
2
3
Adding r back in
+


+  +
Y = C(YD,r) + I(r) + G + CA(q, YD,r)
The impact of r on C and CA is small relative to I
Now R* and Ee shift DD
With sticky prices, R = r
Because of UIP, R = R* + (Ee E)/E = R* + Ee/E 1
So I is a decreasing function of
PREFERENCE AND REVEALED PREFERENCE
Siyang Xiong
Rice University
September 29, 2011
Xiong (Rice University)
ECON 401
September 29, 2011
1 / 21
consumer preferences
Suppose we are given a choice set X .
Let x ; y ; z denote elements in X , i.e., x ; y ; z 2
PREFERENCES
Siyang Xiong
Rice University
September 27, 2011
Xiong (Rice University)
ECON 401
September 27, 2011
1 / 14
consumer preferences
Suppose we are given a choice set X .
Let x ; y ; z denote elements in X , i.e., x ; y ; z 2 X .
I have a binary re
ECON 401: Theorem of Khun and Tucker
Siyang Xiong
Rice University
September 25, 2011
Xiong (Rice University)
ECON 401
September 25, 2011
1 / 18
Another example
A consumer with a utility function given by u .x1 , x2 / D x1 x2 has an
income of 100. The unit
ECON 401: Theorem of Khun and Tucker
Siyang Xiong
Rice University
September 20, 2011
Xiong (Rice University)
ECON 401
September 20, 2011
1 / 21
An example
a rm uses one iput x . 0/ to produce two outputs y . 0/ , z . 0/
by the following technology:
y2 C z
ECON 401: Theorem of Khun and Tucker
Siyang Xiong
Rice University
September 18, 2011
Xiong (Rice University)
ECON 401
September 18, 2011
1 / 17
Constrained optimization
max f .x / s.t. g .x / D 0 and/or h .x /
0.
Use the Theorem of Lagrange to solve
max f
ECON 401: The Envelope Theorem
Siyang Xiong
Rice University
September 15, 2011
Xiong (Rice University)
ECON 401
September 15, 2011
1/9
Sensitivity analysis: the Envelope Theorem
Consider an unconstrained optimization problem in parametric form:
max f .x ,
ECON 401: Theorem of Lagrange: examples
Siyang Xiong
Rice University
September 20, 2011
Xiong (Rice University)
ECON 401
September 20, 2011
1 / 16
examples: consumption Vs leisure
agents get utility from consumption goods x and leisure l : u .x , l /;
for
ECON 401: Theorem of Lagrange
Siyang Xiong
Rice University
September 11, 2011
Xiong (Rice University)
ECON 401
September 11, 2011
1 / 22
Constrained optimization
max f .x /
s.t. g .x / D 0,
and/or h .x /
Xiong (Rice University)
ECON 401
0.
September 11, 2
ECON 401: Quadratic forms and semidenite
matrices
Siyang Xiong
Rice University
September 11, 2011
Xiong (Rice University)
ECON 401
September 11, 2011
1 / 22
identify semidenite matrices
a bijection
f1, 2, ., ng.
: f1, 2, ., ng ! f1, 2, ., ng is called a p
ECON 401: Quadratic forms and semidenite
matrices
Siyang Xiong
Rice University
September 8, 2011
Xiong (Rice University)
ECON 401
September 8, 2011
1 / 15
unconstrained maximization
Throughout the lecture, we consider f : Rn ! R.
Consider the optimization
ECON 401: Optimization
Siyang Xiong
Rice University
August 31, 2011
Xiong (Rice University)
ECON 401
August 31, 2011
1 / 15
examples of optimization continued: consumption Vs
leisure
agents get utility from consumption goods x and leisure l : u .x , l /;