Download Econ8009 International Monetary Economics

Econ8009 International Monetary
Economics
Warwick J McKibbin
Lectures
• 1. Puzzles in International Macroeconomics
• 2. Modeling the International Economy
Using Dynamic Intertemporal GE models
• 3. Some applications
– “International Capital Flows, Financial Reform
& Consequences of Changing Risk Perceptions
in APEC Economies”
Logistics
• Tutorial
– Wednesday Oct 17
– Running simulations of recent events
• Japanese macroeconomic policy
• Sept 11 Terrorist Attacks
• Office Hours
– Coombs room 7101
– Thursday 1.30 to 5pm (please email for appointment)
– [email protected]
Structure of this lecture
• Discuss some puzzles (from Obstfeld and
Rogoff)
• Introduce simplest Intertemporal GE model
– Ramsey model with adjustment costs
– Decentralized Ramsey model
• Show how to extend to two country model
(a simplified G-Cubed model) and how
some stickiness helps the puzzles.
Puzzles in International
Macroeconomics
• Puzzles found throughout the theoretical literature
are because we base our understanding on simple
models whereas the world is more complicated
– Why use simple models?
– What can be done?
• Simple models are not wrong but are incomplete
– stickiness
– intertemporal features
– general equilibrium
Some Puzzles
• Home Bias in trade
• Feldstein-Horioka Puzzle
– Saving and investment highly correlated
• Home bias in equity portfolios
• Low correlation between consumption
across countries
• Failure of Purchasing Power Parity
• Exchange rate disconnect puzzle
Home Bias in Trade
• McCallum (1995) – trade between Canadian
Provinces 20 times greater than with the US
• Explanations
– Classic Armington (1967) model
• Goods from different countries are different
– Frictions
• Exchange risk
• Shipping costs
• Tariffs
Feldstein- Horioka
• National Saving and investment move
together
• Current accounts are small relative to scale
of saving and investment
– Suggest a surprising lack of capital mobility
• Doesn’t seem to fit within country
experience
Feldstein- Horioka
• Explanations
– Developing countries restricted from borrowing
– Nature of shocks
Home Equity Bias
• Most wealth is held in home assets
– French and Poterba (1991) found Americans
held 98% of equity wealth at home
• Diversification suggests much too high.
• Explanations
– Trade versus non trade goods.
International Consumption
Correlations
• International risk pooling suggest that
country specific income shocks should not
affect consumption and consumption
growth acroiss countries should be highly
correlated.
Purchasing Power Parity
• Weak linkage between nominal exchange
rates and relative price levels
• Real exchange rates fluctuate
Exchange Rate Disconnect
• Exchange rates don’t seem to be connected
to fundamentals
Uncovered interest parity
• r it = r ut + ( t e t+1 - et ) + t
• r
= real interest rate
• e
= log of real exchange rate (+=deprec)
• t e t+1 = expected exchange rate in period t+1
given information in period t
• t = wedge (risk premium)
An Alternative Interpretation
et = tT (r us - r is + s ) ds + eT
Obstfeld and Rogoff Solution
• Costs in international trade
• But many other explanations as well.
Macroeconomic Volatility in
General Equilibrium
• McKibbin and Wilcoxen (1998)
The Issue
• Do the various insights we get from partial
equilibrium theory hold in general
equilbrium?
• Fundamental theories
– Consumption smoothing
– Investment smoothing
The Issue
• Together in a closed economy they are
inconsistent!
Illustration
• Single agent Ramsey model
• Decentralized model
The Single Agent Ramsey Case

U =  G(c(t))e-t dt
0
where c(t) is consumption at time t, ρ is the rate of time preference and G is a function giving instantaneous utility, or Afelicity@.
q = F(k, a)
(2)
The capital stock accumulates according to the following equation, where i is the rate of investment and δ is the depreciation rate:
dk
= (i -  )k
dt
h = H(i, k)k
Hi >0
q = c+h
Notice that investment enters gross of adjustment costs.
(3)
(4)
(5)
(7)
Maximizing the household=s utility function subject to the four constraints above is an optimal
control problem. Setting up the Hamiltonian and taking first-order conditions yields the following:
Gc H i = 
(8)
d
=  (  +  - i) - G ( F - H) + G H k
dt
c
k
F(k, a) = c + H(i, k)k
dk
= (i -  )k
dt
where μ is the multiplier associated with the capital stock.
c
k
(9)
(10)
(11)
Now consider what happens at the moment
of implementation of an anticipated change
in a. The change could be a shift in
technology or, more abstractly, a change in
exhaustive government spending.
The relationship between the change in a and consumption can be seen by
totally differentiating (8) and (10) holding μ and k constant. This produces the
following expressions:
Gcc H i dc + Gc H ii di = 0
(12)
and
F a da = dc + H i kdi
(13)
Eliminating dc and rearranging gives:
H i kdi = 1
F a da 1 - 
(14)
where Γ is given by:
G
c H ii
=
2
Gcc H i k
(15)
The left hand side of (14) is the ratio of the change in investment expenditure, ,
to the change in the household=s income, .
The effect of adjustment costs can be seen clearly in the model=s
phase diagram in (K,C) space. To make the discussion somewhat more
concrete, suppose the felicity index G and the production function F take
the forms below:
G(c) = ln(c)

F(k, a) = Ak - a
(16)
(17)
In addition, suppose the investment cost function takes the form:
H(i,k) = i(1 + i)
(18)
The Decentralized Case
• Single Household
• Single Firm
Suppose the representative household maximizes the following
intertemporal utility function:
(19)

U =  ln(c) e-  (s-t) ds
t
It will be subject to the lifetime budget constraint shown below:

- R(s)(s -t)
c(s)
ds = W(t)

e
(20)
t
where R(s) is the long term interest rate:
r(v)
R(s) = 
dv
s-t
s
(21)
t
and W(t) is household wealth at time t, which is equal to the
present value of dividends to be paid by the firm:

(22)
- R(s)(s -t)
W(t) =  D(s) e
t
ds
The first order conditions for this problem can be rearranged to
give the familiar expression below showing how consumption in time t is
related to wealth:
c(t) = W(t)
(23)
Equation (23), which is familiar from the partial equilibrium version of
the permanent income hypothesis, hints at the results to come. Since
(23) holds at all points in time, it must hold immediately before and after
implementation of an anticipated event. Since we have shown that in the
presence of adjustment costs, consumption will jump at implementation,
it must be the case that wealth jumps as well. Since the path of earnings
before and after the tax change is known with certainty in advance, the
only way for wealth to jump is for there to be a discrete jump in the long
run interest rate.
Suppose the firm, for its part, maximizes the present value of its
dividend stream:

- R(s)s
(24)
ds
 D(s)
0
e
where dividends D(s) are equal to output less taxes (a) and
investment spending (h):
(25)

D= k - a - h
As before, we assume that adjustment costs mean the firm must
buy more capital goods than it will actually be able to install. Using the
quadratic investment cost function from above, the cost of investing at
rate i is:
h = i(1 + i)k
(26)
Finally, the capital stock evolves according to the accumulation
equation:
dk
= (i -  )k
(27)
dt
Simulate the model
ρ
δ
α
A
φ
a
= 0.05;
= 0.06;
= 0.3;
= 2.95;
= 1.
= 1.2.
These values were chosen so that the model would loosely approximate
the 1995 U.S. economy: GDP is about 7 trillion dollars, consumption is
4.6 trillion, and investment is about 1.1 trillion.
Shock is 30% rise in a for 10 years
Figs.def
Conclusions
• Conflict between partial and general
equilibrium theoretical insights
• Combining standard intertemporal models
of consumption and investment shows
excess volatility
• Asset prices jump as anticipated events
• Open economy implications
Expand the simple model
• Households max utility (made up of goods
from both countries) subject to
intertemporal budget constraint
• Firms maximize value subject to production
technology and intertemporal budget
constraint
• Government provide public goods.
Extensions
• Sticky wages
– Arbitrary adjustment over time
• Add money
– Technology combined with goods before use
• Trade in assets
– Assume all asset perfect substitutes so equate
expected returns
Assets
With free mobility of capital, expected returns on loans denominated
in the currencies of the various regions must be equalized period to
period according to a set of interest arbitrage relations of the following
form:
j
k
/dt
dE
ik = i j +
j
Ek
(1)
where ik and ij are the interest rates in countries k and j, k and j are
exogenous risk premiums demanded by investors (calibrated in the
baseline to make the model condition hold exactly with actual data),
and Ekj is the exchange rate between the currencies of the two
countries.
Results
• Temporary Rise in Home country TFP
growth
• Permanent Rise in Home Country TFP
growth
Figure 1: Temporary Rise in Home Country TFP
Real Output and Consumption: Home Country
Saving and Investment: Home Country
1.4
0.8
1.2
0.7
0.6
%GDP deviation from Base
% deviation from Base
1
0.8
0.6
0.4
0.2
0
-0.2
1
2
3
4
5
6
7
8
9
0.5
0.4
0.3
0.2
0.1
0
-0.1
10 11 12 13 14 15 16 17 18 19 20
1
2
3
4
-0.4
7
8
Consumption
9
10 11 12 13 14 15 16 17 18 19 20
Saving
Real Private Consumption: Home and Foreign Countries
Investment
Real Output: Home and Foreign Countries
0.8
1.4
0.7
1.2
0.6
1
0.5
% deviation from Base
% deviation from Base
6
-0.3
Output
0.4
0.3
0.2
0.1
0.8
0.6
0.4
0.2
0
0
-0.1
5
-0.2
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.2
-0.2
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.4
Home
Foreign
Home
Foreign
Figure 2: Temporary Rise in Home Country TFP
Current Account and Trade Balance: Home Country
Real and Nominal Exchange Rate: Home Country
0.05
2
0.04
1.5
0.02
0.01
0
-0.01
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.02
% deviation from Base
% GDP deviation from Base
0.03
1
0.5
0
1
-0.03
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.5
-0.04
-0.05
-1
Current Account
Trade Balance
Real
Short and Long Term Interest Rates: Home Country
1
0.4
0.5
0.2
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.5
-1
-1.5
% point deviation from Base
% GDP deviation from Base
Wages and producer prices: Home Country
Nominal
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.2
-0.4
-0.6
-0.8
-2
-1
Wages
Producer Prices
Short
Long
Figure 3:Permanent Rise in Home Country TFP
Real Output and Consumption: Home Country
Saving and Investment: Home Country
2
1.2
1.8
1
%GDP deviation from Base
% deviation from Base
1.6
1.4
1.2
1
0.8
0.6
0.4
0.8
0.6
0.4
0.2
0.2
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Output
1
2
3
4
5
6
7
8
Consumption
9
10 11 12 13 14 15 16 17 18 19 20
Saving
Real Private Consumption: Home and Foreign Countries
Investment
Real Output: Home and Foreign Countries
1.6
2
1.4
1.8
1.6
% deviation from Base
% deviation from Base
1.2
1
0.8
0.6
1.4
1.2
1
0.8
0.6
0.4
0.4
0.2
0.2
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Home
Foreign
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Home
Foreign
Figure 4: Permanent Rise in Home Country TFP
Current Account and Trade Balance: Home Country
Real and Nominal Exchange Rate: Home Country
0.2
4
0.18
3.5
3
0.14
% deviation from Base
% GDP deviation from Base
0.16
0.12
0.1
0.08
0.06
2.5
2
1.5
1
0.04
0.5
0.02
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Current Account
1
2
3
4
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Real
Wages and producer prices: Home Country
Nominal
Short and Long Term Interest Rates: Home Country
1.5
0
1
-0.05
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.1
0.5
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-0.5
-1
-1.5
% point deviation from Base
% GDP deviation from Base
5
Trade Balance
-0.15
-0.2
-0.25
-0.3
-0.35
-2
-0.4
-2.5
-0.45
Wages
Producer Prices
Short
Long
Summing Up
• Modern macro theory when modified to
deal with real world rigidities can help us
understand the real world