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)

– Warwick.mckibbin@anu.edu.au

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 u

t + ( 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)

et = tT (r u

s - r is + s ) ds + eT

An Alternative Interpretation

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

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@.  

(2)

The capital stock accumulates according to the following equation, where i is the rate of investment and δ is the depreciation rate:

(3)

 (4)

(5)

 (7)

Notice that investment enters gross of adjustment costs.

dte t-G(c(t))0

=U

a)F(k, = q

)k-(i = dt

dk

k)kH(i,=h

0 > H i

h+c=q

The Single Agent Ramsey Case

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:

(8)

(9)

 (10)

(11)

where μ is the multiplier associated with the capital stock.

= HG ic

kHG + H) - F(G - i)-+( = dtd

kckc

k)kH(i, + c = a)F(k,

)k-(i = dt

dk

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:

(12)

and(13)

Eliminating dc and rearranging gives:(14)

 

where Γ is given by:

(15)

 The left hand side of (14) is the ratio of the change in investment

expenditure, , to the change in the household=s income, .

0 = diHG + dcHG iicicc

kdiH + dc = daF ia

- 11

= daF

kdiHa

i

kHGHG =

2

icc

iic

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:

(16)

(17)

(c) = G(c) ln

a - Ak = a)F(k,

In addition, suppose the investment cost function takes the form:

(18)i)+i(1 = k)H(i,

The Decentralized Case

• Single Household

• Single Firm

Suppose the representative household maximizes the following intertemporal utility function:

(19)  It will be subject to the lifetime budget constraint shown below:

(20) where R(s) is the long term interest rate:

(21) 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)

 

dse(c) = U t)-(s-

t

ln

W(t) = dsec(s) t)-R(s)(s-

t

dvt-s

r(v) = R(s)

s

t

dseD(s) = W(t) t)-R(s)(s-

t

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:

(23)W(t) = c(t)

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:

(24) where dividends D(s) are equal to output less taxes (a) and

investment spending (h):(25)

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:

(26)

Finally, the capital stock evolves according to the accumulation equation:

(27)

dseD(s) R(s)s-

0

h - a - k = D

i)k+i(1 = h

)k-(i = dtdk

Simulate the model

ρ = 0.05; δ = 0.06; α = 0.3; A = 2.95; φ = 1. a = 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

AssetsWith 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:

(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 Ek

j is the exchange rate between the currencies of the two

countries.

E

/dtdE + i = i j

k

j

k

jk

Results

• Temporary Rise in Home country TFP growth

• Permanent Rise in Home Country TFP growth

Real Output and Consumption: Home Country

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

% d

ev

iati

on

fro

m B

ase

Output Consumption

Saving and Investment: Home Country

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

%G

DP

de

via

tio

n f

rom

Bas

e

Saving Investment

Real Private Consumption: Home and Foreign Countries

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

% d

ev

iati

on

fro

m B

ase

Home Foreign

Real Output: Home and Foreign Countries

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

% d

ev

iati

on

fro

m B

ase

Home Foreign

Figure 1: Temporary Rise in Home Country TFP

Figure 2: Temporary Rise in Home Country TFP

Current Account and Trade Balance: Home Country

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

% G

DP

de

via

tio

n f

rom

Bas

e

Current Account Trade Balance

Real and Nominal Exchange Rate: Home Country

-1

-0.5

0

0.5

1

1.5

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

% d

ev

iati

on

fro

m B

ase

Real Nominal

Wages and producer prices: Home Country

-2

-1.5

-1

-0.5

0

0.5

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

% G

DP

de

via

tio

n f

rom

Bas

e

Wages Producer Prices

Short and Long Term Interest Rates: Home Country

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20%

po

int

de

via

tio

n f

rom

Bas

e

Short Long

Figure 3:Permanent Rise in Home Country TFP

Real Output and Consumption: Home Country

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

% d

ev

iati

on

fro

m B

ase

Output Consumption

Saving and Investment: Home Country

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

%G

DP

de

via

tio

n f

rom

Bas

e

Saving Investment

Real Private Consumption: Home and Foreign Countries

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

% d

ev

iati

on

fro

m B

ase

Home Foreign

Real Output: Home and Foreign Countries

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

% d

ev

iati

on

fro

m B

ase

Home Foreign

Figure 4: Permanent Rise in Home Country TFP

Current Account and Trade Balance: Home Country

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

% G

DP

de

via

tio

n f

rom

Bas

e

Current Account Trade Balance

Wages and producer prices: Home Country

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

% G

DP

de

via

tio

n f

rom

Bas

e

Wages Producer Prices

Short and Long Term Interest Rates: Home Country

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

% p

oin

t d

ev

iati

on

fro

m B

ase

Short Long

Real and Nominal Exchange Rate: Home Country

0

0.5

1

1.5

2

2.5

3

3.5

4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

% d

ev

iati

on

fro

m B

ase

Real Nominal

Summing Up

• Modern macro theory when modified to deal with real world rigidities can help us understand the real world