GRA 6639 – Topics in Macroeconomicsbergholt.weebly.com/uploads/1/1/8/4/11843961/gra6639_lecture_9_-_an_intertemporal...GRA 6639 –Topics in Macroeconomics 10. THE SIMPLEST POSSIBLE

GRA 6639 – Topics in Macroeconomics

Lecture 9 Spring 2012

An Intertemporal Approach to the Current Account

Drago Bergholt ([email protected])

Department of Economics

mailto:[email protected]


2.

INTRODUCTION

Our goals for these two lectures (9 & 11):

- Establish an intertemporal (microfunded) equilibrium model suitable for a systematic

and rigorous study of the current account.

- Use the model to address the following issues:

a. What determines current account surpluses and deficits?

b. How does the current account respond to shocks?

c. Are current account deficits always bad?

d. How is the current account affected by fiscal policy?

e. What determines the world interest rate?

f. What explains the global imbalances that have emerged the last decade?

g. How long can deficits be sustained, and when is a country bankrupt (last lecture)?


3.

INTRODUCTION

Case studies:

- Hopefully, we will also have the time conduct a number of interesting case studies:

a. Why has Norway’s current account grown so much over the last decades?

b. How could (can) the U.S. current account deficit be so large, while the U.S. (and

world) real interest is so low?

c. Why did the world interest rate rise so much in the 1980’s?

d. What’s up with the Greeks (the current financial crises)? Or what separates

Greece from Australia?

e. What is the optimal fiscal policy rule in Norway (handlingsregelen)?


4.

INTRODUCTION

Readings

- Main reference:

Obstfeld, M. and K. Rogoff (1996): “Foundations of international macroeconomics”,

ch. 1.1-1.3 and 2.1-2.3.

- Others:

a. Bernanke, B. S. (2005): “The Global Saving Glut and the U.S. Current Account

Deficit”, speech March 10, 2005.

b. Blanchard, O. and G. M. Milesi-Ferretti (2009): “Global Imbalances: In

Midstream?”, IMF Staff Position Note 09/29.

c. IMF World Economic Outlook Sept. 2011: “Slowing Growth, Rising Risks”, ch.

1-2. Link: http://www.imf.org/external/pubs/ft/weo/2011/02/pdf/text.pdf.

http://www.imf.org/external/pubs/ft/weo/2011/02/pdf/text.pdf


5.

WHAT IS THE CURRENT ACCOUNT?

Definition of the current account

- The change in the value of net claims on the rest of the world.

- The net increase in foreign asset holdings.

Current account =

+ Trade account

Exports – imports of goods and services

+ Primary income account

Payments for use of labor and financial resources

+ Secondary income account

Redistribution (foreign aid, etc.)


6.

WHAT IS THE CURRENT ACCOUNT?

The canonical current account equation

- Let denote the value of an economy’s net foreign assets at the end of period

(in what period is a state variable?).

- Then, the current account at time , , is defined as:

or

- Net export: .

- Gross national product (GNP): .

- The accumulation equation updated:


7.

GLOBAL IMBALANCES

A bird’s view of global imbalances

Source: IMF World Economic Outlook,

September 2011


8.

GLOBAL IMBALANCES

A cross-country perspective


9.

GLOBAL IMBALANCES

A historical perspective: Current accounts in U.S. as share of GDP


10.

THE SIMPLEST POSSIBLE MODEL

Environment

- Small open economy where agents can borrow and lend at a world market interest

rate (the interest rate is given).

- The economy exists for two periods, .

- One (macro) consumption good in each period.

- Endowment economy, output in each period is given as and .

- No investments, no public sector.

- Representative household, population normalized to one.

- Perfect foresight economy (no uncertainty, no shocks).

- Several of these assumptions will be relaxed later.


11.


The representative household’s problem

- Lifetime utility:

( ) ( ), (1)

where is the discount factor, and ( ) , ( ) and ( ) .

- Financial wealth after first period (assume ): .

- Financial wealth after second period: ( ) .

- Why is ?

- The intertemporal budget constraint (combine the two above):

⏟

⏟

(2)


12.



- The representative household’s problem is to maximize (1) subject to (2).

- Solve (2) for :

( )( )

- Insert into (1):

( ) (( )( ) ⏟

)

- First order condition with respect to :

( ) ( )( )

⇒ ( ) ( ) ( ) (3)

- Equation (3) is the familiar (consumption) Euler equation.


13.



- Notice that (3) can be written as:

( )

( )

(4)

- Increasing consumption path if and only if ( ) (why?).

- Optimal consumption level can in principle be found by combining the Euler

equation and the intertemporal budget constraint.

- Special case: If

, the Euler equation implies and the BC yields:

⇒ ( )

(5)


14.


Determination of the current account

- The accumulation equation in our simple model:

, (6)

- Remember the period budget constraints:

Period 1:

Period 2: ( )

- Current account period 1:

- Current account period 2:

( )

- Implied lifetime trade balance: ∑ ( ) ( )


15.


The autarky interest rate

- Imagine the economy were closed (autarky).

- Equilibrium conditions: and .

- The interest rate that satisfies the Euler equation when is called the autarky

interest rate:

( )

( )

(7)

- A decline (increase) in (with fixed) raises (lowers) the autarky interest rate .

- Comparative advantage: Countries tend to import present consumption when autarky

interest rates (the price of present consumption) are high.

- Special case: implies

.


16.


Gains from open capital markets


17.


Gains from open capital markets

- Suppose

:

- Consumption levels in both periods are given by (5).

- The current account becomes:

( )

- The difference between present and future income (i.e. economic growth) is the

main determinant of the current account.

-

depends on the growth rate

, not on the absolute income level.


18.


Summing up

- The absolute income level should not be an important determinant of the current

account.

- Countries with high expected income growth would tend to have current account

deficits, countries with low (negative) growth would tend to have surpluses.

- Patient countries (high ) would run surpluses, impatient ones deficits.

- Current account deficits are not necessarily a bad thing!

- Gains from intertemporal trade as long as .

- Intertemporal trade makes consumption smoothing possible (why is that good?).

- Gains are obtained by trade with someone different from oneself.


19.


Does the model help explain…

- Big deficits in the U.S., large surpluses in China?

- Large surpluses among oil producers?

Extensions

- Investments.

- A public sector.

- Large economies (China and the U.S. are not small economies, they may affect the

world interest rate).


20.

GOVERNMENT CONSUMPTION AND TAXES

Environment

- Now we add a public sector. Assume that public spending is financed by a lump-

sum tax . The government can lend and borrow just as households.

- Household’s (period) utility is separable in private and public consumption (is this a

strong assumption?):

( ) ( )

- need not be equal to , but the lifetime public budget must be balanced.

- The government’s intertemporal budget constraint:

- Disposable (after tax) income: .


21.


Household’s intertemporal budget constraint

- Financial wealth after first period: .


- Household’s intertemporal budget constraint:

⇒

(

)

⇒

(

) (8)

- The Euler equation is unaffected because utility is separable.

- The current account:


22.


Fiscal policy and the current account

- Assume

. The Euler equation then implies and the BC yields:

(

)

⇒ ( )( ) ( )

- The current account:

( )( ) ( )

⇒ ( ) ( )

(9)

- Temporarily high (low) public spending will reduce (increase) the current account.

- Taxes or the government budget does not matter (Ricardian equivalence).


23.

INVESTMENT

Motivation

- So far we have treated output as an exogenous variable. This very unrealistic

assumption can be relaxed.

- Mechanism: Investment in factors used in production increases current output

possibilities.

- An important motivation for borrowing abroad is to finance investments. Norway in

the 1970’s is one example.


24.

INVESTMENT

Environment

- Production function:

( ) (10)

with ( ) , ( ) and ( )

- Assume that initial capital, which is given by nature, fulfills (realistic?).

- Law of motion for capital (we ignore depreciation):

(11)

- Remarks:

a. . Why?

b. ( ).

- Everything else is the same.


25.

INVESTMENT

The current account

- Change in total domestic wealth, i.e. national saving:

( )

- The current account (from the equation above and (11)):

(12)

- Saving:

(13)

- Combining (12) and (13), the current account can be written as:

(14)

- Equation (14) is yet another way to define the current account. Countries with lower

(higher) savings than investments run current account deficits (surpluses).


26.

INVESTMENT

The current account, saving and investment 2006 (percent of GDP)


27.

INVESTMENT

The intertemporal budget constraint

- Financial wealth after first period: .


- Household’s intertemporal budget constraint:

( )( )

⇒

⏟

⏟ ( )

(15)

- Now the representative household must decide how much to invest in addition to

how much to consume.


28.

INVESTMENT


- Notice that the intertemporal budget constraint can be rewritten as:

( )( ( ) ) ( )⏟ ( )

⏟

- Lifetime utility of the representative household, ( ) ( ), becomes:

( ) [( )( ( ) ) ( ) ](16)

- First order conditions:

: ( ) ( )( )

⇒ ( )

( )

: ( )( ) ( ) ( ) ( )

⇒ ( ) (17)


29.

INVESTMENT

The optimal saving plan

- Now there is two ways of saving for the future:

a. Lending in international financial markets with constant returns .

b. Investing in productive capital at home with diminishing returns.

- Equation (17), ( ) , suggests investing at home until the marginal return on

that investment is equal to returns in the capital market.

- Remark: The desired capital stock is independent of preferences.


30.

INVESTMENT

The production possibilities frontier

- The production possibilities frontier (assume ):

- Interpretation: Available technological possibilities for transforming period 1

consumption into period 2 consumption in autarky.

- Rewrite to a function of period 1 variables only:

( ) ( ) ( ) ( )

⇒ ( ( ) ) ( ) (18)

- Notice that:

( ) ( ) ,

( )


31.

INVESTMENT

Investment and the current account

- TBA


32.

INVESTMENT

Comparative statics in the model with investments

- What happens to the current account if:

a. The interest rate increases.

b. There is a positive productivity shock in , the productivity level in period 1.

c. There is a positive productivity shock in , the productivity level in period 2.

d. There is a higher predetermined capital stock (exogenous increase in wealth).

- Preliminaries: Assume . Then (10), (13), (14) and the capital law of

motion yields a current account with capital growth:

( ) ⏟

( )⏟

- This current account identity will be used for comparative statics.


33.

INVESTMENT

( ) ⏟

( )⏟

Case a: A raise in the interest rate

- Substitution effect on saving: Relatively cheaper consumption in period 2

⇒ higher saving ⇒

- Income effect on saving:

a. Net borrowers ( ): Income↓ ⇒ ↓ ⇒ ⇒

b. Net lenders ( ): Income ⇒ ⇒ ↓ ⇒ ↓

- Investment effect: ↓ (from (17)) ⇒

- Net effect: for borrowers, for lenders.


34.

INVESTMENT

( ) ⏟

( )⏟

Case b: Positive productivity shock in

- Saving effect: ⇒

Case c: Positive productivity shock in

- Consumption smoothing effect: ⇒ ↓ ⇒ ↓

- Investment effect: (from (17)) ⇒ ↓

- Net effect: ↓

- Lesson: Higher future productivity lowers today’s current account.


35.

INVESTMENT

( ) ⏟

( )⏟

Case d: Higher initial capital (exogenous increase in wealth)

- Income effect: Increases total wealth, parts of which give ⇒ ↓

- Investment effect: unaffected, so ↓ ⇒

- Last effect dominates because changes one for one with while changes less

than one for one.

- Net effect:

- Lesson: Countries with high capital stocks should tend to have surpluses.


36.

A TWO-REGION WORLD ECONOMY

Introduction

- So far we have looked at a small open economy which, by being small, takes the

world interest rate as given.

- Now it is time to abandon the small economy assumption and study how the world

interest rate is determined, and how it interacts with the current account.

Environment

- The world consists of two countries (regions), Home and Foreign (*)

- We ignore the public sector.

- We look at endowment economies first, but reintroduce production and saving later.

- The period utility, the Euler equation, and the budget constraint are as before (in both

countries).


37.


Global market clearing

- Market clearing in the endowment economy:

- Implied world saving:

- Implied world current account ( and

without investment):

- Walras’ law: Consider an economy with markets. If markets are in

equilibrium, then the last market must also be in equilibrium.

- By Walras’ law the world economy is in equilibrium if:

(19)


38.


Savings and the world interest rate

- The world interest rate is determined by and (the two countries’ net supply of

period 1 consumption). For now, we assume

and

.

- This gives the following world interest rate in equilibrium ( ):


39.


Savings and the world interest rate

- Notice that represents the price of present consumption in terms of future

consumption, i.e. the price of a period 1 surplus country’s export good in terms of its

import good.

- In the figure, clears markets in the sense that Home’s supply (lending) of period 1

consumption to Foreign is equal to Foreign’s demand (borrowing) for period 1

consumption from Home.

- Comparative statics: What happens if increases? What happens if increases?

(Hint: refer to case b. and c. in the small economy model)

- Remark: When drawing the figure, we assumed that

and

. That

assumption is analyzed next.


40.


Consumption and the world interest rate

- is Home’s net supply of period 1 consumption to Foreign, while is

the equivalent supply from Foreign.

- Since , the relationship between (Home) saving and the world interest

rate in our two-period model is:

- Thus, to find

, we need to identify how consumption depends on the interest rate

( is treated as exogenous for now).


41.


A small detour: The elasticity of intertemporal substitution

- From the Euler equation (derivation in class):

( )

( )

⇒ ( ) ( )

( )⏟ ( )

( ) ( )

( )⏟ ( )

( ) (20)

- Definition of the elasticity of intertemporal substitution ( ):

( ) ( )

( ) (21)

- The elasticity of intertemporal substitution is constant when utility is isoelastic:

( )

where and ( ) ( ) (22)


42.


The shape of the savings schedule

- From the budget constraint (2) and the Euler equation (4):

( ) ( ) [( )( ) ]

- Implicitly differentiating with respect to gives (derivation in class):

( ) ( ) ( )( )

( ) ( ) ( ) (23)

- Assume that period utility is given by (22). Then (23) becomes (derivation in class):

( )

(24)

- Result: A rise in the world interest rate has an ambiguous effect on Home’s period 1

consumption.


43.


The effects on saving and consumption of a rise in

- Note that:

( )

- If Home is a borrower in period 1, , then a rise in unambiguously leads to

higher saving and lower consumption.

- As rises however, Home must eventually become a lender, i.e. . If is not

that much higher than , a rising still increases saving and lowers consumption.

- When becomes sufficiently high, saving can actually drop and consumption

increase.


44.


Saving, the current account and the world interest rate revisited


45.


Optimal consumption growth path

- When utility is isoelastic the Euler equation (3) can be written as:

( ) (25)

- Note that the implied optimal growth rate of consumption is:

( )

Remarks:

a. Optimal consumption growth is positive if ( ) .

b. Optimal consumption growth is high in absolute value if is high.

What is the intuition behind these results?


46.


Substitution, income and wealth effects of an interest rate change

- Insert (25) into the budget constraint (2) to find optimal period 1 consumption:

( ) (

) (26)

- Substitution effect: Higher means that the price of current consumption in terms of

future consumption rises. That reduces consumption today (i.e. more saving).

- Income effect: Higher allows higher future consumption. Some of this positive

income effect is spilled over to period 1 through higher consumption today.

- The tension between the two effects above is reflected in ( ) .

- Wealth effect: Higher lowers lifetime income

and reinforces the

substitution effect in lowering current consumption and raising saving.


47.

INVESTMENT, SAVING AND THE METZLER DIAGRAM

Environment

- We now introduce investment to the two-region world economy model.

- Production in Home and Foreign:

( ) and

( )

- We continue to abstract from government sector.

- Besides being large economies, everything else is the same (as in the small economy

model with investment).


48.


Equilibrium

- Equilibrium requires:

- Using (13) this is equivalent to:

- Using (14) there is an implied mutual consistency between current accounts:


49.


Investment schedules

- The investment schedules are given as in (17) (where we use that ):

( ) and

(

)

- A rise in leads to lower and ( and

are predetermined as before).


50.


The shape of the savings schedule

- The intertemporal budget constraint in Home is still (15) (but no government sector).

- The budget constraint (15) combined with the Euler equation gives:

( ) ( ) {( )[ ( ) ] ( ) }

- Implicitly differentiating with respect to in the general case (derivation in class):

( ) ( ) ( )[ ( ) ]

( ) ( ) ( )

- In the isoelastic utility case this becomes very similar to (24):

( )

- Thus, given current account balances, the slope of the savings schedule identical to its

counterpart in the endowment case.


51.


Saving, the current account and the world interest rate revisited


52.


Application 1: An increase in Home’s impatience

- Suppose households in Home become more impatient, represented by a fall in .

- By inspecting the Euler equation we find that lower implies less period 2

consumption relative to period 1 consumption.

- in figure shifts to the left.

- increases to restore equilibrium in financial markets.

- Home saving and investment falls, Foreign investment falls, Foreign saving increases.


53.


Application 2: A rise in Home’s future productivity

- Suppose suddenly is expected to be higher.

- What is the effect on the investment schedule?

( )

⇒ ( )

( )

⇒

|

( )

( )

⇒ The investment schedule skifts outwards.

- What is the effect on the saving schedule?

responds to shifts in productivity as if there are purely exogenous output changes.

⇒ Higher leads to a shift in inwards.


54.


Application 2: A rise in Home’s future productivity

- Assume initially balanced current accounts.

- Home’s current account becomes negative.

- Foreign’s current account becomes positive due to more saving and less investment.

- The world interest rate increases.


55.

GLOBAL IMBALANCES REVISITED

Case study: The global saving glut and the U.S. deficit

- Puzzle: How can the U.S. current account deficit be so large, while the U.S. (and

world) real interest rate is so low?


56.



- Traditional view: “U.S. consumers save too little”.

- But why then the low interest rates?

- Bernanke (2005): A significant increase in global supply of savings can explain the low

level of world interest rates and the U.S. current account deficit.


57.



- Bernanke (2005): “The global saving glut and the U.S. current account deficit”

a. Increase in global saving due to:

- Strong motives for saving in countries with ageing populations (e.g. Germany

and Japan).

- High commodity prices has triggered savings in many (developing) countries.

- Low prospective returns to domestic investment in many industrialized

countries (due to e.g. slowly growing workforces and high capital-labor ratios).

b. Low U.S. saving because of high equity and house prices. Also, anticipations of

high productivity in the U.S. based on experiences from the 1990’s.

- How can we understand this using our two-country model (sketch in class)?


58.



- Important issue: Is the U.S. current account deficit sustainable?

- That is one of the topics next time.


59.

EXERCISES

1. Discuss reasons why a country may find it optimal to run a current account deficit.

2. Consider the two-country endowment model studied in class. Home’s utility is:

( ) ( )

a. Show that Home consumption in period 1 is:

(

)

b. Show that Home saving in period 1 is:

( )( )

c. Compute the interest rate when Foreign has the same preferences, but possible

different endowments and

.

Documents

GRA 6639 – Topics in Macroeconomicsbergholt.weebly.com/uploads/1/1/8/4/11843961/gra6639_lecture_9_-_an_intertemporal...GRA 6639 –Topics in Macroeconomics 10. THE SIMPLEST POSSIBLE