international economics, lecture 1 intertemporal trade and ...international economics, lecture 1...

International Economics, Lecture 1Intertemporal Trade and the Current Account

Dan WalesUniversity of Cambridge

London School of Economics1 October, 2018

Course Overview (Michaelmas Term)

I Three broad topics in international macroeconomics.

1. Real: Current account and international RBC.

2. Nominal: Monetary policy and international pricing.

3. Financial crises and the nominal exchange rate.

I Objectives:I Recent developments in international macroeconomics.

I Develop tools and ideas for writing research papers.

I Deliverables:I Weekly problem sets (two marked at random during the term).

I Exam (January).

I Extended essay (should you choose so).

Cumulative Current Account Balances

Notes: Data taken from IMF April 2018 WEO, (1980 - 2017). Methodology asin Schmitt-Grohe et al. (2016).

Why Focus on the Current Account?

I Indicator of sustainability.I Conventional wisdom: Persistent current account deficits

above 5% of GDP should be alarming.I Reversals are usually associated with slower income growth...

I ...and large currency depreciations.

I Can this country generate future trade surpluses to repay debtburden? Ultimately: is the country solvent?

I Indicator of macroeconomic imbalances.I Clearly highlights which countries are reliant on external

financing, and imbalance between countries.

I But causality is unclear.

I Highlight intertemporal trade.

Current Account Balances

1995 2000 2005 2010 2015 2020 2025

-6

-4

-2

0

2

4

6

8

10

Source: IMF April 2018 WEO.

Plan

Basic Definitions

Two Period Endowment Model (SOE)

Two Period Production Model (SOE)

Two Period Model (Two Country)

Dynamics of the Current Account

Stochastic Infinite Horizon Model

Engel and Rogers (2006)*

Basic Definitions

I Balance of Payments.I Records transactions with the rest of the world.

I Double entry bookkeeping, as each transaction enters twice.

I Comprised of three separate accounts:

BoP = CA + KA− FA = 0.

I Current Account (CA):I Trade balance and net factor income from abroad.

cat ≡ nxt + rbt−1.

I Capital Account (KA):I Net unilateral capital transfers from abroad (Small).

I Financial Account (-FA):I Net acquisition of foreign financial assets. fat ≡ bt − bt−1.

Three Current Account Relationships

I Definitional:cat = nxt + rbt−1 :

as the trade balance and net factor income from abroad.

I Change in net foreign assets:

cat = fat = bt − bt−1,

which uses the BoP relationship (intertemporal approach).Arises as unilateral payments in the capital account are small.

I Difference between savings and investment:

yt = ct + it + gt + nxt ,

yt = ct + it + gt + cat − rbt−1,

cat = rbt−1 + yt − ct − τtsp

+ τt − gtsg

−it ,

which uses the GDP and BoP identities.

Two Period Endowment Model (SOE)

I Small Open Economy (SOE) takes world interest rate, r , asgiven.

I Representative household maximises lifetime utility:

U = u(c1) + βu(c2),

where ct represents real consumption, β ∈ (0, 1) is thediscount factor and the period utility function, u(·), obeysstandard properties [u′(·) >, u′′(·) < 0].

I Subject to period-t budget constraints:

bt + ct = yt + (1 + r)bt−1,

for t = {1, 2} where b0 = b2 = 0 and endowments, yt , areperishable.

Intertemporal Budget Constraint

I Write down the period-t constraints:

b1 + c1 = y1 + (1 + r)b0,

b2 + c2 = y2 + (1 + r)b1.

I Recall b0 = b2 = 0:

b1 + c1 = y1,

c2 = y2 + (1 + r)b1,

I Eliminate b1 to show that:

c1 +c2

1 + r= y1 +

y2

1 + r.

I The present discounted value of lifetime consumption equalsthe present discounted value of lifetime income.

Solution

I Substitute the IBC to rewrite the household problem as:

maxc1

u(c1) + βu(y2 + (1 + r)(y1 − c1)).

I Differentiate to show the first order condition:

u′(c1)

βu′(c2)= 1 + r .

I The marginal rate of substitution between c1 and c2 isequal to the relative price of current consumption vis-a-visfuture consumption.

Autarky vs Openness

I Under autarky household consumes income:

ct = yt ,

bt = 0.

I In a trading equilibrium, in general:

ct 6= yt ,

bt 6= 0.

I Therefore define autarky real interest rate as:

u′(y1)

βu′(y2)= 1 + rAut .

Suppose rAut > r

I Rearrange budget constraints:

c1 = y1 − b1,

c2 = y2 + (1 + r)b1.

I Then, using the FOC of the household problem:

1 + rAut ≡ u′(y1)

βu′(y2)>

u′(c1)

βu′(c2)= 1 + r .

I Reveals:u′(y1)

βu′(y2)>

u′(y1 − b1)

βu′(y2 + (1 + r)b1),

such that rAut > r [rAut < r ] implies an initial currentaccount deficit [surplus], as b1 < 0.

Graphical Representation - Autarky

I Initially consume endowments and receive some autarky levelof utility, uAut .

Graphical Representation - Introduce Trade

I Then, introduce possibility to trade using intertemporalbudget constraint.

Graphical Representation - New Equilibrium

I Under free trade, the small open economy moves to the newequilibrium point on a higher indifference curve, uFT .

Graphical Representation - Current Accounts

I Same diagram also shows the current account in each period.Borrowing today, repaying tomorrow.

Graphical Representation - What Happened?

I Initially the country was relatively well endowed with homeendowment in the second period.

I At the prevailing world interest rate, r , they therefore wish toconsume a little more today, and a little less tomorrow.

I Under free trade, they run a current account deficit todayCA1 < 0 such that c1 > y1...

I ... and a current account surplus tomorrow, CA2 > 0, suchthat c2 < y2.

I Together this smooths consumption between periods, relativeto the autarky case.

I Note: nx2 = −(1 + r)nx1, borrowing is repaid with interest.

Income Shocks and the Current Account

I Consider the model just described and assume (1 + r)β = 1:

u′(c1)

βu′(c2)= 1 + r → c1 = c2,

and we therefore have perfect consumption smoothing.

I Use the IBC to find consumption:

c1 = c2 =(1 + r)y1 + y2

2 + r.

I Use the period budget constraint to solve for current account:

b1 = y1 − c1 =y1 − y2

2 + r.

I Also assume y1 = y2 such that, initially, b1 = 0.

Permanent Shock

I Permanent increase in income: ∆y1 = ∆y2 > 0.

I Consumption in both periods increases to match the newlevel of discounted life-time income:

∆c1 = ∆c2 =(1 + r)∆y1 + ∆y2

2 + r> 0.

I No change to the current account, which is still balanced:

∆b1 = ∆y1 −∆c1 =∆y1 −∆y2

2 + r= 0.

Temporary Shock

I Now consider a temporary increase in income: ∆y1 > 0 but∆y2 = 0.

I Again, consumption in both periods increases to match thenew level of discounted life-time income:

∆c1 = ∆c2 =(1 + r)∆y1

2 + r> 0,

due to the change in y1 only.

I However now the current account moves to surplus, as someof the temporary windfall is saved to smooth consumptionover time:

∆b1 = ∆y1 −∆c1 =∆y1

2 + r> 0.

Intuition

I “If you lose your lunch money one day, it’s not a problem.You simply borrow from a friend. Next time, you pay for hislunch. However if your parents cut your monthly allowance,you will have to change spending plans accordingly” [SGU,forthcoming].

I It is hard to identify whether a change in income is temporaryor permanent. One exception to this are natural disasters.

Two Period Production Model (SOE)I Now introduce production and government spending to the

previous model. Each period, government purchases satisfy:

gt = τt ,

where gt is government spending and τt represent lump-sumtaxes, faced by households.

I Production technology follows:

yt = AtF (kt),

where F (·) obeys standard properties.[F (0) = 0,F ′(·) >,F ′′(·) < 0].

I Capital accumulation:

kt+1 = kt + it ,

where there is no depreciation, k1 is given and investmentmay be negative.

New Intertemporal Budget Constraint

I The series of period-t budget constraints now become:

bt + ct = yt + (1 + r)bt−1 − it − τt ,

where τt represent lump-sum taxes and it is investment.

I Again, eliminate b1 and set b0 = b2 = 0 to show that:

c1 + i1 +c2 + i21 + r

= y1 − τ1 +y2 − τ2

1 + r.

I PDV of lifetime expenditure on consumption and investmentequals the PDV of lifetime income, after tax.

I To move to equilibrium notice:I k3 = 0→ i2 = −k2 and i1 = k2 − k1, with k1 given.

I Taxation is specified exogenously as government consumption.

I Production functions: yt = AtF (kt).

Optimality Conditions

I Combine and rearrange for c2:

c2 = (1 + r)[A1F (k1)−g1− c1−k2 +k1

]+A2F (k2)−g2 +k2,

I Use in optimisation problem:

maxc1,k2

u(c1)+βu(

(1+r)(A1F (k1)−g1−c1−k2+k1)+A2F (k2)−g2+k2

),

I FOCs:

u′(c1) = β(1 + r)u′(c2), (wrt c1)

A2F′(k2) = r . (wrt k2)

I Separation of savings and investment decisions (k2

independent of u).

I No crowing out (k2 independent of gt).

Graphical Representation - Autarky

I Initially consume endowments and receive some autarky levelof utility, uAut . IC tangent to PPF.

Graphical Representation - Introduce Trade

I Then, introduce possibility to trade using intertemporalbudget constraint. BC is tangent to PPF.

Graphical Representation - New Equilibrium

I Under free trade, households/consumption move(s) to thenew equilibrium point on a higher indifference curve, uFT .

Graphical Representation - Current Accounts

I Firms/production move(s) to a new equilibrium point. Thelevel of capital, k2, may be read directly from the graph.

Graphical Representation - What Happened?

I Two distinct procedures:I In the first investment decisions (capital) are made to

maximise the possible size of the economic pie for the Homecountry, given international prices.

I In the second, given this level of income, international pricesand the household discount factor, households chooseconsumption to maximise utility.

Two Period Model (Two Country)

I Two countries: Home and Foreign (denoted by ∗).

I Return to endowment setting. Global equilibrium nowrequires:

yt + y∗t = ct + c∗t .

I May be rewritten in terms of household savings st ≡ yt − ct :

st + s∗t = 0.

I Or in terms of the current account (savings minus investment,but no investment here):

CAt + CA∗t = 0.

I The main change: world interest rate is now endogenous,ensuring equilibrium in the global asset market.

Graphical Representation - Metzler Diagram (Endowment)

I The savings schedule for each country may be plotted.Assume different autarky equilibrium real interest rates.

Graphical Representation - Free Trade I (Endowment)

I To balance the global level of household savings, the interestrate must fall for Home and rise for Foreign.

Graphical Representation - Free Trade II (Endowment)

I Indeed, we may quantify the precise level of r by consideringthe equilibrium condition CAt = −CA∗t .

Graphical Representation - What Happened?

I Under autarky for each country we define rAut and r∗,Aut suchthat:

st(rAutt ) = 0,

s∗t (r∗,Autt ) = 0.

I We assumed the parameterisation gave rAut > r∗,Aut .

I We must have that rAut > rW > r∗,Aut , else:I rW > rAut > r∗,Aut → CAt > 0 and CA∗t > 0 →

CAt + CA∗t > 0.

I rAut > r∗,Aut > rW → CAt < 0 and CA∗t < 0 →CAt + CA∗t < 0.

I Therefore we know that when rAut > rW > r∗,Aut :I CAt < 0, while CA∗t > 0.

I Precise level given by CAt + CA∗t = 0.

Move to a Production Economy

I The analysis for the two country case may be extended for aneconomy with production.

I Notice, in this case, current accounts are given as the balancebetween household savings and investment, CAt = st − it ,such that the real interest rate will be determined by:

st + s∗t = it + i∗t ,

CAt + CA∗t = 0.

I For both endowment and production economies a shock toone country will propagate internationally to the otherthrough changes in the real interest rate.

Graphical Representation - Metzler Diagram (Production)

I Savings and investment schedules are plotted for each country.Assume different autarky equilibrium real interest rates.

Graphical Representation - Free Trade I (Production)

I To balance the global level of savings and investment, the realinterest rate must fall for Home and rise for Foreign.

Graphical Representation - Free Trade II (Production)

I Again, we may quantify the precise level of r by consideringthe equilibrium condition CAt = −CA∗t .

Graphical Representation - Foreign Investment Shock

I The shock shifts the Foreign investment curve to the right,both countries affected. In one case both CA’s close.

Dynamics of the Current AccountI Move from a 2-period setting to infinite horizon. Can do this

in two steps:I Set a finite horizon, T .

I Investigate properties as T →∞.

I Initially extend to a T -period model:I Representative household maximises lifetime utility:

Ut = u(ct) + βu(ct+1) + ...+ βTu(ct+T ) =t+T∑s=t

βs−tu(cs).

I Subject to a series of period-t budget constraints:

bt + ct + it + gt = yt + (1 + r)bt−1,

bt+1 + ct+1 + it+1 + gt+1 = yt+1 + (1 + r)bt ,

· · ·bt+T + ct+T + it+T + gt+T = yt+T + (1 + r)bt+T−1.

I Assume r is constant over time.

Finite Horizon Intertemporal Budget Constraint I

I As before rewrite the budget constraints in terms of NFA:

bt = yt − [ct + it + gt ] + (1 + r)bt−1,

bt+1

1 + r=

yt+1 − [ct+1 + it+1 + gt+1]

1 + r+ bt ,

· · ·bt+T

1 + r=

yt+T − [ct+T + it+T + gt+T ]

1 + r+ bt+T−1.

I Iteratively substitute out to obtain:

bt+T

(1 + r)T= (1 + r)bt−1 +

t+T∑s=t

ys − [cs + is + gs ]

(1 + r)s−t.

Finite Horizon Intertemporal Budget Constraint II

I Our usual assumption of bt = 0 and argument that bt+T = 0will still apply.

I May therefore rewrite the intertemporal budget constraint as:

t+T∑s=t

ys(1 + r)s−t

=t+T∑s=t

cs + is + gs(1 + r)s−t

.

Again, it is clear that the PDV of lifetime income will be usedto cover the PDV of expenditure on consumption, investmentand by the government.

I Could stop here and discuss how this extension to a longertime horizon affects the model. A useful discussion in OR.Instead we proceed directly to the infinite horizon case.

Infinite Horizon Model

I Now allow T →∞.

I Representative household maximises lifetime utility:

U(ct) =∞∑s=t

βs−tu(cs).

I Subject to the intertemporal budget constraint:

∞∑s=t

cs + is + gs(1 + r)s−t

+ limT→∞

bt+T

(1 + r)T= (1+r)bt−1+

∞∑s=t

ys(1 + r)s−t

.

Transversality Condition

I We will assume the terminal transversality condition (TVC):

limT→∞

bt+T

(1 + r)T= 0.

I This is the result of two distinct notions:

1. Optimality condition. With u′(·) > 0 it will never be optimalfor households to allow assets to grow more quickly that thereal interest rate, such that:

limT→∞

bt+T

(1 + r)T≥ 0.

2. No-Ponzi (Madoff) assumption:

limT→∞

bt+T

(1 + r)T≤ 0.

I Continue to normalise initial condition: (1 + r)bt−1 = 0.

Optimality Conditions

I Take FOCs of the infinite horizon problem, subject to initialand terminal conditions:

u′(ct) = β(1 + r)u′(ct+1), (wrt ct , Euler Equation)

At+1F′(kt+1) = r . (wrt kt+1)

I Will hold in every time period.

Analytical Solution for Consumption Profile?

I In general, no. Three special cases:

1. β = 11+r , such that households fully consumption smooth.

2. Iso-elastic utility function (log as special case).

3. Stochastic income, with β = 11+r and quadratic utility.

Permanent Level / Annuity Values

I Consider a constant, xt :

∞∑s=t

xt(1 + r)s−t

=∞∑s=t

xs(1 + r)s−t

,

such that the NPV of this constant, xt , is equal to the NPVof the steam ov the variable xt . Hence:

xt

1− 11+r

=∞∑s=t

xs(1 + r)s−t

,

xt =r

1 + r

∞∑s=t

xs(1 + r)s−t

,

and xt is said to be the annuity value of the series xt .

Special Case 1, β = 11+r

I Assume β = 11+r and rewrite the Euler equation as:

u′(ct) = β(1 + r)u′(ct+1),→ u′(ct) = u′(ct+1),

such that we have full consumption smoothing, ct = ct+1.

I Define household wealth, Wt , as:

Wt = (1 + r)bt−1 +∞∑s=t

ys − [is + gs ]

(1 + r)s−t,

= (1 + r)bt−1 +1 + r

r

[yt − it − gt

].

I But, using IBC and assumption consumption is shown to be aconstant fraction of lifetime wealth, Wt :

Wt =∞∑s=t

cs(1 + r)s−t

=1 + r

rct .

Special Case 1, β = 11+r ctd.

I Using these results we observe:

ct = r · bt−1 +[yt − it − gt

],

such that consumption only responds to changes in the valueof permanent income.

I Turing to the current account:

cat = r · bt−1 + yt − ct − it − gt ,

cat = (yt − yt)− (it − it)− (gt − gt).

I Changes in the current account arise due to temporarydeviations in income, investment and government spendingfrom their permanent levels. Call this the fundamentalequation of the current account.

Special Case 2, iso-elastic utility

I Assume:

u(ct) =c1−1/σ

1− 1/σ,

with σ > 0, and hence u′(ct) = c−1/σt .

I Euler equation may be rewritten as:

u′(ct) = β(1 + r)u′(ct+1),→ ct+1 = βσ(1 + r)σct .

I Substitute to find value of lifetime wealth as:1

Wt =∞∑s=t

cs(1 + r)s−t

=ct

1− βσ(1 + r)σ−1.

1Assume βσ(1 + r)σ−1 < 1.

Special Case 2, iso-elastic utility ctd.

I Thus:

ct =r + θ

1 + rWt ,

where θ ≡ 1− βσ(1 + r)σ.

I And hence, with a slight change to before:

cat = (yt − yt)− (it − it)− (gt − gt)−θ

1 + rWt .

I Similar intuition to before, with the addition of a tilt factor, θ:

I Consumption still a constant fraction of PDV lifetime wealth.

I Current account arises through:

1. Deviations of variables from their permanent level.

2. Difference in household preferences, compared to the marketreal interest rate (tilt factor). More impatient → consumemore today → CA deficit today.

Special Case 2, log utility

I Log utility is a special case of the above, with σ = 1.

I In this case the Euler condition will become:

ct+1 = β(1 + r)ct .

I We may characterise consumption growth patterns using arelationship between β and (1 + r):

I If β > (1 + r) then we have ct+1 > ct as household arerelatively patient (compared to international financialmarkets).

I If β < (1 + r) then we have ct+1 < ct as household arerelatively impatient.

I If β = (1 + r) then we have ct+1 = ct and we recover theperfect consumption smoothing profile of special case 1.

I Intuition may also be given for a fixed β and consideringchanges in r .

Stochastic Infinite Horizon ModelI Introduce concepts allowing income to be stochastic:

I Assume that yt , it and gt follow stochastic processes with

ytiid∼ N (µy , σ

2y ), it

iid∼ N (µi , σ2i ) and gt

iid∼ N (µg , σ2g ).

I Households have rational expectations:I Knows model’s structure and shocks.

I Forecast errors are uncorrelated, after conditioning on theavailable information set.

I Rewrite the household’s optimisation problem as:

max{cs}∞s=t

Et

∞∑t=1

βt−1u(ct),

s.t. Et

∞∑s=t

cs + is + gs(1 + r)s−t

= (1 + r)bt−1 + Et

∞∑s=t

ys(1 + r)s−t

,

and limT→∞

Etbt+T

(1 + r)T= 0.

Optimality Conditions In Stochastic Model

I Euler equation:

u′(ct) = β(1 + r)Et [u′(ct+1)].

I Now “holds in expectation” and takes the uncertainty ofincome fluctuations into account.

Aside: Steady State Indeterminacy*

I A steady state arises when xt = x , ∀t, x . (Long run).

I Three equations specify the equilibrium. In steady state thesemay be written as:

u′(c) = β(1 + r)u′(c), (EE)

r = AF ′(k), (FOC, k)

c + g = rb + AF (k). (IBC)

I EE only restricts the real interest rate, as β(1 + r) = 1.

I From this, the FOC for capital pins down k .

I However, the IBC is then unable to distinguish between thelevel of consumption and international financial assets. Thelevel of financial assets, b, is indeterminate and the steadystate is compatible with any level of foreign assets.

I Schmitt-Grohe and Uribe (2003) document ways to solve this.

Special Case 3, Stochastic Income and Quadratic Utility

I Assume utility is quadratic:

u(ct) = ct −α

2c2t ,

with α > 0 such that u′(ct) = 1− αct .

I The Euler equation takes the form of a random walk2:

u′(ct) = β(1 + r)Et [u′(ct+1)]→ ct = Et ct+1,

I From (abuse of) previous notation we have that:

Wt =1 + r

rct = (1 + r)bt−1 +

1 + r

r

[yt − it − gt

],

where now xt ≡ r1+r

∑∞s=t

Et xs(1+r)s−t .

2Classic reference is Hall (1978).

Special Case 3 ctd.

I With:ct = r · bt−1 +

[yt − it − gt

],

we again have a version of the fundamental equation of thecurrent account:

cat = (yt − yt)− (it − it)− (gt − gt).

where changes are now due to variables varying from theirexpected levels, and the variances of shocks are irrelevant forconsumption decisions (certainty equivalence).

Example - Persistent Income I

I Suppose endowment model, with income following an AR(1)process (SGU 2.2):

yt = (1− ρ)µy + ρyt−1 + εt ,

with εtiid∼ N (0, σ2

ε) and ρ ∈ (−1, 1), empirically ρ > 0.

I Can rewrite:

yt+s − µy = ρ(yt+s−1 − µy ) + εt+s .

I Implies:Et [yt+s − µy ] = ρs(yt − µy ),

I Hence:

yt =r

1 + r

∞∑s=t

Et yt+s

(1 + r)s−t= µy +

r

1 + r − ρ(yt − µy ).

Example - Persistent Income III Using yt , given initial conditions yt−1, bt−1 and an exogenous

shock, εt , we may immediately write down the path forconsumption and the current account:

ct = r · bt−1 + yt = r · bt−1 + µy +rρ(yt−1 − µy ) + rεt

1 + r − ρ,

cat = yt − yt =ρ(1− ρ)(yt−1 − µy ) + (1− ρ)εt

1 + r − ρ.

I With temporary shocks (0 < ρ < 1)I Unexpected positive endowment shocks (εt > 0) leads to

ca > 0.

I Want to smooth consumption gains over time.

I With permanent shocks (ρ = 1)I No effect on current account.

I Income socks reflected one-to-one in consumption.

I Permanent income hypothesis at work (Friedman).

Example - Persistent Income III

I Homework: Go to Matlab, generate the shock.

Impulse Response to Exogenous Income Shock

-5 0 5 10 15 20

0

0.5

1

1.5

-5 0 5 10 15 20

0

0.02

0.04

0.06

0.08

0.1

0.12

-5 0 5 10 15 20

0

0.005

0.01

0.015

Notes: µy = 1, ρH = 0.6, ρL = 0.4, r = 5%. Calibrated for 1% income shock inhighly persistant case. yt and ct shown as % deviation from SS.

Engel and Rogers (2006)*

I Question: Is the (large) US current account (deficit) anoutcome of optimising behaviour?

I Their answer: Perhaps.

I Model: Two country current account model, tweaked toaccount for private forecasters expectations of future incomegrowth.

US Share of AE GDP*

I Key observation: concurrent increase in US GDP as a share oftotal, and increase in CA deficit since 1980s.

Source: Engel and Rogers (2006).

Simple Two Country Model*

I Predictions:I Suppose Et [∆yt+k ] > 0 for some k > 0.

I Then, optimising behaviour suggests home country shouldborrow now and repay later (when they have higher income).Hence CA deficit cat+k−s < 0 (for 0 < s < k).

I A low real interest rate would amplify this mechanism.

I Specifics:I Endowment economies, same log preferences, no government.

I Equilibrium conditions (+ foreign):

ct+1 = β(1 + r)ct , (EE)

bt−1 = Et

[ ∞∑s=t

cs − ys(1 + r)s−t

], (IBC)

ywt = yt + y∗t = ct + c∗t . (Resources)

Use Fractions of World GDP*

I Combine and rewrite the above 3 equations as:

ct = (1− β)

((1 + r)bt−1 + ywt Et

[ ∞∑s=t

βs−tγs

]),

ct = (1 + r)(1− β)bt−1 + ytΓt/γt ,

where γs = YtY wt

is the home country share of world GDP and

Γt = (1− β)Et

[∑∞s=t β

s−tγs

].

I The current account as a percentage of GDP becomes:

catyt

=bt − bt−1

yt=

yt − ct + rbt−1

yt,

catyt

= 1− Γt/γt − [1− β(1 + r)]bt−1

yt.

Economic Mechanism*

I Two key equations:

catyt

= 1− Γt/γt − [1− β(1 + r)]bt−1

yt,

ctyt

= (1 + r)(1− β)bt−1

yt+ Γt/γt .

I Assume, initially, bt−1 = 0 and that γt+k ↑ for some k >> 0.Then ct ↑ and cat ↓.

I Note: The home country share of world output cannot growindefinitely! The current account will rebalance at some pointin the future.

Model Predictions*I The model does well, after several “heroic assumptions” (see

section 2.2) and using private forecasters expectations of USoutput growth to help dynamics.

Source: Engel and Rogers (2006).

Summary

I Introduced basic open economy concepts, and focus oncurrent account.

I Develop both a two-period and infinite horizon model todescribe current account dynamics.

I Three special cases to achieve an analytical solution.

I Application: US current account deficit in early 2000s(discussed findings in Engel and Rogers (2006)).

References I

Engel, C. and J. H. Rogers (2006). The U.S. Current Account Deficit and the Expected Share of World Output.Journal of Monetary Economics 53(5), 1063–1093.

Hall, R. E. (1978). Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence.Journal of Political Economy 86(6), 971–87.

Schmitt-Grohe, S. and M. Uribe (2003). Closing Small Open Economy Models. Journal of InternationalEconomics 61, 163–185.

Schmitt-Grohe, S., M. Uribe, and M. Woodford (2016). International Economics. Princeton, NJ: PrincetonUniversity Press.