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ECON7520 Economic Mechanism

创建日期：2024-05-23 16:33:16

所属分类：经济Economics

标签： ECON7520

Economic Mechanism

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ECON7520: Current Account Determination

1 / 43
Motivation 1: What determines TB and CA?
Question 1: What determines trade balances (TB) and
current account (CA) balances?
Question 2: What are the effects of various economic
shocks on TB and CA?
Temporary output shock
Permanent output shock
Terms-of-trade shock
Question 3: What is the welfare consequence of a CA
policy such as a capital control policy?
2 / 43
Motivation 2: The Case of Chile
Shown: actual real and forecast avg. real price of copper
over the next 10 years produced by Chilean experts.
3 / 43
Motivation 2: The Case of Chile
The Current Account, Chile, 2001-2013
Question: Can we rationalize Chile’s CA movement?
4 / 43
ECON7520
An Economic Model
5 / 43
Key Economic Mechanism
We will study a small open economy model.
The key is the household’s optimal intertemporal
allocation of consumption: The household
makes intertemporal consumption and saving decisions.
smoothes consumption over time by borrowing and lending.
We will see
how the household’s decisions determine TB and CA.
how the household reacts to various shocks, and thus how
TB and CA are affected by those shocks.
6 / 43
Setup: Small Open Economy
Small open economy:
Open: The country trades in goods and financial assets
with the rest of the world (ROW).
Small: The country’s domestic economic conditions don’t
affect the prices of internationally traded goods, services
and financial assets.
Examples of small open economies:
Developed: Netherlands, Switzerland, Austria, New
Zealand, Australia, Canada, Norway
Emerging: Argentina, Chile, Peru, Bolivia, Greece,
Portugal, Estonia, Latvia, Thailand
Examples of large open economies:
Developed: U.S., Japan, Germany, U.K.
Emerging: China, India
Small open economy model: country + ROW.
7 / 43
Setup
Two-period small open economy: periods 1 and 2.
The single consumption good in the economy is
perishable, i.e. cannot be stored across periods.
The single asset traded in the financial market is a bond
(measured in units of the consumption good).
There is a representative household (HH) in the
economy endowed with
B0 units of the bond at the beginning of period 1,
Q1 units of the good in period 1,
Q2 units of the good in period 2.
Interest Rates:
r0 for the initial bond holdings,
r1 for the bonds held at the end of period 1.
8 / 43
Household’s Budget Constraint
The HH can reallocate resources between periods by
purchasing or selling bonds.
The HH’s budget constraint in period 1 is
C1 + B1 = (1+ r0)B0 + Q1 (1)
where
C1 is consumption in period 1,
B1 is the amount of bonds held at the end of period 1.
Analogously, the HH’s budget constraint in period 2 is
C2 + B2 = (1+ r1)B1 + Q2 (2)
where we assume B2 = 0 (transversality condition).
9 / 43
Number of Households, Interpretation of Bt
We assumed there is a single household.
If the HH borrows or lends, it is via the international
financial market.
→ Bt = NIIP at the end of period t.
Alternatively, we could assume the economy is populated
by multiple identical households (see SUW).
All HHs will make identical savings decisions.
→ HH A will never borrow from HH B (either both want to
lend or both want to save).
→ All borrowing and lending occurs on the international
financial market.
→ Bt = NIIP at the end of period t
10 / 43
Intertemporal Budget Constraint
C1 + B1 = (1+ r0)B0 + Q1, (1)
C2 = (1+ r1)B1 + Q2. (2)
By combining (1) and (2) we obtain the HH’s
intertemporal budget constraint
C1 +
C2
1+ r1︸︷︷︸
Consumption Values
= (1+ r0)B0 + Q1 +
Q2
1+ r1︸︷︷︸
Inital Assets + Total Income Values
.
The intertemporal budget constraint describes the
consumption paths (C1,C2) that the HH can (just) afford.
11 / 43
Intertemporal Budget Constraint
The above graph assumes B0 = 0.
The slope of the budget constraint is −(1+ r1). (Can you
prove this?)
12 / 43
Utility Function
The household obtains utility (happiness) from (C1,C2).
The utility function U maps consumption paths (C1,C2) to
levels of happiness:
U(C1,C2).
How can we graphically represent the utility function?
By indifference curves (ICs).
The IC for a given utility level L consists of all consumption
paths (C1,C2) that give the household utility L.
13 / 43
Graph of Indifference Curves
Typical Indifference Curves
Shown are the IC for utility level L1, the IC for utility level L2
and the IC for utility level L3.
14 / 43
Properties of Indifference Curves
By definition,
1 ICs do not intersect.
We assume that U is such that its ICs satisfy:
2 ICs are downward sloping.
True if for each of C1 and C2 “more is better”.
3 The right-upper ICs indicate higher levels of utility.
E.g., in the previous slide, L1 < L2 < L3.
4 ICs have a bowed-in shape towards the origin (convex
toward the origin).
Exercise
Prove 1.
For each of the conditions 2, 3 and 4, what would it mean if
the condition was violated?
15 / 43
Examples of Utility Functions
Utility functions whose ICs satisfy these 4 properties
include:
1 Logarithmic utility function
U(C1,C2) = lnC1 + lnC2
2 Square-root utility function
U(C1,C2) =
√
C1 +
√
C2
3 Cobb-Douglas utility function
U(C1,C2) = (C1)
α
(C2)
1−α
where 0 < α < 1.
In the lectures we focus on the logarithmic case.
16 / 43
Slope of Indifference Curves
Pick any consumption path (C1,C2) on an IC.
The absolute value of the slope of the IC at (C1,C2) is
called the (intertemporal) marginal rate of substitution
(MRS) of C2 for C1.
The MRS is important because it represents trade-offs that
the HH is willing to make:
Keeping the level of the utility same, how much C2 is
needed to make up for a decrease of 1 (small) unit of C1?
The MRS at (C1,C2) equals the amount of C2 that just lifts
the HH back to her original utility level if, starting at
(C1,C2), we take 1 (small) unit of good C1 away from her.
17 / 43
Slope of Indifference Curves (Important)
The MRS at (C1,C2) can be derived as the ratio of the
partial derivatives of the utility function at (C1,C2):
MRS =
U1(C1,C2)
U2(C1,C2)
where
U1 (C1,C2) =
∂U(C1,C2)
∂C1
,
U2 (C1,C2) =
∂U(C1,C2)
∂C2
.
Thus, the slope of the IC containing (C1,C2) at (C1,C2) is
(slope of IC)(C1,C2) = −
U1(C1,C2)
U2(C1,C2)
.
SUW p. 49 reviews how to derive the above formulas.
18 / 43
The Household’s Decision
Maximization Assumption: From the set of all (C1,C2)
that the HH can afford, the HH chooses a (C1,C2) that
maximizes her utility. That is:
HH’s Optimization Problem: The HH maximizes her utility
subject to the intertemporal budget constraint.
Which path(s) will solve the HH’s optimization problem?
To answer this, superimpose the figure of the HH’s ICs on
the on the intertemporal budget constraint graph.
19 / 43
The Optimal Intertemporal Allocation
The above graph assumes B0 = 0.
The optimal consumption path is point B. (Why?)
20 / 43
Properties of Optimal Consumption Path
1 The optimal consumption path (C1,C2) lies on the
intertemporal budget constraint.
2 At the optimal bundle (C1,C2) the IC is tangent to the
intertemporal budget constraint (IBC).
This means that
−
U1(C1,C2)
U2(C1,C2)︸︷︷︸
IC’s slope
= − (1+ r1)︸︷︷︸
IBC’s slope
or, equivalently,
U1(C1,C2) = (1+ r1)U2(C1,C2).
Exercise
Prove that 1 and 2 hold at the optimal consumption path.
21 / 43
Equilibrium
Exogenously given are r0,B0, r
∗,Q1 and Q2. An equilibrium is
a consumption path (C1,C2) and an interest rate r1 such that:
1 Feasibility of the intertemporal allocation
C1 +
C2
1+ r1
= (1+ r0)B0 + Q1 +
Q2
1+ r1
.
2 Optimality of the intertemporal allocation
U1(C1,C2) = (1+ r1)U2(C1,C2).
3 Interest rate parity condition
r1 = r
∗.
This is implied by free capital mobility and means that the
domestic interest rate r1 equals the world interest rate r
∗.
22 / 43
TB and CA in Equilibrium: Intuition
Given the HH’s endowment B0 and (Q1,Q2),
the HH optimally chooses her consumption path (C1,C2),
the HH accordingly adjusts her asset level B1.
Depending on her preference,
the HH will borrow (B1 ≤ B0) to increase consumption
above income in period 1 (C1 > r0B0 + Q1), or
the HH will save (B1 ≥ B0) some of her period 1 income for
consumption in period 2.
Therefore, the HH’s willingness to save determines the TB
and CA.
23 / 43
Trade Balance and Current Account Balance
In this economy,
TB1 = Q1 −C1,
TB2 = Q2 −C2.
And
CA1 = r0B0 + TB1,
B1 = B0 + CA1
CA2 = r1B1 + TB2.
Also, since we don’t have investments in this economy
(I1 = I2 = 0),
S1 = CA1,
S2 = CA2.
24 / 43
ECON7520
Analysis of Various Shocks to the Economy
25 / 43
Temporary vs. Permanent Output Shocks
What is the effect on the current account of an increase or
decrease in output?
Depends on whether the shock is temporary or permanent.
For the analysis, assume:
1 Temporary shock
Output in Period 1 = Q1 −∆
Output in Period 2 = Q2
2 Permanent shock
Output in Period 1 = Q1 −∆
Output in Period 2 = Q2 −∆
The next slides assume that both C1 and C2 are normal
goods (their consumption increases with income).
26 / 43
Temporary Output Shock: Budget Constraint
The above graph assumes B0 = 0.
A is the old and A′ the new endowment point.
27 / 43
Temporary Output Shock: Optimal Allocation
The above graph assumes B0 = 0.
B is the old and B′ the new optimal consumption path.
C1 declines by less than ∆; TB1 deteriorates.
28 / 43
Permanent Output Shock
The above graph assumes B0 = 0.
A is the old and A′ the new endowment point.
B is the old and B′ the new optimal consumption path.
As drawn, TB1 does not change much.
29 / 43
Temporary vs. Permanent Output Shocks: Summary
1 Temporary shock
Relatively small effect on the consumption path (C1,C2).
Temporary negative income shocks are smoothed out by
borrowing from the rest of the world.
Generally, one should expect the borrowing to move the
country’s trade balance and current account significantly.
2 Permanent shock
Relatively large effect on the consumption path (C1,C2).
Generally, one should expect permanent negative income
shocks to lead to similarly sized reductions in C1 and C2.
Generally, one should expect the country’s trade balance
and current account to not be much affected.
30 / 43
Terms of Trade Shocks
Relax the assumption of a single good and consider an
economy which exports endowments of oil (Q1,Q2) and
imports food for consumption (C1,C2).
Then, the HH’s budget constraints for period 1 and 2 are
C1 + B1 = (1+ r0)B0 + TT1Q1, (3)
C2 = (1+ r1)B1 + TT2Q2. (4)
where the terms of trade TTt (t = 1,2) are the relative
price of exports in terms of imports:
TT1 =
PX1
PM1
, TT2 =
PX2
PM2
.
By (3) and (4), the effects of terms of trade shocks can be
analyzed analogously to those of output shocks.
31 / 43
Term-of-Trade Shocks: The Case of Chile
Chile: More than 50% of exports are copper.
A large positive permanent shock hit the copper price
around 2003-2007.
What does our theory predict?
After the shock hits, the current account balance doesn’t
move much because the shock is permanent.
32 / 43
Term-of-Trade Shocks: The Case of Chile
33 / 43
Term-of-Trade Shocks: The Case of Chile
The Current Account, Chile, 2001-2013
34 / 43
Imperfect Information
The theory failed to predict the movement of Chile’s current
account.
What went wrong?
We incorrectly assumed that HHs perfectly foresaw the
nature of the shock.
But until about 2007, Chilean experts didn’t expect the
shock to last long — they expected it to be temporary.
For a temporary positive terms of trade shock, our model
predicts an improvement in CA.
In line with that, the Chilean CA indeed (significantly)
improved in the years 2004-2007.
35 / 43
Capital Controls: Setup
Current account deficits are often viewed as bad for a
country.
As a result, a policy recommendation frequently offered is
the imposition of capital controls.
What’s is the effect of such a policy on the household’s
welfare?
Assume B0 = 0 as a simplification.
Assume the country is a borrower without the policy
(B1 < 0).
Assume the country’s authority introduces a policy that
prohibits borrowing, that is, requires B1 ≥ 0.
36 / 43
Capital Controls: Graphical Analysis
The Optimal Intertemporal Allocation
The optimal allocation moves from B to A.
r1 6= r
∗.
37 / 43
Capital Controls: Result
After this policy is introduced, the HH cannot borrow even
though she likes to.
Therefore, the budget constraints become
C1 = Q1,
C2 = Q2.
As a result, the trade balances are
TB1 = Q1 − C1 = 0,
TB2 = Q2 − C2 = 0.
Thus, the capital control achieves the government’s goal.
However, note that the IC of point A in the above graph is
below the IC of point B.
The household is worse off with the policy because the
policy prevents her optimal intertemporal decision.
38 / 43
ECON7520
An Economy with Logarithmic Preferences
39 / 43
Logarithmic Utility Function
We can solve for the equilibrium if the utility function is
U(C1,C2) = lnC1 + lnC2.
In this case, using the derivative formula
d ln(x)
dx
= 1
x
,
U1 (C1,C2) =
∂U (C1,C2)
∂C1
=
∂ (lnC1 + lnC2)
∂C1
=
1
C1
,
U2 (C1,C2) =
∂U (C1,C2)
∂C2
=
∂ (lnC1 + lnC2)
∂C2
=
1
C2
.
Therefore, the equilibrium condition
U1 (C1,C2) = (1 + r1)U2 (C1,C2)
becomes
1
C1
= (1+ r1)
1
C2
.
40 / 43
Equilibrium under Logarithmic Utility Function
The equilibrium conditions are
1 Feasibility of the intertemporal allocation
C1 +
C2
1+ r1
= (1+ r0)B0 + Q1 +
Q2
1+ r1
. (5)
2 Optimality of the intertemporal allocation
1
C1
= (1+ r1)
1
C2
. (6)
3 Interest rate parity condition
r1 = r .
41 / 43
Equilibrium under Logarithmic Utility Function
From (6), we can derive
C2 = (1+ r1)C1. (7)
By substituting (7) into (5), we obtain
C1 =
1
2
[
(1+ r0)B0 + Q1 +
Q2
1+ r1
]
. (8)
From (7) and (8), we get
C2 =
1
2
(1+ r1)
[
(1+ r0)B0 + Q1 +
Q2
1+ r1
]
. (9)
After substituting r∗ for r1, equations (8) and (9) describe
the equilibrium consumption path.
42 / 43
Summary and Conclusion
Today, we studied:
1 A theory of current account determination.
The HH’s intertemporal allocation decision is the key.
2 Analysis of the effect of various shocks on the CA.
Temporary output shock.
Permanent output shock.
Terms-of-trade shock.
3 Policy analysis: capital controls.
Next week, we will study interest shocks and import
tariffs in today’s setup as well as the current account
determination in a production economy.

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CS 333 CP1406 KIT308 Economics 701 ECON3740 ECE 5759 BFC3340 FINC2012 COMP4500 MATH3871 FIT3080 18-819C Economic ECO202Y5Y PHY100 FINC-780 Econ 100B EC602 IE582 EE450 COMP9517 WRDS 150B ECON 570 LECTURE 2 ECA5101 ECE 4420 ADAD9311 FIT3031 CS 544 MF 703 CS 6140 KIT501 ENGSCI 344 CSC171 IE 332 FINM8007 21S2 COSC 1114 FE545 E471 SIT102 CSC108 MAT301 IAE 101 COP3503 STAT2004 EC 303 CS1026 STAT1203 MATH3171 ISOM5160 IFN657 FIT2014 ACCT2102 DSCI550 STATS 330 ELEC421 COMP3670 QBUS6840 MEES:698B MAST30027 MIET1077 Economics IFT 6758 FIT5122 BUSN5101 CptS 111 HRMT5502 Math2018 PP 312 INFS3200 CZ3005 CSSE1001 SENG 2011 MKTG 553Q BUFN 640 COMP507 ETF5952 DATA 311 ECE4043 BANK3011 finance M3H623544 HW1 INFS 7410 AI6103 STAT3888 INFS3208 ACCT7103 ECOS3013 PSYCH 20B F79MA STAT3006 ENGG952 2X MGSC 7000 ECE4132 MSF 526 MATH 3033 CDS 511 EEEE4120 EEET2465 ECA5103 MATH2070 ELEC3104 BU51019 EEE8147 ENGR20003 COSC 1107 ETF3200 FNCE 435 MSFI 435 ISyE6420 GENG4405 HW ETC5523 IE 7315 MOEC0021 STA 106 ENGG 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