Transcript Document

Chapter 11
Inflation
and Short-Run Dynamics
© Pierre-Richard Agénor and Peter J. Montiel
1


Models of Inflationary Process.
Dynamics of Monetary and Exchange-Rate Rules.
2
Models of Inflationary
Process
“Orthodox” view:
 Inflation results from money creation by governments
faced with limited borrowing options
New structuralists:
 Inflation results from the worker-capitalist conflict over
distribution of income between real wages and profits.
4



Inflation, Money and Fiscal Deficits.
 Adaptive Expectations.
 Perfect Foresight.
Food Supply, Distribution, and the Wage-Price Cycle.
A Structuralist-Monetarist Model.
5
Inflation, Money and Fiscal
Deficits


Closed economy with exogenous output.
Demand for money function takes the Cagan
semilogarithmic form:
m = exp(-a),
 > 0,
(1)
.
m  M/P: M is base money stock and P is price level;
a: expected inflation rate.
6

Government cannot issue bonds to the public and
finances its primary budget deficit d entirely through
seigniorage:
.
d = M/P = m,
(2)
.

  M/M.
Combining (1) and (2)
d =  exp(-a).

(3)
(3): how primary fiscal deficit affects equilibrium rate of
growth of the money stock, and inflation rate.
7




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
“Seigniorage Laffer curve”: two steady-state rates of
inflation that generate any given amount of seigniorage.
Figure 11.1: (3) is plotted.
D: combinations of  and a for which d is constant.
Since (3) indicates that d =  when a is zero, d is
measured by the distance between the origin and the
intercept of the D curve on the -axis.
Since government budget constraint always binds,
economy is always located on the D curve.
Differentiating (1) with respect to time yields
.a
 -  = - .
(4)
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In steady state:
 = a = .

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

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(5)
(4): 45o line in Figure 11.1.
D and the 45o line intersect twice.
Thus there are two potential steady-state positions:
 low-inflation equilibrium (point A);
 high-inflation equilibrium (point B).
At A the elasticity of the demand for real money
balances is less than unity, whereas at point B it is
greater than unity.
Suppose that d is constrained by the amount of revenue
that can be generated through money creation.
10


Inflation rate that maximizes steady-state seigniorage
revenue is s = 1/.
Corresponding level of revenue:
ds = exp(-1)/.




Assume that d that the government wishes to finance is
~
fixed at d.
Depending on size of deficit target, there may be zero,
one, or two equilibria.
Since the government cannot obtain more than ds in the
long-run equilibrium, there is no steady state if d > ds.
~ s
~
For d = d or d < 0, there is a unique steady state.
11


~
0 < d < ds: two steady states, and the economy may be
“stuck” at high-inflation equilibrium (point B).
Two alternative assumptions about the formation of
inflation expectations.
12
Adaptive Expectations

When inflation expectations are adaptive:
.a
 = ( - a),


 > 0.
(6)
Combining (3), (4) and (6) determines the time path of
actual and expected inflation, for a given d.
From (4) and (6), changes in expected inflation are
determined by
.a
 = ( - a)/(1 - ).
13

Actual rate is

 = ( - a)/(1 - ),





which implies that in the steady state  = a = .
With an adaptive expectational scheme, A is a stable
equilibrium whereas B is unstable, if  < 1/.
Points located to the right of B lead to hyperinflation.
Government prints money at an ever-increasing rate.
This prevents a from ever coinciding with the actual
rate of increase in prices.
Although real money balances are reduced at an
increasing rate, rapid printing money helps financing the
deficit.
14







Suppose that the economy is initially at A, and consider
effect of an increase in d.
Small increase: D shifts to the right to D’ but continues
to intersect the 45o line twice.
Increase in d leads to jump in  from A to C.
Then gradual increase in both actual and expected
inflation rate from point C to A’.
Once expectations begin to adjust, demand for real
money balances starts falling.
Government must print money at an accelerated pace
to compensate for the reduction in the inflation tax base.
If increase in d is large, D may not intersect the 45o line
at all (D’’).
15



There is no steady state, and inflation increases
continually.
Economy jumps from A to F and follows a
hyperinflationary path, moving to northeast along D’’.
If bonds can be used as an additional source of
financing, unique steady-state inflation rate is attained
when the government sets a nominal anchor.
16
Perfect Foresight






Rational expectations can be implemented by
 setting    in (6);
 allowing expected and actual prices to jump.
In this case, B is a stable equilibrium and A is unstable.
Since a can jump on impact, all points located on D are
short-run equilibria.
Increase in d leads to an instantaneous jump to a new
equilibrium.
But there is no guarantee that the economy will be on
D’D’.
Thus, inflation may be unnecessarily high under perfect
foresight.
17




So large d leads to hyperinflation only when private
agents have adaptive expectations.
Bruno and Fischer (1990) and Kiguel (1989):
Large d may lead to hyperinflation even under perfect
foresight, if there is sluggish adjustment toward
equilibrium in the money market.
Assume that money market adjusts according to
.
m/m = (lnmd – lnm),
 > 0,
(7)
md: desired real balances;
: speed of adjustment.
18

(7) can be written as
 =  - (lnmd – lnm).



(8)
(8): inflation rate adjusts one-for-one with , but adjusts
partially in response to differences between desired and
actual levels of real money balances.
Thus inflation rate is sticky, but real balances are
predetermined.
Solving for the logarithm
. . of money demand from (1) and
using the identity m  M/P - m in (8) yields
.
m = [/( - 1)](d + m lnm). (9)
19



Figure 11.2: plot (9) for a value of the deficit equal to d0
and  < 1/.
Two equilibria: A is unstable; B is stable.
When   , (9) becomes
.
m  d + -1 m lnm.
If policymaker increases d from d1 to d0:
.
 m = 0 schedule moves down.
 It may no longer intersect the horizontal axis.
 In such conditions system will be unstable:
 decreasing real money balances;
 rising rates of inflation.
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
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Thus too large d leads to a hyperinflationary path.
Under perfect foresight, instability in inflation process
depends on the assumption of sluggish adjustment in
money market.
Increase in money growth creates a temporary excess
supply in the money market.
This leads to an increase in inflation.
Higher inflation rate exerts two conflicting effects on the
equilibrium of the money market:
 it reduces supply of real money balances
(reequilibrate the market);
 it leads to fall in demand for real money balances
(amplify initial disequilibrium).
22



When the system does not possess a stable long-run
equilibrium, the latter effect dominates the former.
This results in accelerating inflation.
Possibility of following unstable inflationary path
becomes more likely if erosion in tax revenue results in
positive relation between d and .
23
Key results:
 Money financing of fiscal deficits may lead to multiple
steady-state equilibria.
 Hyperinflation is an unstable process that emerges as
due to large, unsustainable d financed by money
creation.
 Essential feature of stabilization programs must be a
significant fiscal adjustment.



In small, open countries, additional factor that may
affect inflation in the short run is exchange rate.
Nominal depreciation affects domestic-currency price of
import-competing goods and exportables.
Indirect effect: if cost of imported inputs affects pricing
24
decisions.
Fluctuations in unofficial exchange rate may affect
inflation if domestic price setters take into account
marginal cost of foreign exchange when setting prices.
 Depreciation of exchange rate may affect inflation by
raising nominal wages, through implicit or explicit
indexation mechanisms.
 Despite these effects of exchange rate on inflation,
fiscal deficits play a key role in the long run.
Rodríguez (1978):
 His model explains this result.
 If d is financed through credit creation by the central
bank, monetary expansion leads to an increase in
prices and a progressive erosion of foreign reserves.

25


This triggers a devaluation if the central bank has
limited access to borrowing in international capital
markets.
Devaluation-inflation spiral may develop.
26
Food Supply, Distribution,
and the Wage-Price Cycle





Link between inflation, food supply, and competing
claims for the distribution of income is important in new
structuralist approach to inflation.
Here modified version of a model developed by
Cardoso (1981) s presented.
Closed economy producing two goods:
 agricultural good, yA;
 manufactured good, yI.
~
Food supply is given in the short-run at yA.
Output is demand determined in the industrial sector.
27

Equilibrium conditions in both markets:
+
~
d
yA = cA(y, ),
  PA/PI,
+ +
yI = cI (y, ) + g,
d
cAd: food demand;
y: real factor income;
: relative price of agricultural goods;
cId: private expenditure on manufactured goods;
g: autonomous government expenditure on industrial
goods.
28

Real factor income:
y = y~A + yI.




Assume that direct effect of changes in  on demand is
zero.
0 <  <1 denote marginal propensity to consume.
0 <  < 1: proportion of consumption spent on
agricultural goods.
Equilibrium condition of food market:
y~A = y = (y~A + yI).
(10)
29

Market-clearing condition for industrial goods:
yI = (1 - )(y~A + yI) + g.

Assuming that prices of industrial goods remain
constant and that output in industrial sector responds
gradually to excess demand for manufactured goods:
.
yI = I[(1 - )(y~A + yI) + g – yI],

(11)
I > 0. (12)
Agricultural prices respond gradually to the excess
demand for food:
.
~
PA/PA = A[(yA + yI) - y~A],
A > 0. (13)
30

(12) and (13): dynamic behavior over time of production
in industrial sector and agricultural prices:
.
PA
.
yI




=
-A(1 - )
A
I (1 - ) -I (1 - (1 - ))
PA
yI
For stability, trace of coefficient matrix must be negative
and its determinant positive.
Figure 11.3: equilibrium of the economy.
.
Curve [PA = 0]: combinations of industrial output and
relative price that maintain equilibrium in the food
market.
It has a positive slope.
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Left of it: excess supply of food and falling prices.
Right of it: excess demand and rising food prices.
.
Curve [yI = 0] : equilibrium condition for industrial good
market.
It has a positive slope.
Left of it: excess demand for industrial goods and rising
output.
Right of it: excess supply of manufactured goods and
falling output.
E: steady-state equilibrium.
Economy is at A initially: excess supply of food and
excess demand for manufactured goods.
Increase in output in the industrial sector dampens
excess demand for manufactured goods.
33

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
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
Increase in output in the industrial sector dampens
excess demand for manufactured goods.
This increases income and demand for agricultural
products.
Thus, this reduces excess supply in agricultural sector.
Food prices fall at first and then rise.
Industrial output rises continuously until long-run
equilibrium is reached.
Thus, there is no tendency toward instability since it is
assumed that industrial prices remain constant.
Suppose that industrial sector set prices as a fixed
mark-up  over labor costs.
34

Industrial prices:
PI = (1 + )w,


 > 0.
(14)
Suppose: workers have a constant real wage target *.
Thus, nominal wages are determined by
~
w = P,
(15)
P is consumer price index, defined as
P - PAPI1-,
0 <  < 1.
(16)
35

Using (14), (15), and (16) yields “required” relative price,
consistent with workers' real wage target:
* = [(1 + )*]-1/,


(17)
*: required price ratio.
Rate of change of nominal wages is determined by
difference between * and .
Using (14), rate of change of industrial prices:
.
I = w/w = ( - *),
 > 0,
(18)
: speed of wage adjustment.
36


Thus, * is relative price at which wage inflation is zero
and industrial prices remain constant.
Using (13) and (18),
.
/ = A[(y~A + yI) - y~A] - ( - *). (19)





Figure 11.4: solution of the system consisting of (12),
(13), and (19).
.
Curve AA: identical to curve [PA = 0].
.
.
Curves [yI = 0] and [ = 0]: both upward sloping, with the
former having a steeper slope to ensure stability.
.
Slope of AA is also steeper than slope of [ = 0].
.
AA and [ = 0] intersect at B:  = * and food market is
in equilibrium.
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
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[yI = 0] and [ = 0] intersect at E:  > *.
.
[yI = 0] and AA intersect at G.
 None of the points represents a long-run equilibrium.
Point G:
 Food and industrial goods markets are both in
equilibrium but real wages are lower than desired level.
 Thus, nominal wages increase, raising industrial prices
and lowering the relative price of agricultural goods.
 Negative income effect reduces output in industrial
sector.
Point B:
 Real wages are at the desired level and food market is
in equilibrium.
 But there is an excess demand for manufactured goods.
39

Industrial production begins rising.
 But, increase in income exerts upward pressure on the
relative price of food products.
Point F:
 There is an excess demand in the food market.
 Upward pressure on agricultural prices causes a rise in
nominal wages.
 This leads to an increase in industrial prices and higher
output in that sector.
 If excess demand for food remains large relative to the
difference between actual and desired real wage,
nominal wages and industrial prices increase less
rapidly than agricultural prices.
 Thus,  rises over time.

40







This leads to excess demand for manufactured goods,
and industrial output rises.
.
.
Economy moves toward E, where [yI = 0] and [ = 0]
intersect, and both industrial output and the relative
price remain constant.
But at that point, excess demand for agricultural
products maintains upward pressure on their price.
Since real wage is lower than desired, both nominal
wages and industrial prices continue to rise.
Thus, there is no stable long-run equilibrium.
Outcome may be a self-perpetuating inflationary
process.
Stable, long-run equilibrium can be achieved by
government policies.
41
.
Reduction in g that is large enough
to shift [yI = 0] to the
.
left until it intersects AA and [ = 0] at B can halt
inflationary spiral, at the cost of lower industrial output.
~
 Income policy that reduces  can increase * toward 
and eliminate inflationary cycle.
Price controls:
 It prevents capitalists in the industrial sector from raising
their prices and maintain the relative share of profits in
national income, without necessarily leading to a
reduction in output.
General implication of the analysis:
 When workers' desired real wage is high relative to the
level compatible with long-run equilibrium, inflation
stabilization is impossible to achieve without a shift in
income distribution.
42

A Structuralist-Monetarist Model



Assumption in new structuralist models of inflation:
monetary policy fully accommodates changes in the
price level.
Integrated framework that accounts explicitly for money
supply dynamics in the new structuralist model, is
introduced.
Link between prices, money, and fiscal deficits is
captured by
 introducing food subsidies;
 accounting for the government budget constraint.
43

In the presence of a subsidy at the rate 0 < s < 1, the
consumer price index:
P = [(1-s)PA]dP1-
.
I



Government levies a uniform tax on factor income at the
rate 0 <  < 1.
Its expenditures consist of demand for industrial goods
(g) and food subsidies.
The government budget constraint can be written as
.
~
~
M = PIg + sPAyA - (PAyA+PIyI).
44

In real terms:
.
m = g + (s-)y~A - yI - Im,

(21)
m: real money balances measured in terms of industrial
prices.
Assume: demand for food products is a positive function
of real money balances.
45

Equilibrium condition of the food market in the presence
of food subsidies:
~
~
(1-s)yA = (1-)(yA+yI) + m,



: propensity to consume out of disposable income.
Left-hand side: post-subsidy value of the supply of food,
measured in terms of industrial goods.
Last term on the right-hand side: real balance effect.
Dynamics of output adjustment in the market for
manufactures:
.
~
yI = I[(1-)(1-)(yA+yI) + (1-)m + g - yI].
(23)
46

Assuming that workers pursue a real wage target, the
required relative price:
* = (1-)-1[(1+)*]-1/.

Behavior of relative price is determined by:
.
/ =
~
~
A[(/(1-s))(yA+yI) + (/(1-s))m - yA] - (-*).
(25)

Using (18), (21) can be approximated at t = 0 by
.
m  g + [(s-)y~A - m0] - yI + (0-*)m.
(26)
47







Equations (23), (25), and (26): dynamic system in yI, ,
and m.
Assume: output adjustment in the market for industrial
goods is instantaneous (I  ).
.
Solving (23) for yI with yI = 0 and substituting the result
in (25) and (26) yields a system of two differential
Equations in  and m.
Figure 11.5: graphical presentation of the equilibrium.
.
[ = 0]: positively sloped.
Reason: increase in money holdings raises demand for
agricultural and manufactured goods, requiring an
increase in the relative price of food to maintain
equilibrium.
.
[m = 0]: negatively sloped under the assumption that
48
(s-)y~A > m0.
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w
S
t
r
u
c
t
u
r
a
l
i
s
t
M
o
d
e
l

.
=
0

E
.
m
=
0
m
*
m
S
o
u
r
c
e
:
S
r
i
n
i
v
a
s
a
n
e
t
a
l
.
(
1
9
8
9
)
.
49




Long-run effect of an increase in the subsidy rate on
inflation is ambiguous.
Two opposite effects:
 Increase in subsidy payments increases government
spending and reduces the wedge between the actual
price ratio and its required level which tends to raise
real money balances.
 Higher activity in the industrial sector raises income
tax revenue and reduces the fiscal deficit, exerting a
downward pressure on money growth.
If subsidy rate is high enough initially, raising it further
leads to higher money growth and inflation.
If wages are fully flexible, increasing subsidies on food
is always inflationary.
50
Dynamics of Monetary and
Exchange-Rate Rules


A One-Good Framework.
 Households.
 Government and the Central Bank.
 Money Market Equilibrium.
 Dynamic Form.
 Devaluation Rule.
 Credit Growth Rule.
 Dynamics with Alternative Fiscal Policy Rules.
A Three-Good Model with Flexible Prices.
 Households.
 Output and the Labor Market.
 Central Bank and the Government.
52
Market-Clearing Conditions.
 Dynamic Form.
 Policy Shocks.
Extensions.
 Imported Intermediate Inputs.
 Sticky Prices.


53
A One-Good Framework




Domestic and foreign assets are imperfectly
substitutable in private agents' portfolios.
Small, open economy in which there are four types of
agents:
 producers,
 households,
 government,
 central bank.
All firms and households are identical, and their number
is normalized to unity.
Domestic output consists of a tradable good produced
using only labor, which is supplied in fixed quantity ns.
54





Wages are perfectly flexible, so that domestic
production is fixed.
Purchasing power parity holds continuously.
Under a regime of predetermined exchange rates:
 Domestic currency is depreciated at a constant rate
by the central bank.
 Central Bank’s stock of foreign assets adjusts to
equilibrate supply and demand for foreign exchange.
Under a regime of flexible exchange rates: foreign
reserves of the central bank are constant and rate of
credit growth is predetermined.
Households hold two categories of assets :
 domestic money;
 domestic government bonds.
55







Domestic money bears no interest.
Household borrows on world capital markets subject to
a rising risk premium.
Foreigners do not hold domestic assets.
Domestic interest rate adjusts to maintain equilibrium in
the money market.
Real rate of return on foreign bonds is determined on
world capital markets.
Government consumes goods and services, collects
lump-sum taxes, and pays interest on its domestic debt.
It finances its budget deficit either by issuing domestic
bonds or by borrowing from the central bank.
56
Households

Household's discounted lifetime utility:


0
{
}
c1-
+ lnm
1-
e-tdt,
, > 0
(27)
: constant rate of time preference;
c: consumption.
57

Nominal wealth of the representative household:
A = M + B - EL*,
M: nominal money stock;
B: stock of government bonds;
EL*: domestic-currency value of the stock of foreign
bonds;
E: nominal exchange rate;
L*: foreign-currency value of foreign borrowing by the
household.
58

Real wealth:
a = m + b - L*,
m  M/E: real money balances;
b  B/E: real stock of government bonds.
59

Flow budget constraint:
.
a = y + ib - c -  - (i*+)L* - (m+b), (28)
y: domestic output (constant at y(ns));
: real value of lump-sum taxes;
i: domestic nominal interest rate;
.
  E/E: predetermined rate of depreciation of the
exchange rate;
-(m+b) : capital losses on the stocks of money and
domestic bonds resulting from changes in the exchange
rate;
(i*+): cost of borrowing on world capital markets;
i*: exogenous, risk-free interest rate;
60
: risk premium.

Risk premium:
 = (L*, ),



L* > 0.
Premium is positively related to L*.
Individual default risk: domestic agent's borrowing
options are restricted by his or her capacity to repay.
Flow budget constraint can be rewritten as
.
a = y + ra - c -  - (i*+-r)L* - im,

(29)
(30)
r = i - : domestic real rate of interest.
Households treat y, , i*, i and  as given and maximize
(27) subject to (29) and (30) by choosing a sequence

{c,m,b,L}t=0
.
61

Required optimality conditions:
md = c/i,
(31)
i = (i* +  + ) + L*L*,
(32)
.
c/c = (r-),
(33)
lim(e-ta) = 0.
t


(31): money demand function.
It is obtained from the condition that the marginal rate of
substitution between money balances and consumption
be equal to the opportunity cost of holding money.
62








(33): conventional Euler Equation.
It shows that consumption rises or falls depending on
whether r exceeds or falls below .
(32): arbitrage condition that determines implicitly the
demand for loans.
Suppose: premium rises with the level of private debt.
Optimality: households borrow up to the point where the
marginal return and the marginal cost of borrowing are
equalized.
Marginal return: rate of return on domestic bonds.
Marginal cost of borrowing: i* +  +  + L*L*.
L*L*: increase in the cost of servicing the existing stock
of loans induced by the marginal increase in the risk
premium.
63

Since  is a function of L*, optimal level of borrowing
can be obtained from (32):
L* = (i - i* - )/,


 = 2L* > 0.
Foreign borrowing is positively related to
 difference between domestic interest rate;
 sum of safe world interest rate and devaluation rate.
Demand for foreign loans is proportional to the
differential i - i* - , with a proportionality factor that
depends on the sensitivity of the risk premium to the
level of private debt.
64
Government and the Central Bank



There are no commercial banks in the economy.
Central bank lends only to the government.
Nominal money stock:
M = D + ER*,
(35)
D: stock of domestic credit allocated by the central bank
to the government;
R*: stock of net foreign assets, measured in foreigncurrency terms.
65

Changes in the real credit stock d  D/E:
.
d = (-)d,



: rate of growth of nominal credit stock.
Central bank receives interest on its holdings of foreign
assets and its loans to the government.
Interest rate paid by the government on central bank
loans equals market rate of interest on domestic bonds.
Real profits of the central bank:
cb = (i*+)R* + id,
(37)
R*: real capital gains on reserves.
66




Government's revenue sources: lump-sum taxes on
households and transfers from the central bank.
It consumes goods and services and pays interest on its
domestic debt.
It finances its budget deficit by borrowing from the
central bank or issuing bonds.
Nominal flow budget constraint of the government:
. .
B + D = E(g--cb) + i(B+D),

g: noninterest government spending.
In real terms, and using (37):
. .
d + b - m = g + rb - i*R* - .
(38)
67



(38): government spending plus net interest payments
on the domestic debt, minus lump-sum taxes, and
interest income on reserves, must be financed by
 issuance of bonds;
 increase in real domestic credit;
 seigniorage revenue.
(38) yields government's intertemporal budget
constraint.
It equalizes present value of government purchases of
goods and services to initial holdings of net assets plus
present value of lump-sum taxes subject to the solvency
requirement
lim be-rt = 0.
t
68
Money Market Equilibrium

Equilibrium condition of the money market:
ms = md.

Given (31), the above Equation can be solved for the
market-clearing domestic interest rate:
+
-
i = i(c, m).

(39)
Equilibrium nominal interest rate depends positively on
private consumption and negatively on the stock of real
cash balances.
69
Dynamic Form

Substituting (30), (35) and (38) in the household's flow
budget constraint (28) give the economy's consolidated
budget constraint:
. .
L* - R* = i*(L*-R*) + L* + c + g - y. (40)


This determines the behavior over time of the total stock
of foreign debt.
Counterpart to change in net external liabilities:
 current account deficit (c+g-y) and
 net interest payments on the outstanding foreign debt
i*(L*-R*) + L*.
70

Integrating (40) yields economy's intertemporal budget
constraint:
L*0 - R*0 =




e-i*(y - c - g - L*)dt.
0
Current level of foreign debt must be equal to the
discounted stream of the excess of future output over
domestic absorption (c+g), adjusted for the loss in
resources induced by capital market imperfections.
(33), (34), (36), (38), (39), and (40) describe the
evolution of the economy along any perfect foresight
equilibrium path.
71

The system can be rewritten as:
L* = [i(c,m) - i* - ]/,
.
c/c = [i(c,m) -  - ],
(41)
(42)
. .
L* - R* = i*(L*-R*) + (L*)L* + c + g - y, (43)
. .
d + b + m = g + rb - i*R* - ,
(44)
.
d = (-)d,
(45)
m = d + R*.
(46)
72




(41)-(46): differential equation system with six
endogenous variables, c, b, L*, R*, d, and m.
Note that: capital account and overall balance of
payments are defined in terms of changes in the level of
private foreign debt and official reserves.
This definition do not capture transactions that occur
discretely under a regime of predetermined exchange
rates.
Although the economy's overall stock of foreign debt L*R* is predetermined, official reserves and private foreign
borrowing may jump in response to sudden movements
in domestic interest rates.
73
.
Assume that b = 0, and instead government either
borrows from the central bank or varies lump-sum taxes
to balance its budget.
. . .
 Steady-state solution is obtained by setting c = L* = R*
.
= d = 0.
In the long-run equilibrium:
 Real domestic interest rate must be equal to the rate of
time preference:

~ ~
r =  -  = .

(47)
Rate of domestic credit growth must be equal to the
devaluation rate:
 = .
74

Real money balances are thus
~
~
m = m(c, +).
75
Devaluation Rule


Under a constant rate of devaluation ( = h), rate of
growth of the credit stock must be endogenous if taxes
cannot be adjusted to finance the fiscal deficit ( = 0).
Setting constant stock of government bonds equal to
zero, (44) implies that the evolution of the real stock of
credit over time
.
d = g - i*R* - 0 - hm.

(50)
Path of d given by (50) can be substituted in (45) to
determine :
.
 = h + d/d.
76
.


.
.
From (46), m = d + R*.
Substituting (50) in this expression yields
.
.
m = R* + g - i*R* - 0 - hm.

Using (43):
.
.
m = L* + y - c - 0 - (i* + )L* - hm. (51)

Because the stock of government bonds is normalized
to zero, (28) implies that
m = a + L*,
(52)
which can be substituted in (41) to give
L* = [i(c, a+L*) - i* - h]/.
77

Taking a linear approximation to the function i() yields
L* = (icc + ima - i* - h)/(-im).

Equivalently
+
-
-
L* = (c, a; h),
(53)
where, setting   1/(-im) > 0:
c = ic,

a = im,
 = -.
Substituting (53) in (52) implies that
+ +
-
m = a + L* = h(c, a; h),
hc = c,
ha = 1 + a < 1,
(54)
h = .
78

Substituting (54) in (42) yields
.
+ - - h
h
h
c = c{i [c, h(c, a,  )] -  - } = G(c, a;  ),
(55)
~
~
~
Gc = cic,
Ga = cimha, G = -c.

Substituting (53) and (54) in (51) and rearranging yields
. .
.
a = m - L* = y - c - 0 - [i* + ((c, a; h))]
(c, a; h) - hh(c,a; h).
79

Equivalently
- + +
.
a = (c, a; h),
(56)
where, with a ‘~’ denoting initial steady-state values:
~ ~
~
c = -1 - (+L*L*)c,
~
~
a = -(+L*L*)a - hha,
~
~
 = -(+L*L*)h - m.

Taking a linear approximation of (55) and (56) around
initial steady state yields the following system:
.
c
.
a
=
Gc
c
~
Ga
c-c
a
~
a-a
(57)
80








Consumption is a forward-looking variable, whereas
financial wealth is predetermined at each moment in
time, with an initial value a0.
Determinant of the system (57) is given by Gca-Ga c.
It must be negative for the system to be saddlepoint
stable.
Figure 11.6: diagrammatic solution of the model.
.
CC (along which c = 0) is upward sloping and so is AA,
.
along which a = 0.
Saddlepath stability requires CC to be steeper than AA.
Saddlepath SS: unique path leading to the steady-state
equilibrium (point E).
Suppose that the economy is initially in a long-run
equilibrium position.
81
F
i
g
u
r
e
1
1
.
6
E
q
u
i
l
i
b
r
i
u
m
i
n
t
h
e
O
n
e
G
o
o
d
M
o
d
e
l
c
C
S
A
E
~
c
S
C
a
0
~
a
a
82



Consider the effect of a permanent, unanticipated
reduction in  from h to s < h.
~
Reduction in  raises a~ and lowers c.
From (41) and (47), steady-state level of private foreign
borrowing is
~
(58)
L* = (-i*)/,
~
~
Because a rises, it must be the case that m rises.
Reason:
 From (47) nominal interest rate must be equal in the
steady-state to the rate of time preference plus the
devaluation rate.
 It therefore falls in the same proportion as the
83
devaluation rate so it raises demand for cash balances.






Reduction in  raises private foreign borrowing at the
initial level of domestic interest rates.
Since private financial wealth cannot change, this
portfolio shift must be offset by a rise in real money
balances.
This adjustment takes place through purchases of
foreign currency assets by the central bank
accompanied by a discrete increase in the domestic
money stock.
Consumption falls to place the economy toward new
steady state.
Since real money stock rises and consumption falls,
domestic nominal interest rate falls by less than the
devaluation rate.
84








Increase in foreign borrowing raises risk premium faced
by private agents on world capital markets.
So services account of balance of payments
deteriorates.
At the same time, reduction in private consumption
leads to an improvement in trade balance.
Net effect on changes in private financial wealth is
positive.
Rate of growth of the nominal credit stock falls on
impact.
Since shock is permanent, adjustment path to the new
steady state is monotonic.
Figure 11.7: transitional dynamics.
Economy is initially at point E.
85
F
i
g
u
r
e
1
1
.
7
R
e
d
u
c
t
i
o
n
i
n
t
h
e
D
e
v
a
l
u
a
t
i
o
n
R
a
t
e
i
n
t
h
e
O
n
e
G
o
o
d
M
o
d
e
l
c
C
S
'
A
E
E
'
~
c
A
S
' B
C
~
a
a86






Reduction in  shifts both CC and AA to the right.
Because private wealth is predetermined, consumption
jumps downward from point E to point B, located on the
new saddlepath S’S’, and begins rising afterward.
Nominal interest rate must rise over time to allow real
interest rate to return to its initial steady-state value.
This increase leads to a reduction in private foreign
borrowing.
During the transition current account remains in surplus,
which is large enough to compensate for capital
account deficit.
Therefore, central bank's holdings of foreign assets and
real money stock increase.
87



As a result of both increase in real money balances and
reduction in foreign borrowing, private financial wealth
rises over time.
Assuming that risk-free rate is not too large, rate of
nominal credit growth falls gradually over time toward
lower devaluation rate.
New steady state is reached at point E ’.
88
Credit Growth Rule


Under a constant nominal-credit rule ( = h), foreign
.
reserves of the central bank remain constant (R* = 0),
and devaluation/inflation rate is determined
endogenously.
Setting constant level of official reserves equal to zero
(m = d), (41) yields
+
-
-
 = i(c, d) - i* - L* = (c, d, L*).

This which can be substituted out in (45) to give
.
d = [h - (c, d, L*)]d.
(59)
89


(59) determines changes in the real credit stock.
.
Because R* = 0, (43) can be written as
.
L* = [i* + (L*)]L* + c + g - y.





(60)
This determines changes in private external borrowing.
Difference from previous case: private foreign borrowing
is predetermined at any point in time.
Assume: lump-sum transfers are continually adjusted to
maintain fiscal equilibrium.
Dynamic system consists of (42), (59), and (60).
From (41), i -  = L* + i*.
90

Substituting this result in (42) yields
+
.
c/c = (i -  - ) = (L* + i* - ) = (L*).

Dynamic system:
.
0
c
.
~
d = -cd
.
L*
1
~

0
~
c-c
~
-dd
-L*d
0

~
d-d
~
L* - L*
(61)
~ ~
where  = i* +  + L*L*.
91






Necessary and sufficient conditions for saddlepath
stability: determinant of the matrix of coefficients in (61)
be negative and its trace be positive.
Both conditions always hold.
Consider reduction in rate of expansion of nominal
credit stock, from h to s < h .
In the long run, private foreign borrowing is determined
only by difference between rate of time preference and
risk-free world interest rate, and thus does not change.
Because output is constant, this result implies that
consumption also does not change.
From (59), devaluation rate must fall in the same
proportion as the nominal credit growth rate, to ensure
constant real credit stock in steady state.
92






As a result, domestic nominal interest rate falls also in
the same proportion as nominal credit growth rate.
Because consumption does not change, reduction in
opportunity cost of holding money is unambiguously
associated with increase in real money balances.
Because stock of nominal credit does not change,
nominal exchange rate must undergo a step
appreciation.
There are, therefore, no transitional dynamics.
Economy jumps immediately to new steady state, with
no effect on consumption, current account, private
foreign borrowing, or domestic real interest rate.
Rate of depreciation falls instantaneously to the lower
level of credit growth rate.
93
Nominal interest rate falls also in the same proportion.
 This is associated with a steady-state increase in real
money balances, resulting from an appreciation of the
nominal exchange rate.
Exchange rate and monetary rules may lead to very
different adjustment paths for the main variables
under imperfect capital mobility:
 Models based on the monetary approach to the balance
of payments possess a “dynamic equivalence” property:
steady-state solutions and adjustment paths associated
with a monetary rule or an exchange-rate rule are
identical.
 In the model developed here, behavior of economy
during the transition period is completely different.

94
Under a credit growth rule, there is no transitional
adjustment as such; economy jumps immediately to
the new steady state.
 Under an exchange-rate rule, there are two types of
adjustments:
 those that occur through time;
 those that occur instantaneously.
Depending on the constraints that policymakers face in
the short run, nature of the transitional dynamics
determine adoption of one rule as opposed to the other.


95
Dynamics with Alternative Fiscal Policy
Rules




Adjustment path induced by monetary and exchangerate policy shocks depends on financing rules that
policymakers adopt to close fiscal deficit.
Assume: government does not issue bonds, and the
central bank sets rate of growth of nominal credit so as
to compensate the government for the loss in value of
real outstanding stock of credit due to inflation ( = ).
Government then adjusts lump-sum taxes to close fiscal
deficit.
In this setting, monetary policy and exchange-rate policy
cannot be distinguished.
96


This financing rule satisfies the transversality condition
of the public sector and is therefore sustainable.
.
Because
. credit rule implies that d = 0, Equation (44),
with b = b = 0, can be solved for lump-sum taxes:
 + m = g - i*R*,

m: inflation tax revenue.
. .
As a result of this rule, m = R* (changes in real money
stock reflect only changes in the central bank's net
foreign assets).
97
Agénor (1997b):
 Analysis of the above model under the financing rule.
 Short- and long-run dynamics associated with a
permanent, unanticipated reduction in the rate of
devaluation-credit growth rate are similar to those
reduction in the devaluation rate with credit financing of
the budget deficit.
98
A Three-Good Model with
Flexible Prices





Economy produces two goods:
 nontradable good that is used only for final domestic
consumption;
 exportable good, whose output is entirely exported.
Capital stock in each sector is fixed.
Labor is homogeneous and perfectly mobile.
Households and the government consume home goods
and an imperfectly substitutable importable good.
Prices in the home goods sector and nominal wages are
perfectly flexible.
99
Households



Consumption decision follows a two-stage process:
 determine optimal level of total consumption given
their budget constraint;
 allocate optimal amount between consumption of
home and importable goods.
Under the assumption that labor is supplied inelastically,
representative household's discounted lifetime utility
remains as in (27).
Difference: c and m are measured in terms of price of
consumption basket, P.
100

Real financial wealth of the representative household is
defined as in (28):
a = m + b - l*,
(63)
a and b measured in terms of price of the consumption
basket;
real foreign indebtedness l* now defined as l*  EL*/P.
101

Flow budget constraint:
.
a = y + ib - c -  - (i* + )l* - l* - a,

(64)
y: net factor income;
.
  P/P: overall inflation rate.
-a: capital losses on total wealth due to inflation.
l*: increase in the domestic-currency value of external
liabilities due to exchange rate devaluation.
Using (63), (64) can be written as
.
a = ra + y - c -  - (i* +  +  - i)l* - im, (65)
r = i - : domestic real rate of interest.
102

First stage of the consumption decision process:
household
 treats , , y, i, i* and  as given,
 internalizes effect of her borrowing decisions on ,
 maximizes (27) subject to (29) and (65) by choosing

{c, m, b, L*}t=0
.
103

Optimality conditions:
md
=
c/i
+ -
= m(c, i) ,
i = (i* +  + ) + L*L*,
.
c/c = (r-),
(66)
(67)
(68)
lim(e-ta) = 0.
t

Using linear approximation to , (67) yields a demand
function for foreign loans:
L* = (i - i* - )/.
(69)
104
What is new in this setting?
 Intertemporal Euler Equation (68): overall expenditure
growth depends on real rate of interest measured in
terms of the price of the consumption basket.
 Thus, presence of nontradable goods prevents
equalization of domestic and foreign real interest rates.
 Thus, differential changes in relative price of
nontradable goods across countries imply different real
rates of return even when nominal rates are equal.
105

Second stage of consumption decision process:
household maximizes a homothetic sub-utility function
V(cN, cI), subject to static budget constraint
PNcN + EcI = Pc,

PN: price of the home good;
cI (cN) expenditure on the importable (nontradable)
good.
Since foreign-currency price of the importable good is
normalized to unity, domestic-currency price is nominal
exchange rate.
106


Since household's intratemporal preferences are
homothetic, desired ratio between home and importable
goods depends only on their relative price, not on
overall expenditure.
Thus:
Vc /Vc = z-1.
N

I
z  E/PN : relative price of the importable good in terms
of the home good.
Assume: sub-utility function is Cobb-Douglas, so that
V(cN, cI) = cN cI1-,
0 <  < 1: share of total spending on home goods.
107

Desired composition of spending is thus
cN/cI = z/(1-).

This can be substituted in intratemporal budget
constraint, c = z(cI + cN/z), to give
cN = z1-c,

cI = (1-)z-c.
(70)
From indirect sub-utility function, definition of consumer
price index P:
P = PNE1- = Ez-.
108

Inflation rate:
.
 =  - z/z.
(72)
109
Output and the Labor Market

Technology for the production of tradable and
nontradable goods is characterized by decreasing
returns to labor:
yh = y(nh),

yh’ > 0, yh’’ < 0
h = N, X,
yh: output of good h;
nh: quantity of labor employed in sector h.
From first-order conditions for profit maximization, the
sectoral labor demand functions
d
d
nX = nX(wX),
d
d
nN = nN(zwX),
d
d
nX’, nN’ < 0,
(74)
wX: product wage in the exportable goods sector.
110

Since nominal wages are perfectly flexible, wX can be
solved for from equilibrium condition of the labor market:
d
d
nX(wX) + nN(zwX) = ns,

ns: supply of labor (constant).
Equilibrium product wage is negatively related to real
exchange rate:
wX = wX(z),

wX’ < 0, |wX’| < 1.
(75)
Substituting this result in (74) , and noting that d(zwX)/dz
= 1 + wX’ > 0, yields sectoral supply equations:
s
s
yh = yh(z),
s
s
yX’ > 0, yN’ < 0.
111
Central Bank and the Government


There are no commercial banks in the economy, and
central bank does not provide credit to domestic agents.
Real money supply
ms = zR*.

(77)
Real profits of the central bank, i* + zR*, are
transferred to the government.
112

With lump-sum financing, and setting constant real
stock of government bonds to zero, government budget
constraint
 = z(gI + gN/z) - z(i*+)R*,
(78)
gI and gN: government spending on importable and
nontradable goods.
113
Market-Clearing Conditions

Equilibrium conditions for the home goods market:
yN = z1-c + gN.
s

(79)
Market-clearing interest rate is given by (39).
114
Dynamic Form

Real factor income y:
y = z(yXs + yNs /z).

(80)
Equations (63) and (77) yields
a = z(R* - l*).


Although R*-l* is predetermined, real exchange rate can
change in discrete fashion; net financial wealth a can
also jump on impact.
Using definition of a and (72) yields:
.
. .
a = z(R*-L*) + (-)a.
115
Substituting this result, together with (70), (78), (79) and
(80) in (64) yields

.
.
L* - R* = i*(l*-R*) + (l*, ·)L* +
(1-)z-c
+ gI -
s
y X.
(81)


This represents consolidated budget constraint of the
economy.
Integrating (81) yields economy's intertemporal budget
constraint.
116

From Equations (70) and (79), short-run equilibrium real
exchange rate is obtained as
-
-
(82)
z = z(c; gN),
where
~
zc = /[yN’ - (1-)c],
s
~
zg = 1/[yN’ - (1-)c].
s
N
117

Behavior of the economy over time:
L* = [i(c,m) - i* - ]/,
.
.
.
c/c = [i(c, m) -  + z/z - ],
(84)
z = z(c; gN),
(85)
D = i*D + (L*)L* +
(1-)z-c
m = zR*.

(83)
s
+ gT - yX(z), (86)
(87)
(78) determines residually lump-sum taxes and D = L*R* denotes net external debt.
118

To condense the dynamic form into a system involving
only c and D, note that from (87):
m = z(L*-D),
or, using (83):
m = z{[i(c,m) - (i*+) - D]/}.
119

Substituting (85) in (89) yields
m = z(c;gN){icc - (i*+) - D},
  1/( -im),
so that
?
-
-
-
m = (c, D; i*+ ,gN),
(91)
where
~
c = (ic+zcR*), D = -,
i*+ = -,
~
gN= zgNR*.
120

Substituting (91) in (84) yields
.
.
c/c = {i [c, (c, D; i*+, gN)] -  + z/z - }. (92)



Assume: changes in gN occur only in discrete fashion.
.
.
(85) therefore implies that z = zcc, with zc < 0.
Substituting this result in (92) yields a dynamic equation
.
+ + +
+
-
c = G(c, D; i*, , gN),
~
(93)
~
where, with  = c/(1-czc) > 0:
Gc = (ic+imc), GD = imD, Gi* = imi*+ ,
G = (imi*+-1), Gg = img .
N
N
121

Substituting (91) into (83) yields
+ +
+
L* = (c, D; i*+ , gN),
(94)
where
D = imD/ = -im,
i*+ = -,
~
c = (ic + imc)/ = (ic + imzcR*),
g = img /.
N
N
122

Using (94), (86) can be written as
.
+ + ? - +
D = (c, D; i*, , gN) - gI,
(95)
where
~
~
~
c = -zc[yX’ + (1-)c] + (1-) + (+L*L*)c,
s
~
~ ~
~
D = i* + (+L*L*)D,
 = (+L*L*)i*+,
~
s
~ ~
g = -zg [yX’ + (1-)c] + (+L*L*)g ,
N
N
N
~
~
~
i* = D + (+L*L*)i*+.
123



Partial derivative I * is ambiguous:
 increase in risk-free rate raises debt-service
payments in proportion to initial stock of foreign debt;
 premium-related component of external debt service
also falls along with demand for foreign loans by
private agents.
Net effect on current account cannot be ascertained a
priori.
While highly indebted economies are investigated, it will
be assumed that net effect is positive: rise in risk-free
world interest rate increases current-account deficit.
124

(93) and (95) form dynamic system in c and D, which
can be linearized around the steady state and written as
.
c
.
D


=
~
Gc
GD
c-c
c
D
D-D
~
(96)
Saddlepath stability requires GcD - GDc < 0.
.
.
Steady-state solution is obtained by setting c = D = 0 in
(93) and (95).
125

From (72), steady-state inflation rate and rate of
inflationin nontradable prices are equal to the
devaluation rate:
~
~
 = N = .

In the steady state current account must be in
equilibrium:
~
~- ~
~
~
~
yX(z) - (1-)z c - gI = i*D + (L*, )L*.
s


Real interest rate is equal to rate of time preference,
and household's steady-state level of foreign borrowing
is given by (58).
Figure 11.8: steady-state equilibrium.
126
F
i
g
u
r
e
1
1
.
8
E
q
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C
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1
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9
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,
p
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)
.
127




NN curve in the north-west quadrant: combinations of
private consumption c and real exchange rate z that are
consistent with equilibrium in the market for nontradable
goods (82).
LL curve in the south-west quadrant: combinations of
product wage in the exportable goods sector wX and
real exchange rate that are consistent with labor market
equilibrium (75).
CC and DD curves in the north-east quadrant: similar to
curves in the previous subsection.
Right of CC: domestic real interest rate is higher than
rate of time preference, consumption is increasing, and
real exchange rate is appreciating to eliminate excess
supply of nontradable goods.
128


Left of CC: falling consumption, excess supply of home
goods, and a depreciating real exchange rate.
Saddlepath stability requires that CC curve be steeper
than DD.
129
Policy Shocks
Tax-financed, permanent increase in gN.
 It has no long-term effect on
 domestic nominal interest rate;
 foreign borrowing by the private sector.
 At the initial level of the real exchange rate, private
consumption must fall to maintain equilibrium of the
market for nontradable goods.
 Real money balances must therefore fall, because
domestic interest rates do not change.
 Reduction in private consumption is proportionally less
than increase in government expenditure, so that
 total domestic spending on home goods rises;
130
real exchange rate appreciates to maintain
equilibrium in the home-goods market.
Although real appreciation tends to reduce output of
tradable goods, trade-balance surplus must rise to
maintain external balance, because
 economy's stock of debt D increases;
 services account deteriorates.
This increase in debt results from reduction in net
foreign assets held by the central bank R*.
On impact, private consumption falls because increase
in government spending
 raises households' lifetime tax liabilities;
 thus reduces their lifetime wealth.




131





Real exchange rate may either appreciate or
depreciate, depending on whether total spending on
nontradable goods rises or falls.
If degree of intertemporal substitution in consumption 
is sufficiently low,
 private consumption will change relatively little on
impact;
 total spending will increase;
 this leads to an appreciation of real exchange rate.
Figure 11.9: adjustment path to permanent increase in
gN when  is low enough to ensure that real exchange
rate appreciates.
CC and DD shift to the left in the north-west panel.
NN in the north-east panel shifts inward.
132
F
i
g
u
r
e
1
1
.
9
I
n
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r
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a
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~
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:
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(
1
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b
,
p
.
4
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)
.
~
D
D
133






Private consumption jumps downward from point E to
point A located on the new saddlepath S’S’.
Real exchange rate jumps from point H to point Q
located on the new NN curve.
At the initial level of interest rates and official reserves,
real money stock falls on impact.
Reduction in money demand induced by fall in c is
matched by reduction in supply.
Reason for reduction in supply: valuation effects on
domestic-currency value of official reserves associated
with appreciation of real exchange rate.
If valuation effects are not too large, fall in c leads to
reduction in i, despite upward pressure induced by
reduction in money supply.
134







Private foreign indebtedness therefore falls, and the
economy registers an outflow of capital.
Because stock of foreign debt cannot change on
impact, official reserves must fall.
Current account moves into deficit and remains in deficit
throughout the transition process.
c continues to fall over time, and real exchange rate
depreciates.
Because i falls on impact, it must be rising during the
transition to the new long-run equilibrium in order to
restore equality between r and .
Thus, private foreign indebtedness increases over time
and the economy experiences net capital inflows.
This continues until private borrowing on world capital
135
markets returns to its initial value.
Unanticipated permanent reduction in :
 This has no long-run effects on r or private foreign
borrowing.
 But, although r remains equal to  in the new steady
state, i falls in the same proportion as devaluation rate.
 Reduction in opportunity cost of holding money raises
demand for domestic cash balances.
 Official stock of net foreign assets must thus rise.
 Since private foreign borrowing does not change, the
economy's external debt must be lower in the new
steady state.
 This implies that initial deficit in the services account is
also lower.
136






To maintain external balance, initial trade surplus must
fall (or c must rise).
Increase in c leads to real exchange rate appreciation
and raises further demand for domestic cash balances.
On impact, c falls because the immediate effect of
reduction in  is to increase r, thereby creating an
incentive to shift c toward the future.
Reduction in  also leads to a discrete increase in
private demand for foreign loans, thereby requiring an
offsetting increase in official reserves.
Because c falls and m rises, net impact effect on i is
unambiguously negative.
Fall in c requires a depreciation of real exchange rate to
maintain equilibrium between supply and demand for
137
home goods.








As a result of reduction in c and expansion of output of
tradables induced by depreciation of real exchange
rate, trade balance surplus increases.
Negative income effect associated with increase in
premium-related component of interest payments raises
initial deficit of the services account.
Current account nevertheless improves, and external
debt falls.
Because the shock is permanent, current account
remains in surplus throughout adjustment process.
c increases, and real exchange rate appreciates.
r rises toward its initial steady-state level, given by .
Upper panel of Figure 11.10: dynamics of this shock.
Both CC and DD shift to the left.
138
F
i
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1
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.
1
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3
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D
139
F
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1
1
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1
0
b
R
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d
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t
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D
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R
a
t
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c
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S
D
S
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M
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F
H
E
B
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A
B
D
S
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N
z
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e
m
p
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y
s
h
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c
k
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S
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p
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4
3
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.
S
~
D
D
140
Consumption jumps downward from E to point A on
impact, and begins rising afterward.
 Economy's stock of foreign debt falls during transition to
the new steady state, which is reached at E’.
Temporary reduction in :
 Lower panel of Figure 11.10.
 Because the shock is temporary, optimal smoothing
response for the household is to reduce c by less than
she would, if the shock was permanent.
 Depending on the length of the interval, two adjustment
paths are possible.
If duration of the shock is short:
 c jumps downward from E to A’, and increases until
reaching B’ on the original saddlepath at T.
141

Trade balance improves only slightly, since short
duration of the shock gives agents little incentive to alter
their c path.
 Current account therefore moves into deficit, and
external debt increases until the shock is reversed.
 Thus, c will continue to increase, with current account
moving into surplus, until economy returns to the
original equilibrium point E.
If duration of the shock is sufficiently long:
 c jumps from E to A, and increases until F on the
original saddlepath is reached at T.
 Thereafter, c starts falling along the original saddlepath
SS, reaching the original equilibrium point E.

142
Whereas current account remains in surplus during the
first phase of the adjustment process, it moves into
deficit afterward.
 Point B is reached before period T.
 Thereafter, with c falling between F and E, current
account remains in deficit, and external debt increases.
Difference between long-run predictions under perfect
and imperfect world capital markets:
Under perfect capital markets:
   0.
 Uncovered interest parity condition i = i*+ holds
continuously, and private foreign borrowing can take
any value a priori.

143





Increase in demand for real cash balances induced by
reduction in opportunity cost of holding money is
achieved through increase in both
 money holdings;
 foreign indebtedness.
Household increases borrowing on world capital
markets.
This generates capital inflow which is monetized by
exchanging foreign exchange for domestic currency at
the central bank in such a way that the economy's net
stock of debt remains constant.
There are no real effects, and the adjustment process
displays no dynamics.
Economy jumps instantaneously to the new steady
144
state.
Although the composition of the economy's net external
debt changes, stock of debt and real variables do not.
Capital market imperfections:
  > 0.
 Long-run value of private foreign borrowing is “pinned
down” by the difference between i* and , and therefore
cannot vary across steady states in response to a
change in .
 Thus, increase in real cash balances induced by the
reduction in opportunity cost of holding money cannot
take place directly through inflow of capital and increase
in private foreign indebtedness.
 For official reserves to expand and for money supply to
match the increased demand for money, requires
145
sequence of current account surpluses.



Because higher official reserves imply a reduction in the
economy's net external debt, lower deficit in the
services account must be accompanied by a lower trade
surplus (higher c).
Adjustment process to a reduction in  displays
transitional dynamics as well as real effects in the long
run.
146
Extensions

Imported intermediate inputs and price stickiness in the
nontraded goods sector.
147
Imported Intermediate Inputs


Output of nontraded goods is produced using labor nN
and imported intermediate materials ON according to a
fixed-coefficients technology.
Production function is thus given by
yN = min(nN, ON),

1/: amount of intermediate materials that must be
combined with a unit of labor to produce a unit of the
domestic good.
Factor demand functions:
d
nN = yN,
ON = -1yN.
d
148

Assuming that world price of imported inputs is equal to
unity, in equilibrium price of home goods would be given
by the zero-profit condition:
pN = w + -1E.

This implies that w/E = z - -1.
149
Sticky Prices


Suppose that price of the nontraded good PN is
predetermined and adjusts only gradually in response to
disequilibrium in the market for these goods.
Specifically, consider the price adjustment Equation:
.
s
1-
  PN/PN = [z c + gN - yN] + ,


>0
(99)
: speed of adjustment.
 = 0: model operates in a “Keynesian” mode with fixed
prices.
  : case of perfect price flexibility.
150

.
Since z/z =  - N, using (99) yields
- 0 .
z/z=  - [z1-c + gN - yNs ] -  = (c, z; , gN),

(100)
where c = -.
In contrast to the case of perfect price flexibility, the
relationship is not between rates of change of z and c,
but between rate of change of z and the level of c.
151

Other Equations of the dynamic system are:
L* = [i(c,m) - i* - ]/,
.
.
c/c = [i(c, m) -  + z/z - ],
(101)
(102)
.
D = i*D + (L*)L* + (1-)z-c + gI - yXs(z), (103)
m = zR*.
(104)
L* = (c, D; i*+),
(105)
where c, D > 0, and i*+ < 0.
152

Eliminating L* using (101) and (104) yields
m = z{[i(c,m) - (i*+) - D]/},
which can be written as
+ +
-
-
m = (c, z, D; i*+),

~
where D = -, i*+ = -, c = ic, z = R*, gN = 0.
Substituting this result in (102) yields
.
.
c/c = {i[c, (c, z, D, i*+)] -  + z/z - }.
153

Then, using (100):
.
?
-
+ +
-
-
c = G(c, z, D; i*, , gN),
(106)
with  = c > 0:
Gc = (ic + imc + c), Gz = (imz + z),
GD = imD, Gi* = imi*+,
G = (imi*+ - 1), GgN = gN.

If  is sufficiently high, Gc, Gz < 0.
154

(103) and (105) yield
.
+ -
+ ?
-
D = (c, z, D; i*, ) - gI,
where
~
~
(107)
~
~
D = i* + ( + L*L*)D,  = ( + L*L*)i*+,
~
~
~
i* = D + ( + L*L*)i*+,
~
~
~
c = (1-) + ( + L*L*)c, z = -yX’ - (1-)c,
s
with i* > 0.
155


(100), (106), and (107) represent a dynamic system in
c, z, and D.
Linearizing the model around the steady state gives
.
c
.
z
.
D
~
Gc
Gz
GD
c-c
= c
z
0
c
z
D
z-z
~
D-D
~
156

Determinant of the system's matrix of coefficients A:
|A| = -c(DGz - zGD) + z(DGc - cGD),



It can be established, assuming that D is initially close
to zero, that |A| > 0.
Because |A| is equal to the product of the system's
characteristic roots, there are either two roots with
negative real part or no negative root.
Assume that  is sufficiently high to ensure that trA is
negative:
trA = Gc + z + D.
157


Because trA is equal to the sum of the system's
characteristic roots, there must be at least one root with
negative real part.
Conclusion:
 There are two roots with negative real parts.
 Thus, because z and D are predetermined state
variables, the system is saddlepath stable.
158