3 A fixed exchange rate regime
3.2 Stationary equilibria
A Walrasian steady-state equilibrium is such that fck U and the self-selection constraint (32) does not bind. kˆ,iˆ* and Wˆ denote, respectively, the steady-state capital-labor ratio, net investment abroad and the transfer to producers in a Walra- sian regime. Fˆ is the ratio of investment abroad to total savings in this regime.
From (33): 13
1 1
1 * 1
) 1
( ˆ 1
°°
¿
°°
¾
½
°°
¯
°°
®
»»
¼ º
««
¬ ª
¸¸¹
·
¨¨©
§
»¼
« º
¬ ª
D
D
I I D
V I I
U D
f d
f d
A A r
k (36)
13 Note that, in order for kˆ to be well-defined, V* must be such that U !0.
(34) and (35), respectively, then give Wˆ and Fˆ as a function of kˆ :
) 1 ( ˆ ˆ
G O
W
k (37)
A k
f
d )(1 )
1 (
)ˆ 1 1 (
ˆ 1
D I I O F G
D
(38) where G {W K is the (steady-state) subsidy rate on the capital stock per old pro-
ducer.14
The steady-state the capital-labor ratio in a Walrasian regime (kˆ ) is unaffected by the choice of T and/or [. However, increases in either T or [ increase G,affect- ing the capital subsidy (Wˆ ) and Fˆ .
Increasing either V*,r,Id or If reduces the steady-state capital-labor ratio, inde- pendently of whether a currency board regime or a pure fixed exchange rate regime is in place. This is a result of the direct link between the marginal product of capital and the rate of interest on loans that exists when credit is not rationed. In addition, higher inflation abroad always increases both the subsidy rate G15 and Fˆ .
In a currency board regime, an increase in the world real interest rate r in- creases the real return on the central bank's reserve position, and therefore, it in- creases the subsidy rate on capital (G). The same increase in r also increases Fˆ , through the resulting increase in G and reduction in kˆ . Also, increasing either Id or If always increases both G and Fˆ .
In a pure fixed exchange rate regime increases in r have no direct effect on the government's finances, leaving G unaffected. However, increases in r still lead to increases in
F ˆ
. Also, increases in either Id or If will increase (decrease) G when the foreign rate of inflation is positive (negative). As a result,F ˆ
will be increas- ing in either Id or If for all values but very small values of V*.Steady-state equilibria under a Credit Rationing regime have f’(k)>U, and the self-selection constraint (32) binds. k~
, ~i*andW~ denote, respectively, the steady- state capital-labor ratio, investment abroad and transfer to producers in a Credit Rationing regime. As Ie did before, we also define F~ to be the ratio of investment abroad to total savings in this regime. From (34) and (32) I determine the steady- state capital stock,
14 Notice that
> @
>
( 1)( ) (1 )@
) 1
( ) )(
1 , (
1 1
, *
*
*
f d
f d d
r r Max r
I [ TI
I I [ V TI
V
V G G
{
¿¾
½
¯®
¸
¹
¨ ·
©
§
! must hold for
lending to be positive. This condition is henceforth assumed to hold.
15 This is a result of the increase in domestic seigniorage income associated with a higher value of the money growth rate.
> @
> @
1 1
) 1 )(
1 (
) 1 ( ) 1
~ (
¿¾
½
¯®
D
DS D O
U G S S r A
k x (39)
and F~ from (35)
). 1 )(
1 (
)~ 1 1 (
~ 1
D I I O F G
D
f
A d
k (40)
In contrast with what we observed in stationary equilibria under a Walrasian re- gime, the steady-state capital-labor ratio in a Credit Rationing equilibrium is af- fected by the choice of T and/or [ made by the monetary authority. Increasing ei- therT or [ has a direct positive effect on the government's finances, increasing G.
AsG changes, it alters the incentives of Type 1 agents to misrepresent their type, affecting the self-selection constraint. In order to induce self-selection, there must be a corresponding change in the degree of credit rationing. Of course, as was true previously, the effects of changes in G may vary depending on different assump- tions on parameter values.
Case 1: DS !r(1O)(1D) When Case 1 obtains, an increment in G due to an in- crease in either T or [, ceteris paribus, increases the subsidy received by agents claiming to be of Type 2 and, in this way, affects the self-selection constraint. Given the high probability of repaying loans (S), k~
has to adjust upward to maintain the incentives of agents to self-select. As a consequence, W~ increases and F~ falls.
An increase in the (domestic and) foreign inflation rate V* has some potentially complicated consequences. These are described in the following proposition.
Proposition 7.Let (1 d f)
f d
d
c I I
I I
[ I ¸¸
¹
·
¨¨
©
§
{ , and let Case 1 obtain.
a) When [[0,[c) in a currency board, an increase in V* causes k~
to fall and F~ to increase if
>
( )(1 )( )@
)(
[ TI I I I
[ I TI I
I
{
d f d d
f d f
d
rc
r (41)
holds16.
16 Note that ¸¸
¹
·
¨¨©
§
d f d
rc
I I
I holds. However, for parameter values that seem to obtain in a
Latin American context, rc is fairly large. Thus, this condition is likely to be satisfied in practice.
b)When [[[c,(1Id If)) in a currency board, then an increase in V* causes k~
to fall, whether r<rc holds or not. On the other hand, when r<rc, F~ will be increasing (decreasing) in V* if ¸¸
¹
·
¨¨©
§
¸¹
¨ ·
©
§
!
d f
x d
I I I S S ) 1
( holds17.
c) When r<rc holds in a pure fixed exchange rate regime, an increase in V* causes k~
to fall. F~ is always increasing in V*.
Intuitively, a higher V* increases the net of subsidy effective real interest rate on loans,(1-G)U. This, in turn, affects the incentives of Type 1 agents to misrepresent their type. Given that DS !r(1O)(1D), the capital stock must fall in order to maintain the incentives of agents to self-select.
On the one hand, increments in r in a currency board regime increase the real return on the central bank's reserves, thereby increasing G. However, changes in r also affect the self-selection constraint and k~
must fall. Finally, F~ increases as a result of the higher r. On the other hand, increases in r in a pure fixed exchange rate regime rate do not affect G but they do affect self-selection constraint, and k~ must fall to maintain the incentives of Type 1 agents to self-select. At the same time, when the r rises, so does F~.
Under a fixed exchange rate regime, the only instruments of domestic monetary policy are the reserve requirements Id and If. In a currency board, an increase in If
reduces the capital stock (k~
) but an increase in Id seems to have an ambiguous ef- fect on k~
. In a pure exchange rate regime, increases in either of the domestic re- serve requirements (Id or If) in general reduce the creation of physical capital (k~
).
Case 2: DSr(1O)(1D) When Case 2 obtains, increases in V*, r, or the do- mestic reserve requirements (Id or If) will have the opposite effects on physical capital (k~
) relative to what would be observed when Case 1 obtains.
Steady-state equilibria do (not) display credit rationing if ~) ( )U
'( k !
f . This
condition is equivalent to
>
S S G U@ >
O D DS@
UD (1 )x (1 ) (!)r(1 )(1 ) (42)
whenever DS !()r(1O)(1D). U is a monotonically increasing and concave function of V*, and, if rrc, then (1G)U is also an increasing function of V*. These properties do not depend upon how the domestic money supply is backed in a fixed exchange rate regime. If U(V*) denotes the interest rate on loans as a function ofV*, then U(V*) has the configuration depicted in Figures 4 and 5. When credit rationing can emerge now depends, for given levels of foreign steady-state inflation, on assumptions on parameter values and on the nature of the fixed exchange rate regime in place.
17 Note that when [[[c,(1Id If)) holds,
¸¸
¹
·
¨¨
©
§
t
d f d
rc
I I
I holds.
Case 1:DS !r(1O)(1D) In situations where Case 1 obtains, both the left and the right hand side of (42) are not only negative but also decreasing in the foreign rate of inflation, V*. As stated previously, these properties do not depend upon how the do- mestic money supply is backed in a fixed exchange rate regime. As a result, the scope for credit to be rationed may depend in a relatively complicated way on the rate of foreign inflation. Two of these possibilities are illustrated in Figures 4a, and 4b.
0 Vc* V*
k fc~
Figure 4a. Argentina, Case 1, x large: steady state equilibria, world inflation and credit rationing
Figure 4a When x is relatively large, for low (high) levels of the foreign inflation rate, credit is (is not) rationed.
0 V*c V*
k fc~
Figure 4b. Argentina, Case 1, x small: steady state equilibria, world inflation and credit rationing
V*
U
V*
U
Figure 4b When x is relatively small, ~)
'(k
f lies everywhere above U(V*). Thus, in economies where Case 1 obtains and a fixed exchange rate regime is in place, the scope for credit to be rationed depends in a relatively complicated way on the rate of foreign inflation. In such a situation, increases in the level of steady-state foreign inflation are always detrimental to long-run output. There is no range of inflation rates over which increases in inflation promote real activ- ity.
Case 2: DS r(1O)(1D) In situations where Case 2 obtains (42) can be re- written as
>
(1 S) S(1 G)U@ >
(1 O)(1 D) DS@
U.D x ! r (43)
Notice that the left-hand side of (43) is positive and decreasing in V*, while the right- hand side is also positive but increasing in V*. Again, these properties do not depend upon how the domestic money supply is backed in a fixed exchange rate regime. As a result, two possibilities arise regarding the existence of steady states where credit is rationed. These possibilities are illustrated in figures 5a and 5b.
0
V
c*V
*V
*U f c k ~
Figure 5a. Argentina, Case 2, x small: steady state equilibria, world inflation and credit rationing
Figure 5a When x is relatively small, for low (high) levels of the foreign inflation rate, credit is (is not) rationed.
0
V
*V
*U f c k ~
Figure 5b. Argentina, Case 2, x large: steady state equilibria, world inflation and credit rationing
Figure 5b When x is relatively large, ~)
'(k
f lies everywhere above U(V*)and credit is always rationed.
As a result, in economies where Case 2 obtains and a fixed exchange rate re- gime is in place, low levels of steady-state inflation will in general be associated with credit being rationed. Moreover, there will be inflation thresholds as are ob- served empirically: foreign inflation and output are positively (negatively) corre- lated below (above) the threshold.