In this section we evaluate monetary and macroprudential policy designs in the context of market frictions and capital flows driven by global factors. Sources of inefficiency arise not only from distortions related to nominal rigidities, but also from the fact that only a fraction of households are owners to the markup-charging monopolistically competitive firms. Furthermore, portfolio adjustment costs of private asset holdings drive a wedge between expected returns of domestic and foreign securities, thus a friction in international risk sharing. Financial stability concerns lead many to call for measures that curb foreign exposures that make the economy vulnerable to foreign interest rate or exchange rate shocks, or worries that large capital inflows push up inflation challenges domestic policy makers to find ways to insulate the economy from foreign influences. We compare alternative policies by first considering a macroprudential regulation taking as given the specified interst rate rule. Next we augment the interest rate rule to respond to financial variables and study the policy implications jointly with the macroprudential regulation.
Consider the social welfare function Vt defined by the weighted average of the expected
dis-counted utility of the heterogeneous domestic households VBt and VSt
Vt≡ (1 − βB)VBt+ (1 − βS)VSt,
where
Vit mi,t−1, bi,t−1, b?i,t−1 ≡ max
{cs,ms,ls}∞s=0Et
∞ k=t
∑
βiku ci,t+k, mi,t+k, li,t+k , i∈ {B, S} .
Given the competitive equilibrium conditions and the interest rate rule defined in the pre-vious section, we evaluate the welfare implications of macroprudential policies that respond to international capital flows specified by the rules
τt = c1τt−1+ (1 − c1) τ + (1 − c1) c2 bf t− bf,t−1
(34)
and
τt?= d1τt−1? + (1 − d1) τ?+ (1 − d1) d2 b?Bt− b?B,t−1
(35)
where τt is the tax rate imposed on capital inflows bf,t, broadly interpreted as a measure to discourage foreign liabilities (bf,t is the foreign holdings of domestic bonds), τt? is the tax rate on domestic agents’ holdings of foreign assets or debts that are susceptible to exchange rate or foreign interest rate risks b?i,t, i ∈ {B, S}, c1, c2, d1, and d2 are scalar coefficients, and τ and τ? are the steady state levels of the respective tax rates.
We search numerically the coefficients c1, c2, d1, and d2to maximize the social welfare func-tion (using second-order approximafunc-tions around the non-stochastic steady states) in moderate regions in which stable equilibrium is defined, and we focus our attention to cyclical policies that do not impose permanent wedges into the intertemporal Euler conditions (thus τ?= τ?= 0). We find that rules that are persistent, that is, policy rules with nonzero coefficients relating current tax rates with its one-period lag, are strictly dominated by rules that react only to capital inflows
or foreign debt buildups. Thus the welfare implications of the considered macroprudential policy rules can be summarized by the relation between the policy weights c2, d2and the corresponding conditional welfare levels presented in the following figure.
0 0.5 1 1.5 2
Figure 4: Conditional Welfare of Macroprudential Policy Rules
Althought the two rules target a different set of households, the previous taxes foreign house-holds and results in a perceived difference in the effective interest rates between home and foreign agents regarding the same asset, while the other targets domestic households by discriminating against the currency denominating the asset or debt, the effects are both welfare-improving at the social level but assymmetric at the individual level. By construction the agents differ in their levels of patience toward the future, and a fraction of domestic households borrow in foreign currency while the other lend to the rest of the world. To see how the policies affect the econ-omy as a whole and the two types of agents separately, we first present the impulse response to foreign shocks in which the thick dashed lines represent the policy experiment under the rule τt? = τ?+ d2
b?Bt− b?B,t−1
. In both scenarios, monetary policy follows the given interest rate
rule. We present the effect of the inflow tax (τt) together with the augmented Taylor rule discussed
Foreign Households' Domestic Asset Holdings
0 5 10 15 20
0 10 20 30
Domestic Households' Foreign Asset Holdings
0 5 10 15 20
-60 -40 -20
0 Foreign Reserves
Figure 5: Effect of Macroprudential Policy (τt?) to a Positive Foreign Interest Rate Shock
We next evaluate the two-prone policy mix that allows the government to target international capital flows using both the inflow tax τtand an augmented Taylor rule that respond to a financial variable xt
. Since under our calibration b?B,t is always negative while b?S,t is always positive, the ratio xt/xt−1 is positive, and hence λb> 0 implies that the authority raises domestic interst rate when the economy is accumulating either foreign debt
xt= b?B,t
or foreign asset
xt = b?B,t
. In the following numerical experiment, we denote
Rule 1 = −λbln b?B,t
adjust the policy weight λbin the augmented Taylor rule
ln (Rt) = λRln (Rt−1) + (1 − λR)
λπln (πt) + λy[ln (Yt) − ln (Yt−1)] + ln (R) + Rule k , (36)
k ∈ {1, 2} to maximize the conditional welfare values. We present the four scenarios in the following figure, with the dashed lines denoting the interest-rate response to financial variables without macroprudential policies and the solid lines denoting the joint use of both instruments.
0 0.2 0.4 0.6 0.8 1 1.2
Full Capital Mobility c2 = 0 (Rule 1) Full Capital Mobility c2 = 0 (Rule 2) Macroprudential Policy with c2 = 2.1 (Rule 1) Macroprudential Policy with c2 = 2.1 (Rule 2)
0 0.2 0.4 0.6 0.8 1 1.2
Figure 6: Conditional Welfare of Macroprudential Policy and Augemented Taylor Rule
We find that with the macroprudential policy or not, social welfare is a decreasing function of the the policy weight λbin the augmented Taylor rule, hence the optimized rule goes back to the capital inflow tax with the baseline interest rate rule. However, from our previous discussion and an examination of figure 7, we learn that the social welfare improvements come at the ex-pense of the drastic welfare loss of domestic savers. This observation leads us to consider the
“second-best” policy combination that makes both types of agents “at least not worse-off” with the introduction of the macroprudential policy. We represent the two local solutions associated with Rule 1 and Rule 2 by the points A and B, respectively, in figure 6.
In our numerical experiment, the “second-best” policy rule correspond to the smallest λb in the augmented Taylor rules that make the domestic savers indifferent between the
free-capital-mobility scheme and the macroprudential rules. Since the borrowers are always better-off (than the welfare level corresponding to λb = 0 of the dashed lines) in the considered interval, the policy combinations A, B represent a Pareto improvement from the baseline economy. We plot the impulse response of the three scenarios, baseline, macroprudential policy (c2= 0.021) with baseline interest-rate rule, and macroprudential policy with augmented Taylor rule (Rule 2), in Figure 7.
Foreign Households' Domestic Asset Holdings10
0 5 10 15 20
0 20 40
Domestic Households' Foreign Asset Holdings
0 5 10 15 20
Baseline economy Macroprudential policy only Both instruments
Figure 7: Impulse Responses to a Positive Foreign Interest Rate Shock
4 Conclusion
Consistent with the open economy literature of the study of macroprudential policies, our results show that prudential measures targeting capital flows are generally welfare-improving. However, such welfare gains may not be Parato improvements taking into account the existence of both borrowers and savers in a given economy. We consider two types of macroprudential rules dis-tinguished by the target of taxation. Depending on the policy objective, one can choose to impose the regulation based on residency of the transacting parties or the currency demonination of the
transaction. We show that the traditional instrument policy interest rate can be augmented to respond to foreign debt or asset growth, and the joint use of the monetary and macroprudential policies can achieve an allocation that improves the well being of both types of agents.
As noted in the literature review section, existing researches have repeatedly pointed out that the conduct of monetary and macroprudential policy is a challenging task due to the complicated nature of various forms of financial frictions. The current work seeks to contribute to policy discussions by providing a tractable specification of relevant concerns facing a typical small open economy and presenting the costs and benefits associated with various proposed policy rules.
Future research possibilities include a further look into the interaction with capital flows and inequality or an extension to sector-specific financial regulations within the domestic economy.
Appendices
In this appendix, we summarize the first-order conditions, market clearing conditions, and the policy equations given the functional form of the utility representation. The equations are labeled to correspond to that in the main text, and in order to keep the expressions concise, some variables are substituted out and the resulted equations are labeled starting from (A.1).
1 cBt = φm
1
mBt + βBEt
1
cB,t+1 1 πt+1
(5B) 1
cSt = φm
1
mSt + βSEt
1
cS,t+1 1 πt+1
(5S)
1
cBt1 + Ψ1 bBt− bB = βBEt
1
cB,t+1Rt 1 πt+1
(6B)
1
ln (R?t) = (1 − ρr) ln (R?) + ρrln Rt−1? + εrt (32)
St= (1 − ρs) SPPP+ ρsSt−1+ εst (33)
For k ∈ {0, 1, 2}, with Rule 0 = 0 corresponding to the baseline Taylor rule and
Rule 1 = −λbln b?B,t b?B,t−1
!
and Rule 2 = λbln b?S,t b?S,t−1
! ,
the monetary policy equation is given by
ln (Rt) = λRln (Rt−1) + (1 − λR)
λπln (πt) + λy[ln (Yt) − ln (Yt−1)] + ln (R) + Rule k , (36)
while the macroprudential policy rules are given by
τt = c1τt−1+ (1 − c1) τ + (1 − c1) c2 bf t− bf,t−1
(34)
τt?= d1τt−1? + (1 − d1) τ?+ (1 − d1) d2 b?Bt− b?B,t−1 . (35)
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