Macroeconomic Effects of Capital Account Regulations

Abstract

We analyze the effects of capital account regulations (CARs) across a large sample of emerging economies on a range of macroeconomic outcomes. We use composite indices of these regulations to capture their intensity in coverage and employ an instrumental variables strategy to overcome the endogeneity of regulations to outcomes. We estimate the effects of CARs on real exchange rate appreciation, foreign exchange pressure, crisis resilience, and post-crisis overheating using annual data from 1995 to 2011 for 51 emerging economies. We find that all CARs, except the financial sector-specific restrictions, reduce foreign exchange pressure and real exchange rate appreciation, contributing to greater macroeconomic stability. Our results further indicate that increasing the restrictiveness of CARs in the run-up to the crisis moderates the growth decline, thus enhancing crisis resilience, and that countries that used CARs experienced less overheating from capital inflow surges during post-crisis recovery. The latter two results imply that CARs are useful countercyclical policy instruments. Our estimates provide evidence in favor of models in which imperfect capital mobility can generate sustained effects on real exchange rates.

Appendices

Appendix A

Additional Tables

Table A1 List of Countries

Table A2 Description and Sources of Variables

Table A3 Replication and Extension of Results in Table 7, Klein (2012)—Capital Controls and Change in Real Exchange Rate

Appendix B

Mathematical Appendix

B1. Derivation of the Bond Demand Function

When we substitute the market-clearing condition for nontraded goods $c_{N,t}=y_{N,t}$, the utility function becomes $u(c_{T,t})=u(c_{T,t},y_{N,t})$, and nontraded consumption and endowment cancel from the budget constraint:

$$c_{T,t}+p_{N,t}c_{N,t}+\frac{(1-\tau _{t+1})b_{t+1}}{R_{t+1}}=y_{T,t}+p_{N,t} y_{N,t}+b_{t}-T_{t} \qquad \qquad \qquad ({\rm B}.1)$$

$$c_{T,t}+p_{N,t}c_{N,t}+\frac{(1-\tau _{t+1})b_{t+1}}{R_{t+1}}=y_{T,t}+p_{N,t} c_{N,t}+b_{t}-T_{t} \qquad \qquad \qquad ({\rm B}.1^{\prime })$$

$$c_{T,t}+\frac{(1-\tau _{t+1})b_{t+1}}{R_{t+1}}=y_{T,t}+b_{t}-T_{t} \qquad \qquad \qquad ({\rm B}.1^{\prime\prime }).$$

The consumers budget constraint (1′), after substituting the government budget constraint $T_{t}=\tau _{t+1}b_{t+1} \slash R_{t+1},$ becomes

$$c_{T,t}+\frac{(1-\tau _{t+1})b_{t+1}}{R_{t+1}}=y_{T,t}+b_{t}-\tau _{t+1}b_{t+1} \slash R_{t+1}$$

$$c_{T,t}=y_{T,t}+b_{t}-b_{t+1} \slash R_{t+1}.$$

Substituting this expression into the consumer’s Euler equation, we define an implicit function

$$F=(1-\tau _{t+1})u_{T}(y_{T,t}+b_{t}-b_{t+1} \slash R_{t+1}, c_{N,t})-\beta R_{t+1}u_{T}(y_{T,t+1}+b_{t+1}-b_{t+2} \slash R_{t+2}, c_{N,t+1})=0,$$

which satisfies

$$\frac{\partial F}{\partial b_{t+1}}=-(1-\tau _{t+1})u_{TT}(c_{T,t}, c_{N,t}) \slash R_{t+1}-\beta R_{t+1}u_{TT}(c_{T,t+1}, c_{N,t+1})>0$$

(B.2)

$$\frac{\partial F}{\partial R_{t+1}}=(1-\tau _{t+1})u_{TT}(c_{T,t}, c_{N,t})b_{t+1} \slash (R_{t+1})^{2}-\beta u_{T}(c_{T,t+1}, c_{N,t+1}) \gtrless 0$$

(B.3)

$$\frac{\partial F}{\partial \tau _{t+1}}=-u_{T}(c_{T,t}, c_{N,t}) < 0.$$

(B.4)

The first partial derivative (9) is always positive, which lets us implicitly define a demand function $b_{t+1}(R_{t+1};\tau _{t+1})$ by the implicit function theorem.²⁷

The second partial derivative (10) is negative given that saving b is sufficiently high. Specifically, we rewrite the condition by multiplying (12) by $R_{t+1}$ to derive b under which (12) is less than zero.

$$(1-\tau _{t+1})u_{TT}(c_{T,t}, c_{N,t})b_{t+1} \slash R_{t+1}-\beta R_{t+1}u_{T}(c_{T,t+1}, c_{N,t+1}) < 0$$

Substituting the Euler equation $(1-\tau _{t+1})u_{T}(c_{T,t}, c_{N,t})=\beta R_{t+1}u_{T}(c_{T,t+1}, c_{N,t+1})$ for the second term, we have

$$u_{TT}(c_{T,t}, c_{N,t})b_{t+1} \slash R_{t+1}-u_{T}(c_{T,t}, c_{N,t}) < 0$$

which we rearrange to

$$b_{t+1} \slash R_{t+1} > \frac{u_{T}(c_{T,t}, c_{N,t})}{u_{TT}(c_{T,t}, c_{N,t})}$$

$$\text {or} \; \; \; \frac{b_{t+1} \slash R_{t+1}}{c_{T,t}} > \frac{u_{T}(c_{T,t}, c_{N,t})}{c_{T,t}u_{TT}(c_{T,t}, c_{N,t})} \equiv -\sigma (c_{T,t}),$$

which states that the savings/consumption ratio is higher than the negative of the elasticity of intertemporal substitution $\sigma (c_{T,t})$. We will refer to this condition as Assumption 1. If this inequality holds, the demand function $b_{t+1}(R_{t+1};\tau _{t+1})$ is strictly increasing in $R_{t+1}$, which can be inverted into a strictly increasing inverse demand function $R_{t+1}(b_{t+1};\tau _{t+1})$.

The third partial derivative (11) is always negative—this is because of the assumption that the revenue from CARs is rebated so that CARs have only substitution effects and no income effects.

B2. Proofs

Proof of the First Prediction

Based on the derivation of the bond demand function, we use the implicit function theorem to obtain the partial derivatives listed below.

• 1. We implicitly differentiate consumer’s Euler function to express

  $$\frac{\partial b_{t+1}}{\partial \tau _{t+1}}=-\frac{\partial F \slash \partial \tau }{\partial F \slash \partial b}>0.$$

  Similarly, because $R_{t+1}$ is constant, we can write

  $$\frac{\partial b_{t+1} \slash R_{t+1}}{\partial \tau _{t+1}}=\frac{\partial b_{t+1}}{\partial \tau _{t+1}}=-\frac{\partial F \slash \partial \tau }{\partial F \slash \partial b}>0.$$

  We implicitly differentiate consumer’s Euler function to show

  $$\frac{\partial c_{T,t}}{\partial \tau _{t+1}}=-\frac{\partial F \slash \partial \tau }{\partial F \slash \partial c_{T}}<0$$

  because the denominator is negative

  $$\frac{\partial F}{\partial c_{T,t}}=-(1- \tau _{t+1})u_{TT}(c_{T,t})<0$$

• 2. The derivative

  $$\frac{\partial p_{N,t}}{\partial \tau _{t+1}}=-\frac{\partial p_{N,t}}{\partial c_{T,t}} \frac{\partial c_{T,t}}{\partial \tau _{t+1}}<0$$

  is negative because the first term is positive and the second term is negative.

Proof of the Second Prediction

• 1. Under open capital accounts, first suppose an equilibrium with zero reserves $a_{t+1}=0 \; \forall t$ and denote the associated level of private bond holdings by $\tilde{b}_{t+1}$. When a policy authority accumulates/decumulates reserves $a_(t+1) \ne 0$ in some periods, consumers would adjust their holdings of private bonds such that $b_{t+1}=\tilde{b}_{t+1}-a_{t+1}$ to satisfy the optimality conditions by keeping all other variables unchanged. Therefore, in case of unconstrained access of consumers to capital markets, reserve accumulation loses its effectiveness. This is true even if the government uses price controls $\tau _{t+1}$ to tax international capital flows since the real allocations of the consumer depend only on the level of capital controls $\tau _{t+1}$ and not the level of reserves $a_{t+1}$. Notice that this proposition is a form of Ricardian equivalence—a representative consumer internalizes that government bond holdings are equivalent to private bond holdings, and suffers therefore from the same limitations as Ricardian equivalence. It strictly relies on the assumption that consumers can access bond markets in the same conditions as governments. If the consumers cannot access bond markets in the same conditions as governments, which might be the case if they are perceived to be riskier by international lenders, then Ricardian equivalence fails to hold. Therefore, there might be a case of imperfectly open capital markets due to differences between the perceived riskiness of individuals and governments.

• 2. Closed capital accounts restrict private consumers to a zero international bond position $b_{t+1}=0$. Therefore, reserve accumulation is the only borrowing/lending from international capital markets. Since consumers adjust their optimal allocation by reducing their tradable consumption, reserve accumulation constitutes forced saving and depreciates the real exchange rate. We can show this formally as follows. Since $b_{t+1}=0$, $c_{T,t}+a_{t+1}=y_{T,t}$. By substituting $c_{T,t}=y_{T,t}-a_{t+1}$, we observe that the real exchange rate is a function of reserve accumulation and exogenous tradable and nontradable income under closed capital accounts:

  $$p_{N,t}=\frac{u_{N}(y_{T,t}-a_{t+1}, y_{N,t})}{u_{T}(y_{T,t}-a_{t+1}, y_{N,t})}.$$

  In order to show how the real exchange rate changes in response to a change in reserve accumulation, we take the derivative

  $$\frac{\partial p_{N,t}}{\partial a_{t+1}}=\frac{u_{NT} (-1) u_{T}-u_{N} u_{TT}(-1)}{(u_{T})^2}<0.$$

  The derivative is negative by our earlier assumptions of the utility function. This confirms that a rise in reserve accumulation depreciates the real exchange rate under closed capital accounts.

• 3. Since under open capital accounts a CAR $\tau _{t+1}$ induces private consumers to accumulate $b_{t+1}(R_{t+1};\tau _{t+1})$ bonds, it is equivalent to reserve accumulation $a_{t+1}=b_{t+1}(R_{t+1};\tau _{t+1})$ under closed capital accounts. This implies that any level of reserve accumulation can be replicated by a proportional CAR given that bond holdings $b_{t+1}(R_{t+1};\tau _{t+1})$ are strictly increasing in $\tau _{t+1}$ and their range is $\mathfrak {R}$.

Proof of the Third Prediction

We know from the first prediction that the first component of $FXP_{t}$ responds negatively to a change in capital controls, i.e. the real exchange rate depreciates in response to a rise in capital inflows, $\partial p_{N,t} \slash \partial \tau _{t+1}<0$.

In order to show how the second component of $FXP_{t}$ responds to a change in capital controls, we need to show how reserve accumulation changes in response to a change in CARs. We take the derivative

$$\frac{\partial a_{t+1}}{\partial p_{N,t}} \frac{\partial p_{N,t}}{\partial \tau _{t+1}} <0.$$

The derivative is negative by our earlier assumption about the government’s reaction function and the first prediction. Therefore, the total effect of rise in CARs on $FXP_{t}$ would be negative, i.e. $\partial FXP_{t} \slash \partial \tau _{t+1}<0$.