Language of an NFA

Recently, a number of authors have invoked some sort of restrictions on capital mobility in order to stabilize the international financial system. For example, Krugman (1999) argues that countries which cannot adopt either currency unions or free floating exchange rates should limit capital flows.

Stiglitz (1999) endorses the same view with special reference to developing countries. Eichengreen et al. (1995) argue that as real markets adjust slug-gishly to shocks, a second best can be achieved by “throwing sand in the wheels” of international finance through a global foreign exchange transac-tion tax in the spirit of Tobin (1978). This would help prevent destabilizing speculation in international financial markets and make capital mobility compatible with modest autonomy in monetary and macroeconomic policy.

These views were broadly discussed in the aftermath of the frequent currency crises of the 1990s. In this Section we analyze the effects of such

restrictions on the probability of transmission of crises in the context of our model. We distinguish between the effects of two different measures:

we define the first as capital controls, which can be thought of as an ad-ministrative or direct intervention and amounts to outright prohibition or discretionary approval of certain cross-border capital movements; the sec-ond is a Tobin tax, i.e. a market-based or indirect control which aims at discouraging capital movements through cost-increasing measures.

3.1 Capital controls

As mentioned above, one way to stabilize international financial markets could be by means of administrative restrictions on capital flows. Montiel and Reinhart (1999) show that, unlike policies of sterilized intervention, capital controls exert an effect on the composition of inflows, rather than on their overall volume, in the direction of reducing the share of short-term and portfolio flows with respect to FDI. Furthermore, as documented by Edwards (1999), the introduction of such restrictions involves a number of issues regarding the sequencing of reforms in emerging markets, the effectiveness and timing of controls, the kind of flows to be restricted (whether inflows or outflows), as well as the maturity of capital flows to be discouraged.

The present setup cannot accommodate for such features of capital con-trols. Thus we resort to modeling this restriction introducing a no-short-selling constraint on either dollar- and local currency-denominated risky assets held by private investors:

x^∗m_s , x^m_s ≥ 0 (49)

In order to simplify notation and make the argument clearer, we assume that the marginal effect on expected utility of relaxing the nonnegative con-straints (49) is invariant across different currency-denominated assets issued by the same country, and that the market value of dollar denominated debt is equal to the market value of local currency denominated debt converted to dollars, i.e. B_s^∗m = B_s^m/e^m_s . As shown below, these assumptions allow for the same effect of capital controls on country m’s assets denominated in different currencies.

Proposition 8 The introduction of a no-short-selling constraint on risky assets reduces the probability of currency devaluation.

Proof. When the constraints (49) are added to the model, the Euler

equations (3) and (4) change as follows:

u⁰(C_s− Xs)B_s^∗m = βE_s©

u⁰(C_s+1− Xs+1)¡

I_s+1^∗m + B_s+1^∗m¢ª

+ v_s+1^m (50) u⁰(Cs− X^s)B_s^m

e^m_s = βEs

½

u⁰(Cs+1− X^s+1)

µI_s+1^m + B_s+1^m e^m_s+1

¶¾

+ v_s+1^m(51) where v_s+1^m is the Lagrange multiplier associated with constraint (2) at time s + 1, denoting the increase in expected lifetime utility that would result if the current constraint were relaxed by one unit. It is assumed to be equal across assets issued by the same country. Going again through the steps discussed in Section 2 leads to the following expression for the risk premium on dollar-denominated risky assets under capital controls, for s = t:

E_t(1 + r^∗m_t+1) − (1 + r^∗ft+1) = −(1 + r^∗ft+1)Cov

½βu⁰(C_t+1− Xt+1) u⁰(C_t− Xt) , r_t+1^∗m

¾

− v_t+1^m (1 + r^∗f_t+1) B_t^∗mu⁰(C_t− Xt)

= ρ^m_t+1− Θ^mt+1 (52)

where ρ^m_t+1 is the risk premium we derived in Section 2 under free capital mobility and

Θ^m_t+1 = v_s+1^m (1 + r^∗f_t+1) B_t^∗mu⁰(Ct− X^t).

An analogous expression can be obtained for the risk premium on local currency-denominated risky assets:

E_t

∙ e^m_t

e^m_t+1(1 + r_t+1^m )

¸

− (1 + r^∗ft+1) = −(1 + r^∗ft+1)Cov

½βu⁰(Ct+1− X^t+1) u⁰(C_t− Xt) , r_t+1^∗m

¾

−e^m_s v_s+1^m (1 + r_t+1^∗f ) B^m_t u⁰(C_t− Xt)

= ρ^m_t+1− Θ^mt+1 (53)

where the third equality derives from the assumptions that the risk premium under free capital mobility ρ^m_t+1 is equal across country m’s assets and that B_s^∗m= B^m_s /e^m_s .

The new expression for the probability of devaluation of country m’s currency under capital controls, π^m_t+1, is, therefore:

π^m_t+1= F [απ^m_t+1+ ϕ(ρ^m_t+1− Θ^mt+1) − φ^mt+1] < π^m_t+1 (31’)

since F [·] is an increasing function.

Proposition 8 implies that the introduction of capital controls in the form of administrative measures can help stabilize the international financial system through a reduction of the risk premium and, in turn, a reduction of the probability of currency devaluation. In fact, this leads to a decreasing contagion because as a country’s probability of devaluation is shocked, the effect on the risk premium on other countries’ assets will be damped by the term Θ deriving from capital controls.

3.2 Tobin tax

We now apply our model to answer the following question: do indirect capital controls in the form of a Tobin tax, i.e. a foreign exchange transactions tax, reduce the probability of contagion of financial crises?

One trivial effect of the introduction of a Tobin tax is to reduce the crisis probability through an increase in the fiscal revenues of the emerging market’s government. This can be seen from equations (28) − (31): ceteris paribus, an increase of fiscal revenues will decrease the government deficit and thus improve the fundamentals; this, in turn, will reduce the crisis probability expectations formulated by private agents. However, this is not an effect peculiar to the Tobin tax since it may be exerted by any measure of fiscal consolidation adopted by the policymaker. It is far more interesting, therefore, to detect what is the influence of a Tobin tax on private investors’

equilibrium behavior.

Proposition 9 The introduction of a Tobin tax does not affect the risk premium demanded on risky assets, and thus does not affect the probability of devaluation.

Proof. Remembering that the budget constraint is expressed in dollars, levying a tax with rate τ^m on each foreign exchange transactions modifies

the international investor’s budget constraint (2) as follows:

B_s+1^∗f + XM m=1

x^∗m_s+1B_s^∗m+ XM m=1

x^m_s+1(1 − τ^m)B_s^m

e^m_s = (1 + r^∗f_s )B_s^∗f + +

XM m=1

x^∗m_s (I_s^∗m+ B_s^∗m) XM

m=1

x^m_s

∙(1 − τ^m) (I_s^m+ B_s^m) e^m_s

¸

−Cs (54)

and the FOCs (3) and (4) remain unchanged since:

e^m_s+1(1 − τ^m)¡

I_s+1^m + B_s+1^m ¢

e^m_s (1 − τ^m)B^m_s = e^m_s+1¡

I_s+1^m + B_s+1^m ¢ e^m_s B_s^m .

Proposition 9 implies that levying a tax on foreign exchange transactions leaves unchanged the equilibrium returns on the risky asset and, thus, the representative investor’s equilibrium behavior. Therefore the risk premium and, in turn, the probability of currency devaluation and transmission of crises remain unchanged.

Interestingly enough, this result contradicts Cordella (2003) which as-serts that in a “bank run” model controls in the form of a tax on short-term capital inflows can increase expected returns by preventing bank runs.

This, the argument goes, may lead to an increase of gross investments in the emerging market. Conversely, in the international asset pricing framework here presented the same kind of tax does not affect rates of return implying that the marginal investment decisions are unchanged.

Advocates of the Tobin tax as a mean of stabilization of international financial markets argue that it should be universally and uniformly levied in order to be effective (Eichengreen et al. 1995). Again, in our framework a Tobin tax levied universally on all countries’ securities and with a uniform rate is ineffective.

4 Conclusion

The existing literature presents an unsatisfactory partition of explanations of contagion between theories based on fundamentals and theories based

on investors’ behavior. The model presented in this paper nests both the main sources of contagion of financial crises, and adds another dimension of non-linearity to the Jeanne-Masson model increasing the likelihood of self-fulfilling equilibria. It shows that financial crises can be transmitted across seemingly unrelated countries (e.g. Russia and Brazil) through the risk at-titudes of international investors. Thus, to understand financial crises it is not sufficient to look at the countries in question, but also at the portfo-lios of international investors. International business cycle considerations through the wealth effects can also play a role in the incidence of financial crises. The model also suggests that bond spreads, in the event of a finan-cial crisis, would change in emerging markets depending on the pattern of portfolio holdings of international investors. Better risk-management can help reduce the incidence of financial crises through diversification. The model can help better understand the transmission of crises across markets which do not seem to be directly related to each other by emphasizing the role of capital flows and thus, integrating international trade and finance considerations. Finally, an extension of the model to introduce a no-short-selling constraint shows that frictions in the international capital flows can help reduce the instability originating from the self fulfilling expectations of rational investors.

5 Acknowledgements

We would like to thank V.V. Chari, John Cochrane, Mardi Dungey, Renée Fry, Basant Kapur, Nobu Kiyotaki, Bob Miller, Cheolbeom Park, Richard Pomfret, Roberto Rigobon, Victor Rios-Rull, and Frank Strobel for very helpful comments. We would also like to thank participants at the RS Seminars (University of Essex); the XII International Conference on Bank-ing and Finance (University of Rome “Tor Vergata” 2003); the 4th Annual Conference of the IEFS - UK (City University London 2003); the Interna-tional Bond Market conference - IIIS (Trinity College Dublin 2004); FEMES 2004 (Seoul); the IX SMYE (Warsaw University 2004); 2005 North Ameri-can Winter Meetings of the Econometric Society (Philadelphia); 2005 Sum-mer Workshop in Macroeconomics (Auckland); 10th Australasian Macro-economics Workshop (Melbourne); the CESifo-Delphi Conference (Munich, 2005) for their comments. All errors are ours.

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Pi C 45°

Pi*

Figure 1. Unique equilibrium.

Pi 45°

C

Figure 2. Multiple equilibria.

Pi C(phimax)

C(phimin) 45°

Pi(phimin) Pi(phimax)

Figure 3. Critical values of fundamentals.

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