Capital Flow Deflection Paolo Giordani, Michele Ruta, Hans Weisfeld, Ling Zhu∗ Preliminary Draft: Feburary 16, 2014

Abstract This paper takes a novel look at the coordination problem of capital controls among borrowing countries. In a simple model of capital flows and controls, we show that inflow restrictions imposed by a country distort international capital flows to other countries and that, in turn, such capital flow deflection may lead to a policy response. We then test the theory using data on inflow restrictions and gross capital inflows for a large sample of developing countries between 1996 and 2009. Our estimation yields strong evidence that capital controls deflect capital flows to other borrowing countries with similar economic characteristics. Notwithstanding these strong cross-border spillover effects, we do not find evidence of a policy response.

JEL No.: F3, F4, F5. Keywords: capital flows, capital controls, cross-border spillovers, multilateral institutions.

∗

Paolo Giordani: University Luiss at Rome (e-mail: [email protected]); Michele Ruta: IMF (e-mail: [email protected]); Hans Weisfeld, IMF (e-mail: [email protected]); Ling Zhu: University of Maryland at College Park (e-mail: [email protected]). The authors would like to thank Anton Korinek and seminar participants at University of Maryland at College Park for helpful comments and suggestions. The views expressed in this paper are those of the authors and do not necessarily reflect those of IMF.

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1

Introduction

What type of multilateral institutions do countries need to govern international capital flows? As the size and volatility of capital flows, namely to developing countries (Figure 1), have largely increased in recent years, this question has raised the interest of both academic economists and policymakers. The ensuing debate has led the International Monetary Fund (IMF) to review its position on the liberalization and management of capital flows and to provide a set of recommendations to help countries deal with these flows. Part of this new institutional view is the emphasis on the need for international agreements to coordinate or set the appropriate standards for policy intervention. However, as recognized by the IMF, “much further work remains to be done to improve policy coordination in the financial sector” (IMF, 2012, pg 28). INSERT FIGURE 1 HERE The trade policy literature can be useful to macroeconomists interested in international policy coordination. First, from a methodological point of view, this literature has shown that multilateral institutions are effective when they provide a framework to address relevant cross-border spillovers associated to countries’ unilateral policies. In particular, Bagwell and Staiger (1999 and 2002) have shown that the World Trade Organization (WTO), and its predecessor the General Agreement on Trade and Tariffs (GATT), have effectively improved international trade cooperation because they allow countries to neutralize a relevant trade policy externality, the (intra-temporal) terms-of-trade effect. Second, the trade policy literature may offer useful analogies to the macroeconomic approach to capital flow management. For instance, Costinot et al. (2013) show that, similarly to the terms-of-trade effect in trade policy, unilateral capital controls can aim at manipulating the world interest rate, that is the inter-temporal terms-of-trade. This paper studies the determinants of the coordination problem among borrowing countries that have at their disposal capital controls as the instrument to manage the inflows of capital1 . In the spirit of the trade policy literature, we present a simple framework to identify a cross-border externality associated to the use of capital controls and then empirically test the relevance of this effect. Our key insight is that, just like tariffs in an importing country deflect exports to other markets and may induce a policy response by affected importers (Bown and Crowley, 2006 and 2007), capital controls induce capital flow deflection2 . Two recent event studies focusing on Brazil (Forbes et al. 1

Capital controls encompass a variety of measures, such as taxes, quantitative restrictions or regulations, that affect cross-border financial activities by discriminating on the basis of residency (IMF, 2013). 2 The term “trade deflection” was introduced in Bown and Crowley (2007) to indicate a situation where an increase in a trade barrier in one market determines a change in destination in exports. This is different from the concept of “trade diversion” introduced by Viner (1950), where the reduction of

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2012; and Lambert et al. 2012) provide motivating evidence for our work. In particular, Forbes et al. (2012) find that more stringent capital controls set by Brazil between 2006 and 2011, such as the introduction of a 2 percent tax on portfolio equity and debt inflows in 2009, have led investors to increase the share of their portfolios allocated to other economies, including Indonesia, Korea, Peru and Thailand. Interestingly, all these countries have imposed measures designed to limit capital inflows in 2010-113 . To examine the problem of policy coordination among recipient countries and guide our empirical analysis, we build a parsimonious model based on work by Korinek (2013). In this setting, governments have two main reasons for influencing the volume of capital flows. A first rationale comes from the desire to manipulate the inter-temporal terms-oftrade in their favor as discussed in Costinot et al. (2013). A large country setting capital controls takes into account that its policy choice affects the world interest rate and finds it unilaterally efficient to exploit this market power. The second motive for capital controls is to manipulate the domestic interest rate to address domestic distortions, such as financial fragility4 . In the absence of other instruments, a government may want to use capital controls as a means to influence the domestic interest rate and offset this market failure. We refer to the latter as the domestic motive (as it is often called in the literature), while the first is the terms-of-trade motive. Note that while this model is parsimonious and does not explicitly account for other uses of capital controls, such as targeting the real exchange rate or preserving monetary policy independence (i.e. dealing with the “trilemma”), it captures their essential rationales: capital controls either aim at altering the world or the domestic interest rate or both. In this context, we formally investigate the causes and consequences of capital flow deflection. Inflow restrictions imposed by a large country, or a sufficiently large set of small economies, lower the world interest rate, as they subtract demand for capital from the world market. This change in the world interest rate leads to higher borrowing by recipient countries that have not altered their controls. The cross-border policy spillover effect among borrowers is what we refer to as capital flow deflection. It is insightful to look at this effect of capital controls from the perspective of foreign investors. For them all borrowing countries are identical (by assumption), except for the level of the a tariff granted to a trading partner increases imports from the latter and reduces imports from other (potentially more efficient) exporters. An example of trade deflection discussed in Bown and Crowley (2007) is the steel safeguard, a set of tariffs and quotas, imposed by the US on Chinese exports in 2002. Shortly afterwards, the EU reacted with similar measures, claiming that the change in US policy had deflected Chinese steel exports to its market. 3 In 2010, Peru increased the fee on non-resident purchase of central bank paper to 400 basis points (from 10 basis points), while Thailand imposed a 15 percent withholding tax on non-residents’ interest earnings and capital gains on state bonds. In 2011, Indonesia introduced a limit on short-term foreign borrowing by banks to 30 percent of capital and Korea restored a 14 percent withholding tax on interest income on non-resident purchases of treasury bonds (IMF, 2013). 4 In the words of Keynes (1943), “the whole management of the domestic economy depends upon being free to have the appropriate rate of interest without reference to the rates prevailing elsewhere in the world. Capital control is a corollary to this.”

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policy. As investors perceive a lower price for exporting capital in countries that have set controls, they reallocate their capital to the other borrowers. This insight plays an important role in our empirical strategy. Capital flow deflection, in turn, induces a policy response by borrowers. Importantly, while the spillover effect is independent of the underlying rationale for capital controls, this is not the case for the policy reaction. Specifically, capital flow deflection has an ambiguous impact on the terms-of-trade motive for capital controls. Intuitively, whether the incentive to manipulate the international interest rate increases or decreases as this price falls depends on the elasticity of global savings faced by borrowers. On the other hand, the domestic motive for capital controls is strengthened by capital flow deflection. The higher inflows exacerbate domestic distortions and increase the incentive to manipulate the domestic interest rate to offset them. This result has an interesting corollary. If the primary motive for capital controls is to manipulate the domestic interest rate, then uncoordinated inflow restrictions can magnify exogenous shocks, such as a sudden increase in global liquidity. Intuitively, with capital flow deflection, inflow restrictions are complementary policies, so that a shock initiates a chain reaction and determines a multiplier effect5 . In the empirical investigation, we use a dynamic panel model to estimate the impact of capital controls on inflows to other counties and on the policy response. To our knowledge, this is the first paper that investigates these issues in a cross-section. There is a well known literature on the push and pull factors that determine capital inflows (e.g. Forbes and Warnock, 2012; Ghosh et al. 2013), but these studies generally abstract from the role of capital controls by third countries. Two exceptions, as discussed above, are the event study approach by Forbes et al. (2012) and Lambert et al. (2012) that find evidence of capital flow deflection spurring from the policies implemented in Brazil between 2006 and 2011. A small recent literature examines the factors that cause policymakers to change the level of capital controls (Fratzscher, 2012; Fernandez et al. 2013). These studies, however, disregard the policy response to the inflow restrictions imposed by other borrowers. We use data on gross capital inflows for a large sample of developing countries between 1996 and 2009 and use the so called Schindler index (Schindler, 2009) which allows to identify the measures aiming at restricting inflows. To test the model, we divide countries into groups of likely substitutes based on common characteristics, such as geographic location, export specialization, return and risk. This is an important step, as the model features symmetric countries and, therefore, abstracts from the multiple features of cross-country heterogeneity that may influence investors’decisions in practice. In the first set of regressions, we introduce a variable capturing the level of capital controls in the rest of the group in an otherwise standard push-pull analysis. In the second set of regressions, we use a probit model to estimate the probability 5

Similar arguments have been made by others. In particular, Ostry et al. (2012) and Korinek (2013) talk of the possibility of a “capital control arms race”.

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that capital controls by some countries may trigger a reaction in a country of the same group. We find strong evidence of a capital flow deflection. The spillover effect of inflow restrictions is estimated to be strong and significant among borrowing countries that have similar risk level. Perhaps surprisingly, capital controls have no significant spillover effects on countries in the same region. This finding is consistent with the view that investors are guided by the similarity of economic characteristics of countries, rather than their geographic location -a result that confirms in a cross-section the evidence of existing event studies. Capital flow deflection is also found to be economically relevant. While somehow an extreme case, we estimate that gross inflows to South Africa would have been between .5 and 2.3 percent lower if Brazil had not imposed higher inflow restrictions in 2009. Finally, these results are robust to a number of tests. In particular, spillovers to countries with similar economic characteristics continue to be significant when we use different measures of capital controls or focus on episodes of capital flow surges. Notwithstanding the strength of capital flow deflection, we find no evidence of a policy response. This result is independent of how we group countries and persists even if we focus on small economies, which have no terms-of-trade motives to set capital controls. We see two possible reasons for this somehow puzzling result. The first has to do with the nature of the data on capital controls. The Schindler index, as the other available measures of capital controls, do not record a change in intensity of a measure (say, an increase in the tax on capital inflows), but only whether the measure is in place or not. To the extent that countries react to capital flow deflection by changing the level of existing policies rather than creating new ones, the empirical findings would be biased against a policy response. The second reason has to do with the model we use to guide our empirical analysis. As discussed in a large literature following the seminal work of Bartolini and Drazen (1997), capital controls can work as a signal to markets in presence of uncertainty over the government type. If policymakers anticipate this, they may be more reluctant to use capital controls in the short run in fear that investors will interpret them as a change in the curse of future policies6 . In this case, a policy response can be muted even in presence of capital flow deflection. The rest of the paper is organized as follows. Section 2 presents a simple general equilibrium model of capital flows and establishes the two main results on capital flow deflection. Section 3 brings these two predictions to the data. We first provide evidence of the cross-border spillover effect of capital controls and then we focus on the policy reaction to inflow restrictions. Concluding remarks and policy implications are 6

Some may see this argument as contradicting the notion that capital controls can be a legitimate (even if second-best) instrument to address a domestic distortion. This idea, however, has only recently become widely accepted (for instance, the institutional view of the IMF on capital flow management was published in 2012), while our dataset covers the period 1996-2009. An interesting question is, therefore, if going forward a policy response to capital flow deflection will become a more permanent feature of the international financial system.

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in Section 4. The proofs and a detailed data description are in the technical Appendix.

2

A Two-Period Model of Optimal Capital Controls

In this section we introduce the simplest model of international capital flows. In a multi-country world lasting two periods (t = 1, 2), economic agents face a standard intertemporal consumption decision problem. A single homogeneous tradeable good exists that allows them to shift consumption across the two periods. Each country can introduce capital controls to affect consumers’ decisions. The model is a further simplified version of the framework presented in Korinek (2013). Even this, admittedly highly stylized, theoretical framework is however sufficient to identify the two effects that we are interested in, and that will later be validated empirically: (i) the spillover effect, whereby a borrowing country raising its capital controls contributes to divert part of its capital inflows to other borrowing countries; (ii) the policy response, whereby a borrowing country raises its capital controls in response to an increase in controls by other borrowers. We start by introducing the characteristics of a generic country i.

2.1 2.1.1

cit

Economic Structure of Country i Preferences and Budget Constraint

Country i is populated by a unit mass of identical consumers who value consumption according to the following utility function: U i (c1 , c2 ) = u(ci1 ) + β i u(ci2 ),

(1)

with u0 > 0, u00 < 0 and β i < 1. The intertemporal budget constraint can be written as (ci1 − y1i )(1 + τ i ) =

(y2i − ci2 ) + T i, R

(2)

where yti denotes income of country i at time t, R ≡ 1 + r is the world gross interest rate, and τ i is the capital control policy at time 1, whose revenue is rebated lump-sum, T i = (ci1 − y1i )τ i . A country is defined as borrower (lender) whenever ci1 − y1i > 0 (ci1 − y1i < 0). A τ i > 0 denotes a capital inflow tax when the country is a net borrower, and a capital outflow subsidy when the country is a net lender; a τ i < 0 has the opposite interpretation. In the rest of the paper, we loosely refer to τ i as capital controls.

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2.1.2

Optimal Intertemporal Consumption

In each country i, the representative consumer maximizes her objective function (1) while satisfying the budget constraint (2), and taking both the world interest rate R and the policy τ i as given. Maximization gives rise to the usual Euler Equation: u0 (ci1 ) = β i Ru0 (ci2 )(1 + τ i ), −

−

+

(3)

+

implying consumption demands ci1 (R, τ i ) and ci2 (R, τ i ). A higher interest rate implies higher savings (ci1 ↓, ci2 ↑), and hence a fall in the demand of capital inflows in borrowing countries and a surge in the supply of capital outflows in lending countries. On the other hand, a country i that raises its capital controls (τ i ↑) also stimulates savings (ci1 ↓, ci2 ↑) and hence reduces its demand of capital inflows.

2.2

Optimal Capital Controls and World Market Equilibrium

For a world economy made up of n countries we now characterize the optimal capital control policy of each individual country i and the resulting market equilibrium. Pn world i i The mass of country i is denoted by m ∈ [0, 1], with i=1 m = 1. Hence, mi = 0 implies that country i is small with respect to the world economy. Whether country i is large or small, its national planner maximizes the following social welfare function: Wti (ci1 , ci2 ) = u(ci1 ) + β i u(ci2 ) + e(ci1 − y1i ),

(4)

subject to the budget constraint (ci1

−

y1i )

(y2i − ci2 ) = . R

(5)

Function e(·) captures the possibility that capital inflows be associated with negative external effects such as financial fragility.This externality is defined by the following function  when ci1 − y1i ≤ 0 e(ci1 − y1i ) = −x(ci1 − y1i ) when ci1 − y1i > 0 0 where x(·) is a positive twice continuously differentiable function with x0 (·), x00 (·) > 0.7 If a country is a net lender (ci1 − y1i ≤ 0), the externality is null. If instead a country is a net borrower (ci1 −y1i > 0), the negative externality associated with capital inflows plays a role in the optimal policy problem. As we will further elaborate below (Proposition 7

The convexity of the externality function is a common assumption in the literature (see for instance Korinek, 2013) [...]. Differently from Proposition 1, the validity of Proposition 2 hinges on that hypothesis.

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1), this externality constitutes a reason for policy intervention. We will refer to this as the prudential motive for capital controls. A second source of market failure arises whenever country i is large enough to affect the world interest rate (mi > 0). It is well known in the literature that large countries attempt to exploit their market power by taking advantage of the effect that their policy has on the world interest rate (terms-of-trade effect). For instance, a borrowing country exploits its monopsonistic power in the capital market by taxing capital inflows so as to limit domestic demand and thus keep a ”low” cost of capital R∗ . In solving the optimization problem defined above, the national planner of country i knows that R depends on its own domestic capital demand mi (ci1 − y1i ) through the following marketclearing condition for the world economy, stating that the sum of net supplies of capital for the world as a whole must be null: n X

mi [y1i − ci1 (R, τ i )] = 0.

(6)

i=1

In the rest of the paper, we refer to this second rationale for imposing capital controls as the terms-of-trade motive. We are now ready to formally characterize the optimal capital control for country i. Proposition 1 (Unilateral Optimal Capital Controls) The unilateral optimal policy (τ i∗ ) can be decomposed into a prudential motive (τbi ) and a terms-of-trade motive (τei ), such that 1 + τ i∗ = (1 + τbi )(1 + τei ), (7) with τbi =

n

x0 (ci1 −y1i ) 0 u (ci1 )−x0 (ci1 −y1i )

when ci1 − y1i > 00

when ci1 − y1i ≤ 0

(8)

and τei = mi · ε−i ,

(9)

where ε−i is the inverse elasticity of global savings faced by country i. Capital controls can be imposed for prudential or terms-of-trade reasons. The expression (8) captures the optimal precautionary capital controls of country i. They are null whenever i is a net lending country (ci1 − y1i ≤ 0). In fact, since the externality is null, the solution to the welfare maximization for a rational forward-looking national planner coincides with the utility maximization of the representative consumer, and the optimal prudential policy is no-intervention: τbi = 0. Capital controls are instead strictly positive when country i is a net borrowing country (ci1 − y1i > 0). In particular, 8

the expression x0 (ci1 − y1i )/[u0 (ci1 ) − x0 (ci1 − y1i )] tells us that (i) low levels of current consumption -and thus a high marginal utility of it- imply weak optimal capital controls; (ii) a strong marginal effect of the negative externality implies strong capital controls. Expression (9) is the well known formula for the unilaterally optimal tax of a country that exploits its market power. In particular, a borrowing country faces a positive elasticity (ε−i > 0), and hence taxes capital inflows (τei > 0), while a lending country faces a negative elasticity (ε−i < 0), and hence taxes capital outflows (τei < 0).8 We conclude this section with the definition of equilibrium for this economy. The equilibrium is a configuration in which agents maximize their utility, each national planner implements the unilaterally optimal capital control policy, and the international market for capital clears. Specifically, Definition. (World Market Equilibrium) A world market equilibrium is defined as the triple (cit , τ i∗ , R∗ ) -consumption plans, capital controls, world interest rate- that satisifies (3), (7) and (6).

2.3

Capital Controls’ Spillovers

In this section we introduce the cross-border spillovers associated to capital controls. In particular, we carry out a comparative statics exercise to analyze the effects of a change in the capital control policy by one country on the world interest rate, as well as on the amount and the distribution of capital flows moving from lending to borrowing countries. We start with the following statement. Lemma 1. A rise in the capital controls of a large borrowing country j -or of a non-zero measure of borrowing countries- ( τ j ↑) (i) lowers the equilibrium world interest rate ( dR∗ /dτ j < 0) and P (ii) lowers the total amount of world savings ( d[ i mi [y1i − ci1 (R, τ i )]]/dτ j < 0 ∀i : ci1 − y1i < 0). The findings of Lemma 1 are well-known in the literature (see for instance Korinek, 2013), but we have chosen to display them as they are instrumental to prove our next propositions on the multilateral effects of capital controls. The first of these effects is the spillover effect, which is the impact of more stringent controls on the amount 8

From a global welfare perspective, prudential and terms-of-trade controls have radically different consequences. Prudential controls are efficient both from a unilateral as well as from a multilateral point of view. As it is widely known, policy intervention aimed at exploiting the terms of trade effect is instead sub-optimal. Indeed, it can be proven that aggregate welfare is maximized under the unilaterally optimal policy defined in expression (8).

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of capital inflows accruing to other borrowing countries. This effect is studied in the following Proposition 2 (The Spillover Effect) A rise in the capital controls of a large borrowing country j -or of a non-zero measure of borrowing countries- (τ j ↑) causes an increase in capital inflows in any other borrowing country i, that is: d[ci1 (R, τ i ) − y1i ] > 0 ∀i : ci1 − y1i > 0. dτ j Proposition 2 simply states that, when a borrowing country or region raises its barriers to capital inflows, it contributes to divert part of these flows to other borrowing countries. This diversion is known from the trade policy literature (Bown and Crowley, 2006 and 2007), but has not been formally studied in the context of capital controls. The existence of this cross-country spillover effect will be verified empirically in the second part of this paper. A graphical intuition of the spillover effect is provided in Figure 1, which is divided in three parts. Part (i) draws the world demand (CF D) and supply (CF S) of capital. Parts (ii) and (iii) instead represent the demand of capital for respectively the borrowing country i (CF Di ) and the rest of the borrowing region j (CF Dj ). The initial world market equilibrium is such that R∗ equalizes the supply of capital (measured by the distance AB) to the demand of capital (measured by the distance CD + EF ). A rise in the capital controls of the borrowing region j ( τ j ↑) shifts the demand of capital to the left (from CF D to CF D0 ), thus generating lower world savings and a lower world interest rate R∗0 (Lemma 1). In particular, R∗0 is now such that the new lower capital supply (AB0) equalizes the new lower capital demand (CD0 + EF 0). The spillover effect arises because, as a consequence of a lower interest rate, capital inflows accruing to the borrowing country i increase (by the measure DD0 ). In other words, while less capital flows to borrowing countries as a whole, part of the capital flows previously directed towards region j are now diverted to the borrowing country i. INSERT FIGURE 2 HERE

2.4

Capital Controls’ Responses

We now introduce the policy response of borrowing countries to capital controls imposed by other borrowers. As a first step, the next lemma investigates how the policy maker of a borrowing country reacts to a change in the world interest rate.

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Lemma 2. The effect of an increase in the world interest rate on the optimal capital inflow tax imposed by a borrowing country i can be decomposed into dτbi dτei dτ i∗ = (1 + τei ) + (1 + τbi ). dR dR dR where dτbi dτei < 0 ∀i : ci1 − y1i > 0 and ≶ 0. dR dR A lower world interest rate is a more powerful incentive to current consumption and, hence, to capital inflows in borrowing countries. As a result, the prudential motive for capital controls is enhanced: a borrowing country needs a higher tax on capital inflows to correct the negative externality associated with the larger inflow. The impact of a change in the world interst rate on the terms-of-trade motive for capital controls is instead ambiguous. In fact, recalling that τei = mi · ε−i , the effect of a lower interest rate on the (inverse of the) elasticity of global savings faced by borrowing country i (ε−i ) can either be positive or negative depending on consumers’ preferences. Lemmas 1 and 2 allow us to investigate how the policy maker of country i reacts to changes in the capital controls in the rest of the world. The nature of this policy response depends on the motive (prudential or terms-of-trade) for capital controls. Our findings are summarized in the following Proposition 3(The Policy Response) A rise in the capital controls of a large borrowing country j -or of a non-zero measure of borrowing countries- causes a policy response by country i which can be decomposed into ei dτbi dτ i∗ ei ) + dτ (1 + τbi ). = (1 + τ dτ j dτ j dτ j where dτbi dτbi dR∗ dτei = > 0 and ≶ 0. dτ j dR dτ j dτ j

We have then isolated two, possibly contrasting, forces that discipline the relationship among capital control policies across countries. The presence of a capital inflows’ negative externality contributes to make the policies complementary, while the exploitation of market power for large borrowing countries may or may not act in the same direction. Intuitively, a large borrowing country j raising its own capital controls contributes to lower the equilibrium interest rate and to raise capital inflows in country i (the spillover effect). On the one hand, this excerbates the negative externality and 11

thus leads country i to ”defend itself” from an excessive capital inflow by raising its own capital controls. On the other hand, the effect of country j’s policy measure on the elasticity of global savings faced by country i is ambiguous as it ultimately depends on the preference fundamentals of consumers. Small borrowing countries have, by definition, no market power and set capital controls for prudential reasons only. Consequently, a small borrower reacts to a surge in capital controls in other borrowing countries by unambiguously raising its own barriers. In contrast, if country i is large, the nature of the relationship among capital controls that is, whether capital controls are complements or substitutes - is in general ambiguous. This relationship ultimately depends on the sign of dτei /dτ j , which in turn depends on how the (inverse of the) elasticity of global savings faced by borrowing country i (ε−i ) responds to changes in the capital controls of another borrowing country j. We exploit this distinction between large and small borrowers when testing the policy response to capital controls in the second part of the paper. The policy response identified above contributes to explaining how prudential capital controls respond to exogenous shocks. Taken together, Lemmas 1 and 2 and Proposition 3 delineate a complementary relationship between the world interest rate and prudential capital control policies, whereby a lower interest rate implies higher barriers to capital inflows, and viceversa. Such complementarity may amplify the effects of exogenous shocks to the world economy or to any subset of it Ω ⊂ [0, 1], thus giving rise to what is usually called a multiplier effect. More formally, denote by τcω (R∗ , ρ) the optimal prudential policy function for country ω ∈ Ω, and where parameter ρ captures any feature that affects τcω other than changes in R∗ (such as the endowments ytω , or the discount factor β ω ). We are now ready to formulate the following Corollary 1. (The Multiplier Effect) A shock to a borrowing region Ω ⊂ (0, 1] causes a prudential policy response of each borrowing country ω ∈ Ω which can be decomposed into ω ω −ω ∂ τcω dτc ∂ τc dτcω dR∗ dτd dρ = ∂ρ + dR dτ −ω · dρ > ∂ρ , where −ω refers to the rest of the borrowing region hit by the shock. A multiplier effect characterizes the prudential capital control policy of each country ω, as the total equilibrium response is higher than the partial equilibrium response because (dτcω /dR)(dR∗ /dτ −ω ) > 0. The complementary relationship between τbi and R∗ that gives rise to the multiplier effect is represented graphically in Figure 2. To gain an intuition of this corollary, suppose a non-negligible fraction of borrowing countries are hit by an exogenous shock (ρ ↑) that induces them to raise their barriers to capital inflows, say from point E to E 0 in Figure 2. This surge in capital controls lowers the world interest rate (as proven in point 1 of Lemma 1), which moves from E 0 to E 00 . Each country, however, reacts to 12

a lower value of R by further increasing its optimal capital controls (as proven in point 1 of Lemma 2) from E 00 to E 000 , which in turn triggers a further decrease in the world interest rate, and so on and so forth. As a result of this chain reaction, the aggregate policy response to the shock, as measured by the horizontal distance between point E and point F , exceeds the initial tax imposed by each individual borrowing country, as measured by the length EE 0 . The existence of such magnifying mechansim across prudential capital control policies is verified empirically in the second part of the paper. INSERT FIGURE 3 HERE

3

Empirical Evidence of Spillover Effect and Policy Response

In the previous section, we showed the existence of spillover effect and policy response in Proposition 2 and 3. In this section we are going to investigate their empirical evidence. In particular we use a dynamic panel and push-pull factors models to study the impact of capital inflow controls on gross capital inflows to other countries and inflow controls imposed by other countries . The recent empirical literature starts to differentiate between gross flows and net flows (Forbes and Warnock, 2012). We follow the literature and use the standard definition of gross capital flows and net flows. Gross capital inflow is the net of foreign purchases of domestic assets and foreign sales of domestic assets. In other words, gross inflow measures the change in the stock of gross foreign liability before any valuation adjustment. Gross outflow measures the change in the stock of foreign assets before any valuation adjustment. Net flow is the difference between the two. Capital controls could target either gross inflow or gross outflow. Capital inflow controls target gross inflow and they are restrictions imposed on foreign purchases of domestic assets and/or foreign sales of domestic assets . Inflow controls could be imposed either on the foreigner who trades the domestic asset with a domestic counterpart or the domestic resident who trades the domestic asset with a foreign counterpart. On the other hand, outflow controls target gross outflow and they are restrictions imposed on domestic residents’ purchases of foreign assets or domestic residents’ sales of foreign assets. They could be imposed either on the domestic resident who trades the foreign asset with a foreign counterpart or foreigner who trades the foreign asset with a domestic counterpart. Both Proposition 2 and 3 consider the multilateral impact of an exogenous shock to the tax on capital inflows in the borrowing countries, so we focus on inflow controls instead of outflow controls in the empirical exercise. And for spillover effect, we focus on 13

gross inflow instead of net flow because net flow includes the gross outflow component. Gross outflow is directly affected by inflow controls in the recipient countries as one’s outflow is another’s inflow, but this effect is straightforward and it differs from the spillover effect. Therefore to isolate this direct effect when studying spillover effect, we examine the impact of inflow controls imposed by other countries on one’s gross inflow. And to study policy response, we examine the impact of inflows controls imposed by other countries on one’s inflow controls.

3.1

Data

Our sample consists of 78 less industrialized countries and emerging markets, for simplification we call them as developing countries. Table 1 provides a full list of countries. We focus on developing countries since they are much more likely to employ capital controls than more advanced countries 9 . The sample period spans 15 years from 1995-2009 and the data are in annual frequency. The sample period and data frequency are constrained by the data availability of capital inflow controls. A country is included in our sample only if it has at least ten years’ observations for all variables used in the regression models. INSERT TABLE 1 HERE We use Schindler’s index (2009) as proxy for capital inflow controls. Schindler calculates inflow controls as the average of the restriction dummies on purchase of financial assets 10 locally by nonresidents, sale or issue of financial assets abroad by residents, collective investment by nonresidents to residents, financial credits by nonresidents to residents, inward direct investment, and liquidation of direction investment. Schindler computes outflow controls as the average of the restriction dummies on purchase of financial assets abroad by residents, sale or issue of financial assets locally by nonresidents, collective investments by residents to nonresidents, financial credits by residents to nonresidents, and outward direct investment. Consider an example of Toyota issuing new stocks in New York: if a restriction is imposed by Japanese government on these new stocks, which would be classified as ”sale abroad by residents”, then Schindler would regard it as an inflow control by Japan. It’s true that the location being foreign does not necessarily imply the purchaser of the asset is foreign, e.g. some Japanese investor could buy the new Toyota stock in New York, which is a potential critique of Schindler’s methodology. We suspect such case to be an exception rather than normality. If U.S. government imposes restriction 9

The average inflow restriction index from 1995-2009 is .5 among developing countries, while it is only .2 among more advanced countries. 10 financial assets are: shares or other securities of a participating nature, bonds or other debt securities, other market instruments

14

on Toyota’s new stock issues in New York. Schindler would count this as an outflow control by U.S.. The methodology would suffer from the critique for it’s likely that not all buyers of the new stock are American residents. What is not clear is if ”sale locally by nonresidents” includes sales of domestic bonds locally by nonresidents. If it does, then we have a problem. While the restriction on foreigners liquidating domestic assets by selling it to domestic households seems absent from Schindler’s computation of inflow restriction, he does however include restrictions on ”liquidation of direct (foreign) investment” in computation of inflow restrictions. So our guess is it’s likely his source, IMF’s AREAER do not report the restrictions on foreigners liquidating domestic assets by selling it to domestic households except in the case of direct investment. A more detailed description of the index and its methodology are available in the appendix. Fig 4.a plots the inflow controls by regions with higher number indicates stricter restrictions. We can see there are regional differences as well as some common trends across regions. Asian and former Soviet bloc countries are more likely to have higher inflow restrictions than Latin American and central and east European countries. Countries across all regions tightened inflow controls during the Asian financial crisis, and the high level persisted in most regions except for in central and east European countries which were going through capital account liberations to be qualified for EU membership. During the 2007 financial crisis, most regions tightened inflow controls except for former Soviet bloc countries which loosened the capital controls though they are still very stringent compared to any other region except for Asia. INSERT FIGURE 4 HERE Following Forbes and Warnock (2012) we compute gross capital inflow as the sum of net portfolio investment liabilities, other liabilities, and net foreign direct investment. All components of gross capital inflows are available from IMF’s International Financial Statistics (IFS) database as reported in BPM5 format 11 . Table 2 shows summary statistics of inflow controls, gross inflow, and other variables used in the regression analysis. Table 3 shows the data sources. We have three measures that capture the risk of investing in a country: composite risk, law and order, and property rights. Higher the value in these indices indicate lower risk. Composite risk index is a composite measure of a country’s economic, financial, institutional, and political risks while law and order and property rights indices captures mainly the institutional risk of a country. Therefore we focus on composite risk index as the proxy for country risk for it is a broader measure of risk. Reinhart et. al (2007) complies 11

As Forbes and Warnock (2012) point out, some components of gross inflow has value 0 in some countries, but IFS does not specify whether they are really zero or the data is not available. Hence we tried both interpretations and they lead to the same findings. Below we report the results where gross capital flows are computed by treating a 0 observation as 0.

15

an updated dataset on de facto exchange rate regime based on the IMF’s The Annual Report on Exchange Arrangements and Exchange Restrictions. INSERT TABLE 2 HERE INSERT TABLE 3 HERE

3.2 3.2.1

Empirical Evidence of Spillover Effect Determinants of Capital Flows

We follow the standard empirical literature on capital flows model that incorporates the results from the theoretical model:

12

i ωti = β0 + β1 Rt + β2 τt−1 + β3 τt−i + β4 xit + it

and use a pull-push

(10)

where ωti denotes country’s i’s gross capital inflow as a percentage of its GDP at time t (henceforth subscript t denotes time t, and i denotes country i), Rt is the real world i interest rate, τt−1 denotes country’s i’s capital inflow controls at t − 1,τt−i denotes the rest of the world’s inflow restrictions and it is computed from P j j j6=i yt τt −i (11) τt = P j j6=i yt yti is real GDP, xit is a vector of the rest pull-push factors that determine ωti , and it is the error term with usual assumptions associated with OLS estimation. Empirical model (10) includes Rt and τti as explanatory variables for ωti because the theoretical model predicts that the household’s borrowing and lending decisions should depend on world real interest rate and domestic capital control. In particular our model predicts β1 and β2 to be negative that the households who are borrowers reduce current consumption by borrowing less when real interest rate goes up or when inflow restriction tightens. We also include τt−i as a explanatory variable since the rest of the world constitutes a non-zero measure of countries, hence its capital control must have an impact on the gross inflow to country i by Proposition 2. β3 captures the spillover effect, and our model predicts it to be positive. The rest pull-push factors include global volatility, lagged real GDP growth rate, lagged real GDP growth rate shock, lagged real GDP per capita, and the lagged country’s risk. We include them because they are found to be important determinants of capital flows in Ghosh et al. (2012) and Forbes et al. (2012). We lag all the domestic 12

See Magud et al. 2012 for a survey of the literature

16

pull factors as well as domestic inflow controls so these domestic variables are less likely to suffer from endogeniety problems. Following the empirical literature, we use real US interest rate as proxy for world real interest. Real US interest rate is computed from annualized US three month treasury rate adjusted and US inflation. We follow Forbes et al. (2012) to use VIX as the proxy for global volatility. We follow Ghosh et al. (2012) to use the composite risk index as proxy for country specific risk. Higher the composite risk index number indicates lower risk. The real GDP growth rate shock is the log difference between the real GDP growth rate and its H-P filtered trend. 3.2.2

Benchmark Result

Table 4 shows the OLS estimation results of regression equation (10). Variables are divided into three blocks: global push variables that only vary across time and are invariant across countries; domestic pull factors that vary across both time and countries; and spillover variable–the rest of world’s capital inflow control13 – which also vary both across time and countries. We lag all domestic full factors by one period to reduce their endogeneity with the dependent variable–gross capital inflow. Global push factors and the rest of the world’s capital inflow control are contemporaneous as they are less likely to suffer from endogeneity with the dependent variable. INSERT TABLE 4 HERE Column (1) reports the OLS estimated coefficients when year fixed effects are not included. And column 2 reports the OLS estimated coefficients when year fixed effects are included. We control for year fixed effects to reduce omitted variable bias. Since global push factors do not vary across countries, hence they drop out in the specification with year fixed effects. The last column shows the signs as expected either from the predictions of the theoretical model or from previous findings in the empirical literature. Both specifications are able to explain more than 10% of the variation in gross capital inflows. All variables except for real GDP per capita are significant determinants of gross capital inflow and their coefficients have the same signs as expected. The model in Section 2 predicts the world interest rate–real US inters rate and domestic inflow controls to have a negative coefficient. We expect international investment to be more risk-averse when global volatility is higher, therefore VIX should have a negative coefficient. Higher domestic real growth rate and lower domestic risk make a country more attractive as an investment destination hence we expect both variables to have positive coefficients. Standard small open economy model predicts temporary growth shock to deteriorate current account, so we expect real GDP growth rate shock to have a negate coefficient. It’s not obvious to us what sign the coefficient on real GDP 13

By rest of the world we mean the rest of the developing countries

17

per capita should have. Previous empirical literature find the coefficient to be either insignificant or negative 14 . On the one hand, higher real GDP per capita is associated with higher level of development in financial infrastructure which should lead to more inflow. On the other hand, lower real GDP per capital is also associated with weak economic infrastructure which implies more need for foreign investment and inflow 15 . Our key variable of interest–the rest of world’s capital inflow controls is significant when year fixed effects are not included. But the variable becomes insignificant once we control for the year fixed effects, implying the significant spillover effects found in column (1) are likely to be due to omitted variable bias. In particular some omitted global push factor might cause gross capital inflow and its restriction to move in the same direction in every developing country, which would explain the positive and significant coefficient on the spillover variable in column (1). Therefore the conclusion of Table 2 is that the pull-push model (10) explains gross capital inflows reasonably well and there is some evidence for spillover effect, but the evidence is not robust. The lack of evidence of capital flow deflection for the entire sample is hardly surprising and in line with other studies (Forbes et al., 2012). In particular, note that this exercise is not a good test of the model in Section 2. An underlying assumption of the model is that countries are identical, if not for the capital controls they implement. In other words, there is a single perfectly integrated world capital market, where all these countries are perfect substitutes in the eyes of investors. This assumption clearly does not hold when we consider the entire sample, where countries are highly heterogeneous, but it could be more reasonable when we look at a smaller group of countries with similar characteristics. Specifically, capital flow deflection may be significant within well defined groups of developing economies, while still be on average irrelevant for the broad (and highly heterogeneous) sample. This is precisely what we investigate next. 3.2.3

Spillover Effects within Country Groups

In this subsection we divide countries into groups based on some common characteristics and investigate spillover effects within these groups. In particular we group countries based on geographic locations, export specialization, returns, and risk. By dividing countries into groups we hope to have countries that are close substitutes from international investors perspective in the same group. Then a natural way to group countries together would be based on similar risk or return. Forbes et al. (2012) and 14

Ghosh et al. (2012) find real GDP per capita to reduce the probability of experiencing a net flow surge. Forbes and Warnock (2012) find no evidence that real GDP per capita is associated with gross inflow surge, while they find real GDP per capita to increase the probability of an outflow retrenchment. 15 There could be a threshold in infrastructure that the coefficient would be positive if the level of infrastructure is below the threshold, and the coefficient would be negative if it is above the threshold. But this is beyond the scope of this paper.

18

Lambert et al. (2012) find the recent inflow controls imposed by Brazil to have spillover effect on some Latin American countries, so we also group countries based on geographic location. Furthermore Forbes et al. (2012) found countries exported to China are affected by Brazil’s higher capital inflow restriction, and since these countries are mostly commodity exporters, so we also divide countries based on export specialization. We use composite risk index as proxy for country specific risk and use real GDP growth rate as proxy for country specific return. We divide countries into four groups depending on the countries’ average real GDP growth rates and average composite risk across the sample period, for example a country i is the low return group if its sample average growth rate is in the bottom 25 percentile of all countries. We call these groups as time-invariant groups since the composition of the groups remain the same across the time. Table 1 shows the time-invariant groups based on risk16 . To allow composition of groups to change over time, we also consider time-variant groups, for example: a country i is in the low return group at time t if it is the bottom 25 percentile among all countries at t. So a country could move from the low return group to a medium-low return group as it grows faster over time. Export specialization and geographic regions follow the definitions used in IMF’s World Economic Outlook. There are six geographic regions17 and five export specializations 18 . We modify the pull-push model (10) to capture within-group spillover effect: ωti = β0 + β1 Rt + β2 τti + β3 τtSi + β4 xit + it

(12)

so (12) looks identical to (10) except the rest of the world’s capital inflow restriction τt−1 is replaced by τtSi , which denotes the rest of the i’s group’s inflow restrictions and it is computed from P j j j∈Si yt τt Si τt = P j j∈Si yt where Si is the set of all the other countries that belong to the same group as country i 19 . INSERT TABLE 5 HERE 16

There are 124 countries in the list with 78 of them in bold. All the countries listed have both GDP and capital inflow restriction data available throughout the sample period, which allow for computing the rest of the group’s capital inflow restrictions. The countries in bold are the ones with at least then years of observations for the rest of the explanatory variables, hence are used for regressions. 17 They are: Latin America and Caribbean; Middle East, North Africa, and Pakistan; Developing Asia; Sub-Sahara Africa; Commonwealth of Independent States (former Soviet member countries); Central and Eastern Europe. 18 They are: fuel exporters; manufacturing exporters; primary products exporters; service, income, transfers exporters; diversified exporters. 19 Si excludes i.

19

In Table 5, we only report the coefficients of τtSi – since it is the key variable of our interest and the coefficients of other variables are almost identical to the ones in Table 420 . Each coefficient in Table 5 comes from a different specification of (12), and there are 36 regression specifications in total. Regression specifications differ by countries are grouped (which gives the six rows in the table) and they also differ by the set of controls (which gives the six columns in the table). In columns (1)-(3) and (4)-(6) we control for a different combination of group fixed effects, country fixed effects, and contagion variables, with the number of controls increasing as the column number ascends. All fixed effects are introduced to reduce omitted variable bias. Regional contagion variable is computed as the gross capital inflow to the geographic region (excluding the country itself) as a share of regional GDP21 , and we include it because it is found to be significant in explaining capital flows in Forbes et al. (2012). In addition, we introduce a second contagion variable: group contagion computed as the gross capital inflow the group (excluding the country itself) as s hare of the group’s GDP. We lag the rest of the group’s inflow control by one period in (4)-(6) to alleviate its endogeneity with the dependent variable. The two might be endogenous since the rest of the group might see a higher capital inflow to a member as a signal for capital inflow surge to the entire group, then they might respond by increasing their contemporaneous capital inflow restrictions. The fewer countries in the group, the more sever is the endogeneity. We find strong evidence of within-group spillover effects when countries are grouped based on risk as all coefficients have the correct signs and are either significant or close to be significant in the last two rows. There is some evidence of within-group spillover effects when countries are grouped based on export specialization. All the signs in the second row are positive as expected, and they are significant or close to being significant at 10% level except in columns (1) and (4). We find no within-group spillover effect when counties are grouped by geographic location or returns. To interpret the coefficients and therefore to understand the magnitude of spillover effects, we compute the range of spillover effect of Brazil’s 2009 capital inflow restriction increase on South Africa. Both countries belong to the same time-variant and timeinvariant risk group in 2009. Brazil increased its capital inflow restriction by .42 in 2009, and in the same year South Africa’s gross capital inflow is 5.6% of its GDP. The coefficient estimates of β4 when countries are grouped by risk ranges from 3.84 to 20.93. Using the lowest and highest estimate, our calculation shows that South Africa’s gross capital inflow would have been between 5.12% and 3.28% of its GDP if Brazil didn’t increase its inflow restriction in 2009, which would be a significant difference. In other words we find that Brazil’s introduction of inflow controls in 2009 increased gross inflow 20

The only exception is the coefficient of real GDP per capita: it is negative and significant in the specifications with all the controls except for country fixed effect, but positive and significant with all the controls . P j j j∈Si yt ωt 21 P j j∈S yt i

20

to South Africa by between .5% and 2.3% of its GDP. To get an idea of how large this spillover effect is, compare it to the effect caused by a 1% reduction in real US interest rate. Our estimation from Table 4 predicts a 1% reduction in real US interest rate increases gross inflow by .3%. So spillover effect coming from another country’s change in capital control could be several magnitude higher than the effect of a change in US monetary policy. 3.2.4

Robustness Test

Recent studies such as Ghosh et al. (2012) and Forbes et al. (2012) focus on extreme capital flow periods such as surges. So instead of studying the spillover effects on magnitude of gross inflows, we study the spillover effects on the probability of experiencing a surge with the same push-pull model: i P rob(Surgeit = 1) = Φ(β0 + β1 Rt + β2 τt−1 + β3 τt−i + β4 xit + eit )

(13)

Where Surgeit equals to one if country i experiences a surge at t, and zero otherwise. Following Ghosh et al. (2012), a country is defined to have a net inflow surge in a year if its net inflow to GDP is greater than 70% of its historical values across time and 70% of all countries’ values in that given year. We define gross inflow surge in the same way by replacing net inflow to GDP by gross inflow to GDP. The probit regression results of (13) are reported in Table 6. The results are largely consistent with the findings in Table 5. Interestingly we now also find some spillover effects among groups by returns. To see if our results rely on the use of Schindler’s inflow controls index , we use the measure of financial sector-specific capital controls by Ostry et al. (2012) to proxy for inflow controls. In particular we use Fincont2 in the Ostry et al. (2012) dataset22 . Fincont2 is computed as an average of three components: (1)differential treatment of accounts held by nonresidents; (ii) limits on borrowing from abroad; and (iii) restrictions on maintenance of accounts abroad. The correlation between Schindler’s inflow controls and Fincont2 is .52. We replicate the same regressions as in Tables 5 with Fincont2 as proxy for inflow controls. The results are reported in Table 7. Due to data availability on Fincont2, we have much smaller sample of 36 countries. The explanatory power the model improves. There is no spillover effect when we do not divide countries into groups. Once we divide countries into groups based on risks, we find expected spillover effects in most specifications as in Table 4. To see if the consistent finding of spillover effects among risk groups depends on the composite risk measure, we consider other measures of country risk. In particular, we 22

A more commonly used proxy for capital controls come from Chinn and Ito (2009). However their measure is computed from restrictions on trade in addition to capital flows, hence less refined than Schindler’s index and Fincont2. We find no robust spillover effects when we proxy capital controls with Chinn-Ito index.

21

divide countries based on their index values of law and order and property rights and we still continue to find robust spillover effects among risk groups. As an additional robustness check, we introduce additional controls used in the literature of push and pull factors in regression equation (12), they include: domestic inflation, real effective exchange rate overvaluation, de facto exchange rate regime. The findings in Table 5 are robust to the inclusion of these additional variables. We do not include these variables in our baseline regressions because their coefficients are never significant. Last, we replace the inflow controls by general capital controls, which is the average of inflow controls and outflow controls and redo the regressions in Table 5 and we are able to find consistent results. This result is consistent with the signaling story in Bartolini and Drazen (2007) and reports in Forbes et al. (2012) that some international investors not differentiating between inflow controls and outflow controls and interpreting tighter outflow controls as signal for future tighter inflow controls. . To conclude this section, we have found strong evidence for spillover effects especially when countries are divided into groups based on risk levels, and the spillover effect could be large in magnitude. The lack of evidence of spillover effects at the regional level has more than one explanation. One possibility is that investors, on average, do not see countries in the same region as sufficiently similar to justify reallocation of investment within the group when one country increases capital controls. However, a second explanation is that the capital deflection model presented in the previous section is not the only mechanism in place. For instance, investors may take an increase in inflow restriction in one country as a signal that others will introduce similar measures and, therefore, reduce rather than ` ´ or Ocontagion ` ´ effect is increase investment to the latter. If this Opolicy emulationO O perceived to be stronger among neighboring countries (perhaps because the electorate is more likely to be informed and politicians to be influenced by policy developments in a nearby country), then it is possible that the capital flow deflection to some countries is offset by a spillover in the opposite direction in others, so that the average effect is imprecisely captured in regression analysis and results in an insignificant coefficient.

3.3 3.3.1

Empirical Evidence of Policy Response Determinants of Increase in Inflow Controls

We proved the theoretical existence of capital control policy response in Proposition 3. In this subsection we investigate empirical evidence for policy response. In particular we will consider a probit model of capital inflow restrictions with other countries’ capital inflow restriction as one of the explanatory variables.

22

There is little empirical literature on the determination of capital controls. Fratzcher (2011) studied capital controls largely in the context of more industrialized economies, and are not applicable to developing countries that we study23 . Due to a lack of established empirical literature in the field, we study the determinants of a country’s decision to change capital inflow controls using empirical models with pull-push factors similar to the empirical models in the previous section with additional controls to capture other motives of using capital controls: P r(Incit = 1) = Φ(β0 + β1 ∆τtSi + β2 xit + uit )

(14)

where Incit is a dichotomous variable and it equals to 1 if country i raises inflow reSi striction at time t and 0 otherwise; ∆τtSi = τtSi − τt−1 . Φ is the cumulative normal distribution function. xt includes all the pull and push factors in the previous sections. We find them to be important determinants of gross capital inflows, and since capital inflow restriction are likely to be intensified when there is a gross capital inflow surge, therefore these pull and push factors might also be important determinants of change in capital inflow restriction. In addition xit includes time fixed effects, group fixed effects, region fixed effects, region contagion variable, group contagion variable real effective exchange rate overvaluation (REER), domestic inflation, flexible exchange rate regime dummy, and real GDP. The REER overvaluation is the percentage deviation from the long-term trend computed by applying the Hodrick-Prescott (H-P) filter to REER. The flexible exchange rate regime dummy takes value one if the de facto exchange rate regime is flexible according to the Reinhart et. al (2007) classification. The key variable of interest in this subsection is ∆τtSi . Proposition 3 predicts that the more countries in the group increase their inflow restriction (hence greater is the increase of capital control), the more likely country i is to also increase its inflow restriction as a policy response especially when country i is small. Therefore we expect the coefficient of ∆τtSi to be positive. Real GDP is included since the model in Section 2 predicts that larger countries are more likely to manipulate the inter-temporal terms of trade with their capital control policies, hence we expect it to have a positive coefficient. We include REER overvaluation, domestic inflation, flexible exchange rate regime dummy since a country could impose capital controls for reasons other than precautionary motif and terms of trade manipulation. A country could impose capital control to keep real exchange rate undervalued, or to keep domestic inflation low, or to defend fixed exchange rate. So we expect the REER overvaluation and flexible exchange rate regime dummy to have negative coefficients and the coefficient of inflation should be positive. 23

We tried using the specifications in his paper to study capital controls in developing countries, but the model yield little explanatory power.

23

3.3.2

Regression Result

Table 8 reports the results of the probit regression results of (14) when countries are grouped in six different ways. Due to data availability of inflation and de facto exchange rate regime, our sample size now reduces to 7224 . The probit model has a reasonable good fit as indicated by the Pseudo R-squares. We do not report the coefficients of the traditional pull factors since they are not significant in any specification and to save space. We find no evidence for within-group policy response as all the coefficients of the change of weighted inflow control in the rest of the group (ROG) are insignificant. We do find evidence consistent with terms of trade motive: larger countries are more likely to increase inflow control. We also find the other motives for capital controls to be important. In particular we find that countries are more likely to increase inflow controls when their currencies are undervalued and when they experience high inflation. Interestingly, the probability of increasing inflow controls are independent of exchange rate regimes which contradicts with policy trilemma. But this finding is consistent with the recent empirical development on dilemma versus trilemma by Rey (2013) and theoretical work by Farhi and Werning (2013) that capital controls are desirable even under flexible exchange rate regime. 3.3.3

Robustness Test

As a robustness test, we consider a linear probability model of (14). The OLS regression results of the linear probability model yield the same findings as the probit model. As an alternative to the policy response variable ∆τtSi , we use DtSi which is computed as P j j j∈Si yt Dt Si Dt = P j j∈Si yt where Dtj is a categorical variable and it takes value 1 if country j tightens inflow control at t, −1 if j lowers inflow control, and 0 if there is no change. And we rerun the regressions in Table 8. The results are largely the same except we find policy response within export groups, but it is only significant at 10%. We conduct the same exercises with decrease in inflow control as the dependent variable, and we do not find robust within-group policy response neither. 24

The countries dropped from the sample are Kazakhstan, Namibia, Oman, Sierra Leone, Sudan and Yemen. All the results from the previous subsection on spillover effect are robust to the exclusion of these six countries from the sample.

24

4

Conclusion TBD.

25

References Bartolini, Leonardo, and Allan Drazen (1997). “Capital- Account Liberalization as a Signal.” American Economic Review, Vol. 87 (March), pp. 138-54. Bagwell, K. and R.W. Staiger (1999). ”An Economic Theory of GATT.” The American Economic Review, 89(1), pp. 215-248. Bagwell, K. and R.W. Staiger (2002). ”The Economics of the World Trading System”, Boston, MA: MIT Press. Bown, Chad P. and Meredith A. Crowley (2006). ”Policy Externalities: How U.S. Antidumping Affects Japanese Exports to the E.U.” European Journal of Political Economy v22, n3 (September 2006): 696-714. [Special issue] Bown, Chad P. and Meredith A. Crowley (2007). ”Trade Deflection and Trade Depression.” Journal of International Economics v72, n1 (May 2007): 176-201. Chinn, Menzie and Hiro Ito (2008). “A New Measure of Financial Openness.” Journal of Comparative Policy Analysis 10(3): 309-22. Costinot, Arnaud, Guido Lorenzoni, and Ivan Werning (2013). “A Theory of Capital Controls as Dynamic Terms-of-Trade Manipulation.” Journal of Political Economy, Forthcoming. Farhi, Emmanuel, and Ivan Werning (2013).“ Dilemma not Trilemma? Capital Controls and Exchange Rates with Volatile Capital Flows” Fernandez, Andres, Alessandro Rebucci, and Martin Uribe (2013) “Are Capital Controls Prudential? An Empirical Investigation”. NBER working paper 19671, November 2013. Forbes, Kristin, Marcel Fratzscher, Thomas Kostka, and Roland Straub (2012).“ Bubble thy Neighbor: Portfolio Effects and Externalities from Capital Controls.” NBER Working Paper No. 18052. Forbes, Kristin and Francis Warnock (2012). “Capital Flow Waves: Surges, Stops, Flight and Retrenchment.” Journal of International Economics, Volume 88, Issue 2, November 2012, Pages 235-25. Fratzscher, Marcel (2012). “Capital Controls and Foreign Exchange Policy.” CEPR Discussion Paper 8788, January 2012. Ghosh, Atish R., Jun Kim, Mahvash S. Qureshi, and Juan Zalduendo (2012). “Surges.” IMF Working Paper 1222 Ilzetzki, Ethan, Carmen M. Reinhart, and Kenneth S. Rogoff (2010). “Exchange Rate Arrangements Entering the 21st Century: Which Anchor Will Hold?” Data updated at http://personal.lse.ac.uk/ilzetzki/IRRBack.htm

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IMF (2012). “The Liberalization and Management of Capital Flows: An Institutional View.” International Monetary Fund Position Paper. Korinek, Anton (2013). ”Capital Controls and Currency Wars”,University of Maryland, Mimeo. Magud, Nicolas, Carmen Reinhart, and Kenneth Rogoff (2011). “Capital Controls: Myth and Reality – A Portfolio Balance Approach.” Peterson Institute of International Economics. WP 11-7. Rey, Helene. (2013). “Dilemma not Trilemma: The global financial cycle and monetary policy independence”. Paper presented at the Jackson Hole Symposium, August 2013. Available at http://www.kansascityfed.org/publications/research/escp/escp-2013.cfm Revised version forthcoming as a CEPR Discussion Paper. Shindler, Martin (2009). “Measuring Financial Integration: A New Data Set.” IMF Staff Papers, Vol. 56, No. 1.

27

5

Tables and Figures Figure 1: Gross Inflows (% GDP) to Developing Countries by Region 35# La,n#America#

30# 25#

Middle#East#and#North# Africa#

20#

Asia#

15#

Sub!Sahara#Africa#

10# Former#Soviet#Bloc#

5#

Central#and#East#Europe#

0# 1995# 1997# 1999# 2001# 2003# 2005# 2007# 2009# !5#

Figure 2: The spillover effect (ii) Borrowing country i

(i) World market

R

(iii) Borrowing region j

R

R

CFS

t(j) R* R*’ CFD CFDj

CFD’ CFDi

A

B’

B

C

D

D’

Figure 1: The Spillover E§ect.

28

R

E

F’

F

CFD CFDj

CFD’ CFDi

A

B’

B

C

D

D’

E

F’

F

Figure 1: The Spillover E§ect.

Figure 3: The multiiplier effect in capital controls

R

E’

E

E’’’ E’’

F

b›R, _fi

R D ›bfi

b›R, _ v fi b

Inflow&controls&by&groups& Figure 2: The multiplier e§ect in capital control policies.

Figure 4: Schindler’s Inflow Control Index by Groups 14

A. Country Groups by Regions 0.9& 0.8& 0.7& 0.6& 0.5& 0.4& 0.3& 0.2&

B. Country Groups by Export Specialization La=n&America& Middle&East&and& North&Africa& Asia& SubISahara&Africa& Former&Soviet& Bloc&

0.75& 0.7& 0.65& 0.6& 0.55& 0.5& 0.45& 0.4& 0.35& 0.3& 0.25&

C. Country Groups by Growth Rate Slow&growth&

0.55& 0.5& 0.45& 0.4& 0.35& 0.3&

Manufacturing& Goods&Exporter& Primary&Goods& Exporter& Service&Exporter& Diversified& Exporter&

C. Country Groups by Composite Risk Level

0.65& 0.6&

Fuel&Exporter&

MediumIslow& growth& MediumIfast& growth& Fast&growth&

29

0.7& 0.65& 0.6& 0.55& 0.5& 0.45& 0.4& 0.35& 0.3& 0.25&

High&risk& MediumIhigh&risk& MediumIlow&risk& Low&risk&

Table 1. Country List by Risk High Risk Angola Burkina Faso Congo, Republic of Côte d'Ivoire Dem. Rep. of the Congo Ethiopia Guinea Guinea-Bissau Haiti Iraq Lebanon Liberia Malawi Mozambique Myanmar Nicaragua Niger Nigeria Pakistan Sierra Leone Sudan Togo Turkey Zambia Zimbabwe

High-Moderate Risk Albania Algeria Armenia Bangladesh Belarus Cameroon Colombia Ecuador Ghana Guyana Honduras Indonesia Kenya Madagascar Mali Moldova Mongolia Romania Senegal Sri Lanka Suriname Tanzania Uganda Venezuela Yemen

Low-Moderate Risk Argentina Azerbaijan Bolivia Brazil Bulgaria Dominican Republic Egypt El Salvador Gabon Guatemala India Iran Jamaica Kazakhstan Papua New Guinea Paraguay Peru Philippines Russia South Africa Syria Thailand Ukraine Uruguay Vietnam

Low Risk Bahamas, The Bahrain Botswana Chile China Costa Rica Croatia Hungary Jordan Kuwait Latvia Libya Lithuania Malaysia Mexico Morocco Namibia Oman Panama Poland Qatar Saudi Arabia Trinidad and Tobago Tunisia United Arab Emirates

Data$summary$

Note: Time-invariant groups by composite risk. The countries in bold are used in the regression analysis. All the countries listed are used in computing τ −i and τ Si .

Table 2. Summary Statistics by Country Groups Variable Schindler index (inflows restrictions) Gross inflows (% GDP) VIX Real US interest rate Inflation Real GDP growth rate Nominal GDP per capita in USD (logged) Nominal GDP in USD (logged) Real effective exchange rate Composite risk Law and order Property rights de facto exchange rate regime

Obs 1170 1108 1170 1170 1135 1169 1159 1170 1170 1138 1138 1121 1134

30

Mean 0.49 4.84 21.54 0.94 15.01 4.12 7.42 10.10 106.78 66.24 3.38 0.44 2.17

S.D. 0.34 8.08 6.45 1.63 54.01 4.72 1.17 1.70 33.93 8.72 1.14 0.17 1.15

Min 0.00 -38.99 12.58 -2.36 -9.86 -24.79 4.38 6.47 56.09 28.00 1.00 0.05 1.00

Max 1.00 63.85 34.04 3.18 1061.21 62.19 10.66 15.42 597.37 86.70 6.00 0.90 6.00

Data$source$ Table 3. Data Sources Data

Source

Capital flows Capital controls VIX US three month treasury rate Inflation rate Real GDP growth rate Nominal GDP per capita in US$ Nominal GDP in US$ Real Effective Exchange Rate Composite risk index Law and Order Property Rights de facto Exchange rate regime classification

International Financial Statistics (IFS) Schindler (2009) Yahoo Finance Federal Reserve Economic Data (FRED) World Economic Outlook (WEO) WEO WEO WEO Information Notice System (INS) Political Risk Service (PRS) PRS Heritage Foundation Reinhart et al. (2008)

Gross%inflow%and%inflow%control% Table 4. Determinants of Gross Inflows (1) Global Push Factors Real US interest rate VIX

-0.337** (0.152) -0.132*** (0.0490)

Domestic Pull Factors (all lagged) Real GDP growth rate 0.595*** (0.188) Real GDP growth rate shock -0.434** (0.209) Real GDP per capita (logged) 0.652 (0.571) De jure Capital inflow control -2.468* (1.341) Composite risk index 0.150** (0.0647) Spillovers ROW's inflow control 23.00*** (5.807) Year fixed effects Observations R-squared

(2)

No 1,007 0.135

Expected Signs -

0.504** (0.194) -0.406* (0.207) 0.481 (0.565) -2.455* (1.440) 0.143** (0.0646) 8.013 (27.50)

+ +/+

+

Yes 1,007 0.167

Note: Robust standard errors culstered at countrylevel level in Note: Robust standard errors clustered at country inparentheses. parentheses. *** p< .01, ** p *** p<0.01, ** p<0.05, * p<0.1 < .05, * p < .1

31

Gross%inflow%and%inflow%control% Table 5. Within-group Spillover Effect of Inflow Controls on Gross Inflows Group by geographic location Group by export specialization Groups by returns Time-invariant groups by growth rate Time-variant groups by growth rate Groups by risks Time-invariant groups by composite risk Time-variant groups by composite risk

Year FE Region FE Group FE Contagion variables Country FE Lagged ROG's inflow control

(1)

(2)

(3)

(4)

(5)

(6)

-2.860 (2.983) 0.277 (2.829)

0.610 (4.476) 6.466 (4.455)

-1.012 (4.437) 6.128 (4.611)

-1.799 (3.043) 0.618 (2.938)

3.555 (5.098) 8.260* (4.704)

-1.228 (4.593) 6.610 (4.779)

4.124 (3.999) 1.574 (2.214)

10.03 (6.697) -2.509 (2.176)

10.58 (6.933) -3.191 (2.026)

3.704 (3.700) -0.467 (2.144)

6.476 (4.473) -2.558 (1.825)

5.556 (4.358) -2.361 (1.467)

10.32* (5.831) 8.752*** (2.816)

14.20** (6.352) 4.951** (1.969)

20.93*** (5.852) 3.835** (1.758)

7.434 (5.492) 10.73*** (3.322)

6.005 (5.656) 8.532*** (2.476)

9.968* (5.166) 7.228*** (2.320)

Yes No No No No No

Yes Yes Yes Yes No No

Yes Yes Yes Yes Yes No

Yes No No No No Yes

Yes Yes Yes Yes No Yes

Yes Yes Yes Yes Yes Yes

Note: Robust errors clustered at country coefficient level in parentheses. *** p<0.01, equation ** p<0.05, *(12) p<0.1for 36 different Note: Thestandard table reports the spillover β3 in regression specifications. Robust standard errors clustered at country level in parentheses. *** p< .01, ** p < .05, * p < .1

32

surges& Table 6. Within-group Spillover Effect of Inflow Controls on Gross Inflow Surge

Group by geographic location Group by export specialization Groups by returns Time-invariant groups by growth rate Time-variant groups by growth rate Groups by risks Time-invariant groups by composite risk Time-variant groups by compisite risk

Year FE Region FE Group FE Contagion variables Country FE Lagged ROG's inflow control

(1)

(2)

(3)

(4)

-0.113 (0.665) -0.399 (0.558)

0.245 (1.100) 1.323 (1.259)

0.161 (0.653) -0.388 (0.575)

1.490 (1.307) 1.141 (0.989)

0.781 (0.767) 0.0884 (0.446)

4.330** (1.719) -0.841 (0.512)

0.696 (0.713) -0.207 (0.537)

3.384*** (1.178) -0.702 (0.471)

-0.657 (1.265) 1.746** (0.752)

3.075* (1.815) 1.653** (0.704)

-1.581 (1.199) 1.804** (0.744)

-0.0498 (1.731) 1.635** (0.675)

Yes No No No No No

Yes Yes Yes Yes No No

Yes No No No No Yes

Yes Yes Yes Yes No Yes

Note: The table reports the spillover coefficient β3 in Probit model (13) for 24 different specifications. No country fixed effects for probit models. Robust standard errors clustered at country level in parentheses. *** p< .01, ** p < .05, * p < .1

33

Gross%inflow%and%fincont2% Table 7. Within-group Spillover Effects of Fincont2 on Gross Inflows Group by geographic location Group by export specialization Groups by returns Time-invariant groups by growth rate Time-variant groups by growth rate Groups by risks Time-invariant groups by composite risk Time-variant groups by composite risk

Year FE Region FE Group FE Contagion variables Country FE Lagged ROG's inflow control

(1)

(2)

(3)

(4)

(5)

(6)

-9.591** (3.716) 0.237 (4.012)

-9.452* (4.775) 1.489 (5.113)

-7.622 (5.018) 4.070 (4.993)

-5.820* (3.155) -0.603 (3.760)

-3.263 (3.324) 3.834 (4.175)

-1.396 (3.749) 6.183 (3.833)

6.433 (4.171) -0.599 (2.984)

1.718 (3.284) -2.661 (2.656)

-1.354 (4.027) -1.795 (1.778)

6.721 (4.363) -4.102 (3.494)

2.962 (3.307) -5.990* (3.418)

4.222 (3.773) -4.600* (2.393)

8.253* (4.271) 2.975 (2.293)

0.264 (4.160) 2.280 (1.469)

2.105 (2.641) 0.679 (1.269)

8.906* (4.674) 2.978 (1.918)

1.981 (4.801) 4.065** (1.522)

5.915 (4.716) 2.787 (1.753)

Yes No No No No No

Yes Yes Yes Yes No No

Yes Yes Yes Yes Yes No

Yes No No No No Yes

Yes Yes Yes Yes No Yes

Yes Yes Yes Yes Yes Yes

Note: The standard table reports the spillover β3 in regression Note: Robust errors culstered at country coefficient level in parentheses. *** p<0.01, equation ** p<0.05, *(12) p<0.1with Fincont2 as inflow controls for 36 different specifications. Robust standard errors clustered at country level in parentheses. *** p< .01, ** p < .05, * p < .1

34

Table 12. Policy Response: Probit Model of Increase in Inflow Controls

Table 8. Determinants of Increase in Inflow Controls (1) Domestic Variables (Lagged) REER overvaluation -1.228** (0.574) Inflation 0.0018* (0.0010) Flexible Exchange Rate -0.186 (0.218) Real GDP (logged) 0.110** (0.0441)

(2)

(3)

(4)

(5)

(6)

Expected Sign

-1.240** (0.581) 0.0018* (0.0010) -0.180 (0.240) 0.105** (0.0464)

-1.149* (0.599) 0.0018* (0.0010) -0.234 (0.187) 0.122*** (0.0461)

-1.252** (0.571) 0.0017* (0.0010) -0.181 (0.207) 0.108** (0.0442)

-1.353** (0.581) 0.0019** (0.0009) -0.0587 (0.218) 0.107** (0.0450)

-1.270** (0.594) 0.0019* (0.0010) -0.146 (0.235) 0.108** (0.0437)

+ +

Change of Weighted Inflow Controls in the ROG Group by geographic location

-0.977 (1.100)

Group by export specialization

+ 0.914 (0.977)

Time-invariant group by growth rate

+ -0.130 (1.052)

Time-variant group by growth rate

+ -0.276 (0.281)

Time-invariant group by composite risk

+ -0.490 (1.274)

Time-variant group by composite risk

Observations Pseudo R-squared

938 0.1538

+ 0.192 (0.366)

938 0.1589

938 0.1562

938 0.1558

938 0.1653

+

938 0.1548

Note: The sample consists of 72 countries. Other domestic variables are not insignificant and hence not reported in the table. All regressions control for year fixed effects, group fixed effects, region fixed effects, group contagion, and regional contagion. Robust standard errors clustered at country level in parentheses. *** p< .01, ** p < .05, * p < .1

35

6

Appendix

6.1 6.1.1

Proofs Proof of Proposition 1

Maximizing (4) subject to (5), and taking both market frictions into account negative externality and market power-, we obtain the following Euler equation: u0 (ci1 ) − β i Ru0 (ci2 ) − x0 (ci1 − y1i ) − β i u0 (ci2 )(ci1 − y1i )

dR = 0. − y1i )]

d[mi (ci1

(15)

Let us investigate separately the two distinct motives for policy intervention, starting with the prudential motive. If country i does not affect the world market equilibrium (mi = 0), then it is dR/d[mi (ci1 −y1i )] = 0. Hence, for a borrowing country (ci1 −y1i > 0), the Euler equation above simplifies to u0 (ci1 ) = β i Ru0 (ci2 ) + x0 (ci1 − y1i ).

(16)

In order for (3) to be equal to (16), it must be u0 (ci1 ) u0 (ci1 ) − x0 (ci1 − y1i ) = , βi R(1 + τ i ) β iR from which we obtain the formula for the optimal precautionary capital controls as τbi = x0 (ci1 − y1i )/[u0 (ci1 ) − x0 (ci1 − y1i )]. For a lending country (ci1 − y1i ≤ 0) instead, it is e(ci1 − y1i ) = 0, and thus all frictions disappear. As a result, the solution to the welfare maximization for a rational forwardlooking national planner coincides with the utility maximization of the representative consumer, and the optimal prudential policy becomes τb1i = 0. Hence, depending on whether country i is lender or borrower, its optimal precautionary capital controls can be described by the step function defined in (8). Let us now introduce the terms-of-trade motive. If country i is able to affect the world market equilibrium (mi > 0), then it is dR/d[mi (ci1 − y1i )] 6= 0, and its unilateral optimal policy is found by equalizing Euler equation (15) with the one solved under the decentralized optimization problem (3). After a few algebraic steps, we obtain the optimal policy as 1 + τ i∗ = (1 + τbi )(1 + τei ). The expression for τbi is given in (8), while the one for τei is given by τei = mi · ε−i , where ε−i represents the inverse elasticity of global savings faced by country i, that is 36

(and after defining Y1−i ≡

P

j6=i

mj y1j and C1−i ≡

ε−i =

6.1.2

P

j6=i

mj cj1 ):25

dR Y1−i − C1−i . R d(Y1−i − C1−i )

(17)

Proof of Lemma 1

(i) Define F (R∗ , τ j ) ≡ mj [y1j − cj1 (R∗ , τ j )] +

n X

−j ∗ m−j [y1−j − c−j 1 (R , τ1 )] = 0.

−j=1

as the implicit function of R∗ w.r.t τ j . From the implicit function theorem, we obtain ∂F/∂τ j dR∗ = − , dτ j ∂F/∂R∗ which is strictly negative, as both ∂F/∂τ j and ∂F/∂R∗ are strictly positive.P (ii) World savings are defined as the sum of each individual lending country’s savings, i mi [y1i − ci1 (R, τ i )], with i indexing all countries for which y1i − ci1 > 0. The statement is true given that dci1 (R, τ i )/dR < 0 for any i. 6.1.3

Proof of Proposition 2

The proof follows immediately from point (i) of Lemma 1 together with the fact that dci1 (R, τ i )/dR < 0 where i denotes all borrowing countries (y1i − ci1 < 0) other than j. Formally, dci1 (R, τ i )/dτ j = (dci1 (R, τ i )/dR) · (dR∗ /dτ j ) > 0. 6.1.4

Proof of Lemma 2

(i) Define G(R, τbi ) ≡

x0 (ci1 (R, τbi ) − y1i ) − τbi = 0 i i i b b 0 i 0 i u (c (R, τ )) − x (c (R, τ ) − y ) 1

1

1

as the implicit function of τbi w.r.t. R when country i is a net borrower. By the implicit function theorem, it is dτbi ∂G/∂R =− . dR ∂G/∂ τbi 25

In deriving the expression for ε−i , we exploit the fact that mi (ci1 − y1i ) =

37

P

j6=i

mj (y1j − cj1 ).

The numerator writes as ∂G u0 (ci1 ) · x00 (ci1 − y1i ) − u00 (ci1 ) · x0 (ci1 − y1i ) ∂ci1 = , ∂R [u0 (ci1 ) − x0 (ci1 − y1i )]2 ∂R which is strictly negative, given that u0 , x0 , x00 > 0, u00 < 0, and ∂ci1 /∂R < 0. On the other hand, the denominator can calculated as ∂G u0 (ci1 ) · x00 (ci1 − y1i ) − u00 (ci1 ) · x0 (ci1 − y1i ) ∂ci1 = − 1, [u0 (ci1 ) − x0 (ci1 − y1i )]2 ∂ τbi ∂ τbi which is also strictly negative. It then follows dτbi /dR < 0 for all borrowing countries. (ii) Deriving expression (7) with respect to R we obtain dτ i∗ dτbi dτei = (1 + τei ) + (1 + τbi ). dR dR dR While derivative dτbi /dR is always strictly negative (as just proven in point (i) above) and, for a large borrowing country, it is also τbi , τei > 0, we are now going to prove that dτei /dR may be positive or negative. Knowing that τei = mi · ε−i , and exploiting the expression for ε−i as given in (17), this derivative can be calculated from the implicit function defined by H[τei , R] ≡ mi

dR Y1−i − C1−i ei − τ = 0, R d(Y1−i − C1−i )

Applying the implicit function theorem to function H, we find that dτei /dR is given by the following expression −i −i Y1−i −C1−i mi d(Y1 −C1 ) d2 R [ ( −i −i 2 R dR R d(Y1 −C1 ) <0 >0 ≶0

dH dτei dR = − dH =− i −i −i m d(Y1 −C1 ) dR ei [ ( dτ

R

dτ i <0

Y1−i −C1−i d2 R −i −i 2 R d(Y1 −C1 ) >0 ≶0

+

+

dR ) d(Y1−i −C1−i ) >0

dR ) d(Y1−i −C1−i ) >0

−

− ε−i ] >0

dR −i ε ] dτ i <0

. −1

For ease of reference, the sign of each term is denoted under each of them. Since both the numerator and the denominator can be either positive or negative, the sign of the expression above is ambiguous.

38

6.1.5

Proof of Proposition 3

(i) It is an immediate implication of Lemmas 1 and 2. (ii) Following the same steps as in the proof of point (ii) of Lemma 2, we derive (7) with respect to τ j to obtain ei dτ i∗ dτbi ei ) + dτ (1 + τbi ). = (1 + τ dτ j dτ j dτ j While dτbi /dτ j as well as τbi , τei are always strictly positive, expression dτei /dτ j may be positive or negative. The implicit function defining τei is given by L[τei , τ j ] ≡ mi

Y1−i − C1−i ei dR − τ = 0, R d(Y1−i − C1−i )

where both C1−i and R are functions of τei and τ j . Applying the implicit function theorem to function L, we find that dτei /dτ j is given by the following expression −i −i 2R Y1−i −C1−i mi d(Y1 −C1 ) [ ( d(Y −id−C −i 2 R dτ j R 1 1 ) >0 >0 ≶0

dL dτei dτ j = − =− i −i −i dL m d(Y1 −C1 ) dτ j ei [ ( dτ

R

dτ i <0

d2 R d(Y1−i −C1−i )2 ≶0

Y1−i −C1−i R >0

+

+

dR ) d(Y1−i −C1−i ) >0 dR

d(Y1−i −C1−i ) >0

)−

−

dR −i ε ] dτ j <0

dR −i ε ] dτ i <0

, −1

whose sign, again, is ambiguous as both the numerator and the denominator can be either positive or negative. 6.1.6

Proof of Corollary

The proof of this statement is immediate given that, as proven in Proposition 3, = dτcω /dR · dR∗ /dτ −ω > 0.

dτcω /dτ −ω

39