Optimal tax on capital inflows discriminated by debt-risk profile

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<ul><li><p>Int Tax Public FinanceDOI 10.1007/s10797-013-9300-1</p><p>Optimal tax on capital inflows discriminated bydebt-risk profile</p><p>Julian A. Parra-Polania Carmia O. Vargas</p><p> Springer Science+Business Media New York 2014</p><p>Abstract In this study, the optimal value of a tax on capital inflows is estimated so thatprivate agents internalize the social costs of their borrowing decisions in an economywith financial constraints. A key feature of our model is that we provide a theoreticalfoundation to tax level differentiation by asset volatility. Using Colombian data for the19962011 period (which includes the crisis of 19981999), we find the tax would bearound 1.2%.</p><p>Keywords Optimal tax Capital flows Externalities Financial constraint</p><p>JEL Classification H23 D62 F34</p><p>1 Introduction</p><p>In the traditional views of financial crises (e.g., Krugman 1979; Obstfeld 1994), freecapital flows are desirable and any government intervention in capital markets isregarded as inefficient. Nevertheless, recent economic literature (e.g., Bianchi 2011;Stein 2012) presents new arguments in favor of the idea that financial crisesmay be dueto the fact that private agents do not internalize their contribution to aggregate financialinstability. Consequently, some policy interventions may improve the general welfareof society.</p><p>J. A. Parra-Polania C. O. Vargas (B)Banco de la Repblica (Colombian Central Bank), Carrera 7 No. 14-78, Piso 11,Bogot, Colombiae-mail: cvargari@banrep.gov.co</p><p>J. A. Parra-Polaniae-mail: jparrapo@banrep.gov.co</p><p>123</p></li><li><p>J. A. Parra-Polania, C. O. Vargas</p><p>This paper analyzes the impact that regulation of capital flows can have on socialwellbeing. The analysis is based on a common argument in the current literature,1</p><p>which claims overborrowingwas one of themain causes of the financial crisis of 20082009. Private agents rationally underestimated the social cost of debt repayments.</p><p>Since private participants have a negligible impact on the market, it is rationalfor them to take prices as given. However, in the aggregate, economic agents deci-sions have an effect on prices, and price changes, in turn, affect all economic agents.This is why debt/consumption decisions give rise to pecuniary externalities. Becauseexternalities of this type operate through the price system, their effects are innocuousin complete and competitive markets, as they efficiently reflect the relative scarcityof goods. In contrast, when markets are incomplete, the competitive equilibrium isPareto suboptimal (Geanakoplos and Polemarchakis 1986), and pecuniary external-ities may have real and distortionary consequences (Greenwald and Stiglitz 1986).This is precisely the case of economies that are subjected to financial constraints due,for instance, to the existence of underdeveloped financial markets (e.g., Caballero andKrishnamurthy 2001, 2003, 2004).</p><p>When the financial constraint is binding, debt repayments and limited access tocredit force agents to reduce consumption. This reduction in aggregate demand has anegative effect on asset prices and, because assets serve as debt collateral, borrowingcapacity is further reduced.2 This negative feedback among aggregate demand, assetprices, and limited access to credit gives rise to a downward spiral in the economy,through a debt-deflation amplification mechanism.3</p><p>The problem stems from the existence of the financial constraint combined withthe fact that private agents do not internalize the social cost of their debt decisions. Onthe whole, these decisions have an impact on prices and, ultimately, on the economysborrowing capacity. Hence, they imply a social cost. From this perspective, financialcrises are defined as situations where economies experience a debt-deflation spiral, asdescribed above.</p><p>Seeing as private agents underestimate the social cost of their decisions, relatedeconomic literature suggests adopting prudential capital controls to reduce financialvulnerability in the face of crisis events (e.g., Bianchi and Mendoza 2011; Korinek2011b). One specific proposal is to regulate capital flows by imposing a Pigouviantax on inflows so as to reduce the impact of capital outflows when a financial crisismaterializes (e.g., Jeanne and Korinek 2010a; Korinek 2010). This paper subscribesto that view and, to calculate the optimal tax level, it proposes a model that exhibitsfinancial amplification in which overborrowing is measured as the difference betweenthe level of debt that would be acquired by a central planner (CP) (who internalizes the</p><p>1 See, among others, Jeanne andKorinek (2010a,b), Korinek (2010), Bianchi (2011), Bianchi andMendoza(2011), and Korinek (2011a).2 There is an alternative interpretation with similar results. To honor their debts, private agents need to sellpart of their assets. This fire-sale implies further reductions in asset prices and, consequently, additionalsales of assets and so on (see Aghion et al. (2004), Mendoza (2010), Bianchi and Mendoza (2011), andStein (2012).3 Two seminal works on the idea that financial restrictions may give rise to an amplifying mechanism inbusiness cycles: Bernanke and Gertler (1989) and Kiyotaki and Moore (1997).</p><p>123</p></li><li><p>Optimal tax on capital inflows</p><p>social cost of his decisions) and one that is acquired by private agents in a decentralizedeconomy.</p><p>The model is simple and highly manageable, based on Korinek (2010, 2011a). Asa contribution we incorporate debt volatility into the model by including liabilities inthe financial constraint and the fact that the real value of debt may be subjected touncertainty (due to factors like inflation or devaluation). In doing so, we find a simpleway to lend theoretical support to our empirical estimation of the tax differentiated bythe debt-risk profile. Incorporating suchprofile is relevant for the purpose of calculatingthe optimal tax, because it has an impact on the size of the externality generated byprivate decisions on debt.</p><p>Furthermore, by including liabilities we are incorporating a fact neglected by tra-ditional financial constraints: the lender does not regard as equal two people with thesame income but with different levels of pending debt. In other words, we are takinginto account that liabilities previously acquired but still in force reduce debt capacity.Borrowers are aware of this fact and have incentives to limit their debt. As a result,the externality that arises during crises is smaller than the one calculated without sucheffect.</p><p>Although Korinek (2010) estimates the optimal tax on capital flows for Indonesiaand differentiates it according to the debt-risk profile, this differentiation is made onlyin the empirical part of his paper by assuming the externality grows one-to-one withthe volatility of each financial instrument, but without any basis in the theoreticalmodel.</p><p>Calculating the optimal tax is highly relevant for some emerging economies thatbecome an attractive alternative for investment in the wake of global financial crisisand experience strong capital inflows as a result. Adopting prudential controls mayallow these countries to reduce the future social cost derived from any sudden changein the trend in international investment.4</p><p>We make use of historical data for the Colombian economy to calculate the optimaltax. Our findings suggest the optimal tax on capital inflows is about 1.2%. This issimilar to the results reported in related literature that estimates the optimal tax forother countries.</p><p>We calculate the optimal tax for two types of debt: CPI-indexed Colombian pesodebt, so its real value for the borrower does not vary, and dollar debt, the real value ofwhich changes for the borrower with movements in the nominal exchange rate and theprice level. The optimal tax in the first case was found to be around 1.1%, and about1.21.3% in the second. The difference between the two is small, since Colombiahas not experienced relatively high values for devaluation minus inflation in recentdecades.5</p><p>In the following section, we describe the model and, in Sect. 3, we obtain theequilibrium for both the decentralized andCP cases. In Sect. 4, we derive an expressionfor the optimal tax that implements the CP solution in a decentralized economy. In</p><p>4 Aghion et al. (2004) draw attention to the fact that economies at an intermediate level of financialdevelopment are the most vulnerable to events involving financial instability.5 For instance, during the last crisis (1999), the value of (devaluation inflation)/(1 + inflation) was 24.1%for Colombia. The value for Indonesia during its crisis period was 118%.</p><p>123</p></li><li><p>J. A. Parra-Polania, C. O. Vargas</p><p>Sect. 5, we estimate the value of the optimal tax for the Colombian case. Section 6contains our conclusions.</p><p>2 The model</p><p>The model is based on Korinek (2010, 2011a). As an additional element, we incorpo-rate debt volatility to lend theoretical support to our empirical estimation differentiatedby the debt-risk profile.</p><p>It is a stylized three-periodmodel of financial amplification for a small open endow-ment economy inhabited by a representative consumer. In periods one and three, forthe sake of simplicity, there is merely one type of good, a tradable good (T), whichis the numeraire. In the second period, there is an additional good, a non-tradable (N)with a relative price p2, and, therefore, 1/p2 can be interpreted as the real exchangerate. In the first period, there are no endowments and consumptionmust be financed bydebt. In the second period, the consumer obtains endowments of both types of goods(yT and yN) and, in the third period, he obtains endowment yT of tradable goods.</p><p>Periods one and three are needed only to start the economy with debt and to guar-antee all debt is paid back, respectively. This is why these periods are modeled in thesimplest possible way and all the interesting elements are incorporated into the secondperiod.</p><p>The representative consumer maximizes the following expected utility function(marginal utility is assumed to be positive and decreasing: i.e., u &lt; 0 &lt; u):</p><p>E [U ] = E[u(cT,1)+ u(c2)+ 2cT,3</p><p>], (1)</p><p>where is the discount factor and c2 = cT,2 c1N,2 is a consumption index that aggre-gates tradable (cT) and non-tradable consumption (cN) with shares and 1 ,respectively. E [.] is the expectations operator.</p><p>The consumer may acquire (tradable) one-period debt in periods one (d1) and two(d2). The value of d1 is subject to uncertainty, because the final payment depends onthe state of the debt in period two.We assume there are two states, both occurring withthe same probability (1/2). In the low state (adverse to the borrower), the consumerrepays d1(1+ ), &gt; 0, and, in the high state (favorable to the borrower), he repaysd1(1 ). The expected value of the first-period debt is d1 and its standard deviationis d1 . Therefore, we interpret as debt volatility.6 Debt acquired in period two is notsubject to uncertainty.</p><p>The assumption on different states intends to capture the fact that different assetcategories, which represent debt, may be subjected to uncertainty, and the real value</p><p>6 We assume there is only one type of debt d1in the model; however, the conclusions remain the same ifwe introduce different types of debt (with different risk levels). So, the total amount is equal to the sum ofall types. Given the concavity of the utility function (risk aversion), the consumer acquires different typesof debt only if higher debt volatility implies a lower interest rate (r). For instance, if there are two types ofdebt, one with high volatility h and the other with low volatility l, h &gt; l, it is necessary that rh &lt; rl.In practice, this situation can be observed when an agent borrows in dollars at a low interest rate (but withhigh foreign exchange risk) or borrows in local currency (avoiding exchange risk) at a higher interest rate.</p><p>123</p></li><li><p>Optimal tax on capital inflows</p><p>of debt may change from the moment it is acquired until it is ultimately repaid. Incor-porating the debt-risk profile is relevant for the purpose of calculating the optimaltax, because, as Korinek (2010) and Jeanne and Korinek (2010b) noted, this volatil-ity has an impact on the size of the externality generated by private decisions. Inpractice, there are different asset categories associated with debt (e.g., GDP-indexed,CPI-indexed, dollar debt) and each represents a different risk profile for the borrower(and the lender). Changes in local or international economic conditions may producesignificant variations in the real value of debt repayments. Although these variationsmay be related to endogenous variables (e.g., the real exchange rate), for the sake ofsimplicity, we assume debt states are exogenously determined.</p><p>The interest rate is assumed to be constant and equal to r. We also define the grossinterest rate R 1+r . Taking this rate as given, the representative consumer choosesin period one the d1 level (which is to be paid back in period two, but can be at leastpartially refinanced by d2) and, in period two, the d2 level (which is to be repaid inperiod three).</p><p>Considering all the previously mentioned elements, budget constraints for periodsone, two, and three can be expressed as follows:</p><p>cT,1 = d1/R, (2)ciT,2 + pi2ciN,2 + d1</p><p>(1 I i) = yT + pi2yN + d i2/R, (3)</p><p>ciT,3 + d i2 = yT, (4)where the superscript i {L,H} indicates the debt state in period two, low or high,and I is a binary variable, IL = 1 and IH = 1. In the first period, the consumer mustfinance consumption by borrowing. In the second period, consumption and repaymentof the debt (the value of which depends on the state: L or H) are financed by income(endowments) andnewdebt. It is important to note that consumption anddebt decisionsin the second and third periods depend on the state observed in period two. In the thirdand final period, the endowment is used to finance consumption and to pay off allremaining debt.</p><p>We assume that lenders assess the borrowing capacity of consumers by taking intoaccount the value of their current available resources. However, the credit market isalso subjected to moral hazard. Namely, borrowers could threaten default and, due toimperfect legal enforcement, lenders can recover only a fraction k of the borrowersincome (net of previous-perioddebt).As a result, to prevent fraud, lenders are unwillingto lend more than what they can recover, and the financial constraint is:</p><p>d i2/R k(</p><p>yT + pi2yN d1(1 I i)), (5)</p><p>where k &lt; /(1 ).7 As explained in Sect. 3.1, we assume that parameter valuesare such that condition (5) is binding only for the low state, and therefore the economyis financially constrained only in such state of nature.</p><p>7 Seeing as there is an amplification effect, this condition guarantees the total impact on consumption ofchanges in initial debt converges to a finite value. See Footnote 10.</p><p>123</p></li><li><p>J. A. Parra-Polania, C. O. Vargas</p><p>The foregoing equation introduces a crucial feature of the model; that is, whenevaluating the debt capacity of potential borrowers, lenders take into account not onlythe borrowers assets (endowments)...</p></li></ul>

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