Capital Controls and Monetary Policy Autonomy in a Small Open Economy

K.7 Capital Controls and Monetary Policy Autonomy in a Small Open Economy Davis, J. Scott, Ignacio Presno Please cite paper as: Davis, J. Scott, Ignacio Presno (2017). Capital Controls and Monetary Policy Autonomy in a Small Open Economy. International Finance Discussion Papers 1190. https://doi.org/10.17016/IFDP.2017.1190 International Finance Discussion Papers Board of Governors of the Federal Reserve System Number 1190 February 2017

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1190 February 2017 Capital Controls and Monetary Policy Autonomy in a Small Open Economy J. Scott Davis Ignacio Presno NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

Capital Controls and Monetary Policy Autonomy in a Small Open Economy J. Scott Davis(cid:3)y Ignacio Presnoz Federal Reserve Bank of Dallas Federal Reserve Board of Governors January 2017 Abstract Is there a link between capital controls and monetary policy autonomy in a country with a (cid:13)oating currency? Shocks to capital (cid:13)ows into a small open economy lead to volatility in asset prices and credit supply. To lessen the impact of capital (cid:13)ows on (cid:12)nancial instability, a central bank (cid:12)nds it optimal to use the domestic interest rate to "manage" the capital account. Capital account restrictions a(cid:11)ect the behavior of optimal monetary policy following shocks to the foreign interest rate. Capital controls allow optimal monetary policy to focus less on the foreign interest rate and more on domestic variables. Keywords: capital controls; credit constraints; small open economy JEL Classi(cid:12)cation: F32; F41; E52; E32 (cid:3)Thispaperpreviouslycirculatedunderthetitle"CapitalControlsasanInstrumentofMonetaryPolicy". We would like to thank seminar participants at the Reserve Bank of New Zealand and participants at theCarnegie-Rochester-NYUconference, theHKIMR-BoG-ECB-FRBDconferenceon"Divergingmonetary policies,globalcapital(cid:13)ows,and(cid:12)nancialstability",the2015meetingoftheSocietyforEconomicDynamics in Warsaw and the 2014 Dynare conference in Paris for many helpful comments and suggestions. We would also like to thank Gianluca Benigno, Javier Bianchi, Martin Bodenstein, Luca Dedola, Mick Devereux, Fabio Ghironi, Kevin Huang, Matteo Iacoviello, Gianni Lombardo, Anna Orlik, Fabrizio Perri, and Albert Queralto. The views presented here are those of the authors and should not be interpreted as re(cid:13)ecting the views of the Federal Reserve Bank of Dallas, the Board of Governors of the Federal Reserve System, or any other person associated with the Federal Reserve System. yFederal Reserve Bank of Dallas, 2200 N. Pearl Street, Dallas, TX 75201, USA Email: scott.davis@dal.frb.org zFederal Reserve Board, 1801 K Street, Washington D.C. 20036, USA Email: ignacio.presno@frb.gov 1

1 Introduction Repeated cycles of capital (cid:13)ows into and out of emerging markets are a (cid:12)xture of the (cid:12)nancially integrated global economy. Surges in capital in(cid:13)ows have led to talk of "currency wars" and the danger of overheating in many emerging markets. Likewise, a sudden reversal of capital (cid:13)ows has been blamed for the recent (cid:12)nancial and macroeconomic instability in many emerging markets. Rey (2015) and Forbes and Warnock (2012) show that capital (cid:13)ows into and out of emerging markets are largely driven by global factors. Reinhart and Reinhart (2009) argue that surges in capital in(cid:13)ows into emerging markets are associated with a higher likelihood of banking, in(cid:13)ation, and currency crises, and contribute to economic and (cid:12)nancial instability. Kaminsky et al. (2005) argue that capital in(cid:13)ows are a primary reason for the procyclicality of monetary policy observed in many emerging markets. Rey (2015) argues that this cycle of capital in(cid:13)ows and out(cid:13)ows means that the "trilemma" of international (cid:12)nance is actually more of a "dilemma", and that "independent monetary policies are possible if and only if the capital account is managed." Obstfeld (2015) addresses this same issue and acknowledges that under certain conditions, a central bank with a (cid:13)oating currency has complete monetary autonomy, but he discusses how (cid:12)nancial globalization a(cid:11)ects the trade-o(cid:11)s faced by monetary policy makers.1 Inthispaperweaddressthisissueinadynamic, generalequilibriummodelwherenominal rigidities and credit frictions give rise to welfare reducing distortions. A policy maker sets policy in order to minimize the e(cid:11)ects of these distortions. If there are multiple distortions and only one monetary policy instrument then the policy maker is faced with a trade-o(cid:11). How are these trade-o(cid:11)s in a small open economy a(cid:11)ected by exogenous shocks from the rest of the world that lead to sharp reversals in capital in(cid:13)ows and out(cid:13)ows? How will capital 1The trilemma has been a feature of the international macroeconomics literature since Mundell (1963). The trilemma states that a country cannot simultaneously maintain a (cid:12)xed exchange rate, an open capital account, and monetary policy autonomy. In technical terms, the fact that the combination of a (cid:12)xed exchange rate and an open capital account lead to the loss of monetary policy autonomy is purely mechanical. When a central bank maintains a (cid:12)xed exchange rate, monetary policy takes the form of a rule stating that the nominal exchange rate is held constant. So for instance, in response to a fall in net capital in(cid:13)ows, the central bank is forced to raise the interest rate to attract capital (cid:13)ows and prevent depreciation. 2

account restrictions a(cid:11)ect the trade-o(cid:11)s that the policy maker faces? What implications does this have for the losses due to certain frictions in the economy? This paper shows that a central bank with a (cid:13)exible exchange rate may (cid:12)nd it optimal to use its interest rate instrument to "manage" the capital account (i.e. stabilize capital (cid:13)ows). When borrowers are subject to collateral constraints, changes in capital in(cid:13)ows and out(cid:13)ows can lead to (cid:12)nancial instability. When the amount that individuals can borrow depends on the value of existing collateral at the current market price, a fall in net capital in(cid:13)ows following a foreign shock can push down asset prices and tighten the collateral constraint in the small open economy, leading to a credit crunch. In this case, the central bank of the small open economy will (cid:12)nd it optimal to raise the interest rate in order to attract net capital in(cid:13)ows, even though the foreign shock is leading to a fall in output. Given this (cid:12)nding, we then show how the use of capital controls can free the interest rate from this need to manage the capital account. Similar to how the use of capital controls allows greater monetary policy autonomy in a country with a (cid:12)xed exchange rate, we show how the use of capital controls allows greater monetary policy autonomy in a country with a (cid:13)exible exchange rate. To frame the discussion we begin by presenting some empirical evidence of this channel. In regressions similar to those in Shambaugh (2004), Obstfeld et al. (2005), and Klein and Shambaugh (2015), we show that imposing capital account restrictions leads to a signi(cid:12)cant increase in monetary policy autonomy. This empirical (cid:12)nding is true not only for countries with a pegged currency, where this gain in autonomy is mechanical, but for countries with a (cid:13)oating currency as well. Then, in a DSGE model with both price and credit frictions, we compute optimal monetary policy in a small open economy following an exogenous shock to the foreign interest rate underdi(cid:11)erentlevelsofcapitalaccountopenness. Themodelissolvedwithapiecewiselinear approximation to a non-linear solution, and thus takes account for potential asymmetries that may arise from potentially non-binding collateral constraints. We show how the use of capital controls signi(cid:12)cantly a(cid:11)ects the degree of monetary policy autonomy and allows the central bank to use its monetary policy instrument for domestic stabilization. Finally 3

we consider the welfare implications of the use of capital controls. Capital controls are not costless and reduce the ability of agents in the small open economy to borrow and lend on international markets to smooth consumption, but by limiting the distortionary e(cid:11)ects of (cid:13)uctuations in capital (cid:13)ows, capital controls can result in a net welfare gain. A number of recent papers have addressed the issue of how capital controls can be used to minimize the e(cid:11)ects of distortions arising from (cid:12)nancial frictions. Korinek (2010), Jeanne and Korinek (2010), Bianchi (2011), Benigno et al. (2013), Korinek (2013), and Bianchi and Mendoza (2015) all discuss how the fact that collateral constraints depend on either asset prices or non-traded good prices, which are subject to (cid:13)uctuations from capital in(cid:13)ows, leads to under- or over-borrowing and (cid:12)nancial instability. Speci(cid:12)cally the ine(cid:14)cient level of borrowing is caused by a pecuniary externality, where agents don’t internalize the e(cid:11)ect that their collective actions are having on asset or non-traded good prices and thus collateral constraints. They discuss how counter-cyclical taxes on capital in(cid:13)ows and other macroprudential measures can be used to o(cid:11)set this externality and reduce (cid:12)nancial vulnerabilities. Brunnermeier and Sannikov (2015) and Heathcote and Perri (2016) discuss how capital controls can enhance international risk sharing. Engel (2015) surveys the recent literature on capital controls and macroprudential policy in a world of volatile international capital (cid:13)ows and discusses how capital controls can be used as a macroprudential regulation to correct for certain (cid:12)nancial distortions. However, while the aforementioned papers consider the e(cid:11)ect of distortions arising from (cid:12)nancial frictions or limited international risk sharing, the models exhibit (cid:13)exible prices and do not have a role for conventional monetary policy. Schmitt-Grohe and Uribe (2012b), Schmitt-Grohe and Uribe (2012a) and Farhi and Werning (2012) show how counter-cyclical capitalcontrolspolicycanplayaroleinmacroeconomicstabilizationinasmallopeneconomy with a (cid:12)xed exchange rate, but in these models, conventional monetary policy is dedicated to maintaining a (cid:12)xed exchange rate, and capital controls frees monetary policy from the constraints of the trilemma.2 Our paper will consider the case where monetary policy can be 2Inaddition, somerecentpapers, likeCostinotetal.(2011)andDePaoliandLipinska(2013), Heathcote andPerri(2016),andFarhiandWerning(2014)discusstheoptimaluseofcapitalcontrolsforterms-of-trade manipulation as a way to improve welfare in an open economy. 4

set freely. Aoki et al. (2016) consider the welfare e(cid:11)ects of various permanent and temporary macroprudentialpolices, includingcapitalcontrols, inasmallopeneconomysubjecttoworld interest rate shocks where domestic monetary policy is dedicated to price stability. They (cid:12)nd that capital controls lead to a signi(cid:12)cant welfare improvement when monetary policy is dedicated to domestic stabilization. While not the same, this is similar in spirit to the main (cid:12)ndings of this paper, that capital controls allow optimal monetary policy to focus more on domestic stabilization and less on managing the external accounts. This paper will proceed as follows. Some simple empirical results that frame our discussion are presented in section 2. The theoretical model used to derive the optimal policy results is described in section 3. The calibration of the model and the solution procedure are discussed in section 4 and the results are presented in section 5. Finally section 6 concludes. 2 Empirical Evidence of Capital Controls and Monetary Policy Autonomy We begin by estimating a simple monetary policy rule in a small open economy. Assume that the central bank in country j sets its nominal interest rate with the following Taylor rule: i =(cid:22){ +(cid:18) ((cid:25) (cid:0)(cid:25)(cid:22) )+(cid:18) (y (cid:0)y(cid:22) )+(cid:18) (i (cid:3) (cid:0)(cid:22){ (cid:3) )+m (1) jt j p jt j y jt jt s t t where i is the nominal interest rate in country j, (cid:22){ is the neutral or steady state value of jt j this interest rate, (cid:25) is the in(cid:13)ation rate, y is log GDP, (cid:25)(cid:22) is the in(cid:13)ation target, y(cid:22) is log jt jt j jt potential output, and m is a monetary shock. The interest rate i(cid:3) is the "base" country t t interest rate, the interest rate in the rest of the world, and (cid:22){(cid:3) is the neutral or steady state value of this interest rate. For most countries and most years in this panel data, the base country interest rate is the U.S. Fed Funds rate, but for some countries and some years, the base country interest rate is the interest rate on the British pound or the euro. The data for this empirical exercise is taken from Klein and Shambaugh (2015). See the appendix to this paper for the complete list of countries and their corresponding "base" country. 5

Take the (cid:12)rst di(cid:11)erence of this Taylor rule expression to get: (cid:3) (cid:1)i = c +(cid:18) (cid:1)(cid:25) +(cid:18) (cid:1)y +(cid:18) (cid:1)i +(cid:1)m jt j p jt y jt s t t where c j = y(cid:22) jt (cid:0)y(cid:22) jt(cid:0)1 . It should be noted that this speci(cid:12)cation assumes that the growth in potential is country-speci(cid:12)c and constant across time. This functional form leads to a panel data estimation that can be used to estimate values of the Taylor rule parameters (cid:18) , (cid:18) , and (cid:18) . We consider an unbalanced panel of 129 p y s emerging market and developing countries and 39 years of annual observations, 1973-2011, for a total of 2784 observations. These observations can be divided into 2 subgroups, based on whether the country-year observation has a (cid:13)oating currency or an exchange rate peg. A pegged exchange rate is one where over the course of the year, the exchange rate never varies out of a band (cid:6)2% with the reference currency (the reference currency is the currency of the base country). We then estimate this equation twice, using the panel with countryyear observations where the country has a (cid:13)oating currency and the panel of country-year observations with a (cid:12)xed currency. The results from this estimation are presented in the (cid:12)rst column of table 1. Our results con(cid:12)rmthe(cid:12)ndingsinKleinandShambaugh(2015)andareinagreementwiththetrilemma. The estimated coe(cid:14)cient on the foreign interest rate is higher for a country with a pegged currency than for a country with a (cid:13)oating currency. Furthermore a country with a (cid:13)oating currency is able to place more weight on domestic variables like in(cid:13)ation. But the results in the (cid:12)rst column show that even for a country with a (cid:13)oating currency, the coe(cid:14)cient on the foreign interest rate is positive and signi(cid:12)cant. This itself is interesting given that the theory of the trilemma states that a country with a (cid:13)oating currency should have complete monetary autonomy. Of course the simple fact that a country’s interest rate is correlated with world interest rate is not proof that the central bank lacks monetary policy autonomy, but in this regression we (cid:12)nd that the central bank takes some attention away from domestic conditions like in(cid:13)ation and output and instead puts weight on the foreign interest rate. Furthermore, we explore the possibility that the coe(cid:14)cient on the foreign 6

interest rate, (cid:18) , may be a function of a country’s level of capital account openness. To test s this we consider the same regression speci(cid:12)cation, but in addition to (cid:1)i(cid:3) we include the t interaction between (cid:1)i(cid:3) and K , where K is the value of the Chinn and Ito (2008) capital t jt jt account openness index in country jand year t (normalized on a 0-1 scale, where 0 represents a completely closed capital account and 1 represents a completely open capital account).3 (cid:1)i = c +(cid:18) (cid:1)(cid:25) +(cid:18) (cid:1)y +(cid:18)c(cid:1)i (cid:3) +(cid:18)oK (cid:1)i (cid:3) +(cid:1)m jt j p jt y jt s t s jt t t where the Taylor rule coe(cid:14)cient on the foreign interest rate in a country with a closed capital account is (cid:18)c and the coe(cid:14)cient in a country with an open capital account is (cid:18)c +(cid:18)o. s s s These results are presented in the second column of table 1. The same patterns seen before continue to hold, where the country with the pegged exchange rate places much more weight on the foreign interest rate and less weight on domestic in(cid:13)ation than the country with the (cid:13)oating currency. But in the results for the country with the (cid:13)oating currency, the coe(cid:14)cient on the foreign interest rate is not signi(cid:12)cantly di(cid:11)erent from zero when the country has a closed capital account, but for a country with an open capital account it is signi(cid:12)cantly positive. This suggests that capital controls have an e(cid:11)ect on monetary policy autonomy even for a country with a (cid:13)oating exchange rate. Having presented these suggestive empirical results, we will now turn to a small open economy DSGE framework to see if a model can replicate this relationship between capital controls and monetary policy autonomy in a small open economy. 3 The Model Consider an in(cid:12)nite-horizon model of a multi-sector small open economy that features nominal price rigidities coupled with credit frictions. The source of aggregate uncertainty is shocks to the foreign interest rate. The economy is populated by a representative household, 3This capital account openness variable could potentially be an endogenous variable, since the change in a country’s interest rate may lead them to change their level of capital account restrictions. But in reality, the Chinn-Ito index moves at very low frequency, so the chances of reverse causality from year-over-year change in the nominal interest rate to changes in the Chinn-Ito index are minimal. 7

a representative entrepreneur, a (cid:12)nal good (cid:12)rm, a continuum of intermediate good (cid:12)rms, and a central bank that sets monetary policy and capital controls policy. Financial markets are incomplete and segmented since only households have access to international credit. In this section we will present the model and the key equilibrium conditions; the full set of (cid:12)rst-order conditions and market-clearing conditions is available in the appendix. 3.1 Households Households supply labor to the intermediate good sector and lend to entrepreneurs. They consume from their labor income, interest on savings and pro(cid:12)ts from (cid:12)rms, which they own. Households are risk-averse and derive utility from consumption and disutility from labor e(cid:11)ort. The representative household in the home country chooses consumption, C , labor e(cid:11)ort, t H , and home and foreign bond holdings, B and Bf respectively,4 to maximize expected t t t lifetime utility given by: 1 1+ 1 E (cid:12)t ln(C )(cid:0) H (cid:27)H (2) 0 t t t=0 (cid:20) (cid:21) P with (cid:12) 2 (0;1), > 0, and the Frisch elasticity of labor (cid:27) > 0. H The households’ budget constraint expressed in local currency is given by: P t C t +B t +S t B t f = W t H t +(cid:4) t +(1+i t(cid:0)1 )B t(cid:0)1 +(1(cid:0)(cid:28) t(cid:0)1 ) 1+if t(cid:0)1 S t B t f (cid:0)1 +T t (3) (cid:16) (cid:17) where P is the price of the (cid:12)nal consumption good, W is the nominal wage rate, S is t t t the nominal exchange rate (expressed in units of the home currency per units of foreign currency), (cid:4) is pro(cid:12)t from (cid:12)rms in the intermediate good sector, T are lump-sum transfers t t from the government, and i is the nominal interest rate on home currency bonds purchased t in period t. The interest rate on foreign currency denominated bonds is the combination of 4Throughout the paper, bond holdings denoted with a superscript f are denominated in the foreign currency while bond holdings written without it are denominated in the home currency. 8

a exogenous foreign risk-free rate, i(cid:3) , and a debt-elastic interest premium: t if = i (cid:3) exp (cid:0)(cid:16)B~f t t t (cid:16) (cid:17) where B~f is the aggregate debt in foreign currency bonds. The parameter (cid:16) is positive t implying that borrowing costs are increasing in the home country debt level. It ensures the stationarity of the linear approximation of this small open economy model, as in Schmitt- Grohe and Uribe (2003). Note that the risk premium depends on the aggregate stock of foreign currency denominated bonds across all households, so the representative household does not internalize the e(cid:11)ect of his actions on it. Capital controls are captured by the tax rate (cid:28) that the central bank applies to holdings of foreign bonds purchased in period t; more t detail is provided later in this section. The total proceeds from the capital control taxes and bond adjustment costs are redistributed to the domestic households in a lump-sum fashion via T : t T t = (cid:28) t(cid:0)1 (1+if t(cid:0)1 )S t B~ t f (cid:0)1 The (cid:12)rst order condition of the household’s problem with respect to consumption is: 1 = P (cid:3) t t C t where (cid:3) is the multiplier on the household’s budget constraint (the marginal utility of t income). Consumer price in(cid:13)ation is given by: (cid:25) = Pt (cid:0)1. t Pt(cid:0)1 The households’ (cid:12)rst order condition with respect to domestic currency bond holdings gives rise to the household’s Euler equation: (cid:3) t 1+i = (4) t (cid:12)E ((cid:3) ) t t+1 Household (cid:12)rst-order conditions for home and foreign currency bond holdings yield an un- 9

covered interest parity condition: 1+if (1(cid:0)(cid:28) )E ((cid:3) S ) t t t t+1 t+1 = (1+i )E ((cid:3) ) (5) (cid:16) (cid:17) S t t t+1 t 3.2 Entrepreneurs The representative entrepreneur supplies labor to (cid:12)rms in the intermediate goods sector. In addition, they own capital and rent it (cid:12)rms. They (cid:12)nance this stock of capital partially with their own equity and partially by borrowing in their local currency. The representative entrepreneur in the home country chooses their consumption Ce, t labor e(cid:11)ort, He, investment I , capital stock K , and domestic currency bond holdings b , to t t t t maximize expected lifetime utility given by: 1 E 0 (cid:12)(cid:22)t ln(C t e)(cid:0) (H t e) 1+ (cid:27) 1 H (6) t=0 h i P subject to his budget constraint: P t C t e +P t I t +b t = W t H t e +R t K t(cid:0)1 +(1+i t(cid:0)1 )b t(cid:0)1 (7) where K t(cid:0)1 is his stock of capital at the beginning of the period, R t is the rental rate on capital, and b is his asset position on one-period bonds denominated in local currency.5 t The entrepreneur’s discount factor is (cid:12)(cid:22) , which is less than the household’s discount factor of (cid:12). This simply ensures that in the steady state equilibrium, entrepreneurs borrow and households save. The calibration of both of these discount factors is presented in the next section. Capital accumulation is subject to a constant depreciation rate (cid:14) and investment adjustment costs captured by the function F (I t ;I t(cid:0)1 ). The stock of capital then evolves according 5The restriction that home entrepreneurs cannot hold foreign currency denominated bonds in the model is intended to prevent exchange rate (cid:13)uctuations from having a distortionary balance-sheet e(cid:11)ects on entrepreneurs, as in Cespedes et al. (2004). This would give the central bank even more incentive to sacri(cid:12)ce monetary independence in favor of capital (cid:13)ow and exchange rate stability. 10

to the following capital accumulation equation: K t = (1(cid:0)(cid:14))K t(cid:0)1 +F (I t ;I t(cid:0)1 )I t 2 where F (I t ;I t(cid:0)1 ) = 1(cid:0) (cid:20) 2 It I (cid:0) t 1 (cid:0)1 , with (cid:20) > 0, as in Christiano et al. (2005). (cid:16) (cid:17) Given this investment adjustment costs there is not a one-to-one transformation between (cid:12)nal goods and existing capital. This ensures that the current price of existing capital relative to the price of the (cid:12)nal good is a function of past, present and future investment decisions and the investment adjustment friction parameter, (cid:20). In a competitive market where existing capital can be traded among entrepreneurs, the equilibrium relative price of existing capital, PK, is given by: t (cid:20) I 2 I I I I 2 P = 1(cid:0) t (cid:0)1 (cid:0)(cid:20) t (cid:0)1 t PK +(cid:12)(cid:22)(cid:20)E t+1 (cid:0)1 t+1 PK t 2 (cid:18) I t(cid:0)1 (cid:19) (cid:18) I t(cid:0)1 (cid:19) I t(cid:0)1! t t " (cid:18) I t (cid:19)(cid:18) I t (cid:19) t+1 # (8) As in Liu et al. (2013), due to limited enforcement, entrepreneurs face an occasionally binding collateral constraint, through which they cannot borrow more than a fraction (cid:18) of the discounted expected market value of their capital stock next period: (cid:0)(1+i )b (cid:20) (cid:18)E PK K (9) t t t t+1 t (cid:2) (cid:3) The entrepreneurs’ Euler condition gives rise to the following expression linking the entrepreneurs’ stochastic discount factor with the real interest rate: (cid:3)e 1+i = t (10) t (cid:12)(cid:22)E (cid:3)e +(cid:22) t t+1 t (cid:0) (cid:1) where (cid:3)e is multiplier of the entrepreneur’s budget constraint (the marginal utility of income t for entrepreneurs) and (cid:22) is the Lagrange multiplier associated with the collateral constraint. t When the collateral constraint binds, we observe a wedge given by (cid:22) (1+i ) between the curt t rent shadow value of income and the expected one next period, re(cid:13)ecting the entrepreneur’s limited ability to reallocate wealth to intertemporally smooth consumption. 11

3.3 Firms There are two types of (cid:12)rms, (cid:12)nal goods (cid:12)rms and intermediate goods (cid:12)rms. Final goods (cid:12)rms operate in a perfectly competitive market and simply combine domestically produced and imported intermediate goods to produce a (cid:12)nal good for consumption or investment. Intermediate goods (cid:12)rms are monopolistic competitors and produce a di(cid:11)erentiated intermediate good that can be sold domestically or exported. They set prices according to a Calvo-style price setting framework. 3.3.1 Final Goods Producers A (cid:12)nals good sector produces output in a perfectly competitive market. Each of the (cid:12)nal goods (cid:12)rms combines domestic goods and imports in a CES Armington aggregator: y t = (!)(cid:26) 1 y t d (cid:26)(cid:0) (cid:26) 1 +(1(cid:0)!)(cid:26) 1 [y t m] (cid:26)(cid:0) (cid:26) 1 (cid:26)(cid:0) (cid:26) 1 (11) h i (cid:2) (cid:3) where the parameter (cid:26) is the Armington elasticity between the composites yd and ym, and t t ! is the Armington weight of the former re(cid:13)ecting the degree of home bias in the local production. Final output is used in the home country for consumption of households and entrepreneurs and investment, y = C +Ce +I t t t t From this Armington aggregator function, the demand functions for domestically produced goods and imports are given by: Pd (cid:0)(cid:26) Pm (cid:0)(cid:26) yd = ! t y and ym = (1(cid:0)!) t y t P t t P t (cid:18) t (cid:19) (cid:18) t (cid:19) wherePd isthepriceindexofdomesticallyproducedgoods, Pm isthepriceindexofimported t t goods, and P is the consumer price index in this small open economy. The import price t index is simply the price level in the rest of the world multiplied by the nominal exchange rate Pm = S P(cid:3) . In this small open economy model, we can assume that the price level t t t in the rest of the world remains equal to 1. The consumer price index is given by P = t 12

1 ! Pd 1(cid:0)(cid:26) +(1(cid:0)!)(Pm)1(cid:0)(cid:26) 1(cid:0)(cid:26) . t t h i (cid:0) (cid:1) 3.3.2 Intermediate Goods Producers Thecompositeyd resultsfromcombiningacontinuumofdomesticdi(cid:11)erentiatedintermediate t goods, through a Dixit-Stiglitz aggregator: (cid:27) yd = 1yd(i) (cid:27)(cid:0) (cid:27) 1 di (cid:27)(cid:0)1 t 0 t (cid:16) (cid:17) R where (cid:27) > 1 is the elasticity of substitution across varieties. Exports from domestic intermediate goods (cid:12)rms are aggregated with a similar function: (cid:27) yx = 1yx(i) (cid:27)(cid:0) (cid:27) 1 di (cid:27)(cid:0)1 t 0 t (cid:16) (cid:17) R From these aggregator functions, the demand function for output from intermediate good (cid:12)rm i is given by: P (i) (cid:0)(cid:27) P (i) (cid:0)(cid:27) yd(i)+yx(i) = t yd + t yx t t Pd t Px t (cid:18) t (cid:19) (cid:18) t (cid:19) 1 where Pd = Px = 1 (P (i))1(cid:0)(cid:27)di 1(cid:0)(cid:27) . The Law of One Price holds for each variety i, so t t 0 t the price of exports (cid:16) Rfrom the small o (cid:17) pen economy in the rest of the world are P t x . Therefore St export demand is given by: Px (cid:0)(cid:26) yx = t yx t S (cid:18) t (cid:19) where the constant yx is set to ensure that trade is balanced in the steady state, yx = (1(cid:0)!)y, where y is steady state output in the small open economy. Intermediate good producer i operates a Cobb-Douglas production function: yd(i)+yx(i) = h (i)1(cid:0)(cid:11)k (i) (cid:11) (12) t t t t where the parameter (cid:11) 2 (0;1) is the capital share, common across all varieties, h (i) and t 13

k (i) are the labor and capital employed by the intermediate good (cid:12)rm in period t. t From its cost minimization problem, the demand functions from intermediate good (cid:12)rm i for labor and capital are given by: MC h (i) = (1(cid:0)(cid:11)) t yd(i)+yx(i) (13) t W t t t MC (cid:0) (cid:1) k (i) = (cid:11) t yd(i)+yx(i) t R t t t (cid:0) (cid:1) where MC = Wt 1(cid:0)(cid:11) Rt (cid:11) denotes the marginal cost of production. t 1(cid:0)(cid:11) (cid:11) Market clea(cid:0)ring(cid:1)in th(cid:0)e la(cid:1)bor and capital markets requires that the total demand for labor by (cid:12)rms is equal to the supply of labor from households and entrepreneurs: H +He = 1h (i)di t t 0 t R And the quantity of physical capital employed by (cid:12)rms in period t is equal to the economy’s stock of physical capital at the beginning of the period: K t(cid:0)1 = 1 0 k t (i)di R GDP is simply given by (cid:12)nal demand plus net exports, GDP = y +yx (cid:0)ym. t t t t Price setting. Firms in the intermediate good sector set prices according to a Calvo style pricesettingframework. Inperiodt,each(cid:12)rmwillbeabletochangeitspricewithprobability 1 (cid:0) (cid:24) . For each item sold to the home or the foreign market the (cid:12)rm receives a constant p subsidy of (cid:23). This subsidy is simply introduced to o(cid:11)set the monopolistic competition distortion and remove this steady state ine(cid:14)ciency. The subsidy is (cid:12)nanced through a lump sum tax to (cid:12)rms. Thus a (cid:12)rm that is allowed to change its price in period t, will do so to maximize: 1 maxE (cid:12)(cid:28) ((cid:24) ) (cid:28) (cid:3) (P (i)+(cid:23)) yd (i)+yx (i) (cid:0)MC yd (i)+yx (i) t p t+(cid:28) t t+(cid:28) t+(cid:28) t+(cid:28) t+(cid:28) t+(cid:28) Pt(i) (cid:20)(cid:28)=0 (cid:21) P (cid:8) (cid:0) (cid:1) (cid:0) (cid:1)(cid:9) 14

The price set optimally in period t is given by: E 1 (cid:12)(cid:28) ((cid:24) ) (cid:28) (cid:3) (MC (cid:0)(cid:23)) ! 1 (cid:0)(cid:27) P t d +(cid:28) (cid:0)(cid:26) y + 1 (cid:0)(cid:27) P t x +(cid:28) (cid:0)(cid:26) yx P t (i) = (cid:27) (cid:0) (cid:27) 1 t (cid:28) P =0 E 1 p (cid:12)(cid:28) ( t+ (cid:24) (cid:28) ) (cid:28) (cid:3) t+(cid:28) ! 1 (cid:18) (cid:16) (cid:0)(cid:27) P t d +(cid:28) P (cid:17) t d +(cid:28) (cid:16) (cid:0)(cid:26) Pt y +(cid:28) (cid:17) + t+(cid:28) 1 (cid:16) (cid:0)(cid:27) P t x +(cid:28) P (cid:17) t x +(cid:28) (cid:16) (cid:0)(cid:26) St y + x (cid:28) (cid:17) (cid:19) t (cid:28)=0 p t+(cid:28) (cid:18) P t d +(cid:28) Pt+(cid:28) t+(cid:28) P t x +(cid:28) St+(cid:28) (cid:19) (cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) P If prices are (cid:13)exible, i.e. (cid:24) = 0, then this expression collapses to: p (cid:27) P (i) = (MC (cid:0)(cid:23)) t (cid:27) (cid:0)1 t which implies that the (cid:12)rm will charge a constant mark-up over its marginal cost less the subsidy. To remove the monopolistic competition distortion in the steady state, (cid:23) = MC, (cid:27) where MC is the steady state marginal cost.6 Let P~ (i) denote the price chosen by (cid:12)rm i that can reset prices in period t. Firms that t can reset prices in period t will all reset to the same level, so P~ (i) = P~ . By the law of large t t numbers, only 1 (cid:0) (cid:24) of (cid:12)rms will be able to change their price in a given period, and the p remaining (cid:24) (cid:12)rms keep their prices (cid:12)xed. Thus the price index for domestic traded goods, p Pd, can be written as: t 1 Pd = (cid:24) Pd 1(cid:0)(cid:27) +(1(cid:0)(cid:24) ) P~ 1(cid:0)(cid:27) 1(cid:0)(cid:27) t p t(cid:0)1 p t (cid:18) (cid:19) (cid:16) (cid:17) (cid:0) (cid:1) 3.4 Monetary and Capital Controls Policy Price frictions and credit frictions lead to distortions in the decentralized market allocation. Nominal price rigidities lead to distortions in domestic production resulting from price dispersion. At the same time, due to the credit friction, the borrowing capacity of entrepreneurs is limited by the market value of their collateral. This collateral constraint gives rise to a Fisherian debt-de(cid:13)ation mechanism. A fall in the price of existing capital leads to a tightening of the borrowing constraint. As we discuss later in this section, this leads to a distortion 6Due to sticky output prices, the (cid:12)rm may earn a non-zero pro(cid:12)t in some periods. Firm pro(cid:12)ts, given by (cid:4) (i) = (P (i)+(cid:23)) yd(i)+yx(i) (cid:0)W h (i)(cid:0)R k (i)(cid:0)(cid:23) yd+yx are returned lump-sum to the t t (cid:0) t t (cid:1) t t t t (cid:0) t t(cid:1) households. 15

in the intertemporal savings/investment decisions of entrepreneurs. To minimize the e(cid:11)ect of these distortions, the central bank sets monetary and (potentially) capital controls policy. Monetary policy is given by an optimal simple rule for the nominal risk-free rate, as in Schmitt-Groh(cid:19)e and Uribe (2007). In particular, we restrict our attention to the class of policy rules with the Taylor-rule functional form in (1) where the nominal interest rate is a function of in(cid:13)ation, the output gap, and the foreign interest rate: i = i +(cid:18) (cid:25)d +(cid:18) (og )+(cid:18) (i (cid:3) (cid:0)i (cid:3) ) t ss p t y t s t ss (cid:0) (cid:1) where (cid:25)d is the in(cid:13)ation of domestically produced goods and og is the output gap|that t t is, log GDP minus log GDP in the frictionless economy|, and i and i(cid:3) are the steady ss ss state values of the home and foreign nominal interest rate, respectively.7 The frictionless economy features (cid:13)exible prices, no collateral constraint, an open capital account, and the same steady state as our benchmark economy with price and credit frictions.8 Recall that the tax rate on the return from foreign bond holdings represents capital controls in the model. This is a potential policy instrument that gives the central bank the ability to control net capital in(cid:13)ows. Assume these tax rates take the following functional form: (cid:28) = (cid:31) if (cid:0)i (14) t t t (cid:16) (cid:17) With this functional form, when (cid:31) = 0 the capital account is open. When capital controls are in place, (cid:31) > 0, and whenever there is a di(cid:11)erence between the home and foreign interest rates, the central bank imposes a capital tax (or subsidy) to discourage or encourage net capital in(cid:13)ows. 7The results are robust to adopting other functional forms, such as including the lagged interest rate in the policy rule, and are available upon request. 8In this framework, borrowing constraints are necessary to establish the existence of a steady state. Entrepreneurs and households have di(cid:11)erent discount factors, and a comparison of the expressions for the stochastic discount factors in (4) and (10) shows that if there is no borrowing constraint and in the steady state (cid:22)=0, there would be no steady state equilibrium. Therefore in the model without (cid:12)nancial frictions, we need to impose a constant tax/subsidy on entrepreneur borrowing that encourages entrepreneurs to save and lowers their steady-state discount factor when (cid:22)=0. This constant tax can be calibrated such that the frictionless economy has the same steady state as the economy with (cid:12)nancial frictions, and this steady state tax is described in the appendix. 16

The coe(cid:14)cients of the rules for the interest rate and capital tax rate are then chosen optimally to minimize the following loss function: 1 L = (cid:12)t E (cid:25)d (cid:0)(cid:25)(cid:22) 2 +’E (og )2 (15) 0 0 t 0 t X t=0 (cid:16) (cid:0) (cid:1) (cid:17) with ’ > 0. This loss function depends on in(cid:13)ation in the price index of domestically produced goods, (cid:25)d, not in(cid:13)ation in the consumer price index, (cid:25) , since domestic production t t distortions arising from price dispersion would depend on domestic and not imported prices (see e.g. Woodford (2003)). The central bank’s in(cid:13)ation target (cid:25)(cid:22) is zero. As discussed by Woodford (2002), this is the target that would minimize the distortions arising from sticky prices in the model.9 In what follows we show how the central bank places a non-negligible weight on the foreign interest rate in its simple interest rate rule when (cid:12)nancial frictions lead to signi(cid:12)cant distortions in the economy following a shock to the foreign rate. Also, the exact welfare reducing distortions and the way that capital controls can reduce those distortions are described in the following subsection. 3.4.1 Equilibrium Dynamics after Shocks to the Foreign Interest Rate Following a positive shock to the foreign nominal interest rate, i(cid:3) , the return on foreign t currency denominated bonds increases. This exogenous shock to the foreign interest rate leads to an increase in net capital out(cid:13)ows. As shown in the household budget constraint (3), households will buy more foreign bonds, Bf , and substitute away from consumption t and local bonds, C and B . This fall in consumption will lead to a rise in the household’s t t marginal utility of consumption and thus a rise in the home real interest rate, as seen by the household’s Euler equation (4). As households substitute away from home consumption and local bonds to foreign bonds the home interest rate increases and at the same time, this capital out(cid:13)ow out of the home country causes a depreciation in the nominal exchange rate, represented by an increase in S in the UIP condition (5). These two actions, an increase t 9In this speci(cid:12)cation, future loss is discounted using the household’s discount rate (cid:12). The results are similar when using the entrepreneur’s discount rate (cid:12)(cid:22). 17

in the home nominal interest rate and exchange rate depreciation together ensure that the UIP condition holds in the new equilibrium after the shock to the foreign interest rate.10 The rise in the interest rate leads to a fall in physical capital investment. The fall in physical capital investment leads to a fall in the price of existing capital due to the presence of investment adjustment costs and the declining marginal product of physical capital investment, as shown in (8) (this declining marginal product of physical capital investment means that each new unit of (cid:12)nal good that is allocated to physical capital investment yields less physical capital). The fall in the price of existing capital tightens the entrepreneur’s borrowing constraint (9). The tightening of the borrowing constraint raises the multiplier (cid:22) . The increase in the multiplier distorts the entrepreneur’s intertemporal allocation decit sion in (10). A comparison of the household’s and entrepreneur’s Euler conditions (4) and (10) shows that the fact that the entrepreneur is subject to a collateral constraint leads to distortions in the entrepreneur’s intertemporal allocation decision that is not present for households. In addition to this distortion arising from the borrowing constraint in the model, there are the usual price dispersion distortions arising from the presence of nominal rigidities in the model. Of course, in a model with only price frictions, a monetary policy dedicated to price stability is optimal, as shown in Woodford (2002). A monetary policy where (cid:25)d = 0 t will reduce the value of the loss function in (15) to zero. This is true even when ’ > 0 and the central bank cares about output gap stability as well as in(cid:13)ation stability. If there were only price frictions in the model, by keeping in(cid:13)ation (cid:12)xed at zero, monetary policy will also keep the output gap (cid:12)xed at zero and allocations in the economy with sticky prices and zero in(cid:13)ation will mimic those of the (cid:13)exible price economy. This is the meaning of the well-known "divine coincidence" result in Blanchard and Gal(cid:19)(cid:16) (2007). The presence of both price and credit frictions in the model mean that this "divine 10How much of the adjustment to the new equilibrium is taken up by a rise in the nominal interest rate and how much is done by currency depreciation is determined by the objective of the central bank. The central bank could decide to keep the exchange rate (cid:12)xed, in which case it would raise the home nominal interest rate one-for-one with the foreign nominal interest rate. Alternatively it could decide to hold the nominal interest rate (cid:12)xed and allow the currency to depreciate. But in both scenarios there is a rise in the home real interest rate. 18

coincidence" is no longer possible and perfect price stability is no longer optimal. In this case the central bank could continue to pursue a policy of price stability, but as we will show, the optimal policy of the central bank is to deviate from price stability and place some weight on reducing distortions created by the borrowing constraint. In response to the exogenous increase in the foreign nominal interest rate, the central bank can raise the home nominal interestrate,makinghomecurrencybondsmoreattractiveandcurtailingthecapitalout(cid:13)ows following the shock. In terms of the UIP condition, by raising the home nominal interest rate following the shock, equilibrium can be restored without as much currency depreciation (and thus without as much capital out(cid:13)ow). Capital controls, in the form of the tax rate on foreign bond holdings (cid:28) , can mitigate the t swings in capital out(cid:13)ows following the shock to the foreign interest rate. When (cid:31) is positive inthefunctionalformforthecapitalcontroltaxin(14), thetaxrateonforeignbondholdings will increase following as an exogenous increase in if . Since the return on those bonds is t (1(cid:0)(cid:28) ) 1+if , following an exogenous increase in if an increase in (cid:28) reduces household t t t t (cid:16) (cid:17) incentivetosubstituteawayfromhomecurrencybondstoforeigncurrencybonds. Thereturn to foreign currency bonds net of this capital tax (1(cid:0)(cid:28) ) 1+if (cid:25) 1+(1(cid:0)(cid:31))if +(cid:31)i . As t t t t (cid:16) (cid:17) (cid:31) increases, the e(cid:11)ect of the exogenous shock on the desire to hold foreign bonds diminishes, and when (cid:31) = 1, the exchange rate is nearly (cid:12)xed.11 By using capital taxes to control swings in capital (cid:13)ows following the shock, the central bank can limit the swings in the price of capital that lead to tightening or loosening of the borrowing constraint. Thus with capital controls, the central bank can largely mitigate the e(cid:11)ect of distortions arising from credit frictions. With these credit frictions taken care of by a second instrument, the conditions for the divine coincidence return and the central bank can once again minimize loss by following a policy of price stability. But at the same time these capital controls are not costless. Taxes on the returns to foreign borrowing limit the ability of agents to borrow and lend in international markets to smooth consumption. When determining the optimal value of the parameter (cid:31) the central 11Thus (cid:31)=1 marks the point on the trilemma of international (cid:12)nance where the central bank has a (cid:12)xed exchange rate and an independent monetary policy. 19

bank balances these costs against the bene(cid:12)ts of capital controls in terms of reduced credit distortions and monetary policy more focused on price stability. 4 Calibration and Solution Method The model is calibrated at a quarterly frequency. The model parameters and their values are reported in table 2. The (cid:12)rst seven parameters in the table, the time discount factor, the capital share, the capital depreciation rate, the investment adjustment cost parameter, the probabilitythata(cid:12)rmcannotresetpricesinagivenperiod,andtheelasticitiesofsubstitution across di(cid:11)erentiated intermediate goods, and between home and foreign traded goods, are all set to values commonly used in the literature. The debt elastic interest premium on foreign bonds (cid:16) a(cid:11)ects the volatility of net exports; it is calibrated such that the ratio of net exports to GDP is about two-thirds as volatile as GDP, as reported in Engel and Wang (2011). The weight on domestic goods in the Armington aggregator function, ! is set to match a steady state import share of 50 percent. The parameter ’ describes the weight on the output gap in the central bank’s loss function and it set to 0:1. The di(cid:11)erence between the values of the household and entrepreneur discount factors, (cid:12) and (cid:12)(cid:22) , implies that the (cid:12)rst-order excess return is about 3.6 percent per year.12 The parameter (cid:18) controls the entrepreneur’s steady-state loan-to-value ratio. We use a value of 0:75, which is the value used by Liu et al. (2013). In a model with collateral constraints for multiple types of agents, Iacoviello (2005) estimates this parameter and (cid:12)nds that it lies between 0:55 (for households) and 0:89 (for (cid:12)rms). We will just consider the e(cid:11)ect of shocks originating in the rest of the world on the small open home economy. More speci(cid:12)cally, we analyze the optimal policy response to a shock to the foreign interest rate that would lead to a surge in capital (cid:13)ows into or out of the small open economy. 12Inthenon-stochasticsteadystate,therisk-freeraterisr = 1(cid:0)1,whichre(cid:13)ectsthehousehold’sdiscount (cid:12) rate,(cid:12). Thesteady-statenetreturnoncapital,R(cid:0)(cid:14) = 1(cid:0)1,re(cid:13)ectstheentrepreneur’sdiscountrate(cid:12)(cid:22). The (cid:12)(cid:22) 4 perannumsteady-state(cid:12)rst-orderexcessreturnisthengivenby(1+R(cid:0)(cid:14)(cid:0)r)4(cid:0)1= 1+ 1 (cid:0) 1 (cid:0)1(cid:25) (cid:16) (cid:12)(cid:22) (cid:12)(cid:17) 4 (cid:12)(cid:0)(cid:12)(cid:22) . (cid:0) (cid:1) 20

To calibrate the process for the foreign interest rate shock, we estimate an AR(1) process for the quarter-over-quarter di(cid:11)erence in the U.S. 3-month Treasury bill rates from 1984:Q1 to 2008:Q4: (cid:3) (cid:3) (cid:3) ^{ = (cid:26)^{ +" t i t(cid:0)1 t where "(cid:3) t (cid:24) N(0;(cid:27) " 2 (cid:3) ). The OLS estimates are (cid:26)^ i = 0:59 and (cid:27)^ "(cid:3) = 0:1.13 4.1 Solution Procedure The model is solved by taking a linear approximation of the system’s equilibrium conditions around the non-stochastic steady state. But at the same time we use a piecewise linear technique to approximate a non-linear solution to account for the occasionally binding collateral constraint. Thus we abstract from all nonlinearities in the model except that of the occasionally binding collateral constraint. In the non-stochastic steady state, the collateral constraint binds, and a comparison of the household and entrepreneur Euler equations in (4) and (10) shows that the steady-state value of the Lagrange multiplier of the borrowing constraint, (cid:22), divided by the steady-state value of the entrepreneur’s marginal utility of income is equal to the di(cid:11)erence between household and entrepreneur’s rates of time discounting.14 In the benchmark version of the modelwithoutcapitalcontrols, a21basispointfallintheforeignnominalinterestratewould cause a surge in capital in(cid:13)ows into the small open economy that would push up asset prices to the point where the constraint is no longer binding and (cid:22) = 0. Given the calibration of t the shock process driving the model, this would roughly be a two standard deviation shock to the foreign interest rate. To solve the model and account for the occasionally binding constraint, we adapt the method that Bodenstein et al. (2013) use to study the e(cid:11)ect of the zero lower bound to nominal interest rates. This is based on the method of introducing news shocks into a 13The innovation standard deviation is 10 basis points for the quarterly rates in the model, which corresponds to 40 basis points in annualized rates. 14FromthehouseholdandentrepreneurEulerequations(4)and(10): (cid:3)e t =(1+i )= (cid:3)t . (cid:12)(cid:22)Et((cid:3)e t+1 )+(cid:22)t t (cid:12)Et((cid:3)t+1) So in the steady state, (cid:12)(cid:0)(cid:12)(cid:22) = (cid:22) . (cid:3)e 21

(cid:12)rst-order approximation developed by Las(cid:19)een and Svensson (2009), and then developed into a framework for approximating the solution to non-linear models by Holden and Paetz (2012).15 Here we adapt this method to study the e(cid:11)ect of a non-binding collateral constraint, and this is described in detail in the appendix. When presenting impulse response results, we will present the results to both a positive shock to the foreign interest rate which tightens the collateral constraint and to a negative shock that loosens the constraint to the point where it is non-binding. Optimal policy responses are not symmetric, although we will show that they are very similar. 5 Optimal Monetary and Capital Controls Policy In analyzing optimal capital account management, we present the results in three steps. First, we consider impulse responses, which let us examine how the use of capital controls a(cid:11)ects the conduct of conventional monetary policy. Here monetary policy is chosen with an optimal simple rule, and with this simple rule optimal policy we can show how when credit frictions are present the central bank places a sizable weight on the foreign interest rate in their policy rule and the use of capital controls allows them to reduce this weight. Finally, we will look at measures of household and entrepreneur welfare losses under di(cid:11)erent monetary and capital controls policy regimes to better gauge the costs and potential bene(cid:12)ts of these policies. 5.1 Impulse Responses The responses of home output, investment, in(cid:13)ation, credit constraints (measured by the multiplier on the collateral constraint), the tax on capital (cid:13)ows, the nominal interest rate, the current account to GDP ratio (net capital out(cid:13)ows), and asset prices following a 50 basis point increase in the foreign nominal interest rate are presented in (cid:12)gure 1. The vertical 15AsdescribedbyGuerrieriandIacoviello(2015), inseveralframeworksthismethodyieldsthesamepath for endogenous variables as the OccBin piecewise linear algorithm. We adapted Bodenstein et. al approach instead of OccBin simply for convenience reasons when coding up the model. 22

axis in the plots for output, investment, and the price of capital are percentage deviations from the steady state values. The vertical axis in the plots for in(cid:13)ation, capital taxes, the nominal interest rate, and the current account to GDP ratio are percentage points. Finally, the plot of the multiplier on the borrowing constraint is in levels. The (cid:12)gure presents the responses from the frictionless model (the blue dotted line), and themodelwithbothpriceandcreditfrictionsunderthreepolicyregimes: pricelevelstability with an open capital account (the purple dashed line), optimal monetary policy with an open capital account (the red solid line), and optimal monetary policy with capital taxes of the form described in (14) where the parameter (cid:31) is also chosen optimally (the green starred line). The value of the (cid:31) parameter that would minimize the central bank’s loss function is 0:5. The positive shock to the foreign interest rate triggers an increase in net capital out(cid:13)ows from the small open economy, and the (cid:12)gure shows that in the frictionless equilibrium there is an increase in the current account in the small open economy. In the frictionless economy we observe a slight decrease in asset prices, investment, and output. If price frictions were the only source of distortion in the model, then a monetary policy of domestic price stability would reproduce the allocations of the frictionless equilibrium, as shown in Woodford (2002) and the well-known "divine coincidence" result in Blanchard and Gal(cid:19)(cid:16) (2007). But when credit frictions are also included in the model, limiting entrepreneur borrowing and giving rise to a Fisherian debt-de(cid:13)ation mechanism, this divine coincidence is no longer possible and a policy of price level stability ampli(cid:12)es the negative responses of investment and demand that are seen in the frictionless equilibrium. The fall in the price of physical capital following the decrease in net capital in(cid:13)ows leads to a tightening of the collateral constraint. The credit friction leads to a further decline in investment and output, which leads to an even further fall in asset prices. Thus when the capital account is open and monetary policy is dedicated to domestic price stability, this feedback loop caused by falling asset prices and a tightening credit constraint ampli(cid:12)es the contraction of domestic macro variables following the shock to the foreign interest rate. In the presence of a second source of distortion arising from credit frictions, price level 23

stability is no longer optimal. In this case the monetary policy that minimizes the central bank’slossfunctioncanbesolvedfornumericallyandisplottedwiththeredsolidline. When responding to a shock to the foreign interest rate under optimal policy and an open capital account, the central bank will partially track the foreign interest rate with its nominal rate. By raising the domestic interest rate, it would curtail the capital out(cid:13)ows from the small open economy. As shown in the impulse responses, by doing this the central bank arrests some of this feedback loop where capital out(cid:13)ows lead to falling asset prices and tightening borrowing constraints. The responses of investment and output in the optimal monetary policy case are much closer to the responses in the frictionless equilibrium. But the (cid:12)gure also shows that this policy leads to more in(cid:13)ation variability, as the central bank lessens its focus on price stability, it leans more toward tempering capital (cid:13)ows and minimizing (cid:12)nancial instability. The shock to the foreign interest rate leads to exchange rate depreciation, which leads to an increase in import and consumer prices. If the central bank followed a policy of price stability, it would raise the nominal interest rate to keep that increase in import prices from passing through into domestic in(cid:13)ation. But doing this leads to a greater fall in output, investment, and asset prices. Under optimal policy the central bank will allow more in(cid:13)ation in order to stabilize output. These results are in line with the (cid:12)ndings in Fornaro (2015), who studies exchange rate policy in a small open economy with nominal wage rigidities and collateral constraint. In that model, the central bank (cid:12)nds it optimal to deviate from price stability by engineering an exchange rate depreciation in order to sustain aggregate demand and asset prices. When capital controls are used in addition to optimal monetary policy, the central bank can return its focus to price stability. In this case following the exogenous increase in the foreign interest rate, taxes on foreign returns increase, discouraging capital out(cid:13)ows. This means that the central bank does not need to raise the interest rate along side the foreign interest rate in order to deter capital out(cid:13)ows. The UIP condition (5) shows that when (cid:28) increases following an increase in the foreign interest rate, equilibrium can be restored t without an increase in the local nominal interest rate or a depreciation of the exchange rate. The impulse responses show that for most variables, the responses under optimal monetary 24

policy and an open capital account are similar to those for optimal monetary policy and capital controls, except the responses for in(cid:13)ation. By allowing the central bank to not worry about capital (cid:13)ows and instead return it’s focus to price stability, the policy regime of optimalmonetarypolicyandcapitalcontrolsdeliversmuchmorestableresponsesofdomestic in(cid:13)ation. Figure 2 plots the responses of the same variables to a 50 basis point negative shock to the foreign interest rate. As discussed earlier, when this shock is su(cid:14)ciently large, it will push up asset prices to the point where the collateral constraint becomes slack and remains so for some periods. As discussed earlier, we use a piecewise linear approximation of a full non-linear solution to solve the model given this asymmetry. Given a su(cid:14)ciently large shock, the multiplier on the borrowing constraint falls to zero for a few periods. The responses of the other variables in the model are similar, but not identical, to the case where the constraint is always binding. The collateral constraint still leads to a greater response in these endogenous variables than would have occurred under in a frictionless model, and a monetary policy that deviates from domestic price stability still temper the responses of these variables and bring the economy with a collateral constraint closer to the frictionless economy. The use of capital controls along side optimal monetary policy allows the central bank to stabilize output with greater in(cid:13)ation stabilization. 5.2 Describing Optimal Monetary Policy As discussed earlier, we assume that monetary policy follows a Taylor rule with coe(cid:14)cients chosen to minimize the central bank’s loss function (15). By looking at these response coe(cid:14)cients, we can examine how the use of capital controls a(cid:11)ects the optimal rule for the conventional monetary policy instrument. The optimal coe(cid:14)cients in the Taylor rule are reported in table 3. The table shows that when the capital account is open, (cid:31) = 0, the optimal weight on the foreign interest rate is 0:22, implying that the central bank reduces its focus on price stability and (cid:12)nds it optimal to raise the nominal interest rate by 22 basis points in response to a 100 basis point 25

increase in the foreign interest rate. When the (cid:31) parameter is optimally set, and (cid:31) = 0:5, this coe(cid:14)cient falls to 0:10. In addition, when capital controls are used, the central bank is able to increase its weight on in(cid:13)ation from 5:26 to 8:34, implying a shift towards price stability. Recall that in the case where there are only price frictions in the model, optimal policy is price stability, where (cid:18) ! 1. p The response coe(cid:14)cient on the foreign interest rate is plotted as a function of the (cid:31) parameter in the capital controls rule (14) in the top panel of (cid:12)gure 3. The (cid:12)gure shows that as (cid:31) increases, the coe(cid:14)cient on the foreign interest rate in the central bank’s monetary policy rule decreases. As it can be seen there, as (cid:31) increases from 0 to 1, the optimal coe(cid:14)cient on the foreign interest rate falls from 0:22 to (cid:0)0:02. Recall from the empirical results in table 1 that when the capital account is open, K = 1, the estimated Taylor rule coe(cid:14)cient on the foreign interest rate is 0:26 and when the capital account is closed, K = 0, it is (cid:0)0:02. 5.3 Welfare Analysis In what follows we evaluate the e(cid:11)ect of capital controls on the relative welfare losses of both households and entrepreneurs. After solving for the equilibrium under optimal monetary policy for a given value of the capital controls parameter (cid:31), we can use the equilibrium paths of household and entrepreneur’s consumption and labor e(cid:11)ort, and in(cid:13)ation, to calculate the e(cid:11)ect of distortions arising from price and credit frictions on household and entrepreneur’s welfare given by (2) and (6). Thehouseholdandentrepreneur’swelfarelossundertwodi(cid:11)erentmonetarypolicyregimes, optimal policy and price level stability, are presented in the bottom two panels in (cid:12)gure 3. The vertical axis in these two (cid:12)gure measures the di(cid:11)erence between household or entrepreneur’s welfare in the frictionless equilibrium and the equilibrium with distortions arising from price and credit frictions, as a percent of steady-state consumption. The top (cid:12)gure presents the welfare loss when monetary policy is chosen optimally while the bottom (cid:12)gure shows the results when monetary policy is dedicated to price stability. The horizontal axis 26

in these (cid:12)gures is the capital controls parameter (cid:31), which is taken as given by private agents. First, comparing the losses of the two types of agents in the case of an open capital account, (cid:31) = 0, shows how all agents are a(cid:11)ected by a switch from monetary policy based on price stability to optimal monetary policy. Entrepreneurs see a sizable reduction in their welfare loss when monetary policy diverts its focus from domestic price stability and instead puts some weight on the foreign interest rate in an e(cid:11)ort to control capital (cid:13)ows. They are most a(cid:11)ected by the credit frictions, which leads to distortions in their intertemporal savings/consumption decision. Hence, a monetary policy that attempts to control capital (cid:13)ows and limit these distortions will bene(cid:12)t them. As the capital control parameter (cid:31), increases from zero, entrepreneur’s welfare loss falls but the variation in household’s welfare loss is ambiguous and depends on monetary policy. Capital controls are not costless and they limit the ability to smooth consumption by borrowing and lending in international markets. When monetary policy is dedicated to price stability, and thus the stance of monetary policy does not change as (cid:31) increases, the adoption of capital controls leads to higher household’s welfare loss. But when monetary policy is set optimally, the addition of capital controls actually leads to a change in the stance of monetary policy towards price stability. So even while households dislike capital controls that limit their ability to smooth consumption, they bene(cid:12)t from the fact that capital controls lead to a changed stance of monetary policy. This means that when monetary policy is set optimally, the optimal value of the capital controls parameter from the household’s perspective is (cid:31) = 0:24, which is lower than the (cid:31) = 0:67 favored by entrepreneurs, or the (cid:31) = 0:5 that would minimize total welfare loss, but still greater than the (cid:31) = 0 favored by households when monetary policy is dedicated to price stability, and thus an increase in (cid:31) does not lead to any change in the stance of monetary policy. 6 Conclusion This paper analyzes the interaction of the capital account management with optimal monetary policy in the context of a small open economy. In the presence of occasionally binding 27

collateral constraints, monetary policy will (cid:12)nd it optimal to place a non-negligible weight on the foreign interest rate in their policy rule, and thus deviate from a monetary policy dedicated to domestic goals like price stability. Capital controls help restore monetary policy autonomy. Focusing on a small open economy is a convenient starting point for this analysis since the dynamics associated with the rest of the world are taken as given, regardless of the policy actions in the home country. We see this assumption appropriate for most emerging economies. Extending the setup to a pair of large countries is the next step. First, when the foreign economy is a(cid:11)ected by the policy actions in the home economy, the degree of policy coordination becomes an interesting question to study. Would the two countries cooperate when setting monetary and capital controls policy, or would they compete? This is especially relevant for studying capital controls, since capital controls policy, like tari(cid:11) policy, can be seen as a beggar-thy-neighbor policy and subject to escalation. Would there be substantial bene(cid:12)ts for countries from cooperation when setting monetary and capital control policy? Second, in the setup with two large economies, asymmetries in the strength of credit frictions between them could have an e(cid:11)ect on their optimal capital policies, as the intensity of credit frictions may in(cid:13)uence the central bank’s desirability to manage the capital account. While in our model non-trivial capital controls are optimal in order to restore monetary policy autonomy and to mitigate the e(cid:11)ects of collateral constraints and (cid:13)uctuations in net capital in(cid:13)ows, capital controls are only part of a wider set of macroprudential policies. Some studies show how capital controls and domestic macroprudential regulations can acts as complements (see e.g. Korinek and Sandri (2014)). Empirically we see a connection between capital controls and monetary policy autonomy, which can be measured by using the relatively long time series of the Chinn-Ito index measuring capital restrictions. Whether such a relationship with more general macroprudential policies exists, and how it could be measured, is left for future research. 28

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Table 1: Coe(cid:14)cient from regression of a country’s policy rate on a base country policy rate for di(cid:11)erent subgroups depending on exchange rate (cid:13)exibility and capital account openness. (cid:1)i (cid:1)i i i Peg (cid:1)(cid:25) 1:113 (cid:3) (0:629) 1:262 (cid:3)(cid:3) (0:619) t (cid:1)y 0:327 (0:389) 0:208 (0:383) t (cid:1)i(cid:3) 0:497 (cid:3)(cid:3)(cid:3) (0:030) 0:231 (cid:3)(cid:3)(cid:3) (0:051) t K (cid:2)(cid:1)i(cid:3) 0:583 (cid:3)(cid:3)(cid:3) (0:092) t t Obs. 1188 1188 R(cid:22)2 0:299 0:324 Float (cid:1)(cid:25) 5:253 (cid:3)(cid:3)(cid:3) (0:788) 5:326 (cid:3)(cid:3)(cid:3) (0:788) t (cid:1)y (cid:0)0:516 (0:578) (cid:0)0:526 (0:578) t (cid:1)i(cid:3) 0:117 (cid:3)(cid:3)(cid:3) (0:045) (cid:0)0:022 (0:079) t K (cid:2)(cid:1)i(cid:3) 0:279 (cid:3)(cid:3) (0:130) t t Obs. 1596 1596 R(cid:22)2 0:078 0:081 notes: Standarderrorsareinparenthesis,theadj. R-squaredfromeachregressionispresentedinbrackets,andtheintegerineachsetofresults isthenumberofobservations. ***/**/*denotesigni(cid:12)canceatthe1/5/10%levels. Table 2: Parameter Values Symbol Value Description (cid:12) 0:9887 household discount factor (cid:11) 0:36 capital share in production of value added (cid:14) 0:025 capital depreciation rate (cid:20) 2:48 investment adjustment cost parameter (cid:24) 0:75 probability that a (cid:12)rm cannot reset prices p (cid:27) 10 elasticity of substitution across (cid:12)rm varieties (cid:26) 3 Armington elasticity (cid:16) 0:015 debt elastic interest premium ! 0:50 Armington weight on domestic goods ’ 0:1 Weight on the output gap in the loss function (cid:12)(cid:22) 0:98 entrepreneur discount factor (cid:18) 0:75 borrowing limit 32

Figure 1: Responses to a positive shock to the foreign interest rate in frictionless model Figure 1: Responses to a positive shock to the foreign interest rate in frictionless model (blue dotted line) and in di⁄erent versions of the model with price and credit frictions: price (blue dotted line) and in di(cid:11)erent versions of the model with price and credit frictions: price stability and an open capital account (purple dashed line), optimal monetary policy and an stability and an open capital account (purple dashed line), optimal monetary policy and an open capital account (red solid line), or optimal monetary policy and capital controls (green open capital account (red solid line), or optimal monetary policy and capital controls (green starred line). starred line). 33 33

Figure 2: Responses to a negative shock to the foreign interest rate in frictionless model (bFliugeurdeo2tt:edRelisnpeo)n,saesndtoinadnie⁄gearteinvte vsehrosciokntsootfhteheformeiogdnelinwteitrhestprriacteeainndfrcircetdiointlefrsisctmioondse:l p(rbiclueestdaobtitlietdy lainned),ananodpeinn cdai(cid:11)peitraelntacvceorusniotn(spoufrptlheedmasohdeedl lwinieth), porpitciemaanldmcorneedtiatryfripcotiloicnys: apnrdicaensotapbenilictyapaitnadl aacncooupnetn(creadpistoallidaclicnoeu)n,tor(pouprtpimleadlamshonedetalirnye)p,oolipctyimanadl mcaopniteatalrcyonptorolilcsy (garnedenanstoaprreendclaipniet)a.l account (red solid line), or optimal monetary policy and capital controls (green starred line) 34 34

Figure 3: The Taylor rule coe¢ cient on the foreign interest rate (from projections of nu- Figure 3: The Taylor rule coe(cid:14)cient on the foreign interest rate (from projections of numerical optimal policy onto a Taylor rule) and household and entrepreneur welfare loss as a merical optimal policy onto a Taylor rule) and household and entrepreneur welfare loss as a function of the capital tax coe¢ cient (cid:31). function of the capital tax coe(cid:14)cient (cid:31). 35 35

Table 3: Optimal Taylor rule coe(cid:14)cients in the model with and without capital controls Open Capital Account Optimal Capital Controls (cid:31) = 0 (cid:31) = 0:5 Weight on in(cid:13)ation, (cid:18) 5.26 8.34 p Weight on the output gap, (cid:18) 0.21 0.08 y Weight on the foreign interest rate, (cid:18) 0.22 0.10 s 36