Foreign Dollar Reserves and Financial Stability

Transcription

1 Foreign Dollar Reserves and Finanial Stability Nihar Shah Harvard University Deember 2015 (Updated Deember 28, 2017) Preliminary and inomplete; do not ite. Clik for the latest version of this paper. Countries have aumulated massive foreign reserve portfolios, but the reasons for doing so remain debated. I doument a new empirial fat on the ompositions of foreign reserve portfolios, and argue that the prevalene of the dollar supports an explanation in whih foreign reserves hedge liquidity shoks to dollarized finanial systems. First, I fit a Bayesian dynami linear model to extrat urreny shares for the foreign reserves of seventy-seven developed and emerging ountries, and show that foreign reserves are poorly-diversified and overwhelmingly onsist of dollar assets. Seond, I show that the dollar shares of foreign reserves are explained by the dollarization of their finanial systems liabilities aross ountries, partiularly for ountries that annot easily borrow dollars from the Federal Reserve diretly. Third, I build a model in whih entral banks build up dollar reserves to mitigate liquidity shoks for finanial systems with urreny mismathes, partiularly in the presene of foreign exhange transation osts. address: nshah@fas.harvard.edu. I am grateful to Gita Gopinath, Matteo Maggiori, Kenneth Rogoff, Elaine Chung, Martin Feldstein, Paolo Pesenti, Mikkel Plagborg-Møller, and Team Maxwell for suggestions on this paper. I also want to thank the partiipants of the international eonomis and maroeonomis seminars at Harvard for omments. The omputations in this paper were run on the Odyssey luster supported by the FAS Division of Siene, Researh Computing Group at Harvard. All errors are my own. 1

2 1 Introdution The foreign reserve portfolios of entral banks vary greatly in size and in omposition. For instane, Hong Kong s reserves exeed its GDP while Australian reserves are twenty times smaller than its GDP, and Peruvian reserves are overwhelmingly dollars while Romanian reserves are biased towards euros. The literature has posited both theoretial and empirial explanations to understand why ountries hold foreign reserves, and papers have relied on the one piee of available information the sizes of foreign reserves to test theories. This paper generates a seond piee of information their ompositions by urreny to explain foreign reserves. In this paper, I estimate the urreny omposition of ountries foreign reserves, and show that the urreny shares of ountries foreign reserves an be explained by the foreign urreny shares of their finanial systems liabilities. First, I estimate urreny shares of foreign reserves using a Bayesian dynami linear model, in whih I projet hanges in the size of a ountry s foreign reserves onto the returns of major reserve urrenies. The results are novel, and show that dollars are far more prevalent than believed in foreign reserve portfolios. Seond, I show that the dollar shares of ountries portfolios are orrelated in the ross-setion with the dollar shares of their finanial systems liabilities, partiularly when ontrolling for swap lines a form of emergeny entral bank-to-entral bank lending that substitute for offiial foreign reserves. Third, I explain these findings using a model in whih entral banks use foreign reserves to hedge liquidity shoks to their finanial setors, whih have foreign urreny liabilities partiularly in the presene of foreign exhange transations osts. Separately, the empirial findings also provide suggestive evidene against other explanations for foreign reserves. For instane, they are inonsistent with explanations in whih foreign reserves provide fisal spae to governments during reessions, as these dollar-heavy portfolios are too lightly diversified aross other reserve assets that appreiate during reessions. The paper s main empirial finding is that the dollar shares of foreign reserve portfolios are massive: aross the foreign reserves of seventy-seven emerging and developed ountries, the average dollar share is 80-85%, and this number is fairly stable over time. The euro represents a small share for most ountries; but for a handful of ountries (e.g. Romania and Moroo), its share is omparable or larger than that of the dollar. These results are novel to the literature, as few ountries report the omposition of their foreign reserves publily, and even fewer do so at any reasonable frequeny. The only omprehensive publi soure of information the IMF s urreny omposition of offiial foreign exhange reserves (COFER) data only publishes urreny shares aggregated aross reporting ountries, and 2

3 does not even release the names of the ountries who report to preserve their onfidentiality. As suh, the aggregated estimates are both skewed by large ountries and are inomplete due to non-reporting ountries. For instane, at the start of 2015, the IMF reported that they had reorded the urreny omposition for 55-60% of all foreign reserves, and 65% of those verified reserves were held in dollars. The paper s seond finding is that these dollar and euro shares orrelate with the dollar and euro shares of external finanial liabilities for emerging markets, although not for developed markets. There are two plausible reasons for this divergene. First, developed ountries have been historially more willing than emerging ountries to seek assistane from the International Monetary Fund, as Bird and Mandilaras [2011] find, and thus do not rely upon foreign reserves to stabilize their finanial systems. This weakens the link between the urreny shares of foreign reserves and finanial liabilities for developed ountries. Seond and more reently, developed ountries have largely benefited from swap lines to the Federal Reserve a form of diret lending between entral banks whih provide emergeny dollar funding. The ECB has also established euro swap lines, although these have not been used widely yet. Swap lines generate dollar and euro reserves on demand, and thus substitute for atual dollar and euro reserves during liquidity rises. Indeed, the orrelation between the foreign urreny shares of reserves and banking liabilities holds when restriting to the ountries that historially did not reeive dollar or euro swap lines during rises. To estimate the urreny ompositions of foreign reserves, I develop a dynami linear model that projets returns in a ountry s aggregate portfolio value onto returns in reserve urrenies over time. While the underlying portfolio shares of urrenies are onfidential, this is feasible beause most ountries report the values of their total portfolios at monthly frequenies. To illustrate the ore insight, suppose a portfolio (with unknown dollar and euro shares) grows by 10% (in dollar terms) over a period in whih the euro appreiates by 20% against the dollar. This portfolio must be 50% dollars and 50% euros. In pratie, the methodology is more ompliated for a few reasons. Portfolio weights may hange over time, portfolios may grow or shrink due to inflows and outflows, and the set of potential reserve urrenies is potentially large. Thus, the paper augments the dynami linear model to allow for these ompliations. Finally, limited publi data on urreny shares are available for a handful of ountries and in the aggregate, and so the paper further augments the dynami linear model to inorporate this information, and uses Bayesian algorithms to find solutions. The methodology is novel, and an be applied to other ases in whih the ompositions of liquid portfolios are unavailable. These two fats the prevalene of dollar reserves and the orrelation between dollar (and euro) shares in foreign reserves and finanial liabilities seem most onsistent with 3

4 models of finanial stability, and I develop one. Speifially, I build a model in whih a entral bank hedges liquidity shoks for its banks that have borrowed heaply and exessively in dollars, due to limited liability fritions. The entral bank has one of three hoies to mitigate liquidity shoks: it an print loal urreny and exhange it for dollars, it an hold diversified foreign reserves and exhange those for dollars, or it an hold dollars diretly. However, the entral bank faes foreign exhange osts for the first two strategies, and so it hold dollar reserves ex ante. 1 This model generates a ausal link between dollar shares of foreign reserves and finanial liabilities. The model does not formally inorporate swap lines, but these are natural substitutes in pratie for foreign reserves as they allow entral banks to produe dollars on demand. 2 In addition to supporting an explanation grounded in finanial stability, the empirial findings on the urreny shares an also provide new evidene against ompeting explanations for the purpose of foreign reserves. The literature has used the sizes of foreign reserves to argue against several possible explanations, by showing that foreign reserves are too large to smooth exhange rate flutuations arising from urrent aount imbalanes, to be byproduts of sterilized exhange rate intervention, or to hedge rollover risk for short-term government debt. But size data annot easily distinguish an explanation foused on finanial stability from an alternate explanation: foreign reserves provide fisal spae to governments during reessions, as disussed by Fernandez-Arias and Montiel [2009], or more generally foreign reserves smooth onsumption shoks, as disussed by Dominguez [2010]. However, my findings on the urreny ompositions of foreign reserves are more onsistent with an explanation based on finanial stability than one based on fisal spae. Under the fisal spae explanation, reserve portfolios whih are similar to sovereign wealth funds should be broadly diversified, with meaningful positions in Swiss frans and yen (urrenies that appreiate strongly during global reessions). The overwhelming dominane of dollars in foreign reserve portfolios ontradits this alternate explanation, and supports the finanial stability explanation, in whih foreign reserves mitigate shoks to dollarized finanial systems. 3 1 Although urreny markets are liquid, foreign exhange osts should be oneptualized broadly, e.g. the market pani that may follow large and sudden foreign exhange transations by a entral bank. 2 In the baseline model, liquidity shoks are exogenous and banks are finaned in dollars. In a refinement of the model, liquidity shoks are endogenous, and banks ould be finaned in loal urreny but ruially by investors whose stohasti disount fators are dollar-based. Even in this setting, foreign reserves are neessary to mitigate liquidity shoks. Sine investors are about dollar returns, they may refuse to rollover funding to a solvent and liquid ountry if they antiipate a urreny depreiation. Foreign reserves allow a entral bank to stabilize the exhange rate, whih stops emergent liquidity shoks. The model s preditions are still being developed, and so this model is not presented in this version. 3 In addition, the popularity of swap lines is further suggestive evidene in favor of a finanial stability explanation. Swap lines are a soure of temporary funding that entail no nominal apital gains. Thus, they should only be valuable to mitigate liquidity shoks, and not to inrease a ountry s budget. 4

5 The paper proeeds as follows. Setion 2 reviews the literature on foreign reserves. Setion 3 disusses the empirial framework and the data used to estimate the urreny shares of foreign reserves. Setion 4 douments the results and tests them against finanial liabilities data. Setion 5 develops a model that links foreign reserves and finanial liabilities. Setion 6 onludes. 2 Literature Review This paper ontributes to two groups of literature: on the motivations for holding foreign reserves, and on the dollar s dominane in the international finanial system. With respet to the first strand of literature, reserves are strongly assoiated with lower risks of rises, as Catao and Milesi-Ferretti [2014] find empirially, and poliymakers are broadly advised to follow the Greenspan-Guidotti rule-of-thumb, whih advises foreign reserves in exess of external short-term debt. However, the speifi reason that ountries hold foreign reserves remains ontested. Consider the five most popular (partially overlapping) hypotheses: (i) foreign reserves are the byprodut of sterilized exhange rate interventions, (ii) foreign reserves stabilize exhange rates during urrent aount flutuations, (iii) foreign reserves hedge rollover risk for shortterm government debt, (iv) foreign reserves stabilize onsumption during reessions, and (v) foreign reserves ensure finanial stability. Dominguez [2010] argues against the first explanation by noting that foreign reserve buildups are too large to be aidental. The seond and third explanations have generated more serious debates. For instane, Aizenman and Sun [2012] argues against the seond explanation, noting that ountries were unwilling to spend reserves to stabilize their urrenies during the finanial risis. On the other hand, Dominguez [2012] argues for this explanation, arguing that ountries did atively manage their urrenies during the risis; and Dominguez [2014] disusses examples from non- Eurozone European ountries. The third explanation originates in the literature on original sin (a ountry s inability to issue loal-urreny debt), and reent work inludes Bianhi et al. [2013], who build and alibrate a model to generate poliy reommendations. However, Obstfeld et al. [2010] argue that these two explanations seem largely inonsistent with the sizes of foreign reserve portfolios. They use bak-of-the-envelope alulations to argue that these explanations would require foreign reserves worth % of GDP weekly, whereas in pratie foreign reserves vastly dwarf that estimate, even under extreme assumptions on the length of rises. The fourth and fifth explanations are more onsistent with large foreign reserve portfolios, and have been supported alternately by Fernandez-Arias and Montiel [2009] and Dominguez 5

6 [2010] and by Obstfeld et al. [2010] respetively, among others. Other papers inlude Kim and Ryou [2011], who argue that foreign reserve portfolios largely fail mean-variane effiieny tests, suggesting that they have purposes beyond stores of value. None of these papers utilize portfolio ompositions to test hypotheses, however; and that is where my paper an ontribute to this literature. Finally, Eihengreen et al. [2017] has floated non-eonomi reasons that ountries hold foreign reserves (e.g. to strengthen geopolitial allianes), but that is beyond the sope of this paper. Moreover, a set of papers indiretly argues that foreign reserves are useful for finanial stability by noting that ountries are relutant to turn to the IMF, and foreign reserves substitute for IMF programs. Bird and Mandilaras [2011] and Fernandez-Arias and Levy- Yeyati [2012] argue that the IMF is unpopular for several reasons: programs take a long time to negotiate and often involve onditionality. Furthermore, Joye and Razo-Garia [2011] put forward a model to show why reserves are favored over IMF programs, and note that the programs are often too small in pratie. (They were both insuffiient for the Mexian and East Asian rises of the 1990s, and despite the reent quota expansions, emerging markets often hold reserves many times larger than their IMF alloations.) Finally, while regional funds have emerged, e.g. the Latin Amerian Reserve Fund, Rosero [2014] note that their advantages over foreign reserves are still unproven. Separately, this paper ontributes to the literature on the dollar s dominane in the international finanial system, by establishing its dominane in most ountries reserve portfolios. The dollar s ubiquity has been well-established in other domains, e.g. Gopinath [2015] in trade invoiing and Bruno and Shin [2015] in bank lending. However, there are onerns that foreign reserve portfolios are adjusting away from the dollar. Truman and Wong [2006], Wong [2007], and Wooldridge [2006] disuss the omposition of foreign reserves from limited publi data, and note autiously that these fears may be overstated. My results validate this laim more forefully, showing that the dollar remains as prevalent as ever aross a wider set of ountries. 3 Empirial Framework The paper s ore ontribution is to estimate the urreny omposition of foreign reserves for individual ountries, as most ountries do not report their own breakdown, and the IMF only reports an aggregated and inomplete breakdown to preserve onfidentiality. (In fat, the IMF does not release the names of the ountries who ontribute to the series.) I estimated a modified dynami linear model using Bayesian algorithms. The paper uses two main piees of data: the sizes of reserves holdings at the ountry 6

7 level and reserve urreny returns, and projets the former onto the latter. To illustrate the key insight, onsider the following toy senario: a ountry who passively holds only dollars and euros reports that its foreign reserves have risen (in dollar terms) by 20% over a month. If the euro appreiated against the dollar by by 40% during that month, the portfolio must be 50% dollars and 50% euros. Of ourse, this insight does not generalize to multiple assets without further struture. For instane, onsider a third asset: the Japanese yen. If that appreiates versus the dollar by, say, 20%, the portfolio holdings are indeterminate. More observations alone are insuffiient, as ountries may hange their portfolio weights ontinuously. However, under some reasonable assumptions about portfolio share stikiness and under some prior beliefs on overall portfolio shares (released either in the aggregate by the IMF, or by a few speifi ountries), solutions an be found. As suh, I augment a dynami linear model with a Bayesian prior, and use Bayesian methods (Markov Chain Monte Carlo) to find the solution. In addition, this approah does not aount for flows: portfolios an grow or shrink outside of urreny flutuations, if foreign reserves are atively added. If inflows are orrelated with urreny returns, this an potentially bias the estimated urreny shares. Finding a suitable instrument or bias-free sub-sample is diffiult, and so I use various strutural assumptions to ontrol the bias. This methodology of unovering portfolios is novel, although the general insight has been used to estimate onfidential baskets to whih ountries peg their urrenies. Speifially, Fidrmu [2010], Frankel and Wei [2008], and Frankel and Xie [2010] similarly deompose loal urreny movements into various reserve urrenies, to find the de fato peg. However, in these papers, portfolio weights are muh stikier, and the methodologies do not worry about inorporating prior data or adjusting for flows. 3.1 Data All but a handful of entral banks do not dislose the omposition of their foreign reserves. But the IMF, on behalf of entral banks, reports two key piees of information: the total value of individual entral bank reserves on a monthly basis (e.g. Japan holds $1.212 trillion as of August 2014), and the quarterly omposition of entral bank portfolios in aggregate (e.g. Euros omposed 24.7% of known entral bank portfolios in 2004, worldwide). The paper relies on these two piees of information, along with monthly urreny returns for large reserve urrenies (obtained from the Federal Reserve). The first piee of data the total value of individual entral bank reserves, on a monthly basis are olleted by the IMF for seventy-five entral banks, and by the Federal Reserve 7

8 for two more entral banks. (Supranational entities like the European Central Bank are omitted.) The seventy-seven ountries are broken down by region: twenty-five in Western Europe, fifteen in Eastern Europe, eleven in Middle East and North Afria, twelve in East Asia, and fourteen in the Amerias. Coverage naturally gets better over time, with approximately forty ountries reporting their total values as early as 2000 and almost all ountries reporting by Eah ountry is analyzed from when they start reporting reserves to the IMF (at the earliest, in 2000) until The seond piee of data, formally known as the Curreny Composition of Offiial Foreign Exhange Reserves (COFER) database, is partiularly tantalizing. In its disaggregated form, it is preisely what this paper seeks. Yet the disaggregated version is inaessible; the IMF states: [Composition] data for individual ountries are kept stritly onfidential given the sensitive nature of the data. Aess to individual ountry data is limited to only four IMF staff on a need-to-know basis. No modern papers have bypassed this restrition; to my knowledge, the only exeption is Eihengreen and Mathieson [2000], whih aessed the underlying data two deades ago. Thus, I use the publi and aggregated version, whih is used to onstrut prior beliefs about portfolio omposition. In addition, a handful of ountries report their urreny shares publily, as doumented by Wong [2007] and Truman and Wong [2006]. This information is not inorporated in the urrent paper, but it will be used in a future version. Finally, I use monthly urreny returns, olleted by the US Federal Reserve. Seven urrenies orrespond to approximately 97% of global reserves, and so the set of reserve urrenies is defined as: the dollar, the euro, the pound, the yen, the Swiss fran, the Canadian dollar, and the Australian dollar. While the Chinese yuan has been disussed for several years as an emerging reserve urreny, this has failed to appear in the data, and so it is not inluded. The IMF only broke out the yuan in the Deember 2016 COFER update, and it onstituted a mere 1% of portfolio holdings. Sine the IMF data breaks out gold from urrenies, I also do not onsider gold. Gold may be formally inorporated in a future version, but most ountries have small gold reserves (with a few notable examples, e.g. Switzerland). Finally, foreign reserves are typially invested in riskfree bonds in that urreny than just in the urreny itself. However, the monthly variation in riskfree returns is minusule ompared to the monthly variation in exhange rates, and Wooldridge [2006] similarly notes that foreign reserve managers are largely onerned about urreny rather than interest rate risk. In my speifiation, onstant differenes in riskfree rates aross ountries will be aptured by a onstant. 8

9 3.2 Methodology This setion develops the dynami linear model for estimating the urreny shares. The portfolio size at time t + 1 reflets two omponents: the portfolio size at time t (times the gross return on that portfolio) plus any inflows or outflows: P t+1 = P t (1 + r t+1 ) + F t+1 Therefore, the overall growth rate of the portfolio an be deomposed into the net return and (saled) inflows and outflows: g t+1 = P t+1 P t P t = r t+1 + f t+1 Finally, I deompose the portfolio net return into the weighted return by urreny, where weights an also adjust at every point in time. This formulation in whih oeffiients an hange over time is known as a dynami linear model, and it an be written as: g t+1 = K wt k rt+1 k + f t+1 (1) k=1 In addition, I impose the restritions that weights sum to one and are non-negative, as entral banks do not meaningfully short urrenies in their foreign reserves portfolios. w k t [0, 1] K wt k = 1 k=1 There are three small adjustments. First, I estimate Equation (1) in logs. Seond, I embed the restrition that weights sum to one by using relative returns rather than absolute returns. Third, I allow weights to adjust at annual rather than the monthly level, to keep the parameter spae relatively ompat. In the revised formulation, Equation (2), T (t) is defined as a funtion that onverts a given month t into the orresponding year Flows g t+1 r K t+1 = K 1 k=1 w k T (t)(r k t+1 r K t+1) + f t+1 (2) In Equation (2), the estimation strategy must ontend with f t+1, whih represents ative inflows and outflows from the foreign reserves. Flows are likely orrelated with urreny 9

10 movements, and they are almost always unobserved, although Dominguez et al. [2012] notes that the IMF has reently started requesting more nuaned information that may help in estimating these omponents. Depending on the overage of the results, this may be inorporated in a future iteration of the estimation strategy. This lassi omitted variables problem leads to misleading portfolio estimates. For instane, onsider a defensive entral bank that always inreases its US dollar holdings when negative eonomi shoks hit the world. Sine the dollar also tends to appreiate during suh periods, estimating Equation (2) naively will overestimate the portfolio weight on dollars. Reserves inrease preisely when dollars are performing well, and I will give too muh redit to existing dollar holdings. There are two broad lasses of solutions: an instrumental variables approah, or a strutural approah. The former is virtually impossible: it requires a variable that drives urreny returns (e.g. the dollar-euro exhange rate) but does not affet how a entral bank atively responds. All the lassi maroeonomi drivers of exhange rates (e.g. interest rates, urrent aount imbalanes, et) would not pass the exlusion restrition. The seond solution is more feasible, by using a flexible strutural model to model entral bank hoies. The key assumption is that entral banks respond disproportionately to larger moves in urreny markets, i.e. small shoks trigger no poliy hange, whereas large shoks do. This an be embedded through three steps. First, I inorporate a ubi term for the loal exhange rate against a basket of SDRs (a mix of dollars, euros, yen, and pounds). This allows large movements in the exhange rate to absorb variation in portfolio returns. g t+1 r K t+1 = K 1 k=1 w k T (t)(r k t+1 r K t+1) + 3 βt m (t)e m t (3) Seond, I detrend the portfolio returns using a standard Hodrik-Presott filter, allowing for slow-hanging trends in foreign reserve aumulation. m=0 Finally, I weight the residuals inversely to the size of loal urreny returns, allowing small movements (representing alm and stable times) to drive the model s estimation Weights The dynami linear model in Equation (3) requires further struture, partiularly on timevarying oeffients w t and β t. First, I impose a Markovian assumption on how these oeffiients hange through time; and seond, I parameterize that stohasti proess. First, a dynami linear model imposes the Markovian assumption that the values of these oeffiients at a given point in time are only diretly related to the previous and subsequent values. This assumption seems reasonable: onditional on knowing the portfolio share of 10

11 dollars in 2004, I an assume that the portfolio shares of dollars in 2003 and 2005 are independent. This allows a simplifiation of the standard likelihood funtion into a more tratable representation, where D t represents data and θ all other parameters: P({w j, β j, θ} {D t }) P({D t } {w j, β j, θ})p({w j, β j, θ}) P({w j, β j, θ} {D t }) [ T ] [ t=1 P(D T ] t w j, β j, θ) (t) j=2 P(w j w j 1 ) (4) [ T ] (t) j=2 P(β j β j 1 ) P(w 1 )P(β 1 )P(θ) Seond, I selet the funtional forms for the probability distributions of weights at t + 1, onditional on weights at t. Speifially, weights w t+1 are distributed aording to a produt prior of the trapezoid and normal distribution. The normal distribution omes from IMF s COFER data, whih holds the aggregate portfolio weights aross many ountries. The trapezoid distribution relates w t+1 to w t, and it is alibrated to reflet some portfolio stikiness aross time. (The trapezoid distribution obeys the bounds [0, 1] on portfolio weights, unlike the normal distribution, and so it is very similar to a trunated normal distribution.) Moreover, β t+1 is distributed normally, entered around β t, whih suggests that response funtions of entral banks to loal urreny volatility are stiky aross time. These assumptions of portfolio stikiness seem reasonable, as Lim [2007] shows that portfolio weights are relatively stable in the aggregate data Markov Chain Monte Carlo Finally, I estimate the distribution of parameters in Equation (4) using the Metropolis- Hastings algorithm. This algorithm is applied to eah ountry in isolation, to find eah ountry s set of parameters. The Metropolis-Hastings algorithm stohastially searhes the parameter spae, moving to regions with higher density and away from regions with lower density, using a jumping distribution. While alibrating the jumping distribution an be diffiult in pratie, I use the adaptive MCMC approah given by Roberts and Rosenthal [2009], in whih the distribution is alibrated automatially to yield reasonable searh proesses. Moreover, the exat hoie of a jumping distribution does not affet the long-run onvergene properties, as long as it searhes the parameter spae adequately. I run the algorithm 50 million times per ountry, and disard the first 49 million as the burn-in period. For almost all ountries, the parameter draws appear stationary and onvergene seems reasonable. 11

12 4 Results This setion depits the results from the simulation. First, I show the summary statistis that emerge from the dynami linear model, whih are eonomially interesting on their own. Dollar shares in foreign reserves are large, and this is relatively stable aross ountries and aross time. Euro shares are smaller, and most other urrenies have negligible shares. Seond, I show that the dollar and euro shares of foreign reserves an be explained by the shares of external finanial liabilities denominated in those urrenies. This is suggestive of a model of finanial stability, whih I develop further in Setion Summary Statistis In this setion, I first show the average dollar and euro shares aross ountries, taking the simple average aross different groups of ountries. I also fous on the dollar, euro, pound, and yen; although I also generate results for the Swiss fran, the Australian dollar, and the Canadian dollar. Figure 1 shows the average dollar share by region, and these are uniformly high. Unsurprisingly, the shares are espeially high in the Amerias. More surprisingly, they are espeially high in Europe; but this may be beause holding euros for Eurozone ountries is ineffiient, leaving the dollar as the main reserve asset. Figure 2 shows the average euro share by region, and these are generally low, although the graph masks some large outliers. For instane, a handful of non-eurozone eastern European ountries and Middle East / North Afria ountries (e.g. Romania and Moroo) have enormous euro shares. Figure 3 shows the average shares for the pound and yen. These are uniformly low, but the ontrast is informative. In the offiial COFER statistis, both have omparable shares but in the disaggregated data, the pound appears twie as dominant as the yen. This is suggestive evidene against reserves as a soure of fisal spae during reessions, as the yen (not the pound) is the ultimate safe-haven asset. Finally, Figure 4 shows hanges in dollar and euro shares over time, benhmarked to their shares at the start of the sample (2004). The euro has gained some share at the dollar s expense, but the magnitudes are eonomially small, at approximately one perentage point. However, these small magnitudes may be a funtion of overly tight priors; and so in a future version, I will hek that these findings are robust to looser priors. 12

13 Figure 1: Dollar Shares of Foreign Reserves Notes: The figure depits the average dollar share aross the foreign urreny reserves of ountries in a given region, where dollar shares are averaged first aross time within ountry and seond aross ountries. Dollar shares are extremely high and somewhat heterogeneous, with ountries in Europe and in the Amerias having partiularly high dollar shares. Figure 2: Euro Shares of Foreign Reserves Notes: The figure depits the average euro share aross the foreign urreny reserves of ountries in a given region, where euro shares are averaged first aross time within ountry and seond aross ountries. Euro shares are low and somewhat heterogeneous, with ountries in the Middle East, Afria, and Asia having partiularly high euro shares. 13

14 Figure 3: Pound and Yen Shares of Foreign Reserves (a) Pound Shares (b) Yen Shares Notes: The figures depit the average pound and yen shares aross the foreign urreny reserves of ountries in a given region, where shares are averaged first aross time within ountry and seond aross ountries. Pound shares and yen shares are both low and largely homogeneous, although pound shares are surprisingly higher than yen shares aross the globe. Figure 4: Dollar and Euro Shares over Time Notes: The figure depits the hange, relative to 2004, in the average dollar and euro shares aross global foreign urreny reserves, where urreny shares are averaged aross ountries for eah year. While the euro share has grown at the expense of the dollar share, the growth is small, and the dollar s dominane in foreign reserve portfolios is eonomially stable. 14

15 4.2 Bank Liabilities In this setion, I explain the heterogeneity in urreny shares aross ountries using the heterogeneity in the urreny shares of their finanial liabilities. Speifially, I regress the dollar and euro shares in foreign reserves on the dollar and euro shares in banking liabilities, and show this is signifiant one swap lines a form of diret lending between entral banks that substitutes for offiial reserves are taken into aount. Broadly, I regress the the dollar and euro shares of foreign reserves aross ountries on the dollar and euro shares of their banking systems external liabilities, as alulated from the Bank of International Settlement s Loational Banking Statistis. The BIS data have some known limitations that I address. First, not all ountries report their banking systems positions. However, fifty ountries do, and this inludes most developed ountries (e.g. the US, UK, Germany, and Japan) and many finanial hubs (e.g. Luxembourg, the Cayman Islands, and Jersey) and the number of reporters has grown steadily over time. Seond, a ountry s overage of its own finanial system has grown steadily over time, making earlier reports less representative of the finanial system at that time than later reports. Thus, I first infer ountries external liabilities as equal to the assets held on them by reporting ountries, to bypass the limited overage issue. Seond, I fous on the latest year the data are available to estimate shares, as this has the widest overage both in terms of number of reporting ountries and number of reporting finanial institutions within eah ountry. This regression on its own yields few signifiant results, and is not reported. In Table 1, however, I inlude an indiator for emerging ountries, and the interative term is highly signifiant. This means that, for emerging markets, higher frations of banking liabilities in dollars and euros predits higher dollar and euro shares for foreign reserves. The distintion between developed and emerging ountries may seem arbitrary, but one plausible and onsistent explanation involves swap lines, whih were extended to many developed ountries and to few emerging ountries. Speifially, swap lines are hannels by whih one entral bank an temporarily lend its loal urreny diretly to another entral bank for liquidity management, and these plausibly rowd out foreign reserves as they funtion as temporary and on-demand foreign reserves. For instane, Aizenman et al. [2011] and Morelli et al. [2015] argue that swap lines empirially and theoretially, respetively, substitute for foreign reserves; and Allen and Moessner [2011] argues that foreign urreny banking liabilities diretly predit swap lines. (Moreover, Bordo et al. [2014] who provide a omprehensive history on swap lines note that William Poole, president of the St. Louis Federal Reserve Bank, objeted on extending swap lines to entral banks with large dollar reserves on the grounds of redundany.) Swap lines were partiularly popular during the finanial risis, when ountries finanial systems suffered dollar shortages, and MGuire and 15

16 von Peter [2009], Fleming and Klagge [2010], and Rose and Spiegel [2012] argue that swap lines alleviated these shortages both in the time series and in the ross-setion. As suh, in Table 1, I inlude an indiator for reeiving dollar and euro swap lines during and after the finanial risis. The interative term remains signifiant, although with wider onfidene levels. Of ourse, ountries that have reeived swap lines historially may not predit ountries that will reeive swap lines going forward, and that may partially explain the smaller onfidene intervals. A seond explanation diretly addresses the divide between emerging and developed markets in the ontext of supranational entities like the International Monetary Fund or European Central Bank. Developed ountries everywhere are more willing to turn to the IMF for historial reasons; and Eurozone ountries are of ourse far more able to turn to the European Central Bank for diret assistane during finanial rises. In other words, ountries without swap lines or without aess to supranational entities have to hold reserves expliitly; ountries with swap lines or with aess to supranational entities hold reserves impliitly. 5 Model In this setion, I develop a model to explain the empirial patterns the prevalene of dollar reserves and the orrelation between urreny shares in reserves and finanial liabilities. In the model, a ountry s entral bank provides liquidity to its private banking system who have taken out exessive dollar debt, in order to protet domesti depositors. During liquidity rises, entral banks need to lend dollars, but ruially it faes foreign exhange transation osts during rises (in addition to general osts of inflation). Thus, printing loal urreny or holding other urrenies and swapping those into dollars during rises is more ostly than holding dollars diretly ex ante. Although this model does not inorporate swap lines, this is equivalent to allowing the entral bank to generate dollars during rises diretly, removing the need for dollar reserves. Of ourse, nominal transation osts in foreign exhange markets are tiny. For instane, I examine high-frequeny exhange rate data for the dollar versus the New Zealand dollar (the least liquid of the major urrenies) in August 2011 a month that inluded a 7% drop in the S&P 500, a 20% fall in Frane s CAC 40, and a downgrade in the US redit rating and find that the mean and median transation osts are 2-3 basis points; and even when transation osts rise, they dissipate within a minute or so. However, I oneptualize impliit foreign exhange transation osts during rises to be large, partiularly when entral banks need to swap billions in short intervals. For instane, this might signal bad news to markets, and end up generating market pani and deeper liquidity runhes prematurely. 16

17 Table 1: Explaining Reserve Portfolios by Bank Liabilities Speifiation Dependent Variable: Reserve Share Dollar Euro (1) (2) (3) (4) Bank Share (0.083) (0.078) (0.048) (0.060) Emerging (Indiator) (0.046) (0.034) Bank Share x Emerging (0.099) (0.079) No Swap Lines (Indiator) (0.045) (0.042) Bank Share x No Swap Lines (0.094) (0.085) Constant (0.029) (0.030) (0.029) (0.039) Observations R Notes: The table regresses the dollar and euro shares of ountries foreign reserves on the dollar and euro shares of their banking systems liabilities, aross the set of seventy-seven ountries. Columns (1) and (2) fous on dollars, and Columns (3) and (4) on euros. All speifiations inlude a dummy that is interated with the banking liabilities variable: for Columns (1) and (3), this dummy is an indiator for emerging ountries; for Column (2), this dummy is an indiator for ountries that did not reeive dollar swap lines; and for Column (4), this dummy is an indiator for ountries that did not reeive euro swap lines. Signifiane is assessed at the 10% (*), 5% (**), and 1% (***) level. For all speifiations, the interated term is signifiant, suggesting that for emerging ountries and for ountries without swap lines, the urreny shares of the finanial systems liabilities orrelate with the urreny shares of their foreign reserve portfolios in the ross-setion. 17

18 5.1 Private Banks The agents in the model are banks, who generate liquidity mismathes with dollar debt. As in the standard Diamond and Dybvig [1983] model, banks borrow and lend aross borders to fund long-term assets with short-term liabilities and deposits. Developed markets offer loweryielding projets and heaper funding ompared to emerging markets, and this assumption oupled with limited liability on behalf of banks leads banks to under-hedge dollar debt. Central banks will be introdued later, as trying to protet domesti depositors who have invested in these banks. The liquidity mismath is standard. At t = 0, banks issue short-term debt (expiring at t = 1) and are given long-term deposits (expiring at t = 2) to fund long-term projets (paying off at t = 2). At t = 1, banks issue new short-term debt (expiring at t = 2) to pay off expiring short-term debt. At t = 2, banks ash in assets and settle all remaining liabilities. Deposits Debt Debt t = 0 t = 1 t = 2 Assets Speifially, there are two ountries (the US and Thailand), and eah ountry offers a ontinuum of projets to banks with gross riskless return U[1, R ]. If projets are liquidated early (at t = 1), they yield zero. As suh, a bank that invests x in a ountry gets at t = 2: R R x rdr = R x 1 2 (x ) 2 Banks also raise finaning from risk-neutral lenders in eah ountry, to supplement exogenous deposits D. But finanial markets have supply onstraints, where eah marginal dollar borrowed in eah market has inreasing osts. The osts are governed by a ountry-speifi and time-varying α t for eah ountry : X 0 (1 + α x)dx = X ) (1 + α 2 X Note that in this model, eah ountry only offers projets and funding in its loal urreny, and so raising finaning from US investors is equivalent to raising dollar funding. 18

19 Finally, exhange rates are assumed to be pegged to unity, and there are no impediments to moving funding aross borders in other words, foreign exhange markets are fritionless. As suh, the bank s optimization problem is: ) max (R x (x ) 2 {x},{x 1 } 2 X 1 ) (1 + α 2 X 1 D subjet to budget onstraints at t = 0 (in whih long-term investments are made) and t = 1 (in whih short-term debt is refinaned), and various non-negativity onstraints: X0 + D = X1 = X 0 x, X 0, X 1 0 x ) (1 + α 2 X 0 Now, I introdue a seond state of the world at t = 1: the risis state. Several things happen during a risis. Most importantly, foreign exhange markets develop onvex fritions, paramterized by f for ountry. Suppose a bank wants to move y dollars into a given ountry ; during a risis, the bank will only reeive the following: y 0 (1 f y)dy = y (1 f ) 2 y In addition, during a risis, short-term borrowing osts shift and exhange rates temporarily deviate from unity. These are not important for the results qualitatively, but they both seem empirially valid and make the quantitative results more stark. Banks have limited liability, and an default (whih hanges the ost of borrowing by riskneutral lenders ex ante, denoted by κ). Finally, banks an save through s, although given the limited liability onstraint, they will not do so in pratie. Thus, the bank s optimization problem an be revised. max E s,x,x,y [ max { 0, ) (R x (x ) 2 2 ) }] X,s 1 (1 + α,s 1 2 X 1 D subjet to budget onstraints at t = 0 (in whih long-term investments are made), t = 1 (non-risis state), and t = 1 (risis state), as well as a onstraint for transferring wealth in 19

20 either state and various non-negativity onstraints: X0 + D = s + X 1 + y E = X 0 s + X 1 + y ( 1 f 2 y s + ( 1 + α 0 ) E = X0 y = 0 s, x, X 0, X X 0 x ) 1 κ ( 1 + α 0 2 X 0 ) 1 κ To illustrate with a speifi parameterization, onsider a bank that has liense to raise funds and invest in both ountries (the US and Thailand). Compared to the US, Thailand has more profitable investments but less developed finanial markets. If there is a risis at t = 1 (with p = 0.01), exhange rate fritions appear. In this senario, the osts of funding in the US and Thailand swith and there are no exhange rate hanges. While I an get more dramati results when the osts of funding both rise and the exhange rate flutuates whih is empirially more onsistent this is done to illustrate the importane of foreign exhange fritions, as the overall funding menu offered to the bank is kept the same. At t = 0, the bank has two hoies. It an take a safe plan, in whih it keeps debt low and remains solvent during the risis; or it an take out a risky plan, in whih it takes out high debt and defaults during the risis. In this example, the risky plan is more profitable, and so a risk-neutral bank will implement this. 5.2 Central Banks When private banks default, the entral bank does not sit idle: it wishes to protet depositors, either by bailing out distressed banks or printing the deposits itself. Suppose the heaper option is to bail out distressed banks. If banks short-term liabilities are in foreign urrenies, domesti urreny is useless and so the entral bank an either inur foreign exhange transation osts to gather foreign urreny, or it an lend out of previously aumulated foreign urreny reserves. In this model, entral banks aumulate preautionary savings in foreign urrenies before turmoil. Speifially, if a bank is on the verge of defaulting in a risis, the entral bank an hoose to bail out the bank by extending loans L at t = 1 in eah urreny. These are not gifts, as banks must repay at t = 2. However, banks an borrow these loans without enountering the 20

21 Table 2: Private Bank Optimization Name State Country Variable Safe Plan Risky Plan Debt t = 0 US X Thailand X Investment t = 0 US x Thailand x Debt No Crisis (t = 1) US X 1, Thailand X 2, Inflows No Crisis (t = 1) US y 1, Thailand y 2, Debt Crisis (t = 1) US X 1, N/A Thailand X 2, N/A Inflows Crisis (t = 1) US X 1, N/A Thailand X 2, N/A Expeted Profit The table shows the optimal senarios under the assumption that a private bank wishes to remain solvent or default in a risis. Both plans involve taking heavy US debt and investing in Thailand, although the plan under the default assumption involves more leverage. The plan that defaults in a risis is more profitable, leading to an overly leveraged banking setor in the aggregate. onvex finaning osts or foreign exhange osts. Naturally, entral banks want to minimize the funds transferred, as long as banks pay off their short-term obligations, and so it does not lend wastefully. I assume that bailouts are unexpeted for banks when banks are optimizing. As suh, at t = 1 in the risis state, the entral bank solves the following optimization problem. min X 1,y,L 1 2 β (L ) 2 subjet to a solveny onstraint for the bank to whih it lends at t = 2, a onstraint to ensure that the bank an remain afloat at t = 1, and the usual onstraints on internal transfers and non-negativity. ) (R x (x ) 2 2 s + L + X 1 + y ( 1 f 2 y X 1 ( ) 1 + α 1 2 X 1 + D + ) E = X0 y = 0 X 1 0 ( ) 1 + α X 0 κ L 21

22 This optimization yields a frontier of lending pakages aross the two urrenies dollars and Thai baht depited in Figure 5. A entral bank piks a loan pakage from the line, as that reflets the minimum transfer needed to bail out the bank. Figure 5: Central Bank Lending Notes: The figure depits the lending frontier for a entral bank that hooses to bail out the risky bank in Table 2 during a risis, aross a mixture of dollar and Thai baht lending. The line depits effiient lending mixtures. A loan pakage from the upper-right portion of the graph is gratuitous, and a loan pakage from the lower-left portion is insuffiient to bail out a bank. The next step is determining whih loan pakage to pik (and whether a entral bank even wishes to bail out the bank in the first plae). The one power that it has is the printing press, and it an print domesti urreny although at the ost of inflation π. Now, onsider a entral bank that is determining whether to let a failing bank atually fail or not. If the private bank fails, the entral bank has to print money to over depositors. If the bank lends to it, it must hit the support frontier identified earlier, using existing reserves and freshly printed money. The entral bank an also use foreign exhange markets, although it is subjet to the same fritions during a risis. Thus, the entral bank solves ex ante: min E [ ] π0 2 + π1 2 π subjet to budget onstraints at t = 0 and t = 1 aross domesti and foreign urrenies, and a bailout funtion B( ) that heks whether the lending frontier has been reahed during a bailout, and returns zero if so. π 0 = s 22

23 π 1 + s H + y H ( 1 f H 2 yh ) E H = i L H i + j D j s + y ( 1 f 2 y ) E = i L i Home B ( L H i, L i) = 0 i For instane, onsider the same example. In this example, entral banks find it optimal to bail out their risky banks, versus bailing out depositors diretly. Note, however, that the domiile of the bank matters greatly while Thai and Amerian banks perform the same strategies, their supervisors find it differentially diffiult to mitigate liquidity shoks. The Federal Reserve, whih an print dollars on demand, need not store reserves and an bear inflationary osts if a risis emerges. The Bank of Thailand, whih annot, stores dollar reserves ahead of time to hedge the possibility of a risis. Table 3: Central Bank Optimization Name State Variable Federal Reserve Bank of Thailand Inflation t = 0 π No Crisis (t = 1) π Crisis (t = 1) π Dollar Savings t = 0 s Baht Savings t = 0 s Dollar Lending Crisis (t = 1) L Baht Lending Crisis (t = 1) L Expeted Loss The table shows the optimal plans for eah entral bank if the defaulting private bank is their responsibility. Both entral banks hoose to bail out the defaulting bank, although the Federal Reserve an print dollars as needed and thus stores no reserves. The Bank of Thailand annot, and thus holds large dollar reserves ex ante. This model thus sheds light on why foreign entral banks hold large dollar reserves when their finanial systems are heavily dollarized. Failing to do so would be ostly for the entral bank, whih would either have to inur large transation osts to generate dollars for its finanial system or would have to let its finanial system ollapse. 23