Global imbalances or bad accounting? The missing dark matter in the wealth of nations 1

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1 Global imbalance or bad accounting? The miing dark matter in the wealth of nation 1 Ricardo Haumann Kennedy School of Government and Center for International Development,, Harvard Univerity Federico Sturzenegger Kennedy School of Government, Harvard Univerity and Univeridad Torcuato Di Tella Abtract Thi paper argue that current account tatitic may groly mimeaure the real evolution of a country net foreign aet. The difference may arie due to mimeaurement of FDI, a well a from unreported trade of inurance or liquidity ervice acro countrie. We ugget etimating net foreign aet by capitalizing the ervice flow and etimating the current account from the change in the foreign aet o computed. We call dark matter the difference between our meaure of net foreign aet and that portrayed by official tatitic. When we apply our methodology we find that the US ha ran no current account deficit over the lat two decade, and that global imbalance are relatively mall and very table. The export of dark matter of the US appear to be fairly teady, cating doubt on the need of a major readjutment of the US dollar. Thi verion: December We thank Robert Barro, Eduardo Borenztein, Richard Cooper, Barry Eichengreen, Jeffrey Frankel, Sebatian Galiani, Robert Lawrence, Ugo Panizza, Roberto Rigobon, Dani Rodrik, Andrei Shleifer and eminar participant at the Lunch on International Economic Policy at the Kennedy School of Government, Harvard Univerity for ueful comment. We thank Maria Fernandez Vidal and Victoria Vanaco for able reearch aitance. 1

2 I. Introduction Over the lat couple of year the increaing US current account deficit, currently ticking at over 700 billion dollar a year in 2005 alone, ha led to ignificant concern about the future of the US and the poibility of a major global crii. It come after 27 year of unbroken deficit which have totaled over 5 trillion dollar. Once the maive financing required to keep on paying for uch a widening gap drie up, perhap becaue foreigner become atiated of owning uch a large and rapidly growing amount of American debt, there will be an ugly adjutment in the world economy. The dollar will collape, triggering a tampede away from American debt, interet rate will hoot up and a harp global receion will enue. Martin Wolf (2004 call thi ituation an unutainable black hole and point that The U.S. i now on the comfortable path to ruin. Maurice Obtfeld and Kenneth Rogoff (2005 remark that any ober policymaker or financial market analyt ought to regard the US current account deficit a a word of Damocle hanging over the global economy. More dramatically, Nouriel Roubini and Brad Seter (2005 warn The current account deficit will continue to grow on the back of higher and higher payment on U.S. foreign debt even if the trade deficit tabilize. That i why utained trade deficit will et off the kind of exploive debt dynamic that lead to financial crie. Figure 1 highlight the large and growing yearly and cumulative current account deficit of the US over the lat 25 year which ha made the US the larget net debtor in the world. In addition to depicting a omber cenario, many author have put baic international finance model to work in order to undertand the amount of US depreciation needed to balance the US current account. Obtfeld and Rogoff (2000, 2004 and 2005 uing a two country endowment model etimated a required depreciation of 12 to 14% in their 2000 piece, one of between 20 and 40% in their 2004 piece, and about 33% in their 2005 Brooking Paper. The later etimate were ignificantly larger than the original one conidering that the dollar had already depreciated between 2000 and Blanchard, Giavazzi and Sa (2005 ue a portfolio model to obtain a required depreciation of 65% in a benchmark pecification. Gourincha and Rey (2006 taking account of the pecific tructure of US aet and liabilitie find a required depreciation, for convergence in 5 year to a teady tate, of between 18% and 13% depending on the aumed elaticity of net export. In addition to anticipating a potential adjutment of the dollar the increaing unbalanced poition of the US alo preent everal theoretical challenge. Firt, there i the puzzle of why uch a large and increaing indebtedne ha not led to any viible crii, and why the world i willing to lend continuouly to the US and to do o at urpriingly low interet rate. Or put otherwie, why i the US itelf willing to run uch large current account imbalance? Many rendition, a of recent, have choen to depict the US a an economy out of control, intead of allowing, at leat the poibility, that the outcome may be an equilibrium or optimal repone to underlying fundamental. One popular verion of thee verion i that it i official ource that are keeping demand for US ecuritie artificially large. But while thi may be true it i an unatifactory anwer: why would thee government buy into inevitable capital loe? A econd puzzle i that if the US i a large net debtor, omeone ele i a large net creditor. A we will how below, according to official tatitic thi large creditor i, not Europe (in fact Europe i a debtor a well, but Japan and the ret of the world. Thi implie that, over 2

3 the lat decade, the le developed countrie in the world have been financing the conumption excee of the richet countrie. Thi mean that there i a huge puzzle of why capital i flowing away from the le developed world, not jut why it doe not flow in. The conceptual and practical problem of the traditional rendition are o large that we are compelled to explore if there i omething eriouly wrong about thi worldview. To motivate our analyi let u tart by reviewing ome fact. The Bureau of Economic Analyi (BEA report that in 1980 the US had about 365 billion dollar of net foreign aet (that i the difference between the foreign aet owned abroad and the local aet owned by foreigner. Thee aet rendered at the time a net return of about 30 billion dollar. Between 1980 and 2004, the US accumulated a current account deficit of 4.5 trillion dollar. It i natural to expect the net foreign aet of the US to fall by that amount, to ay, minu 4.1 trillion. If the US paid 5 percent on that debt, the net return on it financial poition hould have moved from a urplu of 30 billion in 1982 to minu 210 billion dollar a year in After all, debtor need to ervice their debt. But the number for 2004 i, till a poitive 30 billion, jut like in According to thi baic arithmetic the US ha pent 4.5 trillion dollar more than it ha earned (which i what the cumulative current account deficit implie for free! To repond to the incongruence of the flow and the aet data two anwer have been uggeted. One note that the US benefited from about 1.6 trillion dollar of net capital gain o that intead of owing 4.1 trillion, it owe only 2.5 trillion (which, at bet, cut the puzzle by le than half, leaving more than a whole other half to be explained. Thi i the official view a repreented by BEA in it rendition of the US international invetment poition, which how a maller deterioration than the cumulative current account meaure (and noticeably how a contant tock of foreign aet over the lat three year in pite of increaing current account deficit. Thi dicrepancy, i, in part, the reult of the US government deciion in the early 1990 to compatibilize it balance of payment tatitic with IMF practice which required excluding capital gain and loe from current account etimate (when theoretically they hould be included. While BEA alo provide a eparate market value etimate that trie to adjut for capital gain we will argue below that meauring thee capital gain from foreign tock market performance may lead to ignificant underetimation of the value of FDI aet. In fact BEA market value etimate i relatively cloe to the book value meaure. Further adjutment are attempted by Lane and Milei Ferreti (2001, 2005 a well a in Gourincha and Rey (2005. Lane and Milei Ferreti, for example, correct official number by adjuting FDI value on the bai of exchange rate change, but thi turn out to deliver only a minor change (a an example, according to thi methodology, in recent year there would be no valuation adjutment for invetment in China a the dollar/yuan exchange rate ha remained contant. Furthermore, becaue their adjutment are motly exchange rate baed, even when they find that the US net foreign aet poition ha been table in pite of increaing current account deficit, they conclude that an important reaon why the hare of US liabilitie in the portfolio of foreign invetor ha been maintained at a relatively table level ha been the operation of the valuation channel of exchange rate adjutment it i not a viable long run trategy to rely on uch valuation gain to ameliorate a tructural reliance on net capital inflow. 3

4 The econd anwer to the incongruence between flow and tock data tree the fact that the US earn a higher return on it holding of foreign aet than it pay to foreigner on it liabilitie a point made early on by Lawrence (1990 and more recently alo highlighted by Obtfeld and Rogoff (2005. The mot careful decription i in Gourincha and Rey who attempt a characterization of thi differential return by documenting how the gro aet poition of the US economy have hown a trend toward larger hare of riky (equity aet on the aet ide and of rikle ecuritie on the liability ide. In fact they find that it i the differential return and not the compoition effect that explain the US net financial income of the US economy. According to them, however, the action eem to be motly in hort term liquid aet with relatively minor effect from FDI. Again, in pite of finding thi return differential to be fairly teady Gourincha and Rey alo conclude on a omber tone. According to them the US ha been able to overcome the debt cot of it growing indebtedne but only a a reult of a concomitant increae in it unchallenged role a provider of liquidity and afety. Thu they alo conclude that foreign lender could decide to top financing the US external deficit and run away from the dollar, either in favor of another currency or require a rik premium on US liquid aet whoe afety could not be guaranteed any longer. In either cae, the repercuion could be quite evere, with a decline in the value of the dollar, higher dometic interet rate and yield, and a global receion. Both explanation require further analyi. Firt if it i true that there have been ignificant capital gain on US foreign aet we need to undertand where do thoe large capital gain really come from.. It i unlikely that they come from exchange rate movement, to the extent that the dollar ha gone up and down ince the 1980 without any clear trend. It eem unlikely that much of the dynamic can be accounted from thi channel, thi being the reaon that Lane and Milei Ferreti till find the US to be a large debtor. So what are the channel by which capital gain take place? Undertanding the ource i critical to ae the potential utainability of thi revalued tock of capital. On the other hand the traditional rendition that US aet abroad deliver higher rate beg the quetion of why are US invetor abroad o much marter than foreign invetor in the US? After all, are global portfolio invetor not free to buy any aet they want? Why would foreigner conitently pick wore aet than American invetor? Finally, in t there omething mileading about calling a country that make money on it financial poition the world larget debtor? The paper i organized a follow. In ection II we preent a new way of meauring current account imbalance for the US. We will ee that our meaure implie a large dicrepancy with official number, at leat for the US. We call thi dicrepancy dark matter. In Section III we dicu the factor that explain the exitence of dark matter and provide a meaure for the US, we how that once dark matter i taken into account the US economy ha not been running current account deficit during the lat two decade. In Section IV we addre the iue that if the US ha not really been running a current account deficit, then omeone abroad ha not really been running a urplu. If o who can thi be? Who are the net exporter and importer of dark matter? In hort we tudy how global imbalance in the world look once dark matter ha been taken into account. Section V conclude with ome cloing thought and uggetion for future reearch. 4

5 Section II. Our view Our view i that the whole debate i the reult of a confuion caued by an unnatural et of accounting rule. All accounting ytem are conitent but arbitrary. They all decribe the ame reality: meauring the temperature of the air in degree centigrade doe not make the world colder than if meaured in Fahrenheit. But not all ytem are equally tranparent. If you chooe to decribe the orbit of the planet auming that they circle the Earth and not the Sun a Ptolemy did, you will have to include a bunch of arbitrary epicycle to make the ytem fit the fact. Thu, we propoe a different way of decribing the fact. We tart from the pirit of current accounting convention. The interet in a concept uch a the current account balance i that it i related to the change in the net aet poition of a country. In fact, mot textbook make the aumption that thee two concept are identical and would write an equation uch a CA = TB + i NFA = NFA where TB i the trade balance and i i the interet earned by the foreign aet poition. It i alo typical to include a footnote aying that thi formulation may be off becaue of potential valuation change, but the idea i that thee change hould not be very peritent. 2 From here, it i eay to derive a rule that guarantee the contancy of the external debt to GDP ratio, d. TB = (i g d where g i the growth rate of the economy. We argue that thee relationhip are in mot analyt mind and explain why people worry about the external poition of the US. In fact, thi i the rationale that we followed in the third paragraph of thi paper, only to find out that it lead to a very large inconitency. The problem come from the fact that given the tandard accounting rule the capital gain can be very ubtantial and peritent making the relationhip between the current account and the change in net foreign aet quite weak. To make thing add up, the current methodology need an ever expanding et of Ptolemaic epicycle, like the 1.6 trillion dollar in capital gain. We propoe a different et of accounting rule, a ytem that recue the relationhip between our definition of the current account and the change in net foreign aet. Firt we adopt a rule for valuing aet. We tart by auming that if an aet conitently pay more than another aet, then it i worth more, even if they both have the ame hitorical cot or book value. We chooe to value the aet on the bai of their return. Thi i jut like valuing a company by calculating it earning and multiplying by ome price-earning ratio, or valuing a property baed on it rental value. A we know from the corporate finance literature for an individual company, the earning of any given year may give u an unreliable meaure of it true earning potential, but if we average over an economy a large and diverified a the US and look at trend over a couple of year, thi imple methodology 2 See for example, Cave et al dicuion of tatitical dicrepancie in the payment account. 5

6 deliver reaonable reult. Of coure, thi open the quetion a to what exactly thi price earning ratio hould be. We will come back to thi at length below. For the purpoe of illutrating the implication let u ue here an arbitrary 5% rate, which implie a priceearning ratio of 20. If we do o we can provide a back of the envelope etimate of US net foreign aet. We know that the US net income on it financial portfolio i 30 billion dollar. Thi i a 5 percent return on an aet of 600 billion dollar. So we would ay that the US i a net creditor for about 600 billion dollar or about 5 percent of it GDP. Secondly, we will define the current account deficit a the change in the net foreign aet poition a jut defined. Since the income flow ha remained fairly table over the lat 25 year, we would ay that o have the US net foreign aet and by implication, the current account ha been broadly in balance. That i why it i till a net creditor. To put i uccinctly we define the current account a the difference in the capitalized value of the ervice flow CA = SF SF r SF = r t+ 1 t t+ 1 r A o t (1 Where the lat equality derive from the aumption that initially aet were properly meaured and earned the return r. Either becaue aet are mimeaured or earn a different rate the ervice flow in period t+1, (1 can be written a o r At A o 0 CA = At = At + r 1 A o t A + = CA r o A + r (2 o o o where A t+1 = At + CA, i,e the value of aet that the economy would have had if aet evolved according to the official current account. A i then the difference between the ervice flow in period t+1 and the ervice flow that hould have occurred if aet had been properly meaured and continued to yield the ame rate. The A term, capitalized, which we add to the official current account, reflect the fact that there are uncaptured return that how up in the income account (in fact it hould be added to GNP and aving a well. From equation (2 we trivially have DarkMatter A r o = = CA CA, which how that thee capitalized unexplained return are equal to the difference between our verion of the current account and the official meaure. It i thi difference what we call dark matter becaue it correpond to aet that we know exit, ince they generate revenue, but cannot be een (or, better aid, cannot be properly meaured. The name i taken from a term ued in phyic to account for the fact that the world i more table than you would think if it were held together only by the gravity emanating from viible matter. 6

7 How doe our accounting change the way we decribe the well known fact that US aet abroad provide a higher return than foreign aet in the US? To illutrate thi conider an aet that the US hold abroad that earn a rate of return r h which i higher than our fixed and arbitrary benchmark rate of 5% 3 and a liability earning r l which i lower than our benchmark rate. If A and L repreent the market value of the aet and liabilitie we would meaure aet and liabilitie a which implie that A h h h r A r A ( r r A = > A = +, r r r * A h ( r r = A + A. r * The econd term, the capitalized value of the return differential of thi invetment, which repreent the uperior ability of US aet to command a return, i what we call export of dark matter. Notice that by capitalizing thi we are implicitly auming that thi return differential will hold, omething to which we will come back below. We will alo argue below that it i correct to conider thi a an aet even when thi interet rate differential compenate for the higher rikine of the flow. Likewie, for liabilitie we have that our meaure of liabilitie L* can be written a which implie that L l l l r L r L ( r r L = < L = +, r r r * L ( r r l L = L. L * If the interet rate paid by the US i lower than our benchmark the econd term how a reduction in liabilitie equal to the capitalized value of that interet differential. We believe the ability of the US to charge lower rate i an aet (a negative liability, the value of which i meaured in the econd term in the previou equation. The value of thi aet i alo an export of dark matter. It will be clear by now that our difference with Gourincha and Rey i that we capitalized the ervice flow differential and add it to the current account. It i the fact that we conider thi a an aet what make our decription of the current account dynamic o different from the tandard rendition. Of coure the reader will wonder to what extent thee export of 3 None of our reult depend on the particular rate choen. In fact uing the US treaury rate we would get baically the ame tory. 7

8 dark matter are utainable or not, particularly taking into account that we conider their capitalized value, which, implicitly aume that the return differential will remain forever. If they are not table or average out to zero, then our accounting will not mean much, nor change ignificantly the concluion obtained from conventional analyi. But if thee export of dark matter are contant and table then they can change our interpretation of the fact. For the US thi eem to be the cae. Figure 2 how by how much the two meaure differ. On the one hand it how the cumulative current account deficit according to official tatitic, which a wa already mentioned, add up to the 4.5 trillion that the US ha overpent between 1980 and The other line how the cumulative change in net foreign aet according to our methodology. The fact that the curve how no meaningful trend (upward or downward i imply indicating that the total ervice flow obtained from foreign aet held by US reident (and thu our meaure of the amount of thoe aet ha virtually not changed. In term of equation (2 it mean that the US ha conitently exported dark matter. In fact, the export of dark matter have been quite imilar to the reported deficit making the actual deficit cloe to zero throughout thi period and thi i why our meaure of cumulative current account add up to virtually zero. There i a large difference between our view of the US a a net creditor with aet of about 600 billion US dollar and BEA view of the US a a net debtor with total net debt of 2.5 trillion. The difference between thee two equally arbitrary tock meaure i the cumulative amount of dark matter, According to our number the US own about 3.1 trillion of unaccounted net foreign aet. Given the ize of the dicrepancy it i difficult to contet the exitence of dark matter. Though we will plunge into methodological dicuion right away, it eem clear that no methodological minutiae will reconcile the fact with the tatitic. We can alo meaure how much dark matter i exported or imported in any given period. For example, the official tory tell u that in the five year period between 2000 and 2004, the US accumulated a current account deficit equal to 2.5 trillion dollar. We find that the net aet of the US went up by over 300 billion dollar. Hence, the country exported ome 2.8 trillion dollar of dark matter in thi period or about 5.3 percent of GDP annually. The exitence of dark matter open up everal important quetion. Firt and foremot what i behind dark matter? What are the economic reaon for it exitence? Anwering thee quetion will provide the firt clue a to the tability of dark matter and whether we hould expect it to be a lating ource for compenating meaured imbalance. Thi i all the more relevant becaue if the US ha maintained it net aet poition a a reult of accumulating dark matter, i thi to be truted a a ource for compenating the meaured trade imbalance of the US in the future? Thi will lead u to an analyi of the tatitical propertie of dark matter. We deal with both thee quetion in the next ection. Section III. Source of dark matter We believe that there are at leat three factor that account for the accumulation of dark matter. They all involve a peritent return differential between US aet and liabilitie. Thi difference in return i the reult of three factor: a return differential for US FDI 8

9 invetment, the ale of inurance, and the proviion of liquidity ervice. The firt channel involve the uperior return of US FDI invetment abroad. Thi arie becaue FDI invetor purchae aet in order to invet, but alo bring with them a blueprint, a product and a buine know-how that i uually poorly accounted for. Becaue of the difficultie in tracking the international operation of American corporation it i likely that the BEA number underetimate their worth. The econd channel may arie becaue the underlying tability of the US economy allow it to ell ome of thi tability to the ret of world, akin to the ale of inurance. The third channel i related to the proviion of liquidity ervice, baically through the ue of the dollar or the lower return on deeply liquid financial market. The different torie can be een a an interpretation of what Caballero, et al (2005 call the US better ability of generating financial aet. Let u dicu each in turn. 4 Foreign Direct Invetment The US Department of Commerce (1990 report that The international invetment poition hould be interpreted with caution becaue it i only a rough indicator, not a precie meaure. On the one hand, US aet abroad probably are undertated becaue direct invetment i carried at book value (p. 21 While the BEA ha introduced a market value alternative to the original meaure, that deliver higher value for FDI, it doe not affect dramatically the value of the net poition a both FDI abroad and foreign FDI in the US get revalued by imilar amount 5. At any rate, it i book value to which equity adjutment are done, o that if initial valuation are incorrect, over the long run thi can deliver a ignificant undervaluation. Lane and Milei Ferreti attempt to correct thi but their exchange rate adjutment turn out to be only marginal. The fact that book value mirepreent the value of firm i well known from the corporate finance literature. Becaue thi i ued to contruct the erie or ued to obtain initial value that are then increaed by equity price, thi may lead to underetimation. In the market value alternative, BEA alo ue, quite reaonably, hot countrie equity market to do uch valuation adjutment. But notice that if US invetment abroad carry the earning potential of US firm, it could be argued, that at leat partially they hould be updated by the value of US tock market that better capture thi earning potential. Taking an extreme view to figure out if thi could lead to underetimation we gro up the tock of FDI every year by that year increae or decline in tock value, and then add the change in the reported tock of FDI (thi difference hould include new flow net of depreciation. According to BEA International Invetment poition the US ha FDI abroad for anything between 2.3 trillion (book value and 3.3 trillion (market value. But if FDI aet are increaed by the value of the US tock market we obtain a value of 7.8 trillion. 6 Obviouly, it i not jutifiable to increae the value of US invetment abroad fully by the value at which invetment appreciated in the US, but it i equally difficult to jutify increaing them only by the value of foreign tock market, thu we conclude that FDI could be eriouly undervalued even in the BEA market etimate. 4 See alo Cooper (2005 who mention mot of thee channel. 5 For a careful (and official decription of the two methodologie ee Kozlow ( We include in addition to FDI, U.S. claim on unaffiliated foreigner reported by U.S. nonbanking concern and U.S. claim reported by U.S. bank, not included elewhere. 9

10 Thi mimeaurement i far from irrelevant. To the extent that there are unreported capital gain, thee hould be included in the current account in US national account, increaing the aving rate and national income. A per the exercie above, the amount of mimeaurement can be ignificant. Caballero et al (2005 ugget that the US together with a few other countrie have a uperior ability to iue financial claim. We ee thi a the poibility of iuing not only better financial intrument but alo of deploying abroad the buine idea that were developed for their home market. Not urpriingly below we will how that the countrie with the larget dicrepancy between reported aet and official number are the US, the UK, Germany and Switzerland, all countrie which export the buine idea developed at home through FDI invetment. Let u illutrate how thi channel work. Imagine the contruction of a foreign operation the value of which tem motly from the know how that invetor bring along. For the ake of the argument let aume that the cot of etting the operation i 100 million and that thi i what i written down in the book. Imagine alo, for the ake of the argument that thee reource were borrowed abroad at, ay, a 5% rate of return. Once the operation i running it yield 20 cent on the dollar in operational revenue. Once financial cot are taken into account, thi invetment generate a net income flow of 15 cent on the dollar even though BEA would ay that the net foreign aet poition i equal to zero (ince the BEA meaure the value of foreign direct invetment at book value. By contrat, we would ay that the aet abroad in reality are not worth 100 million (what BEA would value it but four time that (the capitalized value at our 5% rate of the 20 million per year that it earn. Why can thi firm earn uch a return? Becaue the invetment come with a ubtantial amount of know-how, brand value, expertie, better financial tructure, and better legal protection, all of which generate earning potential. Thee are ource of dark matter and explain why US reident (and the UK a will be hown below can earn more on their aet than they pay on their liabilitie and why foreigner cannot do the ame. Another way to decribe the ame fact i to ay that the US exported 300 million in dark matter and i making a 5 percent return on it. The point i that in the accounting of FDI, the know-how that make invetment particularly productive i poorly accounted for. Inurance Another poible reaon why US aet abroad command a higher return i the fact that the US actually ell inurance to the ret of the world. Thi interpretation (a oppoed to a valuation effect caued by exchange rate move indicate that to the extent that the US economy remain relatively more table than the ret of the world the return differential i bound to remain. In fact, if anything, it eem that the value of thi inurance ha increaed together with the globalization of international financial market. One way the ale of inurance how a dark matter i in the return to bond. In BEA accounting, debt i meaured at market value. Suppoe the US invet in a portfolio of emerging market bond that yield on average 300 bai point over treaurie. And uppoe that it fund thi operation by iuing an equivalent amount of debt at the rate paid by the US Treaury. The BEA would ay that the net aet poition ha not changed. And yet there i a net income 10

11 caued by the 300 bai-point pread. Where doe thi income come from? It i compenation for the fact that the emerging market portfolio i rikier than the liabilitie iued by the US. Thi pread ha two component. Part of it i the ex ante premium required by a rik neutral invetor to compenate him for the expected default. Another part ha to do with compenating the invetor for hi averion toward rik. The firt component hould tend to average zero over a ufficiently long period of time, a the ex ante compenation hould on average cover ex pot loe. The econd component hould have a poitive mean, the ame way inurance companie make money on average. In any cae, both concept involve compenation for the exchange of rik between countrie. It i an unaccounted aet that we would claify a dark matter. 7 A rik premium in favor of the US would appear in equilibrium in a world characterized by financial integration if the US i a more table economy than the ret of the world. US aet would command a higher price becaue they would be demanded by foreigner to lower their rik. To ee thi conider a two country world with uncertainty and with a full array of Arrow- Debreu contingent ecuritie that can be ued to hedge rik. We will conider a one period model, with S potential tate of nature each with probability π(, and therefore p(s price for contingent ecuritie. Global equilibrium require upply and demand in the S contingent market to balance, i.e. * * C ( + C ( = Y ( + Y ( (3 for each tate, where the tar refer, a uual, to the foreign country. C( refer to conumption in tate and Y( i endowment in uch a tate. With CRRA utility of the 1 ρ tandard form C /(1 ρ the tandard Euler equation for the maximization of expected utility implie the tandard price relation of tate contingent claim: C( 1 C( 2 ρ = p1π 2 p π 2 1 (4 and likewie for the other country. Subtituting the equilibrium condition (3, in (4, implie that p1π 2 p π 2 1 Y = Y W W ( 2 ( 1 ρ (5 7 Klingen, Weder and Zettlemeyer (2005 find that emerging market debt ha ex-pot delivered a rate of return of about 1% above equivalent US ecuritie. 11

12 12 where the upercript W indicate world output in that tate. Uing the tandard normalization that 1 ( = S p, equation (5 can be ued to olve for the equilibrium price of contingent ecuritie ( ( = S W W Y Y p ρ ρ π π ( ( (. (6 The fact that all countrie face the ame aet price implie the celebrated relation ( ( ( ( ( ( * 1 * 2 1 Y Y C C C C W W = = And µ = = ( ( ( ( Y C Y C W W while (1 ( ( ( ( 2 2 * 1 1 * µ = = Y C Y C W W, where µ i the hare of the home country in world conumption. The value of µ derive naturally from the budget contraint and equal the hare of the country output relative to world output meaured at the Arrow Debreu equilibrium price. Solving for thi value after ubtituting for the equilibrium price we find that [ ] [ ] = S W S W Y Y Y ρ ρ π π µ 1 ( ( (. (7 The country hare in equation (7 i our object of interet becaue it indicate how much of world wealth the home economy will command. To the extent that an economy ha a more table output profile than the ret of the world, it will be elling inurance to the ret of the world and obtaining an expected payment in return. In hort the world would be giving up ome income to wap, at actuarially diadvantageou term, local output for the home economy output. Equation (5 how that when there i aggregate uncertainty, price will not be actuarially fair, i.e. the market will price in a rik premium to reduce it rik. To illutrate the concept imagine that the home country (purportedly the US i more table than the ret of the world. Without lo of generality and jut to illutrate the intuition conider the cae in which output i contant acro tate of nature in the home economy and volatile abroad. In hort we aume that Y Y = (, for all tate at home. Output in the

13 ret of the world, on the other hand i aumed, without any lo of generality to be W W decribed by Y ( = φ( Y. We alo aume the probability of all tate to be the ame. In thi cae we can ee that (7 eaily implifie to Y = Y [ φ( ] S µ W 1 ρ [ φ( ] S ρ. (8 Notice that if ρ=0, which implie linear utility, ie. no rik averion, µ equal the country hare in world income. On the other hand when ρ, which i the cae with infinite rik averion, indifference curve become Leontieff o it i eay to how that µ = Y W minφ( Y, (9 with intermediate cae in between. Notice that in thi extreme cae, if the foreign country ha output tate with extremely low income, then the home economy virtually conume the whole of world output! The intuition for thi cae i that with infinite rik averion the foreign country i willing to give up everything to improve it conumption in it wort cenario. The difference between expected income in autarky and with acce to international market i the inurance premium that the country charge every period. In a world of complete ecuritie thi payment i fixed and certain, the higher the rik in the world, the higher the payment (and the higher the ex pot profile of conumption. The ituation i illutrated in Figure 3. In figure 3a home country ha a table income profile while the ret of the world ha a trongly kewed income tream. After trading in Arrow Debreu ecuritie the world economy will operate at the diagonal. Notice that if the probability of both tate i not the ame, equation (5 indicate that the price of output in the high income tate i lower than that of the low income tate. So for tranferring income to the ret of the world in thi tate the home economy obtain a compenation that i poitive in expected value. Thi i a way to viualize the inurance premium that create dark matter. 8 Figure 3b illutrate the cae of infinite rik averion. In thi cae the horizontal move for the home economy repreent the gain in income from it moothing ervice. To the extent that the US economy ha a permanently more table output thi value hould be expected to remain, or to grow with the ability of other countrie to participate in world financial market. The capitalized value of the flow that compenate for thi inurance would appear a dark matter. What are the ource of the enhanced tability of the US economy? Shiller (1993, for example, compute the value of claim to output for different countrie and find that the volatility of thee claim i ubtantially maller for the US (ee Obtfeld and Rogoff,, The cae of infinite rik averion implie that the indifference curve become flat immediately away from the 45% degree line. 13

14 Given that Arrow Debreu ecuritie do not exit, one way the exchange of rik take place i by exchanging debt, a explained above. Conider a country ubject to large output hock and therefore to default rik. Thee countrie may be willing to exchange US debt yielding a teady return in exchange for their riky aet. The difference between the two rate of return include the compenation for the expected default but alo will include an inurance premium for the increaed rik. It i thi extra premium that will be captured ex pot in the factor income data. Finally, FDI may be the vehicle for diverifying rik in thi manner. Countrie may buy the more table US equitie or directly invet in the US while the US may ue the reource to invet abroad. Foreign operation will carry an exce return that will compenate for their intability. Thi exce return i the compenation for the export of inurance ervice and will be captured in our framework a dark matter. Liquidity Our third ource of dark matter i the unaccounted value of the liquidity ervice provided by the US. People all around the world need liquid aet and chooe to hold dollar either in (non-interet-bearing cah or in interet bearing intrument that have inordinately deep liquid market. The US can ue the proceed from printing thi money or iuing thee ecuritie to buy aet that generate a larger income and make a return. Again, the BEA would ay that uch a tranaction caue no change in the aet poition. We would ay that the US ha exported dark matter in the form of liquidity ervice and i making a return on it. Thi concept which involve both eignorage and a negative premium on the dollardenominated reerve aet contitute an unmeaured proviion of liquidity ervice which our accounting method would capture a dark matter. Meauring Dark Matter A tated above in order to etimate the value of US net foreign aet we propoe to capitalize the value of the flow of US financial income into a tock meaure. To do o we need to addre the iue of which dicount rate hould be ued and whether dometic and foreign flow hould be dicounted at the ame rate. If the world wa populated by rik neutral invetor or if there were a complete et of contingent claim, a above, then it i trivial that the ervice flow hould be dicounted by ome rik free rate of return. Here we follow thi procedure and dicount all our flow at an arbitrary contant interet rate of 5%. We have everal reaon for chooing thi approach. Firt, in the global economy each financial claim appear twice: a an aet in one country and a liability in another. We hould value that claim equally in both countrie. Hence, it i important that we ue the ame interet rate. It would be problematic if we applied different interet rate for what i in fact the ame aet. Second, we chooe a contant rate o that change in our meaure of aet depend only on change in the income flow of the aet and not on variation in the price-earning ratio. Thi allow a cleaner viualization of the evolution of flow. In fact, the level of the interet rate we chooe i irrelevant for our tory and imilar reult would obtain if we ued an interet rate computed from market rate. Third, our interet i not to capture the market price at which aet trade ex ante in market, but to track the change in a country debt ervice burden. Our accounting convention 14

15 better capture thi, even though it i different from either valuing an aet at book value or at market value, two procedure that are ued imultaneouly and inconitently in current practice. One potential criticim of our approach i that it may lead to an overetimation of US foreign aet to the extent that it dicount the flow obtained from rikier invetment abroad at the ame rik free rate that the US charge on it liabilitie. In doing o, we would increae the value of US aet relative to it liabilitie. However, while it make ene to dicount an ex ante tream of income at a higher rate becaue of the rik of non-payment due to expropriation or default rik, when working with ex pot data it i tandard to dicount at the rik free rate ince the negative contingencie will have already occurred (ee Jorgenon and Sach, If the higher premium arie from the fact that there i a world with rik avere invetor in which non diverifiable rik carry a premium, then to the extent that thi premium i conitently paid (a i any inurance premium and a in our example above, our meaure of the aet will actually include the capitalized value of thi premium. In other word, in our framework, the net rik premium that countrie would collect on account of the fact that invetor that are not rik neutral are willing to pay for non-diverifiable rik hould be conidered an aet and will be counted a an export of dark matter in our methodology. In figure 2 we preented our calculation of US net foreign aet, a the reult of capitalizing at a contant rate of 5% the US ervice flow. Defining dark matter a the difference between our meaure of the net foreign capital aet poition and the implicit aet poition uggeted by the accumulation of current account, we can etimate both the tock of dark matter a well a the yearly export of dark matter. In figure 4 both are expreed a percentage of US GDP. Looking at the empirical evidence We have argued that there are at leat three theoretical reaon for the preence of dark matter in the US: the country i a net provider of knowledge, liquidity and inurance. It i difficult to identify the ource of dark matter coming from each ource a FDI may operate both a a vehicle for export of know how a well a a mean for providing inurance. Debt intrument, in turn, may both be intrument to export inurance but alo liquidity ervice. Figure 5 bear on thi point by howing the net income ariing from three ource a preented in official figure: net income from foreign direct invetment, net payment by the US government and other net private income. The figure how the riing cot of the interet payment on the growing US public debt, which ha been increaingly held by foreigner. However, thi i compenated by an even fater rie in the income generated by FDI. Other net income flow appear to be mall. At firt view, thi ugget that the bulk of the dark matter i in the exce return on FDI. To get a better idea of thi, we take each one of the three income flow categorie and then cale it up by multiplying by our earning ratio of 20. We can then calculate the difference in our valuation of each of thee aet vi a vi BEA valuation and hence the amount of dark matter correponding to each aet cla. Thi i hown in Figure 6. A can be een, there i dark matter in each aet cla. While FDI i the larget long-run ource, the public debt 15

16 how the bigget turnaround reflecting the low interet rate on US Treaurie of the lat few year. Barro (2005 provide a model in which the equity premium puzzle i explained by the poibility of unuual but large negative effect. Thu in hi model, the return on bond fall ubtantially once thee large event are a poibility. Hi model can be ued to explain why the value of inurance provided by the US ha dramatically increaed tarting in 1998 when following the Aian crii we oberved the Ruian default crii. Thi inurance value may have been compounded by the uncertainty deriving from 9/11. Our undertanding of the nature of dark matter i relevant to ae the fragility of the US current account poition. If export of dark matter are compenating the large trade deficit in the US, can it be truted a a way of keeping the net aet poition of the US table in the future? In other word, i dark matter ufficiently table to hold the world together and avoid global financial market from running into a crii? Thi will depend, ultimately, on how teady i the earning power of the aet that make up dark matter. If dark matter jut reflect capital gain aociated ay, with exchange rate or interet rate fluctuation, it would be quite unreliable, a pointed out by Lane and Milei Ferretti. On the other hand if it i the know-how deployed abroad by US corporation, or an inurance premium baed on the tability of US output, it can be expected to be fairly reilient. Figure 4 howed the evolution of accumulated tock of dark matter by the US. The tock tand now at over 40 percent of GDP. Since 1980 it ha fallen only in 6 year and the larget drop, which took place in 1985, wa barely to 1.9% of GDP. In hort it would take an unprecedented deterioration of the value of dark matter to even approximate the net aet poition that today worrie analyt. On average the US ha exported about 2% of GDP per year of dark matter with a tandard deviation of about half a percentage point 9. The reaon for the tability of dark matter are everal-fold. To the extent that FDI aet abroad continue to rie and to generate exce return then we hould expect to meaure a continued export of dark matter. If the ability of the US to provide inurance and liquidity ervice to the ret of the world i baed on ize and a more table economy, to the extent that thee feature perit into the future, the US will increae, not decreae it ale of dark matter. In hort US export of dark matter have good reaon to how the robut pattern they have hown to date in the data. Section IV. A new look at global imbalance With a better undertanding of what dark matter i, we take our exercie to the whole world. In order to have a working benchmark Figure 7a preent the official evolution of the net aet poition of major global player both in US dollar a a hare of each entity GDP. It how a world that i increaingly unbalanced with Japan and the ret of the world financing Europe and (more importantly the US, which appear accumulating a growing external debt. In thee graph the ret of the world i calculated a a reidual to make thing add up to zero. 9 Even though the export of dark matter are conitently of about 2%, they how very little autocorrelation acro year. 16

17 Figure 7b preent the alternative view, which we contruct by capitalizing the net income that each country make on it aet poition. A can readily be inferred, the world look quite different once dark matter i taken into account. Firt and foremot, the US doe not appear a a net debtor but a a net creditor and, a mentioned above, it net foreign aet poition ha remained table over the lat 20 year. Japan, conitent with official data, i a growing creditor, while the European Union and the ret of world are net debtor. Perhap the mot triking feature of Figure 7b i that it how a world that i urpriingly balanced. Net aet poition of all major region are fairly mall under 10 percent of GDP except for Japan which ha a urplu of ome over 30 percent and the ret of world that only recently ha increaed it indebtedne lightly. Figure 8 replicate Figure 2 in Lane and Milei Ferreti, by howing the net foreign aet of a group of countrie a percentage of global GDP. The comparion permit to highlight the imilaritie and difference in the analyi (though ome group of countrie do not coincide exactly due to data availability. The reult are motly identical for Japan (with teady net foreign aet at about 4% of world GDP, the Euro zone (an increaing debtor currently with net foreign debt of about 3% of GDP, and for the Switzerland and Nordic countrie group (with net foreign aet equivalent to about 1% of GDP. Our number how the ame trend throughout the lat two decade but larger net liabilitie for Emerging Aia indicating that they are net importer of dark matter and are only approaching balance in recent year. The difference i larget in the cae of the US. While Lane and Milei Ferreti ee the US a a debtor for about 7% of world GDP for u it i a net creditor for omewhat more the 1% of world GDP. In hort the comparion how that our methodology provide quite imilar reult but for the cae of the US (and concomitantly for the ret of the world. Figure 9 how the evolution of China. It how firt, that China i till a net debtor. However China ha reduced it debt coniderably in recent year a it ha moved it net foreign debt from about 1.2% of world GDP to only 0.4%. Thi reduction in 0.8% of GDP i in itelf large. The improvement i not a large a i uggeted by the official tatitic becaue China remain an important importer of dark matter. Figure 10 how Europe net foreign aet, again a percent of world GDP. Prior to the launching of the euro both European Union and the Euro countrie moved baically in the ame fahion. But they have dramatically diverged in recent year, with the UK increaing very ignificantly it export of dark matter. While the above illutrate our meaure for ome elected countrie, of coure our analyi allow u to replicate it for any country in the world. Thi i what i done in Table 1 that how the reult for the lat five year for the countrie for which we have data. Table 2 calculate the correlation between the official number and our meaure. It confirm that the difference between the two methodologie i indeed important a the correlation are low. However, part of the reaon come from the fact that the US and the UK are large exporter of dark matter. When thee two countrie are excluded, the correlation become poitive and relatively large. However, the correlation are often far from unity, indicating that the tandard preumption that the current account balance i cloely related to the evolution of the net aet poition i not warranted for many countrie. 17

18 Exporter and importer of Dark Matter In order to obtain a better intuition of the movement of dark matter Table 3 rank the exporter of dark matter for the period. Given that ome countrie do not have data for 2004 we have choen to rank the countrie according to their data for The volatility in year to year value of the ervice flow i large and o are export and import of dark matter. We therefore preent the average value for the period. We alo preent only thoe countrie with export or import of dark matter above 1 billion, i.e. thoe that to ome extent are relevant to explain global imbalance. The table undercore the unique role of the US and the UK in explaining the flow of dark matter. The next country in the lit (Mexico i le than one tenth of the UK number and le than one twentieth of the US number. A wa mentioned about the top exporter of dark matter are thoe countrie that provide intermediation of financial ervice and which tranform capital inflow into effective foreign direct invetment. The US, the UK, Germany, Switzerland, and to a leer extent Mexico and Korea all play thi role (the latter two on a regional bai. 10 On the import ide, ix countrie buy at leat 30 billion of dark matter per year over the lat five year. With the exception of France, thee countrie are FDI haven or oil producer. Both fit our pattern, particularly oil countrie for which the increae in the price of oil ha increaed the income of the aet foreigner hold in thee countrie thu increaing the value of their liabilitie above and beyond what would be captured by their current account deficit meaured according to official tatitic. Similarly, countrie like Ireland and Singapore import ignificant quantitie of dark matter, reflecting the ucceful return of FDI in thee countrie. Section IV. Concluion and future reearch In a nut hell our tory i very imple. The income generated by a country financial poition i a good meaure of the true value of it foreign aet. Once aet are valued accordingly the data eem to indicate a large amount of US net foreign aet that are unaccounted for. Since the US ha a net income on it foreign aet poition it i a net creditor, not a net debtor and it net foreign aet poition appear to have been fairly table over the lat 20 year. The difference with the official tory probably come from a combination of mimeaurment, the unaccounted export of know-how carried out by US corporation through their invetment abroad, a well a the ale of inurance and liquidity ervice. The lat three factor relate explicitly to characteritic of the US that cannot be eaily replicated elewhere, and explain why the US look like a conitently marter invetor, making more money on it aet than it pay on it liabilitie and why the ret of the world cannot wie up. In addition, the value of thi dark matter eem to be rather table, indicating that it i likely to continue to compenate at leat partially for the meaured trade deficit. Dark matter alo hed a different light on the often dicued aving puzzle. According to the official tatitic, the US appear a a profligate conumer with dimal aving. However, 10 The role of Switzerland a a provider of inurance ervice, particularly after WWI, i dicued in Kugler and Weder (2004 and