This paper clarifies how the valuation of hidden assets--what we call "dark matter"--changes our assessment of the U.S. external imbalance. Dark matter assets are defined as the capitalized value of the return privilege obtained by U.S. assets. Because this return privilege has been steady over recent decades, it is likely to persist in the future or even to increase, as it becomes leveraged by an increasingly globalized world. Once this is included in future projections of U.S. current accounts, the U.S. external position looks much more balanced than depicted in official statistics.
**********
It is well known that the U.S. economy has been running increasingly large current account deficits since the early 1980s. Current account deficits signal an economy that is spending beyond its means; so it comes as no surprise that the accumulation of deficits during this period, adding up to 5.27 trillion dollars between 1982 and 2005, has significantly increased U.S. net foreign debt--now more than 20 percent of GDP. If those trends were not in themselves cause for concern, in recent years the deficits have escalated in both nominal value and as a percentage of GDP, suggesting that the process cannot continue much longer and that a large and painful reversal may be near.
In a series of articles (2005, 2006a, 2006b--HS hence), we have argued that this concern may be misguided. Our work starts by pointing that such a large increase in debt needs to be reconciled with a rather contradictory fact: that what the U.S. economy pays on its net foreign position seems to have been surprisingly constant in spite of the measured increase in net foreign liabilities. (1) Paraphrasing Bill Cline (2005) we asked in our work if it made sense to call a country that makes money on its net foreign position a debtor. The question we raised in these studies was whether there were hidden assets or services (whose size had increased steadily over recent decades) provided by the U.S. economy, explaining why the net income flow had remained stable in spite of the increase in measured debt. In that work we called these assets "dark matter" and provided evidence for their existence.
In their article, "Borrowing without Debt? Understanding the U.S. International Investment Position" (this issue), Mathew Higgins, Thomas Klitgaard, and Cedric Tille (HKT hence), acknowledge the existence of these intangibles, but argue that dark matter is unable to account for the difference between the stock and flow data, that the methodology for computing it is doubtful, and that it has no substantive implications for the future evolution of U.S. imbalances. Naturally, we believe these claims to be incorrect. After a year of work by us and a number of other scholars, there is growing evidence, both at the micro and macro level on the existence of significant amount of dark matter. (2) Furthermore, we believe that thinking in terms of dark matter radically changes the way in which we evaluate the future evolution of U.S. and global imbalances. To discuss why we believe that dark matter is a sound and meaningful concept--and therefore disagree with HKT--is the objective of this brief paper.
What is dark matter?
Before addressing HKT's concerns let us first briefly clarify the meaning of dark matter. As mentioned above, our motivating fact is that net income from foreign assets seems to be poorly accounted by the change in foreign assets obtained from accumulating the current account or from direct measures of the stock of net foreign assets that some countries estimate. Thus, we propose an alternative way of measuring the current account, one that starts by defining net foreign assets of the country (NFA) as the capitalized value of the net investment income (NII), discounted at a constant rate of interest (r):
(1) [NFA.sub.t.sup.DM] = [NII.sub.t]/r
The inclusion of dark matter is indicated by the superscript DM. Our use of the concept of dark matter corresponds to that used in physics to account for the fact that the universe is more stable than you would think if it were held together only by the gravity emanating from visible matter. In the same way that physicists infer matter in the universe from its gravitational pull (but not from adding up the visible matter), we infer the assets from their returns and not from adding the current account imbalances. As a result, countries with net investment income larger than what is presumed on the basis of their asset base will have dark matter assets, while countries for which the net investment income is too low will have dark matter liabilities.
Choosing to value the assets on the basis of their returns is just like valuing a company by calculating its earnings and multiplying by some price-earnings ratio, or valuing a property based on its rental value. We know from the corporate finance literature that for an individual company the earnings of any given year may give an unreliable measure of its true earning potential, but if we average over an economy and look at trends over a couple of years, this simple methodology delivers reasonable results. Of course, this opens many methodological questions but we refer the reader to Hausmann and Sturzenegger (2006a, 2006b) for further discussion. (3)
With this measure of net foreign assets, we define the current account simply as the change in the stock of net foreign assets, i.e.:
(2) [CA.sub.t] = [NFA.sub.t.sup.DM] - [NFA.sub.t-1.sup.DM] = [[NII.sub.t] - [NII.sub.t-1]]/r.
We can further understand the sources of the stock of dark matter (DM) by noticing that:
(3) DM = [NFA.sub.t.sup.DM] - [NFA.sub.t] = [[NII.sub.t]/r] - [NFA.sub.t]
= [[[~.r]([NFA.sub.t] + [[mu].sub.t])]/r] - [NFA.sub.t] = [[~.r]/r][[mu].sub.t] + [([~.r] - r)/r][NFA.sub.t]
where NFA stands for the official measure of net foreign assets. In this expression we allow for assets to be mismeasured, with [mu] indicating that error in measurement. In addition, we assume assets yield a rate of return [~.r] different from the constant rate used for discounting. The two terms in the last expression of equation (3) allow visualizing that dark matter may have two origins: the capitalized return to unaccounted assets and return "privileges". These privileges may arise because assets abroad earn a higher rate of return or because liabilities at home pay a lower rate. We agree with HKT that it is irrelevant from the perspective of net income to say that the asset base is larger (say, because, assets are mismeasured) and earns a lower yield, or that the asset base is smaller and earns a higher return. In our original work we distinguish the two channels because the underlying economics are different. Thus, although it is useful to useful identify the two channels separately, to study the relevance of dark matter we can assume [mu]=0, associating all the effect to the yield differentials. If so equation (3) becomes:
(4) DM = [([~.r] - r)/r][NFA.sub.t]
Equation (4) gives the capitalized value of the return differential relative to a given benchmark rate. Once a discount rate is chosen we can easily compute this measure for any country in the world. Figure 1 shows the stock of dark matter assets for the United States when a five percent discount rate is used. It has been growing pretty steadily, accelerating towards the end of the period. On average the increase in dark matter assets has averaged 2.4 percent of GDP per year since 1982, but close to five percent of GDP in recent years.
Equation (4) states that dark matter originates in "return privileges", that is, higher relative return for assets than for liabilities. We argue that there are at least three main factors that explain a persistent return differential between assets and liabilities: a return differential for FDI investments, the sale of insurance, and the provision of liquidity services.
The first factor involves the notion that FDI investments abroad are a vehicle for the dissemination of intellectual property such as ideas, blueprints, and knowledge, and that they are the vehicle for unaccounted exports of services produced by headquarters and used by affiliates around the world. FDI investors purchase assets in order to invest, but also bring with them a blueprint, a product, and a business know-how that is usually poorly accounted for. Because of the difficulties in tracking the trade of these services across national borders, it is likely that numbers underestimate both the net worth of the companies or the exports of services of the source countries that are then used by foreign affiliates to generate income, all of which show up as a larger yield for these assets (See Higgins, Klitgaard and Tille, 2005). The second factor may arise because the underlying stability of a given economy may allow some economies to sell some of this stability to the rest of world, and to do so they will charge risk premia and earn a steady flow for these "insurance" services. The third factor is related to the provision of liquidity services, either directly through the use the domestic currency abroad, or because assets with deep markets earn a liquidity premium. In Hausmann and Sturzenegger (2006b), we use a cross section of countries and discuss related literature providing evidence for all of these factors.
By capitalizing the income from these return differentials we are redefining the stock of assets in a way that more explicitly shows the value of underlying capital and services, regardless of whether they are included in official statistics. In other words, capitalizing these steady return differentials allows including in the asset estimates the advantage or disadvantage reflected in the differences in the rates of return, thus providing a more coherent picture of actual global imbalances. As we will show below, assimilating the return differential to an "asset" is tantamount to assuming that this differential will persist in the future. Herein lies the main difference when looking at global imbalances from the perspective of dark matter.
The critique
HKT cast doubt on our valuation procedure by using a simple argument. Accept for a moment that it makes sense to discount the investment income by, say, a constant discount rate and specifically by the five percent rate used in HS. If this is correct, one could apply the valuation procedure not only to the net return but also separately to the income obtained from assets and liabilities. However, when doing so with U.S. data, HKT find that some assets and liabilities are undervalued relative to official numbers. They argue this indicates there is "dark antimatter" rather than "dark matter" in these assets and liabilities, and only because there is larger "dark antimatter" in liabilities does the United States appear as having dark matter assets. They claim this is evidence against the existence of dark matter in U.S. assets.
We believe this misses the point. The underlying framework we use is simply to claim that there has to be a reason why assets deliver ex post different rate of returns (we suggested risk premia, know-how, and liquidity as potential conceptual explanations). We define dark matter for each asset as the capitalized value of the deviations in returns from a benchmark rate, which measures the "return" to these hidden attributes (productivity, risk, or liquidity). For example, the capitalized value of the risk premia of a stock return will be its dark matter, and the liquidity discount on a financial instrument is another source of dark matter.
Thus valued, assets and liabilities may contain positive or negative amounts of dark matter. Assets will contain positive dark matter if their return is larger than a benchmark interest rate. For reasonable rates there is positive dark matter in U.S. FDI assets, but not necessarily so for other assets. Liabilities contain dark matter if their return is below the benchmark. In the case of the United States, this is particularly relevant for debt, which pays low returns and has liquidity advantages. In fact, finding that these assets are worth less than market value is equivalent to confirming the existence of dark matter in liabilities, not the other way around.
HKT associate dark matter to know-how assets, and thus look for it only within U.S. assets, but this misses one of the key sources of dark matter for the United States--the fact that insurance and liquidity considerations allow it to pay much lower rates on its liabilities. Gourinchas and Rey (2006) find it is in debt instruments where the United States commands the highest gross return differential. This turns out to be a critical source of dark matter for the United States, though not unique to it. Kugler and Weder (2004, 2005) show that Switzerland benefits from similar if not larger benefits.
Of course it may be asked whether our measure provides an alternative to market values. We think it does not. But our point remains that it is useful to take into account systematic return differentials when analyzing global imbalances because it is feasible that these assets will be delivering steady return differentials in that future that will be relevant to assess vulnerabilities. By focusing on market values to assess asset positions this feature is totally missed. (4)
Why does it matter?
Having clarified that finding a lower value of U.S. liabilities does not only not pose any problem with the procedure used, but on the contrary is at the core of the argument, we tackle now the question of explaining why we believe that dark matter provides an alternative vantage point for understanding current account imbalances.
To illustrate this, let us use a simple example that roughly relates to the current U.S. net asset position. Imagine a country with foreign assets to GDP of 100 percent and foreign liabilities to GDP of 125 percent. Just for the sake of the argument, imagine that assets yield a 6.25 percent return while liabilities pay five percent, thus yielding a balanced income flow in spite of measured net foreign assets implying net liabilities of 25 percent of GDP.
There are two ways to interpret this result. The conventional way is to say that in this country assets yield a relatively higher rate of return that compensates for the higher liabilities. The dark matter interpretation, on the other hand, would describe this by stressing that the interest differential reflects underlying fundamentals and therefore should be interpreted as the return to an "unobservable" asset. In this example, assets yield 1.25 percent more than liabilities, so there are implicit assets equal to 25 percent of GDP (1.25/.05 to stick to our five percent rate). Of course the returns or the discount factor can be changed, but the underlying story would be the same.
What is the difference between stating that the United States earns a return differential on its assets and liabilities, or that it holds unmeasured assets in an amount equivalent to the capitalized value of the return differentials relative to a benchmark rate? We believe there are basically two differences.
The first is that by assigning asset-type characteristics to these return differentials, we are implicitly assuming that this return differential will persist going forward--i.e., the null hypothesis becomes that the underlying stock of assets and liabilities will continue to deliver such return differentials in the future. Notice that in the traditional interpretation, the null hypothesis is that this will not happen, so that an "explanation" needs to be given every period why the assets are not inducing a commensurate net income flow. (5)
But what evidence is there that these returns are relatively stable? In the case of the United States the evidence is fairly compelling. Figure 2, shows the return differentials computed for assets and liabilities from official U.S. data. It seems that the null hypothesis that these returns will continue to deliver a return differential, at least in the case of the United States, appears perfectly reasonable.
The second reason for the difference is that the value of the unobservable assets may be growing over time. Tracking the stock of dark matter over time is a way of estimating if this is indeed happening. Figure 1 depicted the evolution of the value of these assets for the United States, in fact showing a growing stock of dark matter. This increasing stock of dark matter is probably the combination of a fairly constant yield differential, shown in Figure 2, combined with increased leverage of this differential as gross asset positions increased hand-in-hand with an increasingly intense process of financial globalization.
So when predicting the evolution of U.S. current account imbalances in the future, should the analyses ignore the fact that the United States will continue to master a return differential and that it may be able accumulate dark matter assets? If there is evidence over the last 25 years that it has accumulated dark matter assets at the tune of 2.4 percent per year (and close to five percent over the last five years), doesn't it make sense to extrapolate this trend forward?
Analysts can have their own view on whether the U.S. economy will be able to continue exporting dark matter (i.e. of sustaining a return privilege on its net foreign assets). Our work provides some historical facts that may become guidance as to what to expect for the future. Short as it is, the data for the last 25 years suggest that it may make sense to assume that these increases in the stock of dark matter will persist into the future. In fact, as the world becomes increasingly globalized, it is likely that some of the sources of dark matter may be bound to increase. If so, the deterioration of net income will be significantly slower than what official numbers anticipate.
In the end it boils down to the difference between evaluating the future prospect for a country with net foreign debt of about 25 percent of GDP and running a current account deficit of six percent of GDP with that of a country that has no net foreign liabilities and runs a current account of between one and 3.5 percent of GDP (6). The difference between those two scenarios provides the scope for understanding the relevance of the dark matter approach to interpreting future U.S. and global imbalances.
At a minimum, the dark matter hypothesis focuses the question of the U.S. current account imbalances on the underlying motives for the return differentials. Rather than concentrating on savings behavior, the analysis suggests that it is equally important to evaluate whether the United States will continue to be a safe haven for investments, run a stable and attractive currency, and have the most innovative universities and firms. These issues have been largely absent from the debate on U.S. current account imbalances, but our approach focuses squarely on them.
REFERENCES
Buiter, Willem. 2006. "Dark Matter or Cold Fusion?" Goldman Sachs, Global Economics Paper No. 136.
Caballero, R., E. Farhi, and P. O. Gourinchas. 2005. "An Equilibrium Model of 'Global Imbalances' and Low Interest Rates." Mimeo, MIT. September.
Campbell, John, Karine Serfaty-de Medeiros, and Luis Viceira. 2006. "Global Currency Hedging." Mimeo, Harvard University.
Chari, Anusha and Linda Tesar. 2006. "The Market's Response to Developed-Market Acquisitions in Emerging Markets," Mimeo, University of Michigan.
Cline, W. 2005. The United States as a Debtor Nation. Institute for International Economics.
Gourinchas P.O. and H. Rey. 2006. "From World Banker to World Venture Capitalist: U.S. External Adjustment and the Exorbitant Privilege," in Clarida, R.H. (Ed.). G-7 Current Account Imbalances: Sustainability and Adjustment. Chicago IL: University of Chicago Press.
Hausmann, Ricardo and Federico Sturzenegger. 2005a. "Dark Matter Makes the U.S. Deficit Disappear." Financial Times. December 8, p. A15.
Hausmann, Ricardo and Federico Sturzenegger. 2006a. "Why the U.S. Current Account is Sustainable." International Finance. 9:2, pp. 223-240.
Hausmann, Ricardo and Federico Sturzenegger. 2006b. "U.S. and Global Imbalances: Can Dark Matter Prevent a Big Bang?" Working paper, Kennedy School of Government. November.
Higgins, Mathew, Thomas Klitgaard, and Cedric Tille. 2005. "The Income Implications of Rising U.S. International Liabilities." Current Issues in Economics and Finance, Federal Reserve Bank of New York. 11:12.
Higgins, Matthew, Thomas Klitgaard and Credic Tille. 2007. "Borrowing Without Debt? Understanding the U.S. International Investment Position." Business Economics. January.
Kugler, P. and B. Weder. 2004. "International Portfolio Holdings and Swiss Franc Returns." Mime, University of Mainz.
Kugler, P. and B. Weder. 2005. "Why are Returns on Swiss Franc Assets so Low? Rare Events May Solve the Puzzle." Applied Economics Quarterly. 51:3, pp. 231-246.
Landefeld S. and A. Lawson. 1991. "Valuation of the U.S. Net International Investment Position." Survey of Current Business. May, pp. 40-49.
Meissner, C. and A. Taylor. 2006. "Losing our Marbles in the New Century? The Great Rebalancing in Historical Perspective." Mimeo, London School of Economics.
Mendoza, Enrique, Vincenzo Quadrini, and Jose Victor Rios-Rull. 2006. "Financial Integration, Financial Deepness and Global Imbalances." Mimeo, University of Maryland.
Ulan, M. and W. Dewald. 1989 "The U.S. Net International Investment Position: Misstated and Misunderstood." in J. Dorn and W. Niskanen (Eds.) Dollars, Deficits and Trade. Kluwer Academic Publishers.
Ricardo Hausmann is director of Harvard's Center for International Development and professor of the Practice of Economic Development at the Kennedy School of Government. Previously, he was chief economist of the Inter-American Development Bank, Minister of Planning of Venezuela, and a member of the Board of the Central Bank of Venezuela. He was the chair of the IMF-World Bank Development Committee and economics professor at the Instituto de Estudios Superiores de Administracion (IESA) in Caracas. He holds a PhD in economics from Cornell University.
Federico Sturzenegger is a visiting professor of public policy at the Kennedy School of Government of Harvard University and a professor at Universidad Torcuato Di Tella in Argentina. He has held positions as an assistant professor of economics at UCLA, chief economist of YPF S.A., Dean of the Business School at Universidad Torcuato Di Tella, and Secretary of Economic Policy of the Republic of Argentina. He is a consultant to corporations and international organizations. He holds a Ph.D. in Economics from MIT. In 2005, the World Economic Forum of Davos selected him as one of its Young Global Leaders.
(1) In Hausmann and Sturzenegger (2006b), we show the United States is an outlier, since in most other countries there is a reasonably good link between current account imbalances and changes in net investment income.
(2) In Hausmann and Sturzenegger (2006b), we provide cross-country evidence on the existence of dark matter, but other authors have provided alternative empirical estimates. Meissner and Taylor (2006) present evidence at the macro-historical level. Buiter (2006) provides an estimate for liquidity dark matter. At the micro level Chari and Tesar (2006) provide evidence of dark matter associated with firm takeovers in emerging countries. Campbell et al. (2006) provide a justification for insurance-based dark matter. Theoretical justifications for some other channels are provided in Caballero et al. (2006) and in Mendoza et al. (2006).
(3) This way of computing net foreign assests has been suggested by Cline (2005) and previously by Ulan and Dewald (1989). It was discussed by U.S. government officials, but the Bureau of Economic Analysis eventually discarded it due to the difficulties associated with choosing a discount rate. (See Landefeld and Lawson, 1991)
(4) The exact amount of dark matter is arbitrary, because it depends on the arbitrarily chosen discount rate. If the chosen rate increases, we will find less dark matter in assets and more of it in liabilities. If the chosen rate decreases, we will find more of it in assets and less in liabilities. The net effect, while less sensitive, will also depend on the discount rate used (as an extreme example if we choose the evidently unreasonable low rate of 0.1 percent as a discount factor, we would describe the United States as having net liabilities of seven trillion U.S. dollars, way above its current value, resulting from an asset valuation of 585 trillion and liabilities of 592 trillion--i.e., measuring both assets and liabilities at close to 60 times their market value, though all earning the paltry 0.1 percent return). While describing the data this way would deliver virtually the same message, we believe choosing a reasonable rate of return, close to risk-free rates, provides a more intuitive interpretation.
(5) HKT spend a great deal of their paper explaining "measured" valuation effects that explain why the net foreign asset position has not deteriorated hand-in-hand with the current account. Notice, however, that our valuation effects are larger, even than those described by HKT, as our measurement of net foreign assets is significantly larger than BEA's measurement.
(6) If the U.S. increases it's dark matter assets at 2.5 percent of GDP per year, running a deficit of 6 percent of GDP per year, entails a reduction in its net investment income of .17 percent of GDP per year (assuming an average payment rate of 5 percent), a number that seems a long stretch from being a cause for concern.