Draft: The Trilemma and Long Run Financial Adjustment

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1 Draft: The Trilemma and Long Run Financial Adjustment William Swanson September 13, 2016 Abstract Rich and poor countries have aggregate portfolios that are starkly different. First, Net Foreign Assets in the world are increasingly long in foreign currency denominated assets and exposed to currency appreciations. Second, most large developed countries are investing less in safe foreign exchange reserves, and choosing portfolios that are higher risk and higher return. These two mechanisms will make the strategy of hoarding reserves more effective in depreciating the exchange rate. Why? This should arise from the return and valuation flows of Net Foreign Asset positions. More foreign currency denominated assets implies more valuation effects that works toward stabilizing the exchange rate, e.g. a first order spike in the exchange rate is mitigated by a second order depreciation of foreign assets. Relatively lower returns on these foreign assets will fortify the second order response. Reserves can then act almost like capital controls but their effectives will depend on the currency composition. In this preliminary paper, I demonstrate this mechanism using a simple two-country (and three country) portfolio balance model. Then I test the theoretical predictions using data on currency composition of Net Foreign Assets. Significance and Literature: Since the 1990s, a number of emerging economies have experienced rapid growth and accumulated large foreign exchange reserves. 1 The literature offers two general explanations to connect the rapid growth in output and reserves. First, the foreign exchange reserves are accumulated for mercantilist reasons, in particular to depreciate the exchange rate and shift demand to domestic exports (see Rodrik (2009) or Benigno et al. (2012)). Second, this trend might arise from a precautionary savings motive. The same countries with large reserves also experience extreme capital flows, high volumes of trade and arguably higher consumption risk. The government accumulates reserves to ensure liquidity and solvency when times are 1 China, for example, has accumulated almost 3 Trillion U.S. Dollars worth in reserves, or almost 50% of its GDP, while experiencing 8% growth on average through

2 bad (see Mendoza et al. (2007, 2010) ). Neither of these literatures, however, can easily account for the unprecedented accumulation of reserves in East Asia. A smaller literature, dating back to Krugman (1979) with recent contributions by Blanchard et al. (2005), proposes that reserves are useful when monetary policy is constrained, or the current account is too volatile. The reasoning is that foreign exchange reserves will smooth supply and demand fluctuations for domestic assets when a country has an open capital account. Using sterilized interventions, the central bank absorbs capital inflows and outflows as effectively as if the country had capital controls. This is a variant of the Portfolio Balance Effect, on which there is a long history of empirical papers debating both ways about its existence in the data. (see Rogoff (1980) or Fatum (2015) ). Reserves can then act as a fourth policy alternative to the three traditional ones of the Trilemma making for a Quadrilemma in which a country must choose some combination of monetary policy autonomy, stable exchange rates, freely flowing capital or reserve accumulation. The literature in this field is growing, with notable contributions by Aizenman et al. (2010), Shambaugh (2004), and Aizenman (2011). The reserve accumulation channel seems to operate in the short run, or as long as the Central Bank has exchange reserves or domestic assets to invest. Steiner (2015) shows that, indeed, sterilized interventions can substitute for capital controls which allows countries to relax the constraints of Mundells Trilemma. In the long run, however, an attempt to maintain a pegged exchange rate without capital controls will be overcome by the countries inter-temporal budget constraint, and the exchange rate must be allowed to float or appreciate. For example if the exchange rate is pegged too low, increasing wealth from a trade surplus puts upwards pressure on the exchange rate, forcing the Central Bank to sell domestic bonds. Eventually the process stops when the central bank holds all of its assets in the form of foreign reserves and the exchange rate is allowed to appreciate. 2 2 Steiner (2015) refers to India, at this point, and points out that even this is not a forever binding constraint. In 2007, India was sterilizing international reserve purchases and the Central Bank had negative net domestic assets, so that it was a net debtor with the Indian treasury. 2

3 Rich and poor countries have aggregate portfolios that are starkly different, and these differences increase the effectiveness of reserves in developing countries for manipulating the exchange rate. This is happening for two reasons. First, average NFA for the world is increasingly long in foreign currency denominated assets and exposed to currency appreciations. Table 2 and Figure 1 in the Appendix shows that this is true for the world on average. Currency depreciations on average will incur a valuation effect that works against that same depreciation in the long run. And the same holds for currency appreciations. For example, a U.S. dollar appreciation will incur a negative valuation effect that reduces U.S. wealth and puts downwards pressure on the U.S. dollar. Second, as Gourinchas and Rey (2005) observe, most large developed countries are investing less in safe foreign exchange reserves, and choosing portfolios that are higher risk and higher return. For a poor country with safe investments, low NFA returns will lessen the upwards pressure on the exchange rate. This is compounded by the portfolio compositions of rich countries. As the U.S. earns higher returns on Foreign assets, the relative returns for the poor countries decrease, again dulling the upwards pressure on the poor countries exchange rate. This mechanism has some theoretical support in Quadrini (2015), who argues that much of the buildup of leverage before the 2008 financial crisis may have come from the complementarity between low return investments in developing countries, and high return investment in developed countries. Both the return effect and valuations effects have strengthened since the 1990s. I expect that overtime sterilized interventions will be more effective at manipulating the exchange rate, and therefore, reserves will be increasingly used in the policy mix for developing countries. In the full paper 3, I use the general portfolio balance model first proposed by Blanchard (2005) and later adapted by Steiner (2015) to include central banks interventions. To test my predictions empirically, I construct Trilemma indexes following Aizenman et al. (2009, 2013), but I control for valuation and return effects, and I test for changes in the Trilemma coefficients over time. My empirical model that 3 Available here: 3

4 controls for these effects shows a marked improvement in fit over that of Steiner (2015). 1 Two Country Model I develop an extended version of the model presented in Steiner (2015). The world has two countries, each with wealth W it, that is equal to difference between total assets X i and net debt in that period, F it. Since world net debt sums to zero, F 1t +F 2t = 0, I refer to all debt in terms of country 1 s debt position. I keep debt in terms of country 1 s consumption good, while assets are denominated in the domestic consumption good. The exchange rate, E t, is the price of country 2 s product per unit of country 1 s consumption good, so that an increase in E t is an appreciation of the currency. As in Steiner (2015), I assume that X i is fixed for each country, but F it, W it, and E t can vary over time at discrete intervals. Each country has wealth W 1t = X 1 F it (1) W 2t = X 2 E + F t (2) and can invest share α ij of wealth in country j, so that total assets of Country 1 are X 1 = W 1t α 11 + W 2t E t α 21 (3) and the shares belonging to each country, α ij for i sum to 1. I assume that interest rates, R i = 1 + r i, are set exogenously and are constant through time so that portfolio shares α ij are constant as well. To keep things simple, I track everything in terms of country 1 s debt. Following the standard Portfolio Balance Model, debt evolves according to ( W 2t F t+1 = α 21 R 1 α 12 W 1 1 de ) t R 2 NX(E t ) (4) E t E t A symmetric equations holds for the debt of country 2. I introduce a central bank into 4

5 Country 2 that manipulates the exchange rate relative to Country 1. Here I follow Steiner (2015) closely in defining the balance sheet of the central bank. Country 2 has a central bank with holdings X cb that it splits between domestic bonds B t, and international reserves, IR t. Country 2 invests (1 α cb ) X cb into B, and α cb X cb into IR t. Country 2 still has a private sector that invests α pr X pr of private sectors assets abroad into Country 1. To restate this: IR t = α cb X cb, and B t = (1 α cb ) X cb. Combining positions together we arrive at total Country 2 assets, X 2. X cb = B t + IR t E t (5) X 2 = X cb + X pr (6) All of this together implies that α 21 is a weighted average of the Foreign investment components of the private and public sectors. If I define ω = α pr (X pr E t F 2t ) /W 2, then I can write α 21 as ωα pr + (1 ω) α cb. With these equations in hand, and taking the limit to zero with respect to time, I totally differentiate equation 3, and substitute in Equations 1, 2, 6 and 5. Rearranging for the change in Country 2 s exchange rate, I arrive at de t = (α 11 α pr ) E t df t + X cb dα cb α pr X pr /E t + α cb X cb /E t I use my assumption that the exchange rate is fixed, so that de t = 0. Again rearranging I find an expression for the necessary shift in α cb to maintain exchange rates at their value. The necessary change in α cb will be, dα cb = df 1 E t X cb (α pr α 11 ) (7) For simplicity I assume that all central bank purchases of foreign reserves are completely 5

6 sterilized, so that dir = α pr X cb. Using this in Equation 7, I obtain 4 dir = df 1 (α 11 α pr ) (9) This can be re-written as a simple function of time so that dir t = ABe tγ (10) where A = α 11 α pr, the term B = α 11 (r 1 r 2 ) X 1 NX(E t ), and γ = r 2 + α 11 (r 1 r 2 ). Figure 9 shows the evolution of foreign exchange reserves over time necessary to maintain the exchange rate fixed (i.e. the blue and orange lines). When there home bias in asset holdings, such that α 11 + α 22 > 0.5 reserves will be increasing without bound over time. However, three are two distinct scenarios. When the degree of home bias in country 2 is relatively high (i.e. α pr = 0.1), required reserves are large. When home bias decreases (i.e. α pr = 0.2), the rate and level of required reserve increases is decreasing as well. Therefore, reserves will increase, but at a lower rate. The other parameters of the model are included in Table?? in the Appendix. [DESCRIBE NET EXPORT ASSUMPTIONS] 2 Three Country Model I extend the model in Steiner (2015) to three countries to show that required changes in reserves to maintain a fixed exchange rate are even less strict in a more generalized framework. With three countries, the algebra is more extensive and the details are in the Appendix, however I will explain the key mechanism using general equations. Suppose that Country 2, which as before, pegs its exchange rate to consumption 4 Looking at a re-arranged expression for net debt, it is more clear how I arrived at this expression. df 1 = ((1 α 11 )(r 1 r 2 )X 1 NX(E t )) + F 1 (r 2 + α 11 (r 1 r 2 )) (8) 6

7 good of Country 1. Then similar to before, if there is some force that puts upwards pressure on the exchange rate, perhaps through additional foreign earnings (e.g. an increase in α pr ), then E 2 will increase. However, as shown in the appendix, for most parameter values, exchange rates are negatively related, so that an increase in E 2 will depreciate E 3. de 3t = de 2t K 2 (11) The net effect on F 1,t+1 will depend on the portfolio shares of country 1, 2, and 3. For example, for Country 1, with downward pressure on E 3 and large α 13, F 1,t+1 will tend to decrease. However, with large values for α 12, the df 1t will tend to increase. [ W 2t F 1,t+1 = α 21 ] W 3t R 1 + α 31 R 1 E 2t E 3t ( [α 13 W 1t 1 de 3t E 3t ) R 3 + α 12 W 1t ( 1 de 2t E 2t ) R 2 ] + NX(E 2t, E 3t ) (12) In the end, the pressure on df 1t will determine the size of the necessary change in reserves to maintain the exchange rate. Below, K 3 is a positive constant for most parameter values, and E 2 is assumed to always be constant. dir t = df 1t E 2t K 3 (13) Therefore, as country 1 invest more heavily country 3, country 2 does not need to invest as much in reserves to maintain a pegged exchange rate in the face pressure to appreciate. 2.1 Data This sections explains the calculations and sources for the variables used in the Trilemma test in Table 3. Variable: PORT In the simple two country model, (α 11 α pr ) can vary between 1 and 1. The reserves required to maintain a fixed exchange rate will be decreasing in 7

8 α pr, and increasing in α 11. According to the 2-country model, the buildup of reserves will be equal to zero when α 11 = α pr = 1/2. Reserves will increase without bound as α 11 reaches 1. I define a simple index, P ORT t, to include in the regressions. It is scaled so that it lies between 0 and 1. The variable is defined as the scaled difference between (1) foreign assets of country i denominated in the currency of the base country j (2) and the foreign assets denominated in the domestic currency of the base country j. Base countries are identified according to the Shambaugh (2010) classification. P ORT t,ij = 1 + α pr,ij α jj,t 2 Variable: dnfa For robustness I include the measure in Steiner (2015). This measure is defined as the change in international reserves divided by the change in net foreign assets (from Lane et al. (2007)), constrained to lie between 0 and 1. {{ } } IRit dnf A t = min, 0, 1 NF A it Variable: MI, ERS and KAOPEN These variables are borrowed from Aizenman (2010) and updated to 2015 by Hiro Ito.[EXPLAIN CALCULATIONS]. Regression The basic test of the Trilemma is the regression of the three traditional policy indexes against 1. 1 = αers it + βmi it + γkaop EN it The Figures 2 and 3 show the predicted dependent variables from the in sample indexes. In Table 3, I present the results of this regression and augmented regressions that include variables dnfa and PORT. 3 Conclusion [DISCUSSION AND CONCLUSION] 8

9 4 Appendix 4.1 Figures: Data Figure 1: Home Currency Bias in Net Foreign Assets (a) Data from Aizenman et al (2010) and the updated data set to that paper available through Hiro Ito s website (2015). 9

10 Figure 2: Trilemma Through Time (a) Data from Aizenman (2010) and Hiro Ito s website, International Financial Statistics (used in creating dnfa), Shambaugh (2010) was used for defining the base currency. Figure 3: Trilemma Through Time (a) Data from Lane et al. (2007), Aizenman (2010) and IMF International Financial Statistics. 10

11 Figure 4: U.S. Net Foreign Assets and Valuation Effects (a) Data from Lane et al. (2007) Figure 5: Home Bias in Total Portfolio Holdings (a) Data principally from the CPIS (Coordinated Portfolio Investment Survey) of the IMF. This data includes total public and private debt securities, foreign exchange reserves and equity portfolio holdings. The World Bank Development Indicators Data Base provided supplemental estimates for domestic assets (via market capitalization and domestic and international holdings of public debt). Authors calculations. 11

12 Figure 6: Reserve Accumulation (a) Central Bank Foreign Exchange Reserves minus Gold. Data from World Bank Development Indicators Data Base and International Financial Statistics. 4.2 Figures: Simulated Figure 7: Changes in Foreign Exchange Reserves (Two Countries) (a) Simulated data, authors calculations. 12

13 Figure 8: Changes in Foreign Exchange Reserves (Three Countries) (a) Simulated data, authors calculations. Figure 9: Changes in Foreign Exchange Reserves (Three Countries) (a) Simulated data, authors calculations. 13

14 Figure 10: Wealth of Country 1 and 2 (Three Country Model) (a) High Foreign Investment, i.e. high α 13. Country 1 = Home and Country 2 = Foreign. Simulated data, authors calculations. (b) Figure 11: Wealth of Country 1 and 2 (Three Country Model) (a) Low Foreign Investment, i.e. low α 13. Simulated data, authors calculations. 14

15 Figure 12: Stream Diagrams for F 1t vs. F 2t (a) High Foreign Investment, i.e. high α 13. Simulated data, authors calculations. Notice that the model is converging to a solution. (b) Low Foreign Investment, i.e. low α 13. Simulated data, authors calculations. Notice that the model is diverging from a solution. 4.3 Calibration for Figures The parameters used in Figures 9 were chosen because they resemble a stylized version of the real world, where the U.S. may be Country 1, and Country 2 may be seen as a developing country. 15

16 Table 1: Parameters Used NX -.2 X pr.8 X cb.2 X 1 = X 2 1 R 1 = R E 1 α cb 0.9 α α pr 0.1 [INCLUDE CALIBRATION FIGURES FOR THREE COUNTRY MODEL] 4.4 Tables Table 2: Foreign Assets and Liabilities in Foreign Currency United States Developed Developing Assets Liabilities Assets Liabilities Assets Liabilities % 16% 89% 66% 100% 81% % 16% 63% 32% 100% 41% Difference 16% 0% -26% -34% 0% -40% 16

17 Table 3: Preliminary Results (1) (2) (3) ERS (0.022) (0.022) (0.016) MI (0.026) (0.026) (0.025) KAOPEN (0.018) (0.018) (0.013) dnfa (0.013) PORT (0.027) Observations 1,168 1,168 1,168 R Adjusted R Note: p<0.1; p<0.05; p<0.01 Table 4: Correlation Table ERS MI KAOPEN PORT dnfa ERS MI KAOPEN PORT dnfa

18 5 Three Country Model I extend the model in Steiner (2015) to three countries to show that required changes in reserves to maintain a fixed exchange rate are even less strict in a more generalized framework. With three countries, each country has wealth W 1t = X 1 F 1t (14) W 2t = X 2 E 2t F 2t (15) W 3t = X 3 E 3t + F 1t + F 2t (16) where, as before, X it are fixed while wealth W it and debt F it are permitted to vary over discrete time intervals. I will assume that total global wealth is fixed at 1, i W it = 1, which implies that i X i = 1. Again, debt sums to zero, F 1t + F 2t + F 3t = 0, and each country i invests share α ij of wealth in country j, so that total assets of Country 1 are X 1 = W 1t α 11 + W 2t E 2t α 21 + W 3t E 2t α 31 (17) Net debt evolves over time according to a similar equation to Equation 4 for the two country model [ W 2t F 1,t+1 = α 21 ] W 3t R 1 + α 31 R 1 E 2t E 3t ( [α 13 W 1t 1 de 3t E 3t ) R 3 + α 12 W 1t ( 1 de 2t E 2t ) R 2 ] + NX(E 2t, E 3t ) (18) With another similar equation for the evolution of debt for country 2, I repeat the process for the two country model and solve for dir t in terms of the changes in debt in country 1. dir t = df 1 t E 2t K 3 (19) 18

19 where K 3 is a constant defined as ( ) α23 α 31 + α 13 (α pr α 31 ) α 33 α pr K 3 = α 11 + α 33 α 23 (20) I can now formulate a dynamic system of two differential equations in df 1t and df 2t. I am able to ignore the dynamics of both exchange rates because of my simplifying assumption, namely, because E 2t is pegged and assets X i do not vary over time, I can show that de 3t = de 2t K 2 (21) where K 2 is a constant when E 2t and assets X i are fixed. The constant K 2 will generally positive and equal to ( ) X3 (E 2t E 2t X 1 X 2 ) E 2 (1 X 1 ) K 2 = (E 2t E 2t X 1 X 2 ) 2 (22) with this in hand, the dynamic system for debt will be df 1t = A C df 2t B F 1t + E D F F 2t Where each of the terms in the expression are defined as A = α 31 R 1 + α 13 R 3 + α 12 R 2 1 (23) B = R 1 (α 31 α pr ) (24) C = R 2 (α 32 α 12 ) (25) D = α 32 R 2 + α 23 R 3 + α pr R 1 1 (26) E = R 1σ E 2 + X 3α 31 R 1 E 3 X 1 (α 13 R 3 + α 12 R 2 ) NX t (27) F = α 12 X 1 R 2 α 23R 3 X 2 E 2 σr 1 E 2 + R 2α 32 X 3 E 3 NX t (28) 19

20 References [1] Joshua Aizenman. The impossible trinity from the policy trilemma to the policy quadrilemma [2] Joshua Aizenman, Menzie D Chinn, and Hiro Ito. The emerging global financial architecture: Tracing and evaluating new patterns of the trilemma configuration. Journal of international Money and Finance, 29(4): , [3] Gianluca Benigno and Luca Fornaro. Reserve accumulation, growth and financial crises [4] Olivier Blanchard, Francesco Giavazzi, and Filipa Sa. The us current account and the dollar. Technical report, National Bureau of Economic Research, [5] Rasmus Fatum. Foreign exchange intervention when interest rates are zero: does the portfolio balance channel matter after all? Journal of International Money and Finance, 57: , [6] Paul Krugman. A model of balance-of-payments crises. Journal of money, credit and banking, pages , [7] Philip R Lane and Gian Maria Milesi-Ferretti. The external wealth of nations mark ii: Revised and extended estimates of foreign assets and liabilities, Journal of international Economics, 73(2): , [8] Enrique G Mendoza. Sudden stops, financial crises, and leverage. The American Economic Review, 100(5): , [9] Enrique G Mendoza, Vincenzo Quadrini, and Jose-Victor Rios-Rull. Financial integration, financial deepness and global imbalances. Technical report, National Bureau of Economic Research, [10] Vincenzo Quadrini. The growth of emerging economies and global macroeconomic stability. Technical report, Working Paper, [11] Dani Rodrik. Growth after the crisis [12] Kenneth Rogoff. On the effects of sterilized intervention: An analysis of weekly data. journal of Monetary Economics, 14(2): , [13] Jay C Shambaugh. The effect of fixed exchange rates on monetary policy. The Quarterly Journal of Economics, pages ,

Topic 8: Financial Frictions and Shocks Part1: Asset holding developments

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