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Essays on interest rate determination in open economies

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Essays on interest rate determination in open economies

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Content ESSAYS ON INTEREST RATE DETERMINATION IN OPEN ECONOMIES by Jesus Antolin Sierra-Jimenez A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (BUSINESS ADMINISTRATION) August 2009 Copyright 2009 Jesus Antolin Sierra-Jimenez Dedication a el infinito a el venado azul a mi familia a mako ii Acknowledgments I would like to express my gratitude to my dissertation chair, Fernando Zapatero, for all his encouragement, patience and support. I would like to thank Christopher S. Jones, Vincenzo Quadrini and Aris Protopapadakis for helpful discussions, comments, and suggestions on each of the essays. Finally, I also want to thank John H. Cochrane, Herve Roche, Tano Santos and Costas Xiouros for their advice and support. iii Table of Contents Dedication ii Acknowledgments iii List of Tables vi List of Figures vii Abstract ix Chapter 1: Valuation effects 1 1.1 Introduction 1 1.2 The data on foreign Holdings of U.S. Long Term Treasury Securities and Valuation adjustments 3 1.3 The relationship between Unadjusted Net Purchases and yields: a simple bivariate V AR framework 6 1.3.1 Impulse response functions and OLS slope coefficients 9 1.4 Structural V AR Model 13 1.4.1 Results 18 1.4.2 The Bertaut and Tryon (2007) dataset 21 1.5 Conclusion 23 Chapter 2: Financial integration, interest parity and foreign exchange reserves 25 2.1 Introduction 25 2.1.1 Literature review 28 2.2 The Model 31 2.2.1 Households 32 2.2.2 Firms 39 2.2.3 Treasury department 41 2.2.4 Central bank 42 2.2.5 Market clearing conditions 44 2.2.6 Current account dynamics 45 2.3 Solution method and calibration 45 iv 2.3.1 Solution method 45 2.3.2 Calibration 46 2.4 The effects of central bank accumulation of foreign reserves on interest rates 51 2.5 The forward premium anomaly and UIP 63 2.5.1 Brief review of UIP and the forward premium anomaly 63 2.5.2 Model implications for UIP and the forward premium anomaly 66 2.5.3 Sharpe ratios for carry trade strategies 75 2.6 Conclusion 76 Chapter 3: Currency positions and foreign exchange risk premia 78 3.1 Introduction 78 3.1.1 Related Literature 79 3.2 Data description and return definitions 81 3.3 Results 84 3.3.1 Summary statistics 84 3.3.2 Forecasting regressions 84 3.3.3 Robustness tests 94 3.4 Conclusion 103 References 105 Appendices 110 A Appendix to Chapter 1 110 B Appendix to Chapter 2 112 C Appendix to Chapter 3 113 v List of Tables 1.1 Regressions of the 10 year yield on Net Purchases 12 2.1 Benchmark case parameter values 48 2.2 Sharpe ratios of the carry trade strategy: model and data 75 3.1 Summary statistics 82 3.2 Forecasting regressions: level in CME netlong futures contracts 85 3.3 Forecasting regressions: changes in CME netlong futures contracts 86 3.4 Robustness regressions: AUD, 1 month horizon 88 3.5 Robustness regressions: AUD, 3 month horizon 89 3.6 Robustness regressions: CAD, 1 month horizon 91 3.7 Robustness regressions: CAD, 3 month horizon 92 3.8 Robustness regressions: CHF, 1 month horizon 93 3.9 Robustness regressions: CHF, 3 month horizon 94 3.10 Robustness regressions: EUR, 1 month horizon 96 3.11 Robustness regressions: EUR, 3 month horizon 97 3.12 Robustness regressions: GBP, 1 month horizon 98 3.13 Robustness regressions: GBP, 3 month horizon 99 3.14 Robustness regressions: JPY , 1 month horizon 101 3.15 Robustness regressions: JPY , 3 month horizon 102 vi List of Figures 1.1 Impulse Responses in Bivariate V AR under alternative identification assump- tions: 10 year yield and Net Purchases series both in levels 10 1.2 Impulse Responses in Bivariate V AR under alternative identification assump- tions: 10 year yield in levels and Net Purchases series in first differences 13 1.3 Impulse Responses in bivariate V AR under alternative identification assump- tions: first difference of the 10 year yield and levels of Net Purchases 14 1.4 Impulse Responses in bivariate V AR under alternative identification assump- tions: 10 year yield and Net Purchases series both in first differences 15 1.5 Impulse Responses of the 10 year yield to Foreign Holdings shocks in Structural V AR under alternative specifications 20 1.6 Impulse Responses of the 10 year yield to Foreign Holdings shocks in Structural V AR using the Bertaut and Tryon (2007) dataset 22 2.1 Impulse response of foreign interest rate to domestic CB intervention shock: low and high friction. 52 2.2 Impulse response of foreign inflation rates, foreign marginal utility and international relative prices to a home CB intervention shock. 54 2.3 Impulse responses of foreign bond holdings and foreign agent’s budget con- straint components to home CB intervention shock 56 2.4 Impulse responses of the components of home CB balance sheet and home bond market to a home CB intervention shock. 58 2.5 Impulse response of nominal depreciation and interest rate differential to a home CB intervention shock and home Monetary Policy shock. 62 2.6 Term structures of Fama slope coefficients 67 vii 2.7 Impulse response of home and foreign inflation rates and marginal utilities to a home Monetary Policy shock. 69 2.8 Impulse response of home and foreign agent’s budget constraint compo- nents to a home Monetary Policy shock. 71 2.9 Impulse Responses of international relative prices and home bond market components to a home Monetary Policy shock. 74 viii Abstract This thesis examines how government accumulation of foreign exchange reserves affect interest rates in an open economy. In the first essay, I examine this issue from an empirical perspective. I estimate the impulse response of the 10 year Treasury yield to an exogenous innovation in Foreign Official Holdings of U.S. Long Term Treasury securities in an iden- tified V AR model. I find that a market valuation adjustment done to the data is behind a seemingly negative effect of holdings on yields, and that once we control for this adjust- ment, the effect is not negative. Hence, I find no conclusive evidence of a negative effect on U.S. interest rates from foreign official accumulation of treasury bonds. In the second essay, I analyze the same question from a theoretical perspective. I present a two-country dynamic stochastic general equilibrium model in which central banks accumulate reserves and investigate whether the impulse response of one country’s interest rate is significantly negative after an exogenous shock to the other country’s foreign exchange reserve policy. I find that even in a world in which Uncovered Interest Parity (UIP) does not hold, which renders different currency assets imperfect substitutes, the response of the foreign interest rate to a home country reserve accumulation shock is likely to be negative but small in magnitude. In the third essay, I test for evidence on the mechanism used in the second essay to make different currency assets imperfect substitutes. Specifically, I estimate the elasticity of investments in foreign currencies with respect to expected excess returns. I find that currency flows help predict excess returns, and are statistically significant forecasting variables even in the presence of additional control variables. This means that demand for ix different currency assets is less than perfectly elastic, which lends support to the channel proposed in the second essay to introduce deviations from UIP. x Chapter 1 Valuation effects 1.1 Introduction The level of long term interest rates is an important indicator of the financial conditions that prevail in an economy. This is because they influence the spending decisions of eco- nomic agents on areas such as housing, durable goods or investment in capital goods, and ultimately, the level of Aggregate Demand. Recently, the high level of foreign exchange reserves by Oil and commodity exporting countries, as well as some Industrialized coun- tries, has attracted both attention from the financial press and from the academic literature. More specifically, attention has been drawn to the possible impact that purchases of U.S. Long Term Treasury securities might have on their yields; most notably, on one of the most important financial market prices for the U.S. economy, the 10 year yield. It has been suggested that Foreign Central Bank purchases of Long Term Treasuries have been an important factor contributing to the recent “low” level of long term yields. Although there is vast research on this topic 1 , there is still considerable disagreement about the size of the impact, but not on its existence. Most of the available studies focus on the contemporaneous effects of either interventions or changes in Net Purchases on yield changes. Therefore, because of their focus and estimation techniques, these studies are not designed to estimate the dynamic correlation structure between exogenous innovations in 1 Widely cited examples include Warnock and Warnock (2009), Davis (2004), Roubini and Setser (2005), Bernanke, Reinhart, and Sack (2004), Moec and Frey (2005), Gavila and GonzalezMota (2006) among others. EuropeanCentralBank (2006) contains additional cited references, some of them not publicly available. 1 foreign demand and the levels of yields, and most importantly, cannot be used to asses the direction of causality. Indeed, as Roubini and Setser (2005) indicate, these studies estimate a “static effect”. They even suggest that the impact of central bank demand “may not be linear”. Finally, from a modeling point if view, it is precisely this information about impulse responses of yields to exogenous shocks that constitutes an important guideline in the construction of theoretical models 2 of the yield curve. This paper contributes to the line of research that tries to quantify the impact of for- eigner’s accumulation of Long Term U.S. Treasuries on their prices. First, it casts doubt on the interpretation found in earlier studies that attribute a negative slope coefficient in a regression of the 10 year yield on foreigner’s Net Purchases of Long Term Treasury secu- rities as evidence of a negative causation running from Net Purchases to yields. Using a simple identified bivariate V AR framework, a positive impulse response of the 10 year yield to Net Purchases innovations is obtained. But when the slope coefficient in a simple regression of the 10 year yield on Net Purchases is estimated, it has a negative sign, as the available studies find. Second, the paper highlights the fact that the market value adjustment that is done to the data in order to obtain an estimate of the level of foreign Holdings of U.S. Treasuries is likely causing a mechanical negative relationship between innovations in foreign Holdings and the 10 year yield. When a traditional V AR model of the monetary transmission mech- anism 3 is augmented by including Foreign Holdings of Treasuries and the 10 year yield, the impulse response of the 10 year yield to a Holdings shock is negative only when the Holdings variable includes a significant market-value adjustment. When the price Index used to perform the market-value adjustment is also included in the V AR together with the 2 As emphasized in Christiano, Eichembaum, and Evans (1999) . 3 As used in Christiano et al. (1999) or C. L. Evans and Marshall (1998). 2 Adjusted Holdings variable, the negative impulse response disappears: it becomes posi- tive and after 12 months is not statistically different than zero. The same positive impulse response is obtained when the Holdings variable does not include the market-value adjust- ment. The rest of the paper is organized as follows. Section 1.2 discusses the relevant aspects of the data construction and the potential effect of valuation adjustments. Section 1.3 presents impulse responses of the 10 year yield in a simple bivariate V AR of Net Purchases and yields. In section 1.4, the impulse responses are calculated using a structural model of the economy, for different definitions of the Holdings variable, and using the Bertaut and Tryon (2007) dataset. Section 1.5 concludes. 1.2 The data on foreign Holdings of U.S. Long Term Trea- sury Securities and Valuation adjustments An empirical measure of foreign Holdings (or Net Purchases) of US treasuries is needed to investigate whether exogenous changes in foreign demand for treasury securities have a significant effect on yields. The Treasury International Capital System (TIC) of the U.S. Department of the Treasury reports monthly data 4 on Net Foreign Purchases of long-term U.S. Treasury Securities by major foreign sector, and comprehensive security-level Annual benchmark surveys of Foreign Holdings of U.S. Treasury Securities. In principle, these two sources can be combined to obtain a monthly measure of the level of Foreign Holdings of U.S. Treasury securities. However, some of the necessary adjustments that need to be done to this data induce a mechanical negative relationship between the level of foreign holdings and interest rates. 4 Available atwww.treas.gov/tic/ 3 As explained in Warnock and Warnock (2009) 5 , the data on Net Purchases (flows) can be used to construct estimates of Holdings (stock). Using their terminology and nota- tion, we can form “naive” estimates of the level of Holdings in any montht by using the following formula: h t =h t−1 (1+r t )+ gp t (1−tc)− gs t (1+tc) (1.1) where h t is the naive level of holdings estimated at time t; r t is the return on a price index used to adjust the previous level of holdings for changes in the market value of the securities in the portfolio (the valuation adjustment); gp t and gs t are gross-purchases and sales, respectively, of the security in question; andtc is an constant adjustment factor for transaction costs. h t is called a naive estimate simply because nothing in (1.1) ensures that the level of holdings estimated using that formula will equal the figures reported at the benchmark surveys for December 1978, 1984, 1989 and 1994; March 2000; and June of 2002-2006. For example, if we start from the reported benchmark-survey value of foreign Official Holdings of Long Term U.S. Treasuries at the end of March 2000 and apply equation (1.1) using the TIC data on Net Purchases, and the index return, we will obtain a valueh τ that is in general different than the value reported at the benchmark survey, which we denote as bh τ . This difference, gap τ = bh τ −h τ accumulates the effect of reporting errors in the monthly flows estimates. Therefore, in order to make our inter-survey estimates of holdings consistent with the value reported 5 The subsequent discussion of the adjustment that must be made to the “naive” estimates of holdings to obtain “benchmark-consistent” estimates of foreign holdings follows the exposition in the Appendix of Warnock and Warnock (2009) closely. The reader is referred to that paper for a comprehensive explana- tion of the data, the problems with interpreting the reported numbers, and the methodology used to obtain benchmark-consistent holdings. 4 by the survey at the next survey month, we must allocate gap τ in some way across all inter-survey months in order to make it benchmark-consistent. Specifically, a monthly adjustment adj t that depends on the trading volume registered for that month spreads out gap τ across inter-survey months. Then, the adjustment is applied to the calculation of holdings as follows: ˆ h t = ˆ h t−1 (1+r t )+ gp t (1−tc)− gs t (1+tc)+ adj t (1.2) with the obvious boundary condition ˆ h τ = bh τ . ˆ h t is called the benchmark-consistent level of foreign Holdings of Treasury securities, at market value. The specific procedure used in the present paper is exactly that of Warnock and Warnock (2009) and the reader is referred to that study for specific details on the adjustment procedure. The important point for the purposes of this paper, is to note that ˆ h t depends positively onr t , but sincer t is a weighted average of the market prices of T-Notes and T-Bonds, it is inversely related to their yields. It is precisely this necessary feature of the adjustment to the data that can induce a negative relationship between ˆ h t andy (10) t , the 10 year Treasury yield. In the estimations that follow, 2 different foreign holdings series will be used: an Unad- justed foreign Holdings series obtained from (1.2) but setting r t = 0 for all t; and an Adjusted foreign Holdings series also obtained from (1.2) but using for r t the monthly return on the Lehman Brothers U.S. Treasury Index 6 , as in Warnock and Warnock (2009). In particular, note that the Unadjusted series will be benchmark-consistent by definition, but will not include a market value adjustment; instead, the adjustment for a given month will only be a function of the trading volume in that month. Both holdings series are scaled by the Total amount outstanding of U.S. Long Term debt, so that the empirical measure 6 http://www.lehman.com/fi/indices/pdf/US Treasury Index.pdf 5 more accurately reflects a demand pressure of foreign purchases on yields. See Appendix 1 for a discussion of this point. 1.3 The relationship between Unadjusted Net Purchases and yields: a simple bivariate V AR framework Most of the available studies that try to quantify the impact of foreign Net Purchases of U.S. Treasury securities on their yields, estimate an OLS regression of yield levels or changes, on a measure of either the level or the change in Net Purchases of Treasury securities. How- ever, we cannot deduce the direction of causality from an estimated correlation coefficient. Additionally, regression coefficients do not give information about how the impact spreads over time. In principle, to be able to ascertain whether Net Purchases of Long Term U.S. Treasury securities by foreigner’s have had a negative effect on their yields, we must identify a measure of an exogenous innovation in Net Purchases. A V AR framework seems well suited for this purpose, since at the price of making an assumption about the contemporaneous causality between Net Purchases of Long Term treasuries and yields, we can obtain empirical measures of exogenous innovations in both of these variables that can be used to estimate impulse response functions. This section presents the results of estimating several bivariate V AR models that include Net Purchases of Long Term Treasuries and the 10-year treasury yield. Because each variable can be included either in levels or first differences, 4 separate estimations are considered. And in each of the estimations, the effect of changes in the Wold causal order on the impulse response functions is analyzed. In this way, the results exhaust all possible directions of causality between the variables in a bivariate system, so that a clearer picture 6 of the effects of each variable on the other can be obtained. In addition, the results will be directly comparable to some of the available estimations in the literature. Denote as Y t a vector that includes two variables: either the level or the change in Net Foreign Purchases of Treasuries, denoted asNP t or ΔNP t , respectively, and on the other hand, either the level or the change in the 10 year yield , denoted asy (10) t or Δy (10) t , respectively. For this section, the estimation uses the raw data on Net Purchases of Long Term Treasury securities as available on the TIC website. This means that this data is neither consistent with the benchmark surveys, or has been adjusted to reflect valuation changes. This is done both for comparison purposes, since the estimates available in the literature do not specify if they adjust the data in any way, and in order to obtain an estimate that its free of data manipulation. The V AR model used in this section to investigate the causal relation between Net Purchases and yields is given by A 0 Y t =A(L)Y t−1 +ε t . (1.3) Here,ε t is a vector of structural disturbances, with itsi th entry denoted asε i t . It is assumed thatε t ∼ i.i.d.N(0,I 2 ). This implies that the value ofε j t is interpreted as an exogenous innovation in thej th element ofY t . To achieve identification of the structural shocks from the estimated residuals, an Recur- sive Identification strategy will be employed 7 . This amounts to assuming that only the 7 See Christiano et al. (1999). 7 variables that appear before some variable of interest in the vectorY t can have a contem- poraneous effect on it. This is equivalent to assuming thatA 0 is lower triangular: A 0 =   1 0 a 21 a 22   In the present case of a bivariate V AR, identification of exogenous shocks is simple. For example, if Y t = [NP t ,y (10) t ] , ε NP t has a contemporaneous effect both on NP t and y (10) t , while ε y t affects only y (10) t contemporaneously, and NP t with a 1 month lag. That is, exogenous innovations in Net Purchases of Treasuries cause the 10 year yield, but not otherwise. The estimated model is specified as X t =B(L)X t−1 +u t (1.4) whereB(L) =A −1 0 A(L) and u t =A −1 0 ε t (1.5) Denote the covariance matrix of reduced form disturbances asΣ =E[u t u ′ t ]. Since we don’t have any exclusion restrictions onA(L), ˆ B(L) is obtained using OLS equation by equation, and ˆ Σ is obtained as the sample covariance matrix of the estimated residuals ˆ u t . 8 Impulse responses to structural disturbances are obtained exploiting the fact that a symmetric positive definite estimated ˆ Σ implies that there exist a unique lower triangu- lar Cholesky factor that satisfies ˆ Σ = ˆ P ˆ P ′ . 8 Therefore, from (1.5), we identifyA −1 0 with ˆ P, since Σ =E[u t u ′ t ] =A −1 0 E[ε t ε ′ t ](A −1 0 ) ′ =A −1 0 (A −1 0 ) ′ The method employed to calculate the impulse responses and variance decompositions is outlined in Appendix A. The results to be presented in the rest of the paper concentrate on the 10 year Treasury yield 9 . 1.3.1 Impulse response functions and OLS slope coefficients The V ARs in this section are estimated by ordinary least squares, equation by equation, with data from 1995:01 to 2007:06. Structural shocks are identified using a Cholesky fac- torization of the sample covariance matrix of the estimated residuals. The raw (unadjusted and benchmark inconsistent) monthly data for Net Purchases of U.S. Treasury Bonds & Notes by Foreign Official Institutions 10 is used in this section, mainly to obtain an initial estimate of the effect that is free of additional data manipulation. Only data on Official purchases is used in the estimation because that series has received more attention both in previous studies and in the press. Asymptotic68% standard error bands are calculated using the procedure explained in Lutkepohl (2007). Figure 1.1 presents the impulse responses in a bivariate system that includes both vari- ables in levels. In this case, there are 2 possible orderings of the variables in Y t : either 8 The discussion follows closely the exposition in Hamilton (1994), p.p. 318-324. 9 The results for the 1, 3, 5, and 7 year yields are available upon request. The results are not changed, however, so don’t waste your time 10 Available at http://www.treas.gov/tic/tressect.txt 9 Y t = [NP t ,y (10) t ] or Y t = [y (10) t , NP t ]. In the first case, contemporaneous innovations in holdings cause the 10 year yield, while in the second the opposite holds. Figure 1.1: Impulse Responses in Bivariate V AR under alternative identification assump- tions: 10 year yield and Net Purchases series both in levels 0 10 20 30 40 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 shock of NP t →y (10) t when Y t =[y (10) t ,NP t ] 0 10 20 30 40 −0.05 0 0.05 0.1 0.15 shock of NP t →y (10) t when Y t =[NP t ,y (10) t ] 0 10 20 30 40 −3000 −2000 −1000 0 1000 2000 shock of y (10) t →NP t when Y t =[y (10) t ,NP t ] 0 10 20 30 40 −3000 −2000 −1000 0 1000 2000 shock of y (10) t →NP t when Y t =[NP t ,y (10) t ] The figure plots the impulse response function of each variable to a shock in the other, as indicated in the titles. Identification of structural shocks is achieved using a recursive scheme. The standard error bands are 68% bands calculated using the asymptotic method in Lutkepohl (2007). The sample is monthly from 1995:01 until 2007:07. The foreign Holdings series is neither market value adjusted or benchmark consistent. 10 The top panel includes responses of the 10 year yield to an exogenous innovation in foreign Net Purchases of Long Term Treasury securities under both orderings of the vari- ables inY t . As can be clearly seen, it can hardly be argued that an exogenous innovation in Net Purchases depresses the 10 year yield: if anything, the effect appears to be posi- tive although the standard error bands are wide. However, a possible explanation of why previous studies find negative regression coefficients is given in the bottom panel, which includes the other side of the coin, the responses of Net Purchases to an exogenous change in the market price 11 of the 10 year Treasury Note. Here, the effect is negative, persistent and statistically significant. Therefore, it is possible that the negative regression coefficients previously obtained in other studies reflect this negative effect. Indeed, this intuition is confirmed when an OLS regression is run with the same vari- ables included in the V AR. The first column of Table 1.1, presents the results of a regres- sion of the 10 year yield as independent variable, on an constant and Net Purchases as an explanatory variable. We can see that the estimated coefficient is statistically significant and negative, which is the usual finding on the other studies. However, as was seen before in the analysis of the impulse response functions, there does not appear to be clear evidence of negative causation running from Net Purchases to the 10 year yield. Figures 1.2, 1.3 and 1.4, together with columns (2)-(4) of Table 1.1, present the results for the cases in which the V AR is estimated with any or both variables in first differences. Here, the impulse responses and the OLS evidence confirm the results found before. For example, when the Y t vector is specified as Y t = [y (10) t ,ΔNP t ] or Y t = [ΔNP t ,y (10) t ], the impulse response functions included in Figure 1.2 reaffirm the evidence found before that the response of the ten year yield to an innovation in ΔNP t is positive, while the response ofΔNP t to an innovation iny (10) t is negative at impact and alternates in 11 Which is inversely related to its yield 11 Table 1.1: Regressions of the 10 year yield on Net Purchases (1) (2) (3) 4) y (10) t y (10) t Δy (10) t Δy (10) t Intercept 5.37 5.26 -0.024 -0.018 (30.63) (27.47) (-0.098) (-0.91) NP t -28.65 1.42 (-2.68) (0.67) ΔNP t -4.58 -4.15 (-1.19) (-1.95) R 2 0.05 0.00 0.00 0.02 n 150 150 150 150 This table presents regressions of the 10 year yield on an intercept and for- eign Official Net Purchases as explanatory variable. The dependent variable is indicated in the second row, below the column number: it is the level or the first difference of the 10 year Treasury yield. Explanatory variables are indi- cated in the first column. NP t is foreign Official Net Purchases of Long Term U.S. Treasury securities, from the TIC website. The series is not market-value adjusted or benchmark-survey consistent. All regressions include a constant. t-statistics based on Newey-West robust standard errors (6 lags) are reported in parentheses. The sample is monthly from 1995:01 to 2007:07. sign thereafter. Further, the slope coefficients in the regression between both variables is again negative, although not significant. Finally, the conclusions are similar for Figures 1.3, 1.4 and the associated OLS regres- sions on columns (3) and (4) on Table 1.1. Overall, there does not appear to be any signifi- cant evidence in favor of the hypothesis that foreign Net Purchases for Long Term treasury securities are indeed causing a downward trend in the 10 year yield, at least during the 1995-2007 period. 12 Figure 1.2: Impulse Responses in Bivariate V AR under alternative identification assump- tions: 10 year yield in levels and Net Purchases series in first differences 0 10 20 30 40 0 0.02 0.04 0.06 0.08 0.1 0.12 shock of ΔNP t →y (10) t when Y t =[y (10) t ,ΔNP t ] 0 10 20 30 40 −0.05 0 0.05 0.1 0.15 shock of ΔNP t →y (10) t when Y t =[ΔNP t ,y (10) t ] 0 10 20 30 40 −3000 −2000 −1000 0 1000 2000 3000 shock of y (10) t →ΔNP t when Y t =[y (10) t ,ΔNP t ] 0 10 20 30 40 −3000 −2000 −1000 0 1000 2000 3000 shock of y (10) t →ΔNP t when Y t =[ΔNP t ,y (10) t ] The figure plots the impulse response function of each variable to a shock in the other, as indicated in the titles. Identification of structural shocks is achieved using a recursive scheme. The standard error bands are 68% bands calculated using the asymptotic method in Lutkepohl (2007). The sample is monthly from 1995:01 until 2007:07. The foreign Holdings series is neither market value adjusted or benchmark consistent. 1.4 Structural V AR Model The fundamental economic question that this paper tries to address is whether foreign accu- mulation of U.S. Long Term Treasury securities can be considered an independent risk 13 Figure 1.3: Impulse Responses in bivariate V AR under alternative identification assump- tions: first difference of the 10 year yield and levels of Net Purchases 0 10 20 30 40 −0.04 −0.02 0 0.02 0.04 0.06 shock of NP t →Δy (10) t when Y t =[Δy (10) t ,NP t ] 0 10 20 30 40 −0.04 −0.02 0 0.02 0.04 0.06 shock of NP t →Δy (10) t when Y t =[NP t ,Δy (10) t ] 0 10 20 30 40 −3000 −2000 −1000 0 1000 2000 shock of Δy (10) t →NP t when Y t =[Δy (10) t ,NP t ] 0 10 20 30 40 −3000 −2000 −1000 0 1000 2000 shock of Δy (10) t →NP t when Y t =[NP t ,Δy (10) t ] The figure plots the impulse response function of each variable to a shock in the other, as indicated in the titles. Identification of structural shocks is achieved using a recursive scheme. The standard error bands are 68% bands calculated using the asymptotic method in Lutkepohl (2007). The sample is monthly from 1995:01 until 2007:07. The foreign holdings series is neither market value adjusted or benchmark consistent. factor 12 that drives time-variation in yields. Because if this where the case, then together with the traditional measures of technology, inflation and monetary policy stance, foreign demand variables should be included in general equilibrium models of the term structure. 12 At least for the long-end of the yield curve. 14 Figure 1.4: Impulse Responses in bivariate V AR under alternative identification assump- tions: 10 year yield and Net Purchases series both in first differences 0 10 20 30 40 −0.04 −0.02 0 0.02 0.04 0.06 shock of ΔNP t → Δy (10) t when Y t =[Δy (10) t ,ΔNP t ] 0 10 20 30 40 −0.04 −0.02 0 0.02 0.04 0.06 shock of ΔNP t → Δy (10) t when Y t =[ΔNP t ,Δy (10) t ] 0 10 20 30 40 −3000 −2000 −1000 0 1000 2000 3000 shock of Δy (10) t → ΔNP t when Y t =[Δy (10) t ,ΔNP t ] 0 10 20 30 40 −3000 −2000 −1000 0 1000 2000 3000 shock of Δy (10) t → ΔNP t when Y t =[ΔNP t ,Δy (10) t ] The figure plots the impulse response function of each variable to a shock in the other, as indicated in the titles. Identification of structural shocks is achieved using a recursive scheme. The standard error bands are 68% bands calculated using the asymptotic method in Lutkepohl (2007). The sample is monthly from 1995:01 until 2007:07. The foreign Holdings series is neither market value adjusted or benchmark consistent. So far, the evidence presented in the bivariate case points to a negative answer to the above question. However, the information set in a bivariate V AR estimation is rather lim- ited. It can always be argued that the seemingly positive effect of shocks to Net Purchases 15 on yields includes the effect of other omitted regressors, most notably, macroeconomic vari- ables like technology shocks. Once the effect of other important variables is included, it is still possible that foreign Net Purchases of Long Term Treasuries might have an indepen- dent negative effect on yields. And this would constitute evidence that the foreign sector’s demand for treasuries should be an important ingredient in general equilibrium models of the yield curve. Additionally, the raw data on Net Purchases was not obtained from the cor- responding Holdings series. In particular, the raw data on Net Purchases was not adjusted in any way, which makes it inconsistent with the benchmark-survey levels, and with the nominal increase in the market value of Holdings after a change in market prices. In order to address these potential shortcomings, this section presents identified impulse response functions of the 10 year yield to a shock in foreign Official Holdings estimated from an augmented version of the structural V AR model used to study the monetary trans- mission mechanism. Such model includes a measure of production, consumer prices, com- modity prices, the effective Federal Funds rate and the money supply. In addition to these variables, the macroeconomic V AR employed in this section includes other indicators, such as the price of oil and the exchange rate. The price of Oil is included to control for the fact that the accumulation of foreign exchange reserves by oil exporting countries is obviously correlated with the world price of Oil. The exchange rate is included to control for the impact of foreigner’s accumulation of FX reserves on the value of the dollar and its further feedback effect on yields or consumer prices. Both measures of Unadjusted and Adjusted Foreign Official Holdings of Long Term U.S. Treasury securities are employed, to be able to compare the impulses when the market valuation component is present or not. Finally, the 10 year yield is always present in the estimations. LetY t denote ann y ×1 vector of macroeconomic variables, specified as Y t =[oil t , gdp t , cpi y , ppiidc t , FF t , NBRX t ] (1.6) 16 oil t is the spot price of West Texas Intermediate Oil; gdp t is quarterly real GDP interpolated to a monthly frequency using the method of Chow and Lin (1971) 13 ; ppiidc t is the Producer Price Index of Industrial Commodities ; FF t is the effective Federal Funds rate; and NBRX t is the ratio of non-borrowed reserves to total reserves. In addition to the macro variables vector the V AR includes the level of foreign Official Holdings of Long Term U.S. Treasury securities normalized by the total amount outstand- ing of T-notes and T-bonds 14 , denoted as foi t ; a Trade Weighted Exchange Index of the nominal value of Dollar against Major Currencies, denoted ase t ; and the yield on a nomi- nal zero coupon 10 year bond,y (10) t . Collect all variables into ann×1 vectorX t ≡ [Y ′ t , foi t ,e t ,y (10) t ] ′ , wheren = n y +3. Then, the structural V AR model can be represented as A 0 X t =A(L)X t−1 +ε t (1.7) where ε t = [ε Y t ,ε f t ,ε e t ,ε y t ] ′ is the vector of structural disturbances. It is assumed that ε t ∼ i.i.d.N(0,I n ). To achieve identification of the structural shocks from the estimated residuals, an Recursive Identification strategy will be employed 15 . As in section 2.1, under a Recursive identification strategy,A 0 will be assumed lower triangular. This implies that the ordering of the variables of the vectorX t matters, since then, innovations in all the variables that appear in positioni<j will be assumed to affect contemporaneously the value of variable in positionj, while innovations in the latter not 13 The related variables used for interpolation are: the Industrial Production Index, the Institute for Supply Management’s PMI Composite Index, Total Nonfarm Payrolls (All Employees) from the BLS, and the Index of Capacity Utilization in Manufacturing (NAICS) from the FRB. 14 Obtained from the Monthly Statement of the Public Debt of the United States. 15 See Christiano et al. (1999). 17 affecting the values of the former in the same period. Throughout the analysis,A 0 will be assumed to take the following form: A 0 =             a 11 (ny×ny) 0 (ny×1) 0 (ny×1) 0 (ny×1) a 21 (1×ny) a 22 (1×1) 0 (1×1) 0 (1×1) a 31 (1×ny) a 32 (1×1) a 33 (1×1) 0 (1×1) a 41 (1×ny) a 42 (1×1) a 43 (1×1) a 44 (1×1)             witha 11 and lower triangular with ones on the diagonal, anda 22 =a 33 =a 44 = 1. With this specification, the model will imply that the contemporaneous innovations in all macro variables included inY t will affect the level of foreign Holdings foi t , the exchange rate indexe t and the 10 year yieldy (10) t . At the same time, exogenous innovations in yields are assumed not to have a contemporaneous effect on foi t ore t , but instead to affect them with a lag. On the other hand, innovations in the exchange rate are assumed to have an effect on yields in the same period and on consumer prices with a lag. These are the main identification assumptions regarding the effects of foreign holdings on yields and the exchange rate in this version of the V AR. Notice that macro variables affect all other variables included, both contemporaneously and with a lag. The estimated model and the method used to obtain the impulse response functions are the same as explained in section 2.1. The reader is referred to that section for details. 1.4.1 Results The top left panel (a) in Figure 1.5 plots the impulse responses function of y (10) t for a V AR model that includes the Unadjusted level of Foreign Holdings of Long Term Treasury securities. As can be seen, the impulse response is positive for the first 8 months and then converges towards zero. That is, when the foreign Holdings series is adjusted to 18 be consistent with the benchmark-survey amount outstanding but where no inter-survey adjustment is made for market valuation changes, the effect of a positive innovation in Holdings appears to be positive, not negative. This finding in consistent with the earlier results found in the bivariate V AR, but inconsistent with the available estimates in the literature, most notably Davis (2004). The top right panel (b) in Figure 1.5 plots the impulse responses function ofy (10) t for a V AR model that includes the Adjusted level of Foreign Holdings of Long Term Treasury securities. The Holdings series in this case has been adjusted to reflect the return on an Index of Treasury Notes and Bonds prices, as explained in section 1.2. The effect at impact is strongly negative of about 10bp, significant, and persists for 30 months. But from the discussion of the Valuation effects, we know that it is not surprising that the estimated impulse response is strongly negative and statistically significant. In an effort to separate the valuation effect from the pure demand effect of holdings on yields, the V AR is estimated including as an additional variable the same bond price index used to perform the market valuation adjustment: this should control for the effects of market price movements on the estimated responses. That is, the impulse response of y (10) t to a shock in foi t obtained in this way will include only the effect of changes in the level of Holdings and not the valuation effect. As can be seen in the bottom left panel (c) in Figure 1.5, the impulse responses is again positive for the first 8 months and then converges towards zero: it is almost identical to panel (a). The evidence gives support to the hypothesis that positive innovations in foreign Official Holdings of Long Term Treasury securities do not cause a negative change in the 10 year Treasury yield. As a final robustness check, the bottom right panel (d) in Figure 1.5 presents the impulse response of y (10) t to an exogenous innovation in the bond price index alone, and not to a shock in foi t . By definition, this response should be negative, and this is precisely what 19 Figure 1.5: Impulse Responses of the 10 year yield to Foreign Holdings shocks in Structural V AR under alternative specifications 0 10 20 30 40 −0.05 0 0.05 0.1 0.15 a) shock of Unadjusted foi t →y (10) t 0 10 20 30 40 −0.15 −0.1 −0.05 0 0.05 b) shock of Adjusted foi t →y (10) t 0 10 20 30 40 −0.05 0 0.05 0.1 0.15 c) shock of Adjusted foi t →y (10) t with Index 0 10 20 30 40 −0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 d) shock of Lehman US Treasury Index →y (10) t Impulse response functions of the 10 year yield to innovations in foreign Offi- cial Institution’s holdings of Long Term Treasury securities. Top left: hold- ings are benchmark-survey consistent but NOT adjusted for market valua- tion effects. Top right: holdings is both benchmark-survey consistent AND adjusted for market valuation effects. Bottom left: V AR controlling for the bond price Index. Bottom right: impulse response of the 10 year yield to an exogenous innovation in the Lehman Brothers US Treasury Bond price Index (and not to a shock in Holdings). Identification of structural shocks is achieved using a recursive scheme. The standard error bands are 68% bands calculated using the asymptotic method in Lutkepohl (2007). The sample is monthly from 1995:01 until 2007:07. 20 we obtain: a negative, statistically significant and persistent impulse on the 10 year yield. Notice the remarkable similarity between panels (b) and (d). Overall, the results obtained with the available data do not lend support for the hypoth- esis that foreign Central Bank accumulation of Long Term Treasuries has caused part of the downward shift in long term US yields after 2003. When the valuation adjustment is removed from the series, the effect appears to be positive. 1.4.2 The Bertaut and Tryon (2007) dataset The mechanical negative effect on yields of the valuation adjustment is as evident when the data from Bertaut and Tryon (2007) is employed in the V AR. As in Warnock and Warnock (2009), they construct monthly estimates of U.S. cross-border securities positions obtained by combining the benchmark surveys with monthly transactions data. However, their data has some advantages since they make some simplifications in the numerical pro- cedure used to allocate the gap, and perform additional adjustments to the transactions data. More importantly, they break down the estimated holdings positions into flows, val- uation changes, and other factors. Therefore, it is natural to use their data an compare the impulse response ofy (10) t to an innovation in foreign Official Holdings when the valuation component is either included or absent. The top panel of Figure 1.6 presents the impulse response ofy (10) t to an innovation in foi t as calculated by Bertaut and Tryon (2007), but normalized by the Total Long Term Treasury Debt Outstanding. When the valuation adjustment is present, the response is negative, significant and persistent. This is consistent with the results found so far. Finally, when the market value adjustment component is not included in the Holdings series, the estimated impulse response in the bottom panel of Figure 1.6 is positive for the first 8 months and then converges to zero. That is, the results support the view that a negative effect of holdings innovations on yields is caused by the negative relationship between 21 Figure 1.6: Impulse Responses of the 10 year yield to Foreign Holdings shocks in Structural V AR using the Bertaut and Tryon (2007) dataset 0 10 20 30 40 −0.15 −0.1 −0.05 0 0.05 shock of Adjusted foi→y (10) t 0 10 20 30 40 −0.1 −0.05 0 0.05 0.1 0.15 shock of Unadjusted foi→y (10) t Impulse responses of the 10 year yield to innovations in foreign Official Insti- tution’s holdings of Long Term Treasury securities. The Holdings data is from Bertaut and Tryon (2007). Top figure: the holdings variable is both benchmark- survey consistent and adjusted for market valuation effects. Bottom figure: the market valuation component of holdings is excluded from the series. Identifi- cation of structural shocks is achieved using a recursive scheme. The standard error bands are 68% bands calculated using the asymptotic method in Lutke- pohl (2007). The sample is monthly from 1995:01 until 2006:06 22 prices and yields, and not by the upward demand pressure on prices that is commonly thought to have depressed yields over the last 4 years. Therefore, we conclude that under 2 related methodologies used to obtain accurate data on foreign Official Institution’s Holdings of Long Term Treasury securities, the result is the same: the response of the 10 year yield is not negative. 1.5 Conclusion This chapter has presented evidence of the effect of foreign official institution’s accumula- tion of Long Term U.S. Treasury securities on their prices. The results show that, contrary to the available evidence and common intuition, foreign Central Banks accumulation of Long Term treasuries has not had a direct negative impact on yields: at least, an effect cal- culated from the available data on foreigner’s accumulation of Long Term Treasury securi- ties. At the heart of the conclusion are two observations: first, that it is possible to obtain a negative regression coefficient of yields on Net Purchases while at the same time not have evidence of negative causation running from Holdings or Net Purchases to yields; second, that the market value adjustment done to Net Purchases (flows) to obtain Holdings (stock) creates a mechanical negative relationship between an innovation in Holdings and the 10 year yield. If foreign Official institutions hold more than 60% of the total amount of Long Term Treasury securities outstanding, how is it not possible that their demands have an upward pressure on prices? One possible explanation is that if foreigner’s demand does not exert a price pressure at the auction, we will not observe an effect on yields. For example, if Official Institutions buy at auction a certain amount of T-Notes, and then acquire the rest form third parties, if those third parties did not bid up the price at auction, then we will not observe a negative effect of foreign Holdings on prices. Probably, this will only be reflected 23 at secondary market trades. Overall, the results suggest a complex set of relationships between Treasury issuance, Foreign Central Bank reserve accumulation, and prices. 24 Chapter 2 Financial integration, interest parity and foreign exchange reserves 2.1 Introduction This chapter studies the impact of central bank accumulation of foreign reserves on interest rates and the predictions for uncovered interest parity in a world characterized by imperfect financial integration where private agents face significant costs to change positions in the international bond market. It presents an incomplete-markets two-country monetary model in which the central bank intervenes in the foreign exchange market and conducts domestic monetary policy using an interest rate feedback rule that targets domestic CPI inflation. Open market operations are given by the central bank balance sheet. Bonds in positive net supply are issued by a treasury department. Finally, behavioral constraints are imposed on private agents by the interaction of their budget constraints with the central banks balance sheets and the bond market clearing conditions. The model features two main ingredients: portfolio adjustment costs and international market incompleteness. Portfolio adjustment costs magnify the exchange rate impact of nominal shocks, like a central bank intervention. They can create significant changes in output while at the same time preventing the agents from hedging the shock using assets, with the resulting impact on consumption and interest rates. Additionally, adjustment costs attenuate the relative price effects of monetary policy shocks, given that such costs pre- vent large changes in foreign bond positions which mitigates the impact on the nominal 25 exchange rate. That causes the effect of the shock to be greatest in the prices and allocations of the country in which it originates, and ultimately causes the exchange rate appreciation to be persistent. On the other hand, international asset market incompleteness creates a role for the demand and supply of bonds, and in this way effectively links both agents and the central banks through the budget constraints, balance sheet, and market clearing condi- tions. For example, if the home central bank or the foreign agent are unable or unwilling to buy bonds when the domestic agent needs to sell them, perhaps because of a contractionary monetary policy shock, domestic consumption and marginal utility will be impacted, and in this way interest rates will respond to shocks. The reason to study central bank interventions and uncovered interest parity (UIP) specifically in a world in which private agents face important costs to change foreign bond portfolios, is motivated by the work of Lyons (2001) and Bacchetta and Wincoop (2008). They consider that limited participation and agency costs, or investment fees might be behind the violations of short-run UIP known as the “forward premium anomaly”, as these costs imply that agent’s portfolios react slowly to new information. Collectively, their work points to costs that are difficult to measure but that might be important enough to explain the anomaly. These types of costs are formalized in the model by introducing an interest rate spread on foreign bond holdings that depends on the change in the foreign bond port- folio of the agents, as in Tuladhar (2003); in equilibrium, the spread will be a risk premium that depends on net foreign private assets. There are two main findings in this paper. First, when private agents face important costs in adjusting their foreign bond holdings, a purely nominal shock like an innovation in domestic central bank holdings of foreign exchange reserves decreases foreign interest rates by 2.3 basis points. This is due to the portfolio adjustment costs and the constraints on agent’s bond positions imposed by their budget constraint and the market clearing con- dition. When the home central bank purchases foreign bonds, and the supply does not 26 change, it forces both home and foreign private agents to absorb the shock, i.e., sell some of their holdings to the central bank. In a world without frictions, both agents share this burden equally. In a world with frictions, home agents are constrained and cannot sell their foreign bonds, so foreign agents must sell proportionately more. The muted response of private foreign portfolios implies that the central bank purchase causes a depreciation of the domestic currency that gives rise to changes in relative prices and output. This interacts with the budget constraint and forces greater changes in consumption, marginal utility and ultimately interest rates. Therefore, instrumental in generating this result is the inability of the agent to neutralize adverse changes in real income when his international portfolio holdings are costly to change. The other set of results concerns the predictions of the model for uncovered interest par- ity (UIP). In this respect, the paper finds that both monetary policy and foreign exchange intervention shocks can cause a “forward premium anomaly”, that is, a short-horizon devi- ation from UIP. The mechanism by which monetary policy shocks cause a “forward pre- mium anomaly” is similar in spirit to the conjecture in Froot and Thaler (1990): changes in nominal interest rates reflect changes in real rates, and cause a persistent nominal appreci- ation. In the model, the persistent nominal appreciation, in turn, is caused by the frictions in the international bond market: they bring about smaller changes in relative prices (since portfolios respond less) and on foreign inflation. This causes the nominal exchange rate to mimic the response of the real exchange rate and domestic PPI inflation, which are per- sistent after a domestic monetary policy shock. Additionally, the model is gradually more consistent with UIP at long horizons, as the evidence in the data suggest, giving rise to an upward sloping term structure of Fama regression coefficients. For maturities up to 3 years, the model can reproduce the upward sloping term structure of UIP regression coef- ficients without foreign exchange holdings shocks. This suggests that although part of the 27 story, foreign exchange intervention shocks are not necessary to reproduce the salient fea- tures of the data, as argued in Mark and Moh (2007). In fact, when there are no central bank intervention shocks, monetary policy shocks alone are enough to cause sizeable devi- ations from UIP. Finally, simulated data from the model give Sharpe ratios for carry trade strategies close to the data. 2.1.1 Literature review Froot and Thaler (1990) conjecture that a model capable of generating a forward anomaly would have to feature investors that cannot instantaneously adjust their portfolios in response to an increase in the interest differential. If increases in nominal rates cause increases in real interest rates, this will cause a capital inflow, and a resulting appreciation. Then, the slowly adjusting portfolios will cause the currency to keep appreciating in the following periods after the shock. This gives rise to a negative relationship between inter- est differentials and subsequent exchange rate changes. Although the mechanism proposed in their paper is very similar to the one presented in this paper, they do not formalize their story with a model. This paper’s contribution is to offer a fully specified two-country model in which the above mentioned behavior arises in equilibrium. Bekaert, Wei, and Xing (2007) also speculate that short-term frictions might cause a delayed response of the exchange rate after a change in the interest differential, which is part of the explanation offered by the model in the present paper. Their focus is on studying the empirical implications of imposing both the expectations hypotheses of the term structure of interest rates (EHTS) and UIP over short and long-horizons in a V AR model, rather than to present a theoretical model that can explain short and long-horizon UIP, as we do in the present paper. Also, they do not study the relationship between central bank interventions and UIP violations. 28 Bacchetta and Wincoop (2008) analyze the implications for the forward premium anomaly of introducing infrequent portfolio decisions into an OLG model. They are able to account for both short-term and long horizon evidence on UIP, as well as the delayed overshooting result documented in Eichenbaum and Evans (1995). The main differences between their model and the one used in the present paper is that theirs is one good model with no production or labor markets in which the international transmission mechanism of changes in relative prices cannot be analyzed, and central banks are modeled asymmetri- cally as one sticks to a fixed money supply rule while the other’s interest rate follows an exogenous AR(1) process. Further, they do not have implications for the effects of surprise interventions on yields or on UIP, because in their model central banks do not accumulate reserves. McCallum (1994) shows that if the monetary authorities “lean against the wind” in such a way as to make the interest differential depend on exchange rate depreciation, a bivari- ate system composed of an UIP condition and a rule for the interest differential together can generate a negative correlation between the lagged interest differential and the nomi- nal exchange rate depreciation. Chinn and Meredith (2004) build on McCallum’s idea and extend his model by introducing equations that determine the inflation, output, long-term expected inflation and long-term expected interest rate differentials in order to be able to consider a traditional interest rule for the interest differential that targets the output and inflation differentials. The main difference with the present paper is that their approach directly specifies the world equilibrium conditions instead of deriving them from first prin- ciples, and this requires that the parameters are the same on both countries. Additionally, in their model it is exogenous shocks to the UIP condition that cause a forward premium anomaly, while in the present paper it is the endogenous response of net private assets to monetary policy shocks as a function of financial frictions that gives rise to the anomaly. 29 Their model has no monetary policy shocks. Finally, they do not discuss the sensitivity of their results to key parameters, because their model has no direct mapping to fundamentals. Canzoneri, Cumby, Diba, and Lopez-Salido (2008) (CCDL) also study the effects on the interest rate of a sudden sell-off of reserves by a foreign central bank. They introduce deviations from UIP by assuming a liquidity demand for bonds. In their model, home households hold domestic financial assets only, while the foreign agent must in addition hold domestic bonds for liquidity purposes; on the other hand, the central bank of the coun- try that provides the key currency does not hold foreign reserves. These asymmetries are the main differences with our model. They find that a sell-off of foreign country’s reserves of U.S. Treasury securities calibrated to equal the reserve buildup since 2002 significantly increases home interest rates, similar to our findings. But they focus on a very special (and sizeable) shock to reserves, while in our paper the shock is a typical quarterly standard devi- ation innovation. In addition, their model generates a positive correlation between lagged interest differentials and exchange rate changes, which is the opposite of what is found in the data. The paper that is closest in spirit to ours is Selaive and Tuesta (2003). Their goal is to asses whether financial frictions can help explain the consumption-real exchange rate anomaly of Chari, Kehoe, and McGrattan (2002) in a small open economy (SOE) model. They recognize that costs in taking positions in the international bond market will generate deviations from UIP related to the net foreign asset position of the economy, which is the same mechanism used in the present paper to explain deviations from UIP. One of the key differences between their paper and the present is that they focus on small open economy, while we use a two-country model. Indeed, our model can be seen as a two country version of their small open economy framework, but with one critical difference: in their model, positions in the international bond market are unrestricted, while in our model they are restricted by the bond market clearing condition, and this provides a link between the bond 30 market and the agents budget constraints and central banks balance sheets. And as it turns out, this extra constraint is critical in creating marginal utility effects of interventions and monetary policy shocks. Also, since the foreign country’s variables are modeled as com- pletely exogenous under the SOE paradigm, the effects of domestic shocks on the foreign economy and their sensitivity to frictions cannot be studied. Finally, they do not check their model’s implications for the “forward premium anomaly”, that is, if positive interest rate differentials forecast subsequent exchange rate appreciations, which is one of the main objectives of our paper. 2.2 The Model Consider a world economy consisting of two countries, “home” and “foreign”. In each country, there is a representative household, a continuum of monopolistically competitive firms indexed byj ∈ [0,1], a central bank, and a treasury department. The model used in this paper is a two-country version of the small open economy framework outlined in Gali and Monacelli (2005) augmented to include bonds in positive net supply, a central bank that intervenes in the foreign exchange market, and a constraint on central bank behavior given by its balance sheet. We will see that the constraint on open market operations imposed by the central bank balance sheet makes the effect of official intervention in one country critically depend on the response of consumers on both countries. 31 2.2.1 Households There is a representative consumer in each country that consumes a composite consumption goodC t , demands real balancesm t of (domestic) currency and supplies hours of laborN t to the domestic firms in order to maximize E t ∞ X i=0 (C t+i −θC t+i−1 ) 1−γ 1−γ +V(m t+i )− ℓ(N t+i ) 1+φ 1+φ . (2.1) Preferences display external habit formation, as C t represents aggregate composite con- sumption. The composite consumption index is defined as C t ≡ (1−α) 1/η C η−1 η H,t +α 1/η C η−1 η F,t η η−1 (2.2) whereC H,t is an index of consumption of domestic goods given by C H,t = Z 1 0 c H,t (j) ε−1 ε dj ε ε−1 (2.3) and whereC F,t is an index of consumption of imported goods given by C F,t = Z 1 0 c F,t (j) ε−1 ε dj ε ε−1 (2.4) The parameter α ∈ [0,1] measures the degree of home-bias in preferences; we will assume thatα < 0.5 and this will enable the model to feature real exchange rate fluctua- tions, i.e. PPP will not hold. The parameterη > 0 is the elasticity of substitution between domestic and foreign bundles of goods, whileε>1 is the elasticity of substitution between individual varieties of goods, and is assumed to be the same for both domestic and foreign varieties. The definitions of the composite, domestic and foreign consumption indexes for the foreign householdC ⋆ t ,C ⋆ H,t andC ⋆ F,t are analogous, and they are defined using the same 32 elasticitiesη andε, but we allow for a different home-bias parameterα ⋆ . In each period, from the optimal allocation of a fixed level of expenditures between domestic and foreign consumption indexes we obtain the following demand curves: C H,t = (1−α) P H,t P t −η C t ;C F,t =α P F,t P t −η C t (2.5) where P t ≡ (1−α)P 1−η H,t +αP 1−η F,t 1 1−η (2.6) is the Consumer Price Index (CPI), P H,t ≡ Z 1 0 p H,t (j) 1−ε dj 1 1−ε (2.7) is the domestic Producer Price Index (PPI), and P F,t ≡ Z 1 0 p F,t (j) 1−ε dj 1 1−ε (2.8) is the price index for imported goods in domestic currency. Foreign price indexes P ⋆ t , P ⋆ H,t and P ⋆ F,t are defined in a similar way; P ⋆ F,t would be the price index for imported goods in the foreign economy in foreign currency units. The cost-minimizing demands for domestic and foreign varieties of goods are c H,t (j) = p H,t (j) P H,t −ε C H,t c F,t (j) = p F,t (j) P F,t −ε C F,t (2.9) Here,p H,t (j) is the price in domestic currency of varietyj produced at “home”, while p F,t (j) is the price in domestic currency of varietyj produced abroad. Denote the price in 33 foreign currency units of varietyj asp ⋆ F,t (j). In this paper, it will be assumed that the Law of One Price (LOOP) holds for individual varieties of goods: p F,t (j) = E t p ⋆ H,t (j) p ⋆ F,t (j) = 1 E t p H,t (j). (2.10) E t is the nominal exchange rate, the price of foreign currency in terms of home currency. Then, the LOOP in turn implies that Purchasing Power Parity (PPP) holds between the level of PPI’s across countries: P F,t = E t P ⋆ H,t P ⋆ F,t = 1 E t P H,t (2.11) Note that this does not mean that PPP will hold at the level of CPI’s, simply because of home-bias in preferences. To see this, some notation is in order. Define the real exchange rate as Q t = E t P ⋆ t P t , (2.12) which is interpreted as units of domestic good per unit of foreign good. Also, define the Terms of Trade asS t = P F,t /P H,t , which is the relative price of a country’s imports in terms if its exports. Then, using the home (and foreign) equation for the CPI (2.7), the PPI/CPI index ratioa t = P H,t /P t can be related toS t as a η−1 t =(1−α)+αS 1−η t (2.13) and (a ⋆ t ) η−1 = (1−α ⋆ )+α ⋆ S η−1 t (2.14) 34 Then, it can be shown that the real exchange rate can be expressed as: Q t ≡ S t a t a ⋆ t = α+(1−α)S η−1 t (1−α ⋆ )+α ⋆ S η−1 t 1 η−1 (2.15) As can be seen, PPP at the CPI level will hold (i.e. Q t = 1 ∀t) only if (1−α) = α ⋆ , or if one of the countries does not feature home bias. Hence, we will assume home-bias in preferences which give rise to endogenous real exchange rate fluctuations. It is assumed that markets are complete domestically, but not internationally. The only financial assets available to households of both countries are a nominal bond denominated in domestic and foreign currency, issued by the corresponding treasury departments. The budget constraint of the household is given by : C t + b t − b t−1 R t−1 Π t + Q t b F t − b F t−1 (R ⋆ t−1 +ψ t−1 ) Π ⋆ t + m t − m t−1 Π t ≤w t N t + 1 P t Z 1 0 Γ t (j)dj−τ t + ψ ⋆ t−1 (b F⋆ t−1 ) Π t . (2.16) where ψ t =−δ(b F t −0.99b F t−1 )≃−δ·Δb F t (2.17) Here,b t andb F t are real holdings of the “home” and “foreign” one-period bonds, respec- tively. R t andR ⋆ t are the gross-one period nominal interest rates. N t = R 1 0 N t (j)dj is the total amount of labor supplied by the household, and w t is the real wage. Γ t (j) is the nominal profit of domestic firmj, andτ t is a lump-sum transfer from the “home” treasury department. Finally,Π t = P t /P t−1 andΠ ⋆ t = P ⋆ t /P ⋆ t−1 are the home and foreign gross CPI inflation rates. Notice thatb F t represents aggregate real holdings of foreign bonds, whileb F t is any representative agent’s personal holdings of those bonds. Naturally, the agent takes b F t as given when choosingb F t . 35 Financial friction Following Tuladhar (2003), an interest rate spread 1 ψ t that depends on the change in the foreign bond holdings of the agent is used to obtain a stationary endogenous b F t . This adjustment cost is introduced to formalize the idea that, for the relevant subset of agents willing to engage in cross-country speculation, it is not possible to fully and instantaneously adjust their positions in the international bond market in response to the arrival of new information. As in Tuladhar (2003), we interpret the spread as the existence of capital-market imper- fections like asymmetric information or institutional features that prevent the instantaneous flow of speculative capital to profit from interest rate differentials 2 . For example, Lyons (2001) explains that speculative capital 3 might not be actively trading on the “forward premium anomaly” (the tendency for high interest rate currencies to appreciate) for two reasons. One, an agency friction, is that proprietary traders would not accept a contract that rewards them based on covariances (a factor model), because this ties their compen- sation to securities they do not trade; this makes a contract based on variance optimal, and the Sharpe ratio the natural performance measure. Second, currency speculation Sharpe ratios are usually lower than that of a buy-and-hold strategy on an equity index. With speculative capital out of the picture, this leaves non-leveraged investors (mutual funds) and nonfinancial corporations to speculate. But Lyons considers them to have “competitive disadvantage in implementing pure currency strategies”, and to be “better characterized 1 This type of friction to induce stationary Net Foreign Assets has also been used by Schmitt-Groh´ e and Uribe (2001), Schmitt-Groh´ e and Uribe (2003), Kollmann (2002). A variant of the debt-elastic interest rate mechanism, which has the same implications, is a multiplicative cost function that affects the purchasing price of the bond, as in Benigno (2009), DePaoli (2009). 2 After all, if speculative capital were aggressively trading on the forward premium anomaly, it would have already disappeared. 3 Also called leveraged investors. This group includes entities like hedge funds and trading desks at large banks 36 by limited participation in currency markets, as they do not monitor and trade in currency markets continuously”. This features imply that “their portfolio shifts across currencies are gradual”. It is also assumed that the real cost of changing the bond portfolio ψ t−1 b F t−1 Π ⋆ t is received by the agent in the other country as a “fee”: this explains the last term in (2.16), which is the fee that the domestic agent will receive when the foreign agent changes his portfolio of domestic bonds. The parameterδ controls the quantitative importance of the friction and, as we will see later, effectively determines the response of bond holdings and yields to an exogenous innovation in foreign central bank holdings of domestic bonds, as well as UIP deviations. Optimality conditions Maximization of (2.1) subject to (2.16) gives the following first order conditions: λ t = (C t −θC t−1 ) −γ (2.18) 1=βE t λ t+1 λ t 1 Π t+1 R t (2.19) 1=βE t λ t+1 λ t Q t+1 Q t 1 Π ∗ t+1 (R ∗ t −ψ t ) (2.20) w t =ℓ N φ t λ t (2.21) R t −1 R t = V ′ (m t ) λ t (2.22) The first equation defines the marginal utility of consumption with internal habit for- mation of the difference form; the second is the Euler equation for optimal holdings of domestic bond; the third is the Euler equation for optimal holdings of the foreign bond; the fourth is the FOC for optimal labor supply; and the last one defines optimal holdings of 37 currency. The functionV(•) is not specified, since in the numerical solution of the model, a linear money demand equation is used: lnm t =κ+κ c lnC t −κ R lnR t (2.23) The parameters of the above specification are estimated using an OLS regression from U.S. data. The reason why the money demand equation will be assumed instead of derived endogenously is that the numerical algorithm used to solve the model can give negative nominal interest rates, as in any nonlinear model whose numerical solution around the steady state is represented as a V AR with Gaussian disturbances. The simple linear money demand function (2.23) is introduced to avoid the explosive effect that a negative interest rate can have on the theoretical money demand equation (2.22). This is important because one of the key features of the model is that domestic open market operationsb CB t are derived endogenously using the central bank balance sheet identity. Thus, any instability in money demand will necessarily cause a perverse behavior in the holdings of domestic bonds by the central bank. Incomplete markets and risk-sharing conditions Using the analogous first order condition for optimal holdings of foreign and home bonds by the foreign household, together with the assumption of incomplete markets at the inter- national level, we obtain two distinct risk-sharing conditions: 1=βE t λ t+1 λ t Q t+1 Q t 1 Π ⋆ t+1   1 βE t h λ ⋆ t+1 λ ⋆ t 1 Π ⋆ t+1 i−ψ t   1 =βE t λ ⋆ t+1 λ ⋆ t Q t Q t+1 1 Π t+1   1 βE t h λ t+1 λt 1 Π t+1 i−ψ ⋆ t   38 where, as before, the star ⋆ denotes foreign variables. These are the typical “expectational” risk-sharing conditions, as in Chari et al. (2002) that obtain when markets are incomplete, augmented to reflect the financial friction imposed on the cross-border trading of bonds. Under incomplete markets, the level of financial frictions is important in determining the dynamic properties of equilibrium interest rates. 2.2.2 Firms In each country, there is a continuum of firms indexed byj∈ [0,1] that produce a perfectly tradeable “variety” using the technology: y t (j) =A t N t (j). (2.24) A t is an technology shock, different across countries, but the same for all firms within a country. It is assumed that the log-technology shock follow the AR(1) process: lnA t = (1−ρ A )ln ¯ A+ρ A lnA t−1 +ǫ A t , (2.25) whereǫ A t ∼ N(0,σ 2 A ). Firms are monopolistic competitors that set the price of their product but face real adjustment costs in doing so; this renders their problem dynamic. At any periodt, nominal profits of the generic firmj are given by Γ t (j) =p H,t (j)y t (j)−W t N t − ϑ 2 p H,t (j) p H,t−1 (j) −1 2 P H,t . (2.26) The last term on the right hand side of (2.26) defines the price adjustment costs, as in Rotemberg (1982), Ireland (2004a) or Ireland (2004b). It formalizes the notion of sticky prices in this paper. Quadratic price adjustment costs are a tractable way to obtain an expec- tational Phillips curve, which captures the real effects of nominal variables. Additionally, 39 up to a first order approximation it is similar to the expectations-augmented Philips curve obtained under the Calvo (1983)-Yun (1996) model of sticky prices. The demand curve facing the monopolist is given by y t (j)= p H,t (j) P H,t −ε Y H,t (2.27) y t (j) is total world demand for varietyj produced in the home country, whileY H,t is total aggregate demand in the home country: they are obtained by adding the demand for product j of domestic and foreign households, using (2.5) and (2.9). Since firms are owned by the households and their problem is dynamic, they discount their cash-flows using the nominal pricing kernel of the representative household,M $ t,t+1 = β λ t+1 λt 1 Π t+1 . Then, generic firmj chooses its selling pricep H,t+i (j) to max {p H,t (j)} ∞ X i=0 β i λ t+i λ t P t P t+i Γ t+i (j) subject to (2.27) and (2.24). The first order condition is: P ε H,t p −ε H,t (j)Y H,t ε p H,t (j) W t A t +(1−ε) −ϑ p H,t (j) p H,t−1 (j) −1 P H,t p H,t−1 (j) +ϑβE t " λ t+1 λ t P t P t+1 p H,t+1 (j) p H,t (j) −1 P H,t+1 p H,t+1 (j) p 2 H,t (j) # =0 In a symmetric equilibrium, all firms charge the same pricep H,t (j) = P H,t , and we have y t (j) = Y H,t andN t (j) = N t . Then, the expectations-augmented Phillips curve or aggre- gate supply (AS) equation can be expressed as ϑΠ H,t (Π H,t −1)=ϑβE t λ t+1 λ t a t+1 a t Π H,t+1 (Π H,t+1 −1) +εY H,t w t A t a t − ε−1 ε (2.28) 40 When prices are perfectly flexible,ϑ = 0 and we get that P H,t = ε (ε−1) Wt At ; that is, prices are set as a constant mark-up above nominal marginal cost. The Phillips curve (2.28) says that changes in expected future international prices, viaa t+1 /a t , or movements in expected future domestic inflation Π H,t+1 , or in today’s deviation of the price-marginal cost ratio from the constant mark-up, or in aggregate demandY H,t , will cause changes in domestic PPI inflation today. 2.2.3 Treasury department The government of each country imposes lump-sum transfers to the representative agent, in order to fulfill the debt valuation equation, given an exogenous process for the stock of real government debt. −τ t = sb t − sb t−1 R t−1 Π t + (R t−1 −1)b CB t−1 Π t + Q t (R ⋆ t−1 −1)fx t−1 Π ⋆ t (2.29) Notice that the treasury department does not enjoy seignorage revenues, but does not pay interest on debt held by the central bank. In addition, the domestic central bank pays any interest earned on foreign reserves as “dividend” to the treasury. It is assumed that log-bond supply follows an AR(1) process: lnsb t =(1−ρ sb )lnsb SS +ρ sb lnsb t−1 +ǫ sb t , (2.30) whereǫ sb t ∼ N(0,σ 2 sb ). 41 2.2.4 Central bank Inflation targeting The central bank (CB) of each country conducts monetary policy using an interest rate feedback rule that targets domestic CPI inflation: lnR t = (1−ρ R )lnR t−1 +ρ R [ρ Π (lnΠ t −lnΠ SS )]+ǫ MP t . (2.31) ǫ MP t ∼ N(0,σ 2 MP ) is the monetary policy shock. Notice that we allow for policy “inertia” by including the termlnR t−1 ; this will control the persistence of the short-rate. Foreign exchange (FX) reserve accumulation It is assumed that another entity, perhaps the treasury secretary, instructs the central bank to intervene in the foreign exchange (FX) market to support the domestic currency. The CB purchases foreign currency to maintain the real exchange rate close to an exogenously predetermined target, and its subject to random disturbances, which formalizes the notion of a CB foreign holdings shock, or intervention shock. The reaction function takes the standard form in the literature 4 The central bank intervenes in the FX market according to the rule: ln fx t =ln fx ss +ρ fx ln fx t−1 +ǫ fx t , (2.32) where Δe t ≡ lnE t − lnE t−1 . ǫ fx t ∼ N(0,σ 2 fx ) is the exogenous innovation to central bank reserve accumulation. One of the objectives of the paper is precisely to understand its effects on the level of bond holdings and interest rates. 4 For a comprehensive survey on academic research on the effects of central bank intervention, see Sarno and Taylor (2002). 42 Balance sheet identity Finally, given the FX reserve accumulation policy and the level of real money balances desired by the public as a function of the domestic interest rate, the central bank purchases domestic bondsb CB t through open market operations to fulfill its balance sheet identity Q t fx t − fx t−1 1 Π ⋆ t + b CB t −b CB t−1 1 Π t = m t −m t−1 1 Π t (2.33) The form of the “flow” budget constraint 5 of the central bank used in this paper simply extends that used in Jeanne and Svensson (2007) for the case where the bank holds FX reserves, as in Escude (2007). Notice the assumption that the central bank passes interest payments on domestic bonds and foreign reserves to the treasury as dividend. This is introduced for two reasons. One is that it makes the steady state value ofb CB t consistent with the static balance sheet constraint: fx ss +b CB ss =m ss The other is that it helps the model achieve an endogenous and stationary b CB t variable. If this were not the case, then given that both real money demand m t and real foreign exchange reserves fx t are stationary, equation (2.33) through the term b CB t−1 R t−1 Πt would define an explosive process, given that real interest rates are assumed positive. Also it is necessary to point out that, in the way the model is specified, central bank intervention would actually be unsterilized, that is, money demand would also change. However, quantitatively the response of money demand to an innovation in foreign reserves is almost negligible, so that for practical purposes the intervention can be though of as sterilized. 5 More like an Income Statement, and ignoring changes in Net Worth. 43 2.2.5 Market clearing conditions Aggregate supply The representative firm supplies varietyj to satisfy demand. Some of its output is lost as a consequence of the adjustment costs. In equilibrium, aggregate supply is given by: Y t =A t N t − ϑ 2 (Π H,t −1) 2 (2.34) A similar condition holds for the foreign country, replacing the variables with their ⋆ coun- terparts. Aggregate demand Adding the demands of domestic and foreign households for varietyj, we obtain the fol- lowing demand-side market clearing conditions: Y t =a −η t (1−α)c t +α ⋆ Q η t c ⋆ t Y ⋆ t =a ⋆−η t (1−α ⋆ )c ⋆ t +αQ −η t c t Notice how the real exchange rate affects inversely foreign demand for domestic output, while the PPI/CPI ratio affects domestic demand in the same way. 44 Bond market Both households and central banks invest in bonds of the two currencies. Therefore, the market clearing conditions for domestic and foreign bonds are: b t +b CB t + fx ⋆ t +b F⋆ t =sb t (2.35) b ⋆ t +b CB⋆ t + fx t +b F t =sb ⋆ t 2.2.6 Current account dynamics If we substitute the treasury department’s debt valuation equation (2.29) into the con- sumer’s budget constraint (2.16) and additionally use (2.35) to substitute forsb t , we obtain the current account (CA) dynamics equation Q t b F t + fx t − b F⋆ t + fx ⋆ t = a t Y t −c t + Q t b F t−1 + fx t−1 R ⋆ t−1 Π ⋆ t − b F⋆ t−1 + fx ⋆ t−1 R t−1 Π t + ψ ⋆ t−1 b F⋆ t−1 Π t − Q t b F t−1 ψ t Π ⋆ t . (2.36) This equation says that the change in net foreign assets comes from net exports and from surpluses in interest payments and transactions costs. 2.3 Solution method and calibration 2.3.1 Solution method The model is solved using a first order approximation of the equilibrium conditions around the steady state, also known as first order perturbation method. The software used is dynare++-, version 1.3.6. For details of the solution method, see Kamenik (2007). 45 2.3.2 Calibration The values assigned to the parameters in the simulations are presented in Table 1. Unless otherwise noted, the same values are assumed for both countries. On the consumer side, β is set equal to 0.9926, which corresponds to an annual steady state real interest rate of about3%. The relative risk-aversion parameter is set to a “low” 1.5, to avoid an excessively high elasticity of intertemporal substitution. The home-bias parameterα is set equal to 0.4 as in Gali and Monacelli (2005). The habit formation parameter is set equal to 0.66 as in Rudebusch and Swanson (2008), henceforth RS. For labor supply,ℓ = 4.74, φ = 1.5 as in RS. The elasticity of substitution between domestic and foreign consumption indexesη and between individual varietiesε are set equal to 1.5 and 7.5, respectively, as in Faia and Monacelli (2008) (FM). On the supply side, the Rotemberg adjustment cost parameterϑ is set equal to 75, as in (FM); this is obtained by mapping estimated parameters for the price adjustment frequency in the Calvo model with the coefficient on marginal cost on the Phillips curve under the Rotemberg model. The log-Technology shock parameters ¯ A,ρ A ,σ 2 A are set equal to 1, 0.9 and0.01 2 , respectively. To calibrate the bond supply processessb t andsb ⋆ t , an AR(1) process is estimated using the log-HP filtered real 6 total amount outstanding of marketable treasury bills collected from the Monthly Statement of the Public Debt reports 7 for the period 1978:02-2008:02. ρ sb and σ sb are set equal to 0.8031 and 0.0361 , while sb ss is set equal to the uncondi- tional mean of the ratio of total t-bills outstanding to Personal Consumption Expenditures 8 , which is about 0.10. Notice thatR t in the model refers to the 3 month treasury rate, and 6 All nominal quantities in this paper are deflated using the Price Index for Personal Con- sumption Expenditures from the FRED Database at the Federal Reserve bank of St.Louis website: http://research.stlouisfed.org/fred2/ 7 Which can be found at: http://www.treasurydirect.gov/govt/reports/pd/mspd/mspd.htm 8 This ratio has fluctuated from 0.08 to 0.15 during the 1978 -2002 period. 46 not to all short term bills, which means that the strategy used to calibrate sb t is only an approximation. The parameters of the Taylor rule are standard in the literature: φ R = 0.9, φ Π = 1.5 andσ MP =0.004. Canzoneri et al. (2008) (CCDLS), calibrate the parameters of the rule (2.32) using data on foreign official institutions (FOI) holdings of U.S. Treasury securities from the Flow of Funds accounts of the United States. This number evidently includes holdings of bills, notes and bonds. However, since in this paper the short rate refers to the 3 month rate and the market we model is specifically the market for short-term treasury securities, instead of calibrating fx t to FOI’s holdings of all types of treasury securities, we used data on foreign official institutions holdings of short-term instruments from the Treasury Interna- tional Capital System (TIC) website 9 , for the period 1978:04-2008:06. This provides a more accurate, but still imperfect, measure of the variable whose effects we are trying to trace. The explanation of the procedure as well as the parameter estimates are presented in Appendix 1. We set fx ss = 0.02 because foreign official holdings are about 20% of the total amount outstanding of Tbills. Financial frictionδ A key parameter in the model is the level of financial friction,δ. A first order approximation of the risk-sharing conditions gives E t [Δe t+1 ]−(i t −i ⋆ t ) =ϕΔb F t , (2.37) whereϕ = δβ Π ⋆ ss . This equation says that domestic agents increase their investment of for- eign bonds if the expected excess return, in terms of domestic currencyE t [Δe t+1 ]+i ⋆ t −i t is positive. In Kollmann (2002), a similar equation describes the relationship between the 9 The data can be downloaded from: https://treas.gov/tic/bltype history.txt 47 Table 2.1: Benchmark case parameter values Preferences β = (1.03) −0.25 ,θ = 0.66,γ = 1.5 ξ D = 0.001,ℓ =4.74,φ =1.5,α = 0.4 ε =7.5,η = 1.5 Technology ϑ = 75, ¯ A = 1,ρ A = 0.9,σ A = 0.01 Financial Friction δ =0.0034 andδ = 2.4 Treasury Department sb ss = 0.1,ρ sb = 0.8031,σ sb = 0.0361 Taylor Rule ρ R =0.9,ρ Π =1.5,σ MP =0.004 FX reserve policy fx ss = 0.02,ρ fx = 0.9023,σ 2 fx =0.0050 Bond Supply ρ sb =0.8031,σ sb =0.0361, sb ss =0.10 Unless otherwise noted, the values are the same for both countries. interest rate differential and net foreign assets (NFA) normalized by net exports. That vari- able has a different interpretation thanb F t in this model, which corresponds to a country’s private sector holdings of foreign country’s short-term treasury bills. To obtainδ in (2.37), Kollmann uses an estimate equal to 0.0034 taken from Lane and Lane and Milesi-Ferreti (2002). This number is obtained from a cross sectional regression across countries of their net foreign asset position (which evidently includes asset classes like equity and foreign direct investment) 10 on the real long term interest differential (they motivate their regres- sion equation with a steady state relationship). This approach has two problems: one, it estimates the elasticity of the real interest rate differential to the net foreign asset position of countries, and two, it is not a time series regression of expected returns. In the model, a time series regression with simulated data of the interest differential on Δb F t does not recoverδ. Only a time series regression of realized excess returns Δe t+1 −(i t −i ⋆ t ) can 10 There are some potential shortcomings in using Lane and Milesi-Ferreti’s estimates for the present pur- pose. For example, they estimateδ using real interest rate differentials on government bonds, not short term bills. Additionally, they use two measures of Net Foreign Assets (scaled by exports): one is the cumulative current account, and the other is the fitted value from a cross-country regression. Evidently, these measures include other asset categories other than short-term government bills, like equities, and foreign direct invest- ment. Some of these issues are raised in pp. 112. in their paper. 48 recover the true value ofδ. Therefore, the range of values for the friction parameterδ found in Kollmann (2002) or Lane and Milesi-Ferreti (2002) is not directly applicable to our case. Selaive and Tuesta (2003) estimate a version of (2.37) using GMM and obtain an estimate of 0.0044, but again they use data on Australian net foreign assets. The ideal variable to measure δ in (2.37) would be the change in the Net 11 foreign private asset position of short term government bonds. Such measurement, to the best of our knowledge, does not exist. The closest data that is available, for the U.S., is rest of the world holdings of short term U.S. Treasury securities, which is estimated by the Treasury International Capital System, of the U.S. Department of the Treasury. But this gives only foreigners change in positions of U.S. bills, and data on U.S. residents change in positions of rest of the world short term government bills is not available. Therefore, the net position cannot be constructed. We estimated regression (2.37) using rest of the world private holdings of U.S. short term treasury securities as an imperfect proxy for net foreign private assets, and constructed a FX market turnover weighted average of the 3 month LIBOR interest rates for the main currencies 12 as a proxy fori ⋆ t . The depreciation of the dollar Δe t was measured using the negative of the log growth rate of the Trade Weighted Exchange Index (major currencies) taken from the FRED database at the St. Louis Fed website. This expected returns forecasting regression gave an estimate ofδ of -0.0355 with a Hansen-Hodrick tstat of -1.17, which does not lend much support for high values ofδ. The problem with this approach is that, on top of the fact that the measure is imperfect, given the nature of the hypothesized frictions that make it costly for private agents to adjust portfolios, it is not clear why the interest rates on liquid government securities like 3 month bonds in the data should reflect costs that pertain exclusively to the private sector. 11 In equilibrium, it will be true that, up to a first order approximation,b F t =−b F⋆ t = x t , so that in reality, x t is not “gross” but rather “net” foreign private asset position. 12 Taken from Datastream. The 3 month LIBOR interest rates of the following currencies where used in constructing the “world” interest rate: EUR, JPY , GBP, CHF, CAN, AUD, SEK. 49 There are valid reasons to believe that the true cost to private agents to change inter- national bond portfolios are higher than what the above mentioned estimates suggest. In section 2.1.1 we present a motivation, taken from Lyons (2001), that is based on agency costs together with limited participation by certain agents in the FX market. Another plau- sible explanation is offered in Bacchetta and Wincoop (2008), who document that in the real world, ”there is little active currency management over ... medium term horizons”. They attribute this feature to the fees charged to investors for changing their foreign bond positions: for example, they document that “at20% risk, a typical fee for a currency (hedge) fund is a 1% management fee plus20% of profits” 13 . Along these lines, own calculations indicate that the average expense ratio for short term U.S. government bill mutual funds covered by Morningstar’s website 14 is about 0.0091, while that of foreign exchange funds is 0.0173; this is a considerable difference. Additionally, the mean expense ratio for short term government bond funds is taken across 156 funds, while the same number for FX funds is 30. There is a clear difference in the costs and the number of options for a typical investor if she wanted to invest in foreign currency. Therefore, in order to be able to study the implications of costly foreign bond portfolio adjustment, I choose to study in addition to the baseline case of δ = 0.0034, a case of “high” costs to take positions in the international bond market, whereδ =2.4. This “high” value is chosen so that the model-implied Sharpe ratio for the carry trade strategy is close to the data, taken from Burnside, Eichenbaum, Kleshchelski, and Rebelo (2006) (see Table 2). Also,δ = 2.4 is inside the range of parameter values considered by Tuladhar (2003). As we will see later, at this level of friction, the model features less responsiveb F t andb F⋆ t and has interesting insights into the effects of CB interventions, and deviations from UIP. Finally, notice that since the same level of friction is assumed for both countries, and preferences 13 As in Lyons (2001), the analysis of their model implies that international bond portfolios will adjust slowly to new information. 14 Athttp://www.morningstar.com/. Data as of mid November 2008. 50 are symmetric across consumers, on average neither country looses as a consequence of the transaction costs. However, its effects are crucial for the dynamic response of the world economy to shocks. 2.4 The effects of central bank accumulation of foreign reserves on interest rates In this section we analyze the effect of central bank accumulation of foreign bonds on the foreign interest rate by studying the impulse response functions of interest rates, budget constraints and international relative prices after an intervention shock. This graphical tool allows us to see the dynamic behavior of the variables of interest after the shock. Figure 2.1 presents the impulse response function of the foreign interest rate to an exogenous shock in domestic central bank holdings of foreign treasury’s bonds, for two cases: one in which the level of financial friction isδ = 0.0034 (top row), and another in whichδ = 2.4 (bottom row). Since both countries are symmetric, I only concentrate on the case of the foreign short-rate being shocked by a unitary standard deviation innovation in domestic central bank holdings of foreign bonds. The plots in the top row of Figure 2.1 show the impulse response of the foreign inter- est rate R ⋆ t to a positive one standard deviation innovation in ε FX t . As can be seen in the left box, the effect is negative but very small in magnitude. The response is negligi- ble when compared to other widely studied economic sources of time variation in bond yields, namely, technology and monetary policy (MP) shocks, as the box in the right col- umn shows. The reason for this result is simply that after an exogenous innovation inε FX t , both foreign CPI-inflation Π ⋆ t and foreign marginal utilityλ ⋆ t barely respond to the shock; as the top row of Figure 2.2 shows, the magnitudes are around−2 −7 . In turn,Π ⋆ t does not change because the shock fails to cause quantitatively important changes in foreign PPI 51 Figure 2.1: Impulse response of foreign interest rate to domestic CB intervention shock: low and high friction. 0 5 10 15 20 −6 −4 −2 0 2 4 6 8 x 10 −8 irf of R * t to ε FX 0 5 10 15 20 −1 −0.5 0 0.5 1 1.5 2 x 10 −3 irf of R * t : all shocks Foreign holdings Technology shock Monetary Policy shock 0 5 10 15 20 −6 −5 −4 −3 −2 −1 0 1 2 x 10 −5 irf of R * t to ε FX 0 5 10 15 20 −1 −0.5 0 0.5 1 1.5 2 x 10 −3 irfs of R * t : all shocks Foreign holdings Technology shock Monetary Policy shock Top row: low friction δ. Bottom row: high friction δ. Left column: impulse response of the foreign interest rate to home central bank intervention shock only. Right column: impulse response of the foreign interest rate to all (home) shocks. The numbers are in natural units, i.e.,1.5 −3 means 15 basis points. inflation Π ⋆ H,t or the relative pricesQ t anda ⋆ t , as the plots in the left panel (both rows) in Figure 2.2 show. λ ⋆ t changes by a greater magnitude than foreign CPI-inflation, but it is 52 also very small in absolute terms, as the top-left box in Figure 2.2 shows. This is to be expected since the change in consumptionc ⋆ t is negligible, as the bottom left box in Figure 2.3 shows. At the heart of the almost absent change in consumption is the ability of foreign households to neutralize changes in their domestic bond market with opposite positions in the foreign bond market, to satisfy their budget constraint. This can clearly be seen in the bottom left box on Figure 2.3, which plots the impulse responses of the components of the foreign agent’s budget constraint to theε FX t shock: all the agent needs to do is to substitute domestic bonds with foreign ones. However, things change when the level of the financial friction is “high”,δ = 2.4. The bottom left plot in Figure 2.1 shows that in this case, the foreign interest rate decreases by about 2.28 bp ( annualized) after a positive innovation to ε FX t . The plot on the right indicates that, although still small when compared to policy or technology shocks, now a foreign holding’s shock has a quantitatively important effect. The bigger negative impulse inR ⋆ t has two components. One is the positive expected growth in marginal utility (or a negative expected growth in consumption) that will follow the shock, which is depicted in the top left panel of Figure 2.2; this tends to decrease interest rates. The other is the response in expected CPI inflationΠ ⋆ t+1 which is positive, as can be seen in the same plot; this tends to increase interest rates. As can be seen, the marginal utility effect dominates. Finally, notice that now the response in foreign CPI-inflationΠ ⋆ overshoots its steady state value in period 2 after the shock, and therefore causes a positive expected inflation next periodE t [Π ⋆ t+1 ]. This happens because PPI inflation in the foreign economy next period Π ⋆ H,t+1 will be slightly positive (Π ⋆ H,t is negative), while at the same timea ⋆ experiences a big negative growth fromt tot+1, as seen in the right panel of the bottom row of Figure 2.2. The total effect then follows from the definitionΠ ⋆ t = Π ⋆ H,t a ⋆ t−1 a ⋆ t . 53 Figure 2.2: Impulse response of foreign inflation rates, foreign marginal utility and inter- national relative prices to a home CB intervention shock. 0 5 10 15 −4 −2 0 2 4 6 8 10 x 10 −7 ε FX => Foreign rates: low δ R * π * π * H λ* 0 5 10 15 −4 −2 0 2 4 6 x 10 −4 ε FX => Foreign rates: high δ R * π * π * H λ* 0 5 10 15 −1 −0.5 0 0.5 1 x 10 −6 ε FX => Relative Prices: low δ Q a a * S 0 5 10 15 −4 −2 0 2 4 6 8 x 10 −4 ε FX => Relative Prices: high δ Q a a * S Left column: low friction δ. Right Column: high friction δ. Top row: impulse responses of foreign interest rateR ⋆ t , CPI inflationπ ⋆ t , PPI inflationπ ⋆ H,t , and marginal utilityλ ⋆ t to home CB intervention shock. Bottom row: impulse responses of real exchange rate Q t , terms of tradeS t ; home country PPI-CPI ratioa t , foreign country PPI-CPI ratioa ⋆ t . The numbers are in natural units, i.e.,4 −4 means 4 basis points. Now, the interesting question is: how does increasing the level of financial frictions changes the effect of the foreign holdings shock on interest rates? Since the shock has 54 effects on the bond, currency, and goods markets brought by movements in relative prices and inflation, it is necessary to analyze in some detail how the effects of the shock propagate through both economies in each market. This is what is done next. Effects on bond and currency markets First, when a positive innovation toε FX t hits the economy, the balance sheet of the central bank (2.33) requires that if fx t increases, thenb CB t must decrease; this can be seen in the top row in Figure 2.4. Then, there are two effects on the bond markets of both countries. In the foreign country’s bond market, an increase in the foreign reserves of the home central bank fx t necessarily induces a market clearing decrease of the same magnitude in(b ⋆ t +b F t ), the sum of the holdings of bonds of the private sector; this can be seen in the top left panel of Figure 2.3. In the domestic country’s bond market, a decrease in the holdings of treasury bills of the domestic central bankb CB t necessarily induces a market clearing increase of the same magnitude in(b t +b F⋆ t ); this can be seen in the bottom left panel of Figure 2.4. If domestic and foreign bonds were perfect substitutes and there were no financial frictions, since both representative agents are perfectly symmetric, we would have that Δb ⋆ t = Δb F t = 1 2 Δfx t , and similarly Δb t = Δb F⋆ t = 1 2 Δb CB t , where Δx t = x t −x t−1 . Also, it is important to notice that we will have Δfx t ≃ Δb CB t , as the change in Q t is small in magnitude when compared to the changes in the balance sheet items: this implies that the size of the intervention is| Δfx t | or equivalently| Δb CB t |. Indeed, notice that for the case of low δ, in both the top left panel of Figure 2.3 and bottom left panel of Figure 2.4, the responses of the private agents portfolio holdings lie on top of each other, as they are of the same magnitude and almost indistinguishable from each other. Now, because there is a cost to taking positions in the foreign bond market for both represen- tative agents, we will have that Δb F⋆ t < 1 2 Δb CB t and Δb F t < 1 2 Δfx t . This implies that 55 Figure 2.3: Impulse responses of foreign bond holdings and foreign agent’s budget con- straint components to home CB intervention shock 0 5 10 15 −1 −0.5 0 0.5 1 1.5 x 10 −3 ε FX => Foreign Bond Mkt: low δ b* bF bCB* FX 0 5 10 15 −1 −0.5 0 0.5 1 1.5 x 10 −3 ε FX => Foreig Bond Mkt: high δ b* bF bCB* FX 0 2 4 6 8 10 12 −10 −8 −6 −4 −2 0 2 4 6 x 10 −4 FOREIGN Budet ε FX low δ 0 2 4 6 8 10 12 −10 −8 −6 −4 −2 0 2 4 6 x 10 −4 Foreign Budget ε FX high δ b F * *(1/Q) b * c * a * ⋅Y * m * Left column: low friction δ. Right Column: high friction δ. Top row: impulse responses of components of foreign bond market clearing condition, whereb ⋆ is foreign agent’s holdings of foreign bonds; b F is home agent’s holdings of foreign bonds; b CB⋆ is foreign central bank’s holdings of foreign (treasury bonds); and fx is home central bank’s holdings of foreign bonds (reserves). Bottom row: impulse responses of components of foreign agent’s budget constraint. (Δb F⋆ t +Δb F t )<Δfx t =| Δb CB t |. In fact,Δb F⋆ t andΔb F t will be smaller than 1 2 Δb CB t and 1 2 Δfx t , respectively, the higherδ is. This can clearly be seen from the risk-sharing equation Δb F t = 1 ϕ (E t [Δe t+1 ]+(R ⋆ t −R t )), 56 where ϕ = βδ Π SS . When the level of friction δ is low, we have that 1/ϕ is high and b F⋆ t responds strongly to even small changes in expected nominal depreciation and the interest rate differential, and viceversa whenδ is high. Or, equivalently, whenδ is high, significant changes in the exchange rate and interest rates are needed to induce even small changes in portfolios. This is shown in the top right and bottom right panels of Figures 2.3 and 2.4, respectively: notice how the responses of b F and b F⋆ are smaller than in the case of low δ, with the consequence that now, the position imposed on the agents by the central bank must be absorbed through domestic bondsb andb ⋆ . This observation has important implications for the impact of the foreign exchange intervention on the equilibrium exchange rate. Notice that the home central bank is demanding foreign currency when fx t increases, and this puts upward pressure on the nominal-exchange rate E t ; that is, it tends to depreciate the home currency. But, on the other hand, since private agent’s positions of the other country’s bonds respond in the oppo- site direction, that is Δb F t < 0 (sell foreign currency) when fx t > 0 and Δb F⋆ t > 0 (buy home currency) whenb CB t < 0, then Δb F t and Δb F⋆ t tend to appreciate the home country currency. However, given the existence of a financial friction, the change inb F⋆ t andb F t will be smaller than 1 2 Δb CB t and 1 2 Δfx t , which implies that the combined pressure to appreci- ate the home country currency is smaller than the central bank pressure to depreciate it. This increase in fx t will depreciate the home country currency, but the magnitude critically depends on how muchb F t andb F⋆ t respond to the shock, which in turn depends onδ. As can be seen in the bottom right panel of Figure 2.2, we observe a greater change in relative prices when the financial friction parameterδ is high, and in the top-right panel in Figure 2.5, we see that the impact depreciation of the home currency is much stronger when finan- cial frictions are high. The exchange rate effect gives rise to most of the other changes. 57 Figure 2.4: Impulse responses of the components of home CB balance sheet and home bond market to a home CB intervention shock. 0 5 10 15 −1.5 −1 −0.5 0 0.5 1 1.5 x 10 −3 ε FX => Home.CB.Bal.Sheet: low δ bCB FX m 0 5 10 15 −1.5 −1 −0.5 0 0.5 1 1.5 x 10 −3 ε FX => Home CB Bal.Sheet: high δ bCB FX m 0 5 10 15 −1.5 −1 −0.5 0 0.5 1 x 10 −3 ε FX => Home Bond Mkt: low δ b bF* bCB FX * sb 0 5 10 15 −1.5 −1 −0.5 0 0.5 1 x 10 −3 ε FX => Home.Bond.Mkt: high δ b bF* bCB FX * sb Left column: low friction δ. Right Column: high friction δ. Top row: impulse response of components of home CB balance sheet, where b CB is holdings of home (treasury) bonds; fx is holdings of foreign bonds; and m is money liabilities. Bottom row: impulse response of components of the market clearing condition for home country bonds, where b F⋆ is foreign agent’s holdings of home bonds and fx ⋆ is foreign CB holdings of home bonds (reserves). Effects on relative prices and real allocations Now, consider the effects on relative prices and real allocations of the nominal depreciation of the home country currency. Since demand depends on relative prices, we will analyze first what happens toa t ,a ⋆ t . 58 In the present case of a positive innovation in ε FX t , we have that the resulting depre- ciation of the home country currency increases a ⋆ t = P ⋆ H,t /P ⋆ t and reduces a t = P H,t /P t . The first result can be explained as follows. a ⋆ t = P ⋆ H,t /P ⋆ t goes up because P ⋆ t decreases by more than P ⋆ H,t . There is one force that puts downward pressure on P ⋆ H,t , namely, real wages: as the change in real exchange rates decreases world demand for foreign output rel- ative to home country output, foreign firms decrease the real wagew ⋆ t to induce the agent to work less, i.e., decreaseN ⋆ t . Then, the decrease in real wages causes a decrease in foreign PPI P ⋆ H,t . Next, recall that the foreign CPI P ⋆ t is a weighted average of their domestic PPI P ⋆ H,t and the home country PPI in units of foreign currency P ⋆ F,t . Then, the CPI-index P ⋆ t decreases by more than P ⋆ H,t simply because the impact effect on nominal depreciation of the home country currency (or appreciation of the foreign currency) is many times greater than the decrease in domestic inflation: this means that P ⋆ F,t decreases less than P ⋆ t . This explains whya ⋆ t goes up. Finally, the increasea t follows from the obvious opposite mecha- nism in the home country labor market and the exchange rate depreciation in home currency units. It can be seen in the bottom right plot of Figure 2.2 that the impact change ina t and a ⋆ t is magnified whenδ increases (compare the units between the left and right panels). The effects of the shock on output are thatY t increases whileY ⋆ t decreases. The first result can be explained as follows. Domestic demand for domestic output depends inversely ona t , which in this case decreases; this explains the increase in domestic demand for the domestic good. On the other hand, foreign demand for home goods depends inversely on (a t /Q t ). And as the bottom right plot in Figure 2.2 shows, the nominal home currency depreciation induces a real depreciation. Then, Q t increases and we have that the term (a t /Q t ) decreases by more than a t alone, expanding world demand for domestic output. As world demand for domestic output expands,Y t increases. The increase inY t is greater whenδ is higher. 59 The explanation of the decrease in Y ⋆ t follows the same logic, but with the effects reversed. Foreign demand for foreign output depends inversely ona ⋆ t , which in this case increases; this explains the decrease in foreign demand for their local good. On the other hand, home country demand for foreign output depends inversely on (a ⋆ t Q t ), which increases by more thana ⋆ t alone; this explains why home country demand for foreign out- put decreases. In the end, the result is a fall in world aggregate demand for the foreign country’s good, which causes the decrease inY ⋆ t . The decrease inY ⋆ t is greater whenδ is higher, as can be seen in the bottom right panel in Figure 2.3. Effects on consumption through the agent’s budget constraint Now we need to explain what is the mechanism that causes c t to decrease while Y t increases, and at the same time c ⋆ t to increase when Y ⋆ t decreases. The answer lies in the changes that the foreign exchange intervention by the domestic central bank induces on both agents budget constraints. Since the explanation centers on the foreign interest rate R ⋆ t , we will use the foreign agent’s budget constraint, which is reproduced here in a slightly different way for ease of exposition: c ⋆ t +b ⋆ t + 1 Q t b F⋆ t +m ⋆ t =a ⋆ t Y t +Ω ⋆ t (2.38) where Ω ⋆ t = 1 Π ⋆ t b ⋆ t−1 R ⋆ t−1 +m ⋆ t−1 +δ(b F t−1 ) 2 −τ ⋆ t + 1 Q t Π t b F⋆ t−1 R t−1 −δ ⋆ b F⋆ t−1 (2.39) defines real financial wealth. On impact m ⋆ t changes very little, at least when compared to the other components of the balance sheet of the central bank; this can be seen in the 60 plots at the bottom row of Figure 2.3. Because of this, we concentrate the discussion of the impacts of the shock on the remaining terms:c ⋆ t ,b ⋆ t , 1 Qt b F⋆ t , anda ⋆ t Y ⋆ t . 15 . First, notice that the bottom left plot of Figure 2.2 shows that when δ = 0.0034, the shock toε FX t causes negligible changes in relative prices. Then, it is no surprise to find that after anε FX t shock, the only variables of the foreign agent’s budget constraint that respond are the bond positions variablesb ⋆ t andb F⋆ t ; this can be seen in the bottom left box of Figure 2.3. They change simply to maintain equilibrium in the bond market. The key here is to notice thatb F⋆ t changes as much as b ⋆ t , a direct consequence of the low level of financial friction, or equivalently, their high degree of substitutability. When δ is high, c ⋆ t increases more and the answer as to why it does can be seen in the bottom right box in Figure 2.3, which plots the response of the components of the foreign agent’s budget constraint to the ε FX t shock. On the asset side, we know that Y ⋆ t decreases, but it is actuallya ⋆ t Y ⋆ t what matters, since the nominal profits of the firms are paid at PPI prices, not CPI prices. And sincea ⋆ t increases after the shock, we have that the “real income” of the foreign agent does not decrease as much as Y ⋆ t . 16 . Therefore, the main “income” components of the foreign agent balance sheet decrease after the shock. With real income and real financial wealth decreasing at impact, it might seem counter- intuitive to have increasing consumption, but the key is the change in the portfolio compo- sition of the agent. The big negative change inb ⋆ t forced by the small change inb F⋆ t because of the financial friction, causes the remaining termc ⋆ t to increase, given a mitigated decrease ina ⋆ t Y ⋆ t . In essence, what happens is that the decrease in bond holdings is so big that with a not-so-big decrease in income, consumption must increase. Finally, the obvious opposite effect explains whyc t decreases. The increase inc ⋆ t gives rise to an impact decrease inλ ⋆ that is associated with a positive expected marginal utility growthE t [λ ⋆ t+1 ]−λ ⋆ t , as seen in 15 The evolution over time inΩ ⋆ t reflects past decisions and inflation effects 16 Real financial wealth Ω ⋆ t decreases, mainly from an increase in real taxes that comes with the impulse decrease in inflationΠ ⋆ t 61 the top right box of Figure 2.2. Since the growth in expected marginal utility is greater in magnitude than expected inflation next period, the interest rate decreases. Figure 2.5: Impulse response of nominal depreciation and interest rate differential to a home CB intervention shock and home Monetary Policy shock. 0 5 10 15 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 x 10 −6 ε FX => Δ e t and (R−R * ): low δ Δe t R−R * 0 5 10 15 −1.5 −1 −0.5 0 0.5 1 x 10 −3 ε FX => Δ e t and (R−R * ): high δ Δe t R−R * 0 2 4 6 8 10 12 −0.03 −0.025 −0.02 −0.015 −0.01 −0.005 0 0.005 ε MP => Δe t and (R−R * ): low δ Δe t R−R * 0 2 4 6 8 10 12 −0.03 −0.025 −0.02 −0.015 −0.01 −0.005 0 0.005 ε MP => Δe t and (R−R * ): high δ Δe t R−R * Left column: low frictionδ. Right Column: high frictionδ. Impulse responses of the nominal home currency 1-period log-depreciation rate Δe t = ln E t /E t−1 and the nominal 1-period interest rate differential(R t −R ⋆ t ) to an exogenous home central bank intervention shock (top row) and to an exogenous home Monetary Policy shock (bottom row). The numbers are in natural units, i.e.,0.005 means 50 basis points. 62 2.5 The forward premium anomaly and UIP We have seen that the financial friction can have important effects on the dynamics of interest rates and exchange rates. It is natural then to ask what are its implications for uncovered interest parity, one of the cornerstone conditions in equilibrium international finance models. Special attention will be paid to the short and long-run evidence on UIP. Before explaining the implications of the model for the theory of UIP, it will be useful to briefly review the theory, the way it is tested, and the available empirical evidence. 17 This will help to put the results into context and establish some terminology that will be used when discussing the numerical results of the model. The reader acquainted with the theory of UIP is invited to skip the next section and jump directly to section 2.5.2. 2.5.1 Brief review of UIP and the forward premium anomaly If market participants are risk neutral, then in equilibrium the expected payoff from a strat- egy in which an investor borrows 1 unit of the domestic currency at the log interest rate of i t , converts it into foreign currency at the spot rate ofE t , invests it at the foreign interest rate ofi ⋆ t , and sells the proceeds at the spot price prevailing at the end of one periodE t+1 , should be zero: E t [Δe t+1 ] =i t −i ⋆ t . (2.40) In the last equation, Δe t+1 = e t+1 −e t = ln(E t+1 /E t ) is the log-depreciation rate of the home currency,i t =lnR t is the log nominal interest rate andi ⋆ t =lnR ⋆ t is the log nominal foreign interest rate. On the other hand, a related proposition that is a direct consequence of the absence of arbitrage opportunities is Covered interest Parity (CIP). It states that if arbitrageurs follow a similar strategy but instead of selling spot, they cover their position 17 The next section on UIP draws heavily from chapter 2 in Sarno and Taylor (2002), and from the discus- sion in Backus, Foresi, and Telmer (2001). For a survey of the theory and empirical strategies used in testing UIP, see Engel (1996). 63 in foreign currency by selling the proceeds at the forward price ofF (1) t , the following must hold: f (1) t −e t =i t −i ⋆ t , (2.41) wheref (1) t = lnF (1) t . Therefore, if there are no arbitrage opportunities and market partici- pants are risk neutral, as a consequence of both (2.41) and (2.40) we get that f (1) t =E t [e t+1 ], (2.42) which is known as the unbiasedness hypothesis of the forward rate. UIP is usually tested by running regressions of the form 18 : Δe t+k =α (k) +β (k) (i (k) t −i ⋆(k) t )+ε (k) t (2.43) or Δe t+k =α (k) +β (k) (f (k) t −i (k) t )+ǫ (k) t (2.44) In the data, it is generally found that CIP (No Arbitrage) holds, or that its deviations are within bid-ask spread bounds. For the rest of the paper, equation (2.43) or (2.44) will be refereed to as a “Fama regression”, and the slope coefficientβ (k) will be referred to as a “Fama slope coefficient”. A plot ofβ (k) againstk will be referred to as the “term structure of Fama slope coefficients”. Alvarez, Atkeson, and Kehoe (2005) also refer toβ as “the slope coefficient in the Fama Regression”. As can be seen, regression (2.43) is actually a test of the joint hypothesis that agents are risk neutral and that their expectations are rational, while (2.44) adds the requirement that 18 Examples of studies that use specification (2.44) include Fama (1984), Backus et al. (2001), Burnside et al. (2006), and McCallum (1994). Studies that use specification (2.43) include Chinn (2006), Chinn and Meredith (2004), Chinn and Meredith (2005), and Mark and Moh (2007). 64 the forward rate be an unbiased predictor of future spot rates. Both UIP and the Unbiased- ness Hypothesis require that the estimated coefficients satisfyα (k) = 0 andβ (k) =1 for all k. Short-horizon evidence. A wealth of empirical studies, surveyed in Sarno and Taylor (2002), generally find that estimates of the parameters in both regressions satisfyα > 0 andβ < 0, withβ usually being close to -1. Therefore, the evidence rejects the UIP proposition, and the unbiasedness hypothesis of the forward rate,f (1) t 6=E t [e t+1 ] . Interestingly, some of the most influential studies, such as Fama (1984) or Backus et al. (2001) estimate the regression for short horizons, such as k = 1 or 3 months. A common explanation, among others 19 is that the rejection of the nullβ = 1 reflects the presence of a time-varying risk premium 20 , or that equivalently, agents are not risk neutral. To see this, decompose the forward premium (f (1) t −e t ) into the expected depreciation and a risk-premium, as follows f (1) t −e t =E t [Δe t+1 ]+rp t . (2.45) Sincerp t is imputed into a forward price, it is named a “forward” risk premium. Then, the population slope coefficient in regression (2.44) can be expressed as β = cov(f (1) t −e t ,e t+1 −e t ) var(f (1) t −e t ) = cov(rp t ,Δe t+1 )+var(Δe t+1 ) var(rp t +Δe t+1 ) We see thatβ = 1 only ifvar(rp t ) =0. On the contrary, the finding thatβ < 0 implies that cov(rp t ,Δe t+1 ) < 0 and thatvar(rp t ) > Δe t+1 . Therefore, this evidence formalizes the 19 Again, see Sarno and Taylor (2002) for a discussion of other approaches to explaining the failure of UIP, most notably irrational expectations, rational learning, peso problems in the data, and information processing. 20 The discussion follows Backus et al. (2001) closely. 65 notion that foreign exchange risk premiums are time-varying and negatively correlated with subsequent depreciation rates. This constitutes the so called “forward premium anomaly” or the short-run evidence against UIP. Long-horizon evidence Chinn (2006) and Chinn and Meredith (2004), Chinn and Meredith (2005), perform long- horizon regression tests of (2.43) for maturities grater than 1 year. They cannot reject the null hypothesisβ =1 for the 5 and 10 year maturities for most of the currencies they study (JPY , DEM, GBP, CAN). Most importantly, they find that the term structure of Fama slope coefficients is upward sloping: a plot ofβ k against time delivers an upward sloped line that starts at values close to -1 and ends at numbers close to 1, for the 10 year horizon. This is the long-horizon evidence in favor of UIP. 2.5.2 Model implications for UIP and the forward premium anomaly As before, we will study of the model implications for UIP by analyzing the impulse response functions of interest rates and exchange rates after a monetary policy and inter- vention shock. They are specially suited for this this purpose, since deviations from UIP in the model critically depend on the behavior of the exchange rate in the periods after the shock. The model is consistent with both the short-horizon failure of UIP, and an upward slop- ing term structure of Fama slope coefficients up to the 3-year horizon. In the left panel of Figure 2.6, the model-implied term structure of UIP coefficients is shown together with estimated coefficients for several currencies, taken from Chinn and Meredith (2004). The model captures the general upward sloping pattern up to 10 quarters, and then the term 66 structure becomes flat. The right panel of Figure 2.6 plots the model-implied term struc- ture of Fama slope coefficients for several different values of the parameterδ. As can be seen, violations of UIP are increasing in the level of the friction. Next, we describe in some detail the mechanisms that generate a forward premium anomaly and an upward sloping term structure of Fama slope coefficients in the theoretical model. Of the 4 structural shocks in the model, only monetary policy and foreign holdings shocks generate deviations from UIP. Figure 2.6: Term structures of Fama slope coefficients 0 10 20 30 40 −3 −2 −1 0 1 2 UIP Fama Slope Coeffs: Data and Model dem jpy gbp can model 0 10 20 30 40 −1 −0.5 0 0.5 1 1.5 2 UIP Fama Slope Coeffs: Model, many δ δ=0.01 δ=2.4 The left box plots the term structure of Fama slope coefficients in the model together with the corresponding structures estimated from the data for sev- eral currencies, taken from Chinn and Meredith (2004). The right box shows the model-implied term structures for different values of the financial friction parameterδ. Monetary policy shocks The bottom right plot in Figure 2.5 shows that when δ is high a monetary policy shock causes a forward premium anomaly, or short-term deviation from UIP for two reasons. 67 First, the response of the nominal interest rate differential R t −R ⋆ t is more positive and persistent, and it corresponds to a real interest rate increase in the home country. Second, the home currency depreciation is less negative at impact but the effect takes longer time to dissipate; equivalently, the appreciation does not happen all at once, but is rather spread over time, as conjectured in Froot and Thaler (1990). Then, a positive interest rate dif- ferential today is associated with a negative home currency depreciation tomorrow, and a regression ofΔe t+1 on(R t −R ⋆ t ) will generate a negative slope coefficient. Compared to the case of low δ, why does increasing the level of financial friction increase the impulse response of the interest rate differential to anε MP t shock, while mak- ing more persistent the negative response of Δe t ? In order to answer this question, we must examine the effects of the shock on the two variables of interest, and the role the financial market friction plays in the propagation of the shock. Interest rate differential. Whenδ is low, the interest rate differential increases, but by a small 4 basis points, evidently because interest rates increase in about the same magnitude on both countries: R t increases 15bp whileR ⋆ t increases 11bp. In turn, the nominal home rate increase is accomplished by a stronger negative subsequent marginal utility growth E t [λ t+1 ] that overpowers the effect of decreases in expected inflation E t [Π t+1 ]: this can be seen in the top left panel in Figure 2.7. When δ is high, the interest rate differential increases strongly after the shock: 13bp. This is because the home interest rateR t increases more than in the case of lowδ, to 20bp, while the foreign interest rateR ⋆ t increases less, 7bp. As before, the response of interest rates can be separated into the effect on marginal utility and inflation. In the home country case, expected inflationE t [Π t+1 ] is actually more negative; this would in fact contribute to a smaller response of the nominal rate. Therefore, the strong positive increase in R t is almost entirely a consequence of a more negative expected growth in marginal utility, this can be seen in the top right panel in Figure 2.7. This, in turn reflects a more negative response in consumptionc t to the monetary policy 68 Figure 2.7: Impulse response of home and foreign inflation rates and marginal utilities to a home Monetary Policy shock. 0 2 4 6 8 10 12 −0.015 −0.01 −0.005 0 0.005 0.01 0.015 0.02 ε MP => Home rates: low δ R π π H λ 0 2 4 6 8 10 12 −0.015 −0.01 −0.005 0 0.005 0.01 0.015 0.02 ε MP => Home rates: high δ R π π H λ 0 2 4 6 8 10 12 −4 −2 0 2 4 6 8 10 x 10 −3 ε MP => Foreign rates: low δ R * π * π * H λ* 0 2 4 6 8 10 12 −4 −2 0 2 4 6 8 10 x 10 −3 ε MP => Foreign rates: high δ R * π * π * H λ* Left column: low friction δ. Right Column: high friction δ. Top row: impulse responses of home CPI and PPI inflation rates (π t andπ H,t ), nominal interest rate, and marginal utility to a home Monetary Policy shock. Bottom row: impulse responses of foreign CPI and PPI inflation rates (π ⋆ t and π ⋆ H,t ), nominal interest rate, and marginal utility to a home Monetary Policy shock. The numbers are in natural units, i.e.,4 −3 means 40 basis points. shock. And here is where the level of the financial friction is critical: as can be seen in the top right panel of Figure 2.8, the high level of financial friction prevents the agent from 69 taking a big negative position in the international bond market. Therefore, consumption must decrease by more, and marginal utility increases more at impact, thus causing the subsequent fall in marginal utility growth, or log-change. Notice that the agent cannot just substitute a negative position inb F t with an even more negative position inb t because that would require a market-clearing increase in the bond position of some other agent, either the central bank or the foreign consumer. But as can be seen in the bottom row of Figure 2.9, the home central bank must actually decrease its holdings of home bonds given that the contractionary shock decreases money demand, and by its balance sheet, the bank must conduct an open market operation and sell bonds. On the other hand, the foreign consumer is as constrained in the international bond market as the domestic one, so its real holdings of home country bondsb F⋆ t do increase, but a little. Unable to short bonds to anyone, the home agent is forced to reduce its consumption. A similar mechanism explains why the consumption of the foreign agent does not decrease below its steady state value as much when δ is high. Basically, when δ was low, it was easy to sacrifice consumption to buy real bonds and then finance a persistent level of consumption above real incomea ⋆ t Y ⋆ t in the future, as the bottom left plot of Figure 2.8 shows, specially 6 quarters after the shock. Whenδ is high, the foreign agent cannot take big positive positions in the bond market to invest for the future, so there is no point in sacrificing consumption today, and therefore his decrease in consumption is smaller. This makes both the impact increase in marginal utility and its subsequent negative change much smaller, mitigating the effect onR ⋆ t . Currency depreciation Whenδ is low, the home currency appreciates strongly at impact, but only to return close to its steady state level in the next period and stay at it afterwards; that is, although strong, the policy shock has no persistence onΔe t . In fact, on the period after the shock, Δe t+1 is actually more positive than (R t −R ⋆ t ) and this relationship is maintained for 7 quarters ahead until it dissipates. Because of this, a regression on Δe t+1 on(R t −R ⋆ t ) in fact generates a positive slope coefficient, consistent with UIP. 70 Figure 2.8: Impulse response of home and foreign agent’s budget constraint components to a home Monetary Policy shock. 0 5 10 15 −8 −7 −6 −5 −4 −3 −2 −1 0 1 x 10 −3 HOME Budget ε MP low δ 0 5 10 15 −8 −7 −6 −5 −4 −3 −2 −1 0 1 x 10 −3 HOME Budet ε MP high δ b F *Q b c a⋅Y m 0 5 10 15 −2 −1 0 1 2 3 4 5 6 x 10 −3 FOREIGN Budet ε MP low δ 0 5 10 15 −2 −1 0 1 2 3 4 5 6 x 10 −3 Foreign Budget ε MP high δ b F * *(1/Q) b * c * a * ⋅Y * m * Left column: low friction δ. Right Column: high friction δ. Top row: impulse responses of components of the home agent budget constraint to a home country Monetary Policy shock. Bottom row: impulse responses of components of the foreign agent budget constraint to a home country Monetary Policy shock. b is holdings of own country’s bonds,b F is holdings of the other country’s bonds,c is consumption,m is real money andaY is real income. 71 On the other hand, when δ is high, the home currency’s appreciation is less strong at impact, but critically, is now very persistent. To analyze the behavior of home currency depreciationΔe t whenδ is high, it is useful to use the identityΔe t = Δq t +Π t −Π ⋆ t , which decomposes the depreciation. At impact Δe t decreases less than when δ is low because there is a smaller real appreciation of the domestic currency, a smaller decrease in domestic CPI inflation, and a smaller increase in foreign CPI inflation. But the key is that after the shock, the home currency depreciation remains below its steady state level for many periods, as the appreciation is now persistent. This is in contrast to the case whenδ is low, where impact appreciation is very strong, but almost disappears after the second period. Now, to understand the behavior ofΠ t , we use the identityΠ t =Π H,t −Δa t , whereΔa t = lna t − lna t−1 . Because now the change in the relative price a t is smaller, the response of Π t mimics that of Π H,t . In turn, the response of domestic inflation Π H,t is virtually insensitive to changes inδ, a result that was to be expected given that the contractionary effects onY t must necessarily decrease the real wagew t . 21 Most importantly, the response ofΠ H,t to a home monetary policy shock is always very persistent, as it does not fade away even after 10 quarters; this can be seen in the bottom panels of Figure 2.7. Therefore, the persistent response inΠ t can be explained from the fact that its behavior now mimics that of Π H,t . Finally, since the shock originates in the other country, the effect on foreign CPI inflation Π ⋆ t depends mainly ona ⋆ t , which responds less strongly whenδ is high, because the real exchange rateQ t responds less. Overall, it is the persistent negative response of domestic PPI inflation together with a weak impact on relative prices that causes a persistent home currency depreciation rate below its long run level, or equivalently, a persistent home currency appreciation. These two effects, namely, the persistent positive impulse in the interest rate differential together with a persistent appreciation of the domestic currency explain a negative slope 21 The difference in the response of laborN t can be traced to the less pronounced effect ofλ t . 72 coefficient in a UIP regressions. As the effect dissipates over time, the relationship between these two variables is less strong and regression coefficients decrease in absolute value, thus explaining the upward sloping term structure of UIP regression coefficients. Central bank FX intervention shocks In the top row of Figure 2.5, the response of the interest rate differential and the rate of home currency depreciation to an innovation in home central bank holdings of foreign short-term treasury securities is shown. The response of the interest rate differential(R t − R ⋆ t ) is positive, while that of the rate of depreciation Δe t is positive at impact, negative the next period, and mildly positive afterwards. This means thatβ (1) in regression (2.43) will be negative. Therefore, in this model, foreign holdings shock also cause a short-term deviations form UIP. This feature of the model is consistent with the results in Mark and Moh (2007) modified target-zone model in which surprise central bank interventions cause a forward premium anomaly. The economic mechanism behind UIP deviations after a foreign holdings shock is sim- ilar to what was explained in section 2.4. Specifically, the interest rate differential is more positive than in the case of lowδ because a high financial friction forces greater changes in relative prices and (domestic) bond portfolios, which translate into greater changes in aggregate demand and consumption, and hence, in marginal utility. Home currency depre- ciation is negative after the shock, mainly because domestic CPI inflation Π t undershoots its steady state level after experiencing a drastic increase at impact due to the nominal depreciation 22 , while foreign inflation does the opposite (see the top right plot in Figure 2.2). As both rates of inflation quickly return to their steady state levels 2 periods after the shock, this cause the depreciation to return to its steady state level 2 periods after the shock. This follows from the identity: Δe t = Δq t +Π t −Π ⋆ t . 22 This mechanism is exactly the opposite of what is shown in the top row of Figure 2.2 for the case of foreign rates. 73 Figure 2.9: Impulse Responses of international relative prices and home bond market com- ponents to a home Monetary Policy shock. 0 2 4 6 8 10 12 −15 −10 −5 0 5 x 10 −3 ε MP => Relative Prices: low δ Q a a * S 0 2 4 6 8 10 12 −15 −10 −5 0 5 x 10 −3 ε MP => Relative Prices: high δ Q a a * S 0 2 4 6 8 10 12 −6 −4 −2 0 2 4 6 x 10 −3 ε MP => Home Bond Mkt: low δ b bF* bCB FX * 0 2 4 6 8 10 12 −6 −4 −2 0 2 4 6 x 10 −3 ε MP => Home.Bond.Mkt: high δ b bF* bCB FX * Left column: low friction δ. Right Column: high friction δ. Top row: impulse responses of international relative prices to a home Monetary Policy shock, whereQ t is the real exchange rate, S t is the terms of trade, a t is the home country PPI-CPI ratio, a ⋆ t is the foreign country PPI-CPI ratio. Bottom row: impulse responses of components of the home country bond mar- ket clearing condition to a home Monetary Policy shock. b is home country’s agent holdings of home bonds;b F⋆ is foreign agent holdings of home bonds;b CB is home central bank holdings of home (treasury) bonds; fx ⋆ is foreign central bank holdings of home bonds (reserves). 74 2.5.3 Sharpe ratios for carry trade strategies Deviations from UIP are intimately related to the profitability of currency strategies like the “carry trade”, which involves borrowing currencies with low interest rates, investing in currencies with high interest rates, and leaving the position uncovered hoping to profit from benign exchange rate changes. For example, ifi t is the nominal interest rate in the home country,i ⋆ t is the nominal interest rate in the foreign country andΔe t+1 = ln(E t+1 /E t ) is the realized depreciation of the home currency, then the profitΥ t+1 to the carry trade when i ⋆ t >i t is Υ t+1 = Δe t+1 +i ⋆ t −i t . Table 2.2: Sharpe ratios of the carry trade strategy: model and data δ Data 0.0034 0.01 0.5 1.0 2.0 2.5 3 Mean 0.00002 0.00007 0.0016 0.0027 0.0041 0.0046 0.0051 0.0093 σ 0.03807 0.03797 0.0349 0.0328 0.0299 0.0289 0.0281 0.0502 Sharpe 0.00053 0.00176 0.0457 0.0820 0.1361 0.1590 0.1802 0.1853 This table presents the mean return, return standard deviation and Sharpe ratio for the pay- offs Υ t+1 to the carry trade strategy, defined as Υ t+1 = −Δe t+1 + i t − i ⋆ t when i t > i ⋆ t , or Υ t+1 = Δe t+1 + i ⋆ t − i t when i t < i ⋆ t . Here, i t denotes the log-nominal interest rate of the “home” country, i ⋆ t denotes the log-nominal interest rate of the “foreign” country, and Δe t+1 =ln(E t+1 /E t ) is the depreciation rate of the home country currency, asE t is defined as units of home country currency per unit of foreign country currency. The statistics are obtained using simulated data from the model under different parameter values. Each sim- ulation consists of 2000 quarters, and the statistics are the average across 2000 simulations. The column labeled “data” presents the average figures for the case of no transactions costs presented in Table 2 in Burnside et al. (2006). The units are quarterly simple non-annualized rates. Notice that, as Lyons (2001) pp. 210 notes, the payoff to the carry trade strategy is on average zero when UIP and CIP hold. Therefore, the forward premium anomaly and the profitability of the carry trade strategy are intimately linked, and it is to be expected that 75 the model would be able to reproduce Sharpe ratios for currency strategies close to the data when UIP does not hold. Indeed, this is what we observe in Table 2.2, which shows the average Sharpe ratio for the carry trade strategy for several values of the parameter δ. It can clearly be seen that when financial frictions are low, UIP holds approximately and the Sharpe ratio of the carry trade is close to zero, specially the mean return. On the other hand, for parameter values ofδ close to 3, the Sharpe ratio using simulated data from the model is close to the data(last column), taken from Burnside et al. (2006). 2.6 Conclusion This chapter shows that when there are adjustment costs in changing positions in the inter- national bond market for the private agents of both countries, exogenous innovations in central bank demand for foreign exchange reserves can cause a significant decrease in the foreign interest rate. They can also cause deviations from UIP. Also, increasing the level of portfolio adjustment costs changes dramatically the effects of a monetary policy shock on the exchange rate and interest rates. Specifically, when there are costs that prevent flex- ible adjustment of bond positions to shocks, policy shock can cause deviations from UIP at short-horizons, and change the structure of impulse responses in the model in a way that makes the model consistent with the long-run evidence in favor of UIP. The central features that allow the model to be consistent with the evidence on UIP and that predicts effects on interest rates following central bank interventions are costs to change positions in foreign bonds, and international asset market incompleteness, which creates a role for budget constraints and market clearing conditions. Portfolio adjustment costs effectively prevent any representative agent from instantaneously taking extreme posi- tions in response to shocks. When the shock is in the bond market, the effect is mainly on relative prices, and there is a greater relative price change when agents are unable to change 76 their positions. When the shock is via monetary policy, the effect is mainly on real allo- cations and can be mitigated if portfolios are flexible, but when they are not, consumption must respond more. If any one agent cannot take extreme positions, this limits the extent to which the other agent can absorb either a large short-sell or purchase, or mitigate real income falls. Effectively, both agents and central banks are linked through bond market clearing conditions. 77 Chapter 3 Currency positions and foreign exchange risk premia 3.1 Introduction This paper provides evidence on time variation in foreign exchange risk premia. It exam- ines the empirical performance of two informational variables, aggregate currency order flow and speculative trader’s net futures positions, in explaining the variation in future excess returns for 6 currencies: Australian Dollar (AUD), Canadian Dollar (CAD), Swiss Franc (CHF), Euro (EUR), British Pound (GBP), and Japanese Yen (JPY). The rationale for considering the first variable is as follows: M. Evans and Lyons (2002) have shown that order flow can explain contemporaneous exchange rate changes, and in their model this explanatory power comes from the fact that flows reveal private information to the market. Therefore, it is natural to investigate whether such private information is also related to future exchange rate changes and hence excess returns. On the other hand, the motivation for using the level and the change in the net position of speculators in the CME 1 is that this variable is widely viewed as a measure of speculators expectations about future exchange rate movements 2 . We find that aggregate order flow is not a strong predictor of excess returns, while the net long futures positions is. For all currencies, the net long position is statistically 1 Chicago Mercantile Exchange. 2 See Klitgaard and Weir (2004). Also, see Piazzesi and Swanson (2008) for an application to the Federal Funds futures market 78 significant and can forecast excess returns at the 1 month horizon. For some currencies, like the EUR or JPY , the forecasting power, as measured by theR 2 , is as high as 16.34% and 15.99%, respectively. In general, the forecasting ability is stronger at the 1 month horizon, as only for the AUD, CAD and EUR, can excess returns be significantly forecasted at the 3 month horizon, with theR 2 ’s being 8.42%, 7.96% and 9.85%, respectively. Importantly, different linear transformations of the variables forecast returns at differ- ent horizons and for different currencies. For example, while the net long CME futures positions is a strong predictor of 1 month ahead excess returns for the Euro, with an R 2 of 16.37%, the same variable explains only 4.37% of the variation in CHF excess returns. But when the difference in the net long position is used for the Swiss Franc, the regression specification can explain 9.97% of the variance of future excess returns. For the Yen, a similar conclusion holds: including the level of net long CME positions in the regression equation helps to explain 10.60% of the variance of future excess returns, but when the 1 month change is employed, theR 2 increases to 15.77%. This suggests that the nature of speculation and short term currency movements differ across currencies. 3.1.1 Related Literature Between the many explanations that have been proposed to explain the rejections of UIP, one of the most influential has been Fama (1984), in which it is shown that negative UIP regression coefficients imply the existence of a time-varying and volatile forward risk pre- mium. A large body of work has tried to find a risk premium testing partial equilibrium models. For example, under the portfolio balance model, the risk premium should depend on relative asset supplies. However, in this strand of the literature, most notably Frankel (1982a) and Frankel (1982b), empirical research has generally failed to find predictabil- ity of excess returns using measures of asset supplies. Another approach is to estimate the parameters of the Euler equation of the representative agent in extensions of the Lucas 79 (1982) model. Again, these models were not been completely successful, as the implied parameters (for example, risk aversion coefficients) are usually considered “large”. 3 More recently, some papers have extended either the Campbell and Cochrane (1999) habit-based model or the long-run risks model of Bansal and Yaron (2004) to an inter- national setup in order to account for the forward premium anomaly. These papers try to explain the forward premium anomaly as being driven by exposure to systematic risk. An example of the first approach is Verdelhan (2009), and of the second is Bansal and Shaliastovich (2008). These papers have had success in replicating UIP regression coeffi- cients using simulated data, but only Verdelhan (2009) tests the Euler equation implied by his model, while the latter paper replicates the UIP regression coefficients using simulated data form the model. The paper closest to ours, in the sense that they also focus on forecasting excess returns, is Lustig, Roussanov, and Verdelhan (2009). They sort currencies into portfolios based on their beginning-of-period forward discounts, and find that both the individual portfolio and the average across portfolios log forward discounts can predict excess returns up to the 12 month horizon. The highestR 2 at the 1 month horizon is 7.85%, while it is 17.87% at the 3 month horizon. They also forecast the 12 month ahead excess returns using the 12-month change in Industrial Production (IP) together with forward discounts. Although they find significant predictability, with the highestR 2 being close to 40%, forward discounts loose most of their significance once the growth in IP is included. The main difference between their results and ours is, first, that they use portfolios while we use individual currencies, and that they find predictability at short horizons using market prices, like forward dis- counts, while we forecast short term excess returns with informational variables. Also, their highestR 2 ’s are 7.85% at the 1 month horizon and 17.87% at the 3 month horizon, obtained using the average (across portfolios) forward discount. In our best specification, 3 For a complete survey of this area of research, see Sarno and Taylor (2002). 80 we can forecast 16.34% of EUR excess returns and 15.77% of JPY excess returns at the 1 month horizon. On the other hand, while the forecasting ability of our variables generally decreases with horizon, the forecasting ability of the regressors in their paper generally increases with maturity. The rest of the paper is organized as follows. Section 3.2 describes the data, the inde- pendent variables and explains the definitions used to measure excess returns. In Section 3.3, we present the baseline results, and some robustness tests. Section 3.4 concludes. 3.2 Data description and return definitions Leti (k) t andi ⋆(k) t denote, respectively, the domestic and foreign effective interest rates for risk free loans made between timet andt+k, wheret andk are measured in months. We use data for the Canadian dollar (CAD), the Euro(EUR), the Japanese Yen(JPY), the Pound Sterling(GBP), the Swiss Franc (CHF) and the Australian Dollar (AUS). These are LIBOR interest rates from Datastream. The domestic interest ratei (k) t is the dollar interest rate, as all the excess returns in this paper are measured against the U.S. dollar. Let E t be the nominal exchange rate, expressed in units of domestic currency (i.e. U.S. dollar) per unit of foreign currency (i.e. yen or euro). The exchange rate data for each country are from the FRED Database at the St. Louis Fed 4 . Then, if we denote as Δe t+k = lnE t+k −lnE t the log depreciation rate of the domestic currency between months t andt+k, we can define the excess returns to investing in foreign currency, realized at timet+k, as: xss (k) t+k ≡ Δe t+k +i ⋆(k) t −i (k) t (3.1) 4 http://research.stlouisfed.org/fred2/ 81 Table 3.1: Summary statistics Means AUD CAD CHF GBP EUR JPY xss (1) t 0.001894 0.001467 -0.001685 0.002096 0.003162 -0.003236 xss (3) t 0.002698 0.002751 -0.005502 0.004841 0.008394 -0.008725 i ⋆(1) t −i (1) t 0.001260 -0.000217 -0.002096 0.001031 -0.000180 -0.003185 i ⋆(3) t −i (3) t 0.003725 -0.000672 -0.006243 0.003139 -0.000507 -0.009628 Δx t - -155.4868 -1.131579 36.59211 718.2308 -13.34868 Δ (3) x t - -433.9145 41.92105 36.46711 2012.269 -36.36184 y t 0.244670 0.091339 -0.226961 0.091855 0.391085 -0.250857 Δy t 0.000305 -0.002566 0.004037 -0.002823 0.001444 -0.002793 Δ (3) y t 0.001278 -0.012924 -0.002465 -0.003443 0.003411 0.012093 Standard deviation AUD CAD CHF GBP EUR JPY xss (1) t 0.026647 0.015979 0.024975 0.018889 0.024117 0.025589 xss (3) t 0.060926 0.036533 0.050425 0.039052 0.052844 0.052632 i ⋆(1) t −i (1) t 0.001402 0.000906 0.001204 0.000957 0.001249 0.001383 i ⋆(3) t −i (3) t 0.004276 0.002702 0.003622 0.002909 0.003755 0.004165 Δx t - 5760.870 6606.891 4859.043 16689.44 1534.502 Δ (3) x t - 6996.618 7524.121 8168.591 21297.28 2173.947 y t 0.700163 0.584972 0.623126 0.608774 0.330730 0.509234 Δy t 0.582037 0.477638 0.600765 0.586587 0.229811 0.196932 Δ (3) y t 0.709806 0.630744 0.876732 0.769759 0.376018 0.610592 First order autocorrelation AUD CAD CHF GBP EUR JPY xss (1) t 0.249 0.274 0.250 0.143 0.316 0.219 xss (3) t 0.735 0.734 0.733 0.665 0.707 0.748 i ⋆(1) t −i (1) t 0.975 0.978 0.972 0.967 0.966 0.985 i ⋆(3) t −i (3) t 0.979 0.982 0.975 0.973 0.965 0.986 Δx t - -0.333 -0.407 -0.042 -0.243 -0.282 Δ (3) x t - 0.332 0.288 0.625 0.470 0.550 y t 0.651 0.669 0.530 0.528 0.710 0.620 Δy t -0.314 -0.304 -0.107 -0.239 -0.002 -0.178 Δ (3) y t 0.313 0.381 0.470 0.354 0.543 0.377 Cross-correlations AUD CAD CHF GBP EUR JPY ρ(Δx t ,y t ) - -0.114490 0.009388 0.066779 -0.071316 0.031285 ρ(Δx t ,Δy t ) - -0.013714 -0.120464 -0.005311 0.040668 -0.017989 ρ(Δx t ,Δ (3) y t ) - -0.042140 -0.003280 0.049461 0.010868 0.003264 ρ(Δ (3) x t ,y t ) - -0.067831 -0.053455 0.168305 0.015414 0.025328 ρ(Δ (3) x t ,Δy t ) - 0.153535 -0.190035 0.009893 0.124530 0.055152 ρ(Δ (3) x t ,Δ (3) y t ) - 0.102318 -0.098760 0.089072 0.120520 0.006851 82 We forecast excess returns using two variables. As a measure of aggregate currency order flow 5 , we use U.S. Treasury data on foreign currency holdings of large foreign exchange market participants 6 . If we denote as x t the net position in spot, futures and forward contracts for each currency, then in the regressions we use Δ (k) x t = x t −x t−k , the k-month change in the net position to forecast the k-month ahead excess return. Notice that, in general, x t is a nonstationary variable. We have data on the net position for the CAD, JPY , EUR, CHF and GBP, but not for the AUD. The other variable used is the net long position in currency futures contracts at the CME. This data is made publicly available by the CFTC in their Commitments of Traders Reports. Since we are interested in measuring the effect of positions in contracts used to take advantage of perceived positive excess returns, we concentrate on speculative trader’s (as classified by the CFTC) net positions, as in Brunnermeier, Nagel, and Pedersen (2008). Thus, we denote asy t the net long futures position, as a percentage of the total open interest. As we will see below, we present regression results in which either the levely t or the k-th differenceΔ (k) y t is used, since for some currencies, the changes have superior forecasting power. The changes in the net positions can be naturally interpreted as changes in market participants expectations about future returns. It is important to bear in mind that the CFTC net futures data aggregates positions across all maturities: for example, we have no way to identify whether an observed net long yen position is mainly at the 1, 2 or 3 month horizon. Therefore, we expect that the forecasting power of y t will vary across maturities and possibly by currency, as the investment horizon by foreign exchange speculators is likely to vary depending on the particular currency employed. For example, if most of the speculation in the JPY is short 5 See Wei and Kim (1997), Lyons (2001), and Cai, Cheung, Lee, and Melvin (2001) 6 Those with holdings greater than $50 billion equivalent in foreign exchange contracts on the last business day of any calendar quarter during the previous year (end March, June, September, or December). 83 term, we would expect to see forecastability at the 1 month horizon, but not necessarily at the 3 month horizon. 3.3 Results 3.3.1 Summary statistics Table 3.1 presents summary statistics of the data. Looking at the first order autocorrelation of excess returns xss (k) t , we see that although not a problem for the 1 month horizon, the autocorrelation of realized excess returns at the 3 month horizon will induce serial correlations in the residuals when the forecasting variables are measured at time t and no lags are included. Therefore, in the regressions that follow, the standard errors of the estimated parameters will be obtained using the method of Hansen and Hodrick (1980). In addition, a potential concern with the regressors is that, for each currency, since the U.S. Treasury data on “large” market participants also includes positions in futures contracts, it might be highly correlated with the speculator’s net futures positions data from the CFTC. Table 3.1 shows that this is not the case: for all currencies, the correlation betweenΔx t andy t is fairly small, the largest being -0.19 between the 3-month change in the net position spot, futures and forwards by “large” participants, and the 1-month change in the net long futures position at the CME. Overall, the descriptive statistics suggest that regressions usingΔx t andΔ (k) y t as explanatory variables are not likely to suffer from the multicollinearity problem that would tend to make standard errors large and thus reject significance for the regressors. 3.3.2 Forecasting regressions In this section, we present two main sets of results. The first presents regressions that include as forecasting variables the level of the net long CME futures position, together 84 Table 3.2: Forecasting regressions: level in CME netlong futures contracts Panel I: 1 month horizon AUD CAD CHF EUR GBP JPY intercept -0.0644 0.0855 0.0451 -0.8594 0.1552 0.0359 (-0.2932) (0.6815) (0.2162) (-2.5873) (1.0241) (0.1661) Δ (1) x t - 3.55e-5 -1.4118e-5 2.1929e-5 -2.9778e-6 3.1205e-4 - (1.6348) (-0.4740) (1.7043) (-0.0960) (2.4551) y t 1.0373 0.7308 0.9414 2.9657 0.5925 1.4168 (3.4926) (3.4166) (2.9811) (4.5676) (2.3931) (3.6992) n 152 152 152 104 152 152 adjR 2 0.0681 0.0678 0.0437 0.1634 0.0234 0.1060 Panel II: 3 month horizon AUD CAD CHF EUR GBP JPY intercept -0.3699 0.1817 -0.4595 -1.2463 0.4093 -0.3979 (-0.4973) (0.4213) (-0.6919) (-1.1669) (0.8631) (-0.5614) Δ (3) x t - 1.0375e-4 -1.9866 2.2850e-5 7.1795e-6 1.4423e-5 - (2.1468) (-0.3067) (0.7909) (0.1387) (0.0560) y t 2.6148 1.5150 0.3956 5.2157 0.8105 1.8895 (2.8612) (2.2909) (0.4533) (2.5698) (1.2098) (1.6726) n 152 152 152 104 152 152 adjR 2 0.0842 0.0796 -0.0100 0.0985 0.0036 0.0205 The table presents estimated coefficients in the following forecasting regression: xss (k) t+k = α (k) +β (k) 1 Δ (k) x t +β (k) 2 y t +ε t+k , wherexss (k) t+k is the k month excess return;Δ (k) x t is the change in the net spot, futures, and forward contract positions by “large” market participants as reported by the U.S. Treasury; and y t is the net long futures position of speculators at the CME, expressed as a fraction of the total open interest of noncommercial (speculative) traders . The sample is monthly from 1995:01-2008:08, except for the EUR which is 1999:01- 2008:08. Hansen and Hodrick (1980) t-statistics in parentheses, where the number of lags for each regression is 1 and 2 for the 1 and 3 month forecasting regressions, respectively. with the k-month change in the net spot, futures and forwards position by large market participants. The second presents parameter estimates from a specification that includes the change in the net long CME futures position, together with the k-month change in the net spot, futures and forwards position by “large” market participants. That is, the data for large market participants is always included in difference form, while the CME futures data is used first in levels, and then in differences. 85 Table 3.3: Forecasting regressions: changes in CME netlong futures contracts Panel I: 1 month horizon AUD CAD CHF EUR GBP JPY intercept 0.1892 0.1525 -0.1741 0.2999 0.2118 -0.3325 (0.8873) (1.2031) (-0.9150) (1.3538) (1.4359) (-1.7627) Δ (1) x t - 2.7659e-5 1.9560e-6 1.5877e-5 2.5128e-6 3.1592e-4 - (1.2537) (0.0672) (1.1902) (0.0825) (2.5616) Δ (1) y t 0.6499 0.5689 1.3914 3.3235 0.8316 -4.6946 (1.7679) (2.1378) (4.3462) (3.4307) (3.2961) (-4.8852) n 152 152 152 104 152 152 adjR 2 0.0136 0.0255 0.0997 0.0977 0.0542 0.1577 Panel II: 3 month horizon AUD CAD CHF EUR GBP JPY intercept 0.2689 0.3259 -0.5485 0.7906 0.4843 -0.8926 (0.3504) (0.7410) (-0.8668) (0.9886) (1.0123) (-1.3798) Δ (3) x t - 8.5329e-5 -1.7204e-5 2.4769 1.5403e-5 2.2298 - (1.7272) (-0.2647) (0.7861) (0.2948) (0.0869) Δ (3) y t 0.7136 1.0652 0.3835 -0.3149 0.2314 1.7335 (0.8529) (1.8998) (0.6320) (-0.1712) (0.4659) (2.0437) n 152 152 152 104 152 152 adjR 2 0.0003 0.0542 -0.0079 -0.0097 -0.0100 0.0297 The table presents estimated coefficients in the following forecasting regression: xss (k) t+k = α (k) + β (k) 1 Δx t + β (k) 2 Δy t + ε t+k , where xss (k) t+k is the k month excess return; Δ (k) x t is the k-month change in the net spot, futures, and forward contract positions by “large” market participants as reported by the U.S. Treasury; andΔ (k) y t is the k-month change in the net long futures position of speculators at the CME, expressed as a fraction of the total open interest of noncommercial (speculative) traders . The sample is monthly from 1995:01-2008:08, except for the EUR which is 1999:01-2008:08. Hansen and Hodrick (1980) t-statistics in parentheses, where the number of lags for each regression is 1 and 2 for the 1 and 3 month forecasting regressions, respectively. It is shown that the informational variables have considerable forecasting power at short horizons. For some currencies, the net long futures positions is a good predictor of excess returns, while for others, it is the change in the net long futures positions that does a better job at forecasting returns. The results show that the highest predictive power is generally found at the 1 month horizon. 86 Using the level of net long position in CME futures First we forecast excess returns using the level of speculator’s net long position in CME currency futures contracts, as this variable should include information about the direction in which non commercial traders were betting the currency to move. Table 3.2 presents results of the 1 and 3 month ahead forecasting regressions of currency excess returns using the level of the net long speculator’s CME futures positiony t , together with the k month change in the net spot, forward and futures position by large market participants from the U.S. Treasury. The forecasting regressions used is: xss (k) t+k =α (k) +β (k) 1 Δ (k) x t +β (k) 2 y t +ε t+k k = 1,3 (3.2) The table shows that the CME net long futures position is a strong predictor of future excess returns: for all currencies at the 1 month horizon, and for all but the GBP and JPY at the 3 month horizon, the variable is statistically significant. As explained before, we use Hansen and Hodrick (1980) standard errors, with k-1 lags (1 lag in the case of the 1 month ahead forecasting regression). On the other hand, the changes in the net spot, futures and forward contract positions is significant only for the JPY at the 1 month horizon and the CAD at the 3 month horizon. Therefore, the results suggest that currency flows have limited forecasting ability for future exchange rates. The most significant finding in this table is that the simple model can explain a signif- icant percentage of the variance of future excess returns, and that the forecasting ability of the variables varies across currency and investment horizon. For the AUD, excess returns can be forecasted at the 3 month horizon with an adjustedR 2 of 8.42 percent; for the CAD, at the 3 month horizon with anR 2 of 7.96 percent; a comparatively lower 4.37% of CHF excess returns can the explained by the two forecasting variables. Finally, for the JPY , a highR 2 of 10.60% is obtained when forecasting at the 1 month horizon. 87 Table 3.4: Robustness regressions: AUD, 1 month horizon k = 1 month horizon (a) (b) (c) (d) (i) (j) intercept -0.0024 -0.0032 0.0007 0.0007 0.013729 0.015870 (-0.8493) (-1.1543) (0.1331) (0.1383) (0.958845) (1.102481) Δ (k) x t y t 0.0085 0.0082 0.007852 (2.3973) (2.3678) (2.257550) Δ (k) y t 0.0066 0.0067 0.006030 (1.8293) (1.8824) (1.728657) i ⋆(k) t −i (k) t 1.7493 4.0705 2.2231 4.4664 2.218688 4.113239 (0.9923) (2.7327) (1.2574) (2.9762) (1.188330) (2.439411) IP ⋆ t,t−k 0.5719 0.4301 (0.5340) (0.3993) IP t,t−k -0.1981 -0.2343 (-0.5158) (-0.6039) Π ⋆ t,t−k -2.1860 -2.3078 (-2.1121) (-2.2184) Π t,t−k -0.0189 -0.0590 (-0.0288) (-0.0892) IP ⋆ t,t−12 -0.016603 -0.052457 (-0.066712) (-0.209489) IP t,t−12 0.008155 -0.018388 (0.078764) (-0.177450) Π ⋆ t,t−12 0.211876 0.188280 (0.957214) (0.843441) Π t,t−12 -0.806071 -0.805196 (-2.771278) (-2.748354) n 152 152 152 152 152 152 adjR 2 0.0679 0.0535 0.0768 0.0645 0.0981 0.0859 The table presents regressions of realized excess returns xss (k) t+k to investing in the AUD on currency positions and control variables at timet. The controls are: i ⋆(k) t −i (k) t , the k month interest rate differential; IP ⋆ t,t−k is the arithmetic growth rate of an Index of Industrial Produc- tion for the foreign country, while IP t,t−k is the domestic (U.S.) counterpart; andΠ ⋆ t,t−k is the arithmetic growth rate of a Consumer Price Index for the foreign country, whileΠ t,t−k is the domestic (U.S.) counterpart. The positions variables,Δ (k) x t andΔ (k) y t are defined in Tables 3.2 and 3.3. The regression uses Hansen and Hodrick (1980) standard errors with 1 lag. The highest forecasting ability of all currencies is obtained for the EUR: at the 1 month horizon, the model explains 16.34% of the monthly variation in future excess returns, while at the 3 month horizon, excess returns can be forecasted with anR 2 of 9.85%. The lowest 88 Table 3.5: Robustness regressions: AUD, 3 month horizon k = 3 month horizon (e) (f) (g) (h) (k) (l) intercept -0.0057 -0.0078 -0.0112 -0.0107 0.053989 0.060757 (-0.5995) (-0.7910) (-0.5625) (-0.5124) (1.198380) (1.284403) Δ (k) x t y t 0.0239 0.0240 0.022167 (2.3099) (2.4239) (2.336693) Δ (k) y t 0.0072 0.0064 0.004511 (0.8767) (0.8213) (0.603930) i ⋆(k) t −i (k) t 0.6849 2.8222 1.5512 3.7187 1.441969 3.213844 (0.3609) (1.6222) (0.8215) (2.1239) (0.748130) (1.719979) IP ⋆ t,t−k 1.4657 1.3131 (1.1008) (0.9381) IP t,t−k 0.2086 0.2116 (0.3115) (0.3012) Π ⋆ t,t−k 0.2342 -0.0125 (0.1820) (-0.0092) Π t,t−k -1.8992 -1.8614 (-1.9125) (-1.7886) IP ⋆ t,t−12 -0.140016 -0.252621 (-0.178364) (-0.306031) IP t,t−12 0.148519 0.085273 (0.456845) (0.250519) Π ⋆ t,t−12 0.935124 0.885814 (1.348173) (1.214500) Π t,t−12 -3.172727 -3.205088 (-3.565860) (-3.432709) n 152 152 152 152 152 152 adjR 2 0.0797 0.0333 0.1241 0.0750 0.2090 0.1657 The table presents regressions of realized excess returns xss (k) t+k to investing in the AUD on currency positions and control variables at timet. The controls are: i ⋆(k) t −i (k) t , the k month interest rate differential; IP ⋆ t,t−k is the arithmetic growth rate of an Index of Industrial Produc- tion for the foreign country, while IP t,t−k is the domestic (U.S.) counterpart; andΠ ⋆ t,t−k is the arithmetic growth rate of a Consumer Price Index for the foreign country, whileΠ t,t−k is the domestic (U.S.) counterpart. The positions variables,Δ (k) x t andΔ (k) y t are defined in Tables 3.2 and 3.3. The regression use Hansen and Hodrick (1980) standard errors 2 lags. forecasting ability is in the GBP: although significant, the variables can only explain 2.34% of the variation in future excess returns. 89 Although we do not provide a model of the forecasting relationship and thus cannot expect a particular value or sign for the estimated coefficients, it is worth noting that most of the slope coefficients confirm with simple intuition regarding positions and expected returns: an increase in the net long positions, either in CME futures or in spot and forwards, forecasts higher excess returns. This is consistent with a view in which market participants buy the currency when they expect to profit from it. Using the changes in the net long position in CME futures In this section, we investigate the forecasting ability of the k-month changes in net spot, futures and forward contracts position of large market participants together with the k- month change in the CME net long futures position. We do this because the change in the CME net position, rather than the level at any given point in time, might more accurately reflect changes in market participant’s expectations about future returns. The forecasting regression we employ is the following: xss (k) t+k =α (k) +β (k) 1 Δ (k) x t +β (k) 2 Δ (k) y t +ε t+k k =1,3 (3.3) where, as before, Δx t is the k month change in the net spot, futures and forward con- tract position by “large” market participants, andΔ (k) y t is now the change in the net long position of CME futures contracts by speculative traders, from the CME. The estimated regression coefficients across currencies are presented in Table 3.3. Here we see that the change in the CME net long futures position has quite high forecasting power for the CHF and the JPY at the 1 month horizon: it doubles theR 2 in the case of the CHF and increases it in about 5 percentage points for the JPY . On the other hand, at the 3-month horizon, the same variable has very low forecasting power, with some adjusted R 2 ’s being essentially zero. 90 Table 3.6: Robustness regressions: CAD, 1 month horizon k = 1 month horizon (a) (b) (c) (d) (i) (j) intercept 0.0013 0.0022 -0.0009 -0.0004 0.006040 0.004263 (0.9788) (1.7055) (-0.3802) (-0.1896) (1.065370) (0.746850) Δ (k) x t 3.5272 2.9277 3.9298 3.5679 3.282158 2.751717 (1.6300) (1.3472) (1.7924) (1.6211) (1.553904) (1.295820) y t 0.0064 0.0061 0.006563 (2.7679) (2.6200) (2.792120) Δ (k) y t 0.0055 0.0057 0.005382 (2.1064) (2.1728) (2.102026) i ⋆(k) t −i (k) t 1.5858 3.0488 2.2432 3.8884 -1.208492 0.936491 (1.0735) (2.2062) (1.3768) (2.5797) (-0.598009) (0.493794) IP ⋆ t,t−k 0.2633 0.3257 (0.5754) (0.7085) IP t,t−k 0.1753 0.2708 (0.6944) (1.0651) Π ⋆ t,t−k 0.1395 -0.0040 (0.2646) (-0.0076) Π t,t−k 0.2452 0.3665 (0.4558) (0.6805) IP ⋆ t,t−12 -0.076396 -0.105295 (-0.882935) (-1.208011) IP t,t−12 0.016656 0.074456 (0.225484) (1.022105) Π ⋆ t,t−12 0.604827 0.661813 (2.674321) (2.909097) Π t,t−12 -0.519152 -0.454742 (-2.611014) (-2.267424) n 152 152 152 152 152 152 adjR 2 0.0685 0.0493 0.0560 0.0431 0.0955 0.0760 The table presents regressions of realized excess returns xss (k) t+k to investing in the CAD on currency positions and control variables at timet. The controls are: i ⋆(k) t −i (k) t , the k month interest rate differential; IP ⋆ t,t−k is the arithmetic growth rate of an Index of Industrial Produc- tion for the foreign country, while IP t,t−k is the domestic (U.S.) counterpart; andΠ ⋆ t,t−k is the arithmetic growth rate of a Consumer Price Index for the foreign country, whileΠ t,t−k is the domestic (U.S.) counterpart. The positions variables,Δ (k) x t andΔ (k) y t are defined in Tables 3.2 and 3.3. The regressions use Hansen and Hodrick (1980) standard errors with 1 lag. It is important to notice that for all currencies except the JPY , the estimated coefficient onΔy t is positive. A positive coefficient can be interpreted as speculators increasing their 91 Table 3.7: Robustness regressions: CAD, 3 month horizon k = 3 month horizon (e) (f) (g) (h) (k) (l) intercept 0.0033 0.0050 -0.0026 -0.0018 0.027190 0.023068 (0.7321) (1.1341) (-0.2914) (-0.2070) (1.493714) (1.239480) Δ (k) x t 10.4521 8.9689 11.1103 9.9635 9.073930 7.722694 (2.1785) (1.8584) (2.3206) (2.0873) (2.010576) (1.678513) y t 0.0121 0.0096 0.014192 (1.7432) (1.3473) (2.142463) Δ (k) y t 0.0099 0.0096 0.008618 (1.8072) (1.7736) (1.650544) i ⋆(k) t −i (k) t 1.7613 2.5823 3.0217 3.8613 -0.963038 0.539144 (1.0571) (1.6294) (1.5661) (2.1712) (-0.447502) (0.258199) IP ⋆ t,t−k 0.2478 0.2259 (0.3938) (0.3603) IP t,t−k 0.4286 0.5721 (0.8711) (1.1887) Π ⋆ t,t−k -0.2336 -0.3667 (-0.2368) (-0.3752) Π t,t−k 0.3259 0.4564 (0.3488) (0.4963) IP ⋆ t,t−12 -0.153607 -0.222168 (-0.559521) (-0.787621) IP t,t−12 0.040641 0.170059 (0.175395) (0.721171) Π ⋆ t,t−12 1.606425 1.709377 (2.282072) (2.371298) Π t,t−12 -1.907920 -1.733340 (-2.998515) (-2.662707) n 152 152 152 152 152 152 adjR 2 0.0883 0.0848 0.0835 0.0922 0.1765 0.1569 The table presents regressions of realized excess returns xss (k) t+k to investing in the CAD on currency positions and control variables at timet. The controls are: i ⋆(k) t −i (k) t , the k month interest rate differential; IP ⋆ t,t−k is the arithmetic growth rate of an Index of Industrial Produc- tion for the foreign country, while IP t,t−k is the domestic (U.S.) counterpart; andΠ ⋆ t,t−k is the arithmetic growth rate of a Consumer Price Index for the foreign country, whileΠ t,t−k is the domestic (U.S.) counterpart. The positions variables,Δ (k) x t andΔ (k) y t are defined in Tables 3.2 and 3.3. The regression use Hansen and Hodrick (1980) standard errors with 2 lags. net long position, compared to the last month or three months ago, when they expect sub- sequent positive excess returns. In the case of the JPY , the opposite relationship seems to 92 Table 3.8: Robustness regressions: CHF, 1 month horizon k = 1 month horizon (a) (b) (c) (d) (i) (j) intercept 0.0067 0.0079 0.0091 0.0110 0.024388 0.027259 (1.6927) (2.1259) (2.1324) (2.7449) (3.042195) (3.642751) Δ (k) x t -1.2389 0.4230 -0.9226 0.7872 -1.425702 0.265835 (-0.4204) (0.1495) (-0.3144) (0.2800) (-0.495969) (0.096943) y t 0.0072 0.0067 0.006530 (2.1410) (2.0051) (1.967802) Δ (k) y t 0.0140 0.0139 0.014065 (4.4947) (4.4753) (4.659659) i ⋆(k) t −i (k) t 3.2118 4.6066 4.2916 5.4420 3.839897 5.787452 (1.8525) (2.9884) (2.2762) (3.2624) (1.338842) (2.253248) IP ⋆ t,t−k 0.4256 0.3683 (1.6109) (1.4614) IP t,t−k 0.0442 -0.0219 (0.1173) (-0.0611) Π ⋆ t,t−k 1.2506 0.7975 (1.1342) (0.7562) Π t,t−k -1.0388 -1.2229 (-1.5700) (-1.9430) IP ⋆ t,t−12 0.089612 0.097156 (1.854637) (2.123454) IP t,t−12 -0.048892 -0.033969 (-0.488055) (-0.361169) Π ⋆ t,t−12 0.771147 0.595199 (1.278317) (1.039913) Π t,t−12 -0.938540 -0.915605 (-2.253660) (-2.321976) n 152 152 152 152 152 152 adjR 2 0.0585 0.1439 0.0634 0.1506 0.0820 0.1762 The table presents regressions of realized excess returns xss (k) t+k to investing in the CHF on currency positions and control variables at timet. The controls are: i ⋆(k) t −i (k) t , the k month interest rate differential; IP ⋆ t,t−k is the arithmetic growth rate of an Index of Industrial Produc- tion for the foreign country, while IP t,t−k is the domestic (U.S.) counterpart; andΠ ⋆ t,t−k is the arithmetic growth rate of a Consumer Price Index for the foreign country, whileΠ t,t−k is the domestic (U.S.) counterpart. The positions variables,Δ (k) x t andΔ (k) y t are defined in Tables 3.2 and 3.3. The regression use Hansen and Hodrick (1980) standard errors with 1 lag. hold, as it appears that increases in net long positions in JPY forecast subsequent lower excess returns, at least for the sample period considered. 93 Table 3.9: Robustness regressions: CHF, 3 month horizon k = 3 month horizon (e) (f) (g) (h) (k) (l) intercept 0.0207 0.0197 0.0277 0.0242 0.073546 0.071086 (1.7113) (1.6593) (1.9756) (1.7657) (3.242733) (3.187670) Δ (k) x t -1.5634 -0.9689 0.6192 0.8302 -1.836949 -1.079382 (-0.2529) (-0.1569) (0.1028) (0.1368) (-0.316947) (-0.186466) y t -0.0056 -0.0102 -0.007983 (-0.6406) (-1.1789) (-0.967486) Δ (k) y t 0.0036 0.0019 0.004322 (0.6318) (0.3415) (0.797878) i ⋆(k) t −i (k) t 4.4019 4.0339 5.5129 4.5600 5.686510 4.805087 (2.5068) (2.4522) (2.6685) (2.3820) (2.058580) (1.852023) IP ⋆ t,t−k 0.1512 0.1247 (0.5030) (0.4151) IP t,t−k 0.3710 0.2227 (0.5947) (0.3625) Π ⋆ t,t−k 2.6216 2.4521 (1.5330) (1.4352) Π t,t−k -1.5409 -1.3412 (-1.6769) (-1.4764) IP ⋆ t,t−12 0.285975 0.280943 (2.042715) (2.034575) IP t,t−12 -0.156861 -0.197594 (-0.529668) (-0.683800) Π ⋆ t,t−12 0.597047 0.753072 (0.356834) (0.453992) Π t,t−12 -2.091252 -2.142811 (-1.819182) (-1.874269) n 152 152 152 152 152 152 adjR 2 0.0709 0.0708 0.0946 0.0825 0.1559 0.1533 The table presents regressions of realized excess returns xss (k) t+k to investing in CHF on cur- rency positions and control variables at time t. The controls are: i ⋆(k) t − i (k) t , the k month interest rate differential; IP ⋆ t,t−k is the arithmetic growth rate of an Index of Industrial Produc- tion for the foreign country, while IP t,t−k is the domestic (U.S.) counterpart; andΠ ⋆ t,t−k is the arithmetic growth rate of a Consumer Price Index for the foreign country, whileΠ t,t−k is the domestic (U.S.) counterpart. The positions variables,Δ (k) x t andΔ (k) y t are defined in Tables 3.2 and 3.3. The regression use Hansen and Hodrick (1980) standard errors with 2 lags. 3.3.3 Robustness tests In this section, we augment the regressions presented in the last section by including several control variables. These are: the interest rate differentiali ⋆(k) t −i (k) t , which should be an 94 important determinant of short term speculative investments in currencies; the k-month change in an index of industrial production IP ⋆ t,t−k and IP t,t−k , which should proxy for changes in the real exchange rate; and the k-month CPI inflation rate Π ⋆ t,t−k and Π t,t−k , which is used as a proxy for expected inflation differential over the holding period of the investment. The data sources are explained in the Appendix to the chapter. Controlling for interest differentials, inflation and IP growth The most important finding in Tables 3.4 to 3.15 is that the forecasting ability of currency positions, specially when measured by the net long futures position, is not affected by the inclusion of controls for real activity growth or inflation. Depending on the currency, either the level or the k-month difference in the net long futures position (and sometimes both) is a statistically significant predictor of future excess returns. The level of the net long futures position, which is more likely to include information about trends in exchange rates, is a stronger predictor of future returns for the AUD, CAD (and EUR 7 ), which are known as “commodity currencies” because of their links with the international price of the commodities that their counties produce. And for these currencies, there is strong forecasting ability both at the 1 and 3 month horizons, which supports the view that positions build up on the side of the trade expected to continue for some time. On the other hand, the changes in the net long futures position are stronger predictors of returns for the CHF, GBP and the JPY , which are viewed as “carry trade” currencies (long or short). Indeed, as can be seen in Table 3.1, the CHF and JPY had, over the sample period studied, the lowest interest rate differential vis a vis the U.S. dollar, while the GBP had the second highest differential. Moreover, the strongest forecasting ability of positions 7 The Euro has been lately strongly linked to the world price of oil. See John Auther’s May 7th, 2009 column entitled “Euro and Oil” at the Financial Times website:http://www.ft. com/cms/bfba2c48-5588-11dc-b971-0000779fd2ac.html?_i_referralObject= 733653534&fromSearch=n 95 Table 3.10: Robustness regressions: EUR, 1 month horizon k = 1 month horizon (a) (b) (c) (d) (i) (j) intercept -0.0077 0.0038 -0.0048 0.0073 -0.028921 0.003270 (-2.2958) (1.7401) (-1.1047) (2.0635) (-2.001209) (0.261449) Δ (k) x t 2.2879 1.7494 2.3623 1.8771 2.005302 1.402278 (1.7984) (1.3496) (1.8718) (1.4668) (1.616711) (1.130171) y t 0.0285 0.0278 0.028597 (4.4164) (4.3406) (3.828824) Δ (k) y t 0.0362 0.0363 0.033181 (3.8195) (3.8706) (3.653048) i ⋆(k) t −i (k) t 2.7576 4.4152 2.8015 4.4160 -1.800441 3.980748 (1.6158) (2.5314) (1.6023) (2.4926) (-0.531558) (1.220965) IP ⋆ t,t−k -0.0755 -0.0490 (-0.3116) (-0.1994) IP t,t−k 0.3443 0.2028 (0.7986) (0.4600) Π ⋆ t,t−k -0.4580 -0.7129 (-0.2478) (-0.3796) Π t,t−k -0.6892 -0.8605 (-0.8992) (-1.1053) IP ⋆ t,t−12 0.021784 0.282835 (0.141628) (2.040653) IP t,t−12 0.150314 0.005262 (1.300987) (0.046836) Π ⋆ t,t−12 2.469507 1.259811 (2.543743) (1.306973) Π t,t−12 -1.320808 -1.168884 (-2.779013) (-2.424413) n 104 104 104 104 104 104 adjR 2 0.1757 0.1416 0.1651 0.1381 0.2044 0.1955 The table presents regressions of realized excess returns xss (k) t+k to investing in the EUR on currency positions and control variables at timet. The controls are: i ⋆(k) t −i (k) t , the k month interest rate differential; IP ⋆ t,t−k is the arithmetic growth rate of an Index of Industrial Produc- tion for the foreign country, while IP t,t−k is the domestic (U.S.) counterpart; andΠ ⋆ t,t−k is the arithmetic growth rate of a Consumer Price Index for the foreign country, whileΠ t,t−k is the domestic (U.S.) counterpart. The positions variables,Δ (k) x t andΔ (k) y t are defined in Tables 3.2 and 3.3. The regression use Hansen and Hodrick (1980) standard errors with 1 lag. for these currencies is found at the 1 month horizon, with limited forecasting ability at the 3 month horizon 96 Table 3.11: Robustness regressions: EUR, 3 month horizon k = 3 month horizon (e) (f) (g) (h) (k) (l) intercept -0.0106 0.0091 -0.0323 -0.0067 -0.027718 0.004268 (-0.9870) (1.1487) (-1.8945) (-0.4487) (-0.684307) (0.114060) Δ (k) x t 2.5340 2.6980 1.7715 2.3871 3.838020 4.284998 (0.8850) (0.8719) (0.7102) (0.9030) (1.524302) (1.655363) y t 0.0496 0.0408 0.029455 (2.4565) (2.2737) (1.529657) Δ (k) y t 0.0014 -0.0078 -0.002652 (0.0768) (-0.5011) (-0.173806) i ⋆(k) t −i (k) t 1.8407 2.4102 3.9906 5.0453 -2.505324 -1.075278 (0.9563) (1.1462) (2.1706) (2.6238) (-0.818855) (-0.349631) IP ⋆ t,t−k 1.5845 1.9742 (3.0215) (3.5891) IP t,t−k 0.6279 0.4851 (0.9691) (0.7045) Π ⋆ t,t−k 6.0457 4.2180 (2.1785) (1.4296) Π t,t−k -2.1833 -2.1293 (-2.1136) (-1.9275) IP ⋆ t,t−12 0.499064 0.761253 (1.342550) (2.042342) IP t,t−12 0.203324 0.070613 (0.621331) (0.210248) Π ⋆ t,t−12 7.371417 6.429120 (2.742321) (2.337254) Π t,t−12 -5.446187 -5.505541 (-4.177059) (-4.085278) n 104 104 104 104 104 104 adjR 2 0.1067 0.0092 0.2737 0.2189 0.3015 0.2772 The table presents regressions of realized excess returns xss (k) t+k to investing in the EUR on currency positions and control variables at timet. The controls are: i ⋆(k) t −i (k) t , the k month interest rate differential; IP ⋆ t,t−k is the arithmetic growth rate of an Index of Industrial Produc- tion for the foreign country, while IP t,t−k is the domestic (U.S.) counterpart; andΠ ⋆ t,t−k is the arithmetic growth rate of a Consumer Price Index for the foreign country, whileΠ t,t−k is the domestic (U.S.) counterpart. The positions variables,Δ (k) x t andΔ (k) y t are defined in Tables 3.2 and 3.3. The regression use Hansen and Hodrick (1980) standard errors with 2 lags. In Tables 3.8 and 3.9 it can be seen that the CHF is the only currency for which the interest rate differential is a significant predictor of future excess returns for all specifica- tions at the 1 or 3 month horizons. For the other currencies, the significance of the interest 97 Table 3.12: Robustness regressions: GBP, 1 month horizon k = 1 month horizon (a) (b) (c) (d) (i) (j) intercept 0.0011 0.0007 -0.0004 -0.0014 0.016762 0.015085 (0.4750) (0.3011) (-0.1552) (-0.5320) (2.758720) (2.523091) Δ (k) x t -0.3968 -0.0648 0.6214 0.9755 0.941491 0.951019 (-0.1273) (-0.0212) (0.1952) (0.3145) (0.308917) (0.317030) y t 0.0058 0.0063 0.006471 (2.2941) (2.5008) (2.500766) Δ (k) y t 0.0084 0.0097 0.008223 (3.3430) (3.8343) (3.368054) i ⋆(k) t −i (k) t 0.4988 1.4207 0.1793 1.2026 -1.754073 -0.399226 (0.3100) (0.9146) (0.1109) (0.7802) (-0.991416) (-0.235528) IP ⋆ t,t−k -0.1950 -0.1652 (-0.9677) (-0.8464) IP t,t−k 0.3117 0.4170 (1.1346) (1.5526) Π ⋆ t,t−k 1.0843 1.5485 (1.1118) (1.6072) Π t,t−k -0.2102 -0.3581 (-0.4362) (-0.7604) IP ⋆ t,t−12 -0.217911 -0.136510 (-1.720538) (-1.126986) IP t,t−12 0.021907 0.017530 (0.345525) (0.281176) Π ⋆ t,t−12 -0.098678 0.061724 (-0.408154) (0.266995) Π t,t−12 -0.433727 -0.507693 (-2.296550) (-2.773012) n 152 152 152 152 152 152 adjR 2 0.0174 0.0530 0.0152 0.0651 0.0580 0.0874 The table presents regressions of realized excess returns xss (k) t+k to investing in the GBP on currency positions and control variables at timet. The controls are: i ⋆(k) t −i (k) t , the k month interest rate differential; IP ⋆ t,t−k is the arithmetic growth rate of an Index of Industrial Produc- tion for the foreign country, while IP t,t−k is the domestic (U.S.) counterpart; andΠ ⋆ t,t−k is the arithmetic growth rate of a Consumer Price Index for the foreign country, whileΠ t,t−k is the domestic (U.S.) counterpart. The positions variables,Δ (k) x t andΔ (k) y t are defined in Tables 3.2 and 3.3. The regression use Hansen and Hodrick (1980) standard errors with 1 lag. differential at the 1 month horizon depends on whether the net long futures position vari- able is included in levels or in changes: whenever the level of the net long futures position 98 Table 3.13: Robustness regressions: GBP, 3 month horizon k = 3 month horizon (e) (f) (g) (h) (k) (l) intercept 0.0038 0.0035 0.0098 0.0095 0.074472 0.073659 (0.5496) (0.4913) (0.9824) (0.9441) (4.283864) (4.162316) Δ (k) x t 0.6643 1.2035 0.6449 0.8882 6.639511 7.099888 (0.1265) (0.2269) (0.1243) (0.1708) (1.382128) (1.457880) y t 0.0080 0.0040 0.007526 (1.1860) (0.6230) (1.231575) Δ (k) y t 0.0024 0.0010 0.001125 (0.4929) (0.2042) (0.255114) i ⋆(k) t −i (k) t 0.0830 0.4340 1.0863 1.2876 -2.262554 -1.882295 (0.0499) (0.2600) (0.6648) (0.7968) (-1.360461) (-1.131555) IP ⋆ t,t−k 0.4459 0.4653 (1.1121) (1.1585) IP t,t−k 0.5346 0.5636 (1.3039) (1.3726) Π ⋆ t,t−k -1.5064 -1.4902 (-1.1009) (-1.0749) Π t,t−k -0.7293 -0.7618 (-1.1153) (-1.1608) IP ⋆ t,t−12 -0.278502 -0.206660 (-0.917367) (-0.678654) IP t,t−12 -0.075217 -0.079185 (-0.443981) (-0.456832) Π ⋆ t,t−12 -0.521161 -0.355651 (-0.794435) (-0.537726) Π t,t−12 -1.901347 -1.999644 (-3.598431) (-3.746221) n 152 152 152 152 152 152 adjR 2 -0.0031 -0.0158 0.0648 0.0615 0.1965 0.1849 The table presents regressions of realized excess returns xss (k) t+k to investing in the GBP on currency positions and control variables at timet. The controls are: i ⋆(k) t −i (k) t , the k month interest rate differential; IP ⋆ t,t−k is the arithmetic growth rate of an Index of Industrial Produc- tion for the foreign country, while IP t,t−k is the domestic (U.S.) counterpart; andΠ ⋆ t,t−k is the arithmetic growth rate of a Consumer Price Index for the foreign country, whileΠ t,t−k is the domestic (U.S.) counterpart. The positions variables,Δ (k) x t andΔ (k) y t are defined in Tables 3.2 and 3.3. The regression use Hansen and Hodrick (1980) standard errors with 2 lags. is included in the regression, the interest differential is not significant 8 . This suggests that when the trend is removed from the net long futures positions data, the interest differential, 8 And for the case of the CHF at the 1 month horizon, the interest differential is significant at the 10% level while the level of the net long futures position is at the 5% confidence level. 99 which is itself a very persistent variable, 9 gains significance. Thus, it appears that the infor- mation of interest differentials is mainly about trends. Finally, for the 3 month horizon, the differential is in general only significant when it is accompanied in the regression by the 3 month change in Industrial Production and the 3 month CPI inflation. In general, the results strongly suggest that the positions are concentrated in specific maturities and that the chosen investment horizon varies across currency. Picking-up trends: 12-month growth rates In the last section we saw that the significance of the interest differential, itself a very persistent variable, was sensitive to the inclusion of the futures position data in levels or first differences. From Table 3.1 we see that excess returns gain considerable autocorrelation when measured at the 3 month horizon. On the other hand, the net long futures position data is also highly autocorrelated in levels, much less in first differences, but again significantly autocorrelated when measured at the 3 month change. Because of this, we investigate whether a significant common trend component in real activity or inflation might be behind the forecasting ability of positions data. In this section, we test whether including long horizon changes in industrial production or inflation drives out the forecasting power of the level or 3 month change in the net futures positions. The results on this exercise appear in the two last columns of each of Tables 3.4 to 3.15. As can be seen, the general results for the 1 or 3 month regressions still hold: the net long futures position forecasts excess returns at the 1 or 3 month horizons irrespective of whether the 12 month change in industrial production or inflation are included. For the currencies in which the level of positions displayed forecasting ability at both the 1 and 3 month horizons when 1 or 3 month growth rates in industrial production or inflation were included, the level is still a significant forecasting variable in the presence of 12 month changes in IP t,t−12 or 9 The smallest first order autocorrelation of the interest differential at the 1 month horizon is 0.967 for the GBP. These are even higher at the 3 month horizon. 100 Table 3.14: Robustness regressions: JPY , 1 month horizon k = 1 month horizon (a) (b) (c) (d) (i) (j) intercept 0.0006 0.0050 0.0028 0.0069 0.006012 0.010289 (0.1143) (1.0575) (0.5509) (1.4387) (0.748212) (1.356488) Δ (k) x t 31.2304 32.0904 28.9402 29.9368 30.505312 31.481648 (2.4550) (2.6329) (2.3206) (2.4888) (2.398036) (2.571277) y t 0.0141 0.0141 0.014912 (3.2414) (3.3148) (3.396365) Δ (k) y t -0.0472 -0.0447 -0.046671 (-4.9691) (-4.7915) (-4.927101) i ⋆(k) t −i (k) t 0.0764 2.6023 0.3526 2.8173 0.393715 2.628312 (0.0478) (1.9242) (0.2248) (2.1089) (0.208600) (1.525337) IP ⋆ t,t−k 0.0049 0.0298 (0.0319) (0.2002) IP t,t−k 0.3530 0.2757 (0.9971) (0.8054) Π ⋆ t,t−k 2.1241 1.8044 (2.5822) (2.2676) Π t,t−k -0.9799 -0.8624 (-1.6352) (-1.4893) IP ⋆ t,t−12 -0.032856 -0.001808 (-0.641238) (-0.037209) IP t,t−12 0.064215 0.017593 (0.594710) (0.170886) Π ⋆ t,t−12 -0.020746 -0.012523 (-0.076554) (-0.047982) Π t,t−12 -0.203889 -0.209999 (-0.773407) (-0.828203) n 152 152 152 152 152 152 adjR 2 0.0999 0.1722 0.1274 0.1871 0.0902 0.1559 The table presents regressions of realized excess returns xss (k) t+k to investing in the JPY on currency positions and control variables at timet. The controls are: i ⋆(k) t −i (k) t , the k month interest rate differential; IP ⋆ t,t−k is the arithmetic growth rate of an Index of Industrial Produc- tion for the foreign country, while IP t,t−k is the domestic (U.S.) counterpart; andΠ ⋆ t,t−k is the arithmetic growth rate of a Consumer Price Index for the foreign country, whileΠ t,t−k is the domestic (U.S.) counterpart. The positions variables,Δ (k) x t andΔ (k) y t are defined in Tables 3.2 and 3.3. The regression use Hansen and Hodrick (1980) standard errors with 1 lag. Π t,t−12 . And for those currencies in which the changes in the positions were important in forecasting 1 month returns, the changes in net long futures positions are still important 101 Table 3.15: Robustness regressions: JPY , 3 month horizon k = 3 month horizon (e) (f) (g) (h) (k) (l) intercept 0.0154 0.0190 0.0147 0.0157 0.016440 0.017505 (0.9241) (1.2090) (0.8141) (0.9319) (0.643953) (0.712021) Δ (k) x t 3.3510 4.0211 2.9178 4.4811 -0.691578 1.251747 (0.1312) (0.1621) (0.1127) (0.1785) (-0.026842) (0.049819) y t 0.0102 0.0094 0.012285 (0.8316) (0.7616) (1.011944) Δ (k) y t 0.0179 0.0189 0.017932 (2.1762) (2.2690) (2.198296) i ⋆(k) t −i (k) t 2.2405 2.9031 2.5778 3.2008 2.480395 3.367388 (1.3139) (1.9343) (1.4654) (2.0750) (1.198186) (1.749899) IP ⋆ t,t−k 0.0505 0.0589 (0.1709) (0.2046) IP t,t−k 0.4112 0.4398 (0.6506) (0.7169) Π ⋆ t,t−k 0.3562 -0.1068 (0.2478) (-0.0767) Π t,t−k 0.1509 0.4858 (0.1657) (0.5443) IP ⋆ t,t−12 -0.148585 -0.139261 (-0.929496) (-0.901290) IP t,t−12 0.179525 0.198341 (0.516164) (0.586179) Π ⋆ t,t−12 -0.557882 -0.619757 (-0.651783) (-0.743811) Π t,t−12 -0.035069 0.098256 (-0.042237) (0.120936) n 152 152 152 152 152 152 adjR 2 0.0387 0.0749 0.0211 0.0605 0.0340 0.0676 The table presents regressions of realized excess returns xss (k) t+k to investing in the JPY on currency positions and control variables at timet. The controls are: i ⋆(k) t −i (k) t , the k month interest rate differential; IP ⋆ t,t−k is the arithmetic growth rate of an Index of Industrial Produc- tion for the foreign country, while IP t,t−k is the domestic (U.S.) counterpart; andΠ ⋆ t,t−k is the arithmetic growth rate of a Consumer Price Index for the foreign country, whileΠ t,t−k is the domestic (U.S.) counterpart. The positions variables,Δ (k) x t andΔ (k) y t are defined in Tables 3.2 and 3.3. The regression use Hansen and Hodrick (1980) standard errors with 2 lags. predictors of future excess returns, even when we include 12 month growth rates in real production or inflation. 102 Finally, it is important to notice that of the 4 variables used, the inflation controls are more significant. Specifically, the 12 month U.S. CPI inflation rate 10 is the strongest pre- dictor of excess returns for both maturities considered. Apart from this general finding, the significance of the other control variables is cur- rency specific: for the CAD, the 12 month change in Canadian CPI is a significant forecast- ing variable for all specifications and maturities; for the CHF, the 12 month growth in Swiss industrial production; for the EUR, both the growth in Euro Area industrial production and inflation are important in predicting future returns. 3.4 Conclusion The results support the view that positions data contain information about expectations of short term exchange rate movements. The percentage of variation in excess returns that can be predicted using measures of positions is generally higher at the 1 month than at the 3 month horizon, although for some currencies like the AUD and the CAD, the specifica- tion that uses the level of the CME net long position forecasts a higher percentage of the variation in excess returns at the 3 month horizon. The highest forecasting power is found for the EUR at the 1 month horizon, with anR 2 of 16.34%, and for the JPY again at the 1 month horizon with anR 2 of 15.77%. The forecasting power of currency positions remains after the inclusion of control variables that proxy for real activity and inflation expectations. Importantly, the pattern of forecastability is different across currencies. Excess returns in “carry trade” currencies can be forecasted at the 1 month horizon using changes in posi- tions, while excess returns to investing in “commodity currencies” can be forecasted at the 1 and 3 month horizons using the level of the (net) position. Overall, the results support 10 Or the trend in it. 103 a risk premium explanation for the violations of UIP, and suggest that the risk premium might be related to high frequency time variation in market participants positions. 104 References Alvarez, F., Atkeson, A., & Kehoe, P. (2005). 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(2001, May). Stabilization policy and the costs of dol- larization. Journal of Money, Credit and Banking, 33(2), 482-509. (Part 2: Global Monetary Integration) Schmitt-Groh´ e, S., & Uribe, M. (2003, October). Closing small open economy models. Journal of International Economics, 61(1), 163-185. Selaive, J., & Tuesta, V . (2003). Net foreign assets and imperfect pass-through: The consumption real exchange rate anomaly. (International Finance Discussion Paper No. 764) Tuladhar, A. (2003, May). Monetary policy under imperfect capital markets in a small open economy. The American Economic Review, 93(2), 266-270. (Papers and Pro- ceedings of the One Hundred Fifteenth Annual Meeting of the American Economic Association, Washington, DC, January 3-5, 2003) Verdelhan, A. (2009). A habit-based explanation of the exchange rate risk premium. The Journal of Finance. (Forthcoming) Warnock, F. E., & Warnock, V . C. (2009). International capital flows and u.s. interest rates. Journal of International Money and Finance. (forthcoming) Wei, S., & Kim, J. (1997). The big players in the foreign exchange market: Do they trade on information or noise? (NBER Working Paper no. 6256) Yun, T. (1996, April). Nominal price rigidity, money supply endogeneity, and business cycles. Journal of Monetary Economics, 37(2), 345-370. 109 Appendices A Appendix to Chapter 1 Benchmark consistent flows construction The foreign flows measure used here differs a bit from that proposed by Warnock and Warnock (2006) in that it scales the level of holdings by the total amount outstanding of Long Term Treasury securities, instead of lagged GDP. This is done to obtain a measure of holdings relative to the total supply available: constructed in this way, the holdings variable may better capture the effects of changes in foreign demand on yields: it controls for any increase or decrease in the total amount outstanding of long term bonds. The data for total outstanding Long Term Treasury securities is obtained from the Monthly Statement of the Public Debt, for all months from December 1978 to July 2007. The modification is used because it would seem to better capture a pure demand effect of foreign holdings on the prices of bonds: saying that foreign holdings are an increasingly higher percentage of GDP is not the same as saying that foreign holdings represent a high percentage of the overall securities available. The construction of the basic ”benchmark” adjusted nominal market value series of holdings of Treasuries follows Warnock and Warnock (2006) exactly: the reader is referred to that paper for a detailed explanation of the construction. The only modification that we employ here, is that, since we do not have detailed data on total trading volume exclusively for Non-Official purchases, we conduct the trading volume adjustment suggested in that paper using the Total trading volume data (that includes all foreigners ) for both official and non-official series as a proxy for the volume of Official institution’s purchases. Finally, an estimate of the fraction of total Long Term Treasury securities held by for- eigners is obtained as the ratio of the calculated Benchmark consistent flows to the Total Amount outstanding (which includes Intragovernmental Holdings and debt held by the public) of marketable Notes and Bonds from the Monthly Statement of the Public Debt, as suggested in the FAQ section in the TIC website. 11 . 11 http://www.ustreas.gov/tic/faq2.html q20 110 Impulse Responses and Variance decompositions Equipped with the estimated autoregressive polynomial ˆ B(L), we obtain the moving aver- age representation X t = ˆ C(L)u t =u t + ˆ C 1 u t−1 + ˆ C 2 u t−2 +··· (A.1) where, in general,C(L) is a lag polynomial of infinite length. In practice, we truncate the algorithm at 3 years (36 periods). Then, from the estimated Moving Average representation of the reduced form V AR (A.1), we obtain the Impulse Response function of the vectorX t as Ψ s = ∂X t+s ∂ε t = ˆ C s P where the(i,j) element ofΨ s denotes the response of the i th variable inX t+s to a one unit standard deviation increase in the j th structural innovation. The Mean Squared Error (forecast error variance) matrix of the vectorX t+s is given by MSE(X t+s ) = ˆ Σ+ ˆ C 1 ˆ Σ ˆ C ′ 1 + ˆ C 2 ˆ Σ ˆ C ′ 2 +···+ ˆ C s−1 ˆ Σ ˆ C ′ s−1 The assumption ofε t ∼ i.i.d.N(0,I n ) together with (1.5) imply that Σ = P 1 P ′ 1 + P 2 P ′ 2 +···+ P n P ′ n where P j is the j th column of the Cholesky factor P. Then, the MSE can be expressed as the sum ofn components, each of them corresponding to the contribution of an orthogonalized disturbanceε j t : MSE(X t+s )= n X j=1 MSE j (X t+s ) where MSE j (X t+s )= P j P ′ j + ˆ C 1 P j P ′ j ˆ C ′ 1 + ˆ C 2 P j P ′ j ˆ C ′ 2 +···+ ˆ C s−1 P j P ′ j ˆ C ′ s−1 Finally, the percentage of the total Forecast Error Variance that can be attributed to the j th structural innovation is given by RMSE j (X t+s ) =MSE j (X t+s )./MSE(X t+s ) Notice that./ denotes element by element division. The Forecast Error Variance decompo- sition for each variable uses the diagonal elements ofRMSE j (X t+s ). 111 B Appendix to Chapter 2 Calibration of fx t process 1. Take Monthly nominal holdings of Short-term treasury securities by for- eign official institutions (foi) (Position at end of period in millions of dollars. Source: Treasury International Capital Reporting System, at http://www.ustreas.gov/tic/bltype history.txt) and deflate it using the monthly PCE index to obtain monthly real foi holdings of short-term Treasuries (Billions of Chained 2000 Dollars). 2. Then, convert to quarterly figures by simple averaging quarterly holdings. 3. Next, linearly de-trend by regressing the log of the quarterly real holdings on a con- stant and a time-trend. Save the residuals as linearly detrended quarterly real foi holdings of short term treasury securities, which we will callx t . 4. Then, estimate an AR(1) process forx t . The results are: t-stats Point HH Hansen Newey- estimate s.e Hodrick OLS West r 2 ˆ s 2 Intercept -0.0043 0.01 -0.52 -0.67 -0.56 0.85 0.0050 Slope 0.9023 0.04 20.84 25.93 22.73 112 C Appendix to Chapter 3 Data sources for summary statistics The table presents sample statistics for the variables used in the regressions. xss (k) t is the k-month excess return realized at time t. i ⋆(k) t −i (k) t is the k-month interest differen- tial, not annualized, in natural units. Δ (k) x t is the k-month change in the net position in spot, futures and forward contracts by large FX market participants. Δ (k) y t is the k-month change in the net long futures position of speculators at the CME, expressed as a fraction of the total open interest of noncommercial traders (speculative). The sample is monthly from 1995:01-2008:08, except for the EUR which is 1999:01-2008:08. Exchange rate data is from the FRED Database at the St.Louis Fed. Interest rates are LIBOR quotes from Datastream. “Large” FX market participants position data is from the U.S. Treasury Bul- letin. Speculator’s net futures position data is from the Commitment of Traders report, at the CFTC website. Data sources for robustness regressions The control variables used in the paper are the interest differentiali ⋆(k) t −i (k) t , and growth rates of CPI inflationΠ ⋆ t,t−k , Π t,t−k and Industrial Production IP ⋆ t,t−k and IP t,t−k . The data sources are as follows: • For Australia, we use a cubic spline interpolation of quarterly CPI to obtain a monthly series, and use this to obtain the 1, 3 and 12 month growth rates. As a proxy for Industrial Production, we use a cubic spline interpolation of quarterly GDP to obtain a monthly series, and use this to obtain the 1, 3 and 12 month growth rates. • For Canada, the seasonally adjusted CPI is available at a monthly frequency. As a proxy for real activity, we use growth rates of the Canadian Composite Leading Indicator, also available at the monthly frequency, from Datastream. • For Switzerland, we use a cubic spline interpolation of the quarterly seasonally adjusted Industrial Production Index to obtain a monthly series, and use this to obtain the 1, 3 and 12 month growth rates. We use the monthly seasonally adjusted CPI index to obtain measures of inflation at the 1, 3 and 12 month horizons. • For the Euro area, we use the monthly seasonally adjusted Industrial Production Index (Total Industry) to construct the growth rates used in the regressions. We use the monthly seasonally adjusted HICP Index of Consumer prices to measure infla- tion. • For Great Britain, we use the monthly seasonally adjusted IOP index (all industries) to measure the growth in real production. For inflation, we perform a multiplicative 113 X12 census seasonal adjustment 12 to the CPI (all items), and use the adjusted series to obtain measures of inflation. • For Japan, we use the monthly, seasonally adjusted Index of Industrial Production for mining and manufacturing to obtain growth rates in real activity. For inflation, we perform multiplicative X12 census seasonal adjustment to the CPI (Ten Major group index), and use the adjusted series to obtain measures of inflation. 12 Using the routines in Eviews, version 5.1. 114

Abstract (if available)

Abstract This thesis examines how government accumulation of foreign exchange reserves affect interest rates in an open economy. In the first essay, I examine this issue from an empirical perspective. I estimate the impulse response of the 10 year Treasury yield to an exogenous innovation in Foreign Official Holdings of U.S. Long Term Treasury securities in an identified VAR model. I find that a market valuation adjustment done to the data is behind a seemingly negative effect of holdings on yields, and that once we control for this adjustment, the effect is not negative. Hence, I find no conclusive evidence of a negative effect on U.S. interest rates from foreign official accumulation of treasury bonds. In the second essay, I analyze the same question from a theoretical perspective. I present a two-country dynamic stochastic general equilibrium model in which central banks accumulate reserves and investigate whether the impulse response of one country’s interest rate is significantly negative after an exogenous shock to the other country’s foreign exchange reserve policy. I find that even in a world in which Uncovered Interest Parity (UIP) does not hold, which renders different currency assets imperfect substitutes, the response of the foreign interest rate to a home country reserve accumulation shock is likely to be negative but small in magnitude. In the third essay, I test for evidence on the mechanism used in the second essay to make different currency assets imperfect substitutes. Specifically, I estimate the elasticity of investments in foreign currencies with respect to expected excess returns. I find that currency flows help predict excess returns, and are statistically significant forecasting variables even in the presence of additional control variables. This means that demand for different currency assets is less than perfectly elastic, which lends support to the channel proposed in the second essay to introduce deviations from UIP.

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Creator Sierra Jimenez, Jesus Antolin (author)

Core Title Essays on interest rate determination in open economies

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Business Administration

Degree Conferral Date 2009-08

Publication Date 06/26/2009

Defense Date 05/04/2009

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag financial friction,foreign official holdings,foreign official intervention,general equilibrium,imperfect financial integration,Impulse response function,incomplete markets,OAI-PMH Harvest,perturbation methods,time-varying risk premia,two country model,UIP,Var

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Zapatero, Fernando (committee chair), Betts, Caroline M. (committee member), Jones, Christopher S. (committee member), Protopapadakis, Aris (committee member), Quadrini, Vincenzo (committee member)

Creator Email jasierraji@gmail.com,jesus.sierra@marshall.usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m2320

Unique identifier UC1468315

Identifier etd-Sierra-2976 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-407889 (legacy record id),usctheses-m2320 (legacy record id)

Legacy Identifier etd-Sierra-2976.pdf

Dmrecord 407889

Document Type Dissertation

Rights Sierra Jimenez, Jesus Antolin

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu