Back Matter

### Annex 1. Announcements by the Federal Reserve

Source: Glick and Leduc (2013) and authors’ own compilation.

### Annex 2. Theoretical Framework

Formally, we can follow Wickens (2011) to show why the impact of foreign official holdings of securities on the yield curve can be studied by analyzing its relationship with the term premium.

Let the holding-period return be the nominal rate of return of holding a zero-coupon bond for one period.1 Letting hn,t+1 be the holding-period return on an n-period bond between periods t and t+1, then:

$1+{h}_{n,t+1}=\frac{{P}_{n-1,t+1}}{{P}_{n,t}}=\frac{{\left(1+{R}_{n-1,t+1}\right)}^{-\left(n-1\right)}}{{\left(1+{R}_{n,t}\right)}^{-n}}$

where Pn,t is the price of the zero-coupon bond with n-periods to maturity at time t, and Rn,t the yield to maturity. Letting lower case variables denote logs prices and imposing the no-arbitrage condition for bonds—i.e. that after adjusting for risk, investors are indifferent between holding an n-period bond and a risk-free bond for one period—then we can show that:

${E}_{t}{h}_{n,t+1}=\left(n-1\right)\left({E}_{t}{R}_{n-1,t+1}-{R}_{n,t}\right)=\left({R}_{n,t}-{s}_{t}\right)-{\rho }_{n,t}$

where ρn,t is the risk premium on an n-period bond at time t, ${s}_{t}={r}_{t}^{f}={R}_{1,t}=-\mathrm{ln}{P}_{1,t}$, and Rn,t – st is the term spread.2 Et is the expectations operator. Now, using forward substitution, it is possible to show that:

${R}_{n,t}=\frac{1}{n}\underset{i=0}{\overset{n-1}{\mathrm{\Sigma }}}{E}_{t}\left({s}_{t+i}+{\rho }_{n-i,t+i}\right)$

That is, the nominal yield to maturity is the average of expected future rates plus the average risk premium on the bond over the rest of the life.

Since the Fisher equation defines a one-period real interest rate rt by:

${r}_{t}={s}_{t}-{E}_{t}{\pi }_{t+1}$

where πt denotes the inflation rate at t, then we can show that:

${R}_{n,t}=\frac{1}{n}\underset{i=0}{\overset{n-1}{\mathrm{\Sigma }}}{E}_{t}\left({r}_{t+i}+{E}_{t}{\pi }_{t+1}+{\rho }_{n-i,t+i}\right)$

Long-term interest rates can therefore be decomposed into three components: expectations about the future path of short-term real interest rates, expected inflation, and the term premium.

The presence of the term premium is relevant because it allows supply and demand conditions pertaining specifically to bonds of that maturity to affect pricing.3 To the extent that foreign official holdings of U.S. securities do not affect the path of real interest rate and/or expected inflation, their impact on the shape of the yield curve will only operate through the risk or term premium. In other words, this implies that the impact of foreign official purchases of U.S. Treasuries on the U.S. yield curve can be reduced to an analysis of its relationship with the term premium.4

A key issue then is how to specify the term premium. The standard approach in finance is to rely on affine factor models of the term structure. Based on certain assumptions about how latent factors behave, this approach extracts measures of the term premium directly from the yield curve. This may be contrasted with the general equilibrium approach to asset pricing where the factors are observable macroeconomic variables (Rudebush et al., 2006). More recently, both approaches have been combined through the use of latent and observable variables.

### Annex 3. Cointegration Tests

Annex Table 1.

Lag Selection and Cointegration Tests

Note: * indicates rejection of the null hypothesis.

## References

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We thank Alfred Kammer, Kristina Kostial, and Petya Koeva for their encouragement, support, and feedback. We acknowledge very useful conversations with Daniel Hardy, Wojciech Maliszewski, Ceyda Oner, Andrew Swiston, Neil Meads, Rina Bhattacharya, and useful comments from Emine Boz, Ezgi Ozturk, and participants at the 2015 Annual Conference of the Hungarian Society of Economics. Janyne Quarm provided excellent research assistance.

See discussions in IMF (2016a, 2011b) and Prasad (2014).

In this paper the term uphill capital flows is used loosely to refer to official flows that result from reserve accumulation. Nonetheless, uphill capital flows includes other components such as private capital flows.

This paradox was first pointed out by Lucas (1990) and has been widely discussed since then (see, for example, Gourinchas and Jeanne, 2007 and Boz et al, 2017).

This notion, however, has been increasingly challenged. In particular, the global financial crisis showed that this characteristic depends on the soundness of the sovereign as well as of its financial sector, as these are closely interconnected.

Agency debt, corporate debt, and interest-rate swaps could be considered alternatives but not fully (see, for example, agency debt during the global crisis, or the scandal surrounding the LIBOR rate). Moreover, the corporate market’s potential is limited as the market is fragmented. Globally, the euro, the main competitor of the U.S. dollar, does not have a Eurozone bond market, leaving the German Bunds as the closest alternative to U.S. Treasuries, but without its scale.

For a discussion in a similar context see Kitchen and Chinn (2011).

See Annex I. for more details.

Traditionally, the 2-year maturity was the most liquid (measured by daily turnover) segment of the U.S. Treasury market. However, the daily turnover for the 2-year securities has declined since 2008, with 5-year Treasuries becoming the most liquid segment of the market. This shift likely reflects the sustained levels of low interest rates since the onset of the GFC (Adrian, 2013).

In a zero-lower bound environment, the shadow rate can characterize both the term structure of interest rates and the stance of monetary policy (See Figure 4, bottom left panel).

See Bernanke’s global savings glut hypothesis and Greenspan’s conundrum speech (Bernanke, 2005; Greenspan, 2005, respectively).

Bernanke et al. (2004) find a negative relationship between foreign exchange interventions and U.S. Treasury yields. Specifically, they show that interventions undertaken by the Japanese Ministry of Finance between 2000 and 2004 could have lowered 10-year U.S. Treasury yields by 66 basis points for every purchase of US$100 billion. McCauley and Jiang (2004) find a significant negative relationship between weekly changes in 10-year U.S. Treasury yields and foreign official holdings, with the latter proxied by custodial holdings at the New York Federal Reserve, but only over two short periods in 2000 and 2003. Warnock and Warnock (2005) also found a negative relationship between the 10-year U.S. Treasury yield and foreign inflows between 1984 and 2005. According to their estimates, the presence of foreign investors in the U.S. Treasuries market lowered the 10-year yield by 150 bps between mid-2004 and mid-2005. Foreign official holdings could affect the future path of short-term interest rates if foreign exchange interventions by foreign central banks have an impact on growth and inflation outlook in the United States. For example, interventions aimed at keeping the currency undervalued relative to the U.S. dollar could lower economic growth and inflation in the United States by hurting its competitiveness, thereby triggering looser monetary conditions and lower short-term interest rates. For the purposes of this study we assume that this channel is of second order. However, Sierra (2010) shows that the impact of official and private flows differs: while official flows are similar to relative supply shocks, private flows seem to absorb excess supply. The annual surveys include information on foreign holdings of U.S. securities (stock) at the end of June every year. The TIC S data includes monthly cross-border transactions of securities (flow). The TIC SLT, introduced in 2011, collects data on foreign holdings of long-term securities (stock). While both the annual survey and the TIC SLT provide data on foreign holdings, the former is more detailed and comprehensive. The TIC S is prone to a number of biases, in particular the transaction and custodial bias. Specifically, given that the TIC S data are collected according to the country of the first cross-border counterparty, transactions are often concentrated in financial centers, causing a bias in their geographic distribution. Moreover, foreign private holdings could be overestimated relative to foreign official holdings (e.g., if an official investor holds U.S. securities with a foreign private custodian bank). As the TIC SLT collects information on actual holdings, it does not suffer from the transaction bias. However, it is also subject to the custodial bias that could distort both the geographic distribution (e.g., if a foreign holder has a custodian in a different country) and the size of foreign holdings (e.g., if a U.S. investor has a foreign custodian, foreign holdings of U.S. securities are overestimated). Prior to the estimation of Eq. (2), we tested for the order of integration of ρm, TF,O, TFED, and υ. The Dickey-Fuller, augmented Dickey-Fuller and Phillips-Perron tests are not able to reject the null hypothesis of unit roots for any of these series. The likelihood-ratio tests the null hypothesis of exactly r cointegration relationships versus the alternative of r + 1. Where the null hypothesis is that there are no more than r cointegration relationships. The Jarque-Bera normality test rejects the null hypothesis that the residuals from the term premium equation are normally distributed (Table 2). However, in the case of lower maturities this is mainly due to kurtosis rather than to skewness. As Paruolo (1997) has shown, if the rejection of normality is driven by kurtosis rather than skewness, the Johansen cointegration results are unaffected. This allows us to conclude that the fit of our model is adequate. For a discussion on the role of the SDR see IMF (2016a,b) and Tovar (2017). This is lower than the estimate of 17-20 basis points by Beltran et al. (2013). One of the possible reasons is that foreign official holdings are expressed relative to total outstanding marketable debt in the estimated models, therefore the impact of a US$ 100 billion decrease in demand on yields depends on the stock of debt. As total outstanding debt has been continuously increasing, the impact

Without loss of generality, we work with a zero coupon bond, as the n-period coupon bond can be thought as a collection of pure discount bonds with payoff in period to t to t + n – 1.

Equation (1) is the rational-expectations hypothesis of the terms structure when the risk premium (i.e. the term premium) is omitted.

The presence of idiosyncratic effects associated with a certain maturity of bonds is sometimes linked to the preferred habitat theory, that is, that certain investors have a preference for purchasing assets of specific maturities.

Foreign official holdings could affect the future path of short-term interest rates if foreign exchange interventions by foreign central banks have an impact on growth and inflation outlook in the United States. For example, interventions aimed at keeping the currency undervalued relative to the U.S. dollar could lower economic growth and inflation in the United States by hurting its competitiveness, thereby triggering looser monetary conditions and lower short-term interest rates. For the purposes of this study we assume that this channel is of second order.

Uphill Capital Flows and the International Monetary System
Author: Mr. Balazs Csonto and Mr. Camilo E Tovar Mora