D O C U M E N T O

D E T R A B A J O

Instituto de EconomíaD

OC

UM

EN

TO d

e TR

AB

AJO

I N S T I T U T O D E E C O N O M Í A

www.economia.puc.cl • ISSN (edición impresa) 0716-7334 • ISSN (edición electrónica) 0717-7593

Addicted to Debt: Foreign Purchases of U.S. Treasuries and the Term Premium

David Kohn

4802016

1

Addicted to Debt:Foreign Purchases of U.S. Treasuries and the

Term-Premium*

David Kohn

Universidad Catolica de Chile

Abstract

This paper investigates the effect of purchases of U.S. Treasuries by foreigners

on long-term yields and the term-premium. I set up a consumption-based model

with habit preferences, calibrate it to match the average slope of the yield curve in

the U.S., and find that foreign purchases decreased long-term yields significantly

prior to the financial crisis. Half of this change is explained by a drop in the term-

premium: foreign purchases increase domestic agents’ consumption above their

habit, reducing their risk-aversion and decreasing the term-premium. Finally, I

show that a reversal of foreign inflows results in a sharp increase in long-term yields.

Keywords: term-premium, long-term yields, U.S. Treasury bonds, habits.

JEL Classification: E43, E44, G12, G15.

* Email: davidkohn@uc.cl Mailing address: Pontificia Universidad Catolica de Chile, Institutode Economia, 3er piso, Av. Vicuna Mackenna 4860, Macul, Santiago, Chile. I would like tothank Jaroslav Borovicka, Tim Cogley, Sydney Ludvigson, and Stijn Van Nieuwerburgh for theiradvice and invaluable comments and suggestions. I would also like to thank Virgiliu Midrigan,Matteo Maggiori, Michal Szkup, Fernando Leibovici, Gaston Navarro, Elena Resk, Aitor Erce,and participants at various seminars and conferences, for their helpful feedback and suggestions.

1

1 Introduction

Over the last two decades there has been a dramatic increase in foreign holdings

of U.S. Treasuries. Foreign ownership of U.S. Treasury bills, notes and bonds,

increased from 8.8 percent of GDP in 1994 to 33.6 percent of GDP by the end of

2013.1 Approximately three-fourths of this increase was driven by Foreign Official

Institutions, such as foreign central banks. At the same time, both nominal and real

long-term bond yields declined significantly. Figure 1 depicts the increase in the

ratio of foreign holdings to GDP and the decline in the yield of a 10-year nominal

U.S. Treasury bond.

Figure 1: U.S. Treasury bond yields and foreign holdings of U.S. Treasuries

1990 1995 2000 2005 20100

10

20

30

40

% o

f GD

P

1990 1995 2000 2005 20100

2.5

5

7.5

10

Ann

ualiz

ed %

Foreign holdings US Treasuries10yr nominal yield

Source: Data on nominal zero-coupon yields is from Gurkaynak, Sack, and Wright (2007), updated by Federal ReserveBoard staff. Data on foreign holdings is from Treasury International Capital (TIC) system, U.S. Department of Treasury.

In this paper, I investigate the link between foreign holdings and long-term

yields. While previous empirical studies find a strong relationship between them,

the literature lacks a quantitative asset pricing model to quantify these effects and

1 Over the same period, foreign holdings of U.S. Treasuries increased from 18 percent of totaloutstanding treasury debt to 49 percent of total outstanding treasury debt. Data from TreasuryInternational Capital (TIC) system, U.S. Department of Treasury.

2

analyze counter-factual scenarios. I provide such a model and study the extent to

which the rise in foreign holdings of U.S. treasuries drove the observed decrease

in long-term yields. For instance, in contrast to the empirical studies, the model

allows me to investigate the effects of a potential sell-off of U.S. Treasuries by for-

eign holders, such as the Central Banks of China and Japan, on the term-structure

of interest rates.

Despite the importance of long-term treasury bond yields for macroeconomic

outcomes through their impact on the cost of borrowing, investment, and the prices

of assets such as houses,2 there is still a limited understanding of their determinants.

For instance, while there has been a surge of papers that study the determinants

of global imbalances and short-term interest rates over this period,3 this literature

cannot account for the behavior of long-term yields, which became disconnected

from short-term interest rates over a good part of the recent decade.4

To study the dynamics of long-term yields, I use the model to decompose the

effect of foreign purchases on current and future short-term interest rates, on the

one hand, and on the term-premium, on the other hand. Distinguishing whether

long-term yields are driven by higher expected yields or by a higher term-premium

is key for understanding agents’ expectations about the behavior of macroeconomic

variables and, therefore, for the success of monetary policy.5 Indeed, evidence sug-

gests that the decline in long-term yields over this period was driven by a decreasing

term-premium, as can be seen in Figure 2.6

2 See, for example, Favilukis, Kohn, Ludvigson, and Van Nieuwerburgh (2012).3 For example, Caballero, Farhi, and Gourinchas (2008), Caballero and Krishnamurthy (2009),

Mendoza, Quadrini, and Rıos-Rull (2009), among others.4 See, for example, Greenspan (2005).5 As argued by Bernanke (2006), while high yields due to expectations of higher growth in the

future —and therefore, high future short-term interest rates—, prescribe contractionary measures,high long-term yields due to high risk-aversion and a high term-premium —low future short-terminterest rates— call for the opposite approach.

6 The term-premium is unobservable and there are alternative ways to measure it. However, mostavailable measures suggest a secular decline over this period (Swanson 2007), which led many tobelieve that the decline in the term-premium was the explanation for the Greenspan’s conundrum—See Kim and Wright (2005), Rudebusch, Swanson, and Wu (2006), Backus and Wright (2007).

3

Figure 2: Term-premium for 10-year zero-coupon U.S. Treasury bond

1990 1995 2000 2005 2010−1

0

1

2

3

annu

aliz

ed %

10yr term premium

Source: Data on the term-premium is from Kim and Wright (2005), updated by Federal Reserve Board staff.

In order to understand the role of foreign purchases of U.S. Treasuries as a

driver of the term-premium and the term-structure of interest rates in the U.S., I

set up a standard asset pricing model with three key ingredients: (i) external habit

preferences; (ii) long-term debt; and (iii) non-zero foreign holdings of bonds of

different maturities. These preferences have been shown to capture the size and

time-variation of the risk-premium in the data, thus allowing the model to match

several features of the real and nominal yield curves.7 Therefore, this framework

has the potential to shed light over the macroeconomic drivers of the decline in the

term-premium and long-term yields over the last two decades.

The model consists of an endowment economy inhabited by a domestic repre-

sentative agent and foreign agents. The domestic agent maximizes expected utility

and receives an stochastic endowment every period. The agent can also trade bonds

of different maturities to smooth her intertemporal consumption profile. In par-

ticular, there are two types of bonds: a one-period bond and a perpetual long-term

bond. The latter pays a geometrically declining coupon that determines the duration

7 See, for example, Campbell and Cochrane (1999) and Wachter (2006).

4

of the bond.8 There is no default, so the short-term real bond is risk-less, while the

long-term bond is subject to the risk of capital losses in recessions. An exogenous

stochastic process for inflation allows for the pricing of nominal bonds.

Foreign agents purchase bonds, providing consumption goods in return. They

are represented in the model by a stochastic demand for bonds, which I estimate

from U.S. historical data on foreign holdings of U.S. Treasuries, jointly with en-

dowment growth and inflation. As mentioned above, most of the recent increase

in foreign holdings of U.S. Treasuries was driven by Foreign Official Institutions

(FOI).9 This is important, since it has been argued that the demand from these of-

ficial institutions is fundamentally different from the private sector demand: FOI

purchases are driven by a distinct set of incentives, namely reserve accumulation

and foreign exchange intervention, implying that this demand is significantly more

price-inelastic.10 Thus, these institutions do not behave as the portfolio-maximizers

private agents. Therefore, I take an agnostic modeling approach and estimate these

holdings directly from the data.

In order to study the quantitative implications of the model for bond prices and

the term-premium, I assume that the domestic agent has preferences with external

habits, as studied by Campbell and Cochrane (1999) and Wachter (2006). These

preferences imply that the agent values her consumption relative to a slow-moving

reference level, which can be interpreted as a habit or as the aggregate consumption

in the economy. This feature generates counter-cyclical risk-aversion, which allows

the model to reproduce a large, positive, and counter-cyclical term-premium, as

observed in the data.

I use this model to investigate how much of the drop in long-term yields from

8 As in Hatchondo and Martinez (2009), Arellano and Ramanarayanan (2012), and Rudebusch andSwanson (2008).

9 Foreign Official Institutions are defined as primarily foreign national government institutions in-volved in the formulation of monetary policy, such as central banks, but also include nationalgovernment owned investment funds. See TIC System, U.S. Department of Treasury.

10 See Alfaro, Kalemli-Ozcan, and Volosovych (2011), Donald Kohn (2002).

5

the first quarter of 2000 to the end of 2007 can be explained by foreign purchases

of U.S. Treasuries and how much of this decline was due to changes in the term-

premium.11 Since I study an endowment economy, I decompose observed consump-

tion growth into two components: foreign purchases and the difference between

observed consumption growth and foreign purchases. The goal of this exercise is to

quantify the response of yields to the variation in consumption growth attributable

to foreign purchases.

First, I show that the model delivers realistic implications for the yield curve.

I estimate the stochastic process for the exogenous variables using U.S. data, and

calibrate the preference parameters to match the average term structure of yields

and their standard deviation in the data.

I use this framework to investigate the impact of foreign purchases on long-term

yields and the term-premium. To do so, I compute the implied paths of long-term

yields and the term premium when the domestic agent faces the paths of inflation,

interest rates and consumption observed in the data between 2000 and 2007. Then,

I contrast the yields implied in this case with the ones obtained under the counter-

factual scenario in which foreign holdings stayed constant relative to GDP at their

beginning-of-period’s level.12 The difference between the yields implied by these

scenarios, suggests that foreign purchases reduced long-term yields by 5.5 percent-

age points over this period, and that the term-premium explains half of this effect.

These numbers imply that every 100USD billion of foreign official purchases of

U.S. Treasuries decreases long-term yields by 50 basis points, a number well in-

between estimates from previous empirical studies.13

Foreign purchases reduce bond yields in the model through their impact on

11 I purposely exclude the financial crisis when the Fed instrumented its Large Scale Asset Purchasesprogram. Thus, I avoid confounding the effects of foreign purchases of U.S. Treasuries with thoseof purchases by the Fed.

12 I assume a specific sequence of shocks to foreign holdings such that the stock of holdings overGDP stays constant.

13 See, for example, Warnock and Warnock (2009) and Beltran, Kretchmer, Marquez, and Thomas(2013).

6

expected consumption growth and consumption growth innovations. On the one

hand, foreign purchases increase current consumption and reduce expected con-

sumption growth, since consumption in the following period is expected to be lower

when debt needs to be repaid. This induces agents to save, so short-term inter-

est rates need to decrease to restore the equilibrium in the bond market. On the

other hand, agents are surprised every period by higher-than-expected consumption

growth. This is because new and unexpected foreign purchases of U.S. Treasuries

raise consumption growth above its expected value, which increases surplus con-

sumption —the difference between current consumption and a weighted average

of past consumption or habit. Higher surplus consumption in the model decreases

risk-aversion, leading agents to request a lower term-premium.

Finally, I investigate the effect of a reversal of foreign inflows of U.S. Treasury

debt. Discussion about the sustainability of global imbalances has led to speculation

over the possible consequences of a sell-off of U.S. debt by foreign governments.

I use my model to provide an estimate of the effects of this sell-off on U.S. Trea-

sury yields and bonds’ term-premium. For the baseline counter-factual exercise, I

assume that Foreign Official Institutions decide to stop rolling over 45% of their

U.S. Treasury debt holdings, which is equivalent to the holdings by Chinese and

Japanese FOIs. I use data on the maturity structure of foreign official institutions’

holdings to determine the speed of this adjustment. Beginning in June 2014, for-

eign holdings decline from 23.8 percent of GDP to 12.2 percent of GDP over the

following ten years, with more than two-thirds of that adjustment occurring in the

first three years. My results suggest that long-term bond yields would increase by

5.4 percentage points during the first three years, of which more than 60 percent is

explained by an increase in the term-premium.

My findings suggest that time-varying risk-premia played a significant role in

the recent dynamics of long-term interest rates. In this model, long-term bonds

are risky because of counter-cyclical short-term real interest rates, that cause bond

7

prices to co-vary positively with consumption growth. There is an additional risk-

premium in nominal bonds, due to the negative covariance between consumption

growth and inflation, but it plays a minor role in the dynamics of the term-premium,

which is mostly driven by the real risk-premium. This is in contrast to another po-

tential explanation of time-variation in risk premium, namely that a reduction in

inflation uncertainty has caused a drop in the term-premium, particularly during the

1990s.14 This hypothesis is downplayed by evidence on the U.S. TIPS markets,

however, since inflation uncertainty does not affect the yields of inflation-indexed

bonds and these behaved similarly to nominal bond yields for the period of analy-

sis.15

In the rest of this section, I discuss the related literature. In Section 2, I introduce

the model. In Section 3, I present and discuss the main results from the simulations.

At the end of that section, I study the case of a reversal in foreign inflows to U.S.

Treasuries. Finally, the conclusions are presented in Section 4.

1.1 Related Literature

This paper is related to recent papers that have studied the determinants of global

imbalances, the excess supply of savings, and the behavior of interest rates for safe

assets, as in Caballero (2006), Caballero, Farhi, and Gourinchas (2008), Caballero

and Krishnamurthy (2009), and Mendoza, Quadrini, and Rıos-Rull (2009).16

In contrast to the papers above, I investigate the effect of these flows on long-

term yields, the shape of the term-structure of interest rates, and the term-premium.

14 See, for example, Piazzesi and Schneider (2006) and Bansal and Shaliastovich (2012).15 The model in Piazzesi and Schneider (2006) suggest a flat real yield curve, while the mechanism

in Bansal and Shaliastovich (2012) implies a negatively sloped real yield curve, due to flight toquality in recessions. In U.S. data, however, the real yield curve typically slopes up (Gurkaynakand Wright 2012)

16 Another related strand of literature has focused on documenting the puzzling behavior of cap-ital flows, which flowed from developing countries —mostly Asian countries— to developedeconomies, as in Lucas (1990), Gourinchas and Jeanne (2013), and Alfaro, Kalemli-Ozcan, andVolosovych (2014). For alternative explanations for the global imbalances, see Angeletos andPanousi (2011), Aguiar and Amador (2011), and Maggiori (2013).

8

Since Fama and Bliss (1987) and Campbell and Shiller (1991), there is cumulative

evidence that risk-premia are time-varying and countercyclical,17 and this feature

is needed to capture the upward sloping shape of the yield curve observed in the

data (Backus, Gregory, and Zin 1989). Furthermore, there is wide consensus that

this premium has been declining over the last two decades, as shown by Rude-

busch, Sack, and Swanson (2007). However, despite the recent progress relating

movements in yields and the term-premium with macroeconomic variables, we are

still missing a good understanding of the macroeconomic forces driving the bond

term-premium.18

Related to my findings, there is a large body of empirical evidence that doc-

uments the effects of foreign purchases of U.S. Treasuries on yields and bonds

term-premia. Bernanke, Reinhart, and Sack (2004) finds that Japanese daily inter-

ventions on the foreign exchange market decreased 10-year bond yields during the

period from 2000 to 2004. Warnock and Warnock (2009) further suggests that for-

eign purchases flatten the yield curve with large effects on 10-year yields but not on

2-year yields, for 1984 to 2005. On the same line, Beltran, Kretchmer, Marquez,

and Thomas (2013) results show that an inflow of $100 billion USD reduces the 5-

year premium by 0.46 to 0.50 percentage points. Focusing on forecasting realized

excess returns instead, Sierra (2014) finds that official flows have a negative and

non-linear effect similar to supply shocks.19

These papers point towards a negative correlation between foreign purchases

and either long-term yields or the term-premium. However, they are silent regarding

the mechanism behind these effects. I quantify these effects in a consumption-

based model where bond prices and the term-premium are equilibrium outcomes,

17 See, for example, Ludvigson and Ng (2009), Cochrane and Piazzesi (2005), and Cochrane andPiazzesi (2008).

18 See Gurkaynak and Wright (2012) for a survey on this literature. Rudebusch and Swanson (2008),Rudebusch and Swanson (2012) for some recent examples.

19 See also Bertaut, DeMarco, Kamin, and Tryon (2011) and Bernanke, Bertaut, DeMarco, andKamin (2011).

9

and show how they are affected by foreign purchases of U.S. Treasuries.

An alternative explanation for these facts relies on segmented markets for bonds

of different maturities. Under this setup, the desire of foreigners for bonds of long-

maturities induced a fall in long-term yields and the term-premium. Kaminska

and Zinna (2014) build and estimate a structural arbitrage-free model with these

characteristics, and estimate that foreign purchases of U.S. Treasuries cumulatively

reduced long-term real yields by 80 basis points by 2008.20 While this is an intuitive

argument, it is hard to reconcile with the evidence that the average maturity of

foreign holdings was close to four years, while these purchases affected primarily

yields of longer maturities.

With a quantitative approach closer to the one in this paper, Justiniano, Prim-

iceri, and Tambalotti (2013) use a medium scale DSGE model to study the effects

of both the saving glut and banking glut on interest rates and house prices. Their

model, however, is silent regarding the risk premium and long-term yields, which

are the focus of my paper. Favilukis, Ludvigson, and Van Nieuwerburgh (2012a)

provides an alternative framework21 to study the effects of foreign inflows to safe

assets on welfare. They model foreign holdings of safe assets as following an ex-

ogenous process like I do, but in a setup with production and heterogenous agents.

However, they don’t look at the term structure of interest rates and bonds term-

premium, as I do.

The model in my paper extends Wachter (2006) to allow for foreign holdings

of bonds of different maturities. As such, it also draws on the earlier literature on

habit formation.22 In her model, however, nominal zero-coupon bonds are in zero-

net supply, and consumption is parametrized as a random walk. In this paper foreign

20 A similar model is used by Vayanos and Vila (2009), Kaminska, Vayanos, and Zinna (2011), andHanson and Stein (2014) to study the U.S. term structure of real rates and the long-run real effectsof monetary policy.

21 This is the same framework than in Favilukis, Ludvigson, and Van Nieuwerburgh (2012b).22 Among these: Campbell and Cochrane (1999), Abel (1990), Constantinides (1990), Ferson and

Constantinides (1991), Heaton (1995) and Sundaresan (1989).

10

purchases introduce a predictable component in consumption growth. Furthermore,

bond prices depend on current and past foreign holdings, which is needed to assess

the effects of foreign purchases on bond prices but makes the model challenging to

solve numerically.

2 The Model

In this section, I set up a model to study the effect of foreign purchases of

U.S. Treasuries on long-term bond yields and the term-premium. In the following

section, I solve this model numerically and I use it to investigate the quantitative

impact of foreign purchases of U.S. Treasuries and the counterfactual effect of a

reversal of foreign capital inflows.

The model consists of an endowment economy inhabited by a domestic repre-

sentative agent and foreign agents. The domestic agent maximizes expected utility

with external habit preferences. These preferences allow the model to generate a

positive and sizable term-premium, which is necessary to replicate an upward av-

erage yield curve as observed in the data.23 At the same time, it reproduces a real-

istic volatility of interest rates, because it breaks the link between the intertemporal

elasticity of substitution and the relative risk aversion, implied by standard isoe-

lastic preferences.24 Finally, and directly related to the focus of this paper, these

preferences generate a time-varying term-premium. Below, I briefly describe the

preferences, following Wachter (2006).25

The preferences of the domestic agent depend on an external habit, or subsis-

23 For example, Backus, Gregory, and Zin (1989) shows that an endowment economy with completemarkets and standard CRRA preferences can account for neither the sign nor the magnitude ofaverage risk premia.

24 The difficulty in generating both realistic risk premium and interest rates volatility is known asrisk-free rate puzzle, see Weil (1989).

25 Campbell and Cochrane (1999) presents a similar setup with constant risk free rates.

11

tence level Xt:

u(Ct, Xt) =(Ct −Xt)

1−γ − 1

1− γ

=(CtSt)

1−γ − 1

1− γ

(1)

where St ≡ Ct−Xt

Ctis surplus consumption.

The habit Xt is external, which implies that the agent does not consider the

effect of its decisions on the future level of the habit when deciding its optimal

consumption choice. These preferences are characterized by time-varying relative

risk aversion:

(2) − u′′(Ct, Xt)Ctu′(Ct, Xt)

=γ

St

Risk aversion varies with surplus consumption, which is procyclical: risk aver-

sion is higher in bad times commanding a higher risk premium, and declines during

expansions. This is the force driving time-variation of the term-premium in the

model.

This model can generate a high average value of risk aversion for a small value

of the utility curvature parameter, γ.26 This allows the elasticity of intertemporal

substitution to have a value consistent with a realistic volatility of interest rates.

The process for log surplus consumption is

(3) st+1 = (1− φ)s+ φst + λ(st)(∆ct+1 − Et∆ct+1)

where lower-case letters represent logarithms. Notice that a high value for φ implies

a slow-moving habit.

26 In the time-additive, isoelastic, expected utility, the elasticity of intertemporal substitution is givenby 1/γ, the inverse of the constant relative risk aversion coefficient.

12

The specification of the process for surplus consumption in logarithms ensures

that consumption never falls below the habit. This process is heteroskedastic given

that λ varies over time, and surplus consumption is positively correlated with con-

sumption growth innovations.

The sensitivity of surplus consumption to consumption growth innovations,

λ(st), is defined as in Wachter (2006):

λ(st) =

1S

√1− 2(st − s)− 1 if st ≤ smax

0 if st > smax

smax =s+1

2(1− S2

)

S =σc

√γ

1− φ− b/γ

(4)

where σc ≡ Stdt (∆ct+1 − Et[∆ct+1]) is the standard deviation of consumption

growth innovations, conditional on information at period t.

This function, λ(st), is specifically designed to introduce several important fea-

tures in the process for surplus consumption.27 In particular, when surplus con-

sumption equals its long-run value s, the habit is a function of past consumption.

Moreover, the risk-free rate depends on surplus consumption, with the sign of the

relationship depending on the sign of b.28

Every period the domestic agent receives a stochastic endowment Yt, and has

access to two types of assets: one-period bonds and long-term bonds. I model long-

term bonds as perpetuities that pay geometrically declining coupons, as in Arellano

and Ramanarayanan (2012) and others.29

The lender of these nominal long-term bonds lends qLt Lt units of currency in

27 See Campbell and Cochrane (1999) for more details on this.28 When consumption is a random walk, Wachter (2006) shows that the risk-free rate depends lin-

early on surplus consumption.29 See also Hatchondo and Martinez (2009) and Rudebusch and Swanson (2008).

13

period t and is paid back δn−1Lt units of currency in every period t + n. Then,

defining BLt as the stock of long-term bonds at time t, or the total payments due in

period t on all past issuances,

BLt =

t∑

j=0

δjLt−j = Lt + δLt−1 + ...+ δtL0 +BL0

where BL0 is given.

Notice that the law of motion for BLt can be written recursively as:

(5) BLt = δBL

t−1 + Lt

This formulation alleviates the need for additional state variables which would

be necessary in the case of zero-coupon, long-maturity, bonds. Furthermore δ can

be calibrated to match the average duration of long-term bonds in the data, which

makes this perpetuity an attractive substitute for modeling purposes.

The domestic agent solves every period:

maxCt,BSt ,B

Lt ,Lt

E0

( ∞∑

t=0

βt(CtSt)

1−γ − 1

1− γ

)

s.t.

Ct + qStBSt

Pt+ qLt

LtPt

=Yt +BSt−1

Pt−1

Pt−1

Pt+BLt−1

Pt−1

Pt−1

Pt

BLt =δBL

t−1 + Lt

st+1 =(1− φ)s+ φst + λ(st)(∆ct+1 − Et∆ct+1)

BSt

Pt+BLt

Pt(1 + δqLt ) ≥ bt

(6)

where bt is the natural debt limit.

Foreign agents consist of a stochastic demand for bonds, following a process

14

which I estimate from U.S. data. This modeling assumption responds to the con-

cerns expressed above, that Foreign Official Institutions have an objective function

guided by different incentives than private investors that solve a standard portfolio

choice problem. Therefore, I take an agnostic view of the preferences guiding this

process and, instead, estimate this foreign demand from the data.

Furthermore, I assume that every period foreign agents hold a fixed fraction

of their total stock of bonds in short-term bonds. Then, their portfolio decision is

given by α, the share of short-term bond holdings. While this assumption is not

necessary, it simplifies the problem since it avoids having to keep track of both

long- and short-term foreign holdings. Instead, both are driven by the total foreign

holdings Ft:

F St =αFt

FLt =(1− α)Ft

(7)

where F S are short-term bond holdings and FL are holdings of long-term bonds by

foreigners.

The market clearing conditions for bonds are given by,

BSt + F s

t =0

BLt + FL

t =0(8)

To complete the model, I assume that endowment growth, ∆Yt ≡ log( YtYt−1

),

real foreign holdings over the endowment, ft ≡ Ft

PtYt, and inflation, πt ≡ log( Pt

Pt−1),

follow a VAR(1) process.

15

Xt =(I − A)µ+ AXt−1 + εt

Xt ≡

∆Yt

ft

πt

, εt ≡

ε∆Y,t

εf,t

επ,t

(9)

where A is a 3x3 matrix and εt ∼ N(0,Σ), with Σ also a 3x3 matrix.

This parsimonious specification with only one lag helps keeping the model

tractable.

2.1 Equilibrium bond prices

In this subsection, I obtain the expressions that characterize the equilibrium

policies for bond prices and consumption. Since the problem is not analytically

tractable to get closed form solutions for bond prices, in the next section I solve for

these numerically.

Definition Let endowment growth, foreign holdings, and inflation follow the pro-

cess in Equation 9 and let the fraction of short-term bond holdings be given by α.

An equilibrium in this economy is a sequence of consumption choices and bond

holdings, {Ct, BSt , B

Lt }∞t=0, and bond prices, {qSt , qLt }∞t=0, such that:

1. Given bond prices and the process for endowment growth, foreign holdings

and inflation, the agent chooses consumption and bond holdings to solve the

problem given in Equation 6.

2. Markets for short- and long-term bonds clear (Equation 8).

The first order conditions of the domestic agent’s problem (Equation 6) are:

16

qSt =Et[M$

t+1

]

qLt =Et[M$

t+1(1 + δqLt+1)](10)

where M$t+1 = β

[(Ct+1

Ct

St+1

St

)−γPt

Pt+1

]

The market clearing conditions for bonds (Equation 8) and the agent’s budget

constraint imply,

(11)CtYt

= 1 +(αqSt + (1− α)qLt

)ft −

(1 + (1− α)δqLt

)ft−1

Yt−1

Yt

Pt−1

Pt

Consumption depends both on the endowment and the current account deficit,

which mirrors the foreign purchases of bonds in this economy. Therefore, while

trading bonds, foreigners effectively finance consumption and affect the consump-

tion growth process and bond prices. Also, the current account deficit depends not

only on the quantity of bond purchases, but on its price: for any given demand of

bonds, a higher price will allow higher consumption.

Finally, notice that a higher stock of debt at t− 1 diminishes consumption at t,

since it means higher debt payments at t, and its magnitude depends on the price

of long-term debt, endowment growth from t − 1 to t, and inflation from t − 1 to

t. Due to the existence of long-term debt, a higher price of debt means higher debt

payments; this feature of the model can potentially capture some of the valuation

effects that have been quantitatively important over the recent period in the U.S., as

shown by Gourinchas and Rey (2013). On the contrary, higher inflation dilutes the

value of debt since these are nominal bonds. Endowment growth also appears in

this equation since the stock of debt is normalized by the endowment.

Bond prices are functions of 5 state variables in this problem: qj(st,∆yt, ft, ft−1, πt),

where j = S, L, st is log surplus consumption, ∆yt is endowment growth, ft is the

17

foreign bond holdings over the endowment at t and ft−1 is the one corresponding to

the previous period, and πt is the consumption good price growth. In the next sec-

tion, I solve for these prices numerically, given the exogenous process in Equation 9

above.

3 Quantitative Results

In this section, I present the quantitative findings of the paper. First, I estimate

the process for endowment growth, foreign holdings and inflation from U.S. data

and calibrate the parameters of the model to match the average level of yields over

this period. Then, I use the model to ask how much of the large drop in long-term

yields observed during the 2000s, as shown in Figure 1 above, can be explained by

the dramatic increase in foreign purchases of U.S. Treasuries by Foreign Official

Institutions and how much of this change is attributable to risk compensation. In

the following subsection, I provide an explanation of the mechanism driving these

effects. The section concludes with a counterfactual exercise that studies the re-

sponse of yields and the term-premium to a reversal of foreign purchases of U.S.

treasuries.

3.1 Calibration

I estimate the process for the exogenous variables in Equation 9 from the first

quarter of 1952 to the last quarter of 2007. For endowment economies, a standard

practice in asset pricing models is to estimate endowment growth using consump-

tion growth data. However, in this model consumption growth depends both on

endowment growth and on the change in foreign purchases normalized by the level

18

of the endowment:

∆logCt ≈∆logYt + ∆

[(αqSt + (1− α)qLt

)ft −

(1 + (1− α)δqLt

)ft−1

Yt−1

Yt

Pt−1

Pt

]

⇒∆logYt ≈ ∆logCt −∆

[qtFt − qt−1Ft−1

PtYt

]

where ft ≡ Ft

PtYtand the hat variables are the corresponding proxies in the data for

consumption growth, market value of current and past debt, and nominal endow-

ment, respectively.

As a proxy for ∆yt, I use data on growth of real consumption of nondurables

and services, per-capita, minus the change in foreign purchases of U.S. treasuries

at market value –the change in the flows of foreign holdings of bonds– normalized

by nominal GDP.30 The data on consumption is from BEA and the data on foreign

holdings of treasuries is from the U.S. Treasury, as explained below. Inflation, πt,

is the growth in the U.S. consumer price index from BLS.

Finally, ft is the stock of U.S. Treasuries by Foreign Official Institutions over

nominal GDP.31 Data on U.S. Treasuries holdings by FOIs includes Treasury bills,

bonds and notes.32

I first estimate the VAR process. The choice of the estimation period from the

first quarter of 1952 to the last quarter of 2007 is due to the availability of data and

I exclude the financial crisis subperiod as in the main quantitative exercise. There

are 18 parameters to be estimated corresponding to µ, A, and Σ above. I use a

30 Notice that, in the model, the change in foreign purchases over the endowment is the same asthe change in the current account deficit over the endowment. I could have instead calibrated theprocess using data on the current account. The main findings are robust to this alternative.

31 I normalize foreign holdings by nominal GDP, instead of the endowment constructed as describedabove. Foreign holdings are valued at book value –I subtract capital gains–, except for the con-struction of the endowment series above. Results are robust to these choices.

32 Data from the Flow of Funds, release Z.1, published by the Federal Reserve. These data are basedon the Treasury International Capital (TIC) reporting system and are adjusted by BEA to accountfor systematic and known under- or overestimating of reported transactions, based largely on theannual surveys, and for valuation adjustments.

19

method of moments to match the means of the processes for each of the variables

in the data, the standard deviations, cross-correlations, first order autocorrelations,

and covariances. The target moments are described in table 1 below.

Table 1: Target Moments

Process for ∆Y, qxf and π, 1952Q1-2007Q4

µ∆Y 0.49% Mean endowment growthσ∆Y 0.54% Std endowment growthµπ 0.93% Mean Inflationσπ 0.74% Std Inflationµf 3.81% Mean foreign holdings over GDPσf 2.35% Std foreign holdings over GDPρ∆Y

′ ,∆Y 0.18 AR(1) endowment growthρ∆Y

′ ,f -0.06 Correlation ∆Y′ and f

ρ∆Y′ ,π -0.23 Correlation ∆Y

′ and πρf ′ ,f 0.996 AR(1) foreign holdings over GDPρf ′ ,∆Y -0.07 Correlation f ′ and ∆Y

ρf ′ ,π 0.07 Correlation f ′ and πρπ′ ,π 0.82 AR(1) Inflationρπ′ ,∆Y -0.06 Correlation π′ and ∆Y

ρπ′ ,f 0.09 Correlation π′ and fρ∆Y,π -0.23 Correlation ∆Y and πρf,∆Y -0.08 Correlation ft and ∆Y

ρf,π 0.08 Correlation ft and π

Notes: Sample moments for 1952Q1-2007Q4. ∆Y is consumption growth, where consumption is real per capita consumptionof nondurables and services minus the change in foreign purchases of U.S. treasuries at market value. ft is stock of foreignholdings of U.S. Treasury bills, bonds and notes at book value over nominal GDP. π is U.S. CPI price inflation. Mean andSt. dev. for f are divided by K = 0.224. See the text for explanation on this adjustment. Source: Data on foreign holdingsof U.S. Treasuries from Flow of Funds, Federal Reserve; other data from BEA.

Given this process, I simulate the model and calibrate the preference parame-

ters, at a quarterly frequency, following a Simulated Method of Moments approach.

There are four preference parameters: the utility curvature, γ, the subjective dis-

count factor, β, the persistence of the log surplus consumption, φ, and a parameter

that affects the sensitivity of the log surplus consumption to consumption growth

20

shocks in Equation 4 above, b. As explained below, a large and positive b drives

a large and positive risk-premium, since it commands a countercyclical risk-free

rate. I choose these four parameters to match four targets: the levels and stan-

dard deviations of the yields of the 3-month Treasury Bills at the secondary market

and those of the 4-year, zero-coupon, Treasury Bonds from the Fama-Bliss dataset.

Since even with four parameters I cannot match the targets exactly, I choose them

to minimize the objective function MWM ′, where M is a row vector that consists

of the log-difference between each target moment and its model counterpart. W is a

weighting matrix that allocates the same weight to each of the four target moments

described above.33 Table 2 presents the results of the calibration exercise.34

Table 2: Preference parameters, quarterly

β 0.986b 0.011φ 0.952γ 0.822

Finally, the rate of geometric decline of the coupons for the long-term bond, δ,

is set so that the duration of the perpetuity is 16 quarters, the weighted average ma-

turity of foreign holdings of U.S. Treasury holdings by Foreign Official Institutions

at June of 2014. This implies δ = 0.947.35 The share of short-term foreign pur-

chases, α, is chosen to match the average share of short-term treasuries –Treasury

bills– held by foreigners during the period 1994Q1 to 2007Q4.36

33 I have tried allocating ten times more weight to either the first or second moments. Althoughthe resulting parameter values slightly change, the results of the main quantitative exercise do notchange significatively.

34 Numerically I obtain that, around the parameters chosen, an increase in b increases the level andthe slope while an increase in φ reduces the slope but increases the level. Finally, an increase in βdecreases mean yields but increases the slope.

35 I use an average quarterly yield of 1pp to discount the bonds.36 This fraction has been decreasing over time, but has fluctuated around 18% for the last two

decades. Currently, it is approximately 9%.

21

Table 3: Long-term bonds

δ 0.947 Match maturity of 16 quarters;α 0.18 Mean share short-term Treasuries holdings by foreigners

Scaling foreign holdings. I use a perpetuity to model long-term bonds, whereas

in the data this type of perpetuity bonds is rare. While I calibrate the rate of decline

of the coupons to match the average maturity of these bonds, there is a significant

difference regarding their present value.37 Therefore, I scale down foreign holdings

by a constant factor, to equalize their present values.

In the data, the value of long-term foreign holdings is given by q(16)t F

(16)t , where

q(16)t is the price of a 16-quarter bond at t.38 To equalize their present value with the

present value of a long-term bond in the model, qLt FLt , long-term flows need to be

adjusted:

FLt =

q(16)t

qLtF

(16)t , qLt =

e−yt

1− δe−yt , q(16)t = e−yt16

where yt is the quarterly yield to maturity observed in the data. To avoid further

distortions to the data, I restrict myself to a constant adjustment, and use insteadq(16)

qL, where both prices are obtained using a constant average yield of 1pp, quarterly.

To keep short-term foreign holdings as in the data, α needs to be adjusted con-

sistently. DefineK = α+(1−α) q(16)

qL, then the adjusted share of short-term holdings

and adjusted flows are:

α =α

K, Ft = KFt

37 i.e., a zero-coupon bond of 4 years, discounted by an quarterly average yield of 1% has a price ofe−0.01x16 ≈ 0.85, while a consol has a price of 16e−0.01 ≈ 15.84

38 I am assuming these bonds are zero-coupon as an approximation.

22

Given the calibration above, q(16)

qL= 0.0538, K = 0.224 and α = 0.80.

Solution. As discussed above, bond prices need to be solved numerically. I dis-

cretize the continuous process using a code by Knotek II and Terry (2010), which

is an extension of Tauchen (1986) that allows for a non-diagonal covariance matrix.

Given the number of state variables in my problem, the grid size for each variable

is necessarily small. I use a grid of 11 carefully chosen values for surplus consump-

tion,39 7 equidistant values for income growth, 45 equidistant values for stock of

foreign debt, both at t and t− 1, and 5 equidistant values for inflation. Bond prices

are solved for each grid point and then these prices are linearly interpolated when I

simulate the economy for 440,000 quarters, burning the first 40,000 observations.

I focus the analysis on bond yields, which are related to bond prices as follows:

ySt =log

(1

qSt

), yLt = log

(1 + δqLtqLt

)

where ySt is the yield of a short-term bond at t and yLt is the yield of a long-term

bond at t.

The yield for the perpetuity, derived above, reflects the fact that a unit of this

asset at t is a claim to a unit of consumption plus a unit of the bond at t+1 discounted

by δ.40

Table 4 presents the average yields in the simulation, and their standard devia-

tions, for both real and nominal yields, and compares them with the data.

Although the model cannot match the target moments exactly, the table above

shows that it does a good overall job of matching both sample averages and standard

deviations of yields in the data. I now investigate the extent to which bond yields are

driven by foreign holdings using this model. As mentioned above, a standard model

39 The grid points are carefully chosen so that the model without foreign purchases replicates closelythe results in Wachter (2006).

40 The data is for a yield on a zero-coupon, 16 quarters, bond. Its quarterly yield is given by y(16)t =

− 116 log

(q(16)t

)

23

Table 4: Bond Yields, simulation results and data

Model DataReal Nominal Nominal

E(ySt ) 1.16 4.87 5.13

E(yLt ) 2.97 6.31 6.00

σ(ySt ) 2.49 2.94 2.87

σ(yLt ) 2.78 2.65 2.75

Notes: numbers in the table are simulated moments for the model and sample moments for 1952Q1-2007Q4 for the Data. Inthe data column, ySt is the 3-month yield, and yLt is the 4-year zero-coupon bond yield, from Fama-Bliss dataset.

with constant relative risk aversion would not be able to match these moments.

3.2 Foreign purchases of U.S. Treasuries and the “Savings Glut”

In the previous subsection, I showed that the model can match the main features

of the average yield curve in the data. In this subsection, I use this framework to

study the extent to which foreign purchases of U.S. treasuries contributed to the de-

cline in long-term yields and the term-premium from the first quarter of 2000 to the

last quarter of 2007. Bernanke (2005) and others claim that there was a worldwide

“Savings Glut” during this period: a situation in which there were worldwide excess

of savings, mainly from Asian countries, with respect to investment opportunities.41

In particular, foreign holdings of U.S. treasuries by Foreign Official Institutions

almost doubled over these years, increasing by 1.1 trillion U.S. dollars from 6.4

percent of the U.S. GDP to 11.8 percent of the U.S. GDP. I purposely exclude the

financial crisis period when the Fed instrumented its Large Scale Asset Purchases

program. This strategy allows me to isolate the effect of foreign purchases of U.S.

treasuries.

41 See, for example, Caballero, Farhi, and Gourinchas (2008), Justiniano, Primiceri, and Tambalotti(2013).

24

3.2.1 Effect of foreign purchases on treasury yields and the term-premium

To quantify the effect of foreign purchases of U.S. treasuries on bond yields and the

term-premium over this period, I first compute the equilibrium consumption and

bond prices implied by the model in response to the shocks observed in the data.

To isolate the effect of foreign purchases, I then simulate the path for bond yields

for the case in which both inflation and endowment growth behave as in the data,

but foreign holdings stay constant relative to GDP, at their beginning-of-period’s

level. In both cases, I assume that the agents’ perceived law of motion for the

exogenous process is the one I estimated from the data above.42 Finally, I interpret

the difference between the two paths for bond yields as the quantitative impact that

foreign holdings had on the bonds yield-curve and the term-premium over these

years.43

Figure 3 presents the simulated paths implied by the model for long-term nom-

inal yields, the term-premium, and short-term nominal yields, in the case in which

the sequence of shocks is the one observed in the data –black lines– and their coun-

terparts in the case in which inflation and endowment growth behave as in the data,

but foreign holdings stay constant relative to GDP.

As the top panel in Figure 3 shows, long-term yields in the hypothetical case

with constant foreign holdings follow closely the corresponding yields with positive

foreign purchases until 2003Q1, but then their paths separate from each other. At

the end of the period, long-term yields are 5.5 percentage points higher in the case

in which foreign holdings increase as observed in the data.

Thus, the model suggests that absent the purchases by Foreign Official Institu-

tions over these years, the yields of long-term bonds would have been almost twice

42 Under the lens of the model, the observed increase in foreign holdings was a particular sequenceof transitory shocks.

43 The analysis focuses on short- to medium-term fluctuations, so I first filter out quarterly fluctu-ations by taking 4-quarter moving averages of the series for endowment growth, inflation, andforeign holdings.

25

Figure 3: Nominal yields and term-premium in the model

2000 2001 2002 2003 2004 2005 2006 2007 20080

3

6

9

Long−term yields

annu

aliz

ed %

Baseline∆ f=0

2000 2001 2002 2003 2004 2005 2006 2007 20080

3

6

9

annu

aliz

ed %

Short−term yields

2000 2001 2002 2003 2004 2005 2006 2007 20080

3

6

9

annu

aliz

ed %

Term−premium

as large as they were at the end of 2007.44 While these figures seem surprisingly

large, they are rather in the ballpark of previous empirical estimates. For example,

Warnock and Warnock (2009) results suggest an impact of 68 basis points in 10-

year yields per 100USD billion of foreign inflows to U.S. Treasuries by FOIs, and

Beltran, Kretchmer, Marquez, and Thomas (2013) find that every 100USD billion

of foreign official purchases reduce yields by 39 to 62 basis points.45 In com-

parison, using an asset pricing model instead of a regression analysis, the results

above suggest that every 100USD billion of foreign official purchases reduced 4-

44 As argued above, these flows can be characterized as approximately exogenous to the U.S. econ-omy.

45 Both empirical studies focus on 12-month purchases by Foreign Official Institutions during asimilar time-span to the one studied in this paper. The impact attributed to Warnock and Warnock(2009) is implied by their finding that absent the substantial foreign inflows into U.S. governmentbonds, over the 12 months ending in May 2005, the 10-year Treasury yields would have been 80basis points higher. The figures in Beltran, Kretchmer, Marquez, and Thomas (2013) are from thereported medium-run effects in Table 6 of their paper.

26

year Treasury yields by 50 basis points over this period, well in-between previous

estimates.46

The term-premium. Using the model, long-term yields can be decomposed into

an expected component and a term-premium. The term-premium on long-term

bonds is the risk compensation required by risk-averse agents to hold the risky

bond, where the risk is due to their prices co-varying positively with consumption

growth, so that an agent that might need to sell the bond before maturity would suf-

fer capital losses precisely in those moments where he wants to consume the most

—in recessions–.47 The remaining expected component is a weighted average of

the current and expected future short-term yields. This decomposition is useful, as

mentioned above, to understand the source of the changes in long-term yields and,

thus, agents’ expectations about the behavior of macroeconomic variables, which

are a key input for the success of monetary policy.

Therefore, long-term yields can be decomposed as:

yLt = ySt +(yLt − ySt

)︸ ︷︷ ︸

expected

+(yLt − yLt

)︸ ︷︷ ︸term-premium

where yLt is the yield on the expected discounted value of the coupons, discounted

using the risk-free rate rather than the stochastic discount factor.48

The bottom two panels of Figure 3 show that foreign purchases had a simi-

lar effect in short-term interest rates and the term-premium as in long-term yields.

Absent foreign official purchases, the term-premium would have been almost 3 per-

centage points higher, explaining more than half of the change in long-term yields.

46 Foreign official holdings of U.S. Treasuries increased by almost 1.1USD trillion over this period,while the model suggests that the effect of foreign purchases was to reduce yields by 550 basispoints.

47 In the model, this covariance is caused by short-term interest rates increasing when surplus con-sumption is low, so that bond prices are lower in bad times.

48 The term-premium above is the cleanest concept of risk-premium according to Rudebusch andSwanson (2008), although it cannot be directly observed in the data.

27

Finally, foreign official accumulation of U.S. Treasuries also increased short-term

interest rates by 4.9 percentage points, which implies that they decreased future ex-

pected short-term yields –the “expected” term in the middle of the equation above–.

These numbers are summarized in the top panel of Table 5.

Table 5: Bond yields and term-premium in the model, 2000Q1 to 2007Q4

Panel A: Change in nominal yields

yL yS yL − yS TP

Baseline -0.52 -0.93 0.82 -0.41ft = f2000Q1 5.01 3.99 -1.53 2.55Due to ft -5.53 -4.92 2.35 -2.96

Panel B: Change in real yields

Baseline -1.18 -1.38 0.56 -1.47ft = f2000Q1 5.12 3.68 -1.47 2.91Due to ft -6.30 -5.07 2.03 -3.26

Notes: The line labeled “Due to ft” is the difference between the first and second lines in the table and represents the changein each yields’ component attributable to official purchases of U.S. Treasuries.

Finally, as can be seen in Panel B of Table 5, foreign purchases have a quanti-

tatively similar impact on real yields than in nominal yields. This is because they

affect bond prices mainly through real consumption growth, as we discuss below.

Thus, the model suggests that foreign purchases of U.S. Treasuries have a large

negative effect on long-term yields and the term-premium. Moreover, these seem to

move together. Finally, most of the impact is through real yields. Below, I explore

what drives these findings.

28

3.2.2 Explaining the dynamics of bond yields

The model implies that there was a decrease in yields and the term-premium from

the first quarter of 2000 to the last quarter of 2007 but, had foreign holdings stayed

constant relative to GDP, there would have been an increase in yields and the term-

premium instead. In this subsection, I discuss the main channels through which

foreign purchases of U.S. Treasuries affect bond yields.

Since the main channels of transmission in the model occur through changes in

consumption growth, I focus on real yields. Below, I argue that foreign purchases

affect short-term real yields mainly through their effect on expected consumption

growth, and affect long-term real yields and the term-premium mainly through their

impact on surplus consumption. Then, I show that changes in surplus consumption

are driven by unexpected changes in consumption growth, and decompose these

innovations according to their structural sources.

Short-term yields and foreign purchases. On the one hand, high foreign pur-

chases diminish expected consumption growth, reducing one-period real yields.

Equation 12 shows, using a linear approximation, how expected consumption growth

and foreign purchases are related in the model.49

Et(∆ct+1) ≈Et(qat+1ft+1 − qat ft

)+ Et(∆yt+1)

− Et[(1 + (1− α)δqLt+1)fte

−(∆yt+1+πt+1) − (1 + (1− α)δqLt )ft−1e−(∆yt+πt)

]

(12)

where qat stands for a weighted average of the prices of short-term and long-term

bonds at t, using the share of holdings of each bond as weights, i.e. qat = αqSt +

(1− α)qLt .

First, notice that without foreign holdings (ft = 0 ∀t), expected consumption

growth depends only on expected endowment growth. Since endowment growth

49 Here, I am using log(1 + x) ≈ x.

29

has very low persistence according to my calibration, expected consumption growth

barely moves in this case. Given non-zero foreign holdings, there are two ex-

tra terms: the expected change in the value of foreign purchases from t to t + 1,

Et(∆qat+1ft+1

)and the burden of past debt that needs to be paid at t minus what

was paid at t − 1. As I show below, the latter is the dominant term in the an-

alyzed period, given the stochastic process for foreign holdings and endowment

growth. Therefore, expected consumption growth co-varies negatively with foreign

purchases at t, ∆ft.

The burden of past debt also varies with inflation and endowment growth since

foreign debt is normalized by the nominal endowment, and contains the price of

long-term debt, since the stock of long-term debt appreciates or depreciates with

its price. That is, this model can potentially account for some of the big valuations

effects observed in the data over the last decade in the U.S.

The expected change in the value of foreign purchases from t to t + 1 is not

quantitatively important. First, the process estimated for ft is close to a unit root

process, Et(∆ft+1) ≈ 0.50 On the other hand, variation in bond prices, Et(∆qat+1),

is quantitatively small, as I show below.51

The discussion above suggests that foreign purchases reduce expected con-

sumption growth. To understand the effects of changes in expected consumption

growth on short-term yields, I derive below an expression for the short-term real

yield. To derive this expression, I assume that consumption growth is approxi-

mately log-normally distributed.52 Under these assumptions, the short-term real

yield can be expressed as:

50 Actually, it should be negative due to the slow mean reversion of foreign holdings.51 Notice that Et

(qat+1ft+1 − qat ft

)= qatEt (∆ft+1) + ftEt

(∆qat+1

)+ Et

(∆ft+1∆qat+1

)52 This is exact in the case that consumption is a random walk as in Wachter (2006). In this model

it is only an approximation, since consumption has a small predictable component and there isnon-zero foreign debt.

30

ySt =− log (Et (emt+1))

ySt ≈− log(β) + γEt (∆ct+1) + b(s− st)−γ (1− φ)− b

2

(13)

As Equation 13 shows, a drop in expected consumption growth decreases inter-

est rates, with the magnitude of this effect given by the inverse of the elasticity of

intertemporal substitution.

Figure 4: Short-term real yield and Et(∆ct+1)

2000 2001 2002 2003 2004 2005 2006 2007 2008−2

0

2

4

6Short−term real yields

annu

aliz

ed %

Baseline∆ f=0

2000 2001 2002 2003 2004 2005 2006 2007 2008

0

2

annu

aliz

ed %

Expected consumption growth

2000 2001 2002 2003 2004 2005 2006 2007 2008

0

2

annu

aliz

ed %

Change in official foreign holdings

The two top panels of Figure 4 show real short-term yields and expected con-

sumption growth in the baseline simulation –black solid lines–, and in the case in

which foreign holdings stay constant relative to GDP –red dotted lines–. In the base-

line scenario, real short-term yields move in the same direction as expected con-

sumption growth, declining through 2003 and 2004. In the case of constant foreign

holdings, instead, they increase over 2003 and 2004 driven by surplus consump-

31

tion as explained below. The two bottom panels show that expected consumption

growth co-varies negatively with foreign purchases in the benchmark simulation,

while expected consumption growth barely moves in the case of constant foreign

holdings.

Real short-term yields also depend on surplus consumption, as seen in Equa-

tion 13, with the sign and magnitude of their co-movement determined by the value

of parameter b.53 If b > 0, an increase in st drives short-term interest rates down,

so that short-term yields are counter-cyclical and long-term bonds are risky, com-

manding a compensation for risk.

Long-term yields, the term-premium, and surplus consumption. Foreign pur-

chases affect long-term yields and the term-premium mainly through their effect

on surplus consumption. Figure 5 shows that real long-term yields and the term-

premium co-vary negatively with surplus consumption. Here also, the black solid

lines represent the simulated paths implied by the model when the agents are sub-

ject to the shocks observed in data and the red lines represent the counterfactual

paths in the hypothetical case in which foreign holdings stay constant, relative to

GDP, at their 2000Q1’s level.

To better grasp the intuition of what is driving the effects above, here I write the

risk premium component as a sum of covariances between future bond prices and

future values of the nominal stochastic discount factor. The covariances between

prices and pricing kernels in the future are discounted by δt+1.

qLt − qLt =qSt δEt[qLt+1 − qLt+1

]+ δCovt(M

$t+1, q

Lt+1)

qLt − qLt =∞∑

i=0

δ1+iCovt(M$t+1+i, q

Lt+1+i)Q

St+i

(14)

where Qst+i is the risk-neutral price at t of a unit of consumption at t+ i.

Notice that if the covariances between the stochastic discount factor and the53 This is true even in the case analyzed in this paper where this relationship is not linear.

32

Figure 5: Long-term real yields, term-premium, and surplus consumption

2000 2001 2002 2003 2004 2005 2006 2007 20080

3

6

9an

nual

ized

%

Long−term real yields

Baseline∆ f=0

2000 2001 2002 2003 2004 2005 2006 2007 20080

3

6

9

annu

aliz

ed %

Term−premium

2000 2001 2002 2003 2004 2005 2006 2007 2008

−5

−4

−3

annu

aliz

ed %

Surplus consumption

bond price are negative, both in the present and in the future, the price of a long-

term bond is lower than the risk-neutral price of the same bond. This implies that its

yield is higher than its risk-neutral counterpart, generating a positive term-premium.

For the covariance between the pricing kernel and the bond price to be negative, the

covariance between consumption growth and the bond price needs to be positive.

That is, the term-premium is positive if the bond price is low in states of low con-

sumption growth (i.e., in recessions), and high when consumption growth is high.

Each of these covariances can be written as:

Covt(M$t+1+i, q

Lt+1+i) = ρt(M

$t+1+i, q

Lt+1+i)σt(M

$t+1+i)σt(q

Lt+1+i)

In this model, the driving force behind the variation over time of these covari-

ances is the counter-cyclical risk aversion. An increase in surplus consumption

33

reduces the risk aversion of the agents, given by γSt

, and the market price of risk:

σt(Mt+1)

Et(Mt+1)≈ σt(mt+1) = γ(1 + λ(st))σ∆c,t

Notice that λ(st) is negatively correlated with surplus consumption.

Surplus consumption and consumption growth innovations. The discussion

above suggests that long-term yields and the term-premium are driven by surplus

consumption. To understand what causes the changes in bond prices, we need to

understand what drives surplus consumption in the model. Recall that the log of

surplus consumption is given by the following process:

st+1 = (1− φ)s+ φst + λ(st)(∆ct+1 − Et∆ct+1)

Thus, surplus consumption is positively correlated with consumption growth

innovations: when these innovations are positive, surplus consumption increases,

and when they are negative, it decreases, as shown in Figure 6. Therefore, it is

important to study how foreign purchases affect consumption growth innovations

to understand the effect of foreign purchases on long-term yields.

Equation 15, below, decomposes consumption growth innovations in three terms:

the unexpected change in endowment growth, the unexpected change in the value

of foreign holdings at t, and the unexpected change in the value of foreign holdings

from t to t + 1. The first term, innovations in endowment growth, follows closely

the endowment growth.

∆ct+1 − Et(∆ct+1) ≈∆Yt+1 − Et(∆Yt+1)

− ft[(1 + (1− α)δqLt+1)e−(∆yt+1+πt+1) − Et

((1 + (1− α)δqLt+1)e−(∆yt+1+πt+1)

)]

+(qat+1ft+1 − qat ft

)− Et

(qat+1ft+1 − qat ft

)

(15)

34

Figure 6: Surplus consumption and consumption growth innovations

2000 2001 2002 2003 2004 2005 2006 2007 2008

−2

0

2

annu

aliz

ed %

2000 2001 2002 2003 2004 2005 2006 2007 2008

−4.3

−3.5

−2.7

surp

lus

cons

umpt

ion

st

ε∆ c

The second term measures the unexpected changes in the value of debt. An

unexpected increase in the price of long-term bonds increases the amount that needs

to be paid back at t+ 1, given the same quantity of bonds. An unexpected increase

in inflation, instead, diminishes the burden of the debt at t + 1 for the domestic

agent. Finally, positive endowment growth reduces foreign holdings in terms of the

endowment.

The last term is the unexpected change in the value of foreign holdings from

t to t + 1. Since ft is close to a unit root process, foreign purchases at t + 1 are

almost completely unexpected: ∆ft+1 − Et(∆ft+1) ≈ ∆ft+1. Since new foreign

purchases ∆ft+1 are unexpected, they produce positive innovations to consumption

growth. These innovations accumulate, increasing the persistent surplus consump-

tion, which reduces long-term yields and the term-premium.

As Figure 6 above shows, surplus consumption decreases until 2003Q2, and

then increases until the end of the sample. What caused the negative innovations

in consumption growth in the first part of the sample and the positive innovations

thereafter? To answer this question, Figure 7 shows the decomposition of consump-

35

tion growth innovations, given by the black solid line. As can be seen in the figure,

this line moves almost one-to-one with the dashed green line, which stands for the

innovations to endowment growth, until 2003Q2. This suggests that the decrease

in surplus consumption, on the first part of the sample, was caused by negative

innovations to endowment growth.

Figure 7: ∆c unexpected changes decomposition

2000 2001 2002 2003 2004 2005 2006 2007 2008

−2

−1

0

1

2

annu

aliz

ed %

ε∆ c

εq*f

−f*εq,π,∆ y

ε∆ y

After 2003Q2, the black line moves closer to the dotted blue line, which stands

for the innovations to the value of foreign purchases. That is, the following decline

in surplus consumption is driven by positive innovations to the value of foreign

purchases. This is why, absent these foreign purchases, surplus consumption would

continue to decrease –and long-term yields to increase–, as shown above. Finally,

one can decompose innovations in the value of debt as:

εqf ≡(qat+1ft+1 − qat ft

)− Et

(qat+1ft+1 − qat ft

)

= (ft+1 − ft) qat+1 +(qat+1 − qat

)Et (ft+1)− Covt

(qat+1, ft+1

)(16)

36

In the simulations, I find that unexpected changes in the value of debt are in-

deed driven by changes in inflows of foreign holdings, the first term above, and not

changes in bond prices, captured by the second term.

3.2.3 Model vs. data

Above, I quantified the impact of foreign purchases of U.S. Treasuries on bond

yields and decompose their effect to disentangle the different forces that affect

yields. In this subsection, I contrast the simulated bond yields with the ones ob-

served in the data during the period of analysis.

Figure 8 shows how the model simulated yields –black solid lines and dashed

red lines, as before– compare with the ones observed in the data –blue dashed-

dotted lines–. The data on yields is for a 4-year zero-coupon Treasury bond and the

3-month Treasury-based risk-free rate.

Figure 8: Nominal yields and yield curve slope

2000 2001 2002 2003 2004 2005 2006 2007 20080

3

6

9

Long−term yields

annu

aliz

ed %

2000 2001 2002 2003 2004 2005 2006 2007 20080

3

6

9

annu

aliz

ed %

Short−term yields

Baseline∆ f=0Data

37

In the baseline simulation, long-term and short-term yields are close to their

data counterparts at the beginning and end of the sample. However, the model fit

misses the data during the period 2002 to 2004, with both short- and long-term

simulated yields above the ones in the data. During this period the Fed kept fed

funds target rate low, which has been cited as one of the causes for the housing

boom and posterior bust in the U.S.54 Thus, while the model is useful to isolate the

effect of foreign purchases, it abstracts from other forces such as monetary policy.

Nonetheless, this figure also suggests that foreign holdings are a fundamental

driver of the behavior of yields in the data. This is because the simulated yields in

the counter-factual scenario with constant foreign holdings separate steadily from

those in the data, and are well above the latter at the end of the sample.

In the next subsection, I use this model to analyze the potential consequences of

a reversal of foreign holdings on long-term yields and the term-premium.

3.3 A reversal of foreign purchases of U.S. Treasuries

The dramatic increase in foreign demand for U.S. Treasuries has led to an un-

precedented degree of foreign ownership among total U.S. Treasuries outstanding.

By June 2014, of the 10.7USD trillion in marketable long-term U.S. Treasuries out-

standing, 50.4 percent were foreign-owned. However, this percentage has been de-

clining since the record high of 61.1 percent in June 2008. Of those foreign-owned,

70 percent were owned by Foreign Official Institutions. Furthermore, China and

Japan were jointly responsible for 47 percent of the total long-term U.S. Treasuries

held by foreigners, being by far the largest among such owners.55

The high degree of foreign ownership has led many analysts to question the sus-

tainability of this situation, and discuss the potential economic consequences of a

sell-off of U.S. debt by foreign governments.56 While previous empirical estimates

54 See, for example, Taylor (2007).55 I am including China mainland, Hong Kong, and Japan. Data from http://ticdata.treasury.gov/Publish/shl2014r.pdf

56 See, for example, the discussion in Obstfeld and Rogoff (2010), Bernanke, Bertaut, DeMarco, and

38

might be informative of the impact on bond prices of a decline in foreign owner-

ship, using a model to quantify its impact is paramount to ensure that the estimated

effects take into account possible non-linearities and are consistent with an optimal

pricing behavior by domestic agents. In this section, I use my model to provide

an estimate for the effects of this sell-off of bonds on U.S. Treasury yields and the

term-premium.

For the baseline counterfactual, I assume that Chinese and Japanese Official

Institutions stop rolling over their holdings of U.S. Treasury debt –which account

for 45% of total holdings of short-term and long-term U.S. Treasuries by FOIs–,

beginning in June 2014. The speed of adjustment is given by the maturity structure

of their holdings in the data. Because data on maturity is expressed yearly, I obtain

movements between quarters as the linear interpolation of yearly values. I also

compute the exercise for the case in which 25 percent of FOI’s holdings stop being

rolled over –a number close to the holdings by Chinese FOIs–, and finally for the

case in which only 10 percent of FOI’s holdings of U.S. Treasuries stop being rolled

over.

Furthermore, I assume that shocks to endowment growth and inflation are zero,

and the dynamics of these variables stem from their interaction with foreign hold-

ings, as obtained from the transition matrix estimated above. I initialize these vari-

ables at their average value for 2014.

Finally, I normalize foreign holdings by nominal GDP, assuming that it in-

creases at an annual rate of 4.9 percent, which is the sum of the 10-year ahead infla-

tions expectations of 2.3% and real GDP growth for the next ten years of 2.6%.57 I

assume that foreign holdings of U.S. Treasuries by other countries grow at the same

rate as the U.S. nominal GDP.

Figure 9 shows the path for the exogenous state variables in this exercise. In the

Kamin (2011), Farhi, Gourinchas, and Rey (2011), and Favilukis, Ludvigson, and Van Nieuwer-burgh (2012a).

57 Median forecasts in 2014. Data from Survey of Professional Forecasters.

39

baseline counterfactual, ft falls from 23.8 percent of GDP in 2014 to 12.2 percent of

GDP over the following ten years. Since foreign holdings are mostly concentrated

on short-maturities, two-thirds of this change happens in the first three years.58

The figure also shows the path for the exogenous state variables for the alternative

exercises described above.

Figure 9: Path for exogenous variables

2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 202510

15

20

25

ft

% o

f GD

P

2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 20250

1

2

3

∆ yt

annu

aliz

ed %

45% FOIs25% FOIs10% FOIs

2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 20250

5

10

πt

annu

aliz

ed %

Figure 10 presents the main results for long-term nominal yields and term-

premia. The yields are expressed as differences with respect to their value at

2014Q2. In the baseline counterfactual, long-term yields increase by 5.4 percent-

age points in the first three years, 6.7 percentage points in the first five years, and

then slowly decrease to end the 10-year period 5.1 percentage points higher. Over

the same time-spans, the term-premium increases by 3.3, 4.2, and 3.1 percentage58 In June 2014, 56.1 percent of long-term U.S. Treasury debt by FOIs matures in less than 3 years

and 73.7 percent matures in less than 5 years. Data from Department of the Treasury http://ticdata.treasury.gov/Publish/shl2014r.pdf

40

points, respectively, explaining more than 60 percent of the change in long-term

nominal yields.

Figure 10: Nominal long-term yields, yield slope and term-premium

2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 20250

2

4

6

8Long−term yields

annu

aliz

ed %

45% FOIs25% FOIs10% FOIs

2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 20250

1

2

3

4

5

annu

aliz

ed %

Term−premium

Table 6 summarizes these results and additionally presents the results for alter-

native changes in foreign holdings. The table shows the results for the case in which

45% of holdings of U.S. Treasury debt by FOIs –China and Japan–, 25% –China–,

and 10%, stop being rolled over. Values in parenthesis represent the changes in the

first 3 years.

The exercise above shows that if FOIs stopped rolling over their holdings, it

could have unprecedented consequences on U.S. Treasury bond yields. Further-

more, these effects could be even larger if FOIs sell their holdings before maturity,

initiating a growing spiral in yields and the term-premium. On the other hand, I

assume that these changes are totally unexpected, which implies that these results

should be seen as an upper-bound for the potential change in yields.

41

Table 6: A reversal in foreign official inflows

ft yL TP

China and Japan (over 10 years) -10.4 5.1 3.1(over 3 years) (-6.7) (5.4) (3.3)

China (over 10 years) -5.8 2.0 1.0(over 3 years) (-3.9) (2.4) (1.1)

10% FOIs (over 10 years) -2.3 1.3 0.3(over 3 years) (-1.6) (1.4) (0.3)

Notes: Values in the table above are for 10-year changes for foreign official holdings of U.S. Treasuries in terms of GDP(ft), long-term bond yields (yL), and term-premium (TP ). Values in parenthesis represent the changes in the first 3 years.All numbers expressed in percentages, yields are annualized.

4 Conclusion

Foreign holdings of U.S. Treasuries increased dramatically over the last two

decades, driven primarily by Foreign Official Institutions. Recent empirical papers

suggest that this surge in foreign holdings has contributed to the observed decline in

both long-term yields and the term-premium. However, they are silent regarding the

mechanism driving these effects. In this paper, I set up a consumption-based model

to quantify the contribution of the term-premium to this decline, and investigate the

reasons why foreign purchases reduce term-premia and long-term yields.

To this end, I model the domestic agent’s preferences with external habits,

which assumes that the agent values consumption relative to a reference level or

past consumption. This feature implies a time-varying market price of risk. Fur-

thermore, I allow for positive foreign holdings of bonds, which I estimate from U.S.

data. Then, I use the model to study two questions: first, what was the effect of for-

eign official purchases of U.S. treasuries on the term-premium during the period

from the first quarter of 2000 to the last quarter of 2007. Second, how a reversal

42

of foreign inflows to U.S. treasuries would affect the term-premium and long-term

yields.

The first quantitative exercise suggests that the surge in foreign holdings, by it-

self, decreased long-term yields by 5.5 percentage points from 2000Q1 to 2007Q4,

with a half of this change explained by a drop in the term-premium. Foreign pur-

chases reduce long-term yields in the model because they increase consumption

growth beyond its expected value, which drives up the difference between con-

sumption and the habit. On the one hand, an increase in surplus consumption

reduces current and future interest rates, given that surplus consumption is very

persistent. On the other hand, it also reduces the risk aversion generating a drop in

the term-premium. My results suggest that foreign purchases caused a decline in

the term-premium after the first quarter of 2003.

Finally, I analyze the hypothetical case where FOIs stop rolling over almost

half of their holdings of U.S. treasuries –think of Chinese and Japanese official

institutions–, reducing total foreign holdings over GDP from 24 percent to 12 per-

cent over a ten-year period. In this case, long-term yields increase by 5.1 percentage

points, beginning in June 2014, of which approximately sixty percent –3.1 percent-

age points– are explained by an increase in the term-premium.

I do not study the effects of monetary policy in this paper. In macroeconomic

models with a Taylor rule, the short-term interest rate reflects the policy responses

to shocks in nominal or real variables, which constrains its response to exogenous

shocks. Introducing monetary policy in the current setup would be useful to study

the role of interaction between the Federal Reserve policies and foreign demand for

U.S. treasuries.

Also, the quantitative results hinge on the assumed beliefs of the agents for the

process driving foreign holdings. Since this process is estimated from the data as

being very persistent, agents expect debt to stay constant in the future or mean-

revert slowly. Instead, they are surprised over the period of analysis with larger

43

than expected positive changes in foreign holdings. Allowing for learning on the

law of motion of foreign holdings seems like an interesting avenue to extend this

project.

Notwithstanding the caveats mentioned above, this model provides an explana-

tion for the behavior of term-premia and long-term yields that is consistent with

the empirical evidence. Moreover, my results suggest that in the event of a reversal

of inflows to U.S. Treasuries, like the one we might be currently witnessing, the

term-premium and long-term yields would increase significatively.

References

ABEL, A. B. (1990): “Asset Prices Under Habit Formation and Catching Up With

the Jones,” American Economic Review, 80, 38–42.

AGUIAR, M., AND M. AMADOR (2011): “Growth in the Shadow of Expropria-

tion*,” The Quarterly journal of economics, 126(2), 651–697.

ALFARO, L., S. KALEMLI-OZCAN, AND V. VOLOSOVYCH (2011): “Sovereigns,

Upstream Capital Flows and Global Imbalances,” NBER Working Papers 17396.

(2014): “Sovereigns, Upstream Capital Flows and Global Imbalances,”

Journal of the European Economic Association, 12(5), 1240–1284.

ANGELETOS, G.-M., AND V. PANOUSI (2011): “Financial integration, en-

trepreneurial risk and global dynamics,” Journal of Economic Theory, 146(3),

863–896.

ARELLANO, C., AND A. RAMANARAYANAN (2012): “Default and the Maturity

Structure in Sovereign Bonds,” Journal of Political Economy, 120(2), 187–232.

44

BACKUS, D. K., A. W. GREGORY, AND S. E. ZIN (1989): “Risk Premiums in

the Term Structure: Evidence from Artificial Economies,” Journal of Monetary

Economics, 24, 371–399.

BACKUS, D. K., AND J. H. WRIGHT (2007): “Cracking the Conundrum,”

Brookings Papers on Economic Activity, 38(1), 293–329.

BANSAL, R., AND I. SHALIASTOVICH (2012): “A Long-Run Risks Explanation of

Predictability Puzzles in Bond and Currency Markets,” Unpublished paper.

BELTRAN, D. O., M. KRETCHMER, J. MARQUEZ, AND C. P. THOMAS (2013):

“Foreign holdings of U.S. Treasuries and U.S. Treasury yields,” Journal of

International Money and Finance, 32, 1120–1143.

BERNANKE, B. S. (2005): “The Global Savings Glut and the U.S. Current Ac-

count Deficit,” Homer Jones Lecture, April 14, 2005. http://www. federalre-

serve.gov/boarddocs/speeches/2005/20050414/default.htm.

(2006): Remarks by Governor Ben S. Bernanke at the Economic Club of

New York, New York, New York, March 20, 2006.

BERNANKE, B. S., C. BERTAUT, L. P. DEMARCO, AND S. KAMIN (2011): “In-

ternational Capital Flows and the Returns to Safe Assets in the United States,

2003-2007,” Unpublished paper, International Finance Discussion Papers 1014,

Board of Governors of the Federal Reserve System (U.S.).

BERNANKE, B. S., V. R. REINHART, AND B. P. SACK (2004): “Monetary policy

alternatives at the zero bound: an empirical assessment,” Brookings Papers on

Economic Activity, 35(2), 1–100.

BERTAUT, C. C., L. P. DEMARCO, S. KAMIN, AND R. W. TRYON (2011): “ABS

Inflows to the United States and the Global Financial Crisis,” International Fi-

45

nance Discussion Papers 1028. Board of Governors of the Federal Reserve Sys-

tem (U.S.).

CABALLERO, R. J. (2006): “On the macroeconomics of asset shortages,” National

Bureau of Economic Research.

CABALLERO, R. J., E. FARHI, AND P.-O. GOURINCHAS (2008): “An Equilibrium

Model of ”Global Imbalances” and Low Interest Rates,” American Economic

Review, 98(1), 358–393.

CABALLERO, R. J., AND A. KRISHNAMURTHY (2009): “Global Imbalances and

Financial Fragility,” The American Economic Review, pp. 584–588.

CAMPBELL, J. Y., AND J. H. COCHRANE (1999): “By Force of Habit: A

Consumption-Based Explanation of Aggregate Stock Market Behavior,” Journal

of Political Economy, 107, 205–251.

CAMPBELL, J. Y., AND R. J. SHILLER (1991): “Yield Spreads and Interest Rates:

A Bird’s Eye View,” Review of Economic Studies, 58, 495–514.

COCHRANE, J. H., AND M. PIAZZESI (2005): “Bond Risk Premia,” American

Economic Review, 95(1), 138–160.

(2008): “Decomposing the yield curve,” Working Paper.

CONSTANTINIDES, G. M. (1990): “Habit-formation: A Resolution of the Equity

Premium Puzzle,” Journal of Political Economy, 98, 519–543.

FAMA, E. F., AND R. H. BLISS (1987): “The Information in Long-Maturity For-

ward Rates,” American Economic Review, 77(4), 680–692.

FARHI, E., P.-O. GOURINCHAS, AND H. REY (2011): Reforming the International

Monetary System. Centre for Economic Policy Research.

46

FAVILUKIS, J., D. KOHN, S. C. LUDVIGSON, AND S. VAN NIEUWERBURGH

(2012): “International Capital Flows and House Prices: Theory and Evidence,”

in Housing and the Financial Crisis, ed. by E. L. Glaeser, and T. Sinai. University

of Chicago Press, Chicago, IL.

FAVILUKIS, J., S. C. LUDVIGSON, AND S. VAN NIEUWERBURGH (2012a): “For-

eign Ownership of U.S. Safe Assets: Good or Bad?,” Unpublished paper, New

York University.

(2012b): “The Macroeconomic Effects of Housing Wealth, Housing Fi-

nance and Limited Risk Sharing in General Equilibrium,” Unpublished paper,

New York University.

FERSON, W. E., AND G. M. CONSTANTINIDES (1991): “Habit Persistence and

Durability in Aggregate Consumption,” Journal of Financial Economics, 29,

199–240.

GOURINCHAS, P.-O., AND O. JEANNE (2013): “Capital flows to developing coun-

tries: The allocation puzzle,” The Review of Economic Studies, 1, 1–32.

GOURINCHAS, P.-O., AND H. REY (2013): “External Adjustment, Global Imbal-

ances, Valuation Effects,” Forthcoming, Chapter in Handbook in International

Economics, vol IV, Gopinath, Helpman and Rogoff eds.

GREENSPAN, A. (2005): “Testimony of Chairman Alan Greenspan at the Federal

Reserve Board’s semiannual Monetary Policy Report to the Congress Before

the Committee on Financial Services,,” U.S. House of Representatives, July 20,

2005.

GURKAYNAK, R. S., B. SACK, AND J. H. WRIGHT (2007): “The U.S. treasury

yield curve: 1961 to the present,” Journal of Monetary Economics, 54(8), 2291–

2304.

47

GURKAYNAK, R. S., AND J. H. WRIGHT (2012): “Macroeconomics and the Term

Structure,” Journal of Economic Literature, 50(2), 331–367.

HANSON, S. G., AND J. C. STEIN (2014): “Monetary policy and long-term real

rates,” Journal of Financial Economics.

HATCHONDO, J. C., AND L. MARTINEZ (2009): “Long-duration bonds and

sovereign defaults,” Journal of International Economics, 79(1), 117–125.

HEATON, J. (1995): “An Empirical Investigation of Asset Pricing with Temporally

Dependent Preference Specifications,” Econometrica, 63, 681–717.

JUSTINIANO, A., G. PRIMICERI, AND A. TAMBALOTTI (2013): “The Effects of

the Saving and Banking Glut on the U.S. Economy,” Working Paper.

KAMINSKA, I., D. VAYANOS, AND G. ZINNA (2011): “Preferred-habitat investors

and the US term structure of real rates,” .

KAMINSKA, I., AND G. ZINNA (2014): Official Demand for US Debt: Implications

for US real interest rates, no. 14-66. International Monetary Fund.

KIM, D. H., AND J. H. WRIGHT (2005): “An Arbitrage-Free Three-Factor Term

Structure Model and the Recent Behavior of Long-Term Yields and Distant-

Horizon Forward Rates,” FEDS Working Paper No. 2005-33.

KNOTEK II, E. S., AND S. J. TERRY (2010): “Markov-Chain Approximations

of Vector Autoregressions: Application of General Multivariate-Normal Inte-

gration Techniques,” Working Paper RWP 08-02, The Federal Reserve Bank of

Kansas City.

KOHN, D. L. (2002): “Panel: Implications of Declining Treasury Debt. What

Should the Federal Reserve Do as Treasury Debt Is Repaid?,” Journal of Money,

Credit and Banking, 34(3), 941–945.

48

LUCAS, R. E. (1990): “Why doesn’t capital flow from rich to poor countries?,”

The American Economic Review, pp. 92–96.

LUDVIGSON, S. C., AND S. NG (2009): “Macro Factors in Bond Risk Premia,”

The Review of Financial Studies, 22(12), 5027–5067.

MAGGIORI, M. (2013): “Financial intermediation, international risk sharing, and

reserve currencies,” .

MENDOZA, E. G., V. QUADRINI, AND J.-V. RIOS-RULL (2009): “Financial In-

tegration, Financial Development, and Global Imbalances,” Journal of Political

Economy, 117(3).

OBSTFELD, M., AND K. ROGOFF (2010): “Global Imbalances and the Financial

Crisis: Products of Common Causes,” Asia Economic Policy Conference, pp.

131–173.

PIAZZESI, M., AND M. SCHNEIDER (2006): “Equilibrium Yield Curves,” in NBER

Macroeconomics Annual: 2006, ed. by M. W. Daron Acemoglu, Kenneth Ro-

goff. MIT Press, Cambridge.

RUDEBUSCH, G., B. P. SACK, AND E. T. SWANSON (2007): “Macroeconomic

Implications of Changes in the Term Premium,” Federal Reserve Bank of St.

Louis Review, 89(4).

RUDEBUSCH, G., AND E. SWANSON (2008): “Examining the bond premium puz-

zle with a DSGE model,” Journal of Monetary Economics, 55, S111–S126.

(2012): “The Bond Premium in a DSGE Model with Long-Run Real and

Nominal Risks,” American Economic Journal: Macroeconomics, 4(1), 105–143.

RUDEBUSCH, G., E. SWANSON, AND T. WU (2006): “The bond yield conundrum

from a macro-finance perspective,” Monetary and Economic Studies, 24(S1),

83109.

49

SIERRA, J. (2014): “International Capital Flows and Bond Risk Premia,” Quarterly

Journal of Finance, 4(1).

SUNDARESAN, S. (1989): “Intertemporally Dependent Preferences and the Volatil-

ity of Consumption and Wealth,” The Review of Financial Studies, 2, 73–89.

SWANSON, E. (2007): “What We Do and Dont Know about the Term Premium,”

FRBSF ECONOMIC LETTER, (2007-21).

TAUCHEN, G. (1986): “Finite State Markov-Chain Approximations to Univariate

and Vector Autoregressions,” Economic Letters, 20, 177–181.

TAYLOR, J. B. (2007): “Housing and Monetary Policy,” Remarks prepared for

presentation at the Policy Panel at the Symposium on Housing, Housing Finance,

and Monetary Policy in Jackson Hole, Wyoming.

VAYANOS, D., AND J.-L. VILA (2009): “A preferred-habitat model of the term

structure of interest rates,” National Bureau of Economic Research.

WACHTER, J. (2006): “A Consumption Based Model of the Term Structure of

Interest Rates,” Journal of Financial Economics, 79, 365–399.

WARNOCK, F. E., AND V. C. WARNOCK (2009): “International capital flows and

U.S. interest rates,” Journal of International Money and Finance, 28, 903–919.

WEIL, P. (1989): “The Equity Premium Puzzle and the Risk-Free Rate Puzzle,”

Journal of Monetary Economics, 24(3), 401–421.

50