dissertation l13500 - to print

Economics Dissertation L13500 – Stijn Rasschaert

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School of Economics

L13500 Economics Dissertation (Term 2015-16)

The impact of domestic and foreign macroeconomic fundamentals on

long-term interest rates in the United Kingdom

Stijn Rasschaert (ID: 4215540)

Supervisor: Dr. Margarita Rubio

Date of submission: 20/04/2016

Electronic submission receipt number: 56122152

Word Count: 7422

This Dissertation is presented in part fulfilment of the requirement for the completion of an undergraduate

degree in the School of Economics, University of Nottingham. The work is the sole responsibility of the

candidate


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Table of Contents

Title Page………………………………………………………………………………………..........1

Table of Contents………………………………………………………………………………..........2

1. Introduction…………………………………………………………………………………..........3

2. Background Information……………………………………………………………………..........5

2.1 Bond Market Theory………………………………………………………………...........5

2.2 Existing Literature………….…………………………......………………………………8

3. Econometric Model…………………………………………………………………………........10

4. Data Description..………………………………………………………………………………...11

5. Methodology……………………………………………………………………………………..13

5.1 ARDL Bounds Testing and Diagnostic Checks……....…...….........…........……………16

5.2 Long-run Relationship and Short-run Dynamics………………………………………..19

6. Results………………………………………………………………………………………........22

7. Further Estimation………………………………………………………………………………..25

8. Conclusion & Policy Implications...……..………………………………………………….........27

10. Bibliography……………………………………………………………………………….........30

11. Appendix………………………………………………………………………………………...33


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1. Introduction

In a standard AD-AS framework, real long-term interest rates affect aggregate saving and

investment decisions by firms and households and are therefore fundamental in determining the

output level in an economy (Blanchard 2010). The rate that matters to the real economy is the interest

rate agents lend and borrow at to finance durable goods, mortgages and capital investments. This rate

is set in nominal terms and although it varies depending on specific agent characteristics, it crucially

adjust with changes in the return of a risk-free asset, usually long-term government bond yields.

Therefore, changes in government bond yields will affect the “pass-through rate” and, through

household’s consumption decisions and corporate valuations, affect the real economy.

Sovereign bond yield have received ample coverage recently as the Fed has raised its policy

rate from the zero-lower-bound for the first time since 2008 and other central banks are experimenting

with negative deposit rates. Investors are anticipating the end of a downward bond yield cycle in the

UK and the US as the Bank of England (BOE) and Fed are expected to start raising rates periodically.

However, when the Fed last embarked on a tightening cycle in 2004, Greenspan (2005) noted that

long-term interest rates were at levels lower than expected given the macroeconomic fundamentals,

which he referred to as a “conundrum”. Bernanke (2005) was the first to postulate that Treasury yields

were abnormally depressed because of ‘structural change’ in the investor base that came about

because of an increase in the savings supply from, in particular, Asian and petro-dollar countries with

current account surpluses. Importantly, Vestin et al. (2006) find that the conundrum equally applied

to euro area countries, including the UK. These observations, coupled with the persistent low long-

term rates, which has many economists and policymakers still puzzled, have led to greater research

into the effect of foreign variables on long-term nominal interest rates.

The importance of addressing the issue comes at a relevant time as the pace of structural

changes in Asian economies will significantly affect inflows in developed markets (Hauner 2006).

By augmenting a foreign variable in bond yield models, the existing literature has primarily focused

on determining the effect of foreign inflows on U.S. Treasury securities. However, little empirical

analysis has been done on the UK gilt market, even though gilts also possess a safe haven status and

shares similar characteristics with the US treasuries. Figure 1 shows that the ‘structural change’ is not

only real in the UK but it is a relatively recent phenomenon as foreign participation in UK debt market

took off at the start of the century. Interestingly, there appears to be a strong negative correlation with

bond yields prior to the financial crisis of 2008, which matches observations in the US (Bernanke


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2005). Although the trend shows signs of reversal post-financial crisis, we will demonstrate that this

can largely be explained by the rapid increase in the nominal gilt market.

Figure 1 – Foreign holdings of UK gilts (%) vs 10-year UK gilt yields

By adopting a suitable model for UK long-term bond yield1, this study sets out to empirically

examine the extent to which changes in macroeconomic factors explain the movement of UK long-

term nominal interest rates. The empirical focus is on how foreign ownership has affected yields in

the short and long-run over the past 20 years. To avoid the problem of spurious relationships this

paper adopts an autoregressive distributed lag (ARDL) approach to cointegration set out by Pesaran

et al. (2001). Previous studies have mainly used standard OLS and Johansen cointegration estimation

techniques, which have some flaws as identified in “Section”. As such, we hope that the ARDL

framework will provide a new and better understanding of the topic in a time where investors and

authorities seek to understand the historically low yields.

1 Literature uses nominal 10-year UK gilt yields as a proxy for the long term interest rates as most liquid government bond.

Source: United Kingdom Debt Management Office, Gilt Market Oversees Holdings (1996 – 2015)


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2. Background Information

The existing literature employs two main empirical approaches to modelling nominal bond

yields, financial latent-factor and macroeconomic models (Diebold 2005). Throughout this

dissertation the focus will be on using fundamental macroeconomic factors as these are better suited

for understanding long-term relationships (see e.g. Durré et al 2005). Although there is no accepted

model, past papers like Orr et al. (1995) and Bouis et al. (2014) use monetary policy, inflation

expectations and business cycle factors, relating to real activity and fiscal position, as the standard

skeleton for modelling bond yields. Common amongst the literature is the usage of 10-year

government bonds as a proxy for long-term interest rates because they are the most liquid long-term

bond instruments.

2.1. Bond Market Theory

To understand the choice of variables in our bond yield model we start by considering classical

economic theory, which predicts that the market price of bonds, as for any good or asset, is determined

by the interaction of demand and supply factors. As the price of a bond is inversely related to its yield,

the theory provides a baseline for thinking about a suitable economic model to estimate. Greeenwood

and Vayanos (2010) explain that demand and supply effects were important drivers of yields. Agents

have demand for bonds given as a function of their wealth, expected returns, attitude towards risk,

liquidity preference and expected inflation (Mishkin)2. These are discussed in turn;

Periods of economic expansion, for which real GDP growth is used as a proxy in the literature,

will be characterised by household wealth expansion resulting in an increase in demand for bonds at

any price (income effect). However, countering this effect is the fact that during boom periods other

assets will yield a greater return, causing investors to re-allocate resources away from low return

securities like bonds. Overall, however, Laubach and Williams (2003) find that changes in the

business cycle and expectation of such variations affect bond yields significantly and proportionally.

The expected rate of inflation will have an unambiguous effect as higher inflation expectations will

lower the expected real return of bonds, causing a decline in their demand ceteris paribus. The strength

of the relation is evidenced by the expectation augmented Fisher relationship, first introduced by

Irving Fisher (1930), which posits there is a one-to-one relationship between inflation expectations

and the nominal interest rate. Indeed, although there is limited empirical support for the hypothesis,

the significance of inflation expectations on bond yields is clearly documented, with Barr and

2 Mishkin, F ‘The Economics of Money, Banking and Financial Markets’ Chapter 5, 10th Edition


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Campbell (1997) determining that “almost 80% of the movement of UK long-term nominal rates

appears to be due to changes in expected long-term inflation”. Further, the relative riskiness of

government bonds is primarily related to the government’s ability to honour its repayment of the

principal at maturity. The ability to do so will be gauged by the national debt and deficit. These fiscal

variables will affect the risk premium that investors demand on the bond and hence affect the yield.

Indeed, many studies have demonstrated that fiscal balance variables like total debt/GDP and current

deficit/GDP can significantly affect long-term rates (see e.g. Carporale 2002 and Hoelscher 1987),

hence rejecting Richardian equivalence. Finally, bond prices will have a liquidity premium due to

future uncertainty. We will reduce the influence of these two relative factors (risk, liquidity) by using

10-year UK gilt yields, as these securities have historically been highly liquid and backed by a

reputable government with an independent central bank.

On the other hand, the supply of UK government bonds depends solely on the government

budget deficit, as it is the sole issuer of sovereign debt (Miskin). However, in issuing the bonds, the

government also takes into account the expected inflation, supplying more bonds if expected inflation

is higher. In theory, the equilibrium price of a 10-year bond, and consequently the yield, is reached

at the intersection of supply and demand, with any change in the determinants causing a shift of the

demand/supply curve in the price-quantity space.

Figure 2 – Equilibrium level in the bond market and the determinants of supply and demand

P*

BDemand (Wealth, Risk, Liquidity, Expected Inflation)

BSupply (Government deficit, Expected Inflation)

The y-axis has the price of the bond and the x-axis the quantity demanded. The yield of the bond is inversely

related to the price (yield=1/price). Therefore, an increase in the price will mean a decrease in the yield.

Pri

ce o

f B

ond

(£

)

Quantity of Bonds Q*


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However, there are further factors that augment our understanding of what influences and

determines the level of bond yields. One such factor can be observed by the expectation theory of the

term structure (Lutz 1940), which tries to explain the difference in bond yields at different maturities.

The theory uses the no-arbitrage principle to state that long-term bond yields are equal to the average

of the rates on short-term bonds expected over the life of the bond.3 Hence, a change in 3-month

treasury gilt yields, for example, will immediately affect the 10-year gilt yield, although the

magnitude will depend on how expectations of future 3-month yields alter. Crucially, as the policy

rate, set by the central bank, has a direct impact on the short end of the yield curve (Federal Reserve

Board) it follows, from the expectation theory of the term structure, that it also affects long-term

nominal rates. In fact, all the existing literature uses short-term rates as a proxy for the current

monetary stance in their bond yield model specifications.

However, the persistence of low long-term rates has induced further research into the potential

drivers of bond yields. Bouis et al (2014), for example, find that declines in nominal rates in the 2000s

were primarily due to the purchase of sovereign bonds by foreign central banks in surplus economies,

and recently due to the unconventional monetary policies. The latter was introduced in the form of

asset purchases (QE), following the financial crisis, as a means to stimulate the economy further once

policy rates had reached their effective floor. Joyce et al. (2011), and Vissing-Jorgensen et al. (2012)

studied the significance of central bank purchases of government debt on long-term bond yields and

conclude that QE affected yields primarily through a portfolio balance effect. Indeed, Joyce et al

(2011) find that QE “may have depressed long-term yields by about 100 basis points” in the UK.

Given the magnitude of the purchases, with “BOE’s gilts purchases represent[ing] 29% of the free-

float of gilts”, studies have accepted the importance of QE as a new demand factor to explain the

current depressed yields.

The effect of foreign participation in emerging economy currency bond markets is well

reported (see e.g. Peiris 2010), however, the literature on developed economies has only initiated due

to the increasing financially integration and economists and central banks eagerness to explain the

persistent low bond yields in the US. As Figure 1 illustrates, the coincidence of foreign capital inflows

and low levels of long-term interest rates is applicable to the UK. Foreign purchases of sovereign

bonds by definition increase the demand for domestic bonds and will reduce bond yields as long as

outflows do not offset inflows. Even with outflows and inflows balancing out, foreign participants

may have a greater demand for liquidity and safe haven assets than domestic investors, hence

reducing marginal risk-premia on developed economy bonds. Asian countries, notably China (Yang

3 Relies on the assumption that agents only care about expected return and that the instruments are perfect substitutes


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et al. 2011), have extremely high savings rates and may, for reasons of portfolio diversification, funnel

savings into UK and US bond markets at different levels of risk aversion. Indeed, Vissing-Jorgensen

et al. (2012) conclude that US bond yields have reduced yields by approximately 70 basis points from

1926 – 2008 due to their liquidity and safe status. This safe-haven effect is also reported in core euro

countries (Tristani et al. 2006). China, with “savings rate at 34-53% of GDP in the past three decades

and a surge in the saving rate by 11 percent points from 2000-2008” (Yang et al. 2011) is considered

the main force behind lower bond yields in the U.S and the West, which had and still have massive

public debts (Chimerica).

Therefore, a complete study should test a model that takes into account the standard as well as more

recent domestic and foreign factors.

2.2 Existing Literature

There exists a vast literature that examines capital inflows in emerging economies (Peiris

2010). Warnock & Warnock (2009), however, were the first to quantify the effect of foreign purchases

of US government bonds by creating their own benchmark-consistent capital flows data using TIC4

data. They estimate a simple reduced-form 10-year Treasury yield equation from (1984–2005) by

means of OLS using inflation expectation, interest rate risk-premium, expected real GDP growth,

expected deficit and 12 month foreign flows into Treasuries as explanatory variables. They find that

increasing foreign inflows by 1% of GDP cause a 19 basis point reduction in long rates. The key

strength of this paper is the monthly data frequency used, which is difficult to obtain for the UK

without smoothing from trend for foreign inflows and other non-market variables. One limitation in

their empirical estimation is that they assume the explanatory variables are exogenous and that the

data is stationary, meaning no cointegration. This latter assumption is rather restrictive as Nelson and

Plosser (1982) show that most macroeconomic and financial variables are non-stationary. Bertaut et

al. (2011) employ the same empirical framework and find similar results.

Panel-data studies have also looked at foreign investor flows and its effect on domestic 10-

year bonds. Arslanalp et al (2014) use a panel regression for 22 advanced economies whereby they

regress standard macroeconomic factors plus foreign bond holdings variables. They add to the

literature by splitting foreign ownership of bonds into share owned by foreign central banks and

foreign banks and foreign non-banks, which we shall also consider. This provides a more

comprehensive framework for understanding the effect on bond markets, as Wu (2005) highlighted.

4 TIC - Treasury International Capital Reporting System


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Their results find that foreign ownership is statistically and economically significant in determining

10-year bond yields, although by only 6-10 basis points for 1% increase. However, a limitation of

panel regression studies is that it cannot account for the inherent political and economic structural

differences and it assumes homogeneity, hence focusing on the UK will allow for greater accuracy

as to the magnitude of the effect.

Finally, Beltran et al. (2012) and Carvalho et al. (2014) use more sophisticated empirical

methods to correct the issue of “highly autocorrelated and non-stationary” data by estimating a

VECM. Although this approach allows for estimating both the long-run and short run effects, it has

the disadvantage that estimates will be reliable with fewer variables. For example, Carvalho et al.

(2014) regress 10-year euro area bond yields on short term interest rates, inflation expectations and

a foreign holding variable. They find that a 1 percent point increase in foreign holdings lowers the

long-term bond yield by 13 basis points (1999-2006). Beltran et al. (2012) also confirm the impact

of foreign inflows on US yields. In the methodology section we will discuss why we decided to opt

instead for an ARDL framework, which has not been used in the current literature.


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3. Econometric Model

Our econometric analysis starts with the derivation of a bond yield model that takes into account

theory and empirical findings. Most analysis starts5, like in Caporale and Williams (2002), from the

simplified general term structure model equation of real interest rates (1):

𝑟𝑡𝑙 = 𝑟𝑡

𝑠 + 𝐹(𝑙, 𝑣𝑡) (1)

where 𝑟𝑡𝑙 and 𝑟𝑡

𝑠 represent the real long-term and short-term interest rates respectively and vt is a

combination of variables that influence an agents perception of risk and hence affects the

compensation required for holding longer term (l) asset. If we specify a particular functional form for

F(. , .) then the last term of the RHS of (1) represents the risk-premium on 𝑟𝑡𝑙. The above equation is

a simplification of the expectation hypothesis of the term structure if we make the realistic assumption

that agents are risk-averse (Diebold et al 2005). However, as the real-interest rate variable is not an

observable data point, a proxy is introduced by rearranging the expectation augmented Fisher

equation for r (𝑟 = 𝑖 + π𝑒) and substituting this into Eq(1).

Caporale and Williams (2002) define the vector vt to include expected inflation (πe), real GDP

growth rate (gt), government deficit to nominal GDP (dt) and government debt stock to GDP (bt).

However, following the economic theory and literature presented above, we augment the vector by 3

new explanatory variables; central bank purchases of domestic government gilts (CBt), financial

market volatility (VIXt) and a measure of foreign investor base (FIBt). This latter variable will be

subdivided into foreign official and private holdings, as in Arslanalp et al. (2014), which described

in the following section. The empirical specification we will estimate is:

𝑖𝑡10 = 𝛼0 + 𝛽1𝑖𝑡

𝑠 + 𝛽2𝜋𝑡𝑒 + 𝛽3𝑔𝑡 + 𝛽4𝑑𝑡 + 𝛽5𝑏𝑡 + 𝛽6𝐶𝐵𝑡 + 𝛽7𝑉𝐼𝑋𝑡 + 𝛾𝐹𝐼𝐵𝑡 + 휀𝑡 (2)

where α0 and εt is a constant and error term respectively. Notice that 𝑟𝑡𝑠 is replaced with 𝑖𝑡

𝑠 as we

assume that for short periods both are small and approximately equivalent.

As far as the literature goes, this specification has not been used in previous single-country studies.

One risk with having many explanatory variables (8) is that the model is over-specification and

therefore suffers from multicollinearity. However, over-specification will nonetheless yields an

unbiased estimate using OLS (Baltagi 1998).

5 Alternatively an appropriate model could have been dervied using the function of demand and supply factors


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4. Data Description

Before proceeding, a comprehensive understanding of the data and its manipulation is warranted to

observe the strengths and restrictions of our dataset. As some of our non-market explanatory variables

were unavailable in monthly frequency, we compiled our UK dataset with a quarterly frequency from

1996 to 2015. For consistency end of quarter values are used.

The dependent variable (𝑖𝑡10), the long-term nominal rate, is represented by nominal 10-year

benchmark gilt yields obtained from the Bloomberg Terminal6. This variable measures the

long-term borrowing cost of the UK government.

We use 3-month UK Treasury bill yields for our short-term rate 𝑖𝑡𝑠 (Piazzesi 2003), obtained

from the BOE website7. This variable essentially proxies the monetary policy stance in the

UK and is preferred to the official BOE policy rate because, just like our dependent variable,

it is market-driven.

For inflation expectation, πe, a Bloomberg variable8 is obtained that measures the spread

between 10-year nominal gilt yield and 10-year index linked gilts. This measure provides

market participant long-term inflation expectations and is in preferred to survey based

measures (Kajuth et al. 2008). However, the measure may overstates inflation expectations as

the risk-premium on bonds may alter when there are unexpected changes in inflation (FRB).

It may also understate as inflation-linked bonds, which are not so frequently traded, command

a liquidity premium. Overall, we expect a positive and close to unit impact from the Fisher

relationship equation.

Real GDP growth (gt) is obtained from the UK Office of National Statistics (ONS). We

initially use quarter-on-quarter (QoQ) GDP growth. We also use short-term expectations of

GDP growth by constructing it using the simple adaptive expectation formula where GDP

growth is lagged by one period. The expected impact on yields is ambiguous as Arslanalp et

al. (2012) notes.

UK debt stock to GDP (bt), was directly obtained from ONS. Deficit to GDP ratio (dt) was

calculated by dividing the nominal Public Sector Net Borrowing, available from the office for

6 Value is based on the bid-side of the market. Bloomberg Code, GUKG10:IND, constant maturity. 7 Code IUMAJJNB 8 Bloomberg code UKGGBE10, available also on Datastream


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budge responsibility, by UK nominal GDP. As annual deficit data was only available, we

converted the frequency to quarterly using constant-match-sum in Eviews. These variables

aim to proxy UK fiscal policy.

To quantify the other monetary policy factor QE (CBt) we use data from the Asset Purchase

Facility Database, which reports the total sum of gilts owned by the BOE weekly. Quarterly

frequency was obtained by summing up the data points for the respective weeks.

Bloomberg reports the volatility index (VIX), also known as the global fear factor, which

captures market participants’ expectation of US stock market volatility over the next 30 days.

Even though the VIX is specific to the US stock market, financial integration and the

significant market spill-over effects (see e.g. Hamao et al. 1990 and Forbes et al. 1999), mean

that the variable acts as a global uncertainty instrument and is hence expected to have an

impact on UK bonds.

Data on the share of foreign UK gilt holdings was obtained from the UK Debt Management

Office. Following from Wu’s (2005) critique and the existing literature9 foreign UK gilt share

is further subdivide:

Foreign official holdings10 were estimated as in (Arslanalp et al. 2012) using the

COFER (IMF) dataset, which provides quarterly data on the allocated reserves in the

5 major currencies. In order to calculate this value we assume that the “currency

composition of the unallocated part is the same as the allocated part” and that 80% of

the exchange reserves are in government bonds from that country. To make our

analysis consistent we convert the values obtained in pounds using historical quarterly

exchange-rates.

Foreign Bank and Non-Bank11 share or private holdings was calculated by subtracting

share of foreign central banks from total foreign gilt holdings.

This set of variables is used as it provides information about the monetary, fiscal and economic

condition of the UK economy that can impact Gilt yields. A summary is provided in Appendix1.

9 See e.g. Beltran et al (2010) 10 Includes foreign central banks and other official creditors 11 As defined by IMF’s International Financial Statistics


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5. Methodology

Single-equation bond yield models estimated using ordinary least squares (OLS) are popular

in the literature (Warnock & Warnock, 2009 and Arslanalp, 2014). However, such a methodology

requires making restrictive assumptions about the endogeneity of the variables and their

cointegration. Furthermore, with “data on interest rates, macroeconomic variables, and foreign

holdings often [being] highly autocorrelated or even non-stationary” (Granger and Newbold 1974) it

is highly probable that spurious relationships are obtained that yield faulty empirical observations.

Caporale and Williams (2002), Beltran et al. (2012) and Bandholz et al. (2007) are among the few

that identified this issues and implement more full-system methods to ‘take into account stationarity,

cointegration and exogeneity features of the variables of interest’12. The most common of these

methodologies uses a vector autoregressive (VAR) framework.

By quick deduction, using the Fisher relationship and the expectations hypothesis of interest

rates, we can conclude that our model (2) will have at least two cointegrating relationships; one

between the long-term rate and expected inflation and the other between the long-term and the short-

term rates. The most common method adopted in the literature for determining the cointegration rank

involves the maximum likelihood test based on Johansen (1991) and Johansen-Juselius (1990) in a

VAR model. If the model is found to have one or more conintegrating vectors then a vector error

correction model (VECM) is constructed to produce dynamic short-run and long-run equilibrium

estimates of the variables. A key limitation of using Johansen cointegration test is that it requires that

all variables are unit root processes I(1) and hence of equal order of integration. However, our unit

root tests analysis illustrate that this requirement cannot be statistically confirmed in our case.

Furthermore, in a VECM framework, the greater the number of variables and lags the more

parameters need to be estimated. Hence, the technique works best with large sample observations and

few explanatory variables13, which does not meet our model conditions.

In order to circumvent these issues we will employ the OLS based autoregressive distributed

lag (ARDL) modelling approach to detect long and short-run interaction in our model. Although these

regression models have been used for a long time, the introduction of an ARDL approach to

cointegration (Pesaran et al 1997, Pesaran and Shin 1999) has increased its use in empirical research.

The ARDL framework has greater flexibility as it can be applied irrespective of whether the

12 Caporale and Williams (2002) 13 Advance Time Series Econometrics Notes, Patrick Marsh (Nottingham University)


14

regressors are I(0) or I(1), hence eliminating any uncertainty from unit root tests (Pesaran and Pesaran

1997). Another key advantage is that it follows a general-to-specific modelling approach, ensuring

that our model has sufficient lags to capture the data observations (Laurenceson and Chai 2003).

Furthermore, Pesaran et al 2001 shows that the ARDL approach yields more efficient

(asymptotically) results than standard VECM cointegration approaches for small and finite sample

sizes, which is clearly our case with 81 observations. Crucially, the ARDL framework, like with

VECM, allows for a dynamic error correction mechanism (ECM) to be derived by simple

manipulation, which allows us to observe short-run dynamics and long term equilibrium coefficients.

To appreciate the flexibility of the variables, in terms of their order of integration, we test for

unit roots. Table 1 reports the t-statistics for the Augmented Dickey Fuller (ADF) and Break-Point

unit root test, which clearly demonstrates the art involved in determining whether variables are unit-

root. For example, according to the ADF test the 3-month bill yield has a unit-root at level, I(1),

however, the break-point unit-root test shows it to be I(0). Graphical inspection shows that there was

a visible break in trend and mean at the time of the financial crisis (2008Q2), which follows from the

fact that the BOE rate fell to the 0.05% and 3-month yield closely tracks the policy rate. Therefore,

any definite conclusions about stationarity of variables cannot be reached due to the limited years of

data and because of the significant change in variables post-financial crisis. While we could have

assumed that all our variables were I(1) as Nelson and Plosser (1982) state in their formative paper,

we instead implement an ARDL framework that doesn’t impose any unit-root restrictions on

variables.

Table 1 – Unit-root testing using Augmented Dickey Fuller and Break-point tests

Intercept Intercept + trend Intercept Intercept + trend

it10 -1.808 -3.834** -7.684* -7.685* -4.320 7.838*

πte -4.337* -4.395* -7.835* -7.829* -5.009*** -11.198*

it3M -1.168 -2.949 -6.027* -5.991* -5.583* -6.409*

gt -3.937* -4.021** -10.429* -10.355* -6.803* -7.698*

bt -0.341 -2.045 -2.4900 -2.499 -4.554 -9.673*

dt -1.162 -1.946 -8.703* -8.643* -6.892* -10.046*

CBt -0.225 -1.866 -4.035* -4.164* 4.580 -9.458*

FBNBt -1.909 -1.953 -9.017* -8.962* -3.737 -7.273*

FOHt -1.824 -2.146 -5.702* -5.748* -0.027 -9.561*

VIXt -4.850* -4.937* -12.709* -12.631* -6.032* -7.177*

Note:*, ** and *** indicate significance at 1%, 5% and 10% level respectively

Break-point Unit Root Test

Levels 1st DifferenceVariable Levels

Augmented Dickey Fuller Test

1st Diifference


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In an ARDL model, the dependent variable is assumed to take on a function of past values of

itself, hence the autoregressive part in the name, as well as current and past values of other variables.

The general form is hence equivalent to a VAR representation with the other explanatory variables

and their lags added on. In our case:

𝑖𝑡10 = 𝑐 + ∑ 𝛽𝑖

𝑝

𝑖=1

𝑖𝑡−𝑖10 + ∑ 𝛾𝑖𝑖𝑡−𝑖

0.3𝑀

𝑞

𝑖=0

+ ∑ 𝛼𝑖𝜋𝑡−𝑖𝑒

𝑟

𝑖=0

+ ∑ 𝜈𝑖𝑔𝑡−𝑖

𝑠

𝑖=0

+ ∑ 𝜆𝑖𝑑𝑡−𝑖

𝑡

𝑖=0

+ ∑ ϙ𝑖𝑏𝑡−𝑖

𝑢

𝑖=0

+ ∑ 𝜌𝑖𝐹𝐵𝑁𝐵𝑡−𝑖

𝑣

𝑖=0

+ ∑ 𝜙𝑖𝐹𝑂𝑡−𝑖

𝑤

𝑖=0

+ ∑ 𝜛𝑖𝐶𝐵𝑡−𝑖

𝑥

𝑖=0

+ ϝ𝑖𝑉𝐼𝑋𝑡−𝑖 + 휀𝑡

where (p, q, r, s …) are the maximum number of lag determined using lag selection criteria and the

resulting model being an ARDL(p,q,r,s,t,u,v,w,x). Furthermore, the εt is assumed to be a white noise

process with serially independent errors, a crucial assumption for bounds testing. (Pesaran et al 2001).

In equation (3) we have set the dynamic regressors to be short term nominal rate (𝑖𝑡𝑠), inflation

expectation (𝜋𝑡𝑒), QoQ real GDP growth (𝑔𝑡), debt to GDP (𝑑𝑡), deficit to GDP (𝑏𝑡), quantitative

easing (𝐶𝐵𝑡), private share holdings (𝐹𝐵𝑁𝐵𝑡) and foreign official share (𝐹𝑂𝑡) holdings. We set the

financial market uncertainty component (𝑉𝐼𝑋𝑡) as a fixed regressor not only because index values are

unrelated to their previous values but also because financial market conditions vary rapidly.

A general-to-specific modelling framework was implemented to derive the optimal ARDL

model which fits the data. Khim and Liew (2004) determine that the Akaike information criteria

(AIC) is “superior in the case of small samples” and it “minimises the chances of under-estimation

while maximising the chance of recovering the true lag length”. Indeed, it is well noted in the

literature that the Schwarz Information Criterion (SIC) tends to select a simpler model specification,

therefore, AIC is favoured for the ARDL model. For strength of analysis the model we obtain was

compared with models generated using SIC and Hannan-Quinn Criterion, whereby we obtained

similar results. A drawback of using AIC is that it might lead to “over-fitting”, which could result in

our model being autocorrelated and hence unsuitable. Therefore, as a check we always test for the

presence of serial correlation.

To account for the visible structural break caused by the Great Recession which started late

2007, we introduced a dummy variable (Break) as a fixed regressor. The dummy, that takes a value

of 1 for periods from 2007Q4 to 2009Q2 and 0 for all other dates, was determined by a combination

of structural break-point tests and graphical interpretation. It is crucial to account for this one-off

event as there was a clear deviation in the variables path, which would affect our long-term co-

integration and coefficient results. In addition, since our dependent variable exhibited a clear

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16

declining trend, the model was fitted by introducing a restricted linear trend (Trend).14

Initially, we started off by setting the maximum lags for the independent variable and

dependent variable equal to n= 4, which yielded the parsimonious model ARDL(4,4,0,4,4,0,4,0,4).

However the residuals of the model appeared to be serially correlated. Therefore, I employed a

general-to-specific modelling approach, reducing the maximum number of lags of the independent

variable and re-testing the residual properties. Restricting the max lag to n=2 yielded the optimum

model, ARDL(1,1,0,4,3,1,4,1,4) with no serial correlation:

𝑖𝑡10 = 𝑐 + ∑ 𝛽𝑖

1

𝑖=1


0.3𝑀

1

𝑖=0


0

𝑖=0


4

𝑖=0


3

𝑖=0


1

𝑖=0

+ ∑ 𝜌𝑖𝐹𝐵𝑁𝐵𝑡−𝑖

4

𝑖=0

+ ∑ 𝜙𝑖𝐹𝑂𝑡−𝑖

1

𝑖=0


4

𝑖=0

+ ϝ𝑖𝑉𝐼𝑋𝑡−𝑖 + Ϸ𝐵𝑅𝐸𝐴𝐾𝑇

+ ϻ𝑇𝑅𝐸𝑁𝐷 + 휀𝑡

5.1. Diagnostic Checks

Robustness checks were carried on the model’s residuals. Since lagged values of the

dependent variable enter our model (4) we must check whether residuals are serially independent,

otherwise the parameters estimated will not be consistent. Using the correlogram Q-statistics, the p-

values strongly suggest that residuals are serially independent (Appendix 1.1). We confirm this with

the Breusch-Godfrey serial correlation LM test for lags=2,3, which has greater power. Moreover, we

test residuals for homoskedasticity by applying the Breusch-Pagan-Godfrey test. The p-value (0.457)

suggests we cannot reject null hypothesis, hence our residuals are homoscedastic. Furthermore the

Jarque-Bera statistic suggest that our residuals are normally distributed at the 5% level. Finally, we

applied the Ramsey-Reset test to test whether the estimated model is miss-specified (required because

of the limitations of AIC) but find no statistical evidence for this. All the tests indicate that the model’s

residuals have optimal econometric properties, meaning that the coefficients we will estimate in the

next section will be valid for reliable interpretation.

14 Some explanatory variables also exhibited a trend-like-behaviour, although this may be due to the short time

frame(Appendix 2)

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17

Table 2 – Diagnostic Tests on the ARDL(1,1,0,4,3,1,4,1,4) model

ARDL Bound Testing

To carry out ARDL bounds test we construct a “conditional ECM” (Pesaran et al 2001) from

the ARDL model found in (4):

𝛥𝑖𝑡10 = 𝑐 + ∑ 𝛽𝑖

1

𝑖=1

𝛥𝑖𝑡−𝑖10 + ∑ 𝛾𝑖𝛥𝑖𝑡−𝑖

0.3𝑀

1

𝑖=0

+ ∑ 𝛼𝑖𝛥𝜋𝑡−𝑖𝑒

0

𝑖=0

+ ∑ 𝜈𝑖𝛥𝑔𝑡−𝑖

4

𝑖=0

+ ∑ 𝜆𝑖𝛥𝑑𝑡−𝑖

3

𝑖=0

+ ∑ ϙ𝑖𝛥𝑏𝑡−𝑖

1

𝑖=0

+ ∑ 𝜌𝑖𝛥𝐹𝐵𝑁𝐵𝑡−𝑖

4

𝑖=0

+ ∑ 𝜙𝑖𝛥𝐹𝑂𝑡−𝑖

1

𝑖=0

+ ∑ 𝜛𝑖𝛥𝐶𝐵𝑡−𝑖

4

𝑖=0

+ ϝ1𝛥𝑉𝐼𝑋𝑡 + Ϸ1𝛥𝐵𝑅𝐸𝐴𝐾𝑡

+ ϻ1𝑇𝑅𝐸𝑁𝐷 + 𝛿1𝑖𝑡−110 + 𝛿2𝑖𝑡−1

0.3𝑀 + 𝛿3𝜋𝑡−1𝑒 + 𝛿4𝑔𝑡−1 + 𝛿5𝑑𝑡−1 + 𝛿6𝑏𝑡−1

+ 𝛿7𝐹𝐵𝑁𝐵𝑡−1 + 𝛿8𝐹𝑂𝑡−1 + 𝛿9𝐶𝐵𝑡−1 + 𝑒𝑡

where the first part of equation (5) is the ARDL model (4) differenced. The coefficients 𝛽, 𝛾, 𝛼, …

represent the short run dynamics, while the 𝛿1 𝑡𝑜 𝛿9 represent the long run elasticities. The bounds

test works by computing an F-test for the null hypothesis that there is no long-run equilibrium

relationship between the variables, which is also defined by;

𝐻0: 𝛿1 = 𝛿2 = 𝛿3 = 𝛿4 = 𝛿5 = 𝛿6 = 𝛿7 = 𝛿8 = 𝛿9 = 0

Critical values are reported by Pesaran and Pesaran (1997) for an arbitrary mix of I(0) and I(1)

variables. The test works as follows; if the computed F-statistic falls below the lower bound we

conclude that all variables are I(0), by definition no cointegration is possible. However, if the F-

statistic exceeds the upper bound we can conclude that we have cointegration and hence a long-run

relationship between the variables.15

15 Test is inconclusive if statistic between the bounds

Diagnostic Test Description Lags Test-stat Value Prob. value

2 1.091 0.157

3 0.997 0.165

Breusch-Pagan-Godfrey H0: Residuals are not heteroskedastic - F-stat 0.988 0.457

Jarque-Bera H0: Residuals are normally distributed - Jarque Bera 5.226 0.073

Ramsey Reset H0: No serial correlation Up to 4 fitted terms F-stat 0.316 0.869

Breusch-Godfrey LM H0: Residuals not serially correlated F-stat

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18

Table 3 – ARDL Bounds Testing (F-test) for existence of long-run relationship

The calculated F-statistic is 9.234, which clearly exceeds the 1% critical value for the upper

bound. As a result, the null hypothesis can be strongly rejected, indicating the existence of a stable

long-run relationship among the 8 variables. However, careful note must be made that the critical

bounds reported by Pesaran were generated using sample sizes of 500 and 1000 observations with

20,000 and 40,000 replications respectively. P.K. Narayan (2004) calculates a new set of critical

values for the bounds F-test for sample sizes up to 80, ensuring that we can make reliable inferences

for smaller samples. Using the critical values for 80 observations reported by Narayan (Appendix 3)

we confirm existence of a long-run relationship among the variables for UK.

Test Statistic Value k

F-statistic 9.234 8

SignificanceLower I(0)

Bound

Upper I(1)

Bound

10.0% 2.13 3.09

5.0% 2.38 3.41

2.5% 2.62 3.70

1.0% 2.93 4.06

H0: No long-run relationship exists

Critical Bounds (Pesaran)

Note: k is the number of dynamic regressors


19

5.2. Long-run Relationship and short-run dynamics

To determine the actual long-run relationship between the variables we compute long-run

elasticities using the “conditional ECM” (5). These elasticities determine the total effect an

explanatory variable has on our dependent variable (gilt yield) for the whole period considered. The

coefficients of short-run interest rate is (𝛿2/𝛿1), for inflation expectation (𝛿3/𝛿1) and so on for the

remaining variables.

Table 4 – Long-run relationship, with their standard errors, t-statistics and p-values.

Variable Coefficient Std. Error T-statistic

πte 0.956* 0.245 3.897

it3M -0.135 0.116 -1.162

gt -0.896* 0.346 -2.586

bt -0.015 0.034 -0.436

dt -0.081 0.057 -1.412

CBt 0.011* 0.004 3.192

FBNBt -0.230* 0.046 -4.985

FOHt 0.131* 0.040 3.232

VIXt -0.018** 0.009 -1.946

Break -0.574*** 0.330 -1.736

Trend -0.125* 0.021 -5.836

Note:*, ** and *** indicate significance at 1%, 5% and 10% level

respectively

Long-Run ARDL Coefficient Estimation


20

The short-run dynamics are also obtained using the unconditional ECM and are presented for the

ARDL model in Table. These elasticities calculated the immediate effect of the independent variables

on the dependent variable for the optimal lag length (Alam et al. 2012).

Table 5 – Dynamic short-run effects of stated variables on gilt yields

The coefficient of the error-correction term, CointEq(-1), is found to be negative and

statistically significant at the 1% level. This is what we would expect if there is co-integration between


Δ(πte) 0.592* 0.092 6.448

Δ(it3M

) 0.219* 0.063 3.453

Δ(gt) -0.053 0.058 -0.911

Δ(gt-1) 0.368* 0.077 4.810

Δ(gt-2) 0.221* 0.070 3.157

Δ(gt-3) 0.128** 0.061 2.110

Δ(bt) 0.122* 0.039 3.108

Δ(bt-1) -0.041 0.040 -1.034

Δ(bt-2) -0.107** 0.041 -2.609

Δ(dt) -0.007 0.026 -0.263

Δ(CBt) 0.004 0.003 1.508

Δ(CBt-1) -0.007** 0.003 -2.376

Δ(CBt-2) -0.005*** 0.003 -1.761

Δ(CBt-3) -0.006** 0.002 -2.593

Δ(FBNBt) -0.007 0.022 -0.331

Δ(FBNBt-1) 0.094* 0.024 3.983

Δ(FBNBt-2) 0.112* 0.023 4.854

Δ(FBNBt-3) 0.052** 0.023 2.235

Δ(FOHt) 0.125* 0.030 4.176

Δ(VIXt) -0.007** 0.003 -2.152

Δ(Break) -0.302** 0.153 -1.977

C 4.669* 0.588 7.940

CointEq(-1) -0.569* 0.070 -8.126

Estimation of short-run effects of stated variables on bond yields (quarterly)



21

our variables and it thus provides further evidence of the long-run relationship among our variables

(Kremers et al. 1992 and Banerjee et al. 1998). The magnitude of the coefficient is -0.58, suggesting

that nearly 57% of any disequilibrium between our dependent and independent variables is corrected

within one quarter. In other words, it takes under 2 quarters (1/0.57=1.72) or 5.17 months to fully

correct the disequilibrium. This is a relatively quick adjustment.

Granger Causality Result:

In the ARDL framework we can also test for dynamic short-run causality between our

variables by individually restricting the coefficient of independent variables and its lags equal to zero

(Wald test). If the null hypothesis of no causality is rejected, then we say that the relevant independent

variables Granger-causes bond yields.

Table 6 – Granger Causality Test

Table 6 demonstrates that all variables, apart for deficit/GDP, Granger Causes 10-year gilt yields.

Interestingly, foreign ownership of gilts whether official or from the private sector show high

statistical significance (<1%) for causing bond yields.

Variable F-statistic P-value

πte 16.412* 0.0002

it3M 5.876* 0.0055

gt 2.523** 0.0434

bt 3.401** 0.0112

dt -1.062 0.2938

CBt 5.387* 0.0006

FBNBt 7.331* 0.0000

FOHt 3.756* 0.0005

VIXt 7.029** 0.0112

Note:*, ** and *** indicate significance at

1%, 5% and 10% level respectively


22

6. Results

The long-run coefficients (Table 4) suggest the key drivers of 10-year gilt yields are expected long-

run inflation, real GDP growth, private and official foreign holdings, quantitative easing and VIX.

These are discussed in turn;

The coefficient of inflation expectation suggests that in the long-run a 1% increase in long-

term expected inflation leads to a highly significant increase of 95 basis points in bond yields, keeping

all other variables constant. The result has the predicted sign, while the magnitude might confirm

existence of the Fisher effect. The slightly smaller than 1-to-1 effect as observed also by Caporale et

al. (2002), who find approximately 80 basis point effect, can be explained by the relative stability of

the monetary policy by independent authorities (Keeley and Hutchinson 1986). Overall, however, the

literature finds mixed results with regard to inflation that vary significantly depending on the time

period being considered. The short-run dynamics (Table 5) of a change in expected inflation suggest

a much smaller effect of 59 basis points. However, as in Bandholz et al (2007), assuming a rise in

expected inflation increases 1-for-1 the short-run interest rate (22bp), then overall inflation also has

a 1-to-1 effect in the short-run (59+22=91 basis points).

Surprisingly, the short-term interest rate proxy does not have a significant long-run

relationship with bond yields. We would have expected a strong and positive impact due to the term

structure relationship, whereby interest rates move together and vary only due to term-premia. The

plummeting and stationarity of 3-month gilt yields at unprecedented low levels of around 0.5%

(Appendix 2, figure 2), following BOE’s policy rate setting at the lower bound ever since the financial

crisis, could explain our result. Importantly, however, the short-run dynamics point to the fact that a

100 basis point increase in nominal short-term rate increases the long-term rate by 22 basis points.

This is a much higher response than what Dale (1993), who tries to measure the short-run response

of UK long-term rates to monetary policy actions of the BOE, finds an effect of 4-10 basis points for

1983-1993 sample period. Given that short-term rates are a proxy for the monetary policy rate, our

result suggests that a marginal change in monetary policy has a significant but less than one-to-one

pass-through effect on long-run yields.

Furthermore, the other monetary policy instrument, QE, although highly significant, appears

to have a small effect on long-term interest rates. A £100bn increase BOE gilt purchases increase

yields by 1 basis point. Considering total asset purchases thus far is 375, the total effect on UK long-

term yields is only 3.5 basis points. Indeed, MPC member Martin Weale’s says “[QE] worked through


23

reducing uncertainty rather than through significant reductions in the long rate of interest”16.

However, in our estimated model it is apparent that monetary policy instruments have information to

determine of long-term interest rates.

We find that a 1 percent increase in (QoQ) Real GDP growth decreases gilt yield by

approximately 90 basis points. Arsnalap et al. estimate a similar (48-49 basis point) impact across a

panel of advanced countries. The magnitude of the impact is stronger because QoQ real gdp growth

rate was employed rather than growth rate from same quarter a year ago, which when re-estimated,

yields a 24 basis point effect. The negative impact, although counter to many economic theories, is

consistent with the findings of Baldacci and Kumar (2010) and Caporale et al (2002), who explain

that the negative impact might be because higher incomes lead to higher demand for long-term bonds

due to savings motive.

Unlike previous studies on the US (e.g. Warnock and Warnock 2005), debt to GDP and deficit

to GDP in the UK does not have a significant long-run relationship with our dependent variable, so

we cannot conclude anything about Barro-Ricardian equivalence. This relationship breakdown may

be due to the combination of a short-study timeframe and a period of financial stress (Poghosyan

2012). Indeed it is noted that in countries like the US and UK bond yields have continued their

downward trend despite a piling up of general government debt after the financial crisis. The VIX, in

line with our expectations, suggests that an increase in market fear across agents leads a fall in yields

by 1.8 basis points.

Foreign official and private ownership (%), which have not received much focus in the UK

studies, are both significant at the 1% level emphasising the importance of foreign variables as an

additional determinant of bond yields. Interestingly a 1 percent point increase in foreign private share

of total debt decreases 10-year yields by 23 basis points. The sign and magnitude confirm what

Arslanalp and Poghosyan (2014) find about the UK, where a 1 percent point increase in the share of

government debt held by foreign investors reduced 10-year government bond yields by 20-30 points

in the UK. However, a 1% point increase in foreign official holdings cause an increase in gilt yield

by 13 basis points. Similar results were obtained for the short-run. These result is in sharp contrast

with the –ve sign in Warnock and Warnock (2005) and Beltran (2012) and what we expected. The

following graphs help us understand our results;

16 ‘Unconventional monetary policy’ speech at the University of Nottingham (8 March 2016)


24

0.00

200.00

400.00

600.00

800.00

1,000.00

1,200.00

1,400.00

1,600.00

1,800.00

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014

Po

unds

(£bn)

Foreign Official Holdings (£bn) Total gilt market (£m) -

Figure 3 – Share of Foreign official holdings and 10-year gilts (left) & Nominal Gilt Market (right)

The share of foreign official holdings was clearly increasing just prior to the financial crisis,

after which the foreign official share fell. However, the percentage holdings is affected by changes in

inflows (£) as well as by changes in the supply of gilts. From (right) both have kept on increasing but

the total gilt market has at greater rate after the crisis. Therefore, to gain a deeper understanding of

the dynamics we should look at level data. We cover this in the further analysis (below) where we

find that a 1% increase in the growth of foreign private inflows leads to a 0.02% point decrease in

the long-term nominal interest rate. Likewise a 1% increase in growth in foreign official inflows leads

to a 0.05% point decrease in the nominal rate. Therefore, we find that both types of foreign holdings

act to depress yields and that official holdings has a greater effect than private holdings as in Arsnalalp

(2014).

Per

cent

(%)

0

5

10

15

20

25

30

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014

10-year Gilts

Foreign Official Share


25

7. Further Empirical Analysis

1. Expectations Analysis

In order to ascertain the effect of expectations of variables further tests were performed. Real

GDP growth (QoQ) and debt to GDP were lagged one quarter and the resulting variable used as a

proxy for expectations. Using same methodology, we obtain an ARDL(1,1,0,3,4,4,4,0,3), and we find

that taking expectations doesn’t affect our results significantly (Appendix 4).

2. Growth in Foreign Inflows

The analysis thus far, has focused on a model considering the composition of gilt holdings

from foreign agents as share of gilts outstanding, without accounting for the nominal inflows.

Following from our discussion in the “Results” an increase in foreign holdings (%) requires inflows

to grow at a faster rate than the supply. However, as supply of gilts was expanded rapidly post-crisis,

we adapt the model to capture the effect of inflows by re-estimating an ARDL model using foreign

inflows level data. Therefore, we compute percentage change in foreign private and foreign official

inflows from previous quarter, losing 1 observation in the process.

Figure 4 – Growth in foreign private inflows (left) & growth in foreign official inflows (right)

Time Time

-10

-5

0

5

10

15

20

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014

official_change

-80

-40

0

40

80

120

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014

private_change

Per

cen

tage

(%)

Per

cen

tage

(%)

Figure 4 – Growth in foreign private inflows (left) and growth in foreign official inflows (right) in UK gilt market.

Notice how private inflows have been more volatile, with the start of the financial crisis seeing a flight to safety with

a close to 115% increase in inflows from foreign private sector. Official holdings has been less volatile appearing to

have some seasonality. Interestingly, from 2014 there was a rapid inflow which receded abruptly in the 3rd quarter, at

the same time as the stock market crash in China and the emerging markets.


26

Re-estimating an ARDL model using the same procedure buy only replacing the foreign

variables an ARDL(1,1,0,4,0,0,1,1,2) is obtained;

𝑖𝑡10 = 𝑐 + ∑ 𝛽𝑖

1

𝑖=1


0.3𝑀

1

𝑖=0


0

𝑖=0


4

𝑖=0


0

𝑖=0


0

𝑖=0

+ ∑ 𝜌𝑖𝑃𝐹𝐼𝑡−𝑖

1

𝑖=0

+ ∑ 𝜙𝑖𝑂𝐹𝐼𝑡−𝑖

1

𝑖=0


2

𝑖=0

+ ϝ𝑖𝑉𝐼𝑋𝑡−𝑖 + Ϸ𝑏𝑟𝑒𝑎𝑘𝑇 + ϻ𝑡𝑟𝑒𝑛𝑑

+ 휀𝑡

where growth in private foreign and official foreign inflows is denoted by PFI and OFI respectively.

All other assumptions and specifications are kept constant. Below we display the long-run elasticities,

however, short-run dynamics and diagnostic checks were also carried out and displayed in

Appendix5. These results were already reported in “Results” section.

Table 7 – Long-Run coefficient estimates for model (6)


πte 1.277* 0.293 4.364

it3M -0.062 0.134 -0.463

gte -1.549* 0.367 -4.227

bte -0.045 0.039 -1.132

dt -0.015 0.066 -0.234

CBt -0.001 0.003 -0.237

PFIt -0.020** 0.008 -2.495

OFIt -0.050** 0.025 -2.009

VIXt -0.026*** 0.015 -1.730

Break -0.519 0.489 -1.062

Trend -0.021 0.015 -1.359



(6)


27

8. Conclusion & Policy Implications

This paper investigates the impact of bond yield determinants, particularly foreign flows, using a

novel ARDL modelling and cointegration approach for the UK. We find that foreign ownership as a

share of total gilt no longer yields previous literature results due to the overall pace expansion of the

gilt market. Accounting for this, we do find that a 1% increase in the growth of foreign private and

official inflows leads to a 0.02% and 0.05% point decrease in government bond yields respectively.

Moreover, the robustness of our results is evidenced by the fact that granger-causality runs from

foreign variables to bond yields. We caution, however, that it is possible that our results over-state

the effects of macroeconomic variables due to the limited sample size and possible model miss-

specification. Policy makers should note that it is unlikely that any individual explanation and

macroeconomic variable can account for the level of bond yields in recent years.

Indeed, we determined that long-term yields are affected not only by monetary and fiscal

policies but also by foreign variables. In particular, foreign flows have a statistically significant and

economically large impact on long-term UK rates. Agents must hence understand that ‘normalisation’

of domestic macroeconomic variables may be insufficient to bring long-term rates back to pre-crisis

levels unless there is a similar ‘normalisation’ in foreign investor base. Therefore, our analysis is

consistent with the savings glut hypothesis used by Bernanke to describe the ‘conundrum’. The

discussion of this topic is timely, as a recovering of macroeconomic variables (inflation and economic

growth) to pre-crisis levels and the soon expected BOE rate rise has not impeded the downward path

in bond yields. According to our estimates a 0.50% policy rate hike by the BOE will raise 10-year

gilts yield by 10.95 basis points immediately. However, crucially, only a 2% point increase in the

growth of foreign official and private inflows (assuming they do not affect each other) is needed to

counter the policy rate rise by decreasing yields by 14 basis points.

Policy makers, in financially integrated and open countries, must also note that they may have

less power in affecting long-term interest rates than was previously thought. For example, following

the financial crisis and the Eurozone debt crisis, a divergence of sovereign bond yields was reported

between European peripheral and core economies (Germany, UK). International flows played a

significant role in this divergence as Arslanalp and Poghosyan (2014) determine that while foreign

flows to core economies reduced 10-year bond yields, foreign outflows raised yields in peripherals

like Italy and Spain, 40-70 and 110-180 bp respectively. However, higher long-term rates during

recession periods put further pressure on economies as it increases the government cost of borrowing

and can potentially bring further deflationary pressure by decreasing investment (vice versa for core


28

economies). Hence, policy authorities should be aware of the spill-over effects of foreign inflows

depending on the relative perception of uncertainty foreign agents hold on the country. Furthermore,

the openness of financial markets also means that crisis or extreme uncertainty in excess saving

countries (e.g. China) can have significant spillover effects in other bond markets and consequently

the real economy. Therefore, further research should focus on investigating the effect of foreign

inflow from specific surplus economies to determine its effect on UK gilts.

The downward path of nominal long-term rates that initiated prior to the financial crisis is also

addressed by L. Summers by what he coins secular stagnation. According to this view, “structural

changes in economies lead to an increasing propensity to save, a decreasing propensity to invest and

as a consequence, lower equilibrium real rates”, which in turn leads to “less aggregate demand and

disappointing growth performance”. Indeed, secular stagnation could explain the negative effect of

real gdp growth in our results. However, secular stagnation is a global issue, so we must think about

the aggregate saving-investment balance of the global economy. If there are more countries with

excess saving than those with excess investment then there will be an increasing demand for safe

assets, such as bonds, which will therefore depress yields, especially in developed bond markets

(UK). Successful policy approaches should therefore focus on trying to increase (private and public)

investments domestically while decreasing the excess savings developing and petro-dollar countries

have. However to achieve this, a global contribution is needed.


29

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32

11. Appendix

Appendix 1. Description of Variables Used and their Expected sign before the estimation


33

Appendix 1.1 Correlogram of ARDL(1,1,0,4,3,1,4,1,4) for Q-test

All p-values are greater than 0.05, meaning that the model appears to be serially uncorrelated.

Appendix 2. Graphical analysis of variables used in model (2). Data from 1996Q1-2015Q3

0

2

4

6

8

10

96 98 00 02 04 06 08 10 12 14

10-year Gilts

0

2

4

6

8

96 98 00 02 04 06 08 10 12 14

End of quarter 3 month Treasury Bill (£)

1.5

2.0

2.5

3.0

3.5

4.0

4.5

96 98 00 02 04 06 08 10 12 14

Implied Inflation expectation (market inflation)

-3

-2

-1

0

1

2

96 98 00 02 04 06 08 10 12 14

QonQ Real GDP Growth (% change)

20

40

60

80

100

96 98 00 02 04 06 08 10 12 14

UK Debt as % of GDP

-4

0

4

8

12

96 98 00 02 04 06 08 10 12 14

UK deficit % of GDP

0

4

8

12

16

96 98 00 02 04 06 08 10 12 14

FB NB %

5

10

15

20

25

30

96 98 00 02 04 06 08 10 12 14

FO %

0

100,000

200,000

300,000

400,000

96 98 00 02 04 06 08 10 12 14

Assets purchased by CB (£ millions)

10

20

30

40

50

96 98 00 02 04 06 08 10 12 14

VIX

Foreign Official Holdings share (%) Foreign Private Holdings share (%)


34

Appendix 3. Critical Values for ARDL Bounds testing computed by P.K. Narayan (2004) for smaller

sample sizes (up to 80 observations and 7 variables)

Note: Although we have k=8 in the Bounds Testing we perform, by observing and following the

trend of critical values as we increase one more variable, we can conclude that our F-statistic of

9.23 will be above the critical value for n=80 and k=8.

Appendix 4. Estimation taking expectations of GDP growth and Debt to GDP

Expectations were taken by lagging the each of the values by 1 period. The long-run coefficients

are;


πte 1.163* 0.266 4.377

it3M -0.114 0.122 -0.929

gte -1.078* 0.256 -4.203

bte -0.018 0.039 -0.473

dt -0.117*** 0.065 -1.821

CBt 0.011* 0.004 3.217

FBNBt -0.235* 0.054 -4.375

FOHt 0.119* 0.043 2.758

VIXt -0.028* 0.010 -2.695

Break -0.283 0.369 -0.767

Trend -0.119* 0.026 -4.667




35

Our estimates do not vary significantly, however, in this case we can say something about Baro-

Ricardian equivalence, that is, the hypothesis does not hold.

Bound’s Testing outcome; Our F-test value for this model specification is 7.324, hence we cannot

reject the hypothesis that there is a long-run relationship amongst our variables.

Diagnostic Testing;

Appendix 5 – Short-run dynamics, bound’s test and diagnostic check for ARDL model in Eq. (6)


Δ(πte) 0.641* 0.106 6.036

Δ(it3M

) 0.200** 0.077 2.594

Δ(gt) -0.205* 0.066 -3.099

Δ(gt-1) 0.332* 0.087 3.839

Δ(gt-2) 0.187** 0.089 2.096

Δ(gt-3) 0.105 0.066 1.596

Δ(bt) 0.002 0.032 -0.070

Δ(dt) -0.021 0.033 -0.373

Δ(CBt) -0.004*** 0.003 -1.625

Δ(CBt-1) -0.006*** 0.003 -1.963

Δ(FBNBt) -0.005* 0.001 -4.070

Δ(FOHt) -0.006 0.005 -1.239

Δ(VIXt) -0.010** 0.004 -2.406

Δ(Break) -0.194 0.179 -1.085

C 2.139* 0.362 5.912

CointEq(-1) -0.379* 0.062 -6.089

Estimation of short-run effects of stated variables on bond yields (quarterly)



2 1.484 0.079

3 1.270 0.088






36

ARDL Bounds Test;

Diagnostic Testing;

Test Statistic Value k

F-statistic 6.742 8

SignificanceLower I(0)

Bound

Upper I(1)

Bound

10.0% 2.13 3.09

5.0% 2.38 3.41

2.5% 2.62 3.70

1.0% 2.93 4.06

ARDL Bounds Testing for Cointegration

H0: No long-run relationship exists

Critical Bounds (Pesaran)

Note: k is the number of dynamic regressors


2 0.005 0.993

4 0.539 0.531





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