Have the Federal Reserve’s Unconventional Monetary Policy Measures Weakened the Link between Financial and Real Sectors?

Have the Federal Reserve’s Unconventional Monetary Policy

Measures Weakened the Link between Financial and Real

Sectors?

Yimin Xu - S2343908

Supervisor: Prof. dr. Jakob de Haan

Abstract

Contents

1

Introduction

1

2

Literature Review

4

2.1

Unconventional monetary policy

. . . .

4

2.2

The effectiveness of unconventional monetary policy . . . .

4

2.3

Transmission mechanism of quantitative easing . . . .

7

2.4

The link between financial markets and the real economy

. . . .

7

3

Extending the G&Z Credit Spread Index

10

4

Measuring the Link between Financial and Real Sectors

12

4.1

To measure the strength of real-financial link: data and method . . . .

13

4.2

Going for bonds with longer remaining terms to maturity . . . .

15

4.3

Sequences of real-financial link

. . . .

17

1

Introduction

Since the eruption of the 2007-2008 global financial crisis, central banks of many advanced economies

have adopted unconventional monetary policy measures in order to maintain economic and financial

stabilities. Conventional monetary policy measures are usually aimed at setting target short-term

official interest rates at a favourable level, so as to guide the market interest rates and to in turn

in-fluence the broader economy. In this process, the central banks’ balance sheets are usually passively

affected, and the changes in the sizes and compositions of central banks’ balance sheets are usually

relatively small. Unlike the conventional measures, the recent unconventional monetary policy

mea-sures usually involve active expansions of central banks’ balance sheets, in order to directly change

some “non-standard” market interest rates, especially to lower long-term rates. Typical measures

like quantitative easing programs are even aimed at injecting a certain quantity of liquidity into the

economy by massively purchasing privately owned financial assets from the market (Joyce, Miles,

Scott and Vayanos, 2012).

The effectiveness of unconventional monetary policy measures in releasing policy signals and

their influences on the economy are an important aspect in policy research, and many studies have

looked into this issue. Studies such as Gagnon, Raskin, Remache and Sack (2011), Hamilton and Wu

(2012), Neely (2010) and Krishnamurthy and Vissing-Jorgenson (2011) have investigated whether

unconventional policies have effectively lowered long-term interest rates. Besides, many researchers

focused on the influence of balance sheet policies on output, inflation and unemployment, including

Baumeister and Benati (2010), Gambacorta, Hofmann and Peersman (2014) and Engen, Laubach

and Reifschneider (2015).

What is missing in existing literature, however, is the unintended side effects of unconventional

monetary policy, especially the potential risks that may accumulate following the implementation of

such measures. A recent report by Borio and Zabai (2016), for instance, expressed a few concerns

about unconventional monetary policy. First, it is likely that over time the balance of benefits

and costs of these policy measures could deteriorate, so the effects of these measures are likely to

be diminishing. In the future, it would be increasingly difficult for central banks to rescue the

economy from crises and recessions with these measures. If central banks, in order to stabilize the

economy, should have to rely on increasingly experimental measures that are becoming unpredictable

or even dangerous, the credibility and legitimacy of central banks would come into question. Second,

although the unconventional monetary policy measures are supposed to be exceptional, temporary

and for the use only in specific circumstances, it seems that they are gradually becoming standard and

permanent. Third, in spite of ample evidence supporting the influence of these measures on financial

conditions, their influence on real economy seems to be modest.

Although central banks have

deployed the tools vigorously and beyond what was imaginable before the crisis, output performance

has still been disappointing and inflation has stubbornly remained lower than objectives

_{. Among}

the three aspects of concerns, the third one is especially worrisome, as it implies that there may be

risks accumulating in financial markets. The effects of unconventional monetary policy may not have

been evenly transmitted to the financial and real sectors: financial activities have been fostered, but

without a correspondingly remarkable recovery in real economy. This may be a potential source of

financial risks.

Are recent unconventional monetary policy measures, especially the “quantitative easing”

pro-grams that have vigorously injected great amount of liquidity, creating overheated financial markets,

while not strongly supporting the recovery of real economy? Such worries have recently aroused

anxiety among central bankers and macroeconomists that the rather novel unconventional monetary

policy measures may have unexpected negative effects unknown to us: they may have broken the

link between the financial markets and real economy.

It has been accepted by economists that, unless in extreme cases, financial markets should usually

be linked to real economy: the prosperity in financial markets should match the prosperity in real

economy, and a depression in financial markets are usually preceded or followed by a real downturn

(Mitchell and Burns, 1938). A “false boom” in the financial sector without the support of a strongly

growing real economy will almost always end up with a burst bubble. This study, therefore, is

intended to investigate whether the recent unconventional monetary policy measures of central

banks, especially the QE programs, have indeed weakened the link between the financial and real

sectors, and thus accumulated risks in the economy. In particular, the case of the United States is

taken as an example, because it is easier to access several types of data of the United States, compared

with most of other countries. First, the Federal Reserve is among the earliest central banks that

announced quantitative easing programs after the 2007-2008 crisis, which means by focusing on

the US, we are more likely to have a sufficient number of post-QE observations. This will greatly

facilitate the comparison before and after QE. Second, it is easier to collect price information of

a large number of corporate bonds issued by US companies, which is indispensable to this study.

Third, it is acknowledged that macroeconomic and financial data of the US are relatively more easily

accessible, including a few variables needed for this study such as monthly employment and the yield

curve of risk-free interest rates on different dates.

In order to measure the strength of the real-financial link, a quantitative indicator needs to

be developed that can depict the relationship between the financial and real sectors. It has been

found in previous literature that some financial variables can forecast future real economic variables

(Stock and Watson, 2003). Among all the financial variables, a specific type of credit spread index

that is composed of micro-level data of individual bond prices is found to persistently have a very

good predictive content for real variables (Gilchrist, Yankov and Zakrajˇ

sek, 2009; Gilchrist and

Zakrajˇ

sek, 2012; Faust, Gilchrist, Wright and Zakrajˇ

sek, 2013). This study, therefore, uses the G&Z

type credit spread index constructed following the method introduced in Gilchrist and Zakrajˇ

sek

(2012) to predict 3-month-ahead future employment growth, and then takes the predictive content

of the G&Z credit spread as an indicator of the strength of real-financial link.

health of banks that provide credit will lead to a shrinking credit supply and thereby a hiking credit

spread. The increased funding costs will reinforce the balance sheet problems and lead to poor

performances of companies.

We can develop a hypothetical story how the weakened real-financial link by an expansionary

unconventional monetary policy may possibly be reflected in the damaged predictive power of credit

spreads. As the expansionary measures are implemented, such as large scale asset purchases and

quantitative easing, a large amount of liquidity will be injected into the financial sector. Investors

who have just sold assets to the central bank will then eagerly seek for other opportunities to invest

the proceeds of their sold assets in. With excess demands for investment opportunities, investors

will no longer be as cautious as before about investigating companies’ future profitability, and will

hence invest their money in corporate bonds that they would not have invested in if without excess

cash. As a result, the credit spreads of these corporate bonds will be compressed, but not due to

investors’ optimistic expectations about these companies’ future profitability. The predictive power

of credit spread for real activities will disappear, and if the effects of unconventional monetary policy

on the real sector is modest, then the predictive power of credit spread will be even worse.

The analysis of this study is organized as follows. A G&Z type credit spread index constructed

in Gilchrist and Zakrajˇ

sek (2012) is first replicated and extended forward to 2016. Price information

of over 5,000 individual bonds of US non-financial companies are collected to calculate this credit

spread index, and this index is then used to predict 3-month-ahead future employment growth. The

R

_{of the predicting regression model is estimated as the predictive content, which indicates the}

strength of the real-financial link. In order to measure the strength of the link between financial and

real sectors for different time spots, a moving window approach is adopted in which the predicting

process is carried out repeatedly for each and every time spots in the sample. For every point of

time, a window of a specific width (12, 24, 36 or 48 months) is defined around it, and the predicting

regression model is estimated over this window period. The predictive content of this model is

then calculated and assigned to this time spot, representing the strength of the real-financial link

around it. This moving-window predicting process generates a sequence of R

_{’s from January 1973}

to April 2016, depicting the variations in the strength of the real-financial link over the past 40

years. Afterwards, regression analyses are carried out as an attempt to explain the changes in

the real-financial link. Finally, a dummy variable will enter the regression analyses, as a means

to compare the strength of the real-financial link before and after the implementation of Federal

Reserve’s quantitative easing programs.

The rest of this article follows an agenda like this. Section 2 reviews the literature about

un-conventional monetary policy and the link between the financial and real sectors. Section 3 extends

the G&Z type credit spread index following the method of Gilchrist and Zakrajˇ

sek (2012). Then in

Section 4 the R

_{sequence that depicts the strength of the real-financial link will be generated in}

2

Literature Review

2.1

Unconventional monetary policy

Joyce, Miles, Scott and Vayanos (2012) provide a comprehensive introduction to unconventional

monetary policy implemented by central banks around the world, especially after the outbreak of

the 2007-2008 global financial crisis. Before the crisis, the conventional monetary policy measures

were primarily aimed at achieving low and stable inflation, and the main instrument was a

short-term policy rate that anchors other interest rates in financial markets. The financial crisis, however,

brought about great challenges to the traditional way in which central banks used to formulate their

policies. Firstly, central banks start to realize the importance of including also financial stability

as a target of their monetary policy. This leads to central banks’ adding macro-prudential policy

measures to their policy tool boxes. Secondly, the ability of conventional policy measures to help

the economy recover from the financial crisis and to lead the economy back to a sustainable track

is questioned. For instance, the fact that nominal interest rates cannot go below zero means that

central banks could “run out of bullets” someday, when the economy slipped into a deeper recession

and the policy rate approached its zero lower bound. Besides, due to the large scale of losses after

the burst of bubble, some central banks themselves were caught in solvency risks as well, and became

less reliable in maintaining the relationship between official interest rates and market interest rates.

As a result, other forms of monetary policy are needed for central banks to continue effectively

intervening the economy.

Unlike the conventional monetary policy measures which are targeted at a certain level of

short-term official interest rates, the unconventional monetary policy measures usually require central

banks to actively expand their balance sheets to purchase financial assets, in order to influence

other “non-standard” interest rates and to provide liquidity to the economy at the same time

_{. For}

instance, the “credit easing” policy of Fed was intended to directly lower the mortgage interest rates

and provide credit lines to the economy, by purchasing mortgage-backed securities and expanding

the Fed’s balance sheet. Quantitative Easing (QE), as an outstanding example of unconventional

policies, is also a balance-sheet-expanding process, in which central banks purchase large quantities

of securities from the private sector. As the word “quantitative” indicates, the QE measures are

targeted at increasing the volume of bank reserves by a certain quantity, instead of changing interest

rates. The increased reserves will hopefully promote lending in the economy, driving high demands

and asset prices. Quantitative Easing was first implemented by the Bank of Japan in the 1990s

to mop up the aftermath of the burst of real estate bubble in Japan. After the start of the

2007-2008 global financial crisis, Bank of England and the Fed also turned to QE so as to stimulate

the sluggish economy. The European Central Bank announced in January 2015 an expanded asset

purchase programme, becoming the latest major central bank that adopts the QE measure.

2.2

The effectiveness of unconventional monetary policy

Due to the novelty of unconventional monetary policy measures, we have limited knowledge about

how well they can stimulate economic activities, and therefore since the implementation of such

unconventional policy measures, a large number of empirical studies have been undertaken to

inves-tigate their effectiveness. These studies mainly focus on two issues: whether unconventional policies

can effectively influence their targeted financial market indicators, and whether they can effectively

boost the real economy.

One of the earliest studies on the influence of Fed’s large scale asset purchases (LSAP) project

on financial market indicators is by Neely (2010). An event study was undertaken to show that

the LSAPs not only effectively lowered the US long-term interest rates, but led to significantly

lower long-term rates in international financial markets as well. By using security-level data on

all outstanding Treasury securities, D’Amico and King (2013) showed that the LSAPs considerably

reduced medium- and long-term Treasury yields, and the yields of securities purchased in LSAP

programs fell more than those not included in the purchase programs. In addition to the previous

two studies, Gagnon, Raskin, Remache and Sack (2011) carried out both an event study around the

announcements of LSAP policies and regression analyses on multiple risk premiums, and showed that

the LSAP project effectively lowered the long-term interest rates of several different securities, even

including those that were not in the purchase programs. The effects are economically meaningful and

long-lasting, and led to significantly reduced risk premiums. However, the expectations on future

short-term interest rates were not lowered. Krishnamurthy and Vissing-Jorgensen (2011) emphasized

that the quantitative easing (QE) programs influenced particular assets differently through different

channels, so it was inappropriate to focus on only Treasury rates as a policy target. They concluded

that the mortgage-backed securities purchased in QE1 more effectively lowered mortgage-baked

security yields and corporate yields, while the Treasury purchased in QE2 influenced more directly

the yields of Treasuries and Agencies compared with mortgage-backed securities and corporates.

Fratzscher, Lo Duca and Straub (2013) focused on the spillover effects of the US QEs on other

countries’ financial markets. They found that QE1 lowered the sovereign yields in many countries

especially in the US, and QE2 boosted equities worldwide, but QE2’s effects on yields differed across

the world. Besides, while QE1 led to a portfolio rebalance out of emerging markets into US equity

and bond funds, QE2 triggered an opposite trend.

negative. The effects were passed through to other asset prices more efficiently for the US than

for other countries, and the international spillover effects were also more significant from the US to

other countries than the other way around.

The macroeconomic impacts of unconventional monetary policy is also investigated. Using a

Bayesian time-varying parameter structural VAR model, Baumeister and Benati (2010) found that

a compression in the long-term bond yield spread during the 2007-2008 recession contributed to

output growth and inflation in all the four countries they studied (UK, US, Japan and Euro area).

Additionally, their counterfactual simulations showed the unconventional monetary policies adopted

in UK and US avoided great risks of deflation and output collapses. Chen, C´

urdia and Ferrero (2012)

simulated the influence of the Fed’s second LSAP program in a DSGE model on the US data, and

concluded that the LSAP II program could persistently increase GDP growth, but only by less than

half a percentage point. The marginal contribution of such program to inflation is also very small.

The relatively weak impact, according to the authors, were due to the small degree of financial

market segmentation they estimated. A cross-country analysis was carried out by Gambacorta,

Hofmann and Peersman (2014) using a panel VAR model. Analysing with monthly data from eight

developed countries over the crisis period, they found that the expansion of central banks’ balance

sheets indeed temporarily pushed up output levels. The inflation level was also promoted, but the

effect was weaker and less persistent. In general, the real effects of unconventional monetary policy

are admitted, but it is also found that these real effects could be temporary and modest.

The downside of unconventional monetary policy should not be overlooked. A recent study by

Borio and Zabai (2016) pointed out a few potential risks of adopting unconventional monetary policy

measures. First, these policy measures may be subject to diminishing returns, meaning that in the

future it could be increasingly difficult for central banks to rescue economies out of crises with the

same policy tool, and central banks would have to attempt increasingly experimental policy

mea-sures. Second, although the unconventional measures are supposed to be temporary and exceptional,

they are actually becoming permanent and standard. As more novel policy measures enter central

banks’ toolbox, many measures that were considered as “unconventional” are gradually becoming

“conventional”. Third, in spite of ample evidence supporting the effectiveness of unconventional

monetary policy in influencing financial conditions, their impacts on real economy still seem to be

relatively disappointing. It seems that the effects of these measures are not successfully transmitted

to the real sector.

2.3

Transmission mechanism of quantitative easing

Miles (2011, 2012) described two channels through which the Bank of England could boost the

economy by asset purchasing programmes: portfolio substitution channel and bank funding channel.

The portfolio substitution channel is based on a core assumption that the British government

bonds (gilts) and bank deposits are not perfect substitutes. As the Bank of England purchases

gilts from banks and non-banks, either the central bank reserves held by commercial banks or bank

deposits held by gilt sellers will increase. If deposits (or central bank reserves) and gilts are perfect

substitutes then this operation will not change anything. The economy will be caught in a liquidity

trap and bond yields will not be reduced. However, if it is not the case and the investors who sold

gilts would not like to hold deposit but rather buy other financial assets with the proceeds of gilts,

such as corporate bonds, then the prices of these assets will rise and the premiums will be lower.

As a result, the fund raising costs of many companies will be lower and it will be much easier for

them to borrow money. The higher asset prices will also increase the wealth of the households who

own these assets. This will encourage more household consumptions and promote demands in the

economy.

The bank funding channel functions only when banks are experiencing stress in its availability

of funds and are thus reluctant to lend to firms. The purchasing programmes of BOE will increase

the deposits at individual banks and central bank reserves held by banks. With enough liquidity,

banks will be more willing to grant loans to firms.

Although what is described above is the transmission mechanism of quantitative easing carried

out by the Bank of England, QE programmes of other central banks should take effects in similar

ways. From the description of the transmission mechanism we can find that how well such asset

purchasing programmes boost real economy depends largely on how much of the liquidity injected

will ultimately be invested into production. Unlike conventional monetary policy which is aimed at

changing short-term official interest rates, many unconventional measures such as QE inject liquidity

into the economy. Liquidity is directly injected into financial markets, while the real economy can

be only indirectly affected. If liquidity stays in the financial sector and does not participate in real

production, the rapid increase in asset prices and relatively slow recovery of the real economy will

lead to gradually accumulated risks.

2.4

The link between financial markets and the real economy

The worry stated at the end of Section 2.3 can be translated into the worry that unconventional

monetary policy might have broken the link between the financial and real sectors.

From the

experience in the past economists conclude that a prosperity in financial markets usually precedes

the prosperity in real economy (such as Mitchell and Burns, 1938), and a increase in asset prices

without a corresponding promotion in real economy as a support will always end up with a sharp

fall. A broken link between the financial and real sectors usually means increasing risks in financial

markets.

A report of Bank for International Settlements (2011) made a critical summary of literature on

the transmission channels between the financial and real sectors. In this study the authors discussed

existing literature about both the linkages that run from the real sector to the financial sector and

the linkages that run from the financial sector to the real sector.

The linkages that run from the real sector to the financial sector are discussed in standard

macroeconomics. Weaker macroeconomic conditions will affect the balance sheets of banks and

corporates by reducing their revenues and profits, and in turn increase their default risks.

As

a result, macro stress will be incorporated in financial indicators. Empirical studies supporting

this argument include Alves (2005) and ˚

Asberg Sommar and Shahnazarian (2008). They used the

Moody’s KMV expected default frequencies (EDFs) as an indicator of companies’ credit quality, and

found significant relationships between EDFs and macroeconomic indicators such as GDP,

short-term interest rates and inflation in cointegrated closed-economy VAR models. Using VAR models

and data of balance sheets of Swedish companies, Jacobson, Linde and Roszbach (2005) found that

the macroeconomic condition of Sweden was an important factor explaining the variations in the

default frequency of Swedish companies. Apart from business corporations, banks’ balance sheets

are also influenced by macroeconomic conditions. Marcucci and Quagliariello (2009) found, based

on the data of Italian bank borrowers’ default risks and threshold regression models, that banks’

riskiness are augmented in recessionary periods.

The Research Task Force Transmission Channel (RTF-TC) group identified three channels that

in theory could realize the transmission from the financial sector to the real sector:

1. The borrower balance sheet channel.

2. The bank balance sheet channel.

3. The liquidity channel.

The first two channels are related to the financial accelerator theory discussed in Bernanke and

Gertler (1995): the external financial premiums will be lower for firms with higher net worth, since

these firms tend to have lower risks and more sufficient collaterals. These firms thus have lower

financing costs and can more easily raise funds. Similarly, banks with higher net worth, who have

better access to funds and more sufficient liquidity, will be more willing to grant loans to firms.

Empirical studies supporting the borrower balance sheet channel include Mody and Taylor (2003),

who found evidence for the US financial accelerator by predicting real economic activities during the

1990s using high-yield spread. Other studies like Gilchrist, Yankov and Zakrajˇ

sek (2009) found that

Another group of literature focuses on predicting future real economic variables using financial

indicators.

This group of literature is closely related to the balance sheet channels mentioned

above. Asset prices are forward-looking variables, and investors will take into consideration the

future profitability and solvency of a company when deciding whether to invest in the financial

assets issued by this company. Investors’ expectation about the company’s future performance is

therefore incorporated in asset prices and other related financial indicators such as credit spreads,

term spreads and interest rates. Stock and Watson (2003) provide a comprehensive literature review

on the predictive powers of such financial variables in forecasting output and inflation.

The financial variable that seems the most likely to predict future real performances is stock

prices. After all, the most widely accepted theoretical model for stock pricing is the discounted

future earnings model, suggesting an honest reflection in stock prices of future earnings of individual

firms. However, empirical studies have shown that the link between stock prices and future activities

is unclear. Fama (1981) and Harvey (1989) showed that the predictive content of stock prices for

output was not sufficient in bivariate regressions. Stock and Watson (1989, 1999) and Estrella and

Mishkin (1998) tried linear and probit models and also did not find significant improvement in the

predictive content of stock prices. Goodhart and Hofmann (2000) attempted to predict inflation

with stock prices but found no marginal predictive content of the latter.

Short-term interest rates are also used to predict output and inflation. Sims (1980) and Bernanke

and Blinder (1992) found that interest rates are a better predictor for output than monetary

aggre-gate. However, most of the studies found that once spreads are included, the marginal predictive

contents of interest rates usually become insignificant. Term spreads and default spreads are the two

types of spreads mentioned in Stock and Watson (2003). Term spread is the difference between

long-term and short-long-term interest rates. Several studies found that an inverted yield curve with lower

long-term rates than short-term rates usually signals a recession, of which the most comprehensive is

Estrella and Hardouvelis (1991). They found that in both binary and probit models, terms spreads

had a large in-sample predictive content for output. However, later studies showed that predictive

power of term spreads was not stable. Haubrich and Dombrosky (1996) and Dotsey (1998), for

instance, found that term spread lost its predictive power after 1985 in linear models. Nevertheless,

other studies using binary models to predict recessions could successfully ex post predict the 1990

recession (Estrella and Mishkin, 1998). Default spreads are the differences between interest rates

of bonds with different degrees of default risk. Bernanke (1983) found that the “Baa-Treasury”

spreads could well predict industrial production growth duting the interwar period. Stock and

Wat-son (1989) and Friedman and Kuttner (1992) used the “paper-bill” spread as a predictor for output

growth and got a sufficiently high predictive content. The predictive power of default spreads are,

again, found unstable. Bernanke (1990) predicted output with paper-bill spread on two subsamples

and found that the predictive content weakened during the 1980s. This finding was confirmed by

other studies (Hafer and Kutan, 1992; Emery, 1996).

Recent studies found that credit spreads constructed using micro-level bond price information

has a significant marginal predictive content for real economic variables. Gilchrist, Yankov and

Zakrajˇ

sek (2009) used price information of over 5,000 individual US non-financial corporate bonds,

over the period from 1990 to 2008. It was found that the inclusion of such credit spread indices

significantly improved the predictive content of the model. Gilchrist and Zakrajˇ

sek (2012) also

constructed a “high-information-content” credit spread index using US micro-level bond price data,

but instead of sorting individual bonds into different groups based on their default risks, the authors

calculated a credit spread for each individual bond by subtracting the yield of a synthetic risk-free

bond from the yield of the bond, and composed all these individual spreads into one credit spread

index. The credit spread index was used to predict future real economic variables such as industrial

production and US non-farm payroll employment, and the marginal predictive power of the credit

spread index was sufficiently high. A similar study was undertaken by Gilchrist and Mojon (2014)

for several countries in the Euro area, and again, the predictive content for the entire Euro area

and individual Euro area countries were all substantial. In addition, Faust, Gilchrist, Wright and

Zakrajˇ

sek (2013) forecast real-time economic activities using a Bayesian model-averaging (BMA)

approach. Compared with a autoregressive benchmark, the predictive content of the BMA approach

was significantly improved, and the improvement was almost exclusively contributed by the inclusion

of credit spreads as a predictor.

In this study, a quantitative measure is needed as an indicator of the strength of the link between

the financial and real sectors. Since credit spreads are found to predict future real economic activities

very well, the predictive content of the credit spread index can be used to indicate how intimately

the two sectors are connected. A higher predictive content means that investors can better predict

future economic conditions and they take actions in advance according to their expectations; this

suggests a strong link between the real and financial sectors. If the predictive content is low, then

investors fail to predict future economic conditions that well, meaning that the real-financial link is

weak.

3

Extending the G&Z Credit Spread Index

The first step of this study is to construct a high-information-content credit spread following the

method introduced in Gilchrist and Zakrajˇ

sek (2012), and to extend this G&Z type credit spread

index forward up to the year 2016.

(as is introduced in Gilchrist and Zakrajˇ

sek, 2012):

P

[k] =

X

C(s)D

(t

)

, and

D

(t) = e

Here, P

[k] is the price at time t of the synthetic risk-free security corresponding to corporate bond

k issued by firm i. {C(s): s=1,2,...,S} is the sequence of cash flows of bond k, and thus of the

synthetic security as well. D

_{(t) is the discount factor for the cash flow at time t, with r}

t

being

the risk-free zero-coupon Treasury yield over period t, obtained from the US Treasury yield curve of

G¨

urkaynak Sack and Wright (2007). Out of P

[k] is calculated the yield to maturity y

[k]; this is

the risk-free yield of a synthetic Treasury security, whose duration matches with its corresponding

corporate bond.

The G&Z credit spread is then the difference between the yield of the corporate bond and the

yield of the matching synthetic risk-free security:

S

[k] = y

[k] − y

[k]

, where y

[k] is the yield to maturity of the corporate bond.

Price information of 5,324 outstanding U.S. non-financial corporate bonds are collected from

Thomson Reuters Datastream database. The method described above is carried out to calculate the

credit spread for each of these bonds. However, not all the credit spreads are ultimately adopted

in the construction of the final credit spread index. Also following Gilchrist and Zakrajˇ

sek (2012),

a few criteria should be applied to eliminate extreme observations. First, observations beyond the

range of 5 to 3500 basis points are eliminated. Second, bonds with an issued value of smaller than

$1 million cannot enter the sample as well. Finally, the remaining terms to maturity are limited

between 1 year and 30 years

_.

4,737 out of the 5,324 bonds survive the three criteria mentioned above. Table 1 summarizes

the descriptive statistics of these remaining bonds. Similar to Gilchrist and Zakrajˇ

sek (2012), most

firms have only a small number of bond issues, but the a few other firms have much more. This

unbalanced distribution in this study is even more positively skewed compared with Gilchrist and

Zakrajˇ

sek (2012), with the largest firm having so many as 358 bond issues. Besides, the mean value

of issue of bonds in this study are much higher than that in Gilchrist and Zakrajˇ

sek (2012), while

the minimum and median values of issue are not significantly higher. These facts mentioned above

suggest that this study has in its sample a few firms and bond issues that are much larger than those

included in Gilchrist and Zakrajˇ

sek (2012), while the majorities of the two samples are generally

similar.

Next, the credit spreads calculated from individual bond price information are composed into a

Table 1: Descriptive Statistics of US Non-financial Corporate Bonds

Variable

Mean

Std. Dev.

Min

Median

Max

Number of Bonds per Firm

3.384

11.283

1

2

358

Value of Issue ($ mil.)

1043.302

24879.54

1

250

1250000

Maturity at Issue (yrs)

23.303

13.63

10

27

100

Term to Maturity

19.319

5.85

10

19

30

Coupon Rate (pct.)

6.1

2.05

0.97

6.13

15.5

Credit Spread (bps.)

234

193

5

181

3497

G&Z type credit spread index following the formula:

S

=

1

N

X

X

S

[k]

N

is the number of observations of bonds at time t. It is simply the arithmetic average of credit

spreads of bonds issued by the firms in the sample. Figure 1 compares the credit spread index

constructed in this study with the index of Gilchrist and Zakrajˇ

sek (2012). Xu’s index starts in

January 1990 and extends up to April 2016, while Gilchrist and Zakrajˇ

sek’s credit spread index

ends earlier in September 2010. It can be seen that over the period from January 1990 to September

2010, both indices have rather similar shapes, although the peaks in Xu’s index are usually much

lower. The lower peaks can be explained by the fact that Xu’s sample only includes those bonds

that are still outstanding by April 2016 when this study is carried out. As a result, bonds issued by

the firms who failed to survive the 2008 global financial crisis are automatically filtered out of the

sample of this study. Therefore, firms in Xu’s sample are generally less risky, and thus the credit

spreads of the bonds issued by these firms are relatively lower. The difference between the two credit

spread indices becomes especially visible in crisis times when the market is extremely risk averse.

Another conspicuous difference between the two indices is the small peak in the Xu’s index around

the first half of 1991, which does not appear in the Gilchrist and Zakrajˇ

sek (2012) index. In Section

4 it will be discussed that the predictive power of Xu’s index in predicting employment growth

expectations largely outperforms the Gilchrist and Zakrajˇ

sek (2012) index around 1991, meaning

that this small peak in Xu’s index actually captures some features of credit spreads that is missing in

Gilchrist and Zakrajˇ

sek (2012). Besides, Section 4 will show that in spite of the differences between

the two indices, Xu’s index generally performs no worse than the Gilchrist and Zakrajˇ

sek (2012)

index in predicting employment growth.

4

Measuring the Link between Financial and Real Sectors

In this section an indicator is going to be generated that measures how strong the link is between

financial markets and the real sector. Xu’s extended G&Z type high-information-content credit

spread index is used in this section to predict the 3-month-ahead employment growth, and the R

of the predicting regression model indicates the predictive power, or in other words, the strength of

the real-financial link. In order to measure the strength of the real-financial link for each point of

0 1 2 3 4 5 6 7 8 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Gilchrist and Zakrajsek (2012)

Xu

Figure 1: Credit Spread Indices, January 1990 to April 2016

4.1

To measure the strength of real-financial link: data and method

The condition of real economy is represented with employment in this study. The US non-farm

pay-roll employment index is found on the website of Federal Reserve Economic Data of Federal Reserve

Bank at St. Louis

_{. This is a monthly reported index provided by the US Bureau of Labor}

Statis-tics, which measures “the number of U.S. workers in the economy that excludes proprietors, private

household employees, unpaid volunteers, farm employees, and the unincorporated self-employed”

_.

A simple ordinary least squares model is adopted to predict future employment growth with credit

spread:

∇

_{EM P}

t+h

= β

+ β

GZ

+ 

Here, GZ

is the G&Z type credit spread index constructed in Section 3, and ∇

EM P

is the

annualized growth rate of US employment between month t and t + h:

∇

_{EM P}

≡

12 × 100

h + 1

ln(

EM P

EM P

)

, which can be also interpreted as the h-month-ahead employment growth expectation. In this study

h = 3: Gilchrist and Zakrajˇ

sek (2012) have shown that the G&Z type credit spread index performs

quite well in predicting 3-month-ahead employment growth. Following previous studies

, the R

of

this regression model is estimated to measure the predictive power of the G&Z credit spread index

in predicting employment growth expectation, and is considered as the indicator of the strength of

the US real-financial link.

Such a regression model alone, however, can only generate one R

_{that measures the predictive}

4_{https://fred.stlouisfed.org/series/PAYEMS, retrieved on 15th July, 2016.} 5_{Same as in footnote 4.}

power of G&Z spread index over the entire sample of time. A moving-window approach is therefore

adopted, in order to generate a sequence of R

_{’s depicting the strength of real-financial link at every}

spot of time and illustrating the variations in the link strength over time. For instance, for month

t in the sample, the predicting regression model is estimated over a window period (t −

, t +

),

with w (which can be 12, 24, 36 or 48 months) being the width of the window. The R

_{is estimated}

and is assigned to month t, representing the strength of the US real-financial link around month t.

The window then moves from month t to month t + 1, and the same procedure is carried out once

again over the window period (t + 1 −

2

, t + 1 +

w

2

). As the w-month wide window moves over

every month from month 1 to month T − h, a sequence of R

_{can be generated over the period (}

2

,

T − h −

).

G&Z type credit spread index

Figure 2: ∇

EM P

and G&Z Credit Spread Index

The time range of the moving-window predicting process introduced above is set between January

1973 and April 2016. Data over these more than 40 years are put under the investigation of this

study, so as to capture as many details of the real-financial link as possible. However, due to the

lack of accessibility to data before January 1990

, it is difficult for this study to extend its own

G&Z spread index backward to earlier years. Therefore, this study directly adopts the credit spread

index constructed in Gilchrist and Zakrajˇ

sek (2012) for the period from January 1973 to December

1989. Such a compromise can help extend the time range of this study, but it may also bring about

potential inconsistency in the G&Z spread index as a whole. A robustness check introduced in a

later section is carried out to examine this potential defect.

In order to more smoothly connect the Gilchrist and Zakrajˇ

sek (2012) index with the Xu’s index,

7_{Gilchrist and Zakrajˇsek (2012) rely on the Lehman/Warga database for bond price information of earlier years.}

a technique is applied. First, the growth rate of the Gilchrist and Zakrajˇ

sek (2012) credit spreads

between every pair of neighbouring months from January 1973 to January 1990 is calculated. Then,

the credit spreads for the months between January 1973 and December 1989 that will be used in later

analysis of this study is backward projected based on (1) Xu’s January 1990 credit spread and (2)

these growth rates. For example, using Xu’s January 1990 credit spread and the growth rate between

Gilchrist and Zakrajˇ

sek’s credit spreads of December 1989 and January 1990, the credit spread of

December 1989 can be projected. On that basis, using the just projected December 1989 credit

spread and the growth rate between November and December 1989, the credit spread of November

1989 can also be projected. Repeatedly, the whole index of credit spreads between January 1973

and December 1989 can be projected, which moves in the same way as the Gilchrist and Zakrajˇ

sek

(2012) index, and connects smoothly with the Xu’s index after January 1990.

Figure 2 shows the G&Z type credit spread index used in the predicting process over the full time

range from January 1973 to April 2016, together with the 3-month-ahead employment growth

expec-tation (∇

_{EM P}

t+3

) series over the same period. Figure 2 illustrates generally opposite movements

of both series: in most cases, the G&Z spread index rises when the 3-month-ahead employment

growth expectation drops, and goes low when employment growth expectation hikes. These features

generally supports the argument that credit spread can predict future real economy data.

4.2

Going for bonds with longer remaining terms to maturity

In the next stage, the sequence of R

_{’s will be generated as an indicator of the strength of the}

real-financial link, but before showing and discussing the characteristics of the R

sequence, there is

a small innovation of this study to introduce. As is mentioned in Section 3, Gilchrist and Zakrajˇ

sek

(2012) impose a restriction that only bonds with remaining terms to maturity between 1 year and

30 years can enter their sample. This study, however, goes for bonds with longer remaining terms

to maturity, because G&Z spread indexes composed of relatively longer-term bonds perform better

in predicting employment growth expectations.

Figure 3 plots R

_{sequences estimated from credit spread indexes with different requirements on}

remaining terms to maturity. The heavy blue line belongs to the sequence complying with the 1 to

30 years requirement, as suggested in Gilchrist and Zakrajˇ

sek (2012). It can be seen that compared

with the blue line, most other lines (with longer-term bonds) indicate better predictive power of

G&Z spread index almost over the entire period after the year 2007

_{. The higher predictive powers}

of credit spread indexes constructed using longer-term bonds can be explained by the sensitivity of

bond prices to news on future shocks. Consider a typical coupon bond in the sample of this study:

the price of this bond is theoretically decided by its discounted future cash flows. For a

close-to-maturity bond, the discounted payment of its principal makes up a decisive component of the bond

value. As a result, the bond price may not be sensitive enough to news about a shock in three

months, but will rather be mainly influenced by a shock at around its maturity time. However, for

a bond with a very long remaining term-to-maturity, its principal payment is in remote future and

is heavily discounted, and is therefore not very likely to be such a decisive component in the bond

price. In this case, the effect of a shock in three months will be more visibly reflected in the bond

0.0 0.2 0.4 0.6 0.8 1.0 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Term-to-maturity 1 year to 30 years

Term-to-maturity 10 to 30 years Term-to-maturity over 10 years Term-to-maturity over 20 years Term-to-maturity over 30 years

Figure 3: Sequences of Predictive Powers (window width = 48 months): Different Term-to-Maturity

Requirements

price. An explanation like this, though, cannot explain the poor performance of the G&Z index

composed of the longest-term bonds, those with remaining terms to maturity of more than 30 years.

This, however, is simply because the over-strict requirement on remaining terms to maturity filters

out too many observations, especially for earlier years. Among all the candidate term-to-maturity

requirements, the 10-to-30-years requirement is chosen as the criterion imposed in this study, because

it ensures in most times relatively high R

_{’s compared with other candidates. 2,452 bonds survive}

this stricter requirement and are ultimately used to compose the credit spread in this study. All

these 2,452 bonds are listed in Appendix 1.

Section 3 mentions that, although this study constructs the G&Z spread index using different

data from Gilchrist and Zakrajˇ

sek (2012) (and following a different term-to-maturity requirement

as is just discussed), the predictive power of Xu’s index is generally not worse than the Gilchrist

and Zakrajˇ

sek (2012) index. Figure 4 plots two R

_{sequences generated using respectively Xu’s}

index and that constructed in Gilchrist and Zakrajˇ

sek (2012). It is clear that from January 1990

to September 2010, Xu’s index almost always has R

’s no lower than the other sequence, and even

largely outperforms the Gilchrist and Zakrajˇ

sek (2012) index between late 1991 and early 1994.

This period coincides with the peak that appears in Xu’s index but is missing in the Gilchrist and

Zakrajˇ

sek (2012) index, suggesting that Xu’s index can actually capture more characteristics of

0.0 0.2 0.4 0.6 0.8 1.0 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Predictive power using Gilchrist and Zakrajsek (2012) credit spread index

Predicitve power using Xu's G&Z spread index

Figure 4: Sequences of Predictive Powers (window width = 48 months): Xu’s Credit Spread Index

versus the Gilchrist and Zakrajˇ

sek (2012) Index

4.3

Sequences of real-financial link

Figure 5 displays the R

_{sequences that represent the strength of the US real-financial link from}

January 1973 to April 2016, generated with different widths of moving window. Bubble and recession

periods are also marked in each sub-figure as dummy variables. The NBER based recession indicators

are adopted here to mark recession periods, and the bubble periods are determined based on the

studies of Phillips and Yu (2011); Phillips, Wu and Yu(2011); and Phillips, Shi and Yu (2015)

. The

definitions of bubble and recession periods will be discussed in detail in Section 5. The descriptive

statistics of the R

_{sequences are summarized in Table 2.}

Table 2: Descriptive Statistics of R

_Sequences

Obs.

Mean

Median

Maximum

Minimum

Std. Dev.

R

_{(Win.wid.=12mon)}

₅₀₉

_0.327

_0.276

_0.930

_2.94E-05

_0.278

R

_{(Win.wid.=24mon)}

₄₉₇

_0.366

_0.302

_0.940

_4.76E-06

_0.300

R

_{(Win.wid.=36mon)}

₄₈₅

_0.405

_0.422

_0.932

_5.64E-06

_0.291

R

_{(Win.wid.=48mon)}

₄₇₃

_0.443

_0.458

_0.912

_9.70E-07

_0.278

On average the G&Z type credit spread index alone can capture 32% to 44% of the total variance

of 3-month-ahead employment growth expectations. Considering the fact that the predicting model

is a simple OLS regression model with only one explanatory variable, we can say that the G&Z

type credit spread is indeed a high-information-content predictor for employment data. However,

the predictive power of G&Z index does not always stay at this level. In fact, a remarkable feature

of these R

_{sequences that can be observed from Figure 5 and Table 2 is their high volatilities. All}

9_{However, some adjustments are made upon Phillips et al.’s definitions of bubble periods. These changes will be}

the four R

sequences displayed in Figure 5 frequently fall to extremely low levels that are close

to zero, which means over the window period of, say, 48 months around the low position, credit

spread can explain almost none of the variance of employment growth expectations. This suggests

an extremely weak link between the financial and real sectors. On the other hand, the R

_sequences

also frequently reaches extremely high levels of over 0.8 and even 0.9, suggesting that over the, for

instance, 48 months around the high position, the real-financial link is so strong that credit spread

alone can explain almost all of the variance of the 3-month-ahead future employment growth.

The high volatility of the real-financial link suggests that we need to first find out what factors

are affecting the strength of the real-financial link, before we can compare on a reasonable basis the

strength of the real-financial link before and after the implementation of the US Federal Reserve’s

unconventional monetary policy measures.

A feature that can be observed from Figure 5 is that the real-financial link tends to be weaker

almost every time when there is a bubble or when the economy is in a recession; the R

tends to be

especially low in bubble periods. This feature can be explained in this way. During bubble periods,

the illusion about a long-lasting prosperity drives over-investments in bond markets. Irrationally

high demands for investment opportunities will push high bond prices and thus press down credit

spreads to a excessively low level. Investors care less than necessary about the bond issuers’ ability

to repay, so credit spreads will no longer reflect the riskiness and future profitability of the firm.

The over-optimistic emotion overwhelming the market will weaken the function of financial markets

of providing rational expectations on future real economic performances. Similarly, the pessimistic

emotion during recession periods can also weaken the link between financial markets and real

econ-omy. Due to the fear of loss and unawareness of the date of economic recovery, investors are reluctant

to make any financial investments. The riskiness and future profitability therefore cannot be truly

reflected in bond prices and credit spreads, either.

0.0 0.2 0.4 0.6 0.8 1.0 1973m1 1973m7 1974m1 1974m7 1975m1 1975m7 1976m1 1976m7 1977m1 1977m7 1978m1 1978m7 1979m1 1979m7 1980m1 1980m7 1981m1 1981m7 1982m1 1982m7 1983m1 1983m7 1984m1 1984m7 1985m1 1985m7 1986m1 1986m7 1987m1 1987m7 1988m1 1988m7 1989m1 1989m7 1990m1 1990m7 1991m1 1991m7 1992m1 1992m7 1993m1 1993m7 1994m1 1994m7 1995m1 1995m7 1996m1 1996m7 1997m1 1997m7 1998m1 1998m7 1999m1 1999m7 2000m1 2000m7 2001m1 2001m7 2002m1 2002m7 2003m1 2003m7 2004m1 2004m7 2005m1 2005m7 2006m1 2006m7 2007m1 2007m7 2008m1 2008m7 2009m1 2009m7 2010m1 2010m7 2011m1 2011m7 2012m1 2012m7 2013m1 2013m7 2014m1 2014m7 2015m1 2015m7 2016m1 Bubb le Per iods

Rece ssion Periods

Pred ictive p ower (R-square d), window width = 12 months

(a) Window width = 12 months

0.0 0.2 0.4 0.6 0.8 1.0 1973m1 1973m7 1974m1 1974m7 1975m1 1975m7 1976m1 1976m7 1977m1 1977m7 1978m1 1978m7 1979m1 1979m7 1980m1 1980m7 1981m1 1981m7 1982m1 1982m7 1983m1 1983m7 1984m1 1984m7 1985m1 1985m7 1986m1 1986m7 1987m1 1987m7 1988m1 1988m7 1989m1 1989m7 1990m1 1990m7 1991m1 1991m7 1992m1 1992m7 1993m1 1993m7 1994m1 1994m7 1995m1 1995m7 1996m1 1996m7 1997m1 1997m7 1998m1 1998m7 1999m1 1999m7 2000m1 2000m7 2001m1 2001m7 2002m1 2002m7 2003m1 2003m7 2004m1 2004m7 2005m1 2005m7 2006m1 2006m7 2007m1 2007m7 2008m1 2008m7 2009m1 2009m7 2010m1 2010m7 2011m1 2011m7 2012m1 2012m7 2013m1 2013m7 2014m1 2014m7 2015m1 2015m7 2016m1 Bubble pe riods Recession Perio ds

Predictive power (R-squared), window width = 24 months

(b) Window width = 24 months

0.0 0.2 0.4 0.6 0.8 1.0 1973m1 1973m7 1974m1 1974m7 1975m1 1975m7 1976m1 1976m7 1977m1 1977m7 1978m1 1978m7 1979m1 1979m7 1980m1 1980m7 1981m1 1981m7 1982m1 1982m7 1983m1 1983m7 1984m1 1984m7 1985m1 1985m7 1986m1 1986m7 1987m1 1987m7 1988m1 1988m7 1989m1 1989m7 1990m1 1990m7 1991m1 1991m7 1992m1 1992m7 1993m1 1993m7 1994m1 1994m7 1995m1 1995m7 1996m1 1996m7 1997m1 1997m7 1998m1 1998m7 1999m1 1999m7 2000m1 2000m7 2001m1 2001m7 2002m1 2002m7 2003m1 2003m7 2004m1 2004m7 2005m1 2005m7 2006m1 2006m7 2007m1 2007m7 2008m1 2008m7 2009m1 2009m7 2010m1 2010m7 2011m1 2011m7 2012m1 2012m7 2013m1 2013m7 2014m1 2014m7 2015m1 2015m7 2016m1 Bubble period s Recession pe riods

Predictive power (R-sq uared), wind ow width = 36 months

(c) Window width = 36 months

0.0 0.2 0.4 0.6 0.8 1.0 1973m1 1973m7 1974m1 1974m7 1975m1 1975m7 1976m1 1976m7 1977m1 1977m7 1978m1 1978m7 1979m1 1979m7 1980m1 1980m7 1981m1 1981m7 1982m1 1982m7 1983m1 1983m7 1984m1 1984m7 1985m1 1985m7 1986m1 1986m7 1987m1 1987m7 1988m1 1988m7 1989m1 1989m7 1990m1 1990m7 1991m1 1991m7 1992m1 1992m7 1993m1 1993m7 1994m1 1994m7 1995m1 1995m7 1996m1 1996m7 1997m1 1997m7 1998m1 1998m7 1999m1 1999m7 2000m1 2000m7 2001m1 2001m7 2002m1 2002m7 2003m1 2003m7 2004m1 2004m7 2005m1 2005m7 2006m1 2006m7 2007m1 2007m7 2008m1 2008m7 2009m1 2009m7 2010m1 2010m7 2011m1 2011m7 2012m1 2012m7 2013m1 2013m7 2014m1 2014m7 2015m1 2015m7 2016m1 Bubble pe riods Recession perio ds

Predictive power (R-squared), window width = 48 months

(d) Window width = 48 months

5

Explaining the Variations in the Strength of the

Real-Financial Link

Section 4.3 discusses a remarkable feature of the real-financial link that it is highly volatile over the

past more than 40 years of time, and highlights the necessity to investigate the factors leading to

the variations in the real-financial link before comparing the strength of the link before and after

the implementation of unconventional monetary policy. From Figure 5 a phenomenon is found that

the real-financial link seems to be usually weaker during bubble and recession periods, so bubbles

and recessions are two of the candidate variables to be included in the analysis of this section. Two

other factors, namely the general economic condition (employment growth in this context) and the

volatility of the 3-month-ahead employment growth expectations, are also considered.

It has been found in previous studies that financial market indicators can better predict future

economic slowdowns than booms, and multiple studies attempt to forecast economic recessions in

the history of the US using several financial market indicators, including credit spread

. Financial

markets tend to be more cautious about investment opportunities during bad times than in good

times, and will put more efforts in the investigation of a firm’s future profitability before investing on

financial securities issued by this firm. It is therefore reasonable to hypothesize that the predictive

power of the G&Z spread index is relatively higher when economic growth is slow than when the

economy grows fast.

The volatility of the expectation on economic condition (employment growth) can also be an

influential factor. When the market expects the economic condition to be stable over a certain

period of time, the influence of news about economic conditions on investors’ behaviour will fade.

Instead, other market information (noise) will stand out and disturb credit spread, so credit spread

will predict the real economy less well in economic-stable times. In contrast, when the market

expects a sharp change in the near future in the economy, either a sheer fall or a rapid hike of

economic growth, investors’ attentions will be drawn firmly to real economy news, and financial

market indicators such as credit spread will better reflect investors’ expectations on future real

economy.

The hypotheses are summarized as follows.

Hypothesis 1 The predictive power of the G&Z type credit spread index is negatively related with

the economic condition (trend of employment growth).

Hypothesis 2 The predictive power of the G&Z type credit spread index is positively related with

the volatility of the expectation on the 3-month-ahead employment growth.

Hypothesis 3 The predictive power of the G&Z type credit spread index is lower during bubble

periods.

Hypothesis 4 The predictive power of the G&Z type credit spread index is lower during recession

periods.

The trend of monthly US employment growth is used to indicate the general economic condition

of the United States. The annualized monthly US employment growth is calculated according to

the formula

∇EM P

≡ 12 × 100ln(

EM P

EM P

)

, and short-term fluctuations in the US employment growth series is then filtered out using the

Hodrick-Prescott trend filter. The remaining trend variable of employment growth is denoted as

T rend[∇EM P

].

The volatility at time t of the market’s expectation on future economic condition is measured

with the absolute change in the 3-month-ahead employment growth expectations between months

t − 3 and t + 3:

|∆(∇

_{EM P )|}

t

≡ |∇

EM P

− ∇

EM P

|

If the absolute change is large, it means over the half year around time t there is either a sharp

increase or a sheer drop in employment growth expectations. If the absolute change is small, it

means the economic growth is generally stable over the 6 months around time t.

As is mentioned in Section 4, the bubble and recession periods are represented with two dummy

variables. Recession periods are marked following the NBER recession indicators, and the bubble

periods are determined based on Phillips and Yu (2011); Phillips, Wu and Yu(2011); and Phillips,

Shi and Yu (2015). Technically the exact date of emergence of an economic bubble is usually hard

to define. Phillips et al. provide a solution by date-stamping the beginning and the end of asset

bubbles using rolling-window unit root test techniques. Nevertheless, a problem of Phillips et al.’s

definition of bubble periods prevents it from being directly adopted into this study: their bubble

periods are often too wide, sometimes even covering the NBER defined recession periods. This is

because their method is intended to mark the entire period from the emergence of the bubble until

the point when the bubble completely collapses. The bubble, however, can be considered as already

burst for the period after the moment when the price of the underlying asset starts to fall. Therefore

in this study, the starting dates of bubbles defined by Phillips et al. are accepted, while the ending

dates of bubbles are set at the points when the underlying asset prices start to fall.

Three bubble periods are marked between January 1973 and April 2016: the bubble before Black

Monday in October 1987 (1986M06-1987M09), the dot-com bubble (1995M11-2000M03) and the US

housing bubble (2002M05-2006M11). No bubble periods are defined after the 2008-2009 recession,

because there have not been clear evidence whether there is a bubble in that period. For instance,

in the short report published on the Business Times in June 2013, Phillips and Yu undertook the

same method as they designed in their earlier studies, but used more recent data. According to their

results, no new bubble was found by that time.

The descriptive statistics of the four variables are summarized in Table 3.

Table 3: Descriptive Statistics of the Four Variables

Mean

Median

Max.

Min.

Std.Dev.

Obs

Emp.Grwth.Trend

1.487

1.663

4.172

-2.071

1.330

519

Abs.Chng.Emp.Grwth.Expct.

1.235

0.748

9.307

4.43E-04

1.406

510

Bubble

0.238

0.000

1.000

0.000

0.427

520

Recession

0.144

0.000

1.000

0.000

0.352

499

in 3-month-ahead employment growth expectations: both of them are over 0.4. In order to

sta-tistically test whether there exists multicollinearity, the variance inflation factors (VIFs) are also

calculated as is reported in Table 5. We can see that none of the four variables has a VIF greater

than 5, suggesting that there are no severe multicollinearity problem in the regression models.

Table 4: Correlation Table

(1)

(2)

(3)

(4)

(1)Emp.Grwth.Trend

1

(2)Abs.Chng.Emp.Grwth.Expct.

-0.298

1

(3)Bubble

0.129

-0.300

1

(4)Recession

-0.481

0.422

-0.239

1

Table 5: Variance Inflation Factors

Variable

Coefficient variance

Uncentered VIF

Centerd VIF

Constant

5.93E-04

5.087

NA

Emp.Grwth.Trend

8.38E-05

2.852

1.320

Abs.Chng.Emp.Grwth.Expct.

7.57E-05

2.346

1.301

Bubble

6.93E-04

1.494

1.119

Recession

1.391E-03

1.739

1.486

OLS regression models are estimated to test the hypotheses, with the dependant variables being

the R

_{sequences with different widths of moving windows shown in Figure 5. The regression model}

is formulated as

R

= β

+ β

T rend[∇EM P

] + β

|∆(∇

EM P )|

+ β

Bubble + β

Recession + 

The regression results are reported in Table 6. The adjusted R

_{’s of the four regression models}

range from 0.248 to 0.303, indicating a sufficient but not very high goodness of fit. It can be seen that

in all four cases with different moving window widths, the coefficients of both the trend of

employ-ment growth and the absolute changes in the employemploy-ment growth expectations are statistically and

economically significant, with signs consistent with the hypotheses. The coefficients of Bubble and

Recession are relatively less definite. The coefficients of Recession are all negative (consistent with

Hypothesis 4) and are significant in three of the four regressions, except when the moving window is

24 months wide. The coefficients of Bubble are significantly negative (consistent with Hypothesis 3)

when the moving window is narrow (12 or 24 months wide), but are insignificant when the moving

window is wide (36 or 48 months) and even become positive when the window is 48 months wide.

It is difficult to explain why the coefficients of Bubble become insignificant and even positive, if

we do not take into account the effect on the R

sequence of using wide moving windows. As we

widen the moving window, information over a longer period around time t are used to estimate the

strength of the real-financial link around t. As a result, the R

number assigned to time t is less

accurate. Considering a bubble period, when the window is 48 months wide, information from 2 years

of normal time before and 2 years after the bubble period are included to calculate the link strength

for the bubble period, which will lead to higher-than-real bubble-period link strength estimations.

It can be seen from panel (d) of Figure 5 that although for each bubble period there is still always