DBJ Discussion Paper Series, No.1004

Walking After Midnight:
Measurements and Pricing Implications ofMarket Liquidity on Corporate Bonds
Daisuke Miyakawa(Research Institute of Capital Formation,
Development Bank of Japan)
andShuji Watanabe(Research Institute of Capital Formation,
Development Bank of Japan andFaculty of Economics, Gakushuin University )October

2010

Discussion Papers are a series of preliminary materials in their draft form. No quotations,reproductions or circulations should be made without the written consent of the authors inorder to protect the tentative characters of these papers. Any opinions, findings, conclusions
or recommendations expressed in these papers are those of the authors and do not reflect
the views of the Institute.

Walking After Midnight:
Measurements and Pricing Implications ofMarket Liquidity on Corporate Bonds ∗October 2010
Miyakawa, D. † and S. Watanabe ‡Development Bank of Japan and Gakushuin University

Abstract
This paper proposes a theoretically motivated proxy for the degree of market liquidity in corporate bond market(GAP: the highest minus lowest simultaneously reported spreads among multiple market makers), and studies its
pricing implication by quantifying the correlation between GAP and the median reported spreads among market
makers, which presumably approximate market prices conjectured by market makers. While the issue of market
liquidity has been extensively examined over the last decade for stock and sovereign bond markets, ourunderstanding is still limited for corporate bond market mainly due to the unavailability of widely acceptedliquidity proxies, such as bid-ask spreads in other markets. Through various panel estimations for the medianreported spreads in Japanese corporate bond market, we find that (i) inclusion of the lagged GAP to the standard
multi-factor model significantly improves the explanation power, (ii) the quantitative impact of such an illiquidity
measure on bond spreads becomes larger as credit ratings get worse, (iii) the GAP proxy is valid even after
controlling the persistency on spreads, which has been considered as another proxy for illiquidity in the extant
literature (i.e., resiliency), and (iv) the degree of such persistency increases as the credit ratings of corporate bonds
deteriorate. These results jointly explain how market makers construct their opinions about bond prices by (a)learning from the dispersion of reported prices, (b) recalling the past reporting, as well as (c) considering standard
covariates of bond spreads (i.e., JGB Yield, credit ratings etc). Our results also support the empirical implication
provided by theoretical literature on the correlation between the degree of opinion differences and market liquidity
premium.

Key words: Corporate Bond Spreads; Illiquidity Measure; Difference in Opinion
JEL Classification: E44, G01, G12, C23, C58

We appreciate Yohei Yamamoto (University of Alberta), Kei Kawakami (Melbourne University), and Hidehiko Ishihara (Senshu
University) for their highly suggestive comments. We also thank seminar participants at DBJ Applied Economics Workshop, Tokyo
University Macro-Finance, Monetary Economics and International Finance Workshop, Bank of Japan IMES workshop, Summer
Workshop for Economic Theory 2010 at Hokkaido University, Institution of Statistical Research Summer Conference 2010, andanonymous practitioners in a number of security firms for useful comments and suggestions. We also greatly appreciate forTomonori Matsuki, Takeshi Moriya and Junpei Kanemitsu for their excellent research assistant works.
† Corresponding Author, Associate Senior Economist, Research Institute of Capital Formation, Development Bank of Japan, 1-9-3
Otemachi Chiyoda-ku, Tokyo, 100-0004 JAPAN. E-mail: damiyak@dbj.jp.
‡ Special Visiting Professor, Faculty of Economics, Gakushuin University, 1-5-1 Mejiro Toshima-ku, 171-8588 JAPAN. E-mail:shuji.watanabe@gakushuin.ac.jp. Chief Economist, Research Institute of Capital Formation, Development Bank of Japan, 1-9-3
Otemachi Chiyoda-ku, Tokyo, 100-0004 JAPAN. E-mail: shwatan@dbj.jp.
∗

- 1 -

1. Introduction
During the past financial crisis including the recent episode triggered by "Lehman
shock", we have observed large time-series and cross-sectional variations in asset prices(stock prices, corporate bond spreads etc), which are not necessarily co-moving well withothers, and occasionally show bumpy dynamics (Figure-1). As demonstrated in a numberof extant studies, however, classic asset pricing models focusing on credit risk factors
cannot generally explain these actually observed asset price variations (Collin-Dufresne etal. (2001)). Responding to the presumption that such a misalignment between model
prediction and data is sounding particularly when the liquidity of markets dries up as wellas the volumes and frequencies of trades are plunging, it has been a main concern in thefield of asset pricing over the last decade to search appropriate proxies for liquidity factors.
Following such a strand of literature, this paper proposes one theoreticallymotivated proxy particularly targeting the market liquidity of corporate bonds (GAP: thehighest minus lowest simultaneously reported spreads among multiple market makers).
We study its pricing implication by quantifying the correlation between GAP and the
median reported spread, which we believe approximates the market price conjectured bymarket makers. 1
To motivate the research question featuring corporate bonds and necessitate theusage of the multiple quote data from market makers, we should recall the characteristics
of corporate bond markets. Namely, most of the investors of corporate bonds rely on “buy& hold” type investment strategy, the transaction volume is usually limited and, reflecting
this, market making is not very active for corporate bonds, which is different from themarkets with highly frequent trades as stock market. 2

Under such illiquid market

environment, it is not easy even for the professional market makers to find out a “unique”
market clearing price. As a result, the quote of market makers has some distribution
with non-zero variance and the distribution seldom converges to one point, which reflects

1 In this paper, the asset price of corporate bond is represented by “spread” which denotes the yield difference between corporate bonds and Japanese
Government Bond (JGB).
2 As far as we know, even the U.S. and Euro corporate bond markets do not have highly liquid secondary markets where we can occasionally observe
actual trading prices. Recent initiatives in Asian countries promoting corporate bond markets further exemplify how the current environment in the
Asian corporate bond markets are far behind the U.S. and Euro markets.

- 2 -the divergence or heterogeneity on market maker’s bond evaluation. 3 In this paper, wetake a view that corporate bond market is one illustrative example of such an illiquidmarket generically with low frequencies of trades. Notably, the extant studies for theasset pricing implication of market liquidity have been focusing on the markets having acertain volume of trades most of the time, where researchers could observe actuallytransacted prices without any difficulty, and widely accepted liquidity proxies, such asbid-ask spreads, are available. In the markets for corporate bonds, CDO, ABS, and manyother financial markets, however, we could at most observe quoted prices and/or estimatesprovided by market makers from the reason described above, and it is relatively difficult to
use the liquidity proxies referenced in other markets. 4 Such a nature of the corporatebond markets motivates us to study how multiple market makers construct their opinions
about bond prices, and how the median reported spread vary with the diverged opinions.
The data we analyze is provided by Japan Securities Dealers Association (JSDA).
Consistent with our presumption about corporate bond markets, the data of market
makers’ reporting prices are just indication and no obligation of trade with those prices.
In this sense, what we observe would be rather the market makers’ best guess on themarket clearing prices. 5 Note that a series of extant studies taking into account several
notions of liquidity tend to treat the bond spreads as market-clearing prices and apply the
analytical framework mainly used for more liquid market such as stock markets orsovereign bond markets. The starting point of our paper is to recognize the spreads dataas the evaluation of corporate bonds provided by market makers and study how market
makers alter their conjecture about market clearing prices with considering the variationin the distribution of reported prices by multiple market makers.
In order to preview how the GAP measure is informative, Figure-2 (1) depicts theshare of firms staying under a certain level of GAP (i.e., equal to or smaller than 5, 10, 15,
and 20bp) out of the total sample firms at each date. For example, the share of firms
3 Recent development of market microstructure literature considers this aspect and tries to model how the heterogeneous belief or the disagreement
among market makers on public information generates the dynamics of trade volume (Banerjee and Kremer (2010)) and prices (Tychon and
Vannetelbosch (2005)).
4 In fact, Japan Security Dealers Association (JSDA) from which we obtain our data stores almost no data for bid-ask spreads although they prepare
the category for recording.
5 Even Euro markets cannot provide the complete set of the actual transaction prices in daily base. Recently, the accessibility of the corporate bonddata in the U.S. has been largely improved by FINRA TRACE Corporate Bond Data (http://www.finra.org/).

- 3 -showing GAP smaller than 5bp reached more than 80% in the second half of 2005 where
the market condition was relatively good and the liquidity was presumably high. In
contrast, there were several periods where such a share went below 10% (e.g., 2003,
2008-2009). It seems that these dynamics coincide to some extent with the change inmarket condition. Our guess is if the market is illiquid, such a market condition isrepresented by the larger GAP for a given corporate bond, and the spreads become wider.
Such a view on the correlation between the heterogeneous views about bondprices, which presumably works as a proxy for liquidity, and the corporate bond spreads
has been gradually accepted in theoretical literature (Tychon and Vannetelbosch (2005),
Banerjee et al. (2009), Cao and Ou-Yang (2009), Banerjee and Kremer (2010)). Only a few
studies (Hauweling et al. (2003)), however, establishes the quantitative results directly
corresponding to their theoretical prediction. This paper intends to contribute to thisrecent development of empirical studies by using the GAP measure to proxy the illiquidityof individual corporate bonds. 6
As detailed later, another characteristic of our data is the persistency on thequoted median bond spread provided by market makers.

This property can beunderstood in the context of "resiliency" concept discussed in classic market liquidity
literature (e.g., BIS (1999)), which is another good illustration for illiquid markets.7 This
induces us to consider the time-series measurement of market illiquidity as well as the
cross-sectional measurement such as GAP. As in the extant studies (Nakamura (2009)),
we can infer the illiquidity of corporate bonds by checking whether the reported prices bymarket makers has persistency or some stickiness. If the market becomes highly illiquid,
the lesser portion of their quotes depends on the concurrent information and we willobserve the stronger persistency in their previous quotes.
To summarize, the purpose of our quantitative discussion is to illustrate that themarket makers price corporate bonds not only by (a) considering standard covariates ofbond spreads, but (b) learning from the dispersion of reported prices by other market
6 It is natural to conjecture the positive correlation between the GAP measure and firm's credit worthiness. As we will demonstrate later, the panel
estimation we employ in this paper is suitable to disentangle those two correlated effects.
7 A standard definition of the resiliency is the speed of the restoration of normal market prices. The extant literature has been treating this as one
independent dimension representing market liquidity.

- 4 -makers as illustrated above, as well as (c) recalling the past reports, which eventually gives
us a tip for understanding various other low liquid financial securities such as ABS, CDO,
and securitized products. Another interest of this paper is also in understanding themarket maker's forecast for the market-clearing prices. Shedding light on the pricing
mechanism of those illiquid assets would be very useful to understand the financial
markets that have been facing tremendous difficulty in objective evaluation. 8
Through such an analysis, we also attempt to provide an empirical evidence of theso called "Flight-to-Liquidity" view. If the sensitivity of bond spreads with respect toilliquidity measure differs among different credit ratings, it can be interpreted as thereflection of the investor’s attitude toward low credit quality.
This paper is structured as follows. Section 2 briefly surveys the related
literature.

Before going into empirical studies, we go over a theoretical framework

motivating the following empirical section in section 3. Then, section 4 goes over our
empirical framework and formulates our hypothesis. Section 5 and 6 describe the dataand shows the estimated results, respectively. Section 7 compares our empirical resultswith existing studies. Section 8 concludes and presents future research questions.

2. Related Literature
In this section, we briefly survey the related literature to our study. In the long
strand of asset pricing literature, there are three types of papers we need to consider. The
first group is the theoretical study for the relationship between illiquidity and asset prices.
In the context of market microstructure, there are a few theoretical studies explicitly
modeling the market illiquidity risk considered in our paper. A theoretical model closest
to our motivation is Tychon and Vannetelbosch (2005), which develops a corporate bondvaluation model containing both the credit risk and the liquidity/marketability risk
generated by a matching friction between bondholders and potential investors in asecondary market. They assume that each bondholder is matched with whole populationin illiquid market, which might not result in the match up providing the gain from trade,
8 It is highly difficult to directly observe the prices of so called "Level-3 assets" categorized by U.S. Financial Accounting Standard Boards and SEC.

- 5 -while the matching is guaranteed to always generate the gain in liquid market.9 Theirmain idea is that the liquidity premium is actually coming from the interaction between (i)the difference of matching frictions under the illiquid and liquid market environments, and(ii) the heterogeneity of investors’ valuations. To illustrate, bondholders/investors put
lower relative value on the bonds in the illiquid market than in the liquid market as theheterogeneity of belief becomes larger.

This is because it becomes less likely forbondholders/investors to find an appropriate counterpart to sell the bonds in future as thematching friction is amplified by larger heterogeneity.10 Most of the theoretical models
categorized as “inventory model” share the similar perspective. Although our data is notprecisely an actual transaction price, we believe the GAP measure briefly described in theprevious section can capture the degree of heterogeneity on the belief among market
makers.
The recently developed "differences of opinion literature" (Banerjee et al. (2009),
Cao and Ou-Yang (2009), Banerjee and Kremer (2010)) further pursues this direction.
They construct a theoretic model incorporating investors with heterogeneous belief aboutcommon public information and characterize how such heterogeneous views are reflected
in market maker’s opinion, market prices (average opinion), and trading volumes throughlearning process.11
There also exist several other theoretical explanations for why illiquid financial
securities need to be accompanied with higher premium from the stand point of investor’sliquidity demand (e.g., Holmstrom and Tirole (2001)) or transaction cost (Acharya andPedersen (2005)). 12 Instead of digging into such theoretical pricing foundation of liquidity
risk, we intend to establish empirical findings which can contribute to the development of
those theoretical studies.
Papers in the second category are the ones performing a classic empirical analysis
9 In other words, each bondholder will be matched with the investor who put higher evaluation for the bond held by the bondholder.

They assume
that the liquidity market makes it possible to have such a profitable matching always.
10 Consider the environment with no heterogeneous belief. Regardless of the matching friction, no trade emerges and the heterogeneity among
bondholders/investors do not matter.
11 Easley and O'Hara (2010) constructs a model generating equilibrium quotes and the nonexistence of trading at the quotes, which can be observedin financial crisis period.
12 Liquidity Asset Pricing Model(LAPM) in Holmstrom and Tirole (2001) studies the endogenous determination of liquidity premium, which is treatedas somewhat ad-hoc in the previous literature. Their main idea is (i) investor’s optimal choice generates liquidity preference and (ii) corporate bondspreads are determined in a general equilibrium framework.

- 6 -for corporate bond spreads.

The key implication shared by the literature is theinsufficient ability of macro and/or micro credit factors to explain the corporate bondspreads (e.g., Jarrow et al. (2000), Edwin et al. (2001), Huang and Huang (2003), Eom et al.
(2004)). For example, Collin-Dufresne et al. (2001) confirms that credit risk factors cannot
explain bond spreads even after incorporating various aggregate variables (e.g., S&P 500
returns, the slope of sovereign bond yields, the sovereign yields etc.) into the estimation.
Note this empirical finding is discussed in another form as “Credit Spread Puzzle”. The
seminal works by Hull et al. (2004、2005) show that the default probability implied by the
corporate bond yield in the secondary market is more than ten times that the default rate
calculated from the historical data. They also point out that there exists a significant gap
between corporate bond spread and CDS spread. It is our motivation to fill such aninconsistency between the classic model prediction and the observed data.
These results naturally motivate the third strand of the papers on the empiricalanalysis incorporating illiquidity factor.

This literature starts from choosing anappropriate proxy capturing market-level liquidity. Most of the extant studies (Fleming(2003), Goldreich et al. (2005)) in this direction use the sovereign bond yield which istheoretically not affected by credit factor in order to evaluate the performance of various
proxies. Then, with controlling those established market-level liquidity proxies, several
papers started to further incorporate individual liquidity factor. Amihud (2002) is apioneering paper for measuring such an individual illiquidity by introducing ILLIQ
measure, which is computed as the average of daily variation in stock return13. Including
this ILLIQ measure, Houweling et al. (2005) comprehensively studies several illiquidity
factors associated with individual company and portfolio to a standard multi-factor modeland establishes the illiquidity premium by using the data in euro area. Our paper has avery close motivation to their paper. The difference is that we use panel estimation
techniques to analyze the conditionality of the impacts of market liquidity and verify therobustness by also incorporating a classic liquidity proxy (resiliency) explicitly.
13 Precisely speaking, the ILLIQ measure is computed as the absolute price change divided by trading volume for a given stock on a given day.

For

Since
this ratio is a very noisy measure on any day, in practice, it is averaged over all trading days in a month or year to get a monthly or annual liquidity
estimate for the targeted stock.

- 7 -quantifying the pricing implication of illiquidity risk for stocks, Acharya and Pedersen(2005) directly incorporates the "illiquidity transaction cost" notion to an otherwise
standard CAPM structure and price the illiquidity risk explicitly.14 Apart from these
papers originated from a standard factor model specification, Bao et al. (2008) studies theprice dynamics of corporate bonds and establishes a proxy of corporate bond's market
liquidity from the dynamics. Our paper shares the spirit with their study that the pricedynamics has some information related to market liquidity15.
About Japanese corporate bond market, the existing studies are rather limited.
First, in the recent paper, Hongo and Oyama (2010) studies the mechanism governing thecorporate bond spreads through a model without liquidity factor. Second, the importanceof liquidity factor is studied in Saito et al. (2001) and Hori et al. (2008) by explicitly focusing
on Holmstrom and Tirole (2001) type liquidity demand. Shirasu and Yonezasa (2008) also
challenge the same question by using Japanese corporate bond market data. Third,
Nakamura (2009) employs two methods to quantify the illiquidity risk on bond spreads,
which largely shares its motivation with our paper. One difference is on our novel proxyfor bond illiquidity and the estimation strategy.

3. Theory: Heterogeneous Belief and Corporate Bond Spreads
In this section, we review one theoretical underpinning of the relationshipbetween corporate bond spreads and the distribution of the quote provided by market
makers. Our target is the simple presentation of an economic idea demonstrated in
Tychon and Vannetelbosch (2005), which motivates the following empirical sections; noattempt is made to provide either exhaustive survey or create original theoretical models.

3-1. Model
The economy consists of many risk-neutral potential investors and bond holders.

14 Although our paper does not have an explicit asset pricing formulation as theirs, the model structure is actually an extension of Fama and French(1993). In this sense, we follow to some extent a traditional factor model/CAPM structure.
15 Bao et al. (2008) hypothesizes that the amount of price reversal or the negative of auto-covariance of prices is associated with the illiquidity ofcorporate bonds, with referring to the extant theoretical studies such as Roll (1984). It is one remaining issue how to reconcile their view with thetraditional measurements - tightness, depth, and especially resilience.

- 8 -After a corporate bond with coupon c and principal P is issued in date-1, the bond holder
is randomly matched with a potential investor in each period t until its maturity date T.16

The value of the bond-issuing company Vt follows a binomial process with a probability ofmoving upward (q) and downward (1 − q), respectively.

The default of a bond ischaracterized as the case where Vt goes below its principal P. In the case of default, thebond holder could receive (1 − α)Vt where α denotes the cost of bankruptcy. Figure-3(1) illustrates the considered binomial tree with an absorbing state corresponding todefault.
The heterogeneity of investors and bondholders, which is an essential assumption

for modeling the non-degenerated distribution of the quoted spreads, is represented by{αi }Ii=1 where the type index i takes from 1 to I and the large index corresponds to asmaller bankruptcy cost.17 As a notation, γ(i) and ⋕ (i) denote the probability of being
type−i and the numbers of type−i investor among the global population of investors,

which satisfies the following relation. γ(i) is assumed to be constant over time.
γ(i) =⋕ (i)∑Ij=1 ⋕ (j)Important assumption here is that investors have heterogeneous prior beliefs not
explained by differences in information about bankruptcy cost. The heterogeneity ispotentially obtained, for example, through different abilities and/or evaluation methods.18
The distinction of liquidity and illiquidity markets is modeled through the twodifferent matching schemes in each market. If the market is liquid, the bondholder−k ismatched only with the investors with whom he/she can obtain the gain from trades (i.e.,
matched with the investor−j where j ≥ k). The probability for the bondholder−k to bematched with the investor−i such that i ≥ k is denoted as follows.

16 We omit the description for the primary market, which is detailed in the paper, for the presentation purpose.

17 Thus, the bondholder/investor with a large i put a greater value for a given bond as the collateral value of the bond (1 − α)V is evaluated larger bytthe bondholder/investor.
18 The difference in opinion literature (e.g., Banerjee and Kremer (2010)) intends to explicitly model how such heterogeneity is observed and reflectedin the learning process of each player. Tychon and Vannetelbosch (2005) largely abstracts from the learning aspect and focus on how the degree of agiven heterogeneity affects the corporate bond spreads.

- 9 -

γ(i)

∑Ij=k γ(j)On the other hand, bondholders in illiquid market will be matched with whole population.
Hence, the probability for the bondholder-k to be matched with the investor−i is simplyγ(i).

In each period and node denoted by (t, m) where m denotes the number of

upward moves required for reaching the node, each bondholder−i is matched with apotential investor−j through the matching scheme described above and bargains over thei,jprice pt,m based on the following Nash-bargaining procedure if j ≥ i.
i,j

λ

1−λ

if the market is liquid

i,j

λ

1−λ

if the market is illiquid

plt,m = argmax�πi (t, m) − π0i (t, m)� �uj (t, m) − u0j (t, m)�

pt,m = argmax�πi (t, m) − π0i (t, m)� �uj (t, m) − u0j (t, m)�
Where

πi (t, m): Bondholder ′ s value by selling, π0i (t, m): Bondholder ′ s value by not sellinguj (t, m): Investor ′ s value by buying, u0j (t, m): Investor ′ s value by not buying
λ: Bondholder ′ s bargaining power

i,j

i,j

We can immediately notice that πi (t, m) = pt,m or plt,m , and u0j (t, m) = 0. The rest of thevalues π0i (t, m) and uj (t, m) can be constructed as follows.

11ii� �c + Bt+1,m+1
� + (1 − q) �1+r� �c + Bt+1,m�
1+r

π0i (t, m) = q �11jj� �c + Bt+1,m+1 � + (1 − q) � � �c + Bt+1,m �
1+r
1+r

uj (t, m) = q �
wherei
Bt+1,m+1: Expected value at (t, m)for the bondholder − iThanks to the setting with a finite maturity period, we can solve for all the expected values- 10 -

of the bonds corresponding to both liquid and illiquid markets, hence can obtain all the
prices in every (t, m) backwards by beginning at the end of the binomial tree and solving
for the prices from bargaining problems. 19i,jNote that the difference betweeni,jpt,m and plt,m solely comes from the matching procedures with belief heterogeneity in
illiquid and liquid markets.

By using those prices, the bond values for bondholder−i at (t, m) in liquid andilliquid markets are defined as follows, respectively.

BLit,m =i,j∑Ij=i pt,m ×γ(j): Liquid market∑Ij=i γ(j)
i,j

i
Bt,m
= ∑j pt,m × γ(j): Illiquid market

Then, we can define the liquidity/marketability risk premium in the following form.

jjLPt,m = BLt,m − Bt,m ≡ � BLt,m × γ(j) − � Bt,m × γ(j) ⋯ (1)jjThis premium is originated from both the lack of marketability (i.e., the bond can be traded
only once in a market with heterogeneous prior beliefs) and the lack of liquidity (i.e.,bondholders are matched with population in illiquid market whereas with the investors
providing the gain from trade in liquid case). Note that both the factors are necessary forthe premium. Suppose all the players share a common bankruptcy cost α, then no tradeoccurs and LPt,m becomes zero.20 Given the difference between liquid and illiquid market

structure, the liquidity/marketability risk premium takes a positive value only if theeconomy contains heterogeneous beliefs. And there is a positive correlation between thepremium and the degree of heterogeneous beliefs. We take this point to construct our
testable hypothesis.

19 One trick they invent is to reduce the nodes necessarily considered in order to solve for the prices. We only need to consider the nodes inside thebargaining zone in Figure-3 (2).
20 Similarly, there will be no trade if the frequency of trade is high enough and/or obviously the difference between the liquid and illiquid markets does
not exist.

- 11 -

3-2. Empirical Implication and Hypothesis Formulation
The model presented in the previous section effectively puts a linkage between
the degree of heterogeneous beliefs among bondholders/investors and the relative value ofbonds suffering from matching friction. In particular, the existence of heterogeneous
belief induces the spread difference between the liquid and illiquid markets, which implies
that the larger the heterogeneity of bondholder/investor beliefs, the higher the liquidity
premium is.
Although the model does not explicitly describe market makers, we can apply thecurrent setup to the market with market maker since the candidates for the sources ofheterogeneous prior beliefs discussed in the model (i.e., different information processing
abilities, evaluation methods etc.) are also applicable to market makers. Based on thediscussion above, we construct the first hypotheses we verify in the following sections.

Hypothesis-1: Median quoted spread is positively correlated with the absolute dispersion ofmarket maker’s quoted prices, which is captured by the GAP measure in our setup, evenafter controlling the market factor as well as its individual factors (e.g., credit ratings, thevolatilities of stock returns etc.).

Note that our dataset described in the following section does not contain the actual
transaction price but rather the prices conjectured by market makers. Although theavailable data from JSDA is limited in this sense, we think the data should account toconsiderable extent for the market behavior and its illiquidity. About the (i) market and(ii) individual credit factors, and (iii) the market liquidity factor, we use (i) 10-year JGB
yield minus 2-year JGB yield, 10-Year JGB yield, the growth rate of Nikkei Average Stock
Index, (ii) the unexpected historical volatility of individual stocks, the credit ratings, (iii)
3-month Tibor minus 3-month JGB yield, which represents the tightness of short-term
financial market.21 We will summarize the expected signs of each coefficient in the
21 The unexpected historical volatility is estimated as the residual obtained from the regression of the individual historical volatility on the historicalvolatility of Nikkei average index. Various other potential proxies we used for robustness check are omitted for saving the space. Those additional
results are provided upon request.

- 12 -

following section.
Second, in the extant literature, some conditionality has been pointed out in stock
market return (e.g., Watanabe and Watanabe (2008)). They establish the result that thepricing impact of liquidity risk is larger for the firms with lower credit ratings. The
following hypothesis corresponds to this established empirical fact in other financial
markets.

Hypothesis-2: The impact of the GAP measure onto bond spreads has conditionality.

This can be verified, for example, by checking whether the coefficient associated with the
GAP measure times the standard deviation of the GAP measure is different among thesamples split based on the credit-ratings and/or market conditions. This perspective isalso quite consistent with the widely shared flight-to-liquidity view.
Third, in order to identify the role of the heterogeneous belief, we need to control
the liquidity proxy discussed in the classic market liquidity literature. For this purpose,
we need to control at least one of the individually treated dimensions of market liquidity inliterature such as tightness, depth, and resiliency (BIS (1999)). Considering the data
availability described in the previous section, we feature the resiliency and construct thethird hypothesis.

Hypothesis-3: GAP measure is valid to measure the impact of illiquidity on the spreads
even after controlling the resiliency (i.e., persistency on spreads).

We could conjecture the conditionality considered in the second hypothesis also forthe resiliency factor, from which we can construct our last hypothesis.

Hypothesis-4: The quantitative impact of resiliency has conditionality.

We will test this hypothesis by checking the coefficient representing the persistency on the- 13 -

median reported prices changes as firms' individual characteristics (e.g., credit ratings) andthe market condition of liquidity vary.

4. Empirical Framework
In this section, we go over our empirical framework. Different from the typical
time-series estimation for sorted hypothetical portfolios employed in the extant literature,
we use panel estimation with using a balanced panel data of monthly Japanese corporatebond spreads detailed in the next section. The benefits of employing the panel estimation
are twofold. First, it can fully extract both the time-series and cross-sectional propertiesof our firm-level data. By applying the panel estimation framework to such a data set, we
can examine the potential determinants of individual corporate bond spreads precisely.
Second, our dynamic panel estimation enables us to establish the empirical implication of
our GAP measure with precisely controlling the persistency in median quoted bondspreads.
Following the usual asset pricing literature, we start from an extended version ofa multi-factor model proposed, for example, in Fama and French (1993).

SPit = β1 + β2 Ft +β3 Lt + αi + ϵit ⋯ (2)Here, the dependent variable SPit denotes the spread of firm−i at time−t.

As anexplanatory variable, Ft denotes various market indexes (e.g., stock market index, thegrowth rate of the index, and/or its historical volatility) at time−t. In addition to theseaggregate credit factors, we incorporate the market liquidity factor Lt , which can beproxied by, for example, trading volume of corporate bonds, the number and/or volume of

newly issued corporate bonds, and/or Tibor - JGB spread. We attempt to confirm thateach coefficient has an expected sign implied by the extant theoretical studies, which will
be presented later. As in the standard panel estimations, αi captures the firm-specificindividual effect, which takes either a fixed value (fixed-effect model) or an independent

random variable for each group with mean zero and a standard deviation σα .
- 14 -

Next, we advance to the further extended version of such a basic multi-factor
model by incorporating fit , which denotes the individual firm-specific credit risk factor offirm−i at time−t. Potential proxies could be credit ratings and/or historical volatility ofstock returns.

SPit = β1 + β2 fit + β3 Ft +β4 Lt + αi + ϵit ⋯ (3)The most important twist in this paper is the inclusion of the individual liquidity proxy lit

to the extended multi-factor model above.

SPit = β1 + β2 fit + β3 Ft +β4 Lt +β5 lit + αi + ϵit ⋯ (4)This additional factor is the key object in our paper and represented by GAP, which
denotes the highest minus lowest reported yields among market makers at time−t. 22
Through this model, we try to extract pricing implications of individual liquidity risk in amarket under very low liquidity. Note we observe that most of the corporate bonds
including the one issued by highly rated utility companies etc (e.g., electricity companies)
maintain a significant GAP over our sample period (see Figure-2 (2)). 23 Although we
could potentially use bid-ask spreads under a market environment with high liquidity, we
think that corporate bond markets do not satisfy such a criterion24. To summarize, ourmain concern is how the model (4) is better than (2) and (3), and if the sign ofestimated coefficients is consistent with our predictions.25

The estimation will be implemented through pooled OLS, fixed-effect (within),and random-effect GLS estimations. There are a few points to be discussed for model
selection.

First, we have a hunch that the estimators provided by those three

specifications share a similar feature. This conjecture comes from the fact that the

22 Precisely speaking, we use one-day lagged GAP in order to avoid the simultaneous bias problem.

23 In Japan, utility companies in the electricity and gas industries etc (e.g., Nippon Telegraph and Telephone Corporation, Japan Railway Company)
have been keeping highest ratings from the institutional reason.
24 We think securitization markets all over the world do not necessarily satisfy this condition either, in particular, after the sub-prime shock.
25 The expected signs of macro and micro credit factors and the macro liquidity factor will be discussed in the next section when we present our data.

- 15 -

observed variables stored in financial data tend to be further comprehensive than, forexample, the data in the field of labor economics. From this reason, it is natural to guessthat the individual effect, particularly the firm-specific constant in a fixed-model
specification, is largely washed away by using a rich set of explanatory variables. Second,although the estimated coefficients are largely similar among models, we think that the
random-effect model, which allows the independent random component for each group, fits
the characteristics of our observations relatively well. The inclusion of the appropriate
explanatory variables contributes to capture the level of the individual effect (i.e.,
fixed-effect) but it is safe to assume the variation of the individual effect (random-effect) is
not completely controlled. As we will see later, these two conjectures are confirmed in thefollowing section.
Note that from a technical point of view, we might need to control the level of thequoted yield by following the standard finance literature in order to appropriately
incorporate the GAP variable. One way to do so is to simply include the level of either
highest or lowest quoted spread as well as the GAP itself while another treatment can beconstructing a so called "relative distance measure" as in Houweling et al. (2003), which
divides GAP by some appropriate level variable (e.g., concurrent JGB yield). We employ
the latter method as a robustness check for our results in the later section.
Finally, we extend our model to dynamic panel estimation. Specifically, thelagged dependent variable SPit−1 is incorporated in the model (5). As mentioned in theprevious section, this formulation is motivated by the notion of resiliency. Supposedly, thecoefficient γ takes a value close to one, which implies that the median reported spread has
persistency, if the market exhibits low resiliency.

SPit = γSPit−1 + β1 + β2 fit + β3 Ft +β4 Lt +β5 lit + αi + ϵit ⋯ (5)As Arellano (2003) carefully demonstrates, the dynamic models with lagged dependent
variables are suitable for the estimation of economic variables with adjustment costs- 16 -

and/or habit formation. 26

In the current context, the persistency represents thedependence of market maker’s bond evaluation on the spreads reported in the previous
period. 27 From the practical perspective, this specification actually replicates thepricing/reporting scheme implemented by marker makers such that (1) check the price on
the previous period, (2) add some adjustment with taking into account the concurrent
covariates, and (3) report the prices, which is somewhat resembling "walking after
midnight".28
The estimation for this dynamic model will be implemented through pooled OLS,
fixed-effect estimation, random-effect GLS estimation, Arellano-Bond GMM estimation,and random-effect MLE.29 There are a few points to be discussed for model selection.
First, we have the similar conjecture to the ones for the static model that the estimators
provided by those specifications (i.e., OLS, GLS, GMM, and MLE) look similar. We guessthat this issue is more prominent in the dynamic model since one potentially missed
observation (i.e., a lagged dependent variable) is additionally included in the current
model.
Second, we prefer MLE to the other specifications.

Under the existence ofindividual effect (either fixed or random), OLS obviously could not provide a consistentestimator. Moreover, it is well known that fixed-effect and random-effect estimation witha lagged dependent variable could not give a consistent estimator either. This can beeasily shown by the modified expression of the individual effect model.

SPit = γSPit−1 + αi + ϵit ⇔ SPit = αi (1 + γ + γ2 + ⋯ ) + ϵit + γϵit−1 + γ2 ϵit−2 + ⋯Hence,

SPit−1 = αi (1 + γ + γ2 + ⋯ ) + ϵit−1 + γϵit−2 + γ2 ϵit−3 + ⋯26 The typical example could be the capital investment and employment.
27 As we will detail later, we use monthly data.

28 We appreciate a number of anonymous practitioners for pointing us this practice.

29 We also estimate the model with an AR(1) structure on its disturbance for reference.

- 17 -

This implies that both SPit and SPit−1 are correlated with αi , which leads to asimultaneous bias.

Although Arellano-Bond type GMM estimator, which takes into

account this problem, is widely used for dynamic models, recent studies point out that theover-identification restriction test does not work. For example, Bowsher (2002) explains it
is general that Sargan test based on the full instrument set essentially never rejects when
T (and hence the number of moment conditions) becomes too large for a given value of I.30

Considering that our sample contains a relatively large T = 82, it is problematic to use
GMM.31 In order to apply MLE, in which we can ignore the issue of correlation between
the residuals and lagged dependent variables, to our dynamic model, however, we need toknow the distribution for the initial dependent variable (i.e., SPi0 ) in advance.

Fortunately, the large- T of our sample, in turn, alleviates this problem and we could

almost ignore the initial observation problem. Hsiao (2003) shows that the parameters
estimated through MLE become consistent as N → ∞ for a given T. 32

Third, related to the first point, the bias of pooling OLS/GLS estimator associatedwith the random-effect is shown to be smaller as the time-invariant standard deviation σα

becomes smaller. Hsiao (2003) concisely shows the following expression for the estimated
AR(1) coefficient.

γ� =

and

T
T
∑N
∑N
i=1 ∑t=1 SPit SPit−1
i=1 ∑t=1(αi + ϵit )SPit
=
γ
+
T
2
T
2
∑N
∑N
i=1 ∑t=1 SPit
i=1 ∑t=1 SPit

plimN→∞ γ� ==1
∑N ∑T (α + ϵit )SPit
NT i=1 t=1 i

1 1−γT
1 σ2α[(T − 1) − Tγ + γT ]
)+
cov(y
,
α
i0
i
T 1−γ
T 1−γ

Evidently, the last term of the second expression becomes smaller as σα becomes smaller.

After describing our data in the following section, we show our estimation results

30 The size of T needs to be judged in the comparison with the size of I.

31 Blundell and Bond (1998) also points out that the instruments used in the standard first-differenced GMM estimator become less informative in
two important cases - the value of γ increases toward unity, and the relative variance of the fixed effects increases. We judge the long−T problem ismore prominent in our analysis.
32 The key idea is the effect coming from the initial observation for the estimation of model parameters through MLE becomes almost negligible as thelength of data becomes longer enough. Note that the validity of assuming the normal distribution remains as usual.

- 18 -

and discuss the implication in Section 6.

5. Data
As briefed already, the data is obtained from Japan Securities Dealers Association(JSDA). It contains the reference data about Japanese corporate bond markets. The
data is daily-frequency and consists of the highest, lowest, mean, and median bond yields
among all the yields reported by selected market makers (“member security firms”) after
cutting the outliers based on predetermined percentages. 33 Those member security firms
report the yield of each company’s existing bonds for different maturities by 4:30 pm every
day as if they are asked to price the 500 million yen of the bonds as of 3:00 pm. JSDA
collects the data and release the four reference data mentioned above (i.e., highest, lowest,
mean, and median) on its website at 5:30 pm. 34
From this data, we pick up the median spread as our dependent variable. Since
we use the difference between highest and lowest spreads as GAP measure, the median ismore preferable than mean since it is not directly affected by the highest and lowest
spreads from its arithmetic manner. Considering that the data has high persistency, we
decide on using monthly-frequency data. We also use the 1-day lagged GAP measure inorder to avoid the simultaneous bias.

Table-1 shows the summary statistics of our

explanatory variables with its definition and Table-2 summarizes the correlation.35
For the market-level liquidity proxy (T_JGBGAP) and the individual credit factors(eHV and RATE_RI), we expect the positive correlation with the median reported spread.
For the macro credit factors (JGBSLOPE, JGB10Y, and NKYGROWTH), however, theexisting literature provide mixed predictions. Thus, we would rather treat these variables
as control variables without assigning specific expected signs. GAP and the adjusted GAP
measures are expected to have positive signs on our estimations.

33 The selected market makers are as follows: SMBC Friend, Okasan, Credit Swiss, Cosmo, Goldman Sachs, Citi Group, Shinsei, JP Morgan, Daiwa
SMBC, Deutch, Tokai Tokyo, Nomura, BNP Paribas, Marusan, Mizuo, Mizuho Investors, Mitsubishi UFJ, Merril Rinch Japan, Morgan Stanley, UBS.
If reporting firms are 34 to 40, cut 6 firms from the highest and lowest respectively. The cutting criteria is as follows: 27 to 33 security firms report,
cut 5 from the highest and lowest. 21 to 26 security firms report, cut 4 from the highest and lowest. 15 to 20 security firms report, cut 3 from thehighest and lowest. 10 to 14 security firms report, cut 2 from the highest and lowest. 5 to 9 security firms report, cut 1 from the highest and lowest.
34 If the gap between the highest and lowest (yield) becomes more than 500bp, the data is not released.
35 For the reference for the estimation based on the sample splits detailed later, we also list the summary stats and the correlation tables for thosecases.

- 19 -

While we have almost 120 firms in our original sample, the number of groups (i.e.,
firms) is reduced to about 52 because of the maturity control we explained below. It is
important to note that our sample still contains a large variation in the credit ratings and
GAP measure36. The sample period is 82 months from July 2003 to April 2010.
Although the original data covers bit longer time periods, we focus on the period
over which we can always observe the GAP measure. We also consider the data only forJapanese listed firms which maintain a certain number of issued bonds. This is mainly
because we want to transform the yield data of each corporate bond with various
maturities into specific yields corresponding to maturities 3-year and 5-year, instead ofusing the raw data for corporate bond yields. Most of the existing literature incorporates
the maturities in the explanatory variables instead of adjusting the maturity prior toestimation. From the standard practical manner, the assumption in the extant empiricalstudies that the maturities have a linear relation with the yields is too restrictive.
Evidently, we almost always observe non-linear shaped yield curve in reality. In order tocontrol the heterogeneity in maturity, we use the information of multiple corporate bonds
issued by each company. The different bonds for a given company are used to construct
an interpolated yield curve. Then, our targeted spreads corresponding to maturity 3-year
and 5-year are taken out from the yield curve with considering the concurrent JGB yield
curve. 37 Thanks to this operation, we do not need to control the maturity by including thematurities as explanatory variables. Figure-4(1) and Figure–4(2) show the resulting yield
curves for two firms in our sample. We apply this procedure in order to construct the yield
curves for highest, lowest, mean, and median reported spreads. Considering the shape oftime-series data constructed in this way (see Figure-5), we believe this interpolation does
not generate any severe problems.

6. Estimation Results
In this section, we implement the estimations proposed in the previous section.
36 The current sample is a highly balanced panel data.

We are planning to incorporate the unused data with proper treatment for missing values.
On the other hand, we do notcontain 1-year spreads in our analysis simply because the bonds close to its maturity tend to exhibit irregular dynamics.
37 We gave up to construct 10-year spreads since we do not have enough number of long-term corporate bond data.

- 20 -

First, we apply pooled OLS estimation, fixed-effect estimation, random-effect estimation,and MLE to the static model. The results are summarized in Table-3. The sensitivity
analysis of each coefficient with respect to the credit ratings and/or market conditions isfurther demonstrated in Table-5 (1). Considering the fact that our static panel estimation
potentially suffers from heteroskedasticity, we employ the heteroskedasticity-robust
standard error proposed by White.38
The coefficients of introduced covariates are as follows: First, higher Tibor - JGB
spreads (T_JGBGAP), which represents the tightness in the short-term financial market,
contributes to higher median spread. This is consistent with our prediction that the
spreads are positively correlated with the market-level liquidity index.

Second, theresidual in the regression of the individual stock price volatility on that of Nikkei Index(eHV), which corresponds to the extra volatility of individual firm's value after controllingthe aggregate shock, has a positive effect on the corporate bond spreads. Third, the credit
ratings of each company provided by R&I (RATE_RI), which covers the largest number ofJapanese companies, has the same implication as eHV.
About the GAP variable, we can establish a strong positive correlation between
GAP and median reported spreads. One remarkable point is that the inclusion of the
GAP measure significantly improves the R2 of the model. We also find that the impact of

the GAP coefficients depends negatively on the credit ratings (i.e., as the credit ratings areworse, the GAP coefficients times the standard deviation of GAP becomes larger). 39
Namely, the impact is 0.11 (=1.37×0.08) if the credit ratings at the beginning of oursample period is better than or equal to 4 (i.e., AA-) while it takes almost the double size

0.24 (=1.50×0.16) otherwise.40 The variation of the impact of GAP coefficients withrespect to market condition has a similar feature. If the share of firms satisfying "GAP isequal to or smaller than 10bp" is greater than 75% (i.e., the market condition is GOOD),
the impact of GAP coefficient is 0.13 (2.09×0.06) while it becomes 0.19 (1.12×0.17)
otherwise.41
38 In order to implement the test for model specification, fixed-effect and random-effect models are estimated without this consideration.
39 We transform each rating into numbers.

The detailed computation results are provided upon request.

40 The numbers come from Table-5 (1), Table-1 (2), and Table-1 (3).
41 The numbers come from Table-5 (1), Table-1 (4), and Table-1 (5).

- 21 -

Although it seems that we succeed on improving the model by using the GAP
measure in static panel estimation, the residual plot of the model in Figure-6 tells us a
substantial problem. Apparently, it shows heteroskedasticity. The first component is thelower part of the residual plot (i.e., the spreads of firms with good credit and those of goodmarket environment period), which seems to form the down-sloped concentration. The
second component (i.e., the spreads of firms with weak credit or those of bad environment
period) can be found in the upper scattered portion. Because of the potential omitted
variables that could capture the behavior of the latter component, the static model
generates a bunch of very large positive residuals over the high spread range. These
outliers attract the regression line upward and make the former portion over-estimated.
Before adding another explanatory variable in order to overcome this problem, we
tested a model assuming the serial correlation of the disturbance term (see the first columnof Table-4).

This model seems to partially ease the above problem (see Figure-7).

Evidently, it can explain the behavior of the firms with good credit and good environment
rather well. Unfortunately, this remedy still remains a problem - the upper scatteredportion still exists. Ultimate solution seems to be the adoption of the lagged dependent
variable (i.e., the lagged spread). As already mentioned, the notion of resiliency which
pronounces in illiquid market and the actual reporting procedure, incorporating apersistency term is plausible. We also strengthen this conjecture by taking look at theresidual plot over time horizon (see Figure-6(2) and -7(2)).

It is apparent that theunderestimation is typical under the weak market conditions and the spreads tend to stayat the high level even though its covariates including GAP got back to the normal
situation.
Considering these results, the dynamic models proposed in (5) are estimatedthrough pooled OLS, fixed-effect, random-effect GLS, Arellano-Bond GMM, and MLE. 42

The results summarized in Table-4 shows, that all the estimation methods lead to almost
similar coefficients, which is consistent with our conjecture in the previous section.
42 The default setting of STATA for MLE does assume that initial value is exogenously given and does assume nothing on its distribution. Although
this naïve ML estimation works well and is justified by our discussion in the previous section, it might be better for us to assume the more consistent
distribution derived from the model. We recognize it is our future task to employ the MLE methods proposed in Anderson and Hsio (1982), Bhargava
and Sargan (1983).

- 22 -

Looking at the scattered plot (Figure-8 and -9) corresponding the Arellano-Bond GMM and
MLE estimations for the dynamic model, the problem stemmed from omitted variables
seems to be resolved satisfactorily. 43 We can also confirm that the dynamic panel still
provides similar results as in the static model. 44 One point to be noted for the models
with lagged dependent variable is that the AR(1) coefficient is 0.86 to 0.89, which indicatesa strong auto-correlation. The conjectured persistency of the reported bond spreads issuccessfully confirmed through our dynamic panel estimation.
Another interesting point is that AR(1) coefficient seems to have conditionality on
the credit ratings and/or business cycle. Table-5 (2) summarizes the spectrum of AR(1)coefficient for different levels of credit ratings and market environments. The purpose ofthis additional analysis is to see the AR(1) coefficient with respect to the characteristics ofcross-section and time-series sample variation. 45 It is clear that we have a negative
conditionality of the AR(1) coefficient on credit ratings and/or market conditions. Moreprecisely, the persistency of the median reported spread becomes higher as credit ratings
and/or market conditions get worse, which actually looks like “walking after midnight” (i.e.,
not walk away from the previous step when really dark). In the extant literature, someconditionality has been pointed out in stock market return (e.g., Watanabe and Watanabe(2008)) such that the pricing impact of liquidity risk is larger for the firms with lower credit
ratings.46 As far as we know, however, the conditionality of the resiliency component withrespect to the variations of credit ratings and/or market conditions has never been
analyzed.
Note that σα in the MLE for the dynamic model is substantially smaller thanthat for the static model. We think that this is consistent with the fact that the estimatedcoefficients are almost similar among the estimation methods. If the individual effect is
43 There still remain a very few outliers but we think this is no longer the big problem. It is not difficult for us to identify these outliers and tells thatis the result of detection of window dressing. It is very easy to trim out these by setting a dummy variable.
44 As the coefficient of the slope of JGB yield curve calculated by the difference between 10-year JGB yield and 2-year JGB yield increases, the spreads
decrease. This result is somewhat controversial if we consider the discussion in Fama and French (1993) where the slope index is treated as a risk ora sigh of boom. One interpretation of this result is that the higher 10-year JGB yield is accompanied with boom while the lower 2-year JGB yield isgenerated by easing monetary policy.
45 In order to split the sample, we use (i) whether the credit ratings at the beginning of sample period is better than or equal to 4 (i.e., AA-), or worse
than or equal to 5 (A+), and (ii) whether the share of firms satisfying "GAP is equal to or smaller than 10bp" is greater than 75% (i.e., the market
conditions is GOOD) or not (BAD market condition). Note that if firms in our sample do not have their credit ratings from R&I but from otherrating agencies, we transform those ratings into hypothetical R&I ratings (e.g., AAA=1，AA+=2, and so on). This transformation is done by referringto the companies holding both the R&I ratings and the ratings provided by other agencies.
46 Their analysis is based on the hypothetical portfolio as in the other extant studies and does not employ the panel estimation.

- 23 -

properly controlled, it is natural to have very small variations in the estimators among themodel specifications.
In order to check the robustness of the result, Table-6 reports the revised
regression results in (2) to (4) under an adjusted GAP measure, which is constructed by
dividing the GAP with the concurrent JGB yield. The results obtained in the previous
estimations are all confirmed in this additional estimation.

7. Comparison with existing studies
Mainly because of the data limitation, there are only few studies directlycomparable with our results. As one limited example, Hauweling et al. (2005) employs
the measurement constructed by dividing the standard deviation of market makers
concurrent quotes in a given day by the average quoted spreads in order to construct sorted
hypothetical portfolios. Their main conclusion is such a relative distance measure ofquoted spreads is valid to capture the market liquidity among the other proxies. Our
result presented in the previous section is consistent with theirs.

8. Concluding Remarks
This paper proposes a theoretically motivated proxy for the degree of market
liquidity in corporate bond market (GAP: the highest minus lowest simultaneously
reported spreads among multiple market makers), and studies its pricing implication by
quantifying the correlation between GAP and the median reported spreads among market
makers, which presumably approximate market prices conjectured by market makers.
While the issue of market liquidity has been extensively examined over the last decade forstock and sovereign bond markets, our understanding is still limited for corporate bondmarket mainly due to the unavailability of widely accepted liquidity proxies, such asbid-ask spreads in other markets. Through various panel estimations for the medianreported spreads in Japanese corporate bond market, we find that (i) inclusion of thelagged GAP to the standard multi-factor model significantly improves the explanation
power, (ii) the quantitative impact of such an illiquidity measure on bond spreads becomes- 24 -

larger as credit ratings get worse, (iii) the GAP proxy is valid even after controlling thepersistency on spreads, which has been considered as another proxy for illiquidity in theextant literature (i.e., resiliency), and (iv) the degree of such persistency increases as thecredit ratings of corporate bonds and/or market condition deteriorate. These results
jointly explain how market makers construct their opinions about bond prices by (a)learning from the dispersion of reported prices, (b) recalling the past reporting, as well as(c) considering standard covariates of bond spreads (i.e., JGB Yield, credit ratings etc).
Our results also support the empirical implication provided by theoretical literature on thecorrelation between the degree of opinion differences and market liquidity premium. Our
research complements the limited number of quantitative research about Japanese
corporate bond market and gives some implication for the markets associated withrelatively low liquidity (e.g., ABS, CDO, and/or realty market).
To conclude, we list several future research questions. First, we will consider therefinement of our dynamic panel estimation such as the proper selection of instrument
variables and/or imposing an appropriate structure to the distribution of error term in
MLE. It would be also interesting to construct a static measure representing the pricestickiness (e.g., ILLIQ-type measure and/or the difference of GAP measure). Second, it isnecessary to use our estimated results to motivate theoretical models.

The recent"differences in opinion (DO)" literature surveyed in Section 2 constructs market
microstructure model considering the heterogeneous views among market makers. What
we need to construct is the model where market maker continuously revises its evaluation
about bond spreads and still exhibits the heterogeneity of their evaluations. Studying theprice and trade volume dynamics through such a model is one promising way tounderstand the markets with low liquidity.

It also allows us to understand the

distributional dynamics of market maker’s reporting contents from theoreticalperspectives. Third, our analysis could be refined as in the consistent way with the
CAPM literature with liquidity risk (e.g., Acharya and Pedersen (2005)). Fourth, it isimportant to incorporate the unused data in our original sample with a proper treatment
for missing values. One idea is to apply Tobit-type framework to the original data. Fifth,- 25 -

the determination of GAP and further empirical analysis of the distribution of reported
spreads would be informative research objects. Doubtlessly, we are far away from the fullunderstanding on the sources of belief/evaluation heterogeneity among market makers
and/or investors. One potential candidate generating dispersed reported prices, we areguessing, is the heterogeneity of investor classes and the market makers having tightconnections with those investors in each class. To illustrate, the investors taking “Buy &Hold” strategy would not have urgent needs to commit fire-sales even when the quoted
prices plunge.47 Reflecting this feature, the market makers mainly dealing with thoseinvestors are somehow allowed to be insensitive with the price changes. On the other
hand, the “value-based” investors such as hedge funds are conjectured to be very keen on
the price change since it affects the fair-value of their assets. This keenness could be moresounding in CDS markets where hedging motif is the main driver. Along this line, we areplanning to document the quoted price dynamics in CDS markets and compare it with ourcurrent analysis for corporate bond markets.

Trough such an analysis, we aim atestablishing the relation between the types of investors and price dynamics. We believe
all of these extensions provide further guides for better understanding of corporate bond as
well as securitized products in very low liquid markets.

47 Many corporate bond investors in Japan could be categorized in this group.

- 26 -

<Table and Figure>

Corporate Bond Spreads vs. Nikkei Heikin

%

¥

7000

1.2
9000
1
0.8

11000

0.6

13000

0.4

15000

0.2
17000

Firm-A
3-Yr SPREAD

Firm-B
3-Yr SPREAD

2010/04/01

2010/01/01

2009/10/01

2009/07/01

2009/04/01

2009/01/01

2008/10/01

2008/07/01

2008/04/01

2008/01/01

2007/10/01

2007/07/01

2007/04/01

2007/01/01

2006/10/01

2006/07/01

2006/04/01

2006/01/01

2005/10/01

2005/07/01

2005/04/01

2005/01/01

2004/10/01

2004/07/01

2004/04/01

2004/01/01

2003/10/01

2003/07/01

0

Nikkei Heikin(Right Axis: Reversed)

Figure-1 (1): Corporate Bond Spreads and Stock Index

Corporate Bond Spread vs. Stock Price

%

0.38

¥

2000

%

Corporate Bond Spread vs. Stock Price

¥

300

1.2
350

0.33
2500

1

3000

0.8

400

0.28
0.23

450
500

0.18
3500

0.6
550

0.13
0.4
0.08

600

4000

Firm-A Stock Price(Right Axis: Reversed)

Firm-B
3-Yr SPREAD

2010/01/01

2009/07/01

Firm-B Stock Price(Right Axis: Reversed)

Figure-1 (2): Corporate Bond Spreads and Individual Stock Prices- 27 -

2009/01/01

2008/07/01

2008/01/01

2007/07/01

2007/01/01

2006/07/01

2006/01/01

2005/07/01

2005/01/01

2004/07/01

2004/01/01

2010/01/01

2009/07/01

2009/01/01

2008/07/01

2008/01/01

2007/07/01

2007/01/01

2006/07/01

2006/01/01

2005/07/01

2005/01/01

2004/01/01

2003/07/01

2004/07/01

Firm-A
3-Yr SPREAD

650

2003/07/01

0.2

0.03

%

Figure-2 (1): The distribution of GAP measure

Corporate Bond Spread vs. GAP

%

%

0.38

0.3

0.33

%

Corporate Bond Spread vs. GAP

%

0.5

1.2

0.45
0.4

0.25
1

0.28

0.35

0.2

0.3
0.8

0.23

0.25

0.15
0.18

0.2

0.6
0.1

0.13

0.05

0.08

0.15
0.1

0.4

0.05

Firm-A
3-Yr SPREAD

Firm-A
3-Yr GAP

Firm-B
3-Yr SPREAD

Figure-2 (2): Individual Corporate Bond Spreads and GAP measures- 28 -

Firm-B
3-Yr GAP

2010/01/01

2009/07/01

2009/01/01

2008/07/01

2008/01/01

2007/07/01

2007/01/01

2006/07/01

2006/01/01

2005/07/01

2005/01/01

2004/07/01

2004/01/01

0

2003/07/01

0.2

2010/01/01

2009/07/01

2009/01/01

2008/07/01

2008/01/01

2007/07/01

2007/01/01

2006/07/01

2006/01/01

2005/07/01

2005/01/01

2004/07/01

2004/01/01

0

2003/07/01

0.03

Figure-3 (1): Binomial Tree in Tychon and Vannetelbosch (2005)

Figure-3 (2): Necessary Nodes for Price Computation in
Binomial Tree in Tychon and Vannetelbosch (2005)- 29 -

1.6

%

1.4

1.2

1

0.8

0.6

0.4

0.2

Maturity

0
0

2

4

6

10

8

12

14

16

18

Figure-4(1) Interpolated Yield Curve for Firm-A (July 31st 2003)

2.5

%

2

1.5

1

0.5

Maturity

0
0

1

2

3

4

5

6

7

8

Figure-4(2) Interpolated Yield Curve for Firm-B (July 31st 2003)- 30 -

910

Evolution of Reported Spreads (Firm-B)%

Evolution of Reported Spreads (Firm-A)

%

1.4

0.45
0.4

1.2

0.35
1

0.3
0.25

0.8

0.2

0.6

0.15

0.4

0.1
0.2

0.05

Firm-ASPREADLP3

Firm-ASPREADAP3

Firm-ASPREADMP3

Firm-BSPREADHP3

Firm-BSPREADLP3

Firm-BSPREADAP3

Figure-5 Interpolated Spreads (Highest, Lowest, Average, Median)- 31 -

2010/01/01

2009/07/01

2009/01/01

2008/07/01

2008/01/01

2007/07/01

2007/01/01

2006/07/01

2006/01/01

2005/07/01

2005/01/01

2004/07/01

2004/01/01

2010/01/01

2009/07/01

2009/01/01

2008/07/01

2008/01/01

2007/07/01

2007/01/01

2006/07/01

2006/01/01

2005/07/01

2005/01/01

2004/07/01

2004/01/01

2003/07/01

Firm-ASPREADHP3

2003/07/01

0

0

Firm-BSPREADMP3

3-year SP Residual (y - yhat) by Model-9BBGML_JGB
-2
-1
0
1
2
3

0

2
4
Fitted 3-year SP by Model-9BBGML_JGB

63-year SP Residual (y - yhat) by Model-8BBGML_JGB
-4
-2
0
2
4

Figure-6 (1): Residual Plot of Static Panel Estimation (Random-Effect)

0

20

40
TIME

60

Figure-6 (2): Residual Plot of Static Panel Estimation (Random-Effect)- 32 -

80

3-year SP Residual (y - yhat) by Model-9BBGML_AR1_JGB
1
2
3
4
0

0

.5
1
Fitted 3-year SP by Model-9BBGML_AR1_JGB

1.53-year SP Residual (y - yhat) by Model-8BBGML_AR1_JGB
0
1
2
3
4

Figure-7(1): Residual Plot of Dynamic Panel Estimation (AR(1) on Disturbance)

0

20

40
TIME

60

80

Figure-7(2): Residual Plot of Dynamic Panel Estimation (AR(1) on Disturbance)- 33 -

3-year SP Residual (y - yhat) by Model-8BBGML_AB_JGB
-1
0
1
2
3

0

2
3
1
Fitted 3-year SP by Model-8BBGML_AB_JGB

43-year SP Residual (y - yhat) by Model-8BBGML_AB_JGB
-1
0
1
2
3

Figure-8(1): Residual Plot of Dynamic Panel Estimation (Arellano=Bond)

0

20

40
TIME

60

Figure-8(2): Residual Plot of Dynamic Panel Estimation (Arellano=Bond)- 34 -

80

3-year SP Residual (y - yhat) by Model-9BBGML_AHMLE_JGB
-1
0
1
2
3
4

0

1
2
3
Fitted 3-year SP by Model-9BBGML_AHMLE_JGB

43-year SP Residual (y - yhat) by Model-8BBGML_AHMLE_JGB
-1
0
1
2
3

Figure-9(1): Residual Plot of Dynamic Panel Estimation (Anderson=Hsio)

0

20

40
TIME

60

Figure-9(2): Residual Plot of Dynamic Panel Estimation (Anderson=Hsio)- 35 -

80

Variable

Defininition

Expected Sign

Coorporate bond yield minus
JGB yield
3-month Tibor minus
3-month JGB yield
10-year JGB yield minus
2-year JGB yield

Obs

Mean

Std.

Min

Max

4173

0.40

0.45

-0.11

4.21

＋

4264

0.19

0.14

-0.03

0.54

－/＋
－/＋
－/＋

4264

1.06

0.22

0.69

1.64

4264

1.49

0.20

0.95

1.93

4264

0.00

0.06

-0.24

0.13

＋

4264

0.00

13.69

-76.0383.84

SPt

3-Yr SPREAD

Lt

T_JGBGAPFt

JGBSLOPE (10Y-2Y)

Ft

JGB10YFt

NKYGROWTH

fit

eHV

fit

RATE_RI

R&I credit ratings

＋

4264

5.63

2.53

2.00

11.00

lit

GAP3_1DLAGHighest reported yield minus
lowest reported yield in theprevious day of 3-Yr SPREAD

＋

4172

0.09

0.13

0.00

3.95

lit

GAP3_1DLAG_Adj

GAP3_1DLAG divided by
concurrent JGB yield

＋

4172

0.25

0.34

0.01

8.51

10-year JGB yield
Growth rata of Nikkei
stock index
20-day historical volatility of
individual stock minus
estimated historical volatilityof each individual

Table-1 (1): Summary Stat for All Samples

Variable

Mean

Std.

Min

Max

2029

0.25

0.28

-0.11

4.21

＋

2050

-3.81

12.77

-76.0382.44

R&I credit ratings

＋

2050

3.56

1.71

2.00

9.00

GAP3_1DLAGHighest reported yield minus
lowest reported yield in theprevious day of 3-Yr SPREAD

＋

2029

0.07

0.08

0.01

1.51

GAP3_1DLAG_Adj

GAP3_1DLAG divided by
concurrent JGB yield

＋

2029

0.18

0.22

0.01

3.35

Mean

Std.

Min

Max

2144

0.54

0.52

0.13

4.15

＋

2214

3.53

13.58

-55.67

83.84

SPt

3-Yr SPREAD

fit

eHV

fit

RATE_RI

lit
lit

Defininition
Coorporate bond yield minus
JGB yield
20-day historical volatility of
individual stock minus
estimated historical volatilityof each individual

Expected Sign

Obs

Table-1 (2): Summary Stat for Initially Hi-Rate

Variable

Defininition
Coorporate bond yield minus
JGB yield
20-day historical volatility of
individual stock minus
estimated historical volatilityof each individual

Expected Sign

Obs

SPt

3-Yr SPREAD

fit

eHV

fit

RATE_RI

R&I credit ratings

＋

2214

7.54

1.41

4.00

11.00

lit

GAP3_1DLAGHighest reported yield minus
lowest reported yield in theprevious day of 3-Yr SPREAD

＋

2143

0.12

0.16

0.00

3.95

lit

GAP3_1DLAG_Adj

GAP3_1DLAG divided by
concurrent JGB yield

＋

2143

0.31

0.41

0.01

8.51

Table-1 (3): Summary Stat for Initially Low-Rate- 36 -

Variable
SPt

3-Yr SPREAD

Lt

T_JGBGAPFt

JGBSLOPE (10Y-2Y)

Ft

JGB10Y

Defininition
Coorporate bond yield minus
JGB yield
3-month Tibor minus
3-month JGB yield
10-year JGB yield minus
2-year JGB yield

Expected Sign

10-year JGB yield
Growth rata of Nikkei
stock index
20-day historical volatility of
individual stock minus
estimated historical volatilityof each individual

Obs

Mean

Std.

Min

Max

2499

0.28

0.24

0.03

4.21

＋

2548

0.13

0.09

-0.03

0.32

－/＋
－/＋
－/＋

2548

1.07

0.24

0.69

1.64

2548

1.58

0.19

1.17

1.93

2548

0.00

0.04

-0.11

0.09

＋

2548

-0.86

10.72

-38.1674.70

Ft

NKYGROWTH

fit

eHV

fit

RATE_RI

R&I credit ratings

＋

2548

5.67

2.56

2.00

11.00

lit

GAP3_1DLAGHighest reported yield minus
lowest reported yield in theprevious day of 3-Yr SPREAD

＋

2498

0.06

0.06

0.01

1.51

lit

GAP3_1DLAG_Adj

GAP3_1DLAG divided by
concurrent JGB yield

＋

2498

0.12

0.15

0.01

3.35

Table-1 (4): Summary Stat for Good-State

VariableSPt

3-Yr SPREAD

Lt

T_JGBGAPFt

JGBSLOPE (10Y-2Y)

Ft

JGB10Y

Defininition
Coorporate bond yield minus
JGB yield
3-month Tibor minus
3-month JGB yield
10-year JGB yield minus
2-year JGB yield

Expected Sign

10-year JGB yield
Growth rata of Nikkei
stock index
20-day historical volatility of
individual stock minus
estimated historical volatilityof each individual

Obs

Mean

Std.

Min

Max

1674

0.57

0.60

-0.11

4.15

＋

1716

0.29

0.15

0.07

0.54

－/＋
－/＋
－/＋

1716

1.04

0.19

0.71

1.39

1716

1.37

0.13

0.95

1.60

1716

0.00

0.08

-0.24

0.13

＋

1716

1.27

17.11

-76.0383.84

Ft

NKYGROWTH

fit

eHV

fit

RATE_RI

R&I credit ratings

＋

1716

5.56

2.49

2.00

11.00

lit

GAP3_1DLAGHighest reported yield minus
lowest reported yield in theprevious day of 3-Yr SPREAD

＋

1674

0.15

0.17

0.00

3.95

lit

GAP3_1DLAG_Adj

GAP3_1DLAG divided by
concurrent JGB yield

＋

1674

0.43

0.45

0.01

8.51

Table-1 (5): Summary Stat for Bad-State- 37 -

Variable
SPt

3-Yr SPREAD

Lt

T_JGBGAPFt

JGBSLOPE (10Y-2Y)

Ft

JGB10Y

Defininition
Coorporate bond yield minus
JGB yield
3-month Tibor minus
3-month JGB yield
10-year JGB yield minus
2-year JGB yield

Expected Sign

10-year JGB yield
Growth rata of Nikkei
stock index
20-day historical volatility of
individual stock minus
estimated historical volatilityof each individual

Obs

Mean

Std.

Min

Max

1213

0.21

0.27

0.03

4.21

＋

1225

0.13

0.09

-0.03

0.32

－/＋
－/＋
－/＋

1225

1.07

0.24

0.69

1.64

1225

1.58

0.19

1.17

1.93

1225

0.00

0.04

-0.11

0.09

＋

1225

-3.97

10.09

-32.9874.70

Ft

NKYGROWTH

fit

eHV

fit

RATE_RI

R&I credit ratings

＋

1225

3.56

1.71

2.00

9.00

lit

GAP3_1DLAGHighest reported yield minus
lowest reported yield in theprevious day of 3-Yr SPREAD

＋

1213

0.05

0.07

0.01

1.51

lit

GAP3_1DLAG_Adj

GAP3_1DLAG divided by
concurrent JGB yield

＋

1213

0.10

0.14

0.01

3.35

Table-1 (6): Summary Stat for Initially Hi-Rate & Good-State

VariableSPt

3-Yr SPREAD

Lt

T_JGBGAPFt

JGBSLOPE (10Y-2Y)

Ft

JGB10Y

Defininition
Coorporate bond yield minus
JGB yield
3-month Tibor minus
3-month JGB yield
10-year JGB yield minus
2-year JGB yield

Expected Sign

10-year JGB yield
Growth rata of Nikkei
stock index
20-day historical volatility of
individual stock minus
estimated historical volatilityof each individual

Obs

Mean

Std.

Min

Max

858

0.83

0.70

0.17

4.15

＋

891

0.29

0.15

0.07

0.54

－/＋
－/＋
－/＋

891

1.04

0.19

0.71

1.39

891

1.37

0.13

0.95

1.60

891

0.00

0.08

-0.24

0.13

＋

891

5.77

16.93

-55.6783.84

Ft

NKYGROWTH

fit

eHV

fit

RATE_RI

R&I credit ratings

＋

891

7.42

1.41

4.00

11.00

lit

GAP3_1DLAGHighest reported yield minus
lowest reported yield in theprevious day of 3-Yr SPREAD

＋

858

0.19

0.22

0.00

3.95

lit

GAP3_1DLAG_Adj

GAP3_1DLAG divided by
concurrent JGB yield

＋

858

0.54

0.55

0.01

8.51

Table-1 (7): Summary Stat for Initially Low-Rate & Bad-State- 38 -3-Yr
SPREAD(Lagged)

3-Yr
SPREAD

T_JGBGAPJGBSLOPE(10Y-2Y)JGB10YNKYGROWTHeHV

RATE_RI

GAP3_
1DLAG

3-Yr SPREAD

1.00

3-Yr SPREAD(Lagged)

0.97

1.00

T_JGBGAP

0.42

0.40

1.00

JGBSLOPE (10Y-2Y)

-0.15

-0.12

-0.44

1.00

JGB10Y

-0.17

-0.16

-0.42

-0.07

NKYGROWTH

0.00

0.02

-0.19

0.28

-0.01

1.00

eHV

0.32

0.31

0.09

-0.07

-0.03

0.04

1.00

RATE_RI

0.44

0.45

-0.05

0.03

0.01

0.01

0.33

1.00

GAP3_1DLAG

0.68

0.63

0.31

-0.06

-0.19

0.00

0.26

0.25

1.00

GAP3_1DLAG_Adj

0.59

0.57

0.22

0.16

-0.38

0.07

0.21

0.25

0.89

GAP3_
1DLAG_
Adj

1.00

1.00

Table-2 (1): Correlation Table for All Samples
3-Yr
SPREAD(Lagged)

3-Yr
SPREAD

T_JGBGAPJGBSLOPE(10Y-2Y)JGB10YNKYGROWTHeHV

RATE_RI

GAP3_
1DLAG

3-Yr SPREAD

1.00

3-Yr SPREAD(Lagged)

0.93

1.00

T_JGBGAP

0.34

0.34

1.00

JGBSLOPE (10Y-2Y)

-0.25

-0.23

-0.44

1.00

JGB10Y

-0.05

-0.04

-0.42

-0.07

1.00

NKYGROWTH

-0.03

-0.01

-0.18

0.28

-0.01

1.00

eHV

0.40

0.41

0.06

-0.09

0.00

0.08

1.00

RATE_RI

0.58

0.60

0.02

-0.02

0.00

0.00

0.53

1.00

GAP3_1DLAG

0.72

0.62

0.30

-0.07

-0.14

-0.01

0.31

0.47

1.00

GAP3_1DLAG_Adj

0.48

0.40

0.22

0.19

-0.39

0.09

0.24

0.37

0.85

GAP3_
1DLAG_
Adj

1.00

Table-2 (2): Correlation Table for Initially Hi-Rate
3-Yr
SPREAD
3-Yr SPREAD

1.00

3-Yr SPREAD(Lagged)

0.98

3-Yr
SPREAD(Lagged)T_JGBGAPJGBSLOPE(10Y-2Y)JGB10YNKYGROWTHeHV

RATE_RI

GAP3_
1DLAG

GAP3_
1DLAG_Adj

1.00

T_JGBGAP

0.53

0.50

1.00

JGBSLOPE (10Y-2Y)

-0.12

-0.08

-0.44

1.00

JGB10Y

-0.26

-0.25

-0.42

-0.07

1.00

NKYGROWTH

0.03

0.04

-0.19

0.28

-0.01

1.00

eHV

0.21

0.19

0.13

-0.06

-0.06

0.01

1.00

RATE_RI

0.20

0.21

-0.17

0.14

0.02

0.04

-0.13

1.00

GAP3_1DLAG

0.66

0.62

0.35

-0.06

-0.24

0.00

0.20

0.06

1.00

GAP3_1DLAG_Adj

0.59

0.59

0.25

0.16

-0.42

0.08

0.15

0.10

0.90

Table-2 (3): Correlation Table for Initially Low-Rate- 39 -

1.00

3-Yr
SPREAD

3-Yr
SPREAD(Lagged)T_JGBGAPJGBSLOPE(10Y-2Y)JGB10YNKYGROWTHeHV

RATE_RI

GAP3_
1DLAG

3-Yr SPREAD

1.00

3-Yr SPREAD(Lagged)

0.93

1.00

T_JGBGAP

0.24

0.22

1.00

JGBSLOPE (10Y-2Y)

-0.20

-0.17

-0.50

1.00

JGB10Y

0.07

0.08

-0.22

-0.14

1.00

NKYGROWTH

-0.04

-0.05

-0.23

0.21

-0.05

1.00

eHV

0.30

0.31

0.02

-0.09

0.03

0.10

1.00

RATE_RI

0.49

0.50

-0.03

0.03

0.00

0.01

0.36

1.00

GAP3_1DLAG

0.71

0.57

0.13

-0.05

0.08

-0.08

0.19

0.28

1.00

GAP3_1DLAG_Adj

0.50

0.39

0.00

0.31

-0.33

0.00

0.11

0.27

0.74

GAP3_
1DLAG_
Adj

1.00

Table-2 (4): Correlation Table for Good-State
3-Yr
SPREAD

3-Yr
SPREAD(Lagged)T_JGBGAPJGBSLOPE(10Y-2Y)JGB10YNKYGROWTHeHV

RATE_RI

GAP3_
1DLAG

3-Yr SPREAD

1.00

3-Yr SPREAD(Lagged)

0.98

1.00

T_JGBGAP

0.32

0.29

1.00

JGBSLOPE (10Y-2Y)

-0.14

-0.08

-0.58

1.00

JGB10Y

-0.10

-0.07

-0.22

-0.01

1.00

NKYGROWTH

0.03

0.05

-0.21

0.41

0.04

1.00

eHV

0.33

0.31

0.08

-0.04

-0.03

0.01

1.00

RATE_RI

0.55

0.55

-0.05

0.03

0.00

0.01

0.33

1.00

GAP3_1DLAG

0.63

0.58

0.14

-0.05

-0.12

0.03

0.28

0.34

1.00

GAP3_1DLAG_Adj

0.53

0.52

-0.05

0.21

-0.27

0.12

0.23

0.37

0.89

GAP3_
1DLAG_
Adj

1.00

Table-2 (5): Correlation Table for Initially Bad-State
3-Yr
SPREAD
3-Yr SPREAD

1.00

3-Yr SPREAD(Lagged)

0.90

3-Yr
SPREAD(Lagged)T_JGBGAPJGBSLOPE(10Y-2Y)JGB10YNKYGROWTHeHV

RATE_RI

GAP3_
1DLAG

GAP3_
1DLAG_Adj

1.00

T_JGBGAP

0.14

0.13

1.00

JGBSLOPE (10Y-2Y)

-0.19

-0.18

-0.50

1.00

JGB10Y

0.08

0.10

-0.21

-0.14

1.00

NKYGROWTH

0.00

-0.01

-0.24

0.21

-0.05

1.00

eHV

0.37

0.39

0.01

-0.13

0.04

0.13

1.00

RATE_RI

0.53

0.54

0.01

-0.01

0.01

0.00

0.51

1.00

GAP3_1DLAG

0.81

0.61

0.10

-0.08

0.11

-0.07

0.25

0.42

1.00

GAP3_1DLAG_Adj

0.65

0.43

0.00

0.21

-0.22

0.00

0.20

0.35

0.84

Table-2 (6): Correlation Table for Initially Hi-Rate & Good-State- 40 -

1.00

3-Yr
SPREAD

3-Yr
SPREAD(Lagged)T_JGBGAPJGBSLOPE(10Y-2Y)

3-Yr SPREAD

1.00

3-Yr SPREAD(Lagged)

0.98

1.00

T_JGBGAP

0.37

0.32

1.00

JGBSLOPE (10Y-2Y)

-0.10

-0.03

-0.59

1.00

JGB10Y

-0.14

-0.11

-0.21

0.00

JGB10YNKYGROWTHeHV

RATE_RI

GAP3_
1DLAG

1.00

NKYGROWTH

0.07

0.10

-0.22

0.41

0.04

1.00

eHV

0.20

0.17

0.08

-0.04

-0.01

-0.02

1.00

RATE_RI

0.30

0.32

-0.20

0.14

0.02

0.03

-0.18

1.00

GAP3_1DLAG

0.59

0.54

0.17

-0.07

-0.14

0.03

0.20

0.14

1.00

GAP3_1DLAG_Adj

0.51

0.49

-0.04

0.19

-0.30

0.12

0.14

0.21

0.90

Table-2 (7): Correlation Table for Initially Low-Rate & Bad-State- 41 -GAP3_
1DLAG_
Adj

1.00

(2)
Model 1
3-Yr SPREAD
T_JGBGAPJGBSLOPE (10Y-2Y)
JGB10YNKYGROWTH

Coef.

Std.

1.40940.05300.01670.65150.2414(3)
Model 2***0.05420.03630.1106***e_HV
RATE_RI(4)
Model 3 Pooling

Coef.

Std.

1.44930.04150.02970.5901

0.23900.00390.0926***

0.05180.02940.1102***0.0010***0.0248***

GAP3_1DLAG
GAP3_1DLAG_Adj

Coef.

Std.

0.9239-0.0325
0.0962
0.46980.0861***

0.02120.0196***

0.0944***0.0021
0.05420.0005***0.0029***1.77430.2907***-0.36110.0449***(4)
Model 3 RE

(4)Model 3 FE
Coef.

Std.

0.9837-0.02230.08770.47540.1670***0.0473Std.

0.9686-0.0204
0.08760.47370.1687

Coef.
***

0.0446Std.

1.1903-0.1311
0.33630.42470.00250.07200.0004***0.0057***

0.0365***0.0217***0.0240***0.0733***0.0202***

0.0942***0.00200.06280.0007***0.0130***0.2066***1.60640.2073***0.56380.0145***0.1963**-0.4009

0.1054***-0.7368

0.0614***0.0205***0.0941***0.0007***0.0327**1.5833-0.4758

0.00200.0763Coef.

(4)
Model 3 MLE

3-Yr SPREAD (Lagged)_cons

0.04840.0623-0.4874

0.1729# Obs# Group

4173
52

4173
52

withinbetweenoverall

0.26730.03200.17930.30690.61240.4070

R-sq:

***

4172
52

4172
52

4172
52

0.61510.52730.75180.60290.52690.77190.61200.02880.09050.00000.0905sigma_alphasigma_erho: AR(1) on e

4172
52

0.13670.25920.2178

Note: *** :1%,** :5%, * :10%

Breusch and Pagan Lagrangian multiplier test for random effects
3-Yr SPREAD[FCODE,t] = Xb + u[FCODE] + e[FCODE,t]
Estimated

results:|Var
sd=sqrt(Var)---------+----------------------------3-Yr SPREAD|
0.198782 0.44585
e|0.062577 0.250154
u|0.007534 0.086796
Test: Var(u) = 0
chi2(1) = 4728.20
Prob > chi2 =0.0000Hausman test---Coefficient---|
(b)
(B)
(b-B)
sqrt(diag(V_b-V_B))
|
fixed
.
Difference S.E.
-------------+---------------------------------------------------------------T_JGBGAP|
0.983662 0.968578 0.015085 0.002873
JGBSLOPE (10Y-2Y)|-0.02233 -0.02044 -0.00189 .
JGB10Y|
0.087688 0.087634 5.41E-05 .
NKYGROWTH|
0.475361 0.473703 0.001658 .
e_HV|0.001958 0.001967 -9.14E-06 8.06E-05
RATE_RI|
0.07626 0.062779 0.013481 0.006026
GAP3_1DLAG|
1.583268 1.60639 -0.02312 0.000878-----------------------------------------------------------------------------b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Test: Ho: difference in coefficients not systematicchi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)= -126.77 chi2<0==> model fitted on thesedata fails to meet the asymptotic
assumptions of the Hausman test;
see suest for a generalized test

Table-3: Static Model- 42 -

(5)Dynamic
Model 4 AR1
3-Yr SPREAD

Coef.

T_JGBGAPJGBSLOPE (10Y-2Y)
JGB10YNKYGROWTH

0.4664-0.1087
0.03190.1255e_HV
RATE_RI

0.0002
0.0617

GAP3_1DLAG
GAP3_1DLAG_Adj

0.2900(5)
Dynamic
Model 5 Pooling
Coef.

Std.

0.0409***0.0273***0.02180.0211***0.00010.0078***0.0163***

3-Yr SPREAD (Lagged)_cons

0.01050.0540# Obs# Group4172
52

withinbetweenoverall

0.4261
0.63350.4435R-sq:

0.0496-0.0633
0.0036-0.0206

0.00030.0030(5)
Dynamic
Model 5 FE
Coef.

Std.

0.0193***0.0055***0.00890.02470.0001*0.0008***0.39050.1306***

0.88660.02490.04490.0186

0.0634-0.05770.0043-0.01360.0004-0.0052(5)
Dynamic
Model 5 RE
Coef.

Std.

0.0150***0.0078***0.00870.02580.0001***0.0028*0.40960.0149******0.86820.0053**0.08600.02454116

sigma_alphasigma_erho: AR(1) on e

0.0496-0.0633
0.0036-0.0206

0.00030.0030(5)
Dynamic
Model 5 AB GMM
Coef.

Std.

0.0146***0.0078***0.00880.02590.0537-0.0530-0.0016-0.01260.0004-0.0126

0.0212***0.00870.0258***0.1341

0.39890.0149***0.86250.0367***0.87820.0054***0.13370.0636**0.04240.0198**0.0146

0.4310***0.88660.0048******0.04490.0196**0.00000.09050.0066***0.0077***0.39050.02880.0905***

Std.

0.0148******0.9381
0.99800.95840.00490.0588-0.06180.0043-0.01710.0009***0.9384
0.99720.9565**0.0001**0.0007

4116
52

Coef.

Std.

0.02530.00030.00310.0001

4116
52

(5)
Dynamic
Model 5 AH MLE

0.0002*0.0119

4059
52

4116
52

0.01010.09060.0122

Note: *** :1%,** :5%, * :10%

Breusch and Pagan Lagrangian multiplier test for random effects
3-Yr SPREAD[FCODE,t] = Xb + u[FCODE] + e[FCODE,t]
Estimated

results:|Var
sd=sqrt(Var)---------+----------------------------3-Yr SPREAD|
0.199331 0.446465
e|0.008184 0.090466u|00
Test: Var(u) = 0
chi2(1) = 10.74
Prob > chi2 =0.0010Hausman test---Coefficient---|
(b)
(B)
(b-B)
sqrt(diag(V_b-V_B))
|
fixed
.
Difference S.E.
-------------+---------------------------------------------------------------T_JGBGAP|
0.868186 0.886612 -0.01843 0.00217
JGBSLOPE (10Y-2Y)|
0.063394 0.049639 0.013755 0.003667
JGB10Y|-0.05768 -0.06329 0.005606 .
NKYGROWTH|
0.004342 0.003565 0.000777 .
e_HV|-0.01361 -0.02063 0.007019 .
RATE_RI|
0.000402 0.000274 0.000128 8.56E-05
GAP3_1DLAG|-0.00515 0.002975 -0.00813 0.002671
GAP3_1DLAG|
0.409592 0.390487 0.019105 0.003156-----------------------------------------------------------------------------b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Test: Ho: difference in coefficients not systematicchi2(8) = (b-B)'[(V_b-V_B)^(-1)](b-B)=
110.19Prob>chi2 =0.0000(V_b-V_B is not positive definite)

Table-4: Dynamic Model- 43 -

RE
Model 3Hi-RateStd.
Coef.

3-Yr SPREAD

RE
Model 3
Low-Rate
Std.
Coef.

T_JGBGAPJGBSLOPE (10Y-2Y)
JGB10YNKYGROWTH

0.3968-0.1466
0.12240.1522

0.0960***0.0258***0.0139***0.0600**e_HV
RATE_RI

0.00200.10490.0009**0.0297***

GAP3_1DLAG
GAP3_1DLAG_Adj

1.36780.3602-0.32110.1053RE
Model 3Good-State
Std.
Coef.

1.63070.10100.04700.82340.31820.00140.08300.00090.0228******1.49700.2287***-0.75090.2394RE
Model 3
Bad-State
Std.
Coef.

0.4215-0.10960.06150.29340.0723***0.0241***0.0161***0.0842***0.00150.03920.00120.0093******2.08790.3816***-0.0957

0.0412***0.07130.0275*0.1625***1.29110.0498-0.05190.61410.2265RE
Model 3
Hi- & GoodStd.
Coef.
***

0.07730.04800.1254***RE
Model 3Low- & BadStd.
Coef.

0.1080-0.1475
0.00710.46940.0469**0.0177***0.00180.05160.00200.0246*****0.01300.11140.0006
0.11750.00100.0213******

1.11670.1786***2.47540.1378**-0.5973

0.1771***0.04090.0597***2.09080.3114-0.2066
1.05500.4433***0.1287**0.0799***0.2173***0.00090.17880.00190.0527***1.07700.2160***-1.3460

0.4914***

3-Yr SPREAD (Lagged)
_cons
# Obs
# GroupR-sq:

withinbetweenoverallNote: ***:1%,**:5%, *:10%

2029
25

2143
27

2498
52

1674
52

1213
25

858
27

0.61410.70170.61170.57610.73050.5956

0.49830.77710.63010.4754
0.67610.59010.63020.77870.70410.5192
0.5484
0.5213

Table-5 (1): Static Model (RE) with Sample Split(5)
Dynamic
Model 5 AH MLE
Hi-Rate
Std.
Coef.

(5)
Dynamic
Model 5 AH MLE
Low-Rate
Std.
Coef.

(5)
Dynamic
Model 5 AH MLE
Good-State
Std.
Coef.

(5)
Dynamic
Model 5 AH MLE
Bad-State
Std.
Coef.

(5)
Dynamic
Model 5 AH MLE
Hi- & GoodStd.
Coef.

(5)
Dynamic
Model 5 AH MLE
Low- & BadStd.
Coef.

T_JGBGAPJGBSLOPE (10Y-2Y)
JGB10YNKYGROWTH-0.0150-0.0800
0.0129-0.0299

0.01990.1555-0.07100.01170.02290.0217

***

***

***

***

0.0174***0.0317***0.0251***0.2120-0.1664-0.15240.05920.0470***-0.0385-0.0763-0.0425
0.29980.03310.00720.0838-0.1286-0.1226-0.03450.0247***0.0603-0.0611-0.00960.22780.02090.01060.0446***e_HV
RATE_RI

0.00020.00500.0002

***

***

***

***

0.0017**0.00110.01290.00030.00090.00010.00140.0003***0.00060.00330.00020.00200.00010.00500.0002**0.00070.00820.00020.00240.0048***

GAP3_1DLAG
GAP3_1DLAG_Adj

0.8356

0.0314***0.28510.0161***

1.19480.0313***0.28480.0184***1.7406

0.0436***

0.28810.0249***3-Yr SPREAD (Lagged)

0.73520.0137***0.89830.0060***0.71320.0094***0.90950.0085***0.62070.0150***0.89460.0117***_cons

0.05770.0268**-0.01280.0306

0.05860.0184***0.2671

0.0468***0.14380.0296***0.25250.0902***

3-Yr SPREAD# Obs# Group
Note: *** :1%,** :5%, * :10%

0.0105***0.01190.03472003
25

0.01180.03512113
27

0.00780.0348

2495
52

***

0.0362

1621
52

Table-5 (2): Dynamic Model with Sample Split- 44 -

0.0118***0.0127***0.0572***0.00231212
25

0.0647830
27

3-Yr SPREAD

RE
Dynamic
Dynamic
Dynamic
Model 3Model 4 AR1
Model 5 AB GMM
Model 5 AH MLE(Robustness Check) (Robustness Check) (Robustness Check) (Robustness Check)
Std.
Std.
Std.
Std.
Coef.
Coef.
Coef.
Coef.

T_JGBGAPJGBSLOPE (10Y-2Y)
JGB10YNKYGROWTH

1.1859-0.13110.33770.42370.1676***0.0393***0.0453***0.0868***e_HV
RATE_RI

0.00250.06720.0007***0.0166***

GAP3_1DLAG
GAP3_1DLAG_Adj

0.56690.0648***0.4514-0.1150
0.06860.12120.0415***0.0277***0.0223***0.0214***0.00020.05930.00010.0080***0.09280.0066***

3-Yr SPREAD (Lagged)
_cons

R-sq:

-0.7120# Obs# Groupwithinbetweenoverall
***
**
Note:
:1%, :5%, *:10%0.1523***-0.02140.0554

4172
52

4172
52

0.49140.73140.57400.40190.62040.4177

0.0943-0.0772
0.0404-0.0275

0.0248***0.0112***0.0006-0.01020.00030.11370.05140.88560.07940.0851-0.08100.0370-0.0338

0.0157***0.0083***0.0097***0.00050.00260.0001***0.0008*****0.09700.0061***0.0368***0.90750.0058***0.0403**0.01400.02100.02690.0228**0.0113

4059
52

4116
52

Table-6: Robustness Check (Adjusted Gap: Relative Distance Measure)- 45 -

0.0272

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