israeli government debt: altruistic investors in the absence of arbitrageurs
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Israeli Government Debt:Altruistic Investors in the Absence of Arbitrageurs
Matthew Salzberg
Presented to the Department of Economicsin partial fulfillment of the requirements
for a Bachelor of Arts degree with Honors
Harvard College
Cambridge, Massachusetts
March 17, 2005
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ABSTRACT
In this paper, I examine the market for non-negotiable Israeli government debt in
order to understand unconventional investor motivations. Using a unique dataset
provided by the Israeli government, I find that investors in these bonds partially exhibit
altruistic preferences. In fact, I show that investors increase their demand for bonds in
the face of both greater terrorist attacks and religious holidays as a way of supporting the
state. Furthermore, I find that investors overweight the importance of the nominal yield
on these bonds relative to benchmark investments and underweight the importance of the
Israeli default risk premium. Consequently, the State of Israel is able to uniquely harness
the goodwill of investors in order to raise capital at favorable terms.1
1Acknowledgements: I would like to thank my advisors Professor Jeremy Stein and Professor JeffreyMiron for their valuable advice and continuous feedback during the entire thesis-writing process.Furthermore, the successful completion of this paper was made possible by the wonderful people at theIsraeli Ministry of Finance and the Development Corporation for Israel. Specifically, I would like to thankShirley Strifler, Joseph Rychalski and Raphael Rothstein for being kind enough to assist a completestranger with an unusual data request. I owe thanks to Ryan Geraghty for his thoughtful comments. Lastly,I would like to thank my parents for their continued support. They have been a source of invaluableencouragement and good ideas. Special thanks are deserved by my mother, whose annual purchase ofIsrael Bonds inspired this entire project.
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Table of Contents
Abstract and Acknowledgements 2
Table of Contents 3
I. Introduction 4
II. Literature Review and Background 6
III. Three: Theory: A Model for the Israel Bonds Market 11
IV. Empirical Strategy 16a. The Casual Effect of Altruistic Events on Quantity and Spread 17b. Demand Effects 19
V. Data 24a. Israel Bond Instruments 24b. Constructing Comparable Investment Variables 30c. Constructing Altruism Indicators and Event Variables 32
VI. Evidence 36a. Equilibrium Quantity Results 36b. Event Salience 41c. Equilibrium Yield Changes 43d. Demand-Only Effects 47
VII. Conclusion 50
VIII. References 53
IX. Figures and Tables 54
Mathematical Appendices 76Mathematical Appendix A 76Mathematical Appendix B 77
Appendices 79Appendix A: Israel Bonds Marketing Materials 79Appendix B: Israel Bond Prospectus Features 81
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I. Introduction
Traditionally, economists have viewed financial investors as fully-rational, profit-
seeking individuals. They demand financial assets in an effort to maximize monetary
return while simultaneously minimizing the associated risk. Recently, however, much
interest has been given to behavioral approaches to finance, which take into account a
greater variety of investor motivations. The current debate over Harvard Management
Companys holdings of PetroChina, for example, demonstrates that the investment
decision for some investors includes political and ethical concernsin this case, over
genocide in Sudan. Similarly, ethical investment funds allow investors to maintain
portfolios which only hold those companies that they deem as ethical, or socially
desirable. For instance, some investors choose only to hold environmentally-friendly
stocks. As more and more research has begun to document, the existence of broader
investor motivations in specific markets and circumstances requires a rethinking of
traditional economic models.
Of particular interest to practitioners should be how behavioral approaches to
finance may be used to improve macroeconomic policy outcomes. In other words, can
countries use non-private investor motivations to their advantage? For years,
governments have attempted to use social forces and civically-minded marketing to lower
their cost of debt capital. For instance, the governments of most developed nations used
War Bonds to raise capital during both World War I and World War II. These bonds
partially relied on the patriotic sentiments of citizens to raise capital for the war effort.
During World War I, the United States government marketed both Liberty Bonds and
Victory Bonds as a way to capitalize on the patriotism of its citizens and their support
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for the war. More recently, the United States government began issuing Patriot Bonds
after the 9/11 terrorist attacks, which serve as patriotic versions of U.S. savings bonds. If
investors exhibit altruism or patriotism as motivations for investment decisions
regarding government debt, policy makers might be able to use this information to tailor
capital raising schemes more efficiently and lower a countrys effective cost of debt
capital. Consequently, a lower cost of capital helps save a country money and makes
more investment projects efficient to undertake.
In this paper, I examine one of the largest known governmental programs of this
type, the Israel Bonds program, implemented by the State of Israel. This program
markets non-negotiable government debt to altruistic investors in the United States and
Canada as a way to support the State of Israel. For the purposes of this research, I have
been provided with a unique dataset by the Ministry of Finance of Israel, which allows
analysis of changes in prices (yields) and quantities of these securities. By looking at
various events which are likely correlated with altruistic sentiment, like religious holidays
and terrorist attacks, I examine whether investors in these securities react differently to
political and religious news events than purely profit-seeking individuals.
The next chapter of this paper provides background information on investor
motivations and the Israel Bonds program. In chapter 3, I develop a simple model of the
Israel Bonds market to provide an intuition for how and why altruism enters into the
supply and demand decision. Chapter 4 expands upon this model to explain how it is
possible to identify altruistic effects in an empirical context. Chapter 5 describes the
particulars of my data and chapter 6 reports my findings. Finally, I conclude in chapter 7.
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II. Literature Review and Background
Diverse investor motivations have recently become a subject of research in
finance, notably with regard to investment in ethical funds. The development of these
investment funds, where investors limit their portfolios to specific companies that fulfill a
set of socially responsible criteria, is still relatively new. Cullis, Lewis and Winnett
(1992) document the growth in ethical unit trusts in the United Kingdom. Theoretically,
one would expect that if investors weigh social or ethical factors when making an
investment decision, they must forgo higher levels of financial return per unit of risk.
This is because an investor who is maximizing return will chose a different optimal
portfolio than an investor who is maximizing return with other considerations
simultaneously. The latter investor will substitute between financial return and these
other factors, thereby choosing a portfolio with a less-than-maximum return at a given
risk level.
Empirically, however, the results concerning whether ethical investors receive
lower returns have been mixed. Diltz (1995), Sauer (1997) and Guerard (1997) find that
there is no statistical difference between ethical and non-ethical performance in the
United States. Similarly, Statman (2000) and Gregory, Matatko and Luther (1997)
conclude that there is no difference between the performance of ethical and non-ethical
unit trusts in both the United Kingdom and the United States. Yet, other studies do find
that ethical funds under-perform their benchmarks. For instance, Tippit (2001) finds that
ethical mutual funds in Australia under-perform an index benchmark by 1.5% per annum
Furthermore, Ali and Gold (2002) find that investors lose 0.7% per year when companies
in non-ethical industries are removed from a market portfolio.
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This body of research has focused largely on firm-level securities and diversified
portfolios where there are a variety of outlets and substitutes for a particular type of
ethical investing (i.e. there are many investment outlets for an investor who wants to
support environmentally friendly companies). As a result, an investor may not have to
make as serious a departure from his optimal portfolio in order to invest ethically in these
cases. This is because as more securities become eligible for him, his accessible
investment universe will approach the market and he will be closer to being able to
construct the risk-return maximizing portfolio. Yet, the fact that investors may be willing
to forgo even some financial return in order to invest in these ethical funds indicates
that investor motivations may be more complex than traditional economics suggests.
Unfortunately, little research has been done to see the effects of ethical
investing on the cost of capital of a sovereign government, despite the fact that countries
deliberately market their securities with the hopes of attracting these types of investors.
Notably, governments have tried to tie their bonds to a political or patriotic cause in times
of war. Rockoff (2004) looks at U.S. war bonds from World War I and concludes that
they were, in fact, priced to sell as purely financial investments. His analysis rests on the
fact that the spread between Liberty Bonds and municipal bonds does not shrink after the
armistice that ended the war. The bonds traded during World War I, however, were not
as prominently marketed as later patriotic bond issues and were allowed to trade on the
open market. Since they traded on the market, prices reflected what profit-seeking bond
traders were willing to pay, rather than what the civically-minded investor would pay.
After World War I, however, war bonds were sold as non-marketable securities, which
prevented non-civically minded investors from selling and causing the premium to
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vanish. Many have speculated that the government was more successful in raising debt at
below-market rates during World War II; although, no empirical research has been done
on these bonds.
Perhaps the largest governmental program still at work today is the Israel Bonds
program, which sells Israeli government debt in the United States and Canada as a way
for Diaspora Jews and other investors sympathetic to Israel to support the state. This is
done through a retail agency called the Development Corporation for Israel (DCI), a
NASD-registered broker/dealer headquartered in New York, which markets the debt in
the United States. Since these bonds are non-transferable, arbitrageurs cannot sell and
drive prices towards their fundamental values. As a result, these bonds provide a unique
opportunity to search for price and quantity fluctuations caused by the altruistic sentiment
of investors.
The program has been operating since 1951 and has contributed significantly to
Israels fundraising ability abroad. To date, bond sales have exceeded $25 billion.
Relative to the size of the external debt, the program constitutes a large share of borrowed
funds (Figure 1). Indeed, as of September 2004, Israel Bonds accounted for 33.3% of
Israels external debt of approximately $30 billion and approximately 8% of the countrys
total debt.
While sales from the bonds are designated by Israels Ministry of Finance for
general use, DCI highlights the development projects to which they contribute as part of
the marketing campaign. For instance, the DCI website highlights the fact that the funds
go towards nation-building and economic infrastructure, like agriculture, energy,
security and transportation. In fact, it is explicitly stated in the prospectuses of the Israel
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Bonds that these offerings may have a special appeal to persons with an interest in the
State of Israel rather than the general public. By linking Israels prosperity and security
to sales of these bonds, DCI attempts to capitalize on the goodwill of investors in a way
that is unique among other sovereign nations. Appendix A provides examples of the type
of marketing materials used to sell these bonds.
In a recent paper by the Bank of Israel, Rechavi and Weingarten (2003) argue that
the goal of the Israel Bonds program is partially to decrease the cost of debt of the State
of Israel. In fact, they argue that in the programs early years marketing was done
specifically to those Jews with a direct or indirect tie to the Holocaust. Since these Jews
saw the purchase of Israel Bonds as a way to make a contribution to the State of Israel
(and a good cause), they were willing to invest at rates favorable to the Bank relative to
other credit sources. Rechavi and Weingarten argue that the Second Generation of
Jews is willing to pay a smaller premium to support the State of Israel than the earlier
Holocaust generation; however, they believe that they are still willing to buy the bonds at
submarket rates. Unfortunately, however, no empirical evidence has been shown to
support these claims.
Previous research by Liviatan (1980) suggests, however, that the Israel Bonds
program itself is non-economic in naturethat is, the cost of debt at which Israel is able
to issue securities though the program is not more favorable than the going market rates.
While he observes that the direct interest on the bonds is favorably low, other factors
make the effective interest on the bonds comparable to other credit sources. For instance,
the likelihood that the sale of Israel Bonds crowds out charitable transfers through
charities like the United Jewish Appeal (UJA) may raise the effective cost of the bonds.
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Furthermore, DCI incurs above-average marketing and distribution costs in order to
implement the program. Taken together, he concludes that the overall cost of the loan
resembles that of an ordinary commercial loan from abroad. His analysis, however, only
concludes that at that point in time the effective interest on the bonds is comparable to
other credit sources. Over the years, he admits, the effective interest on these bonds has
varied. In fact, Liviatan (1980) cites the Six Days War as an event which induced
substantial capital inflow through the program. Had investors been fully rational, one
would expect this event to raise the risk premium that investors demand for Israeli debt,
and in turn, make Israel Bonds less attractive investments, all else equal. However, it
seems that the opposite occurs the war caused the bonds to become more attractive
investments. By better understanding investor motivations in these securities, it is
possible that the state can use this information to further tailor the Israel Bond program
and enhance its cost-effectiveness.
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III. Theory: A Model for the Israel Bonds Market
In this chapter, I will develop a simple model of the Israel Bonds market. As with
all economic models, this model greatly simplifies reality. This simplified case, however,
will give the reader a better intuition for how and why altruistic events and interest rates
can factor into both the supply and demand decision. In the next chapter, I will expand
the model to a form that can be easily used to identify these effects in an empirical
context.
The market for Israel Bonds is unique in the world of financial markets.
Traditional theory predicts that frictionless markets permit unlimited arbitrage, driving
security prices to their fundamental values associated with the future cash flows of the
security discounted at a rate appropriate to the risk. In the market for Israel Bonds,
however, arbitrage is impossible. The government mandates that these securities are non-
negotiable, which means that investors can buy, but they cannot sell. Consequently, there
is no guarantee that the prices of these bonds are associated with their fundamental
values. Furthermore, the absence of arbitrageurs means that the traditional finance
conception of inventors with perfectly elastic demand curves is not necessarily a good
description of this market.
Since prices may not reflect their fundamental values, it is reasonable to model
the Israel Bonds market with a system of supply and demand functions. In the model, it
is assumed that demand is a function of the spread of the bond and altruism, which is
exogenously shifted by news events such as terrorist attacks. Investors care about the
spread of the bond (i.e. how much it yields relative to a benchmark investment) rather
than the nominal yield because the bond only constitutes a small part of a diversified
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portfolio of investor holdings. When choosing how to allocate a marginal dollar of
capital, investors will analyze these bonds relative to their other opportunities. As a
result, the spread captures this important opportunity cost of funds2. The demand for
bonds is assumed to be linear and can be described as:
Equation 1.1
Qdt = at + b * st
where Qdt is the quantity of bonds demanded in period t, st is the spread on the bonds in
period t, b is a positive constant, and at is the level of altruism in period t.
Next, I will describe the supply decision. According to the Israeli government,
the Ministry of Finance sets annual fundraising quotas for bond sales planned in
accordance with the governments foreign currency requirements (Rechavi and
Weingarten, 2003). The model assumes that the Ministry sets bond spreads each period
to minimize the cost of debt, while maintaining this exogenous quota 3. The Ministry is
concerned with the spread on the bonds rather than the nominal interest rate because the
Israel Bonds market is only one of several possible avenues to raise capital.
Consequently, the spread will indicate the cost relative to other sources4. The Ministrys
minimization problem overtperiods of changing interest rates becomes:
2 In the model, the spread is assumed to be equal to the nominal yield on the bond minus a comparableinvestment. This comparable investment can be decomposed into two components: the U.S. treasury rate(the return required to compensate investors for the time value of money) and the Israeli default riskpremium (the excess return required to compensate investors for the risk of default on the debt). st = yield (U.S. rate + risk premium) where risk premium is the difference between Israeli tradable debt and the U.S.rate. Since the U.S. rate and the risk premium are determined in different markets, they can be considered
exogenous, and are thus, not included separately in the model for simplicity.3 While it is simplest here to assume supply and demand both react on the same time horizon, in practicethis does not occur. In fact, the Ministry of Finance sets a fixed nominal rate for an entire sales period(generally, one month) and allows investors to buy as many bonds as they demand at that price within theperiod.4 In the model, I assume that the Ministry and investors demand spread relative to the same benchmarkinvestment. In practice, this may not be true. It is possible that unsophisticated investors, or those withaltruistic motivations, may be overly sensitive to the nominal yield and less sensitive to the risk premiumthan rational economic actors. The possibility that investors may get the benchmark rate component of thespread wrong is discussed in more detail in chapter 6.
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minimize (Qst * st)subject to Qst = k
where Qs
t is the quantity of bonds supplied in period t, and k is the annual fundraising
quota. The supply function is defined by the spreads, st,which the Ministry sets each
period to fulfill this condition. Using constrained minimization, one finds that the
Ministry sets each periods spread such that:
dQst/dst * st + Qst = * dQ
st/dst
which implies that rates are set according to the following supply function5:
Equation 1.2
st = + c * Qst
-1
where and c are constants with c > 0. If the Ministry is sufficiently forward looking
and can foresee the shape (or at least form expectations) of the demand function for each
of the tperiods, and one assumes that the demand function changes from period to period
only in terms of the altruism variable, at (which causes shifts in the curve), it follows that
rates will be set lower in periods where anticipatable altruism is higher.
In equilibrium, the quantity supplied must equal the quantity demanded.
Combining equation 1.1 and equation 1.2, and taking comparative statics, it is clear that
in equilibrium:
st = + c * Qdt
-1 = + c * (at + b * st)-1
Equation 1.3
dst/dat = [ - c * Qdt-2 ] / [ 1 + bc * Qdt
-2 ]
Equation 1.4
5 See Mathematical Appendix A for a proof.
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dQt/dat = 1 / [ 1 + bc * Qdt-2 ]
From this, it follows that dst/dat < 0 and dQt/dat > 0 for all upward sloping supply and
downward sloping demand curves. Consequently, it is clear that under these
assumptions, one will observe lower spreads and higher quantities transacted in periods
where anticipatable altruism is higher.
In the model, altruism only enters as a parameter in the demand function when
considering the market within years. This is because when the annual fundraising quota
is constant, the Ministry of Finances only goal is to minimize the cost of debt.
Therefore, movements of prices and quantities within the year must be related to altruism
shocks on demand. It is plausible, however, to think that the Ministrys annual
fundraising quota may change in relation to altruistic events, such that movements in
prices and quantities across years may be the result of both supply and demand shifts.
For instance, the government may have a need for greater capital at times with more
frequent altruistic events like terrorist attacks in order to pay for security needs.
Alternatively, the state may have an interest in encouraging American Jews to hold its
securities to align their financial well-being with the policy preferences of Israel. For
example, if Israel needs U.S. aid, a U.S. bondholder may be more likely to support pro-
Israeli policies if he holds Israeli bonds. If the goal of the program is to maintain contact
with Diaspora Jews and influence country policy preferences in relation to Israel, the
benefits of policy leverage are likely higher in times of turmoil when attacks are high6.
Since the annual fundraising quota changes infrequently, it seems intuitive that
over relatively short time horizons the effect of altruism on supply should be small
6 There is some evidence that this may at least be partially true. Rechavi and Weingarten (2003) explicitlyrecognize one of the programs goals as maintaining contact with Diaspora Jews.
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relative to the effect of altruism on demand. Consequently, it is probably a reasonable
simplifying assumption that the annual fundraising quota may be considered exogenous.
In order to be sure, however, the analysis in this paper will allow for the possibility that
supply may be independently affected by the same events that cause altruism in investors.
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IV. Empirical Strategy
In this paper, I examine the Israel Bonds market in order to determine whether
altruistic investors react differently to political and religious news events than profit-
seeking investors. To do this, I analyze several types of events to find out whether they
cause altruistic shifts in the demand for bonds. The two principal kinds of events
considered are Jewish religious holidays and Israel-specific news events, like terrorist
attacks. I choose these events because of their likely tie to altruistic sentiment for the
State of Israel. It is assumed here that altruism is at least partially caused by empathy
with the misfortune of others. If this is the case, one would expect that terrorism and
violence tend to evoke feelings of community and sympathy in investors. Furthermore,
because of Israels unique significance to the Jewish religion, altruism may also be partly
religiously motivated. While technically religiously-motivated altruism may actually be
guilt or some other emotion, it can be considered as part of altruism for the purposes of
this paper (defined as the selfless contribution to the demand of bonds).
In this chapter, I first examine whether altruism is casually related to the quantity
of bonds transacted. In other words, are higher equilibrium quantities observed following
events that should increase altruism or in periods with more frequent altruistic events?
Secondly, I examine whether altruism is casually related to the equilibrium spreads set
for each period. Do spreads rise or fall in tandem with altruistic events? Finally, I show
how it is possible to use these casual effects to estimate the portion of quantity
movements associated only with demand shocks.
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The Casual Effect of Altruistic Events on Quantity and Spread
To first test whether quantities move in relation to altruistic events, a reduced
form regression will be run in the form:
Regression 1.1
lnQi,t= 0 + 1 * holiday t + 2 * terrorismt+ 3 *US ratei,t
+ 4 *Riskpi,t+ 5 * timevart+ 6 * instrumenti + 7 * dowt
where lnQi,tis the log-transformed sales for instrument i in period t, instrumenti is a
dummy variable for each of the 3 instrument types, holiday tis an indicator of religious
holidays, terrorismt is an indicator of terrorist attacks, dowt is a dummy variable for each
day of the week (to allow for cyclical patterns in sales), timevaris a time variable that
allows for a time trend in the series,Riskpi,tis an interaction variable for each of the i
instruments with the Israeli default risk premium (i.e. a dummy variable for each
instrument multiplied by the spread for that instrument), and US ratei,t is an interaction
variable for each of the i instruments with the appropriately comparable U.S. treasury
rate. Since the quantity data follows a right-skewed distribution, a log transformation is
used to make this variable more closely follow a normal distribution. Consequently, the
regression coefficients, 1 and 2, can be interpreted as percent increases or decreases in
quantity rather than changes in levels.
The nominal yield on Israel Bonds is excluded from this reduced form regression
in order to avoid simultaneity bias. This bias is caused because the spread that the
Ministry of Finance sets is a function of the quantity demanded, while at the same time
the quantity demanded is a function of the spread set. As a result, including the nominal
yield causes correlation between the regressor variable and the error term. In the next
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section, I will explain how I deal with this bias in order to properly identify the effect of
altruism on the demand curve alone. In this reduced form regression, however, the
coefficients, 1 and 2, represent only the effect on equilibrium quantities. In other words,
they are the effect on quantities after both demand andsupply adjust accordingly.
The Israeli default risk premium and the U.S. treasury rate are included in the
regression as controls for the exogenous part of the spread. These rates are the important
benchmarks to which investors and the Israeli government compare the nominal yield of
the bonds when assessing the attractiveness of the investment. They represent a base
return required to compensate investors for the time value of money (the U.S. treasury
rate) and the additional return required to compensate investors for the possibility of an
Israeli default on the debt (the Israeli default risk premium). Notably, the default risk
premium is possibly correlated with the same events that cause shifts in altruism. For
instance, a terrorist attack may simultaneously increase the risk premium that investors
demand and increase sympathy for the state. Empirical research has shown mixed
support for this possibility. Blass, Peled, and Yafeh (2004) argue, for instance, that
Israel-specific events (like terrorism) have little impact on the risk premium relative to
international events from 1996-1999, but do impact the risk premium in 2000.
If the risk premium is also correlated with the quantity of bonds transacted,
omitting it may create a bias in the coefficients of altruistic events. Since the nominal
yields on these bonds change infrequently, changes in the risk premium between sales
periods (when the nominal yield is fixed) may be correlated with changes in the spread
that investors demand to hold the bonds. In fact, between periods, the only movement in
the spread that investors receive results from movement in the exogenous risk premium
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and the U.S. treasury rate. Therefore, including the exogenous benchmark rates is
important in order to prevent omitted variable bias; however, the complexity of how they
enter into the model makes the coefficients estimated for their effect meaningless to
interpret.
Next, I will examine whether spreads move in relation to altruistic events7. A
second reduced form regression is run:
Regression 1.2
Yieldi,t= 0 + 1 * holiday t + 2 * terrorismt
+ 3 *US ratei,t+ 4 *Riskpi,t+ 5 * timevart+ 6 *instrumenti
where Yieldi,t is the nominal rate for instrument i in period t, instrumenti is a dummy
variable for each of the 3 instrument types, holiday tis an indicator of religious holidays,
terrorismtis an indicator of terrorist attacks,Riskpi,tis an interaction variable for each of
the i instruments with the Israeli default risk premium, US ratei,tis an interaction variable
for each of the i instruments with the appropriately comparable U.S. treasury rate and
timevartis a variable that allows for a time trend in the series. Since the spread is only
changed periodically, this regression will be run on the subset of observations that
includes only the times at which the interest rate setting decision is made (generally, this
is 5 days before a monthly sales period begins).
Demand Effects
Once it has been determined that bond sales increase or that bond spreads fall in
tandem with altruistic events, it is interesting to understand which portion of this
7 In this paper, I sometimes use the words yield and spread interchangeably. This is because a changein the yield, when holding the U.S. rate and risk premium constant, is equivalent to a change in the spread.
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variation is the result of the demand curve alone, as the primary motivation of this paper
is to understand unconventional investor motivations. In the model of the Israel Bonds
market presented above, altruism shocks affect the demand curve directly and affect the
supply curve through changes in the annual fundraising quota across years. Therefore,
within years, one expects the spread to fall in conjunction with altruistic events, but
across years, it is possible that a supply effect will offset this fall. Consequently, the net
effect on spreads is indeterminate. Yet, the fact that the spread likely adjusts somehow in
relation to altruistic events implies that the actual effect of altruism on quantity demanded
is different than the casual effect of altruism on equilibrium quantities estimated with
reduced form regression 1.1.
For instance, the model predicts a unit increase in altruism across periods will
result in a decrease in spreads within years. The resultant decrease in spreads, however,
means that there will be an offsetting decrease in demand. Therefore, quantities in
equilibrium within years may actually move less than the full demand shift would predict.
If the effect of exogenous spread movements on quantity demanded can be determined, it
is possible to solve for the other parameters that identify the demand function using
results from regressions 1.1 and 1.2.
In the model presented in chapter 3, quantity demanded is assumed to be a linear
function of spread and altruism, while the spread supplied is a linear function of the
inverse quantity and altruism (since it is allowed that the annual fundraising quota is
related to altruistic events like attacks). Consequently, it is necessary to identify the
following structural regression equations for supply and demand8:
8 In the same way that the right-skewed distribution of quantity is log-transformed to ensure that it followsa more normal distribution, the right-skewed distribution of inverse quantity, which enters the supplyfunction, is log-transformed as well. Since ln(Q-1) = -ln(Q), I expect that the estimated coefficient 1 willtake the opposite sign that the parameterc has in the model from equation 1.2 in chapter 2. Consequently,
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S: Yield= 0 + 1 lnQuantity + aA + 3 US+ 4Risk+ 5X
D: lnQuantity = 0 + 1 Yield+ aA + 3 US + 4Risk+ 5X
whereA represents an indicator of an altruistic event, USrepresents the appropriate U.S.
treasury rate,Riskrepresents the Israeli risk premium, andXrepresents exogenous
controls in the regressions. Combining these structural equations with regressions 1.1
and 1.2, it is possible to solve for the unobservable coefficient a (the effect of altruism
on demand alone) in terms of a (the coefficient on an indicator of altruism in regression
1.1: the causal effect of altruism on equilibrium quantities), a (the coefficient on an
indicator of altruism in regression 1.2: the causal effect of altruism on equilibrium
spreads), 3, 3, and 3 (the coefficients on the U.S. rate from regression 1.1, 1.2 and the
structural demand equation)9. It can be shown that10:
Equation 1.5
a = a - a * [(3 3)/ 3]
In order to properly estimate 3, it is necessary to examine the lag structure of the
Israel Bonds market. The market works in the following way. For each sales period
(generally a month-long period), the Ministry of Finance sets the interest rate at which
each instrument of Israel Bonds will be sold for the duration of the period. Therefore, the
state sets one price for the entire period and allows orders to be filled as investors will
demand within that period. Since supply is fixed to be perfectly elastic within each
period, demand shifts can be recognized by changes in short-term quantity fluctuations.
the resultscan be interpreted to imply a 1 % increase in inverse quantity results in a -1 change in the spreadsupplied.9 For a proof see Mathematical Appendix B.10 As a preview to the reader, the value of a appears not to be statistically different from zero in mostcircumstances. If a is assumed to be zero, the full demand shift, a, is close to a (the amount thatquantities move in equilibrium, estimated in regression 1.1). In other words, almost all of the movement ofquantities in equilibrium can be attributed to demand shifts.
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Notably, within each sales period, the spreads that investors receive change, even
though the nominal yields on the bonds do not. This is because the opportunity cost of
funds, or the bottom half of the spread, varies within periods. For instance, the yield on
Zero Coupon Israel Bonds may be a fixed 6% for a sales period, but within that period
U.S. treasuries and the Israeli risk premium change daily. As a result, the spread, which
is the difference between the bond yield and some combination of U.S. treasuries and the
Israeli risk premium, varies substantially. Since both yields from the U.S. treasury
market and the tradable Israeli debt market can reasonably be taken as exogenous, the
variation of these rates within a given period will trace out the price elasticity of demand.
Furthermore, by using this methodology, it is possible to estimate these elasticities over
longer periods of data than would otherwise be possible. Since changes in the spread
within sales periods are only determined by U.S. treasuries and the risk premium, it is not
necessary to have Israel Bond yield data for this calculation. Therefore, estimates can be
made incorporating data from several years before 2001 when the yield data begins,
improving the overall quality of the estimates.
To identify the price elasticity of demand, a fixed-effects regression, controlling
for each sales period and instrument type, will be run in the following form:
Regression 1.3
lnQi,t= 0 + 3 * US ratei,t+ 4 *Riskpi,t
+ 5 * timevart+ 6 *instrumenti + 7 * dowt+ 8 * periodj
where lnQi,tis the log-transformed sales for instrument i in period t, instrumenti is a
dummy variable for each of the i instrument types, US ratei,tis an interaction variable for
each of the i instruments with the comparable U.S. treasury rate,Riskpi,tis an interaction
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variable for each of the i instruments with the Israeli default risk premium,periodj
represents a dummy variable for each of thej sales periods, dowt is a dummy variable for
each day of the week, and timevaris a time variable that allows for a time trend in the
series. Since many of the indicators of altruistic events used in this paper change slowly
relative to the length of a sales period, they are not used in this regression11.
Including dummy variables for the sales periods in the regression allows analysis
of changes of spreads within periods, when their movement is exogenously determined.
Since changes in the spread are exogenous when controlling for the sales period, 3 can
be interpreted as the effect of a change in U.S. interest rates on the quantity demanded,
holding all other variables constant, including the yield. Specifically, 3 is the price
elasticity of demand the percent change in quantity associated with a unit change in the
treasury rate, all else equal.
11 The point of this exercise is precisely to identify the coefficient a, the effect of altruistic events on thequantity demanded. It is my belief that altruism works over long time horizons. Consequently, it will notbe possible to observe the true value of aby including it in regression 1.3, which only looks within salesperiods (time horizons in the range of one month). Since altruistic events are not correlated with the U.S.treasury rates, omitting them should not bias the regression estimates.
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V. Data
Israel Bond Instruments
For the purposes of this paper, a unique and confidential dataset has been
constructed with information provided by the Israeli Ministry of Finance on the prices
and sales of the Israel Bonds. Data is provided on the yields and quantities at which
several Israel Bond instruments were sold over the 1990-2004 period. The dataset
contains monthly yield information on the Infrastructure and Absorption Issues (Zeros),
the Jubilee Issues Series A (5 years), the Jubilee Issues Series B (10 years), the Chai
Issues, several Canadian Issues and several variable rate (Libor-based) issues from 2001
to 2004. Furthermore, daily data on the quantity of bonds sold for three of these
instrument types (the Infrastructure and Absorption Issues and the two Jubilee Series) is
provided from 1990-2004.
For the purposes of this paper, I will focus entirely on the Infrastructure and
Absorption Issues and the two series of Jubilee Issues sold in the United States. The
limitations of the data provided make these bonds the easy choice, as they are the only
instruments for which daily quantity data is available. Furthermore, they are among the
most popular instruments with investors and therefore the most relevant to policy
considerations. In 2001, the combined dollar value of the Jubilee and Zero Coupon
bonds accounted for 57% of all Israel Bonds sold. This statistic rose to 76% in 2002 and
2003 and looks to be even higher in 2004 (78% as of November 2004).
Additionally, the terms of these particular instruments make them more likely to
be held by individual investors for whom one would expect the altruism effect to be the
greatest. For instance, the Jubilee A and B Series each offer fixed annual interest and the
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Infrastructure and Absorption Issue is a zero-coupon discount bond. These interest
payment methods are simple and therefore more likely to be attractive to individual
investors than variable rate bonds with complex interest calculation methods. Also, these
instruments offer relatively small minimum subscription stipulations. The Zero Coupon
bonds are sold at a minimum face value of $6,000 and the Jubilee Bonds are sold with a
minimum subscription of $25,000 (although subsequent purchases can be as low as
$5,000). Other Israel Bond instruments tend to have higher minimum subscription
requirements. For instance, the 4th Variable Rate Libor notes come in minimum
subscriptions of $100,000 and the 3
rd
Libor Notes come in minimum subscriptions of
$150,000. While the Mazel Tov notes are also sold in much smaller denominations
(minimum subscriptions of $100), they serve primarily as gifts rather than investments
and only constitute a very small part of the Israeli debt. Appendix B provides additional
detail on the terms of these bonds from their prospectuses.
Finally, these three bond instruments offer the greatest chance of finding
systematic variation in the yield spreads. The yields set by the Ministry of Finance
generally change monthly for these instruments, whereas a few other instruments only
change quarterly. For instance, the Mazel Tov Bonds and the Chai Dollar Savings Bonds
only adjust their offered rates every six months. Furthermore, the Libor-tied notes tend to
be a fixed spread over Libor. Only very rarely is the offered spread above Libor changed.
For example, the 4th Variable Rate Libor notes have been a constant 60 basis points above
Libor for the past several years. While the nominal rates on these bonds vary, the fact
that they maintain a constant spread with Libor means that they do not fluctuate period to
period in conjunction with changes in altruism for Israel.
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Each instrument type has gone through several different issues over time. For
instance, the Infrastructure and Absorption Issue (Zero Coupon) was first issued in 1990.
Eventually, when the bonds from this subscription were sold, a second issue was released
in December 1991. As of December 2004, the Zero Coupon Bond is in its 8th Issue.
Similarly, the two Jubilee Series Bonds have each had 4 issues since their release in 1998
until the present day. When analyzing the sales of these instruments over long periods of
time, it is important to ensure that there are no important changes in the terms of their
prospectuses which could significantly alter their attractiveness to investors between
issues.
To ensure cross-comparability, a dataset was manually compiled by looking
through Securities and Exchange Commission filings made by the State of Israel. Copies
of all available prospectuses and registration supplements filed from 1993 until the
present were downloaded from the online Thomson Research database and read for their
essential features. While it was discovered that the essential terms of the bonds remained
constant across issues, the frequency at which Israel updated the nominal interest rates on
the bonds changed significantly. In the early 1990s, the interest rate that the bonds were
being sold at was only updated quarterly. Eventually, this policy changed and rates were
updated approximately every 45 days. More recently, the interest rates offered on the
bonds have become updated monthly. These sales periods, or periods within which the
supply of bonds is fixed, are necessary to understand in order to properly measure the
effect of altruism on demand alone. Therefore, dummy variables are included in the
dataset for each sales period. Table 1 shows the dates of changes from one sales period
convention to another.
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The raw dataset provided by DCI required some alteration to make it suitable for
analysis. Firstly, overlap between consecutive issues of the same instrument was
eliminated in order to make the data easier to work with. Obvious cases where sales for
an issue were recorded at a time when the issue was either not yet being sold or finished
being sold were deleted. Furthermore, when small periods of overlap were found
between one issue and the next, a time was selected to consider the end of the previous
issue and the start of the following one. This time was selected to match as best as
possible the start of a new sales period. In all but one case, such overlap was small and
inconsequential (i.e. only a few days), making it easiest to simply delete the improper
observations. This procedure makes the most sense because it is likely that sales before
the start and end date of the issue were either sales unavailable to the general public,
accounting corrections or coding errors. Therefore, including them in the dataset would
provide no useful information regarding how investors react to altruistic events. Overlap
between the 4th and 5th issues of the Zero Coupon bond, however, was substantial. For a
period of 4 months from January 1997 through April 1997 both issues were sold in
material quantities. Therefore, these sales were added together in the final dataset in
order to prevent underestimation of the true quantity of Zero Coupon bonds sold during
this period.
Furthermore, there were several missing observations in the data. One would
expect that a sales observation would be present for each instrument on every weekday
that the DCI office was open. Instead, there are many weekdays for which there are no
observations. There are three possibilities for why this could be the case. Firstly, it could
be that a missing observation means that sales for that day were zero. Secondly, a
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missing observation could mean that DCI was closed that day for either a holiday or
some other reason. Thirdly, it is possible that the recording of new sales for the day was
simply pushed off until a later date. For instance, it is possible that when sales are low,
paperwork is only processed every other day rather than daily.
After consulting with the National Director of Operations at DCI, it seems most
likely that the missing observations are a mix of both office closings and days with zero
sales. The record keeping system used by DCI was changed in April 2001 when they
changed fiscal agents from Chase Manhattan Bank to the Bank of New York.
Consequently, old sales data was converted manually in order to be compatible with the
new system. DCI believes the data from these two periods to be comparable as a result of
this conversion. Interestingly, before 2001, missing observations are less common and
observations of zero sales are present. After 2001, missing observations are more
common and there are substantially fewer observations listed explicitly as zero.
Furthermore, variation within the data shows that there are several days with low enough
sales such that the presence of a day with no sales is plausible. As a result, I believe that
these missing observations are days with zero sales mixed with a small number of office
holidays.
Since an accurate list of historical office closings is not available, and it is
unlikely that the number of office holidays is large enough (or is sufficiently correlated
with altruistic events) to materially bias regression estimates, the following procedure
was used to handle missing observations. A comprehensive list of United States Treasury
yields was taken from Global Financial Data server. This list was then merged with the
Israel Bond sales data. In the case where both the U.S. Treasury data and the Israel
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Bonds data had no observations for a given day, the day was dropped from the dataset
and considered an office closing. Since the U.S. Treasury data is comprehensive and
from a reliable source, I assume that these observations represent only official market
(and therefore also national) holidays. When either U.S. Treasury data was available or
one of the three Israel Bonds instruments had a sales observation but the others did not,
all missing observations for that day were considered to be zero. Similarly, a very
small number of negative sales, which likely represent accounting adjustments, were
considered zero observations if they were present on a weekday.
Finally, a number of weekend observations were found in the dataset. For these
observations, it is possible that they were properly meant to be included in the previous or
following business day. Feedback from DCI indicates that the sales report was
balanced by month, which means that the sum of the daily data was set to match their
official sales numbers from each month. In addition, these weekend observations can
sometimes be substantially larger-than-average observations, which may influence
regression estimates if improperly handled. Consequently, it is likely that these weekend
observations either represent a residual amount of sales for a week, the sum of sales
coded without dates for the week, or simply an error in the dataset. For these reasons, the
most sensible way to handle the weekend observations is to delete them.
The resulting dataset contains 7148 observations. Since all bonds are non-
negotiable, they are all new issues which mature at a fixed time from the issue date and
cannot be traded, except in special instances. Therefore, each yield and quantity data
point represents the price and amount at issuance of new bonds sold. Figures 2-4 display
some descriptive statistics of the data for each instrument type.
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The main shortcoming associated with this dataset is that the sales records do not
match perfectly with the time that the investment decision is made. Sales are only
recorded when receipt of payment is made to DCI. Since there is paperwork and an
application process to apply for these bonds, there is a lag between the time the investor
decides to buy the bonds and the time the sale is recorded. The Ministry of Finance
suspects that this lag can be anywhere from one day to 2 or more weeks depending on the
circumstances of the investor. To account for this, events will be looked at on a lagged
basis (i.e. number of attacks in the last month) and the evolution of quantity movements
after an event will be analyzed
12
.
Constructing Comparable Investment Variables
Variables are added to the datasets to serve as comparable investments. Ideally, a
non-altruistic security would be used that matches all of the important characteristics of
each Israel Bond instrument so that changes in the spread are only representative of how
much investors are willing to forgo to selflessly support the state (and a fixed illiquidity
premium to compensate for the transfer restrictions of the bonds). Unfortunately, there
exists no one security that matches the Israel Bonds perfectly in all respects. Instead, I
will control for both the U.S. treasury rate (the time value of money) and Israeli default
risk premium (the incremental rational return required to hold Israeli debt instead of U.S.
debt) separately.
Data on United States 5-year and 10-year treasuries are taken from the Global
Financial Data server. These rates, which are the ones that the Ministry of Finance
12 Evidence from the event studies conducted in chapter 6 suggests that this lag time is approximately 5-8business days, or 1-2 weeks.
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claims that it uses when setting the rates for the Israel Bonds, are useful because they will
match the Bonds both in terms of which currency the principal is paid in and in terms of
time to maturity.
Figure 5 shows the U.S. 10-year government bond yield along with the yields on
the Jubilee 10-year and Zero Coupon. Figure 6 shows the U.S. 5-year rate compared to
the Jubilee 5-year. From these figures, it is clear that the nominal yields on these bonds
closely track the comparable U.S. treasury benchmark.
Since the U.S. rates do not account for Israel-specific risk, it is important to
control for the default risk premium as well. Given the constraints of the available data,
it is only possible to control for a spread that will have close co-movement with the actual
risk premium. Since 1-year constant maturity Israeli debt yields are available from the
Thomson DataStream data service, it is possible to calculate the spread between 1-year
tradable Israeli debt and 1-year U.S. treasuries. Since the Israeli debt is denominated in
New Israeli Shequelim (NIS), however, this spread is an imperfect approximation of the
true default risk premium. The calculated risk premium includes expected inflation and
an inflation risk premium in addition to the default and liquidity risks. While liquidity
risk for government debt should be small, expected inflation and the inflation risk
premium likely account for a significant portion of this spread. It would be possible to
eliminate the inflation-related aspects of this spread by converting the currency on the
Israeli bond into U.S. dollars using forward currency rate data. Unfortunately, while
forward currency rates are available at the 1-year horizon from Bloomberg, the frequency
of the observations is too sporadic to be meaningfully employed as a correction in the
spread. Therefore, it will be impossible to eliminate expected inflation and inflation risk
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from this spread. Fortunately, since there is unlikely to be a strong correlation between
altruistic events and inflation, this spread should be an unbiased approximation of the
Israeli default risk premium.
Additionally, it is potentially flawed to use the default risk at the 1-year horizon to
approximate the default risk at the 5-year and 10-year horizons. Theoretically, it is
possible that the default risk premium varies differently at various time horizons.
Therefore, in using this spread I am making the assumption that the Israeli risk premium
is relatively constant across time horizons; however, even if it does vary across horizons,
it should not bias the regression estimates so long as it does not vary systematically with
altruistic events.
Furthermore, because the bonds used as comparable investments have differences
in interest payment conventions and coupon amounts with the Israel Bonds, there will be
slight mismatching in terms of duration. This additional error, however, is only of
second-order importance relative to the correct matching of maturities. Since the largest
cash flow from these securities comes at maturity with the repayment of principal, a close
matching of maturities is significantly more important when calculating the spread.
Constructing Altruism Indicators and Event Variables
Variables are constructed for altruistic events using a historical timeline of
relevant terrorist attacks from the Israeli Ministry of Foreign Affairs website entitled,
Suicide and Other Bombing Attacks in Israel Since the Declaration of Principles (Sept
1993).13 This timeline of events is considered exhaustive and is used to represent the
universe of all possible Israeli terrorist attacks in this period. A total of 121 terrorist
13 http://www.mfa.gov.il/
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attacks are identified from 1993-2004. Each is coded according to date, number of
attacks, number killed, and number wounded, as provided by the timeline14. The number
of Israelis killed or wounded serves as an objective proxy for categorizing the salience of
individual events. The death of the suicide bomber in a terrorist attack is not included in
these tallies because it is unlikely that pro-Israeli altruistic investors consider this a
relevant factor in their perceptions of salience. Tables 2a and 2b provide descriptive
statistics of these variables.
All news events documented on weekends or holidays are moved to the following
business day. This correction is made to ensure that the first day of an event, in event-
time, is the same as the first day an investor can act on the news information (i.e. the day
of the attack). Since Jerusalem is 7 to 10 hours ahead of the United States, in most cases,
investors in the United States will have already incorporated all information from an
event in Israel by the start of that same business day in the United States. In the event
that multiple attacks are coded on the same day, the statistics for both dead and wounded
are added together.
To discern the pattern of sales following an event, dummy variables are created
for consecutive periods of fixed length after an event. For instance, a variable is
constructed that has value of 1 for the first day after an attack and 0 otherwise. Similar
variables are created for the second day, third day, and so on for 75 days following a
terrorist attack. Using these variables will help identify the abnormal sales for each day
following an event. Furthermore, several index variables are created from these events to
14 Where information on the number of killed or wounded is not available from the MFA website, thedataset is supplemented with information from the Jewish Virtual Library.Source: http://www.jewishvirtuallibrary.org/jsource/Terrorism/TerrorAttacks.html
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mimic changes in altruistic sentiment. For example, variables are created for the
frequency of attacks in the last 2 weeks, 1 month and 2 months.
Lastly, religious holidays are coded in a similar manner. Due to the large number
of Jewish holidays, the most important holidays are selectively chosen to be examined.
Allowing for too many religious events to be included in the regression simultaneously
will likely over fit the data. Holidays are selected according to their prominence for
American Jews and their religious/symbolic significance. The holidays analyzed include:
Rosh Hashana (Jewish New Year), Yom Kippur (Day of Atonement/Holiest Day of the
Year), Yom HaShoah (Holocaust Memorial Day), and Yom HaAtzmaut (Israeli
Independence Day). Since Jewish holidays are fully-anticipatable events unlike terrorist
attacks or political developments, I expect that spread changes will be more obvious for
these events than for terrorist attacks. Table 2c contains a calendar of these holidays
from 2000-2005.
Since holidays are cyclical events, it will require caution when interpreting their
effect on sales. Sales in the Israel Bonds market are bound to be very cyclically driven
throughout the year. Much of the variation in sales will be tied to roll-overs of maturing
issues. Furthermore, some institutions may regularly purchase bonds at a particular time
of the year (for instance, at the start of a quarter or a half-year period). Since there will
be little to no variation in the date of a particular holiday (i.e. Rosh Hashanah generally
occurs in September), it will be hard to separate the effect of a particular holiday from
another seasonal or cyclical effect. Additionally, since holidays occur in relatively fixed
intervals, it will be necessary to analyze holidays as groups. For instance, when
analyzing sales after Rosh Hashanah and Yom Kippur, it will be essential to look at sales
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patterns from the start of Rosh Hashanah until long after Yom Kippur. The fact that Yom
Kippur regularly occurs 8 days after Rosh Hashanah makes it impossible to consider its
effects separately. Similarly, Yom HaShoah is shortly followed by Yom HaAtzmaut and
Yom HaZikaron (Israeli Memorial Day), which makes it difficult to identify their effects
separately as well.
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VI. Evidence
The evidence suggests that quantities in equilibrium increase substantially when
attacks are more frequent. Furthermore, there appears to be a significant period
following individual attacks and important holidays with higher than average sales. On
the other hand, there is little statistical evidence that equilibrium spreads move relative to
altruistic events. While there is some evidence that spreads rise when the Israel risk
premium rises to compensate investors for the additional risk, it is found that investors
themselves seem to ignore Israel-specific risk. In fact, they purchase additional bonds
when the default risk premium is higher.
Equilibrium Quantity Results
Table 3 provides details of the regression estimates for equilibrium quantities for
all three instruments and Table 4 provides estimates broken down by instrument type.
Regression estimates are shown for altruistic events measured on the 2 week, 1
month and 2 month time horizons for log-quantity, quantity and a transformed log-
quantity15. I estimate an increase of 6.6% in sales for each additional attack in the last
two weeks, an increase of 6.1% for each additional attack in the last month and an
increase of 4.5% for each additional attack in the last two months. All estimates are
statistically significant at the 1% level, except on the 2 week horizon which is significant
at the 5% level16. While all 3 instruments show sales movements in relation to terrorist
15 While regression results using log-quantity are believed to be the most reliable, specifications usingquantity and a transformed log-quantity are shown to illustrate the effect of how missing observations weretreated on the results. The variable lnQplus is equal to ln(2745+Q) so that observations with Q=0 do nothave to be dropped from the ln(Q) regression. The number 2745 was selected because it is the smallestnon-zero quantity observation in the dataset.16 Since there appears to be serial correlation in the data, Newey-West standard errors are used to correctfor arbitrary heteroskedasticity and serial correlation of 7 lags. Significance is reported throughout thepaper using 7 lags for daily quantity data and 40 lags (approx. 2 months) for less frequent yield data.
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attacks, the Jubilee 10-year appears to move the most with a 16.5% increase in sales per
additional attack in the last 2 week period.
Figure 7 graphs the frequency of attacks over time with average daily sales of the
Zero Coupon bond. As the first Palestinian intifada, or uprising, waned around 1991,
both low attacks and sales are observed. Following the Declaration of Principles in
September 1993 (also known as the Oslo Accords a significant step in the peace
process), attacks briefly rise, as do sales. A period of relative calm and low sales
followed until the start of the most recent intifada (the al-Aksa Intifada) in September
2000. This new intifada ushered in a new wave of violence, and interestingly, also
significantly increased bond sales.
With respect to Rosh Hashana, daily sales are higher on average by 23.5% over
the 1 month period following the holiday and by 29.7% over the 2 month period
following the holiday. These increases are driven strongly by sales of the Zero Coupon
bond, which has 41.1% higher sales in the month long period following the holiday and
56.5% higher sales in the 2 month period following the holiday. Since DCI organizes
extensive marketing of the Israel Bonds to Jews attending religious services on Rosh
Hashanah and Yom Kippur, this result is not surprising. The Zero Coupon bonds are
most attractive to these small investors because they require the smallest minimum
purchase and pay interest using the simplest convention. Consequently, one would
expect that the religiously-motivated sentiment created by these bond drives for small
investors would show up in greater sales of the instruments most attractive to this
investor class.
Different lag specifications were tested and it was found that significance was robust to these changes.
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Regressions 7 and 8 from Table 3 show statistically significant results, which are
opposite those one would expect to find for Rosh Hashanah but consistent with what one
would expect to find for terrorist attacks. In these regressions, a variable lnQplus is used
to represent quantity. This variable represents a transformed log-quantity equal to
ln(2745+Q) so that observations with Q=0 do not have to be dropped from the regression.
Replacing zero values with relatively small numbers, however, can falsely create huge
effects when using logs. Since there is significant uncertainty about the correctness of
the observations with zero values in the first place (see discussion in data section),
these results cannot be trusted without scrutiny. The observations with zero values were
determined by comparing U.S. treasury market data with Israel Bond sales--- if there was
U.S. market data but no Israel Bond observation, it was assumed that the day had zero
sales. It is possible, however, that several holidays that were observed in the Israel Bond
office were not observed by the U.S. market. Specifically, it is likely that the Israel Bond
office was closed for several days during the Rosh Hashanah and Yom Kippur period.
Since these observations were listed as zero rather than dropped (as an office closing
should be), using this specification with logs can negatively bias the coefficient estimate
dramatically. The fact that the coefficient for terrorist attacks seems to match the results
from the other regression specifications, supports this theory because attacks should not
systematically occur near days with different holiday conventions.
The evolution of sales in event time is shown for terrorist attacks, Rosh Hashanah
and Yom HaShoah in Figures 8-16. These figures graph the cumulative abnormal
percent increase (or decrease) for each day following an event. In other words, a straight
line in these figures represents a period of relatively constant above average sales (in the
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amount of the slope of the line, per day). All patterns are found to be statistically
significant, unless otherwise noted. Chi-squared statistics are listed in the appendix with
the corresponding figures17.
Figure 8 provides the pattern of sales for all 3 instruments together for Rosh
Hashana. The findings are consistent with what one would expect. Following Rosh
Hashanah, there is a period of 5 to 8 business days with below-average to normal sales
followed by a steep increase in sales thereafter. During this 5 to 8 business day period,
Yom Kippur occurs and the High Holy Days end. Following the end of the High Holy
Days, bond sales come in daily at 52% higher than average amounts until day 31
18
. From
days 31 to 65, sales slow to 35% above average, until sales return to normal from day 66
to 7519.
Figures 9 and 10 show the pattern of sales following Rosh Hashana for the Jubilee
10-Year and Jubilee 5-Year, respectively. Both instruments follow a similar pattern
indicative of a small surge in sales shortly following the holiday. Both instruments
exhibit average or below-average sales for 5-9 days following Rosh Hashana. After that,
there is a brief period of approximately 7 days with above average sales, followed by a
prolonged period of average sales (as indicated by a flat line in the graph) for about 35
days. This inactivity is followed by another brief surge and then again average sales20.
17
To determine significance of the cumulative abnormal sales, aX2
test was run on the dummy variables foreach day following an attack of a particular salience. The test determined whether the sum of each of the75 coefficients (one for each day after an event) was statistically significant. Newey West standard errorswere used to control for arbitrary hetereoskedacity and serial correlation of up to 7 lags.18 This amount is estimated using the slope of the line from day 9 (13.7%) to day 31 (1159.3%) in Figure 8.19 This amount is estimated using the slope of the line from day 32 (1119.5%) to day 65 (2265.8%) inFigure 8.20 This second surge in sales is likely to be attributable to seasonality in bond sales. Since bond sales can becyclically-driven, it is difficult to separate the effect of a holiday (which also occurs around the same timeevery year) from seasonality.
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The pattern of cumulative abnormal sales for these two instruments is only statistically
significant at the 15% level.
Figure 11 shows a much more prominent effect following Rosh Hashana for the
Zero Coupon bond. For the Zero Coupon, bond sales are average until 11 days following
the holiday. At that point, sales come in daily at 65% above average for the next 60 days,
until they gradually return to normal21. This pattern is found to be statistically significant
at the 1% level. This evidence supports my earlier finding that the Zero Coupon bond is
the primary instrument affected by the High Holy Days season because of its
attractiveness to small investors and its use in religious bond drives.
Figure 12 shows the evolution of sales following a terrorist attack for all three
instruments together. The pattern supports the claim that following a terrorist attack there
is a period of elevated bond sales. For instance, Figure 12 shows a period of
approximately 8 days following an attack with average sales. This period is observed
because of the lag associated with the purchase of these bonds. Immediately following
this period, there is a period of approximately 34 days with consistent above-average
sales of 7.9% per day22. Sales then return to normal levels from day 44 to 75, with a brief
bump from days 60-75. This pattern is mimicked in Figures 13, 14 and 15 for the
Jubilee 10-year, Jubilee 5-year and Zero Coupon bonds, respectively. Notably, the
Jubilee 10-year bond reacts the most predictably to terrorist attacks. These bonds
immediately increase in sales following an attack and remain at elevated levels until
approximately 40 days after the attack when they return to normal levels. These figures
also seem to suggest that the Zero Coupon bondholders react slower to news of an attack
21 This amount is estimated using the slope of the line from day 10 (49.0%) to day 65 (3620.6%) in Figure11.22 This amount is estimated using the slope of the line from day 9 (-20.6%) to day 43 (248.3%) in Figure12.
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then Jubilee bondholders. Figure 15 suggests that it takes approximately 30 days after an
attack before observing above-average sales for these investors. It is possible that these
smaller investors either take a longer time to complete the bond purchase paperwork or
incorporate new information slower than larger investors.
Figure 16 provides the pattern of abnormal sales following Yom HaShoah. The
pattern for Yom HaShoah is much more difficult to explain than the patterns for terrorist
attacks and Rosh Hashana. Yom HaShoah is a much less prominent event than Rosh
Hashana. Furthermore, Yom HaShoah occurs close by to several other important cyclical
events. Passover, Yom HaZikaron and Yom HaAtzmaut all occur within a short period.
In addition, the chi-squared statistic indicates that the cumulative abnormal sales 75 days
from the event is statistically insignificant. The pattern appears to become positive
approximately one month after Yom HaShaoh, which coincides with the month of June,
the cyclical half-point of the year, and then falls sharply again. Therefore, given the
pattern of the variation it seems likely that this event can better be attributed to cyclical
forces (such as bond renewals or other purchases) associated with the 6 month mark in
the year.
Event Salience
Events are further broken down to identify their effect by salience. Terrorist
attacks are divided into a low salience and high salience group according to the number
of people wounded in each attack. Each salience group contains one half of the total
attacks so that the high salience group contains all attacks with over 29 people wounded
and the low salience group contains all attacks with 0 to 28 people wounded.
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The pattern of sales following these events shows that high salience terrorist
attacks increase sales more than low salience events while controlling for the High Holy
Days season. Figure 17 shows the evolution of abnormal sales in event time for the 75
business day period following an attack. After 75 days, the high salience events produce
an average increase in sales of 5.5% per day, while the low salience events produce an
average increase of only 1.9% per day. Cumulative abnormal sales for the low salience
group are found to be statistically insignificant (X2=0.81; P =0.3690), while cumulative
abnormal sales for the high salience group are statistically significant at the 1% level
(X
2
=9.62; P =0.0019).
Additionally, the 11 most salient attacks in terms of number of persons wounded
are identified and examined for their effect. Figure 18 shows the pattern of sales
following these 11 large attacks. Figures 19, 20 and 21 show the pattern of sales after the
attacks for the Jubilee 10-year, Jubilee 5-year and Zero Coupon individually. I find a
consistent pattern of greatly above-average sales following these events. For all three
instruments together, I estimate above-average sales of 23.6% per day over the entire 75
day period tested23. In addition, I estimate above-average sales of 31.3% per day for the
Jubilee 10-year, 24.3% per day for the Jubilee 5-year and 14.9% per day for the Zero
Coupon over the course of the same 75 day period24. The pronounced nature of these
nearly monotonically increasing patterns, along with the steep slopes (indicating
relatively high abnormal sales) suggests that salience is an important factor motivating
bond sales. In fact, I previously found that the average terrorist attack only produces 34
23 This amount is estimated using the slope of the line from day 1 (-43.9%) to day 75 (1707.0%) in Figure18.24 This amount is estimated for the Jubilee 10-year from the slope of the line from day 1 (8.8%) to day 75(2323.1%) in Figure 19; for the Jubilee 5-year from the slope of the line from day 1 (70.9%) to day 75(1728.9%) in Figure 20; and for the Zero Coupon from the slope of the line from day 1 (62.8%) to day 75(1043.2%) in Figure 21.
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days of above average sales with an increase of 7.9% per day. Consequently, it appears
that more salient attacks (as defined by the number of persons wounded) increase sales by
much larger amounts and for much longer periods of time.
Equilibrium Yield Changes
Interestingly, while quantities do move statistically relative to holidays and
terrorist attacks, yields generally do not. Table 5 shows the regression results for all
instruments together looking at events on the 1 month and 2 month horizon. There is no
statistically significant evidence that altruistic events cause yields to move, holding the
U.S. rate and risk premium constant25. The only event variable that moves spreads
statistically significantly is Yom HaShoah. As discussed in the previous section,
however, it appears this variable likely captures the cyclical effect of the half-year.
Consequently, it is not surprising that spreads move concurrently.
Table 6 lists the same results broken down by instrument type. Similarly, few
events are statistically significant aside from Yom HaShoah. Notably, however, there is
statistically significant evidence that spreads move relative to terrorist attacks for the
Jubilee 10-year bonds. In fact, I estimate that spreads increase by 0.019 for every
additional terrorist attack in the past month and that spreads increase by 0.014 for every
additional terrorist attack in the past 2 months for this instrument type. The fact that
there is some statistical evidence that spreads increase when attacks are more frequent
suggests that there may also be a supply effect. If the number of terrorist attacks only
entered into the demand function (through altruism), one would only expect to see yields
25 As noted earlier, yield data is only available from 2001-2004. Since yields only change monthly in thisperiod, the number of observations available is small. As a result, it will be difficult to be statisticallyconclusive about changes in yields.
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fall when attacks are greater. In the next section, I will show that even though spreads
may increase with greater attacks, they do not move enough to fully account for all of the
variation I find in quantities.
Yields in equilibrium are explained very well by movements in the U.S. treasury
rate and the Israeli risk premium. Depending on the instrument, 95% - 98% of the
variation in yields can be explained by these variables. If yields could be explained
perfectly by the U.S. rate and risk premium, it would imply that the Ministry of Finance
sets yields exogenously as a constant spread over these rates. While this is obviously not
the case here, the fact that yields are explained very well by these rates means that this is
close to what happens.
Notably, yields in equilibrium move very strongly with the U.S. treasury rates, but
less so with the Israeli risk premium. Yields for the Jubilee 5-year increase by 0.70 for
every percentage point increase in the comparable U.S. treasury rate, while the Jubilee
10-year yield increases by 0.73 and the Zero Coupon yield increases by 0.68. Figures 5
and 6 show the close co-movement of these rates. Furthermore, the yield increases by
0.03 per percentage point of risk premium for the Zero Coupon and Jubilee 10-year, but
varies statistically insignificantly for the Jubilee 5-year. These findings suggest two
interesting results. Firstly, investors care more about the nominal yield on the bond than
the yield relative to alternative investments. Secondly, investors discount the importance
of the risk premium relative to U.S. treasuries. Assuming that the Ministry of Finance
demands the rational spread, supply can be denoted linearly as:
Yield U.S. Rate Risk Premium = a + b * Qs
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If investors demand a spread that weights the U.S. rate and risk premium separately (by
factors of and ), demand can be denoted:
Qd = c + d * [Yield * (U.S. Rate + * Risk Premium)]
In equilibrium, one would expect that:
dYield/dUS = (1-bd) / (1-bd)
dYield/dRisk = (1-bd) / (1-bd)
Therefore, the finding that dYield/dUS < 1 implies that < 1. In other words, investors
discount the opportunity cost component of the spread relative to the nominal rate.
Similarly, finding that dYield/dUS > dYield/dRisk implies that < 1, or that investors
discount the component of the return they demand from the risk premium relative to U.S.
treasuries. If investors weighted the components of the spread in the same way that the
Bank did, we would observe = = 1 and the nominal yield would move 1 to 1 with the
risk premium and U.S. treasury rate in equilibrium. Additionally, it makes intuitive sense
that the instrument held most by the smallest investors, the Zero Coupon bond, is the one
that puts the most undue emphasis on the nominal yield (i.e. has the lowest estimate of
the movement of yields relative to U.S. treasuries).
While the measure used for the risk premium here is imperfect (i.e. is at the 1-
year horizon and includes expected inflation and an inflation risk premium), it seems
reasonable to assume the inflation is random noise (which should not bias the coefficient
estimate). Furthermore, if anything, using a risk premium on the 1-year horizon should
underestimate the risk premium investors would demand at the 5 or 10-year horizon. The
reason for this is that the chances of defaulting over a longer period should be higher than
the chances of defaulting over a short period. Consequently, one would expect a greater
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than 1 to 1 movement with a 1-year risk premium in this specification. This interesting