debt afford ability paper
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Debt Affordability: A Stochastic Model
Kenneth A. Kriz1
DRAFT FOR JOURNAL REVIEW
Draft Date: 09 May, 2007
JEL classification codes: H74, H63
1 Associate Professor, School of Public Administration, University of Nebraska at Omaha; Mailing Address: Annex27, 6001 Dodge Street, Omaha, NE 68182. Phone: 402.554.2058; Email:[email protected]. The authorwould like to thank Qiushi Wang for his research assistance and Fred Thompson for his comments on the paper aswell as his encouragement in pursuing the topic.
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mailto:[email protected]:[email protected]:[email protected] -
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Debt Affordability: A Stochastic Model
Abstract
Many normative models of debt affordability have been proposed. However, most
have been ad hoc in nature. This paper develops and calibrates a normative model of debt
affordability based on the ex ante stochastic distribution of future changes in tax base.
We find that the most important variables in terms of explaining the likelihood of future
default are tax base volatility, desired future operating (non-capital) expenditure growth,
and the effectiveness of investments financed by debt in increasing economic growth.
Less important factors were initial tax rates, interest rates, and a jurisdictions political
sensitivity to increases in tax rates or cuts in spending.
Introduction
In December 1994, the Board for Orange County, California announced one of
the largest municipal bankruptcies of all time. The renunciations of the actions of the
County Treasurer in precipitating the default on over $1.6 billion dollars of municipal
debt, and the fallout associated with the event, were immediate and drastic. Many
individuals lost their jobs in the resulting budget cuts, political careers were cut short or
at least changed inexorably, and citizens had services reduced or eliminated (Baldassare,
1998). Unfortunately, Orange County was neither the first nor the last municipal
bankruptcy. Beyond explicit bankruptcies which occur at infrequent intervals, there have
been a host ofde facto bankruptcies where spending patterns of subnational jurisdictions
(and even a few sovereign nations) had to be changed dramatically in order to
accommodate debt payments.
Default on debt presents a crisis for most borrowers. In the private sector, default
can cause the loss of control over firm assets. In the public sector, control obviously has a
different meaning. However, in a public default situation citizen owners may lose
control over their jurisdiction, with receivership or loss of access to capital markets as
potential penalties. The political penalties for elected leaders may involve loss of control
through loss of access to their office. Needless to say, there is a lot at risk when
jurisdictions choose to borrow. However, there is also risk that comes from not
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borrowing. Lack of borrowing may produce underinvestment in capital, resulting in
slower than potential economic growth (though there is much debate on this point, see
Munnell (1990) for a review of the seminal literature and Zou (2006) for a recent
contribution). The question thus becomes one of affordable debt levels.
At its heart, the central debt affordability question is: Does the issuance of a bond
issue of size b significantly increase the likelihood that the jurisdiction will not be able to
make payments on its total debtB? A related question is whether the issuance of a bond
issue b makes the level of debtB politically unsustainable. In order to answer these
questions, one needs to realize that there is tremendous uncertainty regarding future
revenues and expenditures. The more uncertain are future revenues and expenditures, the
more likely that the jurisdiction will not be able to service its debt burden. Therefore, the
question of debt affordability is a question of probabilities.
Despite the inherently stochastic nature of the debt affordability question,
previous models of debt affordability have largely taken a benchmarkingapproach
comparing debt levels of a jurisdiction either against some fixed standard or against other
jurisdictions. But there are several reasons why a benchmarking approach may not reflect
the true nature of the debt affordability question. This paper takes a different approach,
one that attempts to model more fully the financial implications of issuing debt. We will
produce a model that takes more fully into account specific financial, economic, and
demographic realities of the jurisdiction. Using this model, jurisdictions will be able to
say not only if a certain level of debt will be affordable, but also the reasons why or why
not this is the case.
Literature Review
The literature on debt affordability is relatively well developed.2 Discussion of
debt affordability issues began with Bernards work on meeting the financing needs of
government. He noted that while the private sector finance literature was replete with
2 As the principal purpose of this research is to develop a radically different method for assessing debtaffordability, the review of past literature will be necessarily brief to leave room for the theorydevelopment. Recent and much more detailed literature reviews can be found in Bartle, Kriz and Wang(2006) from which this review was derived and in Denison and Hackbart (2006).
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articles dealing with debt affordability, public sector researchers had yet to take up the
challenge (Bernard, 1982).
As noted in Ramsey, Gritz & Hackbart (1988), techniques in assessing debt
affordability have generally developed into three approaches: the debt ceiling approach,
the benchmarking approach, and the regression approach. In the debt ceiling approach, a
limited number of measures of debt burden (for example, debt as a percentage of assessed
property value) are calculated, and then compared to some maximum level. Often times
this technique is formalized into statute or constitutionally mandated. For example, in the
state of Minnesota, local debt outstanding cannot exceed 3 percent of the total market
value of property.
In the benchmarking approach, more measures of debt burden are calculated, and
then they are compared against some set of similar jurisdictions. This approach is
formalized in guidelines issued by the Government Finance Officers Association
(GFOA). GFOA recommends several measures of debt burden and debt size be
calculated and compared against a peer group (Miranda & Pincur, 2000). An example of
a benchmark that is commonly cited is the debt to assessed property value ratio.
Presumably, as more debt is issued against a property tax base, it puts a jurisdiction more
at risk to default on the debt.
The final approach used in a few affordability studies is the regression approach.
Here, measures of debt burden for many different jurisdictions are regressed against
different explanatory factors and results are captured. Then any one city can generate a
predicted debt burden against which its current situation can be compared. In essence,
this is just another type of benchmarking. The difference between this and other types of
benchmarking are that instead of measuring a jurisdictions debt burden against some
other set of similar jurisdictions, the debt burden is here compared against a
prototypical case developed statistically. This is the methodology developed in
Ramsey, Gritz, and Hackbart (1988).
As pointed out in Bartle, Kriz, and Wang (2006) hereafter BKW-, the above
methodologies are often problematic in terms of their ability to measure debt capacity
and affordability. They cite three sources of problems. First, benchmark type measures
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and debt limits are often incomplete in that they do not take into account differing
circumstances between jurisdictions. The authors cite the case of Omaha, Nebraska, a
city that is much more reliant on sales taxes than other jurisdictions. Obviously, a debt to
property value measure of affordability for a city with a relatively small property tax does
not make much sense. A similar view was voiced in Denison, Hackbart, and Moody
(2006) who argued that more than one type of debt limit might be necessary due to
different characteristics of jurisdictions. One recent paper that attempts to adjust the
benchmarking approach to take into account some differences between jurisdictions is
that of Brecher, Richwerger, and Van Wagner (2003). They develop measures of the
revenue base for states using representative revenue systems and relate them to general
obligation debt burdens in order to assess the relative likelihood of default. While this
paper is an improvement on previous work, their model is still ad hoc in that it does not
proceed from first principles and does not develop a solution for the relative amount of
revenue volatility that can push a jurisdiction into a dangerous situation with regard to its
debt. Second, BKW cite the static nature of existing debt affordability measures.
Dynamics are mostly left off the table in calculating debt affordability, which seems
strange given the dynamic nature of revenue, expenditures, and economic condition. Last,
debt affordability measures are seen by BKW as mechanical: In essence the city is seen
as having zero probability of encountering financial difficulties as long as its
benchmarking calculations fall below some point, then the probability increases to
certainty of difficulties when some magic point is reached (Bartle, Kriz, & Wang, 2006).
Model
In order to address these difficulties in assessing debt affordability, we take a
different approach than any of those papers discussed above. We model the likelihood of
default on debt given different combinations of revenue base growth, the tax rate of the
jurisdiction, desired growth of expenditures other than capital expenditures, the impact on
revenue base growth of the expenditures that debt will be issued to fund, interest rates,
and the willingness of citizens in a jurisdiction to make large expenditure cuts or tax
increases in the event of a budget shortfall. Our model looks most like that of Thompson
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and Gates (Thompson & Gates, 2006). They address a different question in their paper.
They solve for the sustainable growth in expenditures given debt, revenues, and other
variables. We solve for maximum debt, which is a distinct policy question.
We use a median voter model with an existence theorem regarding the
compensation of a government official to motivate our model setup. Assume that a single
rational, utility-maximizing decision maker rules a jurisdiction consisting of a single
citizen whose utility is a function of government operating and capital expenditures,
along with private consumption from an initial allocation of wealth. Our model initially
occurs across two time periods with decisions made at three points in time. At time t0 the
citizen employs the decision maker and provides him with a fixed wage W0. The wage is
an increasing function of the expected amount of utility generated by government
spending. At time t1, after the first time period, the citizen provides the decision maker
with a fixed wage W1 that holds during the second period. At time t2, the decision maker
pays the decision maker a fixed amount W2which is in essence payment for retention of
the decision makers services over another set of time periods. Since the wage and final
payoff to the decision maker are based on expected future utility, there will be a set of
information and actions by the citizen that will create an incentive for the decision maker
to act in the best interest of the citizen when making choices. However, it is not readily
apparent either to the decision maker or to the citizen what those choices should be. We
turn to the dynamics of the revenue and expenditure generation model for the jurisdiction
to try to reason a set of principles for the determination of optimal debt levels.
Assume that at time t0, the jurisdiction has a balanced budget with no debt
outstanding, so revenues equal operating expendituresR0 = EO0. The decision maker
formulates a first period budget based on projections of future revenuesR1 and future
expenditure needsEO1.
Given this formulation, the required revenues at time t1 are equal to the desired
future expenditureEO1. Assuming that the government cannot run an operating deficit,
required revenues will be equal to actual revenues such thatR1 = EO1. Now assume that
the government wishes to borrow an amountB to finance capital expenditures at time t0.
Also assume that the debt is one-period debt issued at par value at an exogenous and
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fixed interest rate r. While borrowing effectively raises revenue in the first period, the
debt must be repaid in the second period. Now the budgetary constraint in the second
period becomes:
( )rBEOR ++= 1011 (1)
Next we recognize the simple relationship between first period revenue and second
period revenue:
1,001 RRR += (2)
and the relationship between first period expenditure and second period expenditure:
1,001 EOEOEO += (3)
In (2) and (3), the terms with represent the change in revenues and operatingexpenditures, respectively from time t0 to t1. Substituting from (2) and (3) into (1), we
obtain:
( )rBEOEORR +++=+ 101,001,00 (4)
Isolating B and noting thatR0 will equalEO0 by definition, we find the question to the
question of the maximum amount that can be borrowed in period 1:
r
EORB
+
=
1
1,01,0
0 (5)
Equation (5) captures the obvious relationship that the change in revenue from the first
period to the second must be greater than the change in operating expenditures,
otherwise, the jurisdiction will have to default on the bond.3 Also, the higher the interest
3 Note that we preclude borrowing for operating expenditures. If jurisdictions can borrow for operatingexpenditures, this will allow the jurisdiction to avoid default. However, in a multi-period model, cash flow
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rate at which the jurisdiction borrows, the less the jurisdiction can borrow safely.
Therefore, if revenues are less than expected, the citizens of the jurisdiction would have
to accept a cut in operating expenditures or accept a default on the bond issue.
The formulation of (5) yields basic results. But revenues are only partially within
the control of the jurisdiction. Rewriting (5) in terms of the controllable and
uncontrollable portions of tax revenue yields additional insights. Assuming an ad valorem
tax, we can write the revenue term to consist of a tax rate trand a tax base TB:
( )( )1,01,1 +++ ++==
tttttt
ttt
TBTBtrtrR
TBtrR
(6)
where the subscript indicates the time period. We can expand the polynomial in the t+1
period to obtain the following:
1,1,1,1,1 +++++ +++= ttttttttttttt TBtrTBtrTBtrTBtrR (7)
The change in revenue is the difference between revenue in period tand in period t+1.
Substituting from (6) and (7), taking the difference and simplifying yields:
[ ]
1,1,1,1,1,
1,1,1,1,1,
11,
+++++
+++++
++
++=
+++=
=
tttttttttttt
tttttttttttttttt
tttt
TBtrTBtrTBtrR
TBtrTBtrTBtrTBtrTBtrR
RRR
(8)
Thus the change in revenue between periods can be broken down into changes strictly
attributable to changes in the tax base (the first term in (8)), changes strictly attributable
to changes in tax rates (the second term), and changes attributable to both factors (the last
term). Given this and our notation we can rewrite (5) as:
borrowing can also lead to default.
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r
EOTBtrTBtrTBtrB
+
++=
1
][ 1,01,01,001,01,000 (9)
One method of analyzing the maximum amount of debt that a jurisdiction can have
outstanding is to use (9) directly. A common way of expressing debt outstanding is to
standardize the debt figure in relation to some base. Dividing through by the tax base in
the base period standardizes the debt burden to a percentage of tax base in the
jurisdiction:
( )rTB
EOTBtrtrTBtr
TB
B
+
++=
1
][
0
1,01,01,01,01,00
0
0(10)
Equation (10) shows that the maximum ratio of debt to tax base is a function of the
jurisdictions initial tax base and tax rate, changes in the tax base, tax rate, and operating
expenditures between periods and the interest rate on the jurisdictions debt. If we denote
the maximum ratio of debt to tax base asD, analysis of the comparative statics of (10)
shows the following relationships:
Table 1. Determinants of the Maximum Debt to Tax Base Ratio
?
D Sign
TB -
TB +
tr +
tr +
r -
EO -
The story behind equation (10) is that the jurisdiction at the beginning of the
period makes an estimate of the change in the tax base and then sets the proper borrowing
level and changes in tax rates and operating expenditures in order to avoid default. Of
course, relying on a point estimate of changes in tax base exposes the jurisdiction to
significant risk. If the realized change in tax base is far below that which was predicted,
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significant cuts in operating expenditures and/or increases in tax rates may be required.
Assume temporarily that the change in the tax base and the interest rate were
known perfectly. Then determining the maximum borrowing would simply reduce to a
mathematical model of the effects of the choice oftrand the change inEO. The
government could simply set trandEO so as to avoid default in each period. Viewed this
way, it can be seen that default for a bond is some combination of debt burdens, tax base
deficiencies, and unwillingness either by the public or their elected officials (or both) to
make necessary changes in tax rates or expenditures. So a default is at least in some
respects a political event. Jurisdictions could absorb relatively large shortfalls in revenue
through revenue rate and spending adjustments or they can default. Another conclusion
of this analysis is that there is hardly ever a case where one debt-to-tax base figure will
capture the maximum amount that a jurisdiction can safely borrow.
This becomes even more apparent when one relaxes the assumption that the
change in tax base is known. In most cases the change in tax base is wholly stochastic.
The decision to issue debt is now a decision based at least in part on expected growth in
the tax base. In an ex ante sense, that expectation will only be realized within a given
confidence level. In order to analyze the maximum amount of debt, officials must now
assess the likelihoodthat the growth in the tax base will be sufficient to cover debt
payments. To look at this decision, we can rewrite (9) in terms of the change in the tax
base necessary to support debt service:
( )
( ) 1,01,00
01,01,001
TBtrtr
TBtrEOrB=
+
++
(11)
Dividing (11) through by tax base to standardize, we see that the minimum percentage
change in tax base necessary to support a debt of sizeB is a function of that debt size, the
interest rate, the desired expenditure change, and the change in tax rate, standardized to a
percentage of future tax base:
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( )
( )0
1,0
1,000
1,01,001
TB
TB
trtrTB
trEOrB =
+
++
(12)
Comparative statics of (12) tell us something about the relationships between variables.
Jurisdictions with higher debt loads and greater expenditure demand as well as those that
pay higher rates of interest need greater changes in tax base to sustain comparable debt
burdens. And jurisdictions with bigger tax bases and higher tax rates, along with those
that can raise their tax rates more, have an ability to sustain debt loads with smaller
percentage changes in tax base. If we call the right-hand side of (12) Tthe comparative
statics are:
Table 2. Determinants of the Minimum Change in Tax Base Needed to Support Debt of Size B
?
T Sign
B +
TB -
tr -
tr -
r +
EO +
Equation (12) can be generalized for multiple-period debt. The only thing that changes
will be the required debt payment in each period. Given fixed rate debt, in all periods t
prior to maturity m, the required paymentPon the bond will be the interest payment
equal to the face value of the bond times the interest rate and at maturity the payment will
be the last interest payment, or:
( )rBP
mtrBP
m
t
+=
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( )
( )mt
TB
TB
trtrTB
trEOP
mtTB
TB
trtrTB
trEOP
m
m
mmm
t
t
ttt
=
=+
+
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Analyzing the comparative statics in Table 3, we find that the mean growth rate of
the tax base, the tax rate, and the change in tax rate have an inverse relationship with the
probability of default. We also find that the volatility of the tax base, the amount of debt,
the interest rate, and the desired change in operating expenditures have a positive
relationship with that probability.
Table 3. Determinants of the Probability of Default
?
)(
DefP Sign
-
+
B +tr -
tr -
r +
EO +
Simulation
In order to benchmark the relative influence of different variables on the
maximum debt burden, simulations must be run. Equation (17) and Table 3 show the
various factors that might influence the probability of default, but says nothing about the
magnitude of the risk that they introduce. In order to assess relative magnitudes, we
developed Monte Carlo simulations of (17) to study the effects of changes in the
important variables.
In order to develop the simulation, we had to initially set some parameters that
would not change over the simulation iterations. We chose arbitrarily a desired growth
rate of expenditures (EO) of three percent, initial tax rate (tr) of five percent, average
tax base growth rate () of five percent, tax base volatility () of 2.5 percent, risk-free
interest rate (r) at six percent, and debt maturity of 30 years.
Two important policy variables for the simulation are the disposal of surpluses
during the bond payoff period and the default rule the level of expenditure cuts or tax
increases which would produce a situation where either the official would choose not to
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make the payment on the debt or the citizenry would revolt, refuse to make payment, and
fire the official. These are trenchant not only in simulation, but in reality. As Kriz
(2002), Hou (2003) and many others have pointed out, keeping surpluses as savings
(through the use of reserve funds or another mechanism) reduces risk that jurisdictions
will have to reduce expenditures or raise taxes during times of economic downturn. Also
an elected or appointed official must be able to somewhat accurately gauge the
willingness of citizens to bear tax increases or expenditure cuts. With no prior knowledge
of disposal rules, we initially assume that the jurisdiction keeps all surpluses during the
bond payment period and invests them at an annual interest rate of three percent. This
assumption may produce overly optimistic results given the many studies which show
little savings behavior on the part of governments. However, later we will relax this
assumption along and analyze the results, as we will with the parameters we used in
setting up the base simulation.
The other policy variable, the default rule, is difficult to define a priori. So we
estimate our simulations at rule levels ranging from five percent to 30 percent in five
percent steps. That is, we run one simulation with a default rule of five percent, a second
simulation with a default rule of ten percent, etc. The results of the simulations are shown
in Figure 1 below. The lines in the chart are probability contours - estimated probabilities
of default from equation (17) given various combinations of default rules and borrowing
as percent of tax base.
FIGURE 1 GOES HERE. CAPTION: Results from Base Simulation
The results show that at low levels of borrowing, the probability of default is very
low regardless of the tolerance for reductions in expenditures or increases in taxes. But
the probability grows as borrowing increases. This much is probably not unexpected.
However, two more subtle points emerge from Figure 1. First, the increase in default
probability from increases in borrowing is fairly linear until the 50 percent point and then
it becomes exponential. After a certain point, borrowing dominates growth in the tax base
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and overwhelms it. We estimate that point to be when borrowing is greater than 50
percent of the tax base. As borrowing approaches 90 percent of the tax base, it becomes
more likely than not that debt service in a given year will force expenditure cuts or tax
increases of more than 15 percent. The second intriguing result is the relative
unimportance of citizen tolerance for changes in budgets, at least at relatively low levels
of debt. There is statistically no difference in probabilities of default regardless of the
default rule for borrowing under 50 percent of the tax base. It isnt until the buildup of
debt becomes relatively large that citizen tolerance for cuts or increases becomes
important.
Our model suggests that the ratio of the mean growth rate of the tax base to its
standard deviation is vital in determining debt affordability. High volatility in the growth
rate of the tax base compared to the mean growth rate increases the probability that in a
given period the growth of the tax base will be insufficient to cover the required debt
payment and normal operating expenditures. Figure 2 shows the results of our simulation
model when the tax base standard deviation is changed.
FIGURE 2 GOES HERE. CAPTION: Results of Simulation at Different Levels of Tax
Base Volatility
Figure 2 shows that at low levels of tax base volatility compared to mean growth
(which was kept at its base value of five percent) the debt burden can become quite
high (up to 70 percent of the tax base) without the jurisdiction incurring a large
probability of default. After this point is reached, however, the probability of default
grows exponentially. As tax base volatility grows, so too does the probability of default,
until it becomes high and more linear as the base volatility approaches the mean growth
rate of the base.
Desired future expenditure growth is yet another important variable in
determining the likelihood of default. To some extent, taking on debt represents a
tradeoff for jurisdictions. They get capital projects in the current period or near future. In
exchange they tradeoff some amount of future expenditures on operating items, replacing
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those expenditures with payments on the debt incurred to build the capital infrastructure.
Unless tax base growth is sufficient to generate sufficient revenue to offset the debt
service payments, cuts in expenditures, increases in taxes, or default on the debt becomes
likely. Figure 3 demonstrates the extent of the tradeoff.
FIGURE 3 GOES HERE. CAPTION: Results of Simulation at Different Levels of
Desired Future Operating Expenditure Growth
Figure 3 shows clearly that if a jurisdiction has a strong preference for capital
spending (and is thus willing to accept much lower expenditure growth) then default is
unlikely. At a level of expenditure growth three percent below the mean growth rate of
the tax base (desired expenditure growth of two percent versus mean tax base growth rate
of five percent), even with debt apprising 90 percent of the tax base, the probability of
default is a mere 13 percent. However, if citizens of a jurisdiction want their cake and
eat it too, demanding high growth rates of operating expenditure along with new capital
projects, they are likely to run into trouble. At a level of desired expenditure growth one
percent below the mean growth rate of the tax base, default is more likely than not for
any debt level in excess of 45 percent of the tax base.
Interest rates may also affect debt affordability. As interest rates rise, required
debt service rises. Debt service requirements may overwhelm tax base growth. However,
Figure 4 shows the obvious interaction between interest rates and debt levels. At modest
levels of debt, differences in interest rates have very little influence on the probability of
default. However, as debt rises, the probability of default becomes much greater at higher
interest rates.
FIGURE 4 GOES HERE. CAPTION: Results of Simulation at Different Interest Rates
The final variable which is predicted to have an effect on the default probability is
the initial tax rate. The initial tax rate amplifies changes in the tax base, so we expect to
see higher tax rates lead to lower probabilities of default. In practical terms, if
jurisdictions have difficulties collecting revenues then they are less likely to be able to
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collect enough revenues to service debt payments. Figure 5 shows the results of default
probability simulations where initial tax rates are varied. The effects of tax rates are
dramatic. At low tax rates, the default probability climbs dramatically as debt is added,
reaching an asymptotic high above 90 percent. At higher tax rates, the climb is much less
dramatic, with 7 percent tax rate default probabilities only reaching 25 percent.
FIGURE 5 GOES HERE. CAPTION: Results of Simulation at Different Initial Tax Rates
The final variable which must be considered is the endogenous growth in the tax
base caused by adopting the capital project. Since tax base growth is such a strong
determinant of the probability of default, we anticipate that stronger rates of endogenous
growth should have an equally dramatic effect on default rates. In order to analyze
whether this was the case, we created simulations with debt having a multiplier effect
on tax base growth rates. We simulated our base model varying the multiplier in the
range 0 (no endogenous effect) to 2.0 (a 10 percent increase in debt causing a 20 percent
increase in annual growth rates of the tax base). Below (Figure 6) we present the result
only for multipliers from 0 to 0.5, because the results for multipliers greater than 0.5 are
essentially the same as for a multiplier of 0.5. We also present only debt levels of 50% of
the tax base, because this shows the general pattern of results. Figure 6 clearly shows the
dramatic effect we predict. As the multiplier approaches 0.5, the probability of default
goes to less than 1 percent. However, as the multiplier gets smaller, default probabilities
climb dramatically.
FIGURE 6 GOES HERE. CAPTION: Results of Simulation at Different Tax Base
Multipliers
Conclusions/Policy Implications
In this paper we have developed and simulated a model of debt affordability that
takes into account the stochastic nature of revenue growth. Our model has yielded many
important insights into those factors that may go into determining the affordability of
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debt. First and foremost, our model strongly refutes the notion that a single measure of
debt affordability can in any way capture the likelihood that a jurisdiction will default on
its debt. Simple benchmarking exercises are not worthwhile when seen in the context of
the tremendous sensitivity of default likelihood to changes in variables such as tax base
volatility. Even regression approaches taken in isolation can only tell us a limited amount
about the likelihood of default. This is because regression results alone can only tell us
about one variable such as the income elasticity of the tax base, and little about other
factors such as the willingness of the jurisdiction to forego current expenditures to sustain
a capital investment program.
Beyond this, our research indicates several issues regarding the direction and
magnitude of various factors that lead to a jurisdiction being more or less creditworthy.
The first observation yielded by our research is that the political will to sustain debt
service in the face of tax increases or service cuts (as proxied by our default rule variable)
has a negative but very minor effect on the likelihood of default. At low levels of debt in
fact, there is almost no effect of increased political will. At higher levels of debt, the
difference is small but present. This indicates that jurisdictions should worry about
citizen sensitivity to tax and expenditure changes only at higher rates of debt.
The second observation is that revenue base volatility has a strong positive effect
on default probability. The implication here is that borrowing should be primarily
supported by revenue bases which are less volatile. If individual jurisdictions have a
choice, they should borrow more against revenue bases that are stable, such as the
property tax. In a comparative sense, jurisdictions that have lower revenue volatility
should be able to borrow more than those jurisdictions with high volatility.
Another factor that emerges as being very important in determining the likelihood
of default is the desired rate of operating expenditure growth. Operating expenditures
may crowd out the ability of jurisdictions to pay debt service. Jurisdictions that wish to
have high growth rates of operating expenditures can ill afford to burden themselves with
high debt levels. And jurisdictions that have high expectations or requirements for capital
investment must work to restrain other spending pressures to ensure that debt is
affordable.
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Interest rates can play an important role in determining debt affordability. This is
especially true for jurisdictions with high debt loads. These jurisdictions become much
less financially viable as the level of interest rates rises. A possible corollary of this result
is that as interest rates increase, the spread between debt interest costs at issuance of
jurisdictions with low debt and high debt will rise. This would suggest the possibility of a
vicious cycle as interest rates rise where jurisdictions with high initial debt levels must
pay more for their new debt, which reduces the likelihood of repayment on all of their
debt, which in turn increases the interest rate on further debt, and so forth.
Another variable whose impact increases with higher debt levels is the initial tax
rate. The ability to sustain higher tax rates can dramatically affect the likelihood of debt
service payments being made. This suggests that the credit rating practice of trying to
assess the political will to sustain tax rates is sound. Returning to the story of Orange
County, the actual trigger for the countys bankruptcy was the failure to pass a tax
increase in the wake of the pension fund debacle (Baldassare, 1998). This result confirms
our earlier one that jurisdictions with high debt loads must be much more aware of
citizens sensitivity to tax rates.
The final variable which is extremely important in determining the likelihood of
debt repayment is the multiplier effect that is created by the use of debt proceeds. Our
results indicate that public capital investments that are effective create economic growth
which will essentially defease the debt. This would indicate that effective capital
budgeting by jurisdictions is vital to ensure that debt is affordable.
In practical terms, the model which we have developed can be easily analyzed for
a particular jurisdiction and debt issuance decision. Given a set of historical data on tax
base growth, effective tax rates, and debt burdens, debt of a certain level can be analyzed
in terms of how likely it is to be repaid. And the sensitivity of those results can be
calculated with respect to changes in key variables such as the investment multiplier and
tax rate changes. In the end, almost any analytical approach to debt affordability is bound
to make assumptions. Our model makes far fewer assumptions and produces output
which decision makers can use to better guide debt issuance decisions.
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