Arson and the business cycle.
Corrigan, Frank E., III ; Siegfried, John J.
I. Arson and the Economy
Arson causes over $1 billion in U.S. property damage annually
(United States Fire Administration, 2005). Arsonists deliberately burn
structures for various reasons, some which may be sensitive to economic
circumstances. Because insurance usually covers fire damage, the
incentive for owners to set fires deliberately or be neglectful in
maintenance varies with conditions that affect market values relative to
insured values. If insured value exceeds market value, there is an
incentive to commit arson. An owner may deliberately set fire to his
business to avoid losses during a recession or to collect fraudulent
insurance payments when the expected cost of continuing the business
exceeds its expected revenue. A home owner, whose property value has
plummeted, for example, due to a severe downturn in the housing market,
may find it more attractive to collect insurance than to sell, repair,
or continue to live in the structure.
A Fox News Report, broadcast on January 27, 2008, indicated that
some American homeowners were deliberately burning residences because
the slump in U.S. housing prices had driven market values below insured
values. Fire investigators have noted the possibility of financial
circumstances motivating arson. Certified Fraud Examiner Douglas Crewse
claims business owners in financial distress may deliberately set fire
to their business "to avoid insolvency, prevent further losses in
the business, ..., dispose of inventory, liquidate a business due to
unprofitable contracts, or even relocate and/or renovate the
business" (Crewse, 2005). Arson for profit is not limited to
commercial buildings. Fortune magazine reported on January 10, 2008 that
the insurance-industry-funded Coalition Against Insurance Fraud had
warned that "fraud fighters were watching closely for a spike in
arsons by desperate homeowners who could no longer afford their home
payments;" Dennis Schulkins, a claim consultant in State
Farm's Special Investigative Unit asserted that "when the
economy is down, we see an increase in fraud." Of course, increased
risk of criminal prosecution occurs if an arsonist acts on the potential
gain from the insurance contract he or she holds.
In 1979, Thomas Spillman and Thomas Zak investigated the
relationship between arson and the business cycle. They regressed arson
rates on economic activity over time, using the unemployment rate as a
measure of both property values and the opportunity cost of crime.
Because they used quarterly observations from 1963 to 1976 from
Nashville, Tennessee, binary variables were included to adjust for
seasonal variation in arsons. Surprisingly, Spillman and Zak found no
relationship between the unemployment rate and arson. However, their
specification did not directly incorporate property values, but rather
correlated arson with general employment conditions.
Hershbarger and Miller (1978, 275-290) continued this line of
research, relating commercial arsons to the number of business
bankruptcy cases filed, duration of unemployment, and other indicators
of general business vitality. Using annual data for the U.S. from
1964-75, Cloninger (1981, 494-504) found that arson increases as the
yield on business assets falls. Brotman and Fox (1988, 751-754) found no
correlation between dollar losses due to arson and unemployment, but
surprisingly found higher arson losses when the bankruptcy rate is lower
and housing prices are higher. They did not consider, however, the
possibility that arson losses can rise with housing prices while arson
frequency diminishes. In a second empirical study of arson, Cloninger
(1990, 540-545) directly tested the hypothesis that arson is an
attractive form of asset abandonment when property values fall below
replacement values. Using data from 1964 through 1987, he found that
arsons vary inversely with "Tobin's q," the ratio of
market value to replacement value. Finally, Steven Green and Allen
Seward (1998) found cross-section evidence that arsons increase when
housing prices fall and when homeowners are in financial distress.
In this note, we replicate and update the Spillman and Zak study
(1979, 37-43), and then extend it by adding variables reflecting housing
prices to reflect the benefits of arson, leaving the unemployment rate
to reflect the opportunity cost of the crime. After explaining why arson
rates should be more sensitive to contemporaneous housing prices than to
general economic conditions, we test our hypothesis by repeating the
Spillman and Zak tests, adding measures of housing prices to
unemployment rates to distinguish the specific role of housing prices
from general business conditions, which do not always move in the same
direction.
II. The Economic Model
Arson is a pre-meditated crime. A rational criminal considers the
consequences of his actions before committing a crime. To be profitable,
the expected benefits from arson must exceed expected costs. Expected
benefit is the financial gain the arsonist receives by destroying
property, essentially the difference between its insured and market
value. Expected costs are legal penalties imposed on a convicted
arsonist, adjusted for the probability of being caught and the
probability of being convicted.
Arson is financial abandonment. Linking formal financial
abandonment models developed by Robichek and Van Home (1967, 577-89),
Dyl and Long (1969, 88-95), and Joy (1976, 1225-28) to criminal behavior
models created by Becker (1968, 169-217) and Ehrlich (1973, 521-565),
Cloninger (1981, 494-504) shows that abandonment is financially
attractive if the abandonment value (insurance) exceeds the net present
value of expected cash flows over the remaining expected life of an
asset. Arson is the optimal form of abandonment when expected gains from
proceeds of an insurance claim arising out of a fire exceed both
expected gains from a legal sale and the expected net present value of
the flow of utility from continued use of the asset. Normally, insured
value is less than market value of an asset, and expected gain is zero.
However, rapid depreciation of an asset or plummeting demand can lower
market value to such an extent that replacement value exceeds market
value. For example, many structures built during 2005 and 2006 could not
be reconstructed with their 2010 market value.
The devastation caused by Hurricane Katrina in 2005 was blamed for
increased arson in the Gulf Coast area. Arson was suspected as the
probable cause of numerous suspicious fires in New Orleans. According to
the superintendent of one New Orleans area fire department,
"speculation is that some homeowners without flood insurance or
those with a low cap on their [flood] policies may be hoping to cover
themselves by collecting through their fire coverage" (Hunter,
2005). Some homeowners may have perceived the expected gain in potential
property insurance compensation that had not been adjusted for the value
lost as a result of Katrina to exceed the expected cost of being
arrested for arson. Katrina essentially caused a downturn in the local
economy, which lowered a cost (the market value of structures) of
committing arson. The lower cost increased the incentive to commit
arson, with the expectation of greater financial gain in the form of
insurance compensation.
Accordingly, we hypothesize that arson depends on the expected
future value of property (benefits), the direct costs of potential legal
consequences (costs), and time (because of progress in fire avoidance
and suppression technology). Like Spillman and Zak, our empirical model
uses the annual number fires in Nashville, Tennessee judged to be arson
as the dependent variable. These data were collected personally from the
Nashville Fire Marshall's office. We use 31 rather than 14 years of
data, thereby including more business cycles. (1) We use annual rather
than quarterly data because only annual data were collected by the
Nashville Fire Marshall for the entire period we analyze. Annual data
also eliminate concerns about seasonal variation in arson.
We consider two measures of arson. "Arsons" are fires
determined to have been set deliberately. The number of arsons is a
function of the number of structures, which, in turn, depends on
population. "Suspicious fires" is the sum of vandalistic,
arson, and suspicious fires. It is more inclusive than arsons, adding
probable-but-not-surely-determined arsons. "Suspicious fires"
is also a function of population.
We include the unemployment rate as a measure of the opportunity
cost of being apprehended and convicted of arson. But, we add measures
of property values to capture directly and separately from the
opportunity cost of being apprehended and convicted of a crime, the
potential benefits of committing arson. The unemployment rate measures
the percentage of those in the civilian labor force who do not have a
job and are seeking work. During periods of high unemployment, potential
arsonists have less to lose if apprehended and convicted for arson.
Housing markets do not always mimic general business conditions,
because the expected growth in future housing prices depends on current
and recent changes in housing prices (i.e. speculation), as well as on
current and expected future mortgage interest rates. We use two property
value indexes: 30-year fixed rate mortgage rates and a home price index.
When mortgage rates rise, potential homebuyers find it more expensive to
borrow and therefore more expensive to purchase property, thus
decreasing demand for housing and, consequently, housing prices.
Moreover, increases in home mortgage rates reflect increases in other
long-term interest rates, including business loans. As costs of doing
business rise, financial pressures intensify and business asset values
decline.
Average annual interest rates for 30-year fixed-rate mortgages were
obtained from the Federal Home Loan Mortgage Association (FHLMA) [18].
(2) The home price index is average home value in Nashville, tabulated
by the FHLMA. (3) It was set at 100 on January 1, 1987. Each home price
index observation represents year end property values.
While mortgage rates measure property values indirectly, the home
price index measures them directly, giving our model two measures of
property value variability.
A second set of estimates controls for the effect of city size on
the quantity of arsons. The number of structures, potential
"victims" of arson, is roughly proportional to population.
Nashville annual average unemployment rate and population information
were collected from the Tennessee Department of Labor and the U.S.
Census [16, 17]. Population in the model is the number of residents (in
units of 10,000) in the Nashville metropolitan area.
III. The Empirical Model and Results
The equation is estimated with multivariate ordinary least squares
regression. First, the Spillman and Zak study is replicated using
suspicious fires as a measure of arsons, as in their study. Spillman and
Zak used quarterly observations from 1963-1976 in first-difference
equations, regressing suspicious fires on the unemployment rate,
including indicators for seasons. They estimated:
[DELTA]Suspicious [Fires.sub.t] = [[beta].sub.0] + [[beta].sub.1] *
[DELTA]Unemployment [Rate.sub.1] + [[beta].sub.2]*[Q.sub.1] +
[[beta].sub.3]*[Q.sub.2] + [[beta].sub.4]*[Q.sub.3]
Because we use annual data, quarterly indictors are not needed.
Thus, we "replicate" the Zak and Spillman estimates with
first-difference regressions (4) of suspicious fires on the unemployment
rate, using annual data from 1971 through 2003. Then, new estimates are
made, adding the housing market measures. Each dependent variable,
arsons and suspicious fires, is regressed on the unemployment rate, the
mortgage rate, and the home price index:
Arson or Suspicious [Fires.sub.1] = [[beta].sub.0] + [[beta].sub.1]
* Unemployment [Rate.sub.1] +[[beta].sub.2]* Mortgage [Rate.sub.1] +
[[beta].sub.3]* Home Price [Index.sub.t] + [[epsilon].sub.t]
Population is controlled by dividing arsons or suspicious fires by
population.
We replicate Spillman and Zak's 1979 estimates using our more
recent annual data in order to insure that any differences we find
compared to the Spillman and Zak results are not a consequence of the
different data used for estimation. The estimated replication, using
first differences, is:
[DELTA]Suspicious Fires = -2.478 - 2.042 [DELTA] Unemployment Rate
(-0.33) (-0.240)
with t-statistics in parentheses, an adjusted coefficient of
determination of -0.04, and an F-ratio of 0.05. The coefficient on the
unemployment rate is not statistically significantly different from
zero. The results are similar to Spillman and Zak's, with low
explanatory power and no significant coefficients.
The empirical results reported in Table 1, adding direct measures
of housing prices, reveal strong correlations between arson and the
housing market variables, but continued weak associations of arson with
employment conditions. (5) In fact, the estimated coefficient of the
unemployment rate implies that arsons decline during periods of higher
unemployment. This suggests that changes in possible benefits have a
greater effect on decisions to commit arson than changes in potential
costs of being apprehended and punished. In Table 1, each measure of
arson is estimated using the unemployment rate, the mortgage rate, and
the housing price index. Since the unemployment rate, the mortgage rate,
and the housing price index have hypothetical unambiguous effects on
arson, one-tail t-tests are used to determine statistical significance.
The coefficients of both the mortgage interest rate and the housing
price index are statistically significant at the one percent level in
both regressions. Rising property values are associated with less arson.
Importantly, however, the unemployment rate is not significant in either
regression (because its sign is contrary to expectations). The mortgage
rate is significantly correlated with suspicious fires in all four
estimates, and the housing price index is statistically significant in
each regression except the one on suspicious fires that does not control
for population. The adjusted coefficient of determination for the
regression on suspicious fires without controlling for population, the
one in Table 1 closest to the Spillman and Zak replication, is 60
percent vis-a-vis virtually zero for the replication.
The regression on arsons per 10,000 people predicts one additional
arson per 10,000 people annually is associated with a six percentage
point rise in the mortgage interest rate (which would cause a decline in
housing prices). Using Nashville's average annual population of
510,243 over the period of analysis, this means a one percentage point
rise in mortgage rates is associated with 8.6 more arsons per year. A
one percentage point decline in the Housing Price Index is predicted to
be associated with 0.015 more annual arsons per 10,000 people or 0.8
more arsons per year.
Our results concerning the association between arson and general
business conditions are similar to those of Spillman and Zak, namely
fluctuations in unemployment are not correlated with arson. Combined
with the strong direct correlations between arson and property values,
the results indicate that labor market conditions more likely reflect
opportunity costs of committing arson than represent the expected
benefits of arson. Unemployment apparently does not change opportunity
costs enough to alter decisions to deliberately burn structures. As
expected by arson investigators (Crewse, 2005; Hunter, 2005; Scott,
2005), higher property values and lower mortgage interest rates are
associated with fewer arsons.
IV. Conclusion
Estimates using data from Nashville, Tennessee show that
unemployment is not related to the incidence of arson, but that property
values are highly correlated with arson. Although Spillman and Zak did
not detect significant relationships between arson and general business
cycle conditions, arson does appear to be related directly to property
values. In light of the volatile housing market conditions from 2007 to
2011, continued analysis of the relation of arson with the business
cycle during a rapidly changing housing market could further clarify the
connection between arson and housing prices. Similar studies for other
metropolitan areas would help improve our understanding of moral hazard
and indicate whether our conclusions about the causes of arson can be
generalized.
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Notes
(1.) Arson data are unavailable for 1990 and 1998, leaving 31
annual observations from 1971 through 2003, a period covering five
recessions in the United States. Recessions identified by the National
Bureau of Economic Research (2005) are: November 1973-March 1975,
January 1980-July 1980, July 1981-November 1982, July 1990-March 1991,
and March 2001-November 2001.
(2.) Since 1971, the FHLMA has surveyed lenders to determine the
weekly average 30-year fixed-rate mortgage rate. The weekly averages are
compiled into an annual average.
(3.) FHLMA (February 2006) constructs a home price index using
repeat sales of same homes.
(4.) Spillman and Zak (1979, 3743) used a first-difference model
because the original unit regressions "revealed serious first-order
autocorrelation." Our replication similarly exhibits severe serial
correlation, and so we have replicated likewise using first differences.
(5.) The numbers of fires and arsons has decreased over time. A
trend variable could capture changes in fire/smoke alarms, building
codes, etc. that have improved fire safety over time. A time-trend
variable was used in regressions not reported; it did not explain enough
of the variation in arson to warrant the sacrifice of a degree of
freedom. Durbin-Watson statistics in Table 1 show no positive serial
correlation, suggesting that the underlying relationships between the
economic variables and arsons or suspicious fires do not suffer from
serial correlation, and, first differences are not necessary. To confirm
that these correlations are not simply spurious because these variables
have similar underlying trends, a Dickey-Fuller cointegration test is
used to test stationarity of the residuals. Because each regression
exhibits a significant cointegration relationship at the one percent
level, and the original regressions are not spurious, first-difference
regressions are not necessary.
Frank E. Corrigan III, Vanderbilt University
John J. Siegfried, American Economic Association and University of
Adelaide, South Australia
TABLE 1.
Estimates of Arson for Nashville, Tennessee
Suspicious
Independent Variables Arsons Fires
Constant 185.273 156.611
(4.329) (2.783)
Unemployment Rate -10.277 -25.567
(-1.540) (-2.914)
Mortgage Rate 8.565 ** 19.375 **
(2.858) (4.918)
Housing Price Index -0.523 ** -0.247
(-3.144) (-1.131)
Adjusted [R.sup.2] 0.601 0.598
Durbin-Watson Stat 2.281 * 1.780 *
F-statistic 14.036 * 13.894 *
[[beta].sub.1] from Dickey- -1.076 ** -0.835 **
Fuller
[DELTA][e.sub.t] + [[beta].sub.] (-4.922) (-4.226)
[e.sub.t-1] + [[eta].sub.t]
Arsons/ Suspicious Fires
Independent Variables Population /Population
Constant 3.977 3.255
(4.576) (2.962)
Unemployment Rate -0.169 -0.448
(-1.244) (-2.613)
Mortgage Rate 0.168 ** 0.388 **
(2.759) (5.037)
Housing Price Index -0.0146 ** -0.00938 *
(-4.327) (-2.196)
Adjusted [R.sup.2] 0.710 0.688
Durbin-Watson Stat 2.144 * 1.843 *
F-statistic 21.367 * 20.072 *
[[beta].sub.1] from Dickey- -1.052 ** -0.863 **
Fuller
[DELTA][e.sub.t] + [[beta].sub.] (-4.806) (-4.000)
[e.sub.t-1] + [[eta].sub.t]
Number of observations = 31 years
t-scores in parentheses: one-tail tests
* significant at the 5% level.
** significant at the 1 % level.
