Public Finance Seminar Spring 2015, Professor Yinger Property
Tax Capitalization
Slide 2
Class Outline What Is Property Tax Capitalization? How Does
Property Tax Capitalization Arise? How Can One Estimate the Degree
of Property Tax Capitalization? What Are the Implications of
Property Tax Capitalization for Public Policy?
Slide 3
Property Tax Capitalization Introduction The basic bidding
model implies that the price of housing services will be higher in
jurisdictions with lower property taxes. This is called property
tax capitalization. Although he was not the first to estimate
property tax capitalization, Wallace Oates (my professor) brought
new attention to the topic with his famous 1969 JPE paper on the
Tiebout hypothesis. Oates used data for suburbs in NJ and found
evidence of tax and service capitalization (more later).
Slide 4
Property Tax Capitalization What Is Property Tax
Capitalization? It is just the impact of the present value of
expected annual property tax payments on the value of a property.
It can be derived from an asset pricing model or from the household
maximization problem in bidding models.
Slide 5
Property Tax Capitalization Asset Value The value of an asset
equals the present value of the net benefits from owning it.
Without property taxes, the amount someone is willing to pay for a
house is the present value of the rental benefits, or where is the
pre-tax price of housing services, H is housing services, r is the
real discount rate, and L is the expected lifetime of a house.
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Property Tax Capitalization The Magic of Algebra
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Property Tax Capitalization House Value Simplified If the real
value of rental services is constant over time and L is large, this
equation reduces to: The value of a house equals its annual rental
value divided by a discount rate. Because housing lasts a long
time, this is a reasonableand obviously helpfulsimplification.
Slide 8
Property Tax Capitalization Adding Property Taxes The property
tax payment, T, is the product of a nominal tax rate, m, and an
assessed value, A. It is also the product of an effective tax rate,
t, and a market value, V In symbols Annual property taxes represent
an expense for a homeowner.
Slide 9
Property Tax Capitalization Adding Property Taxes, 2 With this
new expense, the house value equation becomes: Note that property
taxes are added as a flow because they must be paid every yeara
flow that is capitalized.
Slide 10
Property Tax Capitalization Adding Property Taxes, 3 This
equation assumes that property taxes are fully capitalized. As we
will see, this might not be the case, so a more general form is:
where is the degree of property tax capitalization; i.e., the
impact of a $1 increase in the present value of property taxes on
the value of a house.
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Property Tax Capitalization The Degree of Property Tax
Capitalization A value of equal to 1.0 corresponds to full
capitalization. A value of equal to 0.0 corresponds to no
capitalization. If equals 0.5 a $1 increase in the present value of
property taxes leads to a $0.50 decrease in the value of a house.
The value of need not be the same under all circumstances.
Slide 12
Property Tax Capitalization The Capitalization Equation Solving
the above for V yields the well-known form for the capitalization
equation: Thus, houses facing higher effective property tax rates (
t ) will have lower values ( V ). The strength of this relationship
depends on .
Slide 13
Property Tax Capitalization How Does Tax Capitalization Arise?
Real estate brokers indicate anticipated property tax payments so
buyers can make comparisons across houses. Lenders require mortgage
plus tax payments to equal a fixed percentage of an applicants
income. An increase in T must be offset by a drop in the mortgage,
and hence a drop in how much the applicant can pay for the house,
V.
Slide 14
Property Tax Capitalization Expectations Another issue is that
the expected lifetime of current tax rates might be N < L. In
this case, we need to use r', not r : This leads to: where ' is the
degree of property tax capitalization after accounting for
differences in expectations.
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Property Tax Capitalization Expectations, 2 Now when we solve
for V we get:
Slide 16
Property Tax Capitalization Expectations The coefficient to be
estimated, , is the expression in front of t, so it includes both '
and the impact of different expectations about the lifetime of a
house and of property taxes. This explains why we need both and ' ;
the first is what we estimate but the second is the underlying
degree of capitalization. It is still not obvious why we need to
consider expectationshold on.
Slide 17
Property Tax Capitalization Property Tax Capitalization Inter-
and Intra-Jurisdiction Variation These equations apply within a
community. Recall that Poor assessments result in higher
assessment-sales ratios, and hence higher effective tax rates, for
some houses than for others. These equations also apply across
communities, which may have very different effective tax
rates.
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Property Tax Capitalization Property Tax Changes Here is a
change form of the equation:
Slide 19
Property Tax Capitalization The Strategy in PTHV In PTHV, this
equation is used to study intra- jurisdictional capitalization,
that is, the capitalization of effective property tax rate
differences within a community. To remove the impact of
inter-jurisdictional tax differences/changes, and of other factors
that vary over time, the dependent variable is deflated using a
housing price index. This removes from V the impact of any change
in the average effective tax rate (among other things) and leaves
just the impact of the change in the deviation from the average tax
rate.
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Property Tax Capitalization The Strategy in PTHV, 2 Now express
the effective tax rate as and put an * on V to indicate deflation.
Deflation implies that Accurate revaluation implies that
Slide 21
Property Tax Capitalization The Strategy in PTHV, 3 Hence:
where and Thus, with data on, an estimate of b, and an assumption
about r, one can obtain an estimate of .
Slide 22
Property Tax Capitalization Error in PTHV These equations
correct an error in PTHV. The algebra in that book mistakenly
ignores the denominator of the previous equation. As we will see
below, this mistake implies that the book understates the value of
by about 30 percent.
Slide 23
Property Tax Capitalization Research Issues in Estimating
First, this estimation involves a non-linear relationship between t
and V, even after taking logarithms, so it cannot be estimated with
linear regression methods. After taking logs, the basic equation
is:
Slide 24
Property Tax Capitalization Research Issue 1, Continued One can
use the approximation ln{1+a} a, but it may not be very good in
this case, because ( /r)t may not be close to zero. A change form
of the equation may work better. It can be estimated with NL2SLS.
With reassessment, it can be estimated in linear form under the
assumption that assessments are accurate, i.e. that
Slide 25
Property Tax Capitalization Research Issue 1, Continued Note
that it is impossible to separate and r in the estimation. One can
only estimate their ratio. This leads to the next issue.
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Property Tax Capitalization Research Issue 2 Second, the value
of the discount rate, r, is not observed, and it is impossible to
estimate r and separately. Most studies follow Oates by estimating
a value of /r, assuming a value for r, and then calculating the
implied value of . The trouble with this approach is that the value
of depends on an untested assumption that varies across studies. In
fact, the most extreme estimates of in the literature, in either
direction, are driven largely by extreme assumptions about r.
Slide 27
Property Tax Capitalization Research Issue 2, continued
Moreover, scholars are amazingly careless about r, often using a
nominal interest rate, when the theory clearly shows that a real
rate, say 3 to 5 percent, is needed. A real rate equals the nominal
or market rate minus anticipated inflation. PTHV takes a long-run,
low-risk nominal rate (as for an investment in housing) and
subtracts anticipated inflation based on a study of the factors
that determine inflation expectations. This leads to a 3 percent
rate.
Slide 28
Property Tax Capitalization Research Issue 3 Third, the
asset-pricing logic behind tax capitalization requires assumptions
about house buyers expectations. To be specific, this logic
predicts that a $1 increase in the present value of future property
taxes will lead to a $1 decline in house value (i.e. ' = 1 ), but
it does not say that current tax differences will be fully
capitalized (i.e. = 1 ) if they are not expected to persist.
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Property Tax Capitalization Research Issue 3, Continued
Virtually all the literature estimates the capitalization of
current property tax differences. Under the assumption that current
tax differences will persist indefinitely, the assumption that = 1
makes sense. In fact, however, current differences may not be
expected to persist. In this case, we can use the result derived
earlier, namely, where N is the length of time current tax
differences are expected to persist. The theory indicates that = 1,
but the estimated clearly need not equal 1, and indeed need not
equal the same value under all circumstances.
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Property Tax Capitalization Research Issue 3, Examples If
current property tax differences across (or within) communities are
expected to disappear in 10 years and r =.03, then this equation
implies that the estimated will be only 26% even if = 1. If
revaluation is scheduled every 6 years, say, then the estimated
should decline as one moves closer to the year of revaluation.
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Property Tax Capitalization Research Issue 4 Fourth, because
t=T/V, one must treat t as endogenous. This endogeneity is both
definitional ( t is a function of the dependent variable) and
behavioral (factors unobserved by the researcher but observed by
the assessor may influence both T and V ). PTHV uses a model of
assessor behavior to identify some instruments and then uses either
NL2SLS or 2SLS.
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Property Tax Capitalization Research Issue 5 Fifth, one must be
careful about omitted variable bias. Good data on housing traits
are needed. This is not quite such a big problem with double-sales
data, which difference out time-invariant traits. Even with
double-sales data, it helps to control for renovations. Deflating V
eliminates the possibility that the estimated impact of a change in
t is biased by the omission of other changes at the jurisdiction
level.
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Property Tax Capitalization Research Issue 6 Sixth, one must
consider itemization. If a taxpayer itemizes on her federal income
taxes, then she gets to deduct property taxes. So a $ 1 increase in
the present value of property taxes does not really cost this
taxpayer $ 1. Estimated capitalization may reflect this effect.
However, mortgage interest payments are also deductible, so an
income tax correction applies to both the numerator and denominator
of the estimated coefficient, /r. If s is the marginal income tax
rate, this ratio with full deductibility of interest cam be written
as [(1-s)]/[r(1-s)] = /r. One might also argue that the denominator
is not the mortgage interest rate, but is instead the opportunity
cost of investing in housing, which is the return on other
low-risk, long-term investments and is unaffected by
deductibility.
Slide 34
Property Tax Capitalization Evidence on Property Tax
Capitalization Every reasonable study of property tax
capitalization finds a statistically significant negative impact of
property taxes on house values. Estimates of vary from 15 to 100
percent. The main reason for this variation appears to involve
expectations.
Slide 35
Property Tax Capitalization The Role of Expectations So far,
current tax differences across houses are implicitly assumed to
persist indefinitely. But if tax differences are not expected to
persist, the capitalization of current differences, , declines. A
difference observed today that will disappear upon sale has no
impact on V. A difference observed today that is expected to last
one year will have only a tiny impact on sales price.
Slide 36
Property Tax Capitalization The Case of Massachusetts In
Massachusetts, revaluations were required by the state supreme
court, but enforcement was weak. Communities knew they could avoid
revaluation for many years. Existing tax differences were expected
to persist, but not forever. PTHV finds that current tax
differences were capitalized at a rate of 32 percent. This is
consistent with the expectation that current tax differences would
disappear in 13 years.
Slide 37
Property Tax Capitalization Corrected Estimates of
Capitalization in Waltham for Property Taxes and House Values
Nonlinear Version (equation (8)) Linear Version (equation (9))
Estimate of b 7.42337.0433 Value of0.0420 Value of 1 - b
0.68820.7042 Original 0.22270.2113 Corrected 0.32360.3000
Understatment (%)31.229.6 Implied N (years)13.212.1
Slide 38
Property Tax Capitalization The Case of Syracuse In Syracuse in
the early 1990s, revaluation had not occurred for decades and did
not appear likely to happen any time soon. But the city council
unexpectedly decided to revalue. A study of capitalization in
Syracuse by a PA Ph.D. student (Eisenberg) found capitalization
rates near 100 percentexactly what the theory predicts when tax
differences are expected to persist. This result applies when
people are borrowing to the limit and not itemizing.
Slide 39
Property Tax Capitalization Stay or Go? If property taxes are
fully capitalized, then any tax changes show up in house values
immediately and there is no way to escape them. An owner with a tax
increase must either stay and pay the higher tax or leave and
suffer a capital loss. An owner with a tax cut gets a capital gain.
Moreover, the loss is the full present value of the future
increases in taxes.
Slide 40
Property Tax Capitalization Property Tax Capitalization &
Public Policy Because of these gains and losses, tax capitalization
has bizarre implications for public policy. Consider revaluation,
which is a systematic revision of all assessed values. Revaluation
leads to capital gains for homeowners who were over-assessed and to
capital losses for homeowners who were under- assessed.
Slide 41
Property Tax Capitalization Capitalization and Policy, 2 For
long-term residents, these changes are fair. A resident who has
been under-assessed for a long time has been given, in effect, a
loan from the city and revaluation just claims back this loan. But
for new residents, these changes are not fair. If someone bought an
under-assessed house one day and the change is announced the next,
this person has a capital loss even though she did not benefit from
the poor assessment system.
Slide 42
Property Tax Capitalization Capitalization and Policy, 3 Two
ways to minimize this fairness problem: First, introduce a long lag
between announcement and implementation. This lag allows owners at
the time of announcement to escape some of the burden of the tax
changes. Second, make sure houses are revalued upon re-sale, which
they were not in Massachusetts or Syracuse.
Slide 43
Property Tax Capitalization Capitalization and Policy, 4 A
revaluation imposes some unfair gains and losses but restores
fairness in the near term and boosts faith in local government.
This trade only makes sense if assessments are updated regularly.
Otherwise, gains and losses are handed out each year as assessment
errors mount. Poor assessments also lead to court cases, which the
city usually loses. People who buy over-assessed property pay low
pricesand then can sue the city for a rebate because of unfairly
high taxes. This happened in Boston, to the tune of tens of
millions of dollars. The only way to avoid this crazy situation is
to keep assessments up to date!
Slide 44
Property Tax Capitalization Capitalization and Policy, 5
Proposition 13 in California represents another unusual case. The
proposition fixes assessment growth at 2%, so the assessment/ sales
ratio, and hence t, declines over time for long-term owners. This
cannot be turned into a capital gain because houses are revalued
upon sale. But it represents a gift to long-term owners and it
discourages mobility. The U.S. Supreme Court said this was legal.
Voters in California and a few other states like this reward to
long-term residents; I dont.