Public Finance Seminar
Spring 2015, Professor Yinger
Property Tax Capitalization
Property Tax Capitalization
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?
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).
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.
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
ˆ
ˆ
ˆ
ˆ
PH
PH
PH
PH
V 

 ... 
y 
L
2
(1

r
)
(1

r
)
(1

r
)
(1

r
)
y 1
L
where P̂ 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.
Property Tax Capitalization
The Magic of Algebra
ˆ
ˆ
ˆ
PH
PH
PH
ˆ
V (1  r )  PH 

 ... 
(1  r ) (1  r )2
(1  r ) L1
and
ˆ
PH
ˆ
V - V (1  r )  - PH 
(1  r ) L
or
ˆ [(1  r ) L 1]
V [1  (1  r )]  PH
or
 1  (1  r ) L 
ˆ
PH
ˆ

V  PH 


r
r


where
r 
r
1  (1  r ) L
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:
P̂H
V
r

The value of a house equals its annual rental
value divided by a discount rate.

Because housing lasts a long time, this is a
reasonable—and obviously helpful—simplification.
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.
T  mA  tV
Property Tax Capitalization
Adding Property Taxes, 2

With this new expense, the house value equation
becomes:
ˆ
PH
V 
y
(1

r
)
y 1
L

L
tV
y

(1

r
)
y 1
ˆ
PH

 tV
r
r

Note that property taxes are added as a flow
because they must be paid every year—a flow
that is “capitalized.”
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:
L
L
ˆ
PH
V 
y
(1

r
)
y 1

 tV
y

(1

r
)
y 1
ˆ
PH

  tV
r
r
where β 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.
Property Tax Capitalization
The Degree of Property Tax Capitalization

A value of β equal to 1.0 corresponds to full
capitalization.

A value of β equal to 0.0 corresponds to no
capitalization.

If β 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 β need not be the same under all
circumstances.
Property Tax Capitalization
The Capitalization Equation

Solving the above for V yields the well-known
form for the capitalization equation:
P̂H
V
r  t

Thus, houses facing higher effective property tax
rates (t) will have lower values (V).

The strength of this relationship depends on β.
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 applicant’s 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.
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:
ˆ
PH
V 
y
(1

r
)
y 1
L

N
 tV
y

(1

r
)
y 1
ˆ

tV
PH



r
r
where β' is the “degree of property tax capitalization” after
accounting for differences in expectations.
Property Tax Capitalization
Expectations, 2

Now when we solve for V we get:
V

1 


ˆ
 t   PH
r


r
or
ˆ
PH
ˆ
ˆ
PH
PH
V


 N ]t




r
r


[1

(1

r
)


t

r 1
 r     t
r 
 r


ˆ
PH

r  t
where
r
   
 r 
ˆ
PH

r (1  t )
r
Property Tax Capitalization
Expectations

The coefficient to be estimated, β, is the expression in
front of t, so it includes both β' and the impact of
different expectations about the lifetime of a house
and of property taxes.

This explains why we need both β and β'; 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
expectations—hold on.
Property Tax Capitalization
Inter- and Intra-Jurisdiction Variation

These equations apply within a community.
◦ Recall that
 A
t  m 
V 
◦ 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.
Property Tax Capitalization
Property Tax Changes

Here is a change form of the equation:
ˆ
ˆ
V1  PH and V2  PH
r   t1
r   t2
so


ˆ
ˆ
PH
PH
1
1
ˆ

V2 V1  V 

 PH 

 r   t2

r   t2 r   t1
r


t
1


  PH



ˆ
  (t2  t1)
    t   V    t 

1 r  t 
 (r   t1)(r   t2 )   r   t1   r   t2 
2






ˆ 
 PH

so
V     t 
V1  r   t2 

Property Tax Capitalization
The Strategy in PTHV

In PTHV, this equation is used to study intrajurisdictional 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.
Property Tax Capitalization
The Strategy in PTHV, 2

Now express the effective tax rate as t  t  (t  t )
and put an “*” on V to indicate deflation.
V *   t     (t2  t1)  [(t2  t2 )  (t1  t1)]
V1*  r   t2 
r   [t1  (t2  t1)  (t2  t2 )]

Deflation implies that
(t2  t1)  0

Accurate revaluation implies that
(t2  t2 )  0
Property Tax Capitalization
The Strategy in PTHV, 3

Hence:
V *    (t2  t2 )  (t1  t1)   t *  bt*
V1*
r   t1
r   t1
where
and
b  
r   t1
  br
1 bt1
Thus, with data on t1 , an estimate of b, and an assumption
about r, one can obtain an estimate of β.
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 β by about 30 percent.
Property Tax Capitalization
Research Issues in Estimating β

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:



ˆ
ln(V )  ln( P)  ln( H )  ln(r )  ln 1 t 
r 

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 (β/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
(t2  t2 )  0
Property Tax Capitalization
Research Issue 1, Continued

Note that it is impossible to separate β and r in the
estimation.

One can only estimate their ratio.

This leads to the next issue….
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 β separately.

Most studies follow Oates by estimating a value of β/r,
assuming a value for r, and then calculating the implied
value of β.

The trouble with this approach is that the value of β
depends on an untested assumption that varies across
studies.
◦ In fact, the most extreme estimates of β in the literature, in either
direction, are driven largely by extreme assumptions about r.
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.
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. β' = 1), but it does not
say that current tax differences will be fully capitalized
(i.e. β = 1) if they are not expected to persist.
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 β = 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,
  

N
[1 (1 r ) ]
where N is the length of time current tax differences are expected to
persist. The theory indicates that β = 1, but the estimated β clearly
need not equal 1, and indeed need not equal the same value under all
circumstances.
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 β will be only 26% even if β = 1.

If revaluation is scheduled every 6 years, say, then the
estimated β should decline as one moves closer to
the year of revaluation.
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.
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.
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, β/r. If s is the marginal
income tax rate, this ratio with full deductibility of interest cam be
written as [β(1-s)]/[r(1-s)] = β/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.
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 β vary from 15 to 100 percent.
◦ The main reason for this variation appears to
involve expectations.
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, β, 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.
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.
Property Tax Capitalization
Corrected Estimates of Capitalization in Waltham for Property
Taxes and House Values
Nonlinear Version (equation
(8))
Linear Version (equation
(9))
7.4233
0.0420
0.6882
0.2227
0.3236
7.0433
0.0420
0.7042
0.2113
0.3000
Understatment (%)
31.2
29.6
Implied N (years)
13.2
12.1
Estimate of b
Value of
Value of 1-b
Original β
Corrected β
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 percent—exactly what the theory predicts when
tax differences are expected to persist.
◦ This result applies when people are borrowing to the limit and
not itemizing.
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.
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 underassessed.
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.
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.
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 prices—and 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!
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 don’t.