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DISCUSSION PAPERS IN ECONOMICS
Working Paper No. 08-12
The Effect of Proposition 13 on Mobility:
A Hazard Rate Approach
Nikolay Dobrinov
University of Colorado
Updated November 2009
November 2008
Center for Economic Analysis
Department of Economics
University of Colorado at Boulder
Boulder, Colorado 80309
© November 2009 Nikolay Dobrinov
The Effect of Proposition 13 on Household Mobility:
A Hazard Rate Approach∗
(Job Market Paper)
Nikolay Dobrinov†
University of Colorado, Boulder
November 9, 2009
Abstract
In 1978 California approved Proposition 13 which limits the annual increase in property taxes for households staying in their homes. Because this is an annual limit, the
annual tax savings increase over time. On moving, a household loses this favorable tax
treatment. In this paper I estimate the extent to which these tax savings reduce household mobility. The study improves upon previous studies because: (1) I use a duration
model to describe the decision to stay in one’s home, and (2) I correct for aggregation
bias, for omitted variables bias, for measurement error bias in household income and
house values, and for the co-determination of property taxes and public service provision. My analysis finds that the hazard rate of duration decreases by 3.6% for each $100
of annual taxes which are saved if the household stays in his home.
JEL: H21, H24, H31, H71, R21, R23, R28.
Keywords: property tax, assessed value, mobility, hazard.
1
Introduction
Under Proposition 131 , enacted in California in 1978, the increase in the assessed value
of a home is limited to no more than 2% per year while the homeowner remains in the
home; the assessed value returns back to market value only upon sale or reconstruction (with
future assessments likewise restricted to the 2% annual limit). Because the market value of
most California properties has increased in many years at annual rates in excess of 10%, the
differential between the owner’s taxes and the taxes the same owner would pay, if he were
∗ I am grateful to my advisers, Charles De Bartolome, Donald Waldman, Thomas Thibodeau, Jeffrey Zax,
and Yongmin Chen for their invaluable advice and suggestions. I also want to thank Erik Johnson, and
seminar participants at the University of North Dakota, and the University of the South, for their helpful
comments.
† Contact: [email protected]; Nikolay Dobrinov, 735 University Ave, Sewanee, TN 37383.
1 Proposition 13 is a ballot initiative to amend the constitution of the state of California. The initiative
was enacted by the voters of California on June 6, 1978, and is embodied in Article 13A of the California
Constitution. It generated several changes in the property tax system, applicable for both residential and
business property: (1) the maximum property tax rate is set at 1% of the assessed value; (2) the assessed
value of each property was rolled back to its value in 1975-76 and since then increases by no more than 2% per
year until the house is sold; (3) upon sale or reconstruction the property is reassessed at its full market value,
and thereafter assessed value growth is limited to a maximum of 2% per year; and, (4) property transferred
to a spouse, between parents and children, etc., is not reassessed.
1
to move to a similar house, increases the longer the homeowner stays in the house and can
become quite large. The loss of property tax relief on moving increases the cost of relocation,
and is thereby expected to delay relocation. In this paper I estimate the extent to which the
tax relief constraints mobility, and I find that the hazard rate of duration decreases by about
3.6% for each $100 increase in property tax relief.
My finding has important policy implications as removing the property tax relief is likely
to increase welfare. Economists view a household as choosing his house size and location to
maximise his utility. When a household moves, his new home reflects his contemporaneous
circumstances. As time moves forward and his circumstances change, the cost of moving may
prevent him from moving although his pre-existing house is no longer the house he would buy
if he were to freely re-choose his house. If he does not move, we can think of the household
as being in short-run equilibrium but out of long-run equilibrium. By increasing the cost of
relocation, the property tax relief hinders his re-optimization. It also hinders Teibout-type2
sorting between jurisdictions, leading to an inefficient matching of households with public
service expenditures3 .
Conceptually we can distinguish between two types of moves: cross-state moves and instate moves. Cross-state moves usually occur after a job change or some other large change
in personal circumstances (e.g. retirement) causes the household to get large benefit by
changing his location4 . In contrast, in-state and particularly local moves may occur after a
small change in household circumstances causes a household to wish to change his housing
bundle. Potential tax effects are more likely to affect the latter group and Table 1 below
shows that this group constitutes between 82% and 88% of all movers5 .
2 Tiebout predicts that residential sorting can lead to efficient provision of local public goods; if relocation is
costless, and if sufficient choice of communities is available, households move to the community that provides
their utility-maximizing combination of taxes and public services.
3 Farnham and Sevak (2006) find that the presence of tax rate and (particularly severe) assessment limits
constrain fiscal sorting. Mullins (2003) suggests that Proposition 13 contributes to an inefficient housing
market because it provides dis-incentives for selling property. Tugend (May 2006) suggests that the problem
of unavailability of housing for new buyers is exacerbated by specifics in the supply and demand of housing
in California. Geographical limits and enacted environmental and growth legislation from cities and counties
make new development increasingly expensive, while high migration and birth rates contribute to higher
demand for housing.
4 Cross-state moves are driven by differentials in economic opportunities, in cost of living, and in socialgroup-specific fiscal benefits (welfare programs, estate/inheritance/gift taxes)(Boehm et al. (1989), Cebula
(1974, 1978, 2006), Davies et al. (2001), Conway and Houtenville (2003)).
5 Quigley and Weinberg (1977) find that for the periods between the end of the second world war and 1970,
on average 19% of the metropolitan households change residences within a year and 70% of these relocations
are within the county. Clark and Dielman (1996) also find that most moves are made over very short distances.
2
Table 1. Distance of relocation for owners.
Previous location
%
Same MSA, central city (to central city)
Same MSA, central city (to suburb)
Same MSA, suburb (to central city)
Same MSA, suburb (to suburb)
Same MSA, total
14.69
11.82
4.52
50.62
81.65
Same state, different MSA, central city
Same state, different MSA, suburb
Same state, non-metro
Same state, total
2.04
3.70
1.18
88.57
Previous location
%
Different state, central city
Different state, suburb
Different state, non-metro
Outside U.S.
Out of state, total
3.68
5.37
1.47
0.91
11.43
Note: The table presents frequencies on ‘Location of previous unit’ for owners (information on renters is not
included). The question was asked by the American Housing Survey to a subsample of 15,901 recent-movers
households (households that bought their home in the last 12 months preceding the month-year of the survey),
representing 36 MSAs in 25 States covered in the period 1984-1994.
Table 2 provides some indication of the frequency of moves and the size of the property
tax relief provided by Proposition 13 in California. Column 3-4 show that a quarter of all
homeowners change residence within three years with the median homeowner relocating every
8th year. Column 7 shows that the median homeowner in California experiences a tax relief
of about $560.
Table 2. Distributions of key variables (period of observation 1984-1994)
Duration
for non-movers
Mean
SD
100% Max
99%
95%
90%
75% Q3
50% Median
25% Q1
10%
5%
1%
0% Min
Duration
for movers
Effective
property tax rate
Property tax relief
for households
in California
CA
NonCA
CA
NonCA
CA
NonCA
All
households
Age<55
households
12.190
11.026
12.068
11.903
10.337
10.394
11.519
11.730
0.0053
0.0027
0.0148
0.0251
766.557
733.411
677.472
636.047
73
44
34
29
18
9
3
1
1
1
1
82
49
37
30
18
8
3
1
1
1
1
71
47
33
25
14
6
3
1
1
1
1
86
53
37
29
15
8
4
1
1
1
1
0.0100
0.0100
0.0096
0.0091
0.0077
0.0052
0.0029
0.0019
0.0014
0.0003
0.0000
0.3830
0.0821
0.0336
0.0263
0.0169
0.0110
0.0073
0.0035
0.0011
0.0000
0.0000
5736
3602
2210
1675
1035
563
248
97
46
17
0
4811
3014
1921
1460
911
506
234
89
45
17
0
Note: The first two columns represent distributions of duration (in years) for households who have not left their
home by the last time they were surveyed. The third and fourth columns represent distributions of duration
for households who were observed to move out within the period of observation. The fifth and sixth columns
represent distributions of effective property tax rates, calculated as self-reported property tax payments divided
by self-reported estimate of current market value of the home. The seventh column represents (based on my
own calculations) the distribution of effective tax savings (in USD) experienced by all California households.
The last column shows distribution of tax savings only for households with oldest spouse of age 54 or younger.
I identify three main contributions to the analysis in the previous literature. To justify
estimation I first provide a theoretical model of the household’s decision to relocate. In this
3
model the household’s moves are positively related to the degree to which a household’s consumption of housing services deviates from an optimal bundle of such services, and negatively
related to the various adjustment costs associated with changing from one dwelling to another.
Next, I estimate the model around the measurable variation in the hazard rate of duration.
Survival analysis, provides a very suitable framework for estimation given the properties of
the duration variable.
To correctly identify the sign and magnitude of the effect of the tax savings on mobility, I
also address a number of data and methodology issues, akin to the ones hindering empirical
analysis of Tiebout sorting. I correct for aggregation bias, for omitted variables bias, for
measurement error bias in household income and house values, and for the co-determination
of property taxes and public service provision.
In my analysis I find that the hazard rate of duration decreases with about 3.6% for each
$100 increase in the tax savings. Furthermore, I find that the hazard rate increases with time,
and the rate of increase of the hazard rate is the same for households residing in and out of
California. The data also reveals that the negative effect of Proposition 13, on the mobility
of households targeted by Propositions 60 and 90 (See Footnote (16).), has been effectively
softened. A more detailed analysis also shows that the main effect of Propositions 13, 60, and
90 on household mobility has been experienced by households that occupy more expensive
dwellings; the mobility patterns of households that experience low levels of tax relief are virtually unaffected. Unlike in previous studies, the data also demonstrates a higher propensity
to move for California households. This further confirms that the effect of Proposition 13 on
mobility has been successfully separated from the effects of other factors.
The rest of the paper is organized as follows. Section 2 discusses in more detail the
advantages of duration analysis, over more standard methods of estimation, in studying this
particular problem, as well as what methodological issues arise in estimation and how these
issues have been addressed in this paper. Sections 3 introduces the theoretical model and
clarifies the transition to empirical estimation of this model. Section 4 discusses the estimation
strategy. Section 5 discusses the data and the key variables to be used in the analysis. Sections
6 and 7 report on the empirical findings and robustness checks. Section 8 concludes the paper.
4
2
Data and methodology issues and their relation to the
literature.
For the purposes of this study, estimation using the framework of duration (survival) analysis
has numerous advantages over standard methods of estimation. First, a hazard rate empirical model preserves the framework of the theoretical model. Second, the variable ‘duration’
can be treated according to its information structure. Duration takes only positive values empirical models that assume duration is normally distributed (Wasi and White (2005), Ferreira (2007)) are therefore less suitable. Furthermore, in measuring duration two decidedly
different types of households are observed: households which move during the period of observation (non-censored observations), and households which do not move within the period
of observation (right-censored households). Excluding households which relocate from the
sample (Wasi and White (2005), Ferreira (2007)) will tend to overestimate duration, while
treating right censored duration as exact (Wasi and White (2005), Ferreira (2007)) will tend
to underestimate duration. The third advantage of using survival analysis is that the estimation process also reveals the duration dependence of the hazard rate. This is important for
our analysis because the tax saving experienced by a household is determined both by the
value of the house and by the duration. A larger house and a longer duration both contribute
towards higher tax savings. Estimating the hazard rate allows for these two channels to be
separated.
To correctly identify the sign and magnitude of the effect of the tax savings on mobility,
I also address a number of data and methodology issues that arise in the analysis. First, I
identify the motivations of potential movers by using cross-sectional data at the household
level. This helps me avoid any aggregation bias6 that may be introduced in studies analyzing
the behavior of population aggregates rather than individual households (e.g. Stochs, Childs
and Stevenson (2001)).
Second, there is a potential collinearity between tax levels and the level of public service
provision, with education providing the largest local public expenditure category.7 Recently,
Johnson and Walsh (2008) and Farnham and Sevak (2006) seek to separate the two effects by
estimating using population groups likely to be unaffected by local educational expenditures.8
6 Farnham
and Sevak (2006), Johnson and Walsh (2008).
(1969), Pollakowski (1973), Lang and Jian (2004), Farnham and Sevak (2006), and Johnson and
Walsh (2008) among others.
8 Farnham and Sevak (2006) assume that empty-nest households are indifferent to school expenditure, while
Johnson and Walsh (2008) assume this holds for second-home owners.
7 Oates
5
I take a similar approach in my analysis by estimating using the subsample of households with
no children of school age (in addition to estimating on the full sample).
Third, unlike in previous studies (e.g. Nagy (1997), Stochs, Childs and Stevenson (2001),
Wasi and White (2006)), I use the control function approach9 , to control for omitted variables,
measurement error in housing values and measurement error in household income10 . Omitted
variables bias results from the fact that the researcher does not observe all the characteristics
of the house and neighborhood that affect household’s utility11 . Since information on these
characteristics is stored in the error term of the model, the house value (as an explanatory
variable) is correlated with the error term in the model. Because the tax savings directly
depend on the value of the home, the estimate of the effect of the tax savings on mobility is
expected to be calculated with bias of unknown sign12 .
A second type of bias arises from limitations in the data sources; data on exact sale prices
and exact income receipts is fairly inaccessible. As a result, most of the researchers use
owner-estimated housing values and self-reported incomes to estimate their models13 . Both
variables, however, have repeatedly been shown to be measured with error in survey data14 ,
and can lead to bias if directly used in estimation.
Fourth, and last, I introduce enough variation at the metro area level and state level by
using a data set that includes 36 metro areas from 25 states. The need for enough variation at
the metro area and state levels is twofold. First, some important control variables (as market
availability or price dynamics), are defined only at a more aggregated level, for instance at
the MSA level. To identify the effect of such variables on mobility there must be enough
variation in these variables. Second, if households of only a few states are included as controls (e.g. Stochs, Childs and Stevenson (2001), Wasi and White (2006), Ferreira (2007)) the
selection of the sample may cause it to appear that households in California are, on average,
less mobile than households in other states. Such a result may further be wrongly attributed
to Proposition 13. It is apparent from Table 2 (columns 1-4) that, when we look across a
larger selection of states, the California housing market is characterized with, on average,
9 The
approach was first developed by Hausman (1978), Heckman (1978) and Smith and Blundell (1986).
instruments must be identified. I discuss my approach in Section 4.1. and in more detail in
Appendix B.
11 Ferreira (2007).
12 In multiple regression models the sign of the bias from omitted variables is difficult to determine (See
Greene (2003, pp.148-149)).
13 Researchers usually use the following data sources: Census, the American Housing Survey, the Health and
Retirement Survey , and the Panel Survey of Income Dynamics, among others.
14 Robins and West (1977), Kish and Lansing (1954), Ihlanfeldt and Martinez-Vazquez (1985), Benı́tez-Silva
et al. (2008), Kiel and Zebel (1999), Kain and Quigley (1972), Goodman and Ittner (1992), Kochar (2000),
Shea (2000), Dahl and Lochner (2005), Luttmer (2005), Kosfeld et al. (2008) among others.
10 Reliable
6
faster turnover than housing markets in other states; among the households which relocate,
the median Californian household relocates every 6th year, while the median non-Californian
household relocates every 8th year. This indicates that the effect of the tax savings on mobility can only be studied via a variable that measures the individual levels of the tax relief
experienced by each household, and this is the approach I take in this paper.
For the reasons given above, my study improves on previous studies. Wasi and White
(2005) use OLS to estimate a linear model of duration (coded in intervals) on the tax saving
and find that duration in owned homes increases by about 0.1 years for every $100 of tax
savings. Nagy (1997) estimates a hazard rate on dummies for metro-area-year, but does not
find a significant effect. One of the probable reasons is that his data set includes observations
from only a short period after Proposition 13 was enacted. Stochs, Childs and Stevenson
(2001) regress aggregated sales rates on dummies for state, and find that California households
are less mobile than households in Illinois and Masachusets. Ferreira (2007) estimates the
effect on mobility of two subsequent amendments, Propositions 60 and 9015 , which allow
households with oldest spouse of age 55 or older to transfer their tax saving to a house of the
same or lower value. Using a probit model Ferreira (2007) finds that due to Propositions 60
and 90, a head of household of age 55 is more mobile than one of age 54.
3
Theoretical framework
The early theoretical literature on mobility is framed in terms of household dis-satisfaction and
the gap that arises over time between the current level and the optimal level (given the current
household characteristics) of housing and public goods consumption16 . A central line of work
is the hypothesis that dissatisfaction with the status quo results from life cycle effects17 .
If the life-cycle hypothesis were correct, changes in household composition, income and job
location lead to shifts in the demand for housing, neighborhood, and fiscal characteristics.
This sequence of maximization problems can be expressed with a simple model in the lines
of Conway and Houtenville (2001) and Farnham and Sevak (2006). Suppose the household
maximises utility over the consumption of a numéraire good, C, a vector of housing and
15 Propositions 60 and 90 were approved in 1986 and 1988 respectively to allow households, in which at least
one of the spouses is 55 years old or older, to transfer their assessed value to a new home with the same or
lower market value. Proposition 60 allowed such transfers only within county, while Proposition 90 allowed
transfers across counties.
16 Rossi (1955), Tiebout (1956), Speare et al. (1974), Brown and Moore (1970), Clark and Cadwallader
(1973), Brown et al. (1970), Moore (1972), Wolpert (1964, 1965, 1966), Fredland (1974), Brown (1975).
17 Brown et al. (1970), Moore (1972), Wolpert (1964, 1965, 1966), Fredland (1974), Brown (1975)
7
neighbourhood characteristics including time-costs to commuting18 , HL, and state and local
public services, G, subject to a budget constraint incorporating state and local income taxes
and other taxes excluding property taxes T, a price per unit consumption of HL, P HL , and
user cost of home ownership p = r + τ − π (as defined by Poterba (1992)), where r is
interest/mortgage rate, τ is effective property tax rate, and π is capital gain. The problem
that a household solves can be expressed as
max U (C, HL, G|W )
C, HL, G
s.th.
Y − T = C + (r + τ − π)P HL HL + M C,
where W represents a vector of household characteristics, which serve as demand shifters,
Y denotes household’s income, and MC denotes costs of moving, implicitly assuming that
a household must relocate to optimize utility. Note that for households with no children
of school age, the local public expenditure G is assumed to drop out of the maximization
problem. If t denotes the number of years since the household moved into the unit (the
duration), the resulting utility of the status quo choice for household i in location k at time
t, given the current value of W, is
HL
Uikt (Yit − Tikt − pikt Pkt
HLkt − M C, HLkt , Gkt |Wit ).
(1)
If Ω(k ∗ ) denotes the set of available housing-community alternatives, the resulting indirect
utility from the optimal choice k 0 ∈ Ω(k ∗ ) is
∗
Vik0 t (pik0 t PkHL
0 , HLk 0 t , Gk 0 t , Tik 0 t |Yit , Wit , M C, Ω(k ))
t
(2)
If we assume that the psychological costs to moving, K, are positive, a static model would
have household i relocating only if
Vik0 t ≥ Uikt + K,
(3)
where the right hand side of inequality (3) serves as a reservation utility for the decision of
household i to relocate after time t19 . Changes to income and life cycle changes in W induce
households to re-consider their choice of k, but do not necessarily induce the household to
18 Commuting
imposes both a monetary and an opportunity cost. The monetary cost enters the budget
constraint, while the time-cost enters the utility function.
19 A parallel to the reservation utility concept is the reservation wage rate in a model of spell of unemployment
(see Lancaster (1979)).
8
move. In particular, the tax relief allows for a lower effective property tax rate (tax payment
divided by home market value) at the status quo choice k, and thus affects the decision to
move (3) through the differential in user costs (pikt − pik0 t )20 .
Estimation of equation (3) can not be done directly. If we could calculate indirect utilities,
if we knew the distribution of reservation utilities, F (Uikt + K), and if we knew the rate at
which offers arrive at time t, ϕ(t), we could calculate a sequence of conditional probabilities
that a household leaves the dwelling within period ∆t, and move to another dwelling given
they have not done so by t
λ(t)∆t = (1 − F (Vik0 t ))ϕ(t)∆t,
(4)
where λ(t) is known in the literature as a hazard or failure rate. Once again, it is worth
emphasising that t measures length of time since household moved in the housing unit, and
not just a calendar year.
In the data, however, we do not observe the sequence of reservation utilities for the household for each period, and we can only specify a regression model around the variation of λ(t)21 .
As Cox (1972) and Lancaster (1979) suggest, it is mathematically attractive to impose that
λ(t) factors into two functions, one that depends on variations in all factors that determine
the household’s decision to relocate, ψ1 (X(t)), and a function that determines how λ changes
over time, ψ2 (t).
λ(t|X(t)) = vψ1 (X(t))ψ2 (t),
(6)
where X is a vector of regressors explaining the shifts in the probability that a household
relocates, and v controls for unobserved heterogeneity, with E(v|X(t)) = 0. The measure of
duration enters the empirical model through the so called ‘baseline hazard’ ψ2 (t). The baseline
hazard is designed to detect the effects of unobservable factors that cause the household’s
propensity to move to change with duration. It is also the sub-function through which we can
detect the effect on mobility from larger tax savings, generated by longer duration.
To estimate the effects of different factors (including time) on the hazard rate, the maximum likelihood estimator (MLE) is employed. Details on how this is achieved are provided
20 By rule, property tax rates in California must be no higher than 1%. Table 2 (column 5) reveals that the
effective property tax rates enjoyed by the majority of households in California are far lower than 1%.
21 The sequence of probabilities λ(t)∆t can be deduced using the law of conditional probability, where
λ(t)∆t = g(t)∆t/(1 − G(t))
(5)
with unconditional probability of moving in period ∆t, g(t)∆t, and a rate of survival by time t, (1 − G(t)).
9
in the next section and in Appendices A and B.
4
Estimation strategy
To estimate the effect of the tax savings on mobility, I first calculate the individual probabilities (the likelihood elements) of the observed duration for each household, and then maximise
the product of these probabilities (the likelihood function) using the maximum likelihood
estimator (MLE). Each probability is a function of the hazard rate, and parameterization of
the probabilities is achieved through the hazard rate. The exact structure of the individual
probabilities depends on the structure of the data at hand, and in what follows I begin the
discussion on estimation with a short discussion on data structure.
To examine the effect of the tax relief on household mobility I assemble a data set with observations on housing units from the American Housing Survey (AHS) (Metropolitan Areas
Sample) for the years 1984-1994. A given housing unit is surveyed up to three times, approximately every fourth year, and this allows observation of a household up to three times.
Through repeated observations on the housing unit, one can deduce whether a household has
moved out between survey waves. The number of times a unit is surveyed for the period
1984-1994, combined with the household’s choice on duration, gives eleven unique types of
housing unit observations as shown on Figure 1. On Figure 1 and in what follows housing
units are indexed by j, households are indexed by i, and the sequence of the surveys is indexed
by m. I further denote the year of the particular survey by bm , the year in which household i
moved into unit j by aji , and the conditioning vector of explanatory variables for household
i observed during survey wave m, by Xim . Lastly, I refer to household i as HHi.
To assign likelihood elements to households we need to follow households within housing
units. For the first unit on Figure 1, the same household is observed in all three survey years,
and during the last survey year the household is recorded to still occupy the unit. Such
a household is represented in the likelihood function with only one likelihood element (one
conditional probability) - an observation that is right-censored in the last (third) wave the
unit was surveyed. In the second housing unit, HH2 is observed during the year of the first
survey and another household, HH3, is observed, during the year of the second survey, to have
moved in the unit at t = a23 . There is no information on whether HH2 has moved out exactly
at t = a23 or at an earlier date. It is also unknown whether the unit was occupied between the
dates of exit of HH2 and entry of HH3. What is known with certainty is that HH2 has moved
10
Observation Periods
Types of
observation
units
II
I
b1
III
b2
b3
aji = a11
1.
aji = a22
a23
a34
a35
2.
a36
3.
a47
a48
4.
a59
5.
a6,11
a6,10
6.
a7,12
7.
a8,13
a8,14
8.
a9,15
9.
a10,16
10.
a11,17
11.
Figure 1: Observation Units.
out at t ∈ (b1 , a23 ], and this is all the information that can be incorporated in the likelihood
element for this household. The second housing unit provides two likelihood elements: one
for the first household, that moved out between the first survey wave and the time the second
household moved in, and one for the second household that was right-censored at the third
survey wave. Housing unit 9 has been observed only once, and HH15 is represented by one
likelihood element with duration censored at the first survey wave.
Suppose the random variable T measures the length of time (the duration) a person/household
resides in a given housing unit before they move out to relocate. Its cumulative distribution
function and survivor function, which measures the probability of remaining in the same
housing unit longer than a period t, are respectively
F (t|X) = P (T ≤ t|X),
t ≥ 0,
S(t|X) = 1 − F (t|X) = P (T > t|X),
where X represents a vector of household, housing, neighbourhood and local fiscal characteristics. The likelihood elements for right-censored and non-censored households differ. HH1,
for instance, is right-censored and is represented in the likelihood function by the probability
11
that the households duration is at least b3 − a11
P (T > b3 − a11 |X13 ) = 1 − F (b3 − a11 |X13 ).
If the censored duration for individual i is represented by ci = b̌−aij , where b̌ is the date of the
last survey the household has been observed, then the likelihood element for a right-censored
observation is
P (T > ci |X̌i ) = 1 − F (ci |X̌i ),
(7)
where X̌i is the conditioning vector of explanatory variables recorded during the last survey
in which the household has been observed.
Appendix A shows that the cdf of T can be specified as a function of the hazard rate of T ,
and that the hazard rate can be further specified to depend on observable and unobservable
characteristics. I assume that the random variable T is distributed Weibull, with a hazard
function, conditional on observed explanatory variables Xi and unobserved heterogeneity vi ,
λ(t; Xi , vi ) = vi exp(Xi β)αtα−1 ,
(8)
where the parameter α takes a value α >=< 1 when the process exhibits positive duration
dependence, no duration dependence, or negative duration dependence, conditional on the
observable factors and on unobservable heterogeneity.
Parameterization of the model is done at this step. I specify the following model for the
hazard rate of household i associated with its current level of the tax savings TˇS i
λi (t|x̌i , TˇS i , vi ; β, π, α) = exp(π TˇS i + x̌i β)αtα−1 v,
(9)
where x̌i is a set of controls for household, housing, neighbourhood, local market, and local
fiscal characteristics, discussed in more detail in the next section. The hypothesis of interest
is H0 : π < 0.
I further assume gamma-distributed unobservable heterogeneity - that is, vi ∼ Gamma(δ, δ),
with E(vi ) = 1, V ar(vi ) = 1/δ. Then from equations (7) and (31, Appendix A) it follows
that the final form of the likelihood element for a right-censored observation is
1 − F (ci |x̌i , TˇS i ; β, π, δ) = [1 − exp(π TˇS i + x̌i β)tα /δ]−δ ,
12
(10)
Now suppose a household was observed to exit the initial state at t ∈ (b1 , b2 ) or t ∈ (b2 , b3 ).
For example take HH4, which is represented in the likelihood function by the following
element
P (b1 − a34 ≤ T < a35 − a34 |X41 ) = F (a35 − a34 |X41 ) − F (b1 − a34 |x14 ).
The likelihood element for an observation that is not right-censored is
P (b̌ − aji ≤ T < aji0 − aji |X̌i ) = F (aji0 − aji |X̌i ) − F (b̌ − aji |X̌i ),
where i0 indexes the household that moves in unit j after household i has moved out.
Using equation (31, Appendix A), we can write this likelihood element as
F (aji0 − aji |x̌i , TˇS i ; β, π, δ) − F (b̌ − aji |x̌i , TˇS i ; β, π, δ) =
[1 − exp(π TˇS i + x̌i β)(b̌ − aji )α /δ]−δ − [1 − exp(π TˇS i + x̌i β)(aji0 − aji )α /δ]−δ
(11)
If yji = 1 when the observation is right-censored and yji = 0, when the observation is not
censored, the likelihood and loglikelihood functions are respectively
}1−yji
{
}y {
L(θ) = Πi 1 − F (ci |X̌i ) ji F (aji0 − aji |X̌i ) − F (b̌ − aji |X̌i )
LL(θ) =
∑[
{
}
yji lg 1 − F (ci |X̌i )
i
{
}]
+ (1 − yji ) lg F (aji0 − aji |X̌i ) − F (b̌ − aji |X̌i ) ,
(12)
where θ = {β, π, α, δ} denotes the set of all paramaters to be estimated in the process of
maximising the log likelihood function, with likelihood elements substituted from equations
(10) and (11). The model can be further enhanced by estimating a separate α parameter
for the state of California. assumed that the unobservable heterogeneity is factored out as in
equation (25). Once the parameters are estimated, the hazard rate can be calculated and the
estimates β̂, α, π are interpreted as semi-elasticities through the log of the hazard rate
log λ = π̂ TˇS i + x̌i β̂ + α̂ log t + log α̂ + log v̂.
13
(13)
4.1
Controlling for omitted variables and measurement error
Suppose tax saving, TS, is correlated with the error term v due to omitted variables or
measurement error; the procedure when income is measured with error is analogous. The
approach is to first write a control function for the variable correlated with the error term, and
then estimate the hazard rate and this control function simultaneously. The two important
equations in our extended model are
λ(t|x̌1 , TˇS, v; β1 , π, α) = exp(π TˇS + x̌1 β1 + v)αtα−1
TˇS = x̌1 β21 + x̌2 β22 + u = x̌β2 + u,
(14)
(15)
where x̌1 is the main vector of explanatory variables, x̌2 is the vector of ‘instrumental’
variables, the vectors β1 and β2 are the vectors of parameters to be estimated for each
equation, and u and v represent the unobserved heterogeneity in each equation. Because
TS is measured with error it is correlated with v, and we can not assume that u and v are
uncorrelated. The standard approach (Wooldridge (2002, p.472)) is to assume that u and v
are jointly normally distributed, and estimate the correlation between the two error terms, ρ,
in the process of simultaneous estimation of equations (14) and (15). Testing for dependence
between TS and v can be easily achieved through a t-test on the significance of the correlation
coefficient ρ. Furthermore, the credibility of the instruments is tested with an F-test on the
joint significance of the instruments in equation (15) (Deaton (1997)). Because the procedure
is fairly technical, the reader is referred to Appendix B for full details, including definition
and descriptive statistics of the instruments used in the analysis.
5
5.1
Data
AHS data
The primary goal of the American Housing Survey is to measure the quality of the housing
stock in the U.S.. At each survey wave, information is collected on the quality and structural
characteristics of the housing unit, the quality of the neighborhood, housing unit costs (outstanding mortgage payments, property tax payments, purchase price, current market value,
utility costs), household composition, household income, and the date the household moved
in. The location of the housing unit is identified at the state, county, and metro area level.
The household can be precisely matched to neighborhood characteristics through questions
14
that the household representative answers on her/his opinion about such neighborhood characteristic, and through additional information the survey representative is required to collect
(through personal observation) on key neighborhood features. Once a household moves out
it is not followed to its new location.
The data set covers 36 metro areas (MSAs) from 25 states, of which 6 metro areas are
located in California22 , for the period 1984-199423 . For the empirical analysis the sample is
restricted to one observation per household, and only to owners who have complete data on
all key variables of interest. This leaves us with 86,728 unique household observations24 .
5.2
Variables definition and descriptive statistics
The factors that determine the decision to move through inequality (3) can be divided in
four subsets: (1) property tax liability, affecting the decision to move through differentials
in the user-cost, r ; (2) housing unit and neighborhood characteristics, affecting the decision
to move through the differentials in the vector HL; (3) household characteristics, affecting
the decision to move through shifts in W and Y or through differences in the psychological
costs, K, experienced by different demographic groups; and, (4) housing market characteristics
affecting the decision to move through the market availability, Ω(k ∗ ), or through differentials
in the user cost, r. Definitions of key variables and their descriptive statistics are presented
in Table 3.
22 The MSA’s covered are (number of observations in the sample in parenthesis): Anaheim-Santa Ana, Ca
(4779); Los Angeles-Long Beach, CA (3615); San Francisco-Oakland, CA (5818); Riverside-San BernardinoOntario, CA (4939); San Diego, CA (4588); San Jose, CA (5668); Atlanta, GA (2976); Baltimore, MD
(2764); Birmingham, AL (5018); Boston, MA (4295); Buffalo, NY (4671); Chicago, IL (2691); Cincinnati,
OH (2143); Cleveland, OH (4989); Dallas, TX (3804); Denver, CO (2957); Detroit, MI (6153); Hartford,
CT (3049); Houston, TX (2137); Indianapolis, IN (5331); Kansas City, MO (1938); Memphis, TN (5417);
Miami, FL (2441); Milwaukee, WI (4716); Minneapolis-St-Paul, MN (4842); New Orleans, LA (2394); New
York-Nassau-Suffolk-Orange, NY (1772); Oklahoma City, OK (4972); Philadelphia, PA (2166); Phoenix, AZ
(4581);Pittsburgh, PA (3105); Providence-Pawtucket-Warwick, RI-MA (5088); Salt Lake City, UT (5685);
San Antonio, TX (2687); Tampa-St. Petersburg, FL (4466); Washington, DC (5590).
23 All units were re-sampled (all units in the sample discarded and new units drawn) in 1984 and 1995, and
I choose to use a sample for the years 1984 through 1994 for two reasons. First, for the surveys before 1984
information on the housing unit value has been measured in intervals, and information on housing unit living
area (in sq.ft.) has not been reported at all. Second, the metro areas in the sample for 1995 and after are
not surveyed in regular intervals. A large portion of the metro areas are surveyed only once or surveyed in
intervals of 6-8 years.
24 From a total of 172,537 household observations collected by AHS for the period 1984-1994, the households
which have complete data on key variables for each year they have been observed are 140,226. Since some of
the households are surveyed more then once, this leaves us with 86,728 unique household observations.
15
Table 3. Key variable definitions and descriptive statistics.
Property tax liability
Mean
SD
TAXRLF55
tax relief/savings, as defined in equation (16) (AHS);
TAXRLF
tax relief/savings, as defined in equation (17) (AHS);
TAXRLF*AGE55 AGE55=1 if in CA and AGE≥ 55; AGE=0 else (AHS);
AMTX
effective yearly property tax payments (in 1000s) (AHS,
BLS);
$678
$766
$678
0.944
$636
$733
$636
0.812
0.842
27.488
6.449
0.364
19.772
1.718
0.748
0.434
49.471
0.723
0.895
16.131
0.448
0.306
0.678
0.467
0.052
0.055
0.341
$37.489
0.221
0.227
0.474
$26.439
2.001
1.013
0.097
0.018
0.070
0.122
0.028
0.014
0.235
0.176
0.424
0.381
12.090
11.301
11.754
11.504
Housing unit and neighbourhood characteristics
DTCH1
OLDH
ROOMPER
HOWNH
=1 if one housing unit in building and also detached (AHS);
how many years since the housing unit was built (AHS);
number of rooms in housing unit per household member
(AHS);
=1 if neighbourhood quality, self rated 8 and higher on a
scale from 1 to 10 (AHS);
Household characteristics
AGE
GENDER
WHITE
MARR
CHILD3
CHILD6
CPLWORK
ZINC
CARS
age of HH head (AHS);
=1 if household head is male (AHS);
=1 if white or white-hispanic, ref. group: non-WHITE
(AHS);
=1 if household head is married, ref. group: ‘not married’
(AHS);
A FIRST CHILD of AGE ∈ [1, 3] in HH (AHS);
A FIRST CHILD of AGE ∈ [4, 6] in HH (AHS);
=1 if household head and spouse both have jobs (AHS);
total yearly income of all household members (in 1,000s)
(AHS, BLS);
number of cars and trucks owned by HH (AHS);
Housing market characteristics
MG30YR
NGAINL2
SALEPERC
METRO
STATECA
current (YEAR of survey) 30-Year mortgage fixed-rate
(Freddie Mac);
Net nominal rate of capital gain from housing value
appreciation for the last two years before the date of the
survey (OFHEO);
(available housing units for sale)/(number of housing units
owned) in MSA-YEAR (AHS);
=1 if central city (AHS)
=1 if the HH lives in California (AHS)
Measures of duration
DUR1
DUR2
duration of right-censored observations (in years) (AHS);
duration of households who moved out (in years) (AHS);
Analysis sample n=86,728
Note: All income and price variables are deflated using CPI (provided by the Bureau of Labor Statistics) except
for the variable NGAINL2. HH stands for ‘household’. AHS stands for American Housing Survey. BLS stands
for Bureau of Labor Statistics. OFHEO stand for Office of Federal Housing Enterprise Oversight.
5.2.1
Property tax liability
The main variable of interest, TAXRLF55, is calculated as the dollar value of the tax savings
experienced by a California-based household25
25 According to Mullins and Cox (1995), in the period I study, 1984-1994, the sample includes metro areas of
only one other state that imposed an assessment growth limitation - Phoenix, Arizona. Assessment increases
16

0







0
TAXRLF55 =







MarketValue*1% - AmountTaxPaid
if STATE 6= California
if STATE=California
and YEAR≥1986 and AGE≥55
else,
(16)

 0
TAXRLF =

if STATE 6= California
(17)
MarketValue*1% - AmountTaxPaid else,
where property tax rate is assumed to be equal to 1% (as noted in Footnote 1, page 1) due
to the provisions of Proposition 13. The condition AGE≥ 55 subsets households in which the
head of the household or the spouse of the head is of age 55 or older. Such subsetting reflects
the provisions of Propositions 60 and 90, enacted in 1986 and 1988 respectively, which allow
households with oldest spouse of age 55 or older to transfer their tax savings to a house of the
same or lower value in the same county; households with oldest spouse of age 55 and older
are assumed to experience no constraint in mobility from the tax savings they enjoy in their
present home26 .
I further define the variable TAXRLF (eq.(17)), which assumes that households with oldest
spouse of age 55 or older do not benefit from Propositions 60 and 90. Using this variable in
the model, instead of the variable TAXRLF55, and additionally including an interaction term
(TAXRLF*AGE55) of this variable with a dummy for household in California with oldest
spouse of age 55 and older (past year 1986), allows for simultaneously testing the effects of
Proposition 13, 60, and 90. In particular if the coefficient to the variable TAXRLF*AGE55 is
positive (while the estimate to TAXRLF is negative) this indicates that Proposition 60 and
90 alleviated the (supposedly) negative effect of Proposition 13 on mobility among households
of age 55 and older.
As noted in Section 4, since one of the components of the variable TAXRLF55 is the selfin Arizona are limited to the greater of 10% of value or 25% of difference between current year full cash value
and prior year limited value. However, based on the Housing Price Index, the nominal growth rate of housing
prices in Phoenix for the period 1984-1994 ranged from -1% to 8% per year. Based on this information I
assume that the assessment increase constraint in Arizona is not binding.
26 Proposition 90 was not mandatory and there is clear evidence that very few counties adopted it. Upon
approval only a few, albeit relatively large, counties in California adopted Proposition 90 immediately, namely:
Alameda, Contra Costa, Inyo, Kern, Los Angeles, Marin, Modoc, Monterrey, Orange, Riverside, San Diego,
San Mateo, Santa Clara, and Ventura (Ferreira (2007)). Today (as of June 2008) only seven counties accept
Proposition 90: Alameda, Los Angeles, Orange, San Diego, San Mateo, Santa Clara, and Ventura (WEISS
& WEISSMAN, INC). However, Ferreira (2007) shows that Proposition 60 and 90 have a clear effect on the
mobility of 55 years old and older. For this reason in the formulation of this variable it is assumed that
Propositions 60 and 90 offset the effect of Proposition 13 on mobility for this group of households.
17
reported market value of the house, and since self-reported market value is measured with
error, I test whether TAXRLF55 is also measured with error.
The variable AMTX represents effective property tax payments (self-reported, actual
yearly tax payment made), and reflects the findings of Farnham and Sevak (2006) that, as a
result of Tiebout type sorting, cross-state, empty-nest movers experience large gains in the
form of reduced exposure to local school expenditure and property taxes, while local emptynest movers experience no fiscal adjustment. The variable affects the decision to move (3)
through the user cost rikt . Since 82% of the moves in the sample are local, we would expect
the effect of AMTX on mobility to be insignificant.
5.2.2
Housing unit and neighborhood characteristics
The set of variables on housing and neighborhood characteristics, DTCH1, HOWNH, OLDH
and ROOMPER reflect the findings that such characteristics have a significant effect on
the choice of a house and location27 . One would, for instance, expect households to prefer
detached, one family houses, over all other types of construction. A household occupying a
detached, one family house, would be less likely to relocate.
5.2.3
Household characteristics
The set of variables on household characteristics and life cycle effects - AGE, CARS, CHILD3,
CHILD6, CPLWORK, GENDER, MARR, WHITE, and ZINC - reflect the strong agreement
among researchers on what factors, among many, are important. The prevailing results are
that28 : (1) a recent change in marital status increases mobility; (2) the birth of the first child,
the move of the first child from pre-school to elementary school, and the moment child rearing
ceases are related to significant changes in housing consumption; (3) increases and decreases
in family size increase mobility significantly; (4) there is an inverse relationship between the
age of the household head and mobility, with the effect possibly being non-linear; (5) white
individuals have higher mobility rates than African-Americans and Hispanics; (6) education
and income levels have no clear effect on mobility; (7) a job change often acts as a trigger for
a residential move even for a change of workplace within the metro area; and, (8) dual earner
27 Boyce (1969), Droettboom et al. (1971), Greeberg and Boswell (1972), Moore (1972), Varady (1974),
Molin (1999).
28 The reader is referred to Quigley and Weinberg (1977) for a very detailed review of early studies that mainly
relate the household’s decision to relocate to factors leading to a gap between current housing consumption
and preferred housing consumption, and Dielman (2001) for more recent studies that focused attention on
more refined choice making processes within the household, and on market conditions that strongly constrain
the ability of a household to move when they need to adjust their housing consumption.
18
households relocate less often than one earner households.
Since changes in household composition are not observed in our data set, the variables I
create attempt to, as closely as possible, incorporate the findings in the previous literature:
The variables CHILD3 and CHILD6 are calculated to reflect the previous findings that the
birth of the first child, and the transition of the first child from pre-school to elementary
school, are important predictors of change in the level of housing consumption. The variable
CARS is intended to proxy for the importance of commuting time. The more cars the family
has, the more flexible are household members in commuting. The variable CPLWORK is
introduced due to previous findings that double earner households relocate less often. The
variable MARR acts as a proxy for a household with more than one choice maker (more
then one set of preferences). The variable AGE proxies for various life-cycle effects as well as
psychological costs of relocation. Furthermore, the variable AGE is important because older
households would tend to remain in their homes longer, and accumulate larger than average
tax savings. Omitting the variable AGE from the main equation, may tend to overestimate
the effect of TAXRLF55 on mobility. The variable GENDER can affect the decision to
relocate through the cost parameter K (costs of relocation perceived differently by male and
female household heads) or through the vector W if the frequency of job change is different
for male versus female workers. The variable WHITE is included based on consistent findings
in previous studies that mobility depends on race.
Finally the variable ZINC serves as a demand shifter through income, Y . Since ZINC
is measured with error (as noted in Section 3), I control for the measurement error bias in
estimation.
5.2.4
Housing market characteristics
The variables MG30YR, NGAINL2, SALEPERC, METRO, and STATECA reflect the recent, in the empirical literature, findings that local and non-local market characteristics, and
local market constraints, affect the incentive and ability of households to obtain their optimal bundle of housing/location characteristics. Four major results have emerged from this
discussion: (1) costs of moving (as measured by mortgage rates or other financial or psychological costs) are inversely related to household mobility29 ; (2) availability of alternative
dwellings is positively related to mobility30 ; (3) investment incentives are high in the list of
29 Weinberg
(1975), Amundsen (1985), Quigley (1987).
(2000), Dieleman et al. (2000), and Grling and Friman (2001).
30 Strassmann
19
priorities for buyers, and capital gains differ substantially across time and metro areas31 ; and
(4) the propensity to move and the resulting market ’turnover’ vary considerably from place
to place
32
.
The variable MG30YR is derived from the ‘15-Year and 30-Year Fixed-rate Historic Tables’
provided by Freddie Mac. It represents the 30-Year fixed mortgage rate and is expected to
affect the household’s decision to move (3) through the user cost rik0 t . However, since the
data does not include a variable that measures the business cycle, MG30YR may take the
role of a proxy for employment rate (for example). Mortgage rates are usually high in ‘good’
times, when people have high expectations about the future. For that reason the variable
MG30YR may affect the decision to move through the expected future disposable income,
which can not be measured in our data.
The variable NGAINL2 is designed to measure the household’s expectations about future
local housing market capital gains, and affects the decision to move (3) through the user cost,
r. It is calculated as the average nominal capital gain from holding a house as an asset in a
given MSA for the last two years
NGAINL2MSA,t =
HPIMSA,t − HPIMSA,t−2
,
HPIMSA,t−2
where HPI represents the housing price index for each metro area, provided by the Office of
Federal Housing Enterprise Oversight.
To control for market supply of housing units for sale in a given MSA-YEAR (MSA-YEAR
≡ particular metro area in a particular year), the variable SALEPERC is calculated as the
total number of vacant housing units for sale in the given MSA-YEAR over the total number
of owner occupied housing units for the same MSA-YEAR33 . A second variable, METRO
(=1 if housing unit is in central city), is formulated to control for the supply of land, which
Brasington (2002) finds is an important determinant for the magnitude of capitalisation of
taxes and public services in housing values. The variables SALEPERC and METRO affect
the decision to move (3) through the distribution of market availability Ω(k 0 ).
Finally, the variable STATECA controls for the observed in the data, higher propensity
to move in California.
31 Case
and Shiller (1988), Poterba (1992), Dieleman et al. (2000).
(1998), Pawson and Bramley (2000).
33 To obtain correct values of the variable, each observation of a housing unit for sale and each observation
of owner-occupied housing unit is inflated by its corresponding ’pure weight’, PWT (provided by AHS), where
PWT measures the inverse of the probability that the housing unit is sampled. All weighting in the sample,
when necessary, is achieved using the variable PWT.
32 Lu
20
6
Results
The model is estimated on two separate samples: all households, and households with no
children of school age (66% of all households). The objective is to control for the possible
collinearity between property tax levels and local public expenditure.
For each sample the model is estimated three times: a baseline model with no corrections,
based on specification (9); a model with corrections for omitted variables and measurement
error in TAXRLF55, based on specification (14)-(15); and, a model with corrections for measurement error in household income, ZINC, based on specification (14)-(15)(but this time
controlling for income and not tax savings). Controlling for omitted variables and measurement error is achieved via a two-step procedure described in detail in Appendix B34 . In the
second step of the procedure, simulation of an error term is used to approximate an integral.
Each model is estimated based on 600 draws (per observation) of the iid, normally distributed
error term35 . Furthermore, the standard errors of all estimates in the second step are corrected for the additional variation introduced by the two-step process using the covariance
matrix suggested by Greene (2003, p.510). The important parameters that result from this
procedure are the F statistic, measuring the joint significance of the instruments in the first
step, and the correlation coefficient ρ, which measures the correlation between the error term
v in the main equation (14) and the error term u in the control function (15). The standard
error of the correlation coefficient is calculated using the Delta method (Greene (2003, p.913)),
and a t-test of the hypothesis H0 :ρ = 0 reveals whether the problem of omitted variables or
measurement error is present in the data.
A caveat in the data is a possible influence of outliers in self-reported dollar-valued variables (e.g. income, tax payments, home value, etc.). All dollar-valued variables are topcoded36 by the AHS at the 97th percentile. I further winsorize37 the lower tail of the distributions of these variables at the 1st percentile. All models are estimated on the top-codedwinsorized samples.
In all models that I present in this and next section estimation revealed that TAXRLF55
34 An alternative approach is to estimate the full information maximum likelihood (FIML), which is more
efficient than any two-step estimator, but at the same time far more computationally-intensive. Estimation
of FIML was attempted, but due to the large number of estimates, the large number of observations, and the
complexity of the model, the estimation procedure would either not converge or the Hessian would not be
correctly calculated.
35 To determine the appropriate number of draws for consistent estimation, I estimated one of the models
repeatedly increasing the number of draws with a 100 at each step. I found that estimates and standard errors
settle down in models estimated with more than 600 draws.
36 Any value in the top 3% tail of the distribution takes the value of the 97th percentile. This is done by
the AHS to maintain confidentiality.
37 Any value in the lower 1% tail of the distribution takes the value of the 1st percentile.
21
is not related to the error term in equation (14) due to omitted variables or measurement
error. For brevity I present results only for the baseline models and models with correction
for measurement error in household income.
The main results are presented in Table 4. Results for a modification of the models in
Table 4, where the metro-state area dummy variables are replaced by an indicator variable
for residence in California, are presented in Table 538 .
Tax savings, TAXRLF55, is consistently negatively related to mobility across models. The
magnitude of this effect, however, is not stable because each of these models incorporates a
different set of assumptions. We focus on the models in Table 4, as those are more precise
than the models in Table 5 (judging by the magnitudes of the log-likelihoods for each model).
Specifications (2) and (4) rely on the assumption of correlation between household income
(ZINC) and the error term in equation (14). This correlation however is not confirmed for
the specification that includes metro-state indicator variables as controls: the correlation
coefficient ρ is insignificantly different from zero in both models, given the confirmed by the
F statistic validity of the instruments. For that reason specifications (2) and (4) are invalid,
and we focus on specifications (1) and (3).
The most important difference between models (1) and (3) should be revealed through
differences in the estimated effect of the tax payment, AMTX, on the hazard rate. However,
it appears that the effect of the tax payments on mobility is insignificant in both models.
To a large extent this may result from the predominantly local moves in the sample;
this result complies with the findings of Farnham and Sevak (2006) that, among empty-nest
households, only households that migrate across states are able to reduce their exposure to
local expenditure and property taxes. Further evidence that the two models are very similar
are the consistent estimates of all parameters and their standard errors. It appears there is
no ground for rejecting model (3) on the basis of collinearity between tax levels and school
expenditure levels. However, since model (1) is theoretically more correct than model (3)39 ,
I choose model (1) to discuss the effect of the selected factors on the hazard rate of duration.
All estimated effects are interpreted as semi-elasticities of the hazard rate with respect to the
factors that determine mobility (see equation (13)).
38 More controls could be included in the models, however, estimation with maximum likelihood requires a
careful balance between specifying a meaningful model and being able to estimate it. The models in Table
4 and 5 represent a measured selection of controls, which comply with the theoretical framework and the
empirical literature on mobility.
39 Data on local school expenditures can be used to purge the effect of local spending from the variable
AMTX. Using the residuals from such a regression to estimate model (3), would make models (1) and (3)
more comparable. The assembling of a data set on local school expenditure is in progress.
22
Table 4. Hazard rate determinants: MSA controls; controlling for measurement error in ZINC
HHs with no child of school age
(1) Baseline model
(2) Control function
Full sample
(3) Baseline model
(4) Control function
TAXRLF55
-0.000362***
(0.000060)
-0.000526***
(0.000112)
-0.000365***
(0.000048)
-0.000330***
(0.000099)
AMTX
0.000
(0.000)
-0.445***
(0.035)
-0.031***
(0.001)
0.039***
(0.010)
0.145***
(0.029)
-0.073***
(0.001)
0.055*
(0.032)
0.328***
(0.054)
0.014
(0.038)
0.451***
(0.047)
0.319***
(0.072)
0.173***
(0.034)
0.005***
(0.001)
-0.255***
(0.016)
53.178***
(0.908)
3.730***
(0.133)
15.731***
(2.446)
0.074**
(0.031)
Yes
0.000
(0.000)
-0.495***
(0.059)
-0.035***
(0.002)
0.039**
(0.017)
0.198***
(0.050)
-0.073***
(0.003)
0.066
(0.056)
0.386***
(0.096)
0.075
(0.067)
0.662***
(0.081)
0.255**
(0.127)
-0.031
(0.083)
0.007*
(0.004)
-0.265***
(0.038)
52.956***
(1.922)
2.637***
(0.216)
15.533***
(4.270)
0.221***
(0.054)
Yes
0.000
(0.000)
-0.479***
(0.030)
-0.028***
(0.001)
0.069***
(0.008)
0.134***
(0.023)
-0.074***
(0.001)
0.053**
(0.027)
0.241***
(0.040)
0.038
(0.032)
0.511***
(0.043)
0.400***
(0.042)
0.146***
(0.025)
0.005***
(0.000)
-0.212***
(0.012)
53.112***
(0.757)
3.629***
(0.110)
15.740***
(1.952)
0.052**
(0.026)
Yes
0.000
(0.000)
-0.431***
(0.065)
-0.029***
(0.002)
0.066***
(0.017)
0.220***
(0.050)
-0.075***
(0.003)
0.187***
(0.059)
0.212**
(0.085)
0.031
(0.071)
0.320***
(0.096)
0.364***
(0.090)
-0.017
(0.067)
0.007**
(0.004)
-0.232***
(0.033)
52.924***
(1.900)
2.531***
(0.220)
15.543***
(4.143)
0.079
(0.057)
Yes
1.976***
(0.023)
1.947***
(0.034)
-8.543***
(0.184)
1.959***
(0.049)
2.062***
(0.068)
-8.547***
(0.367)
1.991***
(0.019)
1.988***
(0.030)
-8.684***
(0.147)
1.983***
(0.046)
2.087***
(0.071)
-8.768***
(0.338)
DTCH1
OLDH
ROOMPER
HOWNH
AGE
GENDER
WHITE
MARR
CHILD3
CHILD6
CPLWORK
ZINC
CARS
MG30YR
NGAINL2
SALEPERC
METRO
MSA dummies
α
α(CA)
Const
ρ
-0.848
(0.587)
1583.237***
F(6,n) first step
LL (log lik)
n (# of obs.)
-69722.477
57,758
-70181.648
57,758
Note: See the note to Table 5 below.
23
-0.835
(0.567)
2223.398***
-105990.239
86,728
-107109.236
86,728
Table 5. Hazard rate determinants: no MSA controls; controlling for measurement error in ZINC
HHs with no child of school age
(5) Baseline model
(6) Control function
Full sample
(7) Baseline model
(8) Control function
TAXRLF55
-0.000696***
(0.000060)
-0.000629***
(0.000100)
-0.000649***
(0.000051)
-0.000786***
(0.000081)
AMTX
-0.000***
(0.000)
-0.412***
(0.031)
-0.033***
(0.001)
0.054***
(0.009)
0.096***
(0.026)
-0.069***
(0.001)
0.075***
(0.030)
0.408***
(0.049)
-0.010
(0.035)
0.468***
(0.043)
0.420***
(0.063)
0.201***
(0.031)
0.004***
(0.001)
-0.228***
(0.015)
50.252***
(0.522)
1.992***
(0.089)
8.022***
(0.804)
0.087***
(0.027)
1.099***
(0.083)
1.890***
(0.016)
1.629***
(0.026)
-7.914***
(0.117)
-0.000
(0.000)
-0.378***
(0.052)
-0.034***
(0.001)
0.049***
(0.017)
-0.000
(0.034)
-0.070***
(0.002)
0.129***
(0.040)
0.674***
(0.081)
-0.100**
(0.049)
0.727***
(0.074)
0.000
(0.097)
0.295***
(0.055)
0.006*
(0.003)
-0.241***
(0.034)
52.706***
(1.400)
2.224***
(0.203)
13.435***
(1.431)
0.154***
(0.035)
0.780***
(0.154)
1.920***
(0.052)
1.835***
(0.067)
-8.837***
(0.346)
0.000
(0.000)
-0.385***
(0.029)
-0.031***
(0.000)
0.076***
(0.008)
0.096***
(0.023)
-0.075***
(0.001)
0.065**
(0.027)
0.365***
(0.039)
-0.046
(0.032)
0.624***
(0.043)
0.489***
(0.041)
0.175***
(0.025)
0.005***
(0.000)
-0.214***
(0.012)
53.065***
(0.675)
2.461***
(0.082)
15.554***
(0.713)
0.101***
(0.024)
0.903***
(0.075)
2.001***
(0.019)
1.809***
(0.027)
-8.593***
(0.108)
0.000
(0.000)
-0.378***
(0.044)
-0.029***
(0.001)
0.049***
(0.014)
0.000
(0.027)
-0.073***
(0.002)
0.129**
(0.034)
0.674***
(0.061)
-0.100**
(0.041)
0.727***
(0.063)
0.000
(0.056)
0.295***
(0.039)
0.006***
(0.002)
-0.241***
(0.023)
52.706***
(1.091)
2.224***
(0.170)
13.435***
(1.173)
0.154***
(0.029)
0.780***
(0.128)
1.919***
(0.039)
1.836***
(0.055)
-8.837***
(0.249)
DTCH1
OLDH
ROOMPER
HOWNH
AGE
GENDER
WHITE
MARR
CHILD3
CHILD6
CPLWORK
ZINC
CARS
MG30YR
NGAINL2
SALEPERC
METRO
STATECA
α
α(CA)
Const
ρ
-0.858**
(0.346)
1604.000***
F(6,n) first step
LL (log lik)
n (# of obs.)
-70810.776
57,758
-70941.684
57,758
-0.858***
(0.238)
3543.300***
-107602.699
86,728
-107794.920
86,728
Note: The variable TAXRLF55 is measured in dollars. α is the parameter of the Weibull distribution measuring duration
dependence of the hazard rate. A separate parameter, α(CA), is estimated for California households. Models (2,4,6,8) control
for measurement error in ZINC, using a two-step procedure. The second step of models (2,4,6,8) requires simulation of the
error term, and the models are estimated with 600 draws of the error term per observation. The standard errors for models
(5) and (6) are corrected for the two-step procedure using the approach suggested by Greene (2003, p.510). ρ is the correlation
between the error terms of the main equation (14) and the control function (15) in the two-step procedure. A t-test on H0 :
ρ = 0 reveals whether ZINC is measured with error. F denotes the F-stat measuring the joint effect of the instruments on
ZINC in the first step of the two-step procedure. ***, **, and * indicate significance at the 1, 5, and 10% levels.
24
The tax savings has the predicted negative effect on mobility. Since the tax savings is
measured in dollars, the hazard rate decreases by about 3.6% for every $100 increase in the
tax savings. This results in about 20% decrease in the hazard rate for the median California
household.
More information is revealed by the estimates on the duration dependence of the hazard
rate. The effect of time on the hazard rate is measured by the estimate of the Weibull
distribution parameter α, and is common for all households. When duration is Weibull
distributed, the hazard rate increases with time if α > 1, and the data consistently shows
that the hazard rate of duration increases over time (α̂ = 1.976)40 ; the longer a household
occupies a house, the higher the probability the household will relocate. It comes in support of
the hypothesis that, over time, as circumstances change, a household grows more dis-satisfied
with their current choice of house and location.
The more important for us result, however, is revealed through estimation of two separate
duration dependence parameters: one for households in California, α̂(CA)= 1.947, and one for
households outside of California, α̂ = 1.976. The hazard rate for California-based households
increases at the same rate41 as the hazard rate of households outside of California. It appears
that the effect of tax savings on the hazard rate is not propagated through duration: if
you compare two households with the same duration but different levels of tax savings, the
influence of duration on their probability to relocate at that particular moment is exactly the
same for both households. In other words, we can reject the hypothesis that because savings
increase with duration, the duration dimension of the tax saving will have any influence on
the probability to move. The only thing that appears to be important is the level of the
tax relief: the effect of tax savings on mobility is stronger for higher levels of tax savings no
matter how much time it took for these tax savings to accumulate.
The justification for such an interpretation of this results comes from the fact that the
value of the tax savings depends both on the value of the house, and on the length of time
a household remains in their home. The two effects are separated by the inclusion of both
variables on the right hand side of the equation estimating the hazard rate. Then, the effect
of the variable TAXRLF55 would more precisely be interpreted as the shift in the hazard rate
from an increase in tax savings for a given duration. This is the effect of higher tax savings
on mobility due to higher value of the house. The effect of the duration component of the tax
40 α̂
is significantly different from 1 because it is more than three standard deviations from 1.
that α̂(CA)= 1.947 is only about 1.2 standard deviations away from α̂ = 1.973.
41 Note
25
savings on mobility is incorporated in the parameter α.42
From the last two results it may appear that households in California are less mobile
than households outside of California. However, the estimate of the effect of the dummy
variable STATECA (Table 5, models 6 and 8) on mobility reveals exactly the opposite effect.
California-based households are statistically significantly more mobile than households outside
of California. This last result in no way contradicts the previous two results; the propensity
to move and the tax savings do not change the hazard rate over time, instead, for any value
of duration, they only act as shifters of the hazard rate.
The estimates of the coefficients to the control variables have the predicted signs and
meaningful magnitudes. A few results deserve attention. First, the effect of the current
mortgage rate on mobility is very strong, but consistently positive and significant. It appears
that mortgage rates indeed serve as a proxy for business cycle effects. The negative effect of
high mortgage rates on the propensity to buy a house is trumped by the prospects for low
unemployment rate and stable future incomes. Third, the variable NGAINL2 has a positive
and significant effect on mobility. This shows that investment considerations are of high
importance for home owners, and that markets that offer higher capital gains will exhibit
higher rates of turnover.
7
Robustness checks
The first robustness check I perform is to split the sample in three by year of observation.
The resulting three subsamples include observations for the periods 1984-1987, 1988-1991, and
1992-1994 respectively. The models are estimated only on the first two subsamples because
the third subsample includes only censored observations. The results are presented in Table
6, Panels A and B. The estimated magnitude of the estimated effect of tax relief on mobility
tends to vary over the years. This may be a result of unobserved local market factors or
unobserved business cycle factors.
A potential concern with our measure of tax relief is the large number of households (nonCalifornian) for which tax relief takes a value of zero. I re-estimate the models from Table
5 using only observations for Californian households. The results are presented in Table 6,
Panel C. The estimated magnitude of the estimated effect of the tax relief on the hazard
rate slightly decreases when we exclude households from controlling MSAs, which should be
42 Because we explicitly control for unobserved heterogeneity in the model, the parameter α incorporates
only the effects of factors working towards a change in the propensity to move over time.
26
expected.
Table 6. Robustness of the results to subsamples based on year of observation,
and based on location (controlling for measurement error in ZINC )
HHs with no child of school age
Baseline model
Control function
Full sample
Baseline model
Control function
Panel A: Subsample with observations for 1984-1987
TAXRLF55
-0.001763***
(0.000434)
-0.001733***
(0.000197)
-0.001434***
(0.000090)
-0.001786***
(0.000167)
LL (log lik)
n (# of obs.)
-42,997
14,036
-42,868
14,036
-66,412
21,333
-65,377
21,333
Panel B: Subsample with observations for 1988-1991
TAXRLF55
-0.000323***
(0.000083 )
-0.000310***
(0.000130)
-0.000349***
(0.000060)
-0.000320***
(0.000098)
LL
n
-26,894
19,904
-26,642
19,904
-40,202
29,860
-40,336
29,860
Panel C: Subsample with observations for Californian households only
TAXRLF55
-0.000534***
(0.000077)
-0.000561***
(0.000090)
-0.000505***
(0.000062)
-0.000548***
(0.000086)
LL
n
-14,459
10,477
-14,485
10,477
-21,057
15,236
-21,102
15,236
Yes
No
Yes
No
Yes
No
All models
MAIN CONTROLS
MSA dummies
Yes
No
Note: This table represents the sensitivity of the hazard rate to variation in the tax relief for subsamples of
the data. In Panel A only observations for the period 1984-1987 are included. On Panel C only observations for
California based households are included. The variable TAXRLF55 is measured in dollars. The control function
models control for measurement error in ZINC, using a two-step procedure. The second step of the control function
models requires simulation of the error term, and the models are estimated with 600 draws of the error term per
observation. The standard errors for these models are corrected for the two-step procedure using the approach
suggested by Greene (2003, p.510). ***, **, and * indicate significance at the 1, 5, and 10% levels.
The last subsampling allows for a better understanding on the types of households who’s
mobility is affected by Proposition 13. Table 7 presents results on subsamples of households
based on the value of the dwelling the household occupies. The whole sample is divided into
four subsamples, each including 25% of the households, with dwellings of lowest value in the
first subsample, and dwellings with highest value in the last subsample. Comparing Panels
A, B, C, and D it is clear that the mobility of households that occupy dwellings of lower than
median value has not been affected by the tax relief. Richer households tend to benefit to
a larger extent from the tax savings induced by Proposition 13, by accumulating larger tax
savings.
27
Table 7. Robustness of the results to subsamples based on housing value (controlling for measurement error in ZINC )
HHs with no child of school age
Baseline model
Control function
Full sample
Baseline model
Control function
Panel A: Subsample with housing values below 1st quartile
TAXRLF55
-0.000548
(0.000879)
-0.000254
(0.001293)
0.000105
(0.000832)
-0.001264
(0.001162)
LL (log lik)
n (# of obs.)
-14,775
15,096
-14,812
15,096
-20,951
21,493
-21,025
21,493
Panel B: Subsample with housing values between 1st and 2nd quartiles
TAXRLF55
-0.000516
(0.000595 )
0.000195
(0.000880)
-0.000317
(0.000520)
0.000670
(0.000797)
LL
n
-17,550
14,569
-17,637
14,569
-26,629
21,659
-26,779
21,659
Panel C: Subsample with housing values between 2nd and 3rd quartiles
TAXRLF55
-0.000880***
(0.000221)
-0.000943***
(0.000350)
-0.000999***
(0.000186)
-0.001114***
(0.000292)
LL
n
-19,067
14,065
-19,186
14,065
-29,506
21,670
-29,649
21,670
Panel D: Subsample with housing values between 3rd and 4th quartiles
TAXRLF55
-0.000299***
(0.000069)
-0.000354***
(0.000106)
-0.000299***
(0.000056)
-0.000343***
(0.000089)
LL
n
-17,604
13,723
-17,717
13,723
-27,909
21,519
-28,114
21,519
Yes
Yes
Yes
Yes
Yes
Yes
All models
MAIN CONTROLS
MSA DUMMIES
Yes
Yes
Note: This table represents the sensitivity of the hazard rate to variation in the tax relief for subsamples based
on house value. The observations in the main sample are sorted in ascending order by house value and separated
in four subsamples. The variable TAXRLF55 is measured in dollars. The control function models control for
measurement error in ZINC, using a two-step procedure. The second step of the control function models requires
simulation of the error term, and the models are estimated with 600 draws of the error term per observation. The
standard errors for these models are corrected for the two-step procedure using the approach suggested by Greene
(2003, p.510). ***, **, and * indicate significance at the 1, 5, and 10% levels.
7.1
Assessing the effects of Propositions 60 and 90
In this subsection I present results from models where the main variable of interest, TAXRLF55,
was replaced by the variables TAXRLF and TAXRLF*AGE55. I have two goals in doing this:
(1) redefine the main variable of interest and check for robustness of the results in the previous
section; (2) investigate whether Propositions 60 and 90 indeed, as found in Ferreira (2007),
alleviate the negative effect of Proposition 13 on households in California with at least one
spouse of age 55 or older. I re-estimate the models of this and previous section and the results
are presented in Tables 8-10.
28
Table 8. Hazard rate determinants: MSA controls; controlling for measurement error in ZINC
HHs with no child of school age
Baseline model
TAXRLF
TAXRLF*AGE55
AMTX
DTCH1
OLDH
ROOMPER
HOWNH
AGE
GENDER
WHITE
MARR
CHILD3
CHILD6
CPLWORK
ZINC
CARS
MG30YR
NGAINL2
SALEPERC
METRO
MSA dummies
α
α(CA)
Const
Baseline model
Control function
-0.000547***
(0.000123)
0.000184***
(0.000086)
-0.000475***
(0.000131)
0.000249***
(0.000089)
-0.000464***
(0.000097)
0.000174**
(0.000074)
-0.000418***
(0.000101)
0.000245***
(0.000072)
-0.000
(0.000)
-0.485***
(0.070)
-0.031***
(0.002)
0.045***
(0.013)
0.114***
(0.031)
-0.072***
(0.003)
0.121***
(0.038)
0.291***
(0.091)
-0.009
(0.050)
0.422***
(0.094)
0.331***
(0.114)
0.184***
(0.057)
0.004***
(0.001)
-0.243***
(0.033)
53.155***
(1.891)
3.889***
(0.277)
15.750***
(4.937)
0.086*
(0.050)
Yes
-0.000
(0.000)
-0.454***
(0.070)
-0.029***
(0.002)
0.014
(0.013)
-0.000
(0.031)
-0.068***
(0.003)
0.118***
(0.039)
0.586***
(0.101)
-0.237***
(0.052)
0.446***
(0.096)
0.154
(0.119)
0.278***
(0.074)
0.007**
(0.003)
-0.268***
(0.041)
52.962***
(2.020)
2.741***
(0.258)
15.551***
(5.075)
-0.071
(0.052)
Yes
0.000*
(0.000)
-0.452***
(0.061)
-0.028***
(0.001)
0.061***
(0.010)
0.108***
(0.025)
-0.074***
(0.002)
0.117***
(0.033)
0.247***
(0.069)
-0.048
(0.042)
0.546***
(0.086)
0.397***
(0.067)
0.173***
(0.043)
0.005***
(0.001)
-0.230***
(0.025)
53.068***
(1.573)
3.433***
(0.221)
15.656***
(3.888)
0.072*
(0.042)
Yes
0.000
(0.000)
-0.463***
(0.059)
-0.026***
(0.002)
-0.005
(0.011)
-0.000
(0.025)
-0.069***
(0.002)
0.110***
(0.033)
0.547***
(0.075)
-0.237***
(0.043)
0.453***
(0.085)
0.162**
(0.068)
0.243***
(0.053)
0.008***
(0.002)
-0.277***
(0.031)
52.960***
(1.708)
2.744***
(0.213)
15.551***
(4.027)
-0.054
(0.042)
Yes
1.967***
(0.048)
2.004***
(0.073)
-8.544***
(0.375)
1.829***
(0.047)
1.932***
(0.074)
-8.547458***
(0.409)
1.979***
(0.038)
2.071***
(0.064)
-8.609***
(0.297)
1.854***
(0.038)
1.952***
(0.063)
-8.479***
(0.313)
ρ
-0.867***
(0.282)
2406.700***
F(6,n) first step
LL (log lik)
n (# of obs.)
Control function
Full sample
-69361.691
57,758
-69618.135
57,758
Note: See the Note to Table 9 on next page.
29
-0.878***
(0.225)
3379.400***
-105542.312
86,728
-105897.660
86,728
Table 9. Hazard rate determinants: no MSA controls; controlling for measurement error in ZINC
HHs with no child of school age
Baseline model
TAXRLF
TAXRLF*AGE55
AMTX
DTCH1
OLDH
ROOMPER
HOWNH
AGE
GENDER
WHITE
MARR
CHILD3
CHILD6
CPLWORK
ZINC
CARS
MG30YR
NGAINL2
SALEPERC
METRO
STATECA
α
α(CA)
Const
Baseline model
Control function
-0.000888***
(0.000133)
0.000575***
(0.000086)
-0.000967***
(0.000163)
0.000613***
(0.000094)
-0.000768***
(0.000102)
0.000525***
(0.000072)
-0.000857***
(0.000130)
0.000563***
(0.000078)
-0.000
(0.000)
-0.432***
(0.069)
-0.034***
(0.002)
0.061***
(0.013)
0.124***
(0.032)
-0.074***
(0.003)
0.085**
(0.039)
0.406***
(0.089)
0.042
(0.050)
0.488***
(0.095)
0.420***
(0.114)
0.209***
(0.057)
0.004***
(0.001)
-0.274***
(0.033)
53.084***
(1.629)
2.698***
(0.205)
15.538***
(1.784)
0.100**
(0.047)
0.986***
(0.182)
1.996***
(0.046)
1.845***
(0.067)
-8.353***
(0.274)
-0.413
(0.067)
-0.413***
(0.067)
-0.033***
(0.002)
0.054***
(0.012)
0.124***
(0.031)
-0.072***
(0.003)
0.107***
(0.038)
0.630***
(0.097)
-0.089*
(0.052)
0.618***
(0.097)
0.082
(0.123)
0.211***
(0.078)
0.007*
(0.004)
-0.258***
(0.047)
52.712***
(2.560)
2.260***
(0.211)
13.433***
(1.753)
0.105**
(0.046)
0.826***
(0.189)
1.985***
(0.072)
1.917***
(0.188)
-8.814***
(0.433)
0.000
(0.000)
-0.379***
(0.058)
-0.031***
(0.001)
0.080***
(0.010)
0.106***
(0.025)
-0.074***
(0.002)
0.074**
(0.033)
0.392***
(0.067)
-0.033
(0.042)
0.626***
(0.085)
0.494***
(0.066)
0.181***
(0.043)
0.004***
(0.001)
-0.220***
(0.024)
53.050***
(1.390)
2.561***
(0.168)
15.547***
(1.433)
0.108***
(0.039)
0.863***
(0.151)
1.995***
(0.038)
1.861***
(0.058)
-8.663***
(0.221)
-0.000
(0.000)
-0.388***
(0.058)
-0.031***
(0.002)
0.062***
(0.010)
0.102***
(0.025)
-0.074***
(0.003)
0.088***
(0.032)
0.674***
(0.061)
-0.110**
(0.045)
0.642***
(0.086)
0.159**
(0.071)
0.122**
(0.058)
0.008**
(0.003)
-0.230***
(0.038)
52.706***
(2.250)
2.247***
(0.180)
13.434***
(1.405)
0.102***
(0.038)
0.808***
(0.157)
2.001***
(0.063)
1.916***
(0.076)
-8.850***
(0.359)
ρ
-0.889***
(0.334)
2454.700***
F(6,n) first step
LL (log lik)
n (# of obs.)
Control function
Full sample
-70424.886
57,758
-70455.700
57,758
-0.886***
(0.292)
3585.600***
-107123.944
86,728
-107177.487
86,728
Note: The variable TAXRLF is measured in dollars. α is the parameter of the Weibull distribution measuring duration
dependence of the hazard rate. A separate parameter, α(CA), is estimated for California households. The models for which
the control function approach is used are estimated in the usual way as the models in Tables 4 and 5 (See the note to Table
5). ***, **, and * indicate significance at the 1, 5, and 10% levels.
30
Tables 8 (including MSA dummies) and 9 (not including MSA dummies) reveal that the
negative effect of Proposition 13, on the mobility of households targeted by Propositions 60
and 90, has been effectively softened.
In addition to the main results presented in Tables 8 and 9, table 10 also reveals that
the main effect of Propositions 60 and 90 is observed among households occupying the most
expensive houses in California. This is in line with the fact that older households occupy their
houses longer than average and thus would tend to live in more expensive houses given the
incentives presented by Proposition 13.
Table 10. Robustness of the results to subsamples based on housing value (controlling for measurement error in ZINC )
HHs with no child of school age
Baseline model
Control function
Full sample
Baseline model
Control function
Panel A: Subsample with housing values below 1st quartile
TAXRLF
-0.000111
(0.001478)
-0.000870
(0.001409)
0.000522
(0.001380)
-0.000221
(0.001322)
TAXRLF*AGE55
0.001150
(0.001360)
0.001234
(0.001291)
0.001145
(0.001268)
0.001218
(0.001187)
LL (log lik)
n (# of obs.)
-14,773
15,096
-14,830
15,096
-20,896
21,493
-21,008
21,493
Panel B: Subsample with housing values between 1st and 2nd quartiles
TAXRLF
-0.000221
(0.001112)
0.001070
(0.001095)
0.000239
(0.000916)
0.001394
(0.000956)
TAXRLF*AGE55
0.000705
(0.001360)
0.001166
(0.001291)
0.000696
(0.000831)
0.000908
(0.000818)
LL
n
-17,550
14,569
-17,628
14,569
-26,623
21,659
-26,751
21,659
Panel C: Subsample with housing values between 2nd and 3rd quartiles
TAXRLF
-0.001804***
(0.000453)
-0.001133***
(0.000462)
-0.001860***
(0.000360)
-0.001231***
(0.000369)
TAXRLF*AGE55
0.000220
(0.000383)
0.000483
(0.000390)
0.000334
(0.000340)
0.000343
(0.000343)
LL
n
-19,054
14,065
-19,189
14,065
-29,468
21,670
-29,644
21,670
Panel D: Subsample with housing values between 3rd and 4th quartiles
TAXRLF
-0.000493***
(0.000137)
-0.000556***
(0.000144)
-0.001802***
(0.000120)
-0.000474***
(0.000113)
TAXRLF*AGE55
0.000165*
(0.000096)
0.000258***
(0.000098)
-0.004829***
(0.001063)
0.000252***
(0.000082)
LL
n
-17,598
13,723
-17,712
13,723
-28,180
21,519
-28,088
21,519
Yes
Yes
Yes
Yes
Yes
Yes
All models
MAIN CONTROLS
MSA DUMMIES
Yes
Yes
Note: This table represents the sensitivity of the hazard rate to variation in the tax relief for subsamples based on
house value. The observations in the main sample are sorted in ascending order by house value and separated in four
subsamples. The variable TAXRLF is measured in dollars. The control function models control for measurement
error in ZINC, using a two-step procedure. The second step of the control function models requires simulation
of the error term, and the models are estimated with 600 draws of the error term per observation. The standard
errors for these models are corrected for the two-step procedure using the approach suggested by Greene (2003,
p.510). ***, **, and * indicate significance at the 1, 5, and 10% levels.
31
8
Conclusion
In this paper I estimate the effect of the property tax savings, induced by Proposition 13,
on the hazard rate of duration. To correctly quantify this effect I overcome a number of
identification issues typical of empirical models in Tiebout sorting. I find that the hazard rate
of duration decreases with about 3.6% for each $100 increase in the tax savings. Furthermore,
I find that the hazard rate increases with duration and that the rate at which the hazard rate
increases with duration for households located in California is not statistically significantly
different from the rate at which the hazard rate increases with duration for households located
outside of California (see Footnote 41 on p.25). It appears that the effect of tax savings on the
hazard rate is not propagated through duration, but only through the level of the tax saving
(which depends on the value of the house for a given duration). The data also reveals that
the negative effect of Proposition 13, on the mobility of households targeted by Propositions
60 and 90, has been effectively softened. A more detailed analysis also shows that the main
effect of Propositions 13, 60, and 90 on household mobility has been experienced by households
that occupy more expensive dwellings; the mobility patterns of households that experience
low levels of tax relief are virtually unaffected. Unlike in previous studies, the data also
demonstrates a higher propensity to move for California households. This further confirms
that the effect of Proposition 13 on mobility has been successfully separated from the effects of
other factors. My analysis gives one more confirmation that households decisions to relocate
are affected by local tax policy. It compliments the results in Farnham and Sevak (2006) and
Johnson and Walsh (2008) that households respond to local tax incentives in their across-state
relocation decisions, by showing that intra-metro area moves are also affected by local tax
policy.
Our understanding of the effect of the limit in increase of assessed value on mobility
can further be augmented by answering two additional questions: first, how much of the
disincentive to relocate was capitalised in housing values; and, second, to what extent is
the negative effect of the tax savings on mobility exacerbated by a network effect, where
households willing to sell cannot do so, because they cannot find an adequate house to move
to. Answering these questions is a subject of ongoing and future research.
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Appendices:
A
The Hazard function with observable explanatory variables and unobserved heterogeneity
The exposition in Appendix A closely follows Wooldridge (2007).
The random variable T measures the length of time a person/household resides in a given
housing unit before they move out to relocate. One can easily show (see Wooldridge (2007))
that the cumulative probability, the survival function and the density can be expressed as
functions of the hazard rate:
[ ∫ t
]
F (t) = 1 − exp −
λ(s)ds ,
t ≥ 0.
(18)
0
[ ∫ t
]
S(t) = exp −
λ(s)ds
(19)
0
[ ∫ t
]
f (t) = λ(t) exp −
λ(s)ds
(20)
0
The shape of the hazard function is of primary interest. The simplest case is a constant
hazard function, λ(t) = λ, with T following an exponential distribution, with cdf F (t) =
1 − exp(−λt). In this case the process is memoryless, but the hazard rate can also be duration
dependent. An often used distribution which allows for duration dependence is the Weibull
distribution with
F (t) = 1 − exp(−γtα ),
γ, α ≥ 0;
(21)
f (t) = γαtα−1 exp(−γtα );
(22)
λ(t) = γαtα−1 .
(23)
35
When α >=< 1 the hazard is respectively monotonically increasing, constant, and monotonically decreasing for all t.
For modeling purposes, the hazard function can be specified to depend on observable
characteristics and unobservable heterogeneity. The most widely used class of models, first
suggested by Cox (1972), is the proportional hazard model
λ(t, x(t), v) = v k(x(t))λ0 (t),
(24)
where v > 0 represents the influence of unobservable heterogeneity (independent from the
observable factors) on the hazard, k(x(t)) > 0 is a function of the explanatory variables, which
can be time varying or time-invariant, and λ0 (t) is called the baseline hazard. The model is
called proportional because λ0 (t) measures the duration dependence, which is common for
all households, while k(x(t)) serves to shift the hazard function through the influence of the
regressors.
Typically k(·) is parametrised as k(x(t)) = exp(x(t)β) (which is always positive), where
β is a vector of parameters to be estimated, and the error term v is assumed to be supported
on v ∈ [0; ∞].
If F (t|x(t), v; β) is the cdf of T conditional on (x(t), v), the distribution of T conditional
only on x(t) can be obtained by integrating out the unobservable effect, v. Because v and x
are independent, the cdf of T given x(t) is
∫
F (t|x(t); β, ρ) =
∞
F (t|x(t), v; β)h(v; ρ)dv
(25)
0
where the density of v, h(v; ρ), is assumed to be continuous and depends on the unknown
parameters ρ.
For a random draw i from the population, a Weibull hazard function, conditional on
observed effects xi (t) and unobserved heterogeneity vi is
λ(t; xi (t), vi ) = vi exp(xi (t)β)αtα−1
(26)
[
]
∫ t
α−1
F (t|xi (t), vi ; β) = 1 − exp −vi
exp(xi (s)β)αs
ds .
(27)
Then, from equation (18)
0
36
I assume gamma-distributed unobservable heterogeneity - that is, vi ∼ Gamma(δ, δ) - then
E(vi ) = 1, V ar(vi ) = 1/δ and
h(v; δ) = δ δ v δ−1 exp(−δv)/Γ(δ).
Denoting ξ(t, xi (t), β) =
∫t
0
(28)
exp(xi (s)β)αsα−1 ds, and using equations (25) and (28), we can
integrate out the unobservable heterogeneity to find the distribution of T conditional only on
the observable explanatory variables, xi (t)
F (t|xi (t); β, δ) = 1 − [1 − ξ(t, xi (t), β)/δ]−δ .
(29)
Further, assuming xi (t) = xi we can write
∫
t
αsα−1 ds = exp(xi β)tα .
ξ(t, xi , β) = exp(xi β)
(30)
0
and the cdf of Ti conditional on the observable explanatory variables xi is
F (t|xi ; β, δ) = 1 − [1 − exp(xi β)sα /δ]−δ .
(31)
Finally, another way to incorporate the unobservable heterogeneity is by parameterising
k(x(t)) = exp(xi (t)β + vi ). This allows to relax the assumption that v is independent of x.
B
Controlling for omitted variables and measurement
error in prices and income
In this section I describe the procedure I use to estimate the hazard rate when one of the
explanatory variables is correlated with the error term in the model. For the exposition in
this section I assume this variable is the tax savings, TS, but the derivations when income is
measured with error are analogous.
In nonlinear estimation controlling for measurement error is a somewhat more complicated
procedure than the instrumental variables approach. We need to simultaneously estimate the
hazard rate and a control function for the variable correlated with the error term in the hazard
37
rate. The two important equations in our extended model are
λ(t|x1 , T S, v; β1 , π) = exp(πT S + x1 β1 + v)αtα−1
T S = x1 β21 + x2 β22 + u = xβ2 + u,
(32)
(33)
where x1 is the main vector of explanatory variables, x2 is the vector of ‘instrumental’ variables, the vectors β1 and β2 are the vectors of parameters to be estimated for each equation,
and u and v represent the unobserved heterogeneity in each equation. The parameters of
the two equations are identified when β22 6= 0. Because TS is correlated with v we can not
assume that u and v are uncorrelated. The standard approach (Wooldridge (2002, p.472)) is
to assume that u and v are jointly normally distributed


(u, v) ∼ N (0, Ξ),
σu2

Ξ=
ρσu σv
ρσu σv 
,
σv2
(34)
where (u, v) is independent from x. Since u ∼ N (0, σu2 ) then T S|x ∼Normal. The model is
applicable when E(v|T S) 6= 0. Under joint normality of u and v we can write (Wooldridge
(2007, p.473), Greene (2003, p.868))
v=
σv
Cov(u, v)
u+ε=
ρu + ε = θu + ε,
σu2
σu
(35)
where E(ε|u, x) = 0 and thus E(ε|T S) = 0. Since u and v are jointly normal then ε is also
normal43
ε ∼ N (0, σv2 (1 − ρ2 ))
(37)
Then we can write the hazard rate as
λ = exp(x1 β1 + πT S + θu + ε)αtα−1
= exp(x1 β1 + πT S + θ(T S − xβ2 ) + ε)αtα−1
= exp(ε) exp(zψ)αtα−1
(38)
The model can be estimated in two steps, where in the first step we estimate equation
43
V ar(ε) = V ar(v) −
„
Cov(u, v)
2
σu
38
«2
V ar(u) = σv2 (1 − ρ2 )
(36)
(33) by OLS or ML, save the residuals, û, and their standard error, σ̂u , and in the second
step we estimate equation (32) by ML, using the estimated in the first step residuals and
their standard error. To estimate standard errors for the two-step procedure a correction to
the standard errors in the second step is needed because in equation (32) we do not use the
true value of β2 but its estimate from the first step, β̂2 , and in such cases the variance of β̂1
depends on the variance of β̂2 . The procedure for calculating the corrected standard errors
of β̂1 is described in Greene (2003, p.510).
Once we estimate û and σˆu in the first step, we can use equation (21) to write the likelihood
elements for the censored and uncensored observations
∫
f (T > ci |z, û, σ̂u ) =
+∞
−∞
[
]
1 − exp(−ez ψ +ε cα
)
f (ε)dε,
i
f (b − aij ≤ T < ai0 j − aij |z, û, σ̂u ) =
∫ +∞ [
]
exp(−ezψ +ε (b − aij )α ) − exp(−ez ψ +ε (ai0 j − aij )α ) f (ε)dε,
(39)
(40)
−∞
where from equation (37) we have f (ε) = √
1
2 (1−ρ2 )
2πσv
{
}
ε2
exp − σ2 (1−ρ
.
2)
v
The conditional probabilities (39) and (40) are usually averaged out for ε through simulation (Train (2003))44 or quadrature method (Waldman (1985)). Summing up the logs of
the likelihood elements (39) and (40) over all households and maximising gives the MLE of
β1 , π, σε , θ, α. Once θ and σε are estimated, one can easily derive ρ̂ and σ̂v . Testing for the
credibility of the instruments is done with an F-test on the joint significance of the instruments in the first regression (Deaton (1997)). Testing for dependence between TS and v can
be easily achieved through a t-test on the significance of the correlation coefficient ρ. For the
purposes of the t-test the variance of the correlation coefficient is derived from the covariance
matrix of θ and σε using the Delta method (Greene (2003, p.913)).
Credible instruments must be used to control for the omitted variables and measurement
error in prices and income. It is fairly difficult, however, to find instruments that are correlated
with the house value but uncorrelated with any of the unobservable determinants of utility
a household experiences from living in their current house. To instrument for housing values
I use some of the instruments suggested by Capozza and Hesley (1990), Capozza and Sick
(1994), and Capozza and Seguin (1995).
44 Consistency and efficiency of simulation assisted estimators are discussed in Train (2003 pp.241-242,246247 ).
39
Appendix Table 1. Key instrumental-variables definitions and descriptive statistics.
INC
POP
POPGR
average household income in MSA-YEAR (in 1,000s) (AHS,
BLS);
yearly average-income growth rate for MSA-YEAR (AHS,
BLS);
total population of MSA-YEAR (in 1,000,000s) (AHS);
yearly population growth rate for MSA-YEAR (AHS);
QALIM
QBUS
QINT
QRENT
QSS
QWELF
=1
=1
=1
=1
=1
=1
INCGR
if
if
if
if
if
if
income
income
income
income
income
income
from
from
from
from
from
from
alimony (AHS);
business (AHS);
interest (AHS);
rent (AHS);
social security (AHS);
welfare programs (AHS);
Mean
SD
$24.758
$4.602
-0.006
0.030
2.165
0.004
1.676
0.030
0.039
0.144
0.396
0.124
0.301
0.020
0.192
0.351
0.489
0.329
0.459
0.140
Note: All income variables deflated using CPI (provided by the Bureau of Labor Statistics). AHS stands for
the American Housing Survey. BLS stands for the Bureau of Labor Statistics.
Since about 82% of the households relocate within the metro area, aggregate measures of
characteristics of the metro area should determine prices but not the decision to move. Four
variables are calculated as measures of metro area characteristics. The population variable
POP is calculated by inflating the number of persons per household, using PWT, and then
the numbers are summed within each MSA-YEAR to calculate the population of the MSA for
the given survey year. The variable INC is calculated by averaging out the household income,
using PWT to weight the income of each household. The growth rates, POPGR and INCGR,
represent average yearly growth rates between the year of the current survey and the year of
the previous survey45 . To control for measurement error in income I use dummy variables
that identify whether a household has income from business, interest, rent, welfare programs,
social security, and child alimony46 . These variables are based on questions asked separately
from the questions calculating the total self-reported income, and are hypothesized to be
unrelated to the unobservable determinants of household utility. All instrumental variables
with their descriptive statistics are listed in Appendix Table 1.
45 In most occasions consecutive surveys for a given metro area are taken each four years, but sometimes
the gaps are longer or shorter. To maintain consistency of the growth rates calculated for each MSA-YEAR,
an average yearly growth rate is calculated.
46 Authors have used a variety of instruments for income depending on the nature of the problem they study.
Some of the widely used instruments are lagged income, educational level, and industry/occupation codes.
40
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