1 INEQUALITY IN HOUSING AFFORDABILITY: MEASUREMENT AND ESTIMATION Danny Ben-Shahar and Jacob Warszawski* ABSTRACT This research proposes and examines new measures for assessing the state of housing affordability inequality. We employ a large micro-level dataset by which we estimate and evaluate the time-varying housing affordability inequality in Israel over the period 1992-2011. Results show that our developed housing affordability inequality Gini coefficient has considerably increased in the past decade. Moreover, controlling for changes in net income inequality and macroeconomic conditions, housing affordability inequality is found to positively correlate with average housing prices (computed in net-income terms). Furthermore, our method allows for an examination of segmentation in housing affordability. We find that segmentation particularly prevails across the household head’s gender, family status, working status, and the number of income providers in the household. Research outcomes may direct decision-makers in designing policies aiming to reduce inequality and segmentation in housing affordability. Current Version: September 18, 2014 Key Words: Housing affordability; Inequality; Gini; Atkinson; Decomposition; Segmentation. JEL Codes: I32, R31, Z13 * Danny Ben-Shahar, Alrov Institute for Real Estate Research, Faculty of Management, Tel Aviv University, Tel Aviv, 6139001, Israel, email: [email protected]; and Jacob Warszawski, Faculty of Architecture and Town Planning, Technion – Israel Institute of Technology, Technion City, Haifa 32000, Israel; email: [email protected]. The authors thank Roni Golan, Ofer Huberman, and Doron Sayag for their invaluable assistance in generating the dataset and Shlomo Yitzhaki and seminar participants at the Technion and the 2014 International AREUEA meetings and the 2014 Israel Regional Science meetings for helpful comments.
Transcript
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INEQUALITY IN HOUSING AFFORDABILITY: MEASUREMENT AND ESTIMATION
Danny Ben-Shahar and Jacob Warszawski*
ABSTRACT
This research proposes and examines new measures for assessing the state of housing affordability inequality. We employ a large micro-level dataset by which we estimate and evaluate the time-varying housing affordability inequality in Israel over the period 1992-2011. Results show that our developed housing affordability inequality Gini coefficient has considerably increased in the past decade. Moreover, controlling for changes in net income inequality and macroeconomic conditions, housing affordability inequality is found to positively correlate with average housing prices (computed in net-income terms). Furthermore, our method allows for an examination of segmentation in housing affordability. We find that segmentation particularly prevails across the household head’s gender, family status, working status, and the number of income providers in the household. Research outcomes may direct decision-makers in designing policies aiming to reduce inequality and segmentation in housing affordability.
* Danny Ben-Shahar, Alrov Institute for Real Estate Research, Faculty of Management, Tel Aviv University, Tel Aviv, 6139001, Israel, email: [email protected]; and Jacob Warszawski, Faculty of Architecture and Town Planning, Technion – Israel Institute of Technology, Technion City, Haifa 32000, Israel; email: [email protected]. The authors thank Roni Golan, Ofer Huberman, and Doron Sayag for their invaluable assistance in generating the dataset and Shlomo Yitzhaki and seminar participants at the Technion and the 2014 International AREUEA meetings and the 2014 Israel Regional Science meetings for helpful comments.
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1 INTRODUCTION
Housing is commonly the single largest expenditure item for most households, while
poor and near-poor families often devote half their income to housing (Quigley and
Raphael, 2004). It is not surprising, then, that the recent social protests occurring in
many Western cities around the world were largely incited by requests for a supply of
housing at affordable prices. This further explains the major interest that the general
public, policymakers, and regulators have in the discussion of housing affordability.
Various ratios are found in the literature for measuring housing affordability.
Among these are housing-loan-repayment-to-income, ongoing-housing-cost-to-
income, debt-to-housing-price, and housing-price-to-income (see, for example, Myer
and Engelhardt (1996), Thalmann (1999), Quigley and Raphael (2004), Brounen et al.
(2006), Stone (2006), Norris and Shiels (2007), Kim and Cho (2010), and Haffner and
Heylen (2011).1 Also, while the state of housing affordability is commonly explored
by focusing on an average and/or median figure, some studies further explore
affordability among populations stratified by socio-economic and demographic
characteristics such as income, poverty status, race, and ethnicity (see, for example,
Quigley and Raphael, 2004; Meen, 2011).
Surprisingly, however, to the best of our knowledge previous research has
never attempted to develop a measure that summarizes and examines the state of
housing affordability inequality.2 In this study, we assume this task by adapting a
widely accepted measure for estimating income equality to the context of housing
affordability—thereby developing a novel approach for assessing the state of housing
affordability inequality. Further, we empirically examine the factors that associate
1 Studies of housing affordability alternatively adopt the residual income approach, by which they examine how costs of basic goods net of housing costs associate with income (e.g., Whitehead, 1991; Stone, 2006; Kutty, 2005; & Chen et al., 2010). One of the controversies surrounding both the ratio and the residual income approaches concerns the threshold above which affordability may become increasingly subjective, as well as the definition and measurement of affordability below that threshold (Stone, 2006). 2 Matlack and Vigdor (2008) associate the rise in household income inequality with the deterioration of housing affordability for poor households by focusing on residual income and the rent-per-income ratio. Our study thus differs from that of Matlack and Vigdor (2008) on three central issues. First, we do not include subjective estimates of household basic needs for goods. Moreover, we consider the entire distribution of household housing affordability as opposed to focusing on the lower tail of the affordability distribution (the latter also associates with Whitehead, 1991; Stone, 2006; & Kutty, 2005). Finally, we develop a Gini measure that summarizes the level of housing affordability inequality.
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with the time-varying dynamics of the derived housing affordability inequality
measure.
The Gini coefficient is commonly used in socio-economic literature to
estimate the state of income inequality (see, for example, Alderson and Nielsen, 2002;
Jäntti and Jenkins, 2010; Leigh, 2007; Frank, 2009).3 The methodology for estimating
the income Gini coefficient has been extended and implemented, however, to measure
the state of inequality in other areas such as education and human capital (Földvári
and Leeuwen, 2011), fossil resource consumption (Papathanasopoulou and Jackson,
2009), ecological entitlements (Ruitebeek, 1996), innovative activity states and R&D
spillovers (Audretsch and Feldman, 1996), firm size across industries and locations
(Jovanovic, 1982), and child achievements (Sastry and Pebley, 2010).
In the housing literature, the Gini coefficient approach has been applied by
Buckley and Gurenko (1997) to measure the effect of housing subsidies on living
space inequality; by Landis et al. (2002) to measure inequality in housing values,
housing costs, and monthly rent; and by Henley (2003) to study changes in the
distribution of housing wealth. Robinson et al. (1985) applied the Gini coefficient to
measure inequality in housing consumption. Also, studies by Tilly (2006) and
Matlack and Vigdor (2008) discuss the association between income inequality and
housing affordability challenges at the bottom of the income distribution. More
recently, Dewilde (2011), Dewilde and Lancee (2012), and Norris and Winston
(2012a,b) relate income inequality to homeownership and homeownership inequality.
In this study, we propose and compute a Gini coefficient of housing
affordability inequality based on the net income-to-housing price ratio. Intuitively, a
household net income-to-housing price ratio measures the share (portion) of the
housing unit that a household’s periodic net income could purchase, had it designated
its entire net income to the purchase of a housing unit identical to the one in which it
resides.4 Similar to the income Gini coefficient, our derived housing affordability
3 Recall that the Gini coefficient measures the area between the Lorenz curve and a hypothetical line of absolute equality, and is expressed as a percentage of the total area under this line. The Gini coefficient thus commonly ranges from zero (perfect equality) to one (complete inequality). For alternative measures of inequality as well as criticism and limitations of the Gini measure, see, for example, Cowell (2000). 4 Intuitively, a household housing price-to-net income ratio can be interpreted as the number of time periods it would take one to complete the purchase of a dwelling unit, had the household earmarked its entire net income to purchase a unit identical to the one in which it resides. Formulation of the Gini
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inequality measure thus indicates on the micro-level degree of inequality in household
ability to purchase a housing unit—measured by the portion of the housing unit that a
household’s periodic net income could purchase.5 We further estimate the factors that
associate with our proposed housing affordability inequality measure and, following
Yitzhaki and Lerman (1991), Lambert and Aronson (1993), and Cowell (2000), we
examine segmentation in housing affordability by stratifying the household sample
according to various socio-demographic and locational characteristics.
The analysis is based on a large micro-level sample representative of all
households in Israel over the period 1992–2011. The data include 156,583
observations of household socio-economic, demographic, locational, and dwelling
unit characteristics (see further details in the Data section below).6 Results show that
housing affordability inequality, as assessed by our proposed housing affordability
Gini coefficient, exhibits a substantial increase over the past decade. This increase is
accompanied by a more moderate increase in equivalent net income Gini coefficient.
Empirical examination of the time-varying housing affordability inequality measure
reveals a highly significant positive correlation with average housing prices (in net
income terms), controlling for changes in net income inequality and macroeconomic
conditions. In addition, we find that while housing affordability has considerably
dropped for all socio-demographic segments over the 1992–2011 period, meaningful
segmentation in housing affordability particularly prevails across household head
gender, household family status, household head working status, household number of
income providers, and household geographical location. Finally, we show that our
coefficient method prevents us, however, from applying it directly to the housing price-to-net income ratio. Instead, the net income-to-housing price ratio may both conform to the Gini methodology and be consistent with the literature that measures housing affordability. 5 Ultimately, in computing the housing affordability inequality, one might wish to focus on household “required” amount of housing services (given the household demographic characteristics) and thereby avoid potential “noise” in focusing on the actual housing unit that one occupies (i.e., omitting possible under- and over-consumption of housing). This exercise is, however, beyond the scope of this study. 6 The interest in studying housing affordability of homeowners is threefold. First, as homeowners comprise a dominant share of the housing market, examining their incomes and the values of dwelling units (thus studying their housing affordability status) indicates the likelihood of non-owners attaining ownership. Also, it particularly indicates the potential of homeowners to filter-up in the housing market. Finally, examining a time-series of housing affordability figures of homeowners allows policymakers to draw conclusions with respect to the time-varying level of housing prices in income terms (see, among others, Fingleton, 2008; Fisher et al., 2009).
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evidence on housing affordability inequality is robust to replacing the Gini coefficient
method with the Atkinson index approach.
The main contribution of the research is twofold. First, we propose and
implement a novel approach for assessing the state of housing affordability inequality
based on the Gini coefficient methodology. Moreover, by exploring the factors that
correlate with the level of inequality and specifying the population segments that
particularly contribute to the level of inequality, we provide decision makers
regulating housing prices and housing welfare with a toolbox and practical evidence
that can motivate the design of effective policies aimed at promoting housing
affordability where it is especially needed.
The organization of the paper is as follows. The next section describes the
methodology, while Section 3 presents the data, including variable definitions and
related summary statistics. Section 4 presents related statistical results on the
correlation between housing affordability inequality and average housing prices, and
Section 5 assesses the robustness of the outcomes to the Gini coefficient specification.
Section 6 examines socio-demographic segmentation in housing affordability, and,
finally, Section 7 provides a summary and concluding remarks.
2 METHODOLOGY
Given the individual household net income variable, we first compute the quarterly
net income Gini coefficient (denoted by GW) for the period 1992–2011. We then
compute the quarterly housing affordability Gini coefficient (GH) based on household
i net income-to-housing price ratio (Wi/Pi). In deriving the housing affordability Gini
coefficient, we adapt the method of computing the income Gini coefficient by
substituting the individual net income variable with the individual net income-to-
housing price ratio. Inequality in the net income-to-housing price variable essentially
indicates inequality in the share of a household’s own housing unit that the individual
household can afford, given its individual periodic net income.7
7 Formally, the housing affordability Gini coefficient is then computed as follows: , where and The weighted average of all surveyed household housing affordability is estimated with: , where is the observation weight of household (percentage weight), is the number of members in household , is household i’s net income-to-housing price ratio, and is the number of households surveyed (in a given quarter). For more on the Gini coefficient computation, see Araar and Duclos (2013).
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Following the derived time-series of GW and GH coefficients, we can write
(1)
𝐺𝐻𝑡 = 𝛼! + 𝛼!×𝐺𝑊𝑡 + 𝛼!× 𝑃𝑊 𝑡
+ 𝛼!×𝐶𝑂𝑁𝑇𝑅𝑂𝐿𝑆𝑡 + 𝑢𝑡,
where t is a time period index (in quarters), GW and GH are net income and housing
affordability Gini coefficients, respectively, P/W is the average housing price-to-net
income ratio (across all households at time t), CONTROLS is a matrix of
macroeconomic variables, including gross domestic product (GDP), housing
construction ends (HE), housing construction starts (HS), unemployment rate (UR),
nominal bond rate (BR), construction price index (CI), and new Israeli sheqel-to-
dollar exchange rate (EX). Also, 𝛼! − 𝛼! are parameters, 𝛼! is a vector of parameters,
and u is a random disturbance term.
According to equation (1), time-varying inequality of housing affordability not
only associates with net-income inequality, but also may correlate with the average
housing price (in net income terms, i.e., average housing price-to-net income ratio) as
well as changes in macroeconomic indicators. (For more on the correlation between
macroeconomic indicators and housing prices see, for example, Adams and Füss,
2010; Kim and Cho, 2010; Schnure, 2005; Ortalo-Magné and Rady, 2006; Case and
Quigley, 2008; Sutton, 2002; and Poterba, 1984. On the correlation between
macroeconomic indicators and income inequality, see, for example, Achdut, 1996;
Blejer and Guerrero, 1990; Milanovic, 2002; Heshmati, 2004; and Jäntti and Jenkins,
2010. On the correlation between macroeconomic indicators and housing affordability
see, for example, Malpezzi, 1999; Mostafa et al., 2006; and Ben-Shahar and
Warszawski, 2011.)
In the last part of our study, we stratify the household sample by socio-
demographic and locational characteristics. We then decompose the derived housing
affordability Gini coefficient (GH) into within-segment, between-segment, and overlap
components of inequality. In other words, for a given stratification, we compute (a)
the weighted-average of the housing affordability Gini coefficient by segments (the
within-segment component); (b) the weighted-average Gini coefficient if each
household in a segment had maintained the segment average housing affordability
level (the between-segment component); and (c) the sample Gini coefficient net of the
within- and between-segments, that is, the residual part (the overlap component)—
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following Yitzhaki (1994), the overlap component is a measure for segmentation in
the population. (For a complete discussion on the properties of the overlap component,
see Frick et al., 2006.)
3 DATA
Data for this study come from three sources. First, 156,583 micro-level observations
on individual household socio-economic, demographic, and dwelling unit
characteristics are provided by the Household Income and Expenditure Surveys
conducted by the Israel Central Bureau of Statistics for the years 1992–2011. Each
quarterly independent cross-section sample has between 1,041 and 2,921 observations
and is representative of all households in Israel (see Central Bureau of Statistics,
1993–2012). Table 1 shows the number of cross-sectional observations per quarter for
the 1992–2011 period. Table 2 presents the household socio-demographic and
dwelling unit characteristics in the dataset and the 1992 and 2011 shares of each
characteristic within the sample. Socio-demographic characteristics include family
status, the household head’s gender, the number of members in the household, the
household head’s years of education, last formal education, and age, the number of
household income providers, and the household head’s working status, occupation,
and industry. Dwelling unit characteristics include the number of rooms and location.
Another source of data is all housing transactions in Israel for the period
1992–2011, recorded by the Israel Tax Authority—a total of 729,505 observations of
transacted dwelling unit prices and attributes. Based on this data, we generate a
quality-adjusted price for the dwelling unit of each household in the Household
Income and Expenditure Surveys. (A detailed description of the procedure by which
we produce the quality-adjusted price that is “matched” to each household is provided
in the appendix.)
A final source of data includes macroeconomic indicators for the period 1992–
2011 obtained from the Bank of Israel and the Israel Central Bureau of Statistics.
These include the Gross Domestic Product in dollars (GDP), number of housing
construction ends (HE), change in the unemployment rate (ΔUR), change in the
mortgage rate (ΔMR), change in the rate of change in the construction index (ΔCI),
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change in the one-year bond rate (ΔBR), change in the new Israeli sheqel-to-dollar
exchange rate (ΔEX), and change in the number of housing construction starts (ΔHS).8
Table 3 presents summary statistics for household net income, net income-to-
housing price ratio, housing price-to-net income ratio, and the macroeconomic
variables. It follows that the mean monthly net income was 2,053 dollars, with a
standard deviation equal to 554 dollars (1USD ≈ 4 New Israeli Sheqels). The mean
housing price-to-net income and net income-to-housing price were about 112 and
0.0144, respectively, with standard deviations equal to 10.97 and 0.00134,
respectively. (See Table 3 for summary statistics of the macroeconomic variables.)
Exhibit 1 displays the sample quarterly average and deciles of the housing
price-to-net-income ratio (P/W) over the period 1992–2011.9 Interestingly, the
average ratio approximately overlaps the seventh decile (note that a higher decile
associates with a greater housing price-to-net income ratio, i.e, a lower level of
affordability). Moreover, while the top decile of the housing price-to-net income
ratios (10% of the population with greatest affordability) ranges from 31 to 46 over
the examined period, the lowest decile (lowest 10%) experiences equivalent figures in
the 181–286 range. Namely, had households earmarked their entire net income for
purchase of a housing unit, the top (bottom) housing affordability decile would have
needed 31-46 (181–286) months to complete the purchase. At the same time, the
housing price-to-net income ratio of the third, fifth, and seventh deciles ranges in the
48–71, 69–100, and 99–145 figures, respectively.
Exhibit 2 shows the time-varying series of the sample quarterly average
housing price-to-net income ratio over the period 1992–2011. Interestingly, the
average price-to-net income ratio not only exhibits a positive slope over the examined
period (as seen by the linearized trend); in addition, it experiences a sizable shift from
the 100–110 levels in the 2000–2007 years to the 115–135 levels in the post-2007
period. Note in particular the sharp increase from a level of 98 in 2008Q1 to 137 in
8 The unit root hypothesis could not statistically be rejected for the time-series of the unemployment rate (UR), mortgage rate (MR), rate of change in the construction index (CI), the one-year bond rate (BR), the new Israeli sheqel-to-dollar exchange rate (EX), and the number of housing construction starts (HS). We thus specified these non-stationary control variables in first difference terms (difference between their time t and t-1 values) for which the unit root hypothesis was statistically rejected. 9 In the derivation of the average housing price-to-net income ratio, the lowest and highest 0.5 percent of the observations were omitted to mitigate the effect of outliers. Results, however, are robust to the inclusion of these outliers (available by request).
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2011Q4. In the next section, we examine the relationship between this phenomenon
and the attained level of inequality in housing affordability.
4 RESULTS
Based on the series of individual household net income W and net income-to-housing
price ratio W/P, we first compute the annual net income Gini and housing
affordability Gini coefficients, GW and GH respectively, for the period 1992–2011 (see
Table 4 for summary statistics of GW and GH). Exhibit 3 shows the computed housing
affordability and net income Gini coefficients for the years 1992–2011. Note that the
level of housing affordability inequality has not only experienced an upward trend
since the year 2000, peaking in 2008 with a Gini coefficient of 0.352, but also that its
increase has exceeded that of the net income Gini coefficient in the post-2000 decade.
Columns (1) and (2) in Table 5 present the outcomes from the estimation of
equation (1) (full model and stepwise regression, respectively). Results show that the
housing affordability Gini coefficient is, as expected, positively correlated to a high
degree with the net income Gini.10 Interestingly, however, the housing affordability
Gini is also positively correlated with average housing price-to-net income ratio at the
5% significance level (t-value equals 2.36). As the standard deviation of the housing
affordability Gini coefficient equals 0.0174 (see Table 4), the estimated coefficient on
the housing price-to-net income variable indicates that a ten-unit increase in the
housing price-to-net-income ratio associates with a rise in the housing affordability
Gini coefficient equal to just over 10% of its standard deviation. Put differently, the
sharp rise in the average price-to-net income ratio over the 2008–2011 period (from
98 in 2008Q1 to 137 in 2011Q4—see, once again, Exhibit 3) associates with an
increase in housing affordability Gini coefficient equal to 40% of its standard
deviation.11 Finally, concerning the control variables, it follows that the housing
affordability Gini negatively correlates with the number of housing construction ends
10 Also note that the computed Pearson correlation between W and W/P is equal to 0.65 and between W and P is equal to 0.45. 11 Note that, while the derived Gini coefficient is based on the individual household net-income and housing price, it does not immediately follow that the level of the inequality measure should correlate (either positively and or negatively) with the average housing price-to-net income ratio. Interestingly, however, as described above, our findings indicate that, when average housing price-to-net income rises, households at the lower tail of the housing affordability distribution are adversely affected at a greater degree than those at the higher tail of the distribution.
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and the change in the new Israeli sheqel-to-dollar exchange rate at the 1% and 10%
significance levels, respectively, and positively correlates with the level of gross
domestic product with a five-period lag at the 1% significance level.12
5 ROBUSTNESS TEST: HOUSING AFFORDABILITY ATKINSON INDEX
In this section we assess the robustness of our findings by generating and estimating
an alternative to the housing affordability Gini coefficient. Specifically, we derive a
housing affordability Atkinson index and re-estimate the model in (1).
Recall that the Atkinson index had originally been developed to measure
income inequality (see Atkinson, 1970), allowing for varying levels of inequality
intolerance. It was later adapted to measure inequality of, for example, ecological
entitlements (Ruitebeek, 1996) and the geographical distribution of general
practitioners (Gravelle and Sutton, 2001). Also, Robinson et al. (1985) applied the
Atkinson index method to measure inequality in housing consumption.13
Similar to our derived housing affordability Gini coefficient, we derive an
Atkinson index of housing affordability inequality—AH(ε), where ε is an inequality
aversion parameter—based on the net income-to-housing price ratio.14 In the context
of housing affordability, the Atkinson index can be interpreted as the share of
individual housing affordability (in W/P terms) that may be disposed so as to generate
the same level of social welfare that could be achieved if the mean level of W/P were
to be equally distributed among all households.15
12 While other lags in the level of Gross Domestic Product were found to correlate with the housing affordability Gini coefficient, the highest statistical significance was obtained for the five-period lag reported above. Results obtained for other lags are available from the authors upon request. Also, based on macro-level data, Ben-Shahar and Warszawski (2011) find a negative correlation between the average housing price-to-net income ratio and lagged unemployment rate (also see Jäntti and Jenkins, 2010). 13 As noted by Robinson et al. (1985), the Atkinson index “is particularly important in the case of a commodity such as housing which is widely regarded as a ‘necessity’ and, as such, the plight of those at the bottom end of the distribution is likely to be of special concern” (p. 251). 14 Formally, the housing affordability Atkinson index is computed as follows: , where and and where ε is an inequality-aversion parameter. All other variables are as described above. For more on the Atkinson index computation, see Araar and Duclos (2013). 15 Recall that according to Yitzhaki (1983), we have , where is the average income, is the equally-distributed-equivalent income, and is the Atkinson index as a function of the level of inequality-aversion parameter, ε.
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In accordance with equation (1), we then estimate
(2)
𝐴𝐻𝑡 = 𝛽! + 𝛽!×𝐴𝑊𝑡 + 𝛽!×𝑃𝑊 𝑡
+ 𝛽!×𝐶𝑂𝑁𝑇𝑅𝑂𝐿𝑆𝑡 + 𝑣𝑡,
where t once again denotes a time-period index (in quarters), 𝐴𝐻 and 𝐴𝑊 are the
derived housing affordability and net income Atkinson indices, respectively, for
ε=0.5,16 𝛽! − 𝛽! are estimated parameters, 𝛽! is a vector of parameters, 𝑣 is a random
disturbance term, and the remaining variables are as described above.
Similar to equation (1), in equation (2) we focus on estimating the correlation
between housing affordability inequality (this time estimated by the housing
affordability Atkinson index) and the average housing price (in net income terms).
Again, we control for changes in net income inequality and time-varying
macroeconomic conditions.
Outcomes are robust to the Atkinson specification. In particular, Exhibit 4
shows the computed housing affordability and net income Atkinson indices over the
period 1992–2011. A couple of points are worth noting. First, while in 2000Q4 the
housing affordability Atkinson index equaled 0.074, its level rose by about 27% to
equal 0.094 in 2011Q4. Following Atkinson (1970), the latter implies that all
households could have disposed 7.4% and 9.4% of the total net income-to-housing
price W/P in 2000Q4 and 2011Q4, respectively, so as to generate the same level of
social welfare that could have been achieved if the mean level of W/P had been
equally distributed among all households (see, for example, Yitzhaki, 1983).
Moreover, the pattern previously observed with the Gini coefficient now repeats with
the Atkinson index. That is, the sharp increase in the housing affordability Atkinson
index in the last decade led it to generally exceed the equivalent increase in the level
of the net income Atkinson index.
Further, columns (3) and (4) in Table 5 present the outcomes from the
estimation of equation (2) (full model and stepwise regression, respectively). Results
indicate that the housing affordability Atkinson index is positively correlated not only
with the net income Atkinson index but also with average housing price (in net
income terms)—both at the 1% significance level. Specifically, a ten-unit change in
16 Empirical studies commonly focus on the inequality-aversion parameter ε ranging between 0.5 and 2.5 (e.g., Biewen and Jenkins, 2006). Consistent with the literature, we compute AH for ε=0.5. Unreported results are qualitatively robust to increasing the level of ε.
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the average housing price-to-net income ratio corresponds to a change in the housing
affordability Atkinson index equal to about 21% of its standard deviation. Results
further show that the housing affordability Atkinson index negatively correlates with
the number of housing construction ends and the change in the new Israeli sheqel-to-
dollar exchange rate at the 1% and 10% significance levels, respectively, and
positively correlates with gross domestic product (with a five-period lag) at the 1%
significance level.
6 SEGMENTATION IN HOUSING AFFORDABILITY
We stratify the household sample by socio-demographic characteristics and
decompose the derived housing affordability Gini coefficient into within-segment,
between-segment, and overlap components (see Yitzhaki and Lerman, 1991; Lambert
and Aronson, 1993; Cowell, 2000). A relatively low overlap component in the
decomposition of the Gini coefficient implies a relatively heterogeneous population
(i.e., high level of segmentation) across the stratified characteristic. Table 6 shows the
decomposed components of the housing affordability Gini coefficient by socio-
demographic segments and the computed housing affordability Gini coefficient and
the average housing price-to-net income ratio by segments for the years 1992 and
2011.17
It follows that in 1992 and 2011, a relatively high level of segmentation (i.e.,
low overlap component) persists for the household head gender stratification,18
household family status (divides into married, divorced, widowed, single, and living
separately), the household head working status (divides into wage-employee, self-
employed, and non-worker), the number of household providers (divides into zero-,
one-, two-, three-, and four-provider segments), and the geographical region where
the household resides (divides into nine regions as determined by the Israel Central
Bureau of Statistics—see regions in Table 2).
It also follows that male-headed households experience a sharp increase in the
average housing price-to-net income ratio during the examined period (from 79 in
17 On social inequality in the context of homeownership in Israel, see, for example, Lewin-Epstein et al. (2004). 18 Household head gender is generally determined by the gender of the person who is the main income provider in the household. See Israel Central Bureau of Statistics (2013a) for further details.
13
1992 to 116 in 2011) that is accompanied by an increasing housing affordability Gini
coefficient (from 0.30 to 0.34, respectively). Also, the traditional discrepancy in the
price-to-net income ratio between male- and female-headed households maintains
over the examined period, where female-headed household figures rise from 125 in
1992 to 139 in 2011.19
While experiencing an increased average housing price-to-net income ratio
from 77 to 116 over the 1992–2011 period, married households capture the top spot in
housing affordability among the family status segments. The divorced segment
experiences increasing levels of inequality and average housing price-to-net income
ratio (from 0.32 and 113, respectively, in 1992, to 0.34 and 137, respectively, in
2011).20 The share of single household heads in the population almost doubles from
7% to over 13% over the 1992–2011 period (see Table 2), while both its housing
affordability Gini and average housing price-to-net income ratio sharply increase
(from 0.31 to 0.37 and from 100 to 206, respectively).
With respect to household head working status, average housing price-to-net
income rises over the 1992–2011 period from 65 to 106 for wage employees, from 77
to 119 for the self-employed, and from 148 to 221 for non-workers. These are coupled
with an increased housing affordability Gini coefficient, most notably for the non-
worker segment rising from 0.31 in 1992 to 0.37 in 2011, while the wage-employee
and self-employed segments increase from 0.26 and 0.29 to 0.32 and 0.34,
respectively, during that period.
Note the considerable difference among the zero-, one-, and two or more
provider segments. The two or more provider subgroup maintains not only the lowest
level of average housing price-to-net income ratio (at 37–54 and 61–86 in 1992 and
2011, respectively), but also a relatively low level of housing affordability inequality
19 Compare to the findings of Laux and Cook (1994), and Saegert and Clark (2006), who show that female-headed households in the U.S. exhibit both lower levels of housing affordability and greater income inequality (also see Edwards, 2001). 20 Weiss (1984) and others find that income drops considerably after marital dissolution and maintains its low level some five years following the dissolution, while expenditures at the same time maintain their pre-dissolution levels. For more on single-parent household housing consumption see, for example, Saegert and Clark (2006).
14
(Gini coefficient of 0.25–0.28 in 2011).21 In contrast, as expected, the no-provider
household segment experiences the greatest levels of both average housing price-to-
net income ratio and housing affordability inequality, reaching figures of 221 and
0.37, respectively, in 2011. Correspondingly, in 2011, the one-provider segment
attains an average price-to-net income ratio of 150 and a housing affordability Gini of
0.33.
Interestingly, inequality in housing affordability among geographical regions
has dramatically increased over the 1992–2001 period (the overlap component in the
decomposition of the Gini coefficient has decreased from 53% to 38% over this
twenty-year period). While in 2011 the North and Krayot regions maintain the
greatest level of affordability with an average housing price-to-net income ratio equal
to 73 and 69, respectively (up from 58 and 67, respectively, in 1992), Jerusalem and
Tel Aviv sit at the bottom of the list with an average ratio equal to 206 and 182 (up
from 108 and 111, respectively, in 1992). The sharp increase in the average housing
price-to-net income ratio in Jerusalem and Tel Aviv (as compared to North and
Krayot) can be attributed, among other possible reasons, to the sharp rise in real estate
prices in those specific regions since 2007.22 Jerusalem and Tel Aviv further lead all
regions in the level of inequality with a Gini coefficient of 0.32 in 2011.
Several final points are worth noting. First, a relatively low level of
segmentation is found for the number of members in household and the household
head’s age, years of education, last formal education, occupation, and industry.
Further, for some of these household stratifications, we find that segmentation has
somewhat diminished (the overlap component has increased) during the 1992–2011
period (the exceptions are the household head years of education, last formal
education, and the number of members in household, whose overlap component
experienced a marginal decline). These trends are nonetheless generally accompanied
by a sharp increase in segments’ average housing price-to-net income ratio. Finally, it
should be stressed that the segmentation in affordability analysis proposed here allows
21 This outcome is consistent with the assertion of Cancian and Reed (1998), Heathcote et al. (2010), and others that the net effect of the increased participation of females in the labor force reduces overall inequality. 22 Specifically, while average housing prices increased in the Krayot and North regions by 40% and 57%, respectively, over the period 2006–2011, in Tel Aviv and Jerusalem they increased by 80% and 61%, respectively (Israel Central Bureau of Statistics, 2006–2012).
15
for the identification of population subgroups (according to socio-demographic and
locational characteristics) that particularly “contribute” to the level of housing
affordability inequality and may thus provide policymakers with high-resolution
information on where policy measures that promote equal housing affordability
opportunities are to be implemented.
7 SUMMARY AND CONCLUSIONS
Housing is commonly the single largest expenditure item for most households and
generally demands more than half the income of poor and near-poor families. In this
study, we develop measures (for the first time, to the best of our knowledge) by which
the state of housing affordability inequality could be summarized and examined.
Particularly, we adapt the Gini coefficient and Atkinson index methods for
estimating income inequality to the context of housing affordability and estimate the
factors that associate with the time-varying housing affordability inequality measures
in Israel over the period 1992–2011.
Results show that the time-varying household housing affordability Gini
coefficient and Atkinson index are positively correlated with average housing price
(in net income terms), controlling for changes in net income inequality and
macroeconomic conditions. Further, we detect considerable segmentation in housing
affordability for household head gender, household family status, household head
working status, number of household providers, and household geographical
residence.
As the state of housing affordability is a constant source of political interest,
our developed method for estimating housing affordability inequality and the
outcomes on its positive correlation with average housing prices and, further, its
capacity to identify socio-demographic segmentation in housing affordability may
assist policymakers in designing policies that would increase housing affordability
where it is particularly needed, thereby effectively reducing inequality and
segmentation in housing affordability.
Several major tasks face future researchers in this area. Methodologically, the
estimation of housing affordability potentially suffers from a bias caused by
household over- and under- consumption of housing. Refined measures of housing
affordability inequality may attempt to address this possible bias. Further, while there
exist various approaches for computing housing affordability, none of the prevailing
16
methods points to a formally derived threshold (benchmark) below which a household
is categorized as sub-affordable. Finally, empirically, a panel analysis of housing
affordability Gini coefficient across different economies may shed light on the
regimes and specific policies that are most effective in promoting housing
affordability equality.
17
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22
Exhibit 1: Housing Price-to-Net Income Ratio by Deciles, 1992–2011
Exhibit 2: Average Housing Price-to-Net Income Ratio, 1992–2011
Note: The dashed line in Exhibit 2 represents the regression line obtained from estimating 𝑃
𝑊𝑡= 𝑎! +
𝑎!×𝑡 + 𝑒𝑡, where t is a time period, 𝑎! and 𝑎! are parameters, and 𝑒𝑡 is a random disturbance term.
10
60
110
160
210
260
Price-‐to-‐Net Income Ra
:o
10% 30% 50% 70% 90% Average
75
85
95
105
115
125
135
145
Price-‐to-‐Net Income Ra
:o
Average P/W Regression Line (Average P/W)
23
Exhibit 3: Housing Affordability Gini and Net Income Gini Coefficients, 1992–2011
Exhibit 4: Housing Affordability Atkinson and Net Income Atkinson Indices, 1992–2011
0.29
0.3
0.31
0.32
0.33
0.34
0.35 Gini Coe
fficien
t
Housing Affordability Gini Net Income Gini
0.07
0.075
0.08
0.085
0.09
0.095
0.1
0.105
Atkinson
Inde
x
Housing Affordability Atkinson Net Income Atkinson
24
Exhibit 1: Housing Price-to-Net Income Ratio by Deciles, 1992–2011
Exhibit 2: Average Housing Price-to-Net Income Ratio, 1992–2011
Note: The dashed line in Exhibit 2 represents the regression line obtained from estimating 𝑃
𝑊𝑡= 𝑎! +
𝑎!×𝑡 + 𝑒𝑡, where t is a time period, 𝑎! and 𝑎! are parameters, and 𝑒𝑡 is a random disturbance term.
10
60
110
160
210
260
Price-‐to-‐Net Income Ra
:o
10% 30% 50% 70% 90% Average
75
85
95
105
115
125
135
145
Price-‐to-‐Net Income Ra
:o
Average P/W Regression Line (Average P/W)
25
Exhibit 3: Housing Affordability Gini and Net Income Gini Coefficients, 1992–2011
Exhibit 4: Housing Affordability Atkinson and Net Income Atkinson Indices, 1992–2011
0.29
0.3
0.31
0.32
0.33
0.34
0.35 Gini Coe
fficien
t
Housing Affordability Gini Net Income Gini
0.07
0.075
0.08
0.085
0.09
0.095
0.1
0.105
Atkinson
Inde
x
Housing Affordability Atkinson Net Income Atkinson
26
Table 1: Number of Observations on Individual Household Socio-Demographic Characteristics Quarters, 1992–2011
Notes: Observations indicated in Table 1 come from Household Income and Expenditure Surveys conducted by the Israel Central Bureau of Statistics. The 1994 data has been omitted because of a surveying error made by the Israel Central Bureau of Statistics in that year, where non-wage employed household heads were omitted from the survey. The original total number of observations over the 1992–2011 period was 246,015. Because of missing observations, the final sample included a total of 156,583 observations
73% 64% Wage employee Household Head Working Status
9% 12% Self employed 16% 19% Not working
1% 5% Other
28
Table 2 (continued): Household Socio-Demographic and Dwelling Unit Characteristics and Their Share in the Sample
Share in the Population Category
Household and Dwelling Unit Characteristics 2011 1992
12% 10% Academic profession
Household Head Occupation
12% 10% Technical 5% 6% Managers
13% 10% Office workers 16% 13% Agents, sales workers, and service workers
1% 28% Skilled agriculture workers 17% 5% Skilled industrial and construction workers
6% 10% Unskilled workers
18% 9% Other 1% 1% Agriculture
Household Head Industry
13% 23% Manufacturing 1% 1% Electricity and water supply 5% 7% Construction
11% 11% Wholesale and retail trade, and repairs 3% 2% Accommodation services and restaurants 6% 7% Transport, storage, and communications 3% 3% Banking, insurance, and other financial institutions
12% 7% Business activities 3% 5% Public administration
11% 7% Education 8% 5% Health, welfare, and social work services 4% 4% Community, social, personal, and other services 1% 9% Services for households by domestic personnel
18% 8% Other 14% 5% 5
Number of Rooms in a Dwelling Unit
2% 2% 4.5 30% 22% 4
6% 7% 3.5 33% 39% 3
5% 10% 2.5 9% 15% 2
11% 9% Jerusalem
Geographical Region of
Dwelling Unit
10% 14% Tel-Aviv 7% 7% Haifa
15% 19% Gush Dan 19% 19% Center 15% 12% South 11% 11% Sharon
9% 6% North 3% 3% Krayot
Note: Segments with an insignificant share in the sample (below 1%) are excluded from the table.
29
Table 3: List of Variables, Definitions, and Summary Statistics
Max Min Std Mean Definition Variable 3,040 893 554 2,053 Per quarter average monthly net
income (in dollars) W
137.48 92.39 10.97 112.29 Per quarter average housing price-to-net income
P/W
0.0168 0.0117 0.00134 0.0144 Per quarter average net income-to-housing price
W/P
55,887 9,662 12,324 32,857 Quarterly level of gross domestic product (in millions of dollars)
GDP
20,500 6,770 3,099 10,226 Per quarter number of housing construction ends
HE
1.4 -1.93 0.613 -0.051 The difference between two consecutive quarters of unemployment rate
ΔUR
1.28 -0.9 0.366 -0.019 The difference between two consecutive quarters of mortgage rate
ΔMR
5.2 -7.8 2.43 -0.02 The difference between two consecutive quarters of the rate of change of the construction index
ΔCI
3.6 -2.3 1.064 -0.132 The difference between two consecutive quarters of the 12-month bond rate
ΔBR
0.386 -0.375 0.15 0.018 The difference between two consecutive quarters of the new Israeli Sheqel-to-dollar exchange rate.
ΔEX
8310 -6140 1776 4.05 The difference between two consecutive quarters of housing construction starts
ΔHS
Note: Table 3 presents variable description and summary statistics for net income (W), housing price-to-net income ratio (P/W), net income-to-housing price ratio (W/P), and macroeconomic variables in equations (1) and (2). Testing for unit roots, we could not reject the hypothesis of a unit root in UR, MR, CI, BR, EX, and HS. We thus compute the first difference (between period t and t-1) for these variables and substitute those into the estimation of equations (1) and (2).
30
Table 4: Summary Statistics of Housing Affordability and Net Income Gini Coefficients and Atkinson Indices
Max Min Std Mean Definition Inequality Measure
0.352 0.294 0.0174 0.32 Housing affordability Gini coefficient GH 0.35 0.311 0.011 0.327 Net income Gini coefficient GW
0.101 0.070 0.0087 0.083 Housing affordability Atkinson index for ε=0.5
AH
0.1017 0.0789 0.0055 0.0873 Net income Atkinson index for ε=0.5 AW
31
Table 5: Outcomes Obtained from the Estimation of Equation (1)
Notes: Table 5 reports OLS regression results from estimating equation (1). The first column reports outcomes obtained from estimating the full model, while the second column reports outcome of stepwise procedure with 10% significance threshold. The t-values are in parentheses below the coefficients. Significant values at the 10%, 5%, and 1% levels are marked with one, two, and three asterisks, respectively.
Dependent Variable
(1) (2) (3) (4)Full Model Step-Wise Full Model Step-Wise
55%53% Overlap=71470.270.18Electricity and water supply
149760.360.27Construction
108890.300.26Wholesale and retail trade, and repairs
127870.340.26Accommodation services and restaurants
105780.310.28Transport, storage and communications
97770.280.26
Banking, insurance and other financial institutions
Relative Contribution to
GiniDecomposition
Component
Housing Price-to-Net Income Ratio
Housing Affordability
GiniCategoryHousehold
Characteristic
Household Head Working
Status
Household Head
Occupation
Household Head Industry
34
Table 6 (continued): Gini Coefficient, Price-to-Income Ratio, and Gini Decomposition According to Socio-Demographic Subgroups, 1992 versus 2011
Note: Data on household head industry and occupation have been collected only since 1995. Hence, Gini coefficients for the household head industry and occupation that appears in the 1992 column represents 1995 figures.
201119922011199220111992
102750.300.28Business activities
90630.300.23Public administration
130810.340.26Education
115790.340.28Health, welfare and social work services
