II. ESTUDIOS SOBRE LA FORMACIÓN PERIODÍSTICA EN ESPAÑA
3.3. Otras opciones barajadas para el análisis
As described in Section 2.3.1, a common way to proxy neighborhood quality or health in neighborhood change research is by using economic indicators, such as property value or the change in property value. Underlying this choice is the Hedonic Pricing Model, which asserts that the values of non- separable housing features (such as an additional bedroom or which school district the property belongs to) are capitalized into the price of the property.
This section will briefly outline hedonic pricing theory. It begins with an introduction to household sorting theory, which is presupposed by hedonic price theory. Hedonic pricing theory is introduced next, as well as a short discussion of potential modeling issues and possible solutions.
123
Household Sorting
Household sorting is the tendency for individuals (or households) to divide themselves into homogeneous communities. These “communities” are usually envisioned at the neighborhood or municipal scale. There are two major models of household sorting as advanced by Tiebout (1956) and Alonso (1964).
The Tiebout hypothesis of household sorting is based upon households “voting with their feet” to choose their preferred household location. They choose the community that offers the mix of public goods and taxes that best fits their preferences (Tiebout, 1956). This model presupposes that homebuyers are (perfectly) mobile, have perfect information, have a choice of communities characterized by various combinations of public goods and taxes, and can recognize the differences between them (Fischel, 2001).
A wide array of econometric studies providing evidence to support the Tiebout model have been carried out, beginning with Oates’ 1969 study of New Jersey communities. These studies measure capitalization79 of various local services into home values. A survey of the various empirical studies of
Tiebout capitalization can be found in Dowding, John, and Biggs’ 1994 article. The article refers to several studies which have shown evidence for household sorting by race, homeownership, population density, income and age.
The second theory of urban household sorting is Alonso’s (1964) generalization of Von Thünen’s (1826) locational theory, which posits that bid-rent functions can be used to determine household locations as a function of income. The original model assumes a monocentric city which contains all employment in its central business district and has consistent transportation costs for all households (Alonso, 1964). Hanushek and Yilmaz’s 2007 article lists an array of empirical studies that support Alonso’s hypothesis. While most empirical studies have examined either the Tiebout or the Alonso model of household location, Hanushek and Yilmaz incorporate both. Contrary to the Tiebout model, which bases location choice on household preference, as well as to Alonso’s assertion that locations are determined by income, real jurisdictions are determined by mixtures of income and preferences. Hanushek and Yilmaz constructed a theoretical model, which contained high and low income households, each of which had either high or low valuation of education. It was seen that the two theories complement one another and have results that are more consistent with what is observed empirically (Hanushek & Yilmaz, 2007). De Bartolome and Ross also created a monocentric model with two jurisdictions that showed both jurisdictional and transportational differences to be incorporated into house values, explaining empirical intrajurisdictional income mixing (2003).
These models, and extensions thereof, posit that households move to communities that best satisfy their preference mix. A large number of empirical studies lend strong support to this theory (see Dowding et al., 1994 and Hanushek & Yilmaz, 2007 for examples). It should be noted, however, that these models are based on assumptions of perfect mobility and perfect information, among others. Any deviations from these assumptions must be taken into account when constructing models and interpreting results.
79 Capitalization is the incorporation of the value of local services and amenities (and other factors) into the value of the product—in this case the house.
124
Hedonic Pricing
Hedonic pricing, a type of regression analysis, is often used to determine the effect of specific characteristics on housing values. Said another way, housing can be conceptualized as a “bundle of attributes” (Rosen, 1974). Hedonic pricing is then used to infer the marginal value (price) of individual attributes of properties in specific real estate markets. Hedonic pricing models are constructed by estimating a regression with purchase price or assessed value as the dependent variable. This dependent variable is regressed on a set of independent variables that represent the attributes that comprise the whole, as well as a term representing the time of the valuation if necessary (Meese & Wallace, 1997). By regressing various amenity and disamenity levels on prices, one can determine the marginal willingness to pay for these amenities.
This subsection describes the theoretical origins of hedonic pricing, discusses the specifics for hedonics applied to housing, introduces the model’s functional form, and reviews common methodological issues and ways to remedy them.
Economic theory states that the value of future costs and benefits associated with an asset will be reflected in the value of that asset; in other words, projected future values are capitalized into the present value (Fischel, 2001). The concept of capitalization is closely related to hedonic pricing theory, in that for any factor capitalized into the price of a property, one can determine the implicit price of the capitalized factor using a hedonic pricing model, given that sufficient data are available.
Development of the hedonic pricing method is generally attributed to Griliches (1967) and Rosen (1974), while the first housing capitalization study was done by Oates (1969). Oates tested Tiebout’s hypothesis of household sorting against empirical evidence drawn from New Jersey communities and found that the tax rate was negatively capitalized into home values while the public school expenditure rate per student (a proxy for school quality) was positively capitalized (Oates, 1969). Since then hedonic pricing models have been used to investigate the implicit prices of a wide variety of phenomena, including, for example, tax rates (Palmon & Smith, 1998), school quality (Black, 1999; Brasington & Haurin, 2006; Goodman & Thibodeau, 1998; Jud & Watts, 1981), crime (Tita, Petras, & Greenbaum, 2006), land scarcity (Jud & Winkler, 2002), expected future economic growth (Smith, 2006), and noise pollution from airports (Püschel & Evangelinos, 2012)
Applied to housing, the attribute (independent) variables include can be divided into four categories: (1) structural qualities that vary from house to house, such as age, lot size, and the number of bathrooms; (2) socioeconomic characteristics of the surrounding area, such as poverty rate, race, and education levels; (3) jurisdictional characteristics such as school quality and the local property tax rate; and (4) locational characteristics such as promixity to the central business district, major transportation routes, and environmental amenities and disamenties (e.g. landfills, waterfront location, heavy industry) (Bowen et al., 2001; Li & Morrow-Jones, 2010). Many researchers include change variables, such as the change in poverty rate, to capture neighborhood change in the recent past and the possible impacts of policy interventions, both of which may influence housing price (Li & Morrow-Jones, 2010). When the model includes observations across multiple years, a time variable can be included to account for inflation and market trends in house prices over time.
A major advantage of hedonic pricing models is the ability to determine the marginal willingness to pay for various housing and community attributes. For example, it is likely difficult to determine the
125 disamenity value of living in a community affected by airport noise pollution. One possibility would be to ask residents how much they would need to be compensated to move there. But this process would be highly labor-intensive, and in many cases people do not actually know what avoiding this disamenity is worth to them. A simpler and cleaner solution is to create a hedonic pricing model using real market data instead of hypothetical statements by respondents that includes both properties affected and unaffected by airport noise pollution, and examine the significance and magnitude of the noise pollution coefficient. To do so, one needs only data on home values, whether a property is affected by noise pollution or not, and the appropriate control variables.
The basic functional form of a hedonic pricing model is shown in Equation (3.1), where P represents the price or value, and f is a function of S, structural characteristics of the property; E, socioeconomic characteristics of the surrounding area; J, jurisdictional characteristics; and L, locational characteristics. From this function, the price of any characteristic of the property can be determined by taking the partial derivative of the equation with respect to the characteristic. Equation (3.2) shows Equation (3.1) translated into standard econometric form, where 𝛽0 represents the intercept, and 𝑋𝑠
,
𝑋𝐸,
𝑋𝐽,
and 𝑋𝐿 represent vectors of structural, socioeconomic, jurisdictional, and locational characteristics,
respectively. 𝛽𝑠
,
𝛽𝐸,
𝛽𝐽,
and𝛽𝐿 represent the implicit marginal prices of the aforementioned vectors of characteristics—that is, the regression coefficients—and µ represents the error term.𝑃 = 𝑓(𝑆, 𝐸, 𝐽, 𝐿)
(3.1)
𝑃 = 𝛽
0+ 𝛽
𝑠𝑋
𝑠+ 𝛽
𝐸𝑋
𝐸+ 𝛽
𝐽𝑋
𝐽+ 𝛽
𝐿𝑋
𝐿+ 𝜇
(3.2)
Despite the inclusion of locational characteristics, there may be additional spatial determinants of house prices that are not included in the model. There are two spatial concepts necessary to understanding these. The first is spatial heterogeneity, where there may be variation in price due to the absolute location of a property within the study area. This is evidenced by variation in the mean, variance, or covariance across the study area (Bowen et al., 2001). An example of spatial heterogeneity would be a study area where older properties in one area have high prices while older properties in another area, perhaps more isolated from the central city or of a less desirable architectural style, have lower prices. In this case an indicator for the age of the house would not capture this dependency. The second concept is spatial dependence, where the interdependence of prices is due to the relative locations of properties. That is, spatial dependence occurs where prices “follow” the prices of nearby properties, with the result being a spatially correlated error term (Bowen et al., 2001). A simple example of spatial dependence is the use of comparables in real estate pricing; that is, properties are priced based on the prices of similar, nearby properties. Thus, real estate prices are likely to “follow” one another, but due to a reason that is not incorporated in the model represented in Equations (3.1) and (3.2).
To address possible spatial heterogeneity and spatial dependence, it is possible to add a spatial congruity matrix, W, to Equation (3.2). The matrix includes wjk elements, where j and k index all
126 observations in a pairwise fashion, and wjk represents the spatial relationship between observation j
and observation k.80 W can be incorporated into the hedonic pricing model as shown in Equation (3.3):
𝑃 = 𝛽
0+ 𝛽
𝑠𝑋
𝑠+ 𝛽
𝐸𝑋
𝐸+ 𝛽
𝐽𝑋
𝐽+ 𝛽
𝐿𝑋
𝐿+ 𝜌W𝑃 + 𝜇
(3.3)
where W𝑃 represents the spatial relationships between observations and ρ is the spatial autoregressive coefficient. If ρis significantly different from zero, it indicates the spatial relationship specified in W accounts for some variation in property prices and thus must be included in the model to prevent underspecification.81
When spatial correlation is present, but not accounted for in the model, it is incorporated into the error term, µ, resulting in an improperly specified µ. The impacts of this are manifold: marginal price estimates may be biased; the intercept estimate will be biased; error terms may be severely misestimated; and the estimate of the standard error of marginal price estimates will be biased. Together, the result is that the confidence intervals and hypothesis tests based on the model’s estimates will be misleading (Bowen et al., 2001).
Several diagnostic tools exist for determining whether spatial autocorrelation is an issue, including the use of variograms, the Moran’s I measure, and the Geary’s C measure. The results of these diagnostics determine whether a specific model requires the incorporation of spatial variables.
In addition to deviations from the model’s assumptions, there are some important methodological issues to consider when developing a hedonic pricing model. These include the choice of indicators, multicollinearity, and selection bias. These issues are discussed in the remainder of this subsection. Roback states, “theory does not tell us which attributes are goods; theory only tells us how people behave with respect to goods” (1982). That is, hedonic pricing theory itself does not provide any guidance as to which characteristics to include in a hedonic pricing model; rather, the theory simply requires a fully-specified model. That is, all characteristics that have a significant effect on prices must be included in the model. As it is not possible to know which characteristics are significant a priori, the researcher depends on previous research, experience, and to some extent luck when it comes to selecting characteristics for a hedonic pricing model (Bowen et al., 2001; Roback, 1982). Of course, data availability plays a role in model specification as well.
A second issue in variable selection is multicollinearity, or when variables are highly correlated with one another. When variables displaying a high degree of multicollinearity are included in a regression, small changes in the indicator values can result in drastic changes to the coefficient estimates for these indicators. Thus, while many indicators may influence the asset price (the dependent variable in hedonic regressions), in many cases it is not possible to include all of them due to these issues. For example, in this research, the female-headed household rate and the poverty rate are highly correlated. Thus only one may be included in the hedonic model without casting significant doubt on the interpretability of the coefficient estimates.
80 There are several ways to specify this spatial relationship; see Bowen, Mikelbank, & Prestegaard, 2001. 81 It is important to note that ρ only indicates whether the W chosen is significant, not whether there is any form of significant spatial dependence in the model. See Bowen et al., 2001 for more discussion of this.
127 Gatzlaff and Haurin describe the problem of sample selection bias in property hedonic pricing models, demonstrating that in many instances the set of homes that are sold cannot be presumed random (1998). For example, during the foreclosure crisis, foreclosed homes often cycled through many transactions, while activity in the traditional residential market slowed well below normal levels. A solution, the censored regression technique, is outlined where data for unsold properties is used to determine the probability of a sale, resulting in a selection bias correction variable that is incorporated to generate an unbiased estimate (Gatzlaff & Haurin, 1998).
Extension to the Community Level
This research investigates the effects of policy interventions on neighborhoods and communities, rather than the effects on individual households or properties. Thus, the quantitative model used in this research examines the effects of policy interventions in the real estate submarkets found in Cuyahoga County, Ohio. To do so, a hedonic pricing model is created at the Census Tract level, a proxy for communities, rather than at the property level. This means that the dependent variable is based on the total residential property value at the Census tract level, instead of using the values of individual properties. This extension is not problematic as the underlying theory is the same, where supply and demand determine prices and the slope of the demand curve reveals marginal willingness to pay. For examples of research using this approach, see Buettner & Ebertz (2009), Roback (1982), and Rosen (1979).
General Equilibrium
General equilibrium is a theoretical economics concept, which asserts that there exists a set of stable prices in an economy that results in a stable equilibrium; that is, a situation where prices and demand levels are stable. Further, economic theory asserts that in cases of non-general equilibrium, market forces will, in the absence of external shocks, move prices and demand levels toward general equilibrium.
General equilibrium is an ideal state, rather than a true representation of real markets. Thus, all applications of econometric models deviate from the abstraction of general equilibrium to some extent. What is important is to consider the extent of the deviations and their impact on model results. To meet the requirements of general equilibrium, prices and demand levels must be stable. In the case of the foreclosure crisis, which is examined in this research, the assertion that prices and demand levels for housing are stable is clearly false. However, one can assert that even during times of market instability, the market is moving toward general equilibrium.
In particular, three assumptions of hedonic pricing theory are violated in the model used in this research: (1) perfect mobility, (2) perfect information, and (3) land scarcity. The first asserts that residents have perfect mobility—that is, no moving costs—when determining their housing location. This assumption can obviously never be met, but in the case of the foreclosure crisis mobility was more greatly restricted. In 2013, Jim Rokakis estimated that 40% of Cuyahoga County homeowners owed more on their mortgages than the value of the property (Pagonakis, 2013a), meaning that these homeowners were essentially immobile. Secondly, the perfect information assumption means that all homeowners and homesellers have perfect information on all houses, with no cost of attaining this information. Again, this assumption is clearly an ideal that is not achieved in reality. In the case of this research, the deviation is greater than that typically seen on the real estate market. As will be
128 discussed in Section 4.2.3, the housing market in Cuyahoga County was essentially comprised of two separate markets during and after the foreclosure crisis: a sluggish market with “normal” property prices and a more active market for properties affected by foreclosure, sold at immense discounts. In the foreclosure-impacted market in particular, potential purchasers have particularly poor information, resulting in market distortions. Finally, the third assumption states that land is a scarce good. In the case of Cuyahoga County, there is an oversupply of land—in 2013 there were over 26,000 vacant properties (Pagonakis, 2013b). This weakens the assumption substantially.
This research examines a weak market city during a recession, which implies that hedonic estimates will be lower than those seen in strong market cities and during boom times. Despite this, these depressed prices do accurately reflect amenity values in Cuyahoga County during the study period. The caveat is that these estimates cannot be expected to hold during other parts of the housing and economic cycles, nor in strong market cities. A second caveat is based on Mikelbank et al.’s (2008) article The Sky Isn’t Falling Everywhere, which provides strong evidence for the existence of two submarkets in Cuyahoga County: one dominated by the impacts of foreclosures and a much smaller submarket consisting of properties (relatively) untouched by the foreclosure crisis. It was not possible to create two quantitative models to separately represent each of these markets. Instead, one