The accuracy of self-reported dwelling valuation

Journal Pre-proof The Accuracy of Self-Reported Dwelling Valuation Aviad Tur-Sinai , Larisa Fleishman , Dmitri Romanov PII: DOI: Reference: S1051-1377(17)30046-3 https://doi.org/10.1016/j.jhe.2019.101660 YJHEC 101660 To appear in: Journal of Housing Economics Received date: Revised date: Accepted date: 3 February 2017 5 November 2019 18 November 2019 Please cite this article as: Aviad Tur-Sinai , Larisa Fleishman , Dmitri Romanov , The Accuracy of Self-Reported Dwelling Valuation, Journal of Housing Economics (2019), doi: https://doi.org/10.1016/j.jhe.2019.101660 This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Inc. ฀฀฀฀฀฀฀฀฀ Highlights  Self-reported estimates of dwelling values are higher than the mean market prices.  People who occupy dwellings in the lowest eight deciles of prices are upward-biased.  People who live in the most expensive dwellings understate the value of their homes.  The self-reported valuation bias is systematically associated with owner's traits.  The frequency of dwelling sales has an effect on the self-reported valuation bias. 1 ฀฀฀฀฀฀฀฀฀ The Accuracy of Self-Reported Dwelling Valuation Running head: Self-Reported Valuation Bias over the Distribution of Dwelling Prices Aviad Tur-Sinai Department of Health Systems Management, The Max Stern Yezreel Valley College, Yezreel Valley, Israel & University of Rochester Medical Center, School of Nursing, NY, USA Email: [email protected] ORCID: 0000-0002-4802-455X (Corresponding author) Larisa Fleishman Israeli Central Bureau of Statistics Email: [email protected] Dmitri Romanov Israeli Central Bureau of Statistics Email: [email protected] Corresponding Author: Aviad Tur-Sinai, Ph.D. Tel: 972-50-5315682 Fax: 972-4-6423522 E-mail address: [email protected] The Max Stern Yezreel Valley College, Yezreel Valley, 1930000, Israel 2 ฀฀฀฀฀฀฀฀฀ Abstract Owners‘ valuations of dwelling prices are central in the construction of price indices and households‘ economic behavior. We analyze the variation of the self-reported valuation bias over the distribution of dwelling sale prices, using a dataset of observations from a Household Expenditure Survey merged with the national sample of housing sale transactions by census tract. We find that self-reported estimates of dwelling values are, on average, 20% higher than the mean market prices of houses in the corresponding census tracts. Estimates reported by people who occupy dwellings in the lowest eight deciles of the price distribution are upward-biased, whereas those who live in the most expensive dwellings more typically understate the value of their homes. The self-reported valuation bias is systematically associated with owner's traits and with dwelling and neighborhood characteristics. Misspecification might be another potential explanation for that bias. The frequency of dwelling sales in the respondent's tract was found to have an effect on the self-reported valuation bias. Key words: sale price, subjective asset valuation, census tract, hedonic price model JEL Codes: P22, R20, R21 3 ฀฀฀฀฀฀฀฀฀ 1. Introduction The value of a dwelling in the free market may be estimated in several ways: by a professional appraiser, by setting a price in a sale transaction, and according the property‘s owner subjective judgment. Among these methods, sale price in the free market is considered the best estimate of a dwelling‘s value, consistent with the conventional definition of the American Institute of Real Estate Appraisers (1988). In economic research, however, the use of subjective valuations by property owners is more common, for two main reasons. First, information about sale prices usually originates in reportage to the tax authorities, which usually fails to provide researchers with data that offer sufficiently large samples at an appropriate spatial resolution to meet research needs. Second, many surveys report the subjective valuation of a dwelling together with characteristics of the property and its owner—information that is seldom available in the sale-transaction data that are reported to the tax authorities. Obviously, then, owner valuations elicited by surveys are very useful provided that they furnish an unbiased estimate of the prices of dwellings if the dwellings were sold that very day. Hence the immense importance of a study that tests the extent of accuracy of subjective dwelling valuations, the differences between these valuations and appraiser‘ estimates and sale prices, and the factors associated with these differences. The accuracy of subjective dwelling valuations has been researched for nearly five decades, mainly on the basis of U.S. data. Although the estimates of the bias range from minus 2 percent to 16 percent, it would be fair to sum up by saying that in most scholars‘ opinion, dwelling owners tend to overvalue their properties by about 5 percent. This study augments the research literature on this topic in several ways. First, we focus on investigating the accuracy of subjective valuations across a distribution of dwelling values. Research thus far has not addressed the issue of whether the valuations of inexpensive and expensive properties are biased in the same direction and whether the bias is homoscedastic. Second, the study is based on a unique database that covers more than a decade and combines dwelling valuations culled from a large national survey with data on sale transactions at the level of census tract. Third, along with the dwelling and owner indicators that the survey provides, we augment the analysis with demographic 4 ฀฀฀฀฀฀฀฀฀ and socioeconomic indicators of the population of the census tract and the spatial environment of the dwelling. This allows us to see whether misspecification may be a potential explanation for dwelling valuation bias. Fourth, given information about the change in transaction prices in a census tract over time, we investigate the correlation between the dwelling valuations reported in the survey and dwelling prices in the tract within a one-year window before and after the date of participation in the survey. Thus, we determine how long it takes for homeowner valuations to internalize ―news‖ about housing prices in the neighborhood. The rest of this paper is organized as follows: Section 2 presents theoretical background on the accuracy of subjective dwelling valuations. Section 3 describes our sources of information, defines the variables, and presents descriptive statistics. Section 4 presents the statistical models. Section 5 gives the results; Section 6 discusses them and concludes. 2. Theoretical background The ramified research literature on various aspects of dwelling values bases its conclusions on the valuation of dwellings by their owners. The data for these studies originate in a large number of household surveys that ask, ―What do you think your home is worth? That is, what do you think you could get for your home if you sold it now?‖ 2.1. Accuracy of subjective valuations The accuracy of subjective dwelling valuations has been examined in a number of studies that focus on the investigation of two main questions. The first is how to measure the extent of accuracy. The second question asks why subjective dwelling valuations differ from the benchmark chosen for the comparison. Earlier studies focused on validating homeowners‘ subjective valuations as an estimate of their dwellings‘ ―true‖ value and compared owners‘ subjective valuations with those of appraisers (Kish and Lansing, 1954), with valuations for the purpose of real-estate taxation (Robins and West, 1977), and with subjective valuations by owners of other properties (Follain and Malpezzi, 1981). In 5 ฀฀฀฀฀฀฀฀฀ particular, Ihlanfeldt and Martinez-Vazquez (1986) found that subjective dwelling valuations are upward-biased, whereas Follain and Malpezzi (1981) found them to be downward-biased. Other studies tackle the subject by comparing self-reported dwelling value with sale prices in transactions consummated (Kiel and Zabel, 1999; Benitez-Silva et al., 2009), or predicted market price estimated by a standard hedonic model (Kuzmenko and Timmins, 2011). The findings show that, on average, homeowners tend to evaluate their properties above the market. 2.2. Sale transactions vs. subjective valuation—methodology issues Every seller in the housing market sets an asking price. The asking price represents an opening position in bargaining with the potential buyer of the property (Arnold, 1999). Accordingly, it should exceed or at least be equal to the threshold price at which the seller is willing to sell the property; otherwise, the transaction will not be consummated (Quan and Quigley, 1991). People often demand much more to ‗give up‘ an object (Willingness-to-Accept - WTA) then they would be willing to pay to acquire it (Willingness-to-Pay – WTP) (Kahneman et al., 1991). This phenomenon called by Thaler (1980) as an endowment effect, could drive home owners to attach excessively high values to their property (Huck et al., 2005). Thus, people value their own houses more than is justified by what the market will pay. Moreover, Hovenkamp (1991) claims that the WTA-to-WTP ratio is much higher for poor than it is for the rich. Kain and Quigley (1972) found that homeowners who answered an item relating to property value typically had higher levels of schooling and income, younger age, and less longevity as homeowners. They also found that the response rate among owners of inexpensive properties exceeded that of owners of expensive dwellings. Gonzalez-Navarro and Quintana-Domeque (2009), in contrast, found no relation between item non-response, dwelling value and homeowner characteristics. DiPasquale and Somerville (1995) found that the closer the purchase of the property is to the survey date, the more accurate the subjective valuation of the dwelling becomes. In contrast, Kiel and Zabel (1999) found a longer term of ownership results in greater accuracy in dwelling valuation; whereas Agarwal (2007) claims that a shorter term of ownership increases the likelihood of an upward valuation bias. 6 ฀฀฀฀฀฀฀฀฀ Subjective dwelling valuations are based on different levels of importance that homeowners attribute to a wide range of dwelling indicators and aspects, including physical-structural characteristics, location characteristics, neighborhood quality, and environmental utilities and disutilities (Hu, Geertman, and Hooimeijer, 2014). The marginal contribution of these indicators to dwelling value is usually estimated in a hedonic price model pioneered by Rosen (1974). The factors related to subjective dwelling valuation may be sorted into several groups. The first group includes structuralphysical characteristics of the property, e.g., lot size for low-rise dwellings, dwelling floor space, number of bathrooms, heating and air-conditioning systems (e.g., Emrath, 2002), number of floors in the building (Zabel and Kiel, 2000), and fireplace, terrace, and parking (Arguea and Hsiao, 2000). The second group of factors relates to homeowner characteristics such as ethnic origin, age and income (Coate and Vanderhoff, 1993; Kiel and Zabel, 2008), schooling and gender (Kiel and Carson, 1990), marital and employment status (Ihlanfeldt and Martinez-Vazquez, 1986). The third group is composed of environmental utility and disutility factors, such as proximity of dwelling to open spaces and bodies of water (Emrath, 2002), exposure of dwelling to road noise (Nijland and Wee, 2008), proximity to an airport (Ihlanfeldt and Martinez-Vazquez, 1986). The fourth group includes location characteristics such as good access to public transport (Emrath, 2002) and location of dwelling relative to city center (Kiel and Carson, 1990). Most researchers who use subjective dwelling evaluations, base themselves on Goodman and Ittner (1992) and Kiel and Zabel (1999), who show that the difference between subjective valuation and transaction prices does not systematically correlate with dwelling indicators, dwelling location, or homeowner indicators. Kain and Quigley (1972) found that homeowner‘s schooling is the only variable that correlates significantly with the difference between subjective dwelling valuation and appraiser‘s estimate. Others claim, however, that the use of subjective-evaluation data is suitable for certain purposes only. Steele and Goy (2002) and Rouwendal and Alessie (2002), for example, use subjective housing valuations as an indicator of change in dwelling prices over time but are reluctant to use such valuations as an indicator of price level. . 7 ฀฀฀฀฀฀฀฀฀ 2.3. Reasons for the bias in subjective valuation The finding of most of the studies is that owners‘ valuation of their properties is upward biased by around 5 percent on average, although estimates of the bias size fall into a broad range from –2 to 16 percent (e.g., Goodman and Ittner 1992). Moreover, the bias may also vary over time, principally during the periods of significant movements in housing market (Anenberg, 2011). As to the reasons for the bias in subjective valuations, various studies yield clashing findings. For example, according to Agarwal (2007), a downward bias is typical for older homeowners and those of higher income. Ihlanfeldt and Martinez-Vazquez (1986) find a significant relation between the bias in subjective valuation and homeowner characteristics and property indicators. Similarly, Benitez-Silva et al. (2009) find that accuracy in subjective housing valuation correlates with homeowner‘s schooling and income and fluctuates with economic conditions in the housing market at the time the dwelling is purchased. Kuzmenko and Timmins (2011) show that the bias in self-reported values are correlated with variables typically included in hedonic models, indicating potential problem of biased coefficients estimated in these models. Goodman and Ittner (1992), in contrast, find no relation between characteristics of the property or the residential area and bias in subjective dwelling valuation. Gonzalez-Navarro and QuintanaDomeque (2009) find that homogeneous building in a neighborhood considerably adds to the accuracy of the subjective valuation of a property situated in that neighborhood. 3. Database and descriptive statistics This study is based on data from Household Expenditure Surveys for the years 1997–2008. The survey is conducted annually by the Israel Central Bureau of Statistics on the basis of a national sample of more than 6,000 households. Since our study focuses on examining the extent of accuracy of homeowners‘ subjective valuations, it includes only owner-occupier households, which account for 71 percent of the survey population. The survey data furnish much information about demographic, social, and economic indicators of the household and its head, who is determined by the members of the household, and also characteristics of the property. 8 ฀฀฀฀฀฀฀฀฀ The survey data were matched with information about sale-transaction prices by census tracts. The sale-transaction file is obtained by the Central Bureau of Statistics from tax authorities on an ongoing basis. In 1997–2008, the pooled file contained 612,000 transactions. 3.1. Database construction The consolidated file of twelve survey years includes 72,400 household records. In the first stage, the records were geo-referenced by a GIS system at the level of structure and census tract: 63,300 records were anchored, while 9,100 records—representing, largely, a population living in small and rural localities and collective communities, in which there is no regular housing market— were deleted from the file. Next, 18,000 records of households that occupied housing not their own were dropped from the file. The survey question that relates to dwelling valuation is, ―What sum could you obtain if you sold the dwelling today?‖ The respondent is asked to give a point estimate, i.e., without choosing within a range of values pre-specified in the questionnaire. The valuations are usually expressed by respondents in dollar terms; they are translated into the local currency (NIS—New Israel Shekel) terms during data editing. Of 45,300 geo-referenced records of owner-occupier households, around 7,000 respondents provided no information about the value of their dwellings; these cases were deleted from the file. The item non-response rate for the subjective-valuation question was 15 percent on average in the research period but was found to have trended up over the years, from 5 percent in the late 1990s to 24 percent in 2007 and 30 percent in 2008. Then, 2 percent of the observations were excluded due to outlier subjective valuation (under NIS 150,000 and over NIS 3,200,000). Concurrently, 2 percent of outlier observations of transaction prices (under NIS 75,000 and over NIS 3 million) were also deleted from the national file of sale transactions from which an average dwelling price by census tract is calculated. After removing the outlier observations, we linked each record in the survey to an average price of transactions carried out in the same census tract in the three months preceding the survey interview. Of the 37,800 sound records in the survey, 26,700 were linked to an average transaction price in a given census tract at a three-month lag. The research population in the final file added up to 21,238 9 ฀฀฀฀฀฀฀฀฀ observations relating to the sixty largest cities in the country (where 68 percent of the population of Israel lived in 2007). A general note about the representativeness of the Household Expenditure Survey and the legitimacy of pairing the survey observations with the average dwelling price by census tract is in order. It deserves emphasis that spatial spread of the survey sample does not correspond to the distribution of dwelling values. This is due to the random-systematic sampling of dwellings in all localities countrywide, which assures the same ultimate probability of a dwelling being sampled among all dwellings1 In other words, local averages prices should be interpreted as a noisy signal of a specific value that an owner is asked to estimate. Thus, each annual sample accurately represents the population of dwellings in Israel. Furthermore, as the observations in the survey sample are placed in census tracts by random selection, they should be representative, within the expectation, of housing conditions and average dwelling value in each region individually. Thus it is justified to compare the subjective dwelling valuations in the survey sample with the average transaction price in the census tracts where the survey respondents dwell. 3.2. Choice of time window for comparison of subjective valuations and transaction prices Previous studies that compared the accuracy of subjective valuations with transaction prices did so in different windows of time, paying no explicit attention to the question of the interval of time in which ―news‖ about transaction prices in the survey respondents‘ residential environment ―trickle down‖ to individuals‘ dwelling evaluations. This question is definitely a topic for a separate study. We have no specific information that can point to a mechanism of internalizing ―news‖ about the state of the housing market in the individual‘s neighborhood in estimates of the value of her dwelling. We can, however, look into the variation of a correlation between subjective valuation by the survey participants and the sale-transaction prices over time and choose an optimum time lag for the analysis of the factors that affect the accuracy of the subjective evaluations. 1 For further details about the sampling method used in the Household Expenditure Survey, see Household Expenditure Survey 2007, CBS, 2009. 10 ฀฀฀฀฀฀฀฀฀ In practice, we linked every observation in the survey to an average price of sale transactions in its census tract during the periods of 0-3, 4-6, 7-9, and 10-12 months before the date of the survey interview. This examination was done for various deciles of distribution of subjective valuations, because we assumed that there are differences in the pace of pass through from obtaining information about the value of dwellings in the residential surroundings and the individual‘s formulation of her subjective valuation, and these differences correlate with housing value. Table 1 shows the correlation between subjective valuation, expressed in the survey, and the average price of transactions in the census tract where the dwelling is located, at various periods of time before the survey reportage. (Table 1 about here) That table shows that for each period, the correlation is greater at the extremes of the valuation distribution than in the middle of the distribution. At each point of the valuation distribution, the correlation coefficients for different periods are dispersed in a range of roughly 0.05, with wider dispersion at the extremes of the distribution. Two periods, 0-3 months and 7-9 months before the reported valuation in the survey, stand out in terms of a stronger correlation between valuation and average transaction price in the census tract for the same number of deciles in the valuation distribution. In reference to all time windows, the correlation is stronger at the extremes of the estimated value distribution than in the middle. Thus, in the 7-9 month period the coefficient of correlation is highest for inexpensive dwellings in the main. Yet, compared with the 7-9 month period, the coefficient of correlation in the period of three months before the survey is also higher in deciles 4 and 9 and also attains higher statistical significance for most of the valuation distribution. Thus, three months before the survey is the period of time for which the rest of the study will be performed. 3.3. Bias in subjective valuation Figure 1 contrasts subjective dwelling valuations, reported in the survey, with the average price of transactions in a census tract across the distribution of dwelling prices (Figure 1A). This picture reflects a great deal of variance in the extent of (in)accuracy of the subjective valuations as against the prices of dwellings actually sold. In particular, one may see that an upward bias in valuation is typical 11 ฀฀฀฀฀฀฀฀฀ of people who live in dwellings that are valuated in the lowest eighty percentiles of the distribution; it reaches more than 50 percent at the lowest decile of the distribution (Figure 1B). In contrast, the subjective valuation is downward biased in the uppermost decile of the dwelling-price distribution and comes to roughly (-) 5 percent in the uppermost percentile. The average bias is about 20 percent; the bias of the median-priced dwelling is 8 percent. Furthermore, Figure 1B shows that the bias is highly heteroscedastic at the low end of the distribution of dwelling prices, whereas variance declines slowly in the upper 70 percentiles of the distribution. (Figure 1A and Figure 1B about here) Figure 2 completes the picture in Figure 1 and presents the bias in subjective home valuation (Yaxis, in percent) across the distribution of home prices by years. The figure shows that owners of relatively inexpensive homes (second decile) typically over-value their dwellings, the size of the bias ranging from 30 percent to 50 percent over the years. Interestingly, in this decile there was a perceptible increase in the bias in 2001–2003, which were down years in the Israeli housing market. In contrast, valuation bias among owners of expensive (ninth decile) dwellings varied within a narrower range of 0–13 percent, with a downward trend over the years. The bias in subjective home valuation in the fifth decile was 10–30 percent, with a downward trend after 2005. From the data in Figure 2, one may infer that the distribution of bias in home valuation was rather stable during the research years. Therefore, as the study continued, the analysis was conducted for the research years en bloc. (Figure 2 about here) From the foregoing figures, one may infer the existence of a bias in subjective estimation of dwelling value in comparison with market price. In addition to this descriptive picture and before estimating models to test for the precipitants of the bias, we performed a preliminary statistical test to show that subjective valuation is indeed biased relative to market prices. Namely, we estimated a univariate regression model for subjective valuation of dwelling i in statistical tract j (Evaluationij) as a function of mean transaction price in the same tract (Pricei). We also estimated the model for an inverse relation, i.e., mean transaction price in a statistical region as a function of subjective valuation. The results of the estimations in these models—α= 5.50, β=0.58, α= 4.61, β=0.66, respectively— 12 ฀฀฀฀฀฀฀฀฀ allowed us to reject the null hypothesis (α= 0, β=1) which assumes the absence of bias, and to infer the existence of bias in subjective valuation relative to market price. 3.4. Descriptive statistics Before discussing the variables used in our analysis, it is instructive to learn about the dynamics of dwelling prices in Israel over the research period. Figure 3 depicts the indices of ex ante average dwelling price for the selected percentiles of the dwelling-price distribution over the years. (Figure 3 about here) The prices of inexpensive dwellings (second decile) generally decreased since 1999, while the prices in the middle of the distribution rose moderately over the last decade. In contrast, the prices of expensive dwellings (ninth decile) soared by more than 50 percent during the research period. This rapid growth may serve an explanation for a downward bias in the subjective dwelling valuations of owners of expensive dwellings, who may not have kept up with the pace of increase in the prices of their properties. Basing ourselves on the findings of the earlier studies discussed in Section 2, we selected and defined variables for both analysis of the accuracy of subjective valuations and quality adjusted house values at the census tract level. Some of the variables are self-evident; others require explanation. Table 2 defines the variables that we used in the study and presents their means and standard deviations. (Table 2 about here) In the group of variables that represent the characteristics of a dwelling, we defined the Repairs variable as denoting dwelling-renovation investment in the twelve months preceding the survey date, including interior modifications of dwelling structure, closing of terraces, construction of walls, and replacement of flooring, kitchen cabinets, etc. The group of variables representing physical characteristics of homes that have been transacted during the research period at the level of census tract includes five ‗THFirstHand‘ variables. Each of these variables indicate the time lag between the year of dwellings‘ construction and year of its transacting by building company, ranging from one year to five years or more. There are observable differences in sell prices of ‗first-hand‘ dwellings 13 ฀฀฀฀฀฀฀฀฀ transacted as a function of marketing time: the shorter is the duration of marketing time of residential housing, the higher sell prices are expected for dwellings to be transacted. The group of variables that reflect homeowner and residential-area indicators includes variables for ethnic affiliation and immigrant status. The Jewish population accommodates ethnic groups of Sephardi and Ashkenazi origin. There are perceptible differences between these groups in respect of various socio-economic indicators. Another group of variables relates to immigrants from the Former Soviet Union (hereafter - FSU) who reached Israel after 1989. The mass arrival of immigrants of common origin, mostly of lower– middle socioeconomic class, strongly affected patterns of home purchase, concentration in specific geographic areas, residential environment, and property values countrywide. Another group of immigrants, originating in Ethiopia, is of much lower socioeconomic status than FSU immigrants due to lack of schooling, difficulties in social integration, and severe reliance on welfare services and state subsidies. Accordingly, they have a perceptible effect on the residential environment even though they are much fewer in number than FSU immigrants. 4. Econometric model Let us define X and Z1 as vectors of the explanatory variables that, together, reflect homeowner indicators, dwelling and residential-environment characteristics, and factors related to subjective valuation. (The partitioning of these variables between X and Z1 is unimportant for the moment.) We denote by v the white-noise error term, assuming that it is i.i.d. for every I and j. This allows us to formulate a model for the subjective valuation of dwelling I in census tract j as a hedonic price model in the following manner: (1) ln(Valuation ij )  βX ij  γZ1ij  vij Similarly, we define the price model of the same dwelling, if it was sold: (2) ln(Pr ice ij )  X ij  Z2ij  w ij Some explanatory variables (vector X) in Model (2) are identical to the subjective valuation model; the others (Z2) represent factors that affect the dwelling price but not the subjective valuation 14 ฀฀฀฀฀฀฀฀฀ of the dwelling by its owner, e.g., indicators relating to the other party to the sale transaction. Factor w is the white-noise error term, i.i.d. for every I and j. Subtracting Equation (2) from Equation (1), we obtain a model of bias in subjective dwelling valuation relative to the price of the same dwelling in a sale transaction: (3.1) ln(Valuation ij / Pr ice ij )  (β  κ)X ij  γZ1ij  πZ2ij  v ij  w ij According to Model (3.1), the bias of the valuation relative to the price of the same dwelling is a function of factors X, Z1, and Z2. However, if the sale-transaction price of the dwelling for which the subjective valuation was reported is not known, information about the log-average price in a sample of sale transactions in the census tract of the dwelling may be used instead. We denote 1 n 1 n  n  n ln(Pr ice ij )   X ij   Z2 ij   w ij , or ln(Pr ice j )  X j  Z2 j  w j :  n i 1 n i 1 n i 1 n i 1 (3.2)  ln( Valuation ij )  ln(Pr ice j )  β(X ij  X j )  γZ1ij  π Z2j  v ij  w j  Model (3.2) states that the relative bias in valuation as against the log-average transaction price in the census tract depends, among other things, on factor (X ij  X j ) , meaning that the variables that affect both the valuation and the price may appear in the regression in the form of deviations from the mean value in the census tract corrected by factor   . With the foregoing general model in mind, we begin by describing the empirical model of the subjective valuation. This model is based on a hedonic price model, in which the explained variable is (the natural logarithm of) the subjective valuation of dwelling I in census tract j in year t. For the sake of convenience in presenting the model, we aggregate the explanatory variables in five groups as shown in Table 2: (4) ln( Valuation ijt )  1 Household i  μ 2 Personal i  μ 3 Asseti  μ 4 AvgTract jt  5 Area i  μ 6 ln( Avg Pr iceCT jt ) μ 7 ln(dUSD t )   8 NumTransactCTjt  μ 9 Year t   ijt The first group of variables (Household) includes indicators of an owner-occupier household: number of persons, average income per capita in household, and size of the mortgage loan that the household took in order to buy the dwelling. The second group of variables (Personal) relates to 15 ฀฀฀฀฀฀฀฀฀ homeowner characteristics: sex, age, marital status, years of schooling, and origin—Israel-born and, if not, whether or not immigrated in the 1990s, and Sephardi or Ashkenazi origin. The third group (Asset) includes dwelling indicators: whether it is a stand-alone house or an apartment in a condominium building, number of rooms, age of building, whether purchased by the household or obtained as a gift or an inheritance, whether acquired during the twelve months preceding the survey date, whether equipped with an air conditioner, a heating system, and a garden, and whether renovated in the past year. The fourth group (AvgTract) includes indicators of the census tract in which the dwelling is located: proportion of males, average age of residents of the tract, their distribution by origin, and their average income. The fifth group of variables (Area) includes environmental characteristics of the dwelling‘s nearest surroundings: number of roads of different types in the various ranges (5–50 meters) from the building, distance to the Mediterranean sea shore, and a number of schools within 500 meter from the building. In addition to these variables, which are customarily included in a hedonic price model, we inserted four variables into the set of the explanatory variables. The first is (the natural logarithm of) the average price of sale transactions in the census tract in the three months preceding the subjective valuation offered in the survey (AvgPriceCT), which is meant to represent the information base via which the homeowner subjectively valuates her dwelling, net of dwelling quality and other factors for which we control. In order to make an accurate comparison between each subjective dwelling value and average prices in the census tract, we created a cell with all the properties in a census tract with identical characteristics as the dwelling has (age, house type, number of rooms, air conditioner, heating system) and plugged in the mean sale price for transactions that census tract-year. The distribution of cell sizes ranged between 22-45 observations of sale transactions in the census tract observation in the three months preceding the subjective valuation offered in the survey. Since the relation between this variable and an explained variable is log-logarithmic, the parameter  6 denotes the elasticity of the subjective valuation relative to the average sale-transaction price in the census tract. It may be considered as the rate of pass-through from census-tract transaction prices to 16 ฀฀฀฀฀฀฀฀฀ individual‘s subjective valuation. Accordingly, we would expect this parameter to be positive, within the range of 0–1. The second variable, denoted as dUSD, is (the natural logarithm of) the change in the exchange rate (NIS/dollar) in the three months preceding the survey date. The reason for including this factor is that both the dependent variable and the average price of sale transactions in the census tract are expressed in NIS (local currency) terms, while, until the late 2000s, dwelling prices have been cited usually in dollar terms. If subjective dwelling valuations are formulated in dollar terms and are ―anchored‖ to the dollar prices of sale transactions with a three-month lag, one would expect localcurrency valuations to fluctuate in tandem with exchange-rate fluctuations. That is, formation of valuations in dollar terms would imply a positive parameter  7 ; the stronger the dollar-terms rigidity of prices is, the closer to 1 its estimate would be. The third variable is the number of sales transactions in the census tract in the three months preceding the individual‘s subjective valuation (NumTransactCT). This variable is meant to express the ability to sell dwellings in the census tract. The less salable the dwellings are, the higher their owners‘ valuation should be, for any given condition of demand. Thus, one should expect the estimate of parameter  6 to be negative. Finally, the model includes a fixed effect for the year in which the subjective valuation of dwelling I was given (Year). This effect should represent all idiosyncratic effects that may influence the valuation of dwellings countrywide in a given year. The white-noise error term,  ijt , represents random effects associated with subjective dwelling valuation that are not reflected in the foregoing explanatory variables. We posit that  ijt ~ N(0,  2 ) for every t, j, and I, and sustains all assumptions of the OLS regression model. The main equation in our study estimates the effect of the aforementioned explanatory factors on the percent of bias in subjective dwelling valuation relative to the average sale-transaction price of dwellings in the census tract in the three months preceding the survey. We define this relative bias as ln(Valuation Avg Pr iceCT ) . The model is the following: 17 ฀฀฀฀฀฀฀฀฀ (5) ln( Valuation ijt Avg Pr iceCT jt )   1 Household i   2 Personal i   3 Asset i   4 AvgTract jt  5 Area i  6 ln(dUSD t )   7 NumTransactCTjt  8Year t  u ijt Notably, once the explanatory variable in Model (2) is defined as the log of the relation between subjective valuation and average sale-transaction price in the census tract, it follows that Model (5) is a private case of Model (4), under assumption of  6  1 . In other words, once we assume unit elasticity of the subjective valuation relative to the average transaction price in the census tract, we derive the relative-bias model from the hedonic price model with a specification that includes average transaction price in census tract as an explanatory variable. Assumption  6  1 may, of course, be tested empirically. Comparing empirical Model (5) with general Model (3.2), we notice several differences. The first is the addition of a time dimension originating in the accumulation of survey years in the database of the study. The second difference is the omission of the Z2 group of variables, those that affect dwelling price but not subjective valuation. This omission may introduce a bias onto the estimates of the model if elements of the vector Z2 are correlated with elements of the vectors X and/or Z1. The third difference is that elements of the vector X appear in level and not in the form of a deviation from the mean in the census tract, for the model includes also a group of indicators of the population of the census tract (AvgTract) that reflects differences between characteristics relating to homeowner and those pertaining to neighborhood population. We subject Model (5) to two sensitivity analyses. In one of them, we estimate the model for a subsample of 3.5 percent of observations—including only dwellings that, according to the survey reportage, were purchased during the twelve months preceding the survey. It should be noted that reportage of dwelling purchases in the survey is done via a retrospective questionnaire that does not note the date of the purchase. Thus, it may be flawed in its attribution of purchases to the twelvemonth ―window‖ before the survey date, as some transactions preceding the window are reported as having taken place within the window while others carried out during the window are forgotten (Kennickell and Starr-McCluer, 1997). It stands to reason that these homeowners, who as recent purchasers of their dwellings were exposed to conditions of the local housing market, were more 18 ฀฀฀฀฀฀฀฀฀ aware than others of the value of their dwellings; therefore, we would expect their valuations to be more accurate. The second sensitivity analysis concerns the possibility of small-sample bias at the level of census tract. As stated, the study was performed on the basis of a national survey that has the inherent disadvantage of lacking uniform coverage at census-tract resolution. To determine how seriously this affects the estimates and the size of the subjective-valuation bias, we limited the sample to census tracts in which no fewer than ten, twenty, and thirty observations were found in a census tract in the research years. 5. Estimation results This part of the study presents the results of the empirical analysis on the basis of the models described above. First, we estimated the subjective valuation model for housing value (4) on the basis of the hedonic approach. Table 3 shows the results of the model, which tests the influence of the explanatory variables described in Table 2 on subjective dwelling valuation. The natural logarithm of subjective valuation relative to dwelling value served as a dependent variable in the model. The model was estimated both for the full sample of 21,238 observations (Model A) and for the subsample of 738 observations that comprise dwellings purchased in the twelve months preceding the survey date (Model B). By estimating Model B for a subsample of dwellings for which the transaction price, it becomes possible to perform a sensitivity analysis for the parameters of Model (4) and determine whether the average transaction price in a census tract is a good proxy for dwelling prices actually paid and reported by those surveyed out of total household expenditure in the year preceding the survey; these were included in the estimations. (Table 3 about here) The model for the full sample explains some 70 percent of variance in subjective dwelling valuation. Most of the explanatory variables are significant at a 1 percent level and the directions of their effect correspond to those known in the literature on the estimation of hedonic models (Arguea and Hsiao, 2000; Zabel, 2004; Kiel and Zabel, 2008, etc.). 19 ฀฀฀฀฀฀฀฀฀ The findings of the model attest, among other things, to the importance of household indicators and homeowner‘s personal indicators in explaining variance in the subjective valuation of owned dwellings (Kiel and Zabel, 1997). In particular, it appears that older people, those of Israel nativity, the better educated, and those of higher income attribute greater value to their dwellings than do others. Household size was also found directly related to subjective dwelling valuation, much as Zabel (2004) observed as well. The model findings also show that the higher the monthly mortgage payment, the lower is one‘s subjective dwelling valuation—consistent with the outcome reported by Xu (2008). Furthermore, it is seen in the model that subjective dwelling valuation is greater when the dwelling is acquired not on the free market but by inheritance or as a gift. Among physical dwelling characteristics, several variables—e.g., number of rooms, heating conditions, stand-alone private residence (as opposed to a condominium), and private garden—stand out for the strength of their influence on subjective dwelling valuation. As expected, a strong and positive relation was observed between average sale transaction price in a given census tract and subjective dwelling valuation (0.3 elasticity). Also, a negative relation was found between subjective valuation and number of transactions in a given census tract in the three months preceding the sample. Namely, lack of up-to-date information about dwelling prices in the respondent‘s census tract of residence induces a stronger bias in valuating h/her own dwelling. The significant effect of the variables that were chosen to characterize the residential environment confirms the importance of economic and demographic indicators of residents in the respondent‘s neighborhood for subjective dwelling valuation. In particular, an older and more affluent population in the neighborhood elevates subjective dwelling estimation whereas concentrations of immigrants from the Former Soviet Union or from Ethiopia have a downward effect. The last-mentioned finding is consistent with the results of another study performed in Israel (Fleischman, Gubman, and TurSinai, 2015). As expected, a significant positive relation was found between subjective valuation and change in the U.S. dollar exchange rate in the three months preceding the survey date. The 0.6 elasticity shows that volatility in the dollar exchange rate has a perceptible effect on subjective dwelling value. 20 ฀฀฀฀฀฀฀฀฀ Furthermore, the model findings confirm the importance of indicators that reflect the effect of environment and location on dwelling valuation. A case in point is the dual effect of the proximity of roads to the dwelling: Noise from a main highway near the dwelling (up to 5 meters) lowers valuation whereas the presence of roads at a distance of 30–50 meters increases it, evidently because the easy access to the beach that nearby roads provide is another environmental utility that boosts dwelling value. Also, the presence and number of schools in the neighborhood was found positively related to dwelling valuation. These findings correspond to those of studies that focused on environmental effects of dwelling value (Bourassa, Hoesli, and Sun, 2005; Nijland and Wee, 2008). In principle, the model findings are consistent with those of previous studies (Kiel and Zabel, 2008; Zabel, 2004; Arguea and Hsiao, 2000). Model B, estimated for a relatively small subsample, is of much higher quality than Model A (0.83 vs. 0.70, respectively) even though it yielded fewer significant variables. The probable reason for this is that this model (B) includes an explanatory variable that reflects dwelling prices actually paid (Price). Interestingly, this variable does not switch off in the model with that of average price in census tract (AvrPriceCT), as one would expect. Both variables enter the model at a high level of significance and have similar estimators: 0.31 for Price and 0.29 for AvrPriceCT). In other words, each of these variables has its own role to play in forming the dwelling valuation and each provides relevant complementary information for this purpose. As for the size of parameter µ 6 in Model (4) above, it should be noted that the estimator of AvrPriceCT (0.31) (Table 3, Model A) is far below 1. This means that the bias model (5) cannot be treated as a specific case of the subjective-valuation model (4). Model (5) examines the factors of bias in the subjective valuation relative to the average price of sales transactions in the same census tract (three months before the survey). The model was estimated using the OLS method. Table 4 shows the results of the estimation of the model for both the full sample (Column A) and a subsample of dwellings acquired in the year preceding the survey (Column C). (Table 4 about here) 21 ฀฀฀฀฀฀฀฀฀ The purpose of the latter estimation is to analyze the sensitivity of the estimates to the timeliness of information about dwelling value that new homeowners possess relative to that in the possession of those who bought their dwellings long ago. Table 4 also presents a model with fixed effects for census tracts (Column B). Model A explains almost 29 percent of variation in the subjective valuation bias. It was found that the subjective valuation bias is positively related with the number of rooms and the existence of air-conditioning and heating systems and private gardens. Furthermore, owners of low-rise private homes are inclined to overestimate the value of their dwellings to a larger degree than owners of apartments in condominium buildings, ceteris paribus. The extent of the bias is also affected by household and homeowner characteristics. In particular, we found that the Israel-born typically overvalue their dwellings while immigrants tend to undervalue them, and that older and higher-income homeowners tend to overvalue. These findings, while consistent with those of Ihlanfeldt and Martinez-Vazquez (1986), clash with those of Agarwal (2007). Notably, the finding that immigrants tend to undervalue their dwellings suggests an anchoring bias. If the immigrants come from countries where a similar dwelling would have a lower market value, they may attach too much weight to their estimate of what their dwelling would be worth in their previous country and not enough weight to its value in their new country. A possible explanation for the positive relation between income and size of subjective dwelling valuation bias may be found in the domain of economic psychology. Home ownership is one of the most important factors, along with current income, in measuring an individual‘s economic well-being. When a person‘s income and general well-being improve, her subjective standards for the estimation of her proprietary status also escalate, and these subjective standards usually go up long before her objective economic situation changes (Lewis, Webley, and Furnham, 1995). It follows that an increase in homeowner‘s income magnifies the bias in her dwelling valuation. Interestingly, no significant relation was found between homeowner‘s level of schooling and bias in dwelling valuation when household income is controlled for. As to the effect of longevity of ownership, represented by the variable Bought12months, on the extent of the bias, we found that the valuations of new owners, i.e., those who reported having bought 22 ฀฀฀฀฀฀฀฀฀ their dwellings in the twelve months preceding the survey data, were more upward-biased than those of the other participants in the sample, although the estimate was significant at a relatively low .10 percent level. This latter result corresponds to the findings of Kiel and Zabel (1999) and Agarwal (2007) but clashes with other studies, such as Kain and Quigley (1972) and Goodman and Ittner (1992). Given the low significance level of this variable, the question of the reliability of reportage on purchases within the twelve-month window (as mentioned in Section 4) and uncertainty about what the respondent means when reporting the purchase of a dwelling (signing the contract, paying some or all of the purchase price, or moving in), this finding should be treated cautiously. The larger the mortgage payments are, the smaller the bias. Similarly, the estimation shows that homeowners who acquired their dwellings by inheritance or gift tend to overvalue them relative to those bought their dwellings on their own. As expected, a negative relation was found between the number of sale transactions in the census tract and the size of the valuation bias. In other words, the lack of up-to-date information about housing prices in a survey respondent‘s area of residence causes a larger upward bias, ceteris paribus. As for the effect of neighborhood indicators, the negative estimate of IncomeCT (in Column A) shows that owners of dwellings in low-income census tracts typically overestimate the value of their dwellings relative to the average price of dwellings recently sold in the same tract. Given the robust direct relation between household income and dwelling value, the price level of dwellings in these tracts is also probably relatively low. As has been shown in research of life- and income-satisfaction, while an increase in individual‘s income and proprietary status improves one‘s well-being—having magnified the bias in homeowner‘s dwelling valuation—the effect of income in the individual‘s reference group (e.g., neighbors) is mostly negative (Easterlin, 1995). The effect of additional variables that characterize the demographic composition of the survey participants‘ residential environment reinforces this finding. In particular, an upward bias in valuation is typical of homeowners who live in tracts populated by concentrations of immigrants from the FSU and Ethiopia. This effect, combined with the fact that a higher share of these groups of immigrants in the tract has a negative impact on subjective dwelling valuation (as found in the empirical model of the subjective valuation), leads to the conclusion that the heavier presence of immigrant populations 23 ฀฀฀฀฀฀฀฀฀ in a neighborhood depresses the average dwelling price more than it does the inhabitants‘ subjective valuations. As to dwelling environment and location characteristics, it turns out that a stronger bias in dwelling valuation is typical of households in neighborhoods that are noted for the presence of schools and accessible road systems that are nearby but not too close to the building. As expected, a significant positive relation was found between the bias in dwelling valuation and changes in the dollar exchange rate in the three months preceding the survey—the time when interviewees in the survey were exposed to information about prices of transactions in their near vicinity. The elasticity found, 0.75, indicates a high degree of inelasticity of dwelling price valuations in dollar terms throughout the research period. Column B of Table 4 presents a model with a fixed effect for census tracts. Most explanatory variables that are indicative of household, homeowner‘s personal traits, and physical properties of the dwelling are statistically significant; their effect on the valuation bias resembles the effect in Column A in terms of both the size of the estimates and the direction of their effect. In contrast, no significant impact was observed for the indicators of census-tract population; this seems to be a direct outcome of specifying the model with fixed effects for census tracts as opposed to a model accommodating only fixed effects for years, as shown in Column A. Column C of Table 4 presents results for the subsample of respondents who acquired dwellings during the year preceding the survey date, with the same explanatory variables that were used in the estimation of Column A. This model also includes a variable reflecting the price actually paid for the dwelling reported in the survey (Price). The significance of the explanatory variables in this model is lower due to the very small sample size, but its explanatory power (0.33) surpasses that of the full sample, evidently due to the inclusion of the price actually paid for the dwelling. As for the statistically significant variables, no dramatic differences were found between the estimates for the subsample of new homeowners and the full sample, either in the estimates of the variables or in the direction of their effect. It turns out, however, that among all dwelling physical characteristics that were included in the model, only the number of rooms was found to be correlated positively with the 24 ฀฀฀฀฀฀฀฀฀ bias of dwelling valuation. Furthermore, ownership of low-rise private dwellings induces a larger bias than apartments in condominium buildings. Among the household traits, only income was found to be significant and it tends to increase the bias. As for the effect of indicators relating to the population of the respondent‘s residential area, the findings for the subsample resemble those described for the full sample. Notably, however, exchangerate fluctuations (dUSD) had no statistically significant effect on the subjective valuation bias of new homeowners. This finding may follow from the fact that having recently reported their own transaction for tax purposes in local currency, new homeowners do not return to dollar terms when formulating their updated asset valuations. Using the correlation matrix we show that the characteristics correlated with bias are uncorrelated with differences in asset characteristics from census tract means (see Appendix A). The mean subjective-valuation bias that was found for the subsample of dwellings purchased in the twelve months preceding the survey (19.3 percent) is significantly smaller than the mean bias for the full sample (26.8 percent). This stands to reason because new homebuyers are more familiar with the local housing market than others are. Lastly, we examined the sensitivity of the estimates in Model (5) to a possible small-sample bias at the level of census tract, a spatial resolution that does not presume uniform coverage in the national survey on which the study is based. To examine how seriously this affects the quality of the estimates and the size of the dwelling-valuation bias, we ―filtered‖ the full sample by imposing a minimum threshold of sample size in a census tract: no fewer than ten observations (Column A), twenty observations (Column B), and thirty observations (Column C) in all research years. Table 5 shows the results of the estimation for these downsized samples. (Table 5 about here) First, it should be noted that the mean bias in dwelling valuation is basically the same in all three models, although as the threshold size of the sample of observations in the census tract rises, the mean bias decreases and the fit of the model improves. At the same time, the number of statistically significant explanatory variables decreases steadily from Column A to Column C, evidently due to the drastic contraction of sample size from 19,200 to 12,960 to 5,240, respectively. 25 ฀฀฀฀฀฀฀฀฀ The major contribution of personal indicators to the level of the subjective dwelling-valuation bias weakens as the sample size in the census tract decreases. Among the personal indicators that affect dwelling-valuation bias, one may note the stability in the variables of per-capita household income as well as immigrant and marital status. (The contribution of two latter variables strengths as the sample size in the census tract decreases.) In contrast to the homeowner personal indicators, the effect of most dwelling physical indicators actually gains strength as the threshold of sample size in the census tract goes down. In other words, the marginal effects on the dwelling-valuation bias of better housing conditions (number of rooms, air conditioning, heating system), and of ownership of private houses as opposed to apartments in condominium buildings, rise with an decrease in the sample size in the census tract. Notably, the impact on subjective-valuation bias of most census-tract population and environmental indicators, as well as the effect of the exchange rate, becomes stronger in the transition from Column A to Column C. Consequently, despite certain differences in the estimates and significance levels of the explanatory variables, generally the difference in sample size in a census tract has no meaningful effect either on the size of the subjective-valuation bias or on the factors affecting it. 6. Discussion and conclusion The use of subjective valuations of dwellings by their owners as an estimate of dwelling value is very common in economic research. This study examined the reliability of subjective dwelling valuations. The results of our study indicate that, on average, homeowners tend to overestimate the value of their dwellings by 20 percent and exhibit a median bias of 15 percent. These estimates are much higher than the size of biases found in previous research. This fact may be attributed to a wider spread between the asking price of a property and the sales price in the Israel‘s real-estate market than in the US market that was mostly analyzed in the literature. This study elicited several new findings. First, by investigating bias size across a distribution of dwelling prices, we found wide variance in the accuracy of the subjective valuations as against 26 ฀฀฀฀฀฀฀฀฀ transaction prices. The valuations of inexpensive and costly dwellings are biased in different directions: estimates reported by people who live in dwellings belonging to the first eight deciles of the price distribution are upward-biased in the lowest decile of the distribution, whereas people who occupy the most expensive dwellings more typically understate the value of their homes. A possible explanation for the downward bias at the upper end of the dwelling-value distribution may be proffered on the basis of Veblen‘s (1899) theory of conspicuous consumption. According to the ―Veblen-goods‖ concept, the price that an individual is willing to pay for an expensive and prestigious property reflects both the utility that the property confers and the ―prestige‖ value that its acquisition may signal to the individual‘s reference group. Econometric checks corroborate the Veblen-effect (Bagwell and Bernheim, 1996). Over time, however, the ―prestige‖ aspect tends to dissipate and makes no further contribution to the property owner‘s gratification (Ackerman, 1997). Thus, in the response to the survey question about the valuation of an owner-occupied dwelling, the weight of the ―prestige‖ element is greatly reduced whereas the practical utility of property use internalizes stronger familiarity with the property specification in terms of its characteristics and immediate vicinity that were unfamiliar when the property was acquired. Accordingly, the explanation for the undervaluing of the costliest dwellings seems to lie, at least partly, in the difference between considerations of practical utility, that guide homeowners in their valuation of properties they live in, and a higher valuation of real estate in their vicinity among those who have just bought a dwelling in the neighborhood, ostensibly driven by the Veblen-good effect. It may be reasonable to assume households use transaction price information in their area as a noisy signal of the value of their own home. Therefore, another possible explanation for the undervaluation of the most expensive properties is that prices increased more quickly in the prestige segment of Israel‘s real-estate market than in other market segments during the research years. In areas with strong price growth we would might get undervaluation while in areas with falling prices we would get overvaluation. For this reason, the valuations of owners of expensive properties may not have kept up with the pace of increase in the prices of their properties. An upward bias at the lower end of the dwelling-valuation distribution may take shape if liquidity constraints among owners of inexpensive dwellings bring about a price level for such 27 ฀฀฀฀฀฀฀฀฀ dwellings that is under fair market value. Liquidity constraints have a strong effect on consumer behavior generally and housing purchase and selling behavior specifically (Maki, 1993; Genesove and Mayer, 1997). Studies focusing on the investigation of interrelations of liquidity constraints and changes in property prices indicate that low income homeowners, who usually also have a high loanto-value ratio, are especially inclined to negative income shocks. These may be manifested in liquidity constraints and the ―fire sale‖ disposal of dwellings at under-market prices in order to smooth consumption or pay debts (Brunnermeier, 2009). Indeed, Genesove and Mayer (1997, 2001) corroborated that homeowners with high loan-to-value ratios tend to set higher asking prices. This bias is observed even at times of downturns in the housing market, when sellers of inexpensive dwellings expect to take a financial loss when selling their properties. Another plausible explanation for the overvaluation of inexpensive dwellings by their owners is that certain utilities of home ownership (e.g., stability, local welfare services, community support etc.) are much more important for low-income persons that for high-income persons (Denton, 2001)—an importance that may be ―translated‖ into the overvaluing of the least expensive dwellings by resourcepoor persons. In addition to all the foregoing, one may relate to misspecification as a potential explanation of the valuation bias. A homeowner may identify traits that correlate with fundamental valuation factors that should enter our equations in ways that we do not consider or with fundamental factors that we simply do not observe. In these cases, statistical significance in either of the two equations ((4) or (5)) may be the result of error in this respect. Also, different types of dwellings experienced different rates of price increase during the sample period. It may be reasonable to assume that households use transaction price information in their area as a noisy signal of the value of their own home. Then, we would obtain undervaluation in areas with strong price growth and overvaluation in areas with falling prices. It stands to reason that this is exactly the result we would obtain when we compare expensive homes (hence rich owners) with inexpensive ones (hence poor owners). In an attempt to determine the most relevant period of time during which subjective valuations internalized ―news‖ about housing prices in the neighborhood, we tested the correlation between dwelling valuations reported in the survey and housing prices in the same area within a window of 28 ฀฀฀฀฀฀฀฀฀ one year around the survey participation date. We found that the interval of three months before the survey date delivers the best correlation between valuations and average transaction prices in a given census tract for most of the dwelling-value distribution. Our findings confirm the existence of a significant and systematic relation between bias in homeowners‘ dwelling valuations and dwelling physical indicators, homeowner personal indicators, and census-tract population characteristics. This finding clashes with the conventional wisdom in the estimation of hedonic price models and housing-demand models based on homeowners‘ subjective valuations, which denies the existence of any correlation between dwelling-valuation bias and dwelling-owner indicators, dwelling characteristics, and residential-environment indicators. This conventional wisdom is based on the studies of Kain and Quigley (1972) and Goodman and Ittner (1992), which found no statistical relation between bias and the aforementioned factors. We found no dependency between the average valuation bias and sample size in the census tract for which the bias was examined. In other words, in a national survey that poorly reflects local spatial resolution, sample size in small areas seems to have no dramatic effect on owners‘ valuations of their dwellings. To apply the conclusions of this study to other time windows or other geographical locations, additional tests are of course necessary; we intend to perform them in continuing research. The observation of a mean bias in subjective valuation relative to actual dwelling prices masks quite a bit of variation across the valuation distribution, and the bias may even change signs as it crosses the distribution. This finding entails further testing and efforts to understand why owners of expensive dwellings behave so differently from owners of lower-priced accommodations. 29 ฀฀฀฀฀฀฀฀฀ Disclosure Statement No potential conflict of interest was reported by the authors. 30 ฀฀฀฀฀฀฀฀฀ References Ackerman, F., 1997. 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Rosen, S., 1974. Hedonic prices and implicit markets product differentiation in pure competition, Journal of Political Economics 82, 34–55. 33 ฀฀฀฀฀฀฀฀฀ Rouwendal, J., Alessie, R., 2002. House Prices, Second Mortgages and Household Saviings—An Empirical Investigation for the Netherlands, 1987–1994, Tinbergen Institute Discussion Papers, TI 2002-074 /3. Quan, D. C., Quigley, J. M., 1991. Price formation and the appraisal function in real estate markets, Journal of Real Estate Finance and Economics 4, 127–146. Steele, M., Goy, R., 2002. Do sales prices overstate underlying house prices in market downturns? Evidence from the Canadian House price crash of 1991, Canadian Journal of Administrative Sciences 19, 333–345. Thaler, R., 1980. Toward a positive theory of consumer choice, Journal of Economic Behavior and Organization, 1, 39–60. Veblen, T., 2007. The Theory of the Leisure Class, Cosimo, Inc. New York NY., originally published in 1899. Xu T., 2008. Heterogeneity in housing attribute prices, International Journal of Housing Markets and Analysis, 1, 166-181. Zabel, J. E., 2004. The demand for housing services, Journal for Housing Economics 13, 16–35. Zabel, J.E., Kiel, K.A., 2000. Estimating the demand for air quality in four US cities, Land Economics 76, 174–194. 34 ฀฀฀฀฀฀฀฀฀ Figure. 1. Subjective valuation vs. average dwelling price in census tracts, by percentiles of dwellingprice distribution, 1997–2008 A. Logarithm of subjective valuation and average dwelling price B. Average bias of subjective valuation and its standard deviation 35 ฀฀฀฀฀฀฀฀฀ Figure. 2. Average bias of subjective valuation, by selected percentiles of annual dwelling-price distribution, 1997–2008 Figure. 3. Average price of dwelling, by selected percentiles of annual dwelling-price distribution, 1997–2008 (in current prices, index 1997=100) 36 ฀฀฀฀฀฀฀฀฀ Table 1 Correlation between subjective valuation and average price in sales transactions in census tract, by deciles of valuation and period of time between valuation and sales transactions, 1997-2008 Spearman coefficient of correlation Deciles of subjective valuation 1 2 3 4 5 6 7 8 9 10 months, before the survey 0-3 4-6 7-9 10-12 0.236 0.152 0.139 0.096 0.066 0.099 0.088 0.060 0.098 0.246 0.246 0.143 0.143 0.111 0.061 0.088 0.072 0.052 0.108 0.240 0.260 0.165 0.158 0.086 0.049 0.091 0.087 0.072 0.089 0.239 0.250 0.142 0.145 0.108 0.060 0.088 0.082 0.087 0.103 0.211 Table 2 Descriptive Statistics of Households, Their Dwellings and Transacted homes, 1997–2008 Name of variable Definition of variable Characteristics of household* Persons Number of persons in household Income (Ln of) Monthly monetary income per capita (NIS) Mortgage (Ln of) Mortgage loan repayment, or zero if none (NIS) a Characteristics of head of household* Male Male (%) Age Age (years) IsraelBorn Israel-born (%) Immigrant1990 Immigrated in or after 1990 (%) ImmEuropeAmerica European or American born, not incl. immigrants in or after 1990 (%) ImmAsiaAfrica Asian or African born, not incl. immigrants in or after 1990 (%) Married Married (%) Education Schooling (years) Characteristics of dwelling* Valuation (Ln of) Subjective valuation of dwelling (NIS) Purchased Dwelling purchased (vs. inherited or received without pay) (%) Bought12months Dwelling purchased during twelve months preceding survey (%) Price (Ln of) Dwelling price, if purchased during twelve months preceding survey (NIS) House House (vs. dwelling in condominium building) (%) Rooms Total rooms in dwelling BuildingAge Age of building (years) AirConditioner Air conditioner in dwelling (%) Heating Heating system (%) Garden Garden (%) Repairs (Ln of) Expense on major repairs in dwelling in 12 37 Avg. (S.D.) 3.3 (1.7) 8.04 (0.69) 3.52 (3.69) 55.7 52.1 (15.6) 44.3 14.0 24.0 17.7 73.5 13.1 (4.6) 13.41 (0.54) 92.5 3.6 13.25 (0.57) 27.4 3.8 (1.1) 24.5 (14.8) 75.6 9.7 2.2 1.08 (2.327) ฀฀฀฀฀฀฀฀฀ months preceding survey, or zero if none (NIS) b Characteristics of census tract** AvgPriceCT (Ln of) Average price in sale transactions three months before survey in census tract (NIS)*** NumTransactCT Number of sale transactions three months before survey in census tract (%) MaleCT Men in census tract (%) AgeCT Average age in census tract (years) IsraelbornCT Israel-born in census tract (%) Immigrant1990CT Immigrated in or after 1990 in census tract (%) ImmEuropeAmericaC European-American born, not incl. immigrants in or T after 1990, in census tract (%) ImmAsiaAfricaCT Asian-African born, not incl. immigrants in or after 1990, in census tract (%) EthiopiaCT Ethiopian-born, not incl. immigrants in or after 1990, in census tract (%) IncomeCT (Ln of) Avg. income from wages and business per capita in census tract (NIS)*** 13.29 (0.50) 3.4 (3.1) 48.8 38.3 (8.5) 57.2 15.0 16.0 10.8 1.0 10.32 (0.63) Table 2 (continue) Descriptive Statistics of Households and Their Dwellings, 1997–2008 Name of variable Definition of variable Environmental characteristics of surroundings**** RoadArea Number of roads within 50 meters from the building Road5mArea Existence of a motorway within 5 meters from the building (%) SchoolArea Number of schools within 500 meters from the building SeaArea Distance to the Mediterranean sea shore (km) c Avg. (S.D.) dUSD 0.003 (0.04) (Ln of) Rate of change of the US dollar exchange rate in three months preceding the survey date Characteristics of transacted homes***** THPrice (Ln of) Transacted home price (NIS) THStoreyRatio Ratio: Storey at which the apartment is located, to the number of floors in the building THNumStorey Number of floors in the building in which transacted apartment is located THAge Age of transacted dwelling THRooms Total rooms in transacted dwelling THGardend Dwelling with private garden (%) THPenthoused Penthouse (%) THDuplexd Duplex (%) THCottaged Cottage (%) THHoused Private House (%) e THFirstHand1 Dwelling sold a year after it was constructed (%) THFirstHand2 e Dwelling sold two years after it was constructed (%) THFirstHand3 e Dwelling sold three years after it was constructed (%) THFirstHand4 e Dwelling sold four years after it was constructed (%) THFirstHand5 e Dwelling sold five or more years after it was constructed (%) THSecondHand ‗Second-hand‘ transactions between private owners (%) 38 8.1 (10.7) 8.1 4.8 (4.8) 5.31 (..32) 13.29 (0.78) 0.51 (0.34) 5.6 (4.4) 21.3 (20.9) 3.6 (1.2) 0.76 0.56 0.40 5.04 0.35 4.2 1.1 0.4 0.2 1.8 75.8 ฀฀฀฀฀฀฀฀฀ *Source: Household Expenditure Survey, authors‘ calculations. **Source: Population Register, authors‘ calculations. ***Source: Israel Tax Authority, authors‘ calculations. ****Source: GIS data, authors‘ calculations. ***** Source: Tax Authority, authors‘ calculations a. 48.4 percent of households in the sample reported paying mortgage. b. 18.5 percent of households in the sample reported some repairs in their dwellings in 12 months preceding survey. c. Aerial distance from the building if it is located within 1 km from the shore, otherwise aerial distance from the city center. d. These variables denote various kinds of dwellings vs. dwellings in condominium building (in %) e. These variables denote ‗first-hand‘ transactions between building companies and private owners accomplished more then year after home construction vs. ‘first-hand‘ transactions accomplished in a year of home construction. Table 3 Estimates of Subjective Valuation Model* Variables Intercept Persons Income Mortgage Male Age IsraelBorn Immigrant1990 ImmEurope America Married Education Purchased House Rooms BuildingAge BuildingAgeSq Full sample Estimate (Standard error) (A) 6.918* (0.116) 9.915* (0.002) 9.980* (0.004) -9.996* (0.001) -9.984* (0.004) 9.991* (0.0002) 9.927* (0.006) -0.073* (0.008) -0.031* (0.007) 0.040* (0.006) 0.004* (0.0005) -9.807* (0.008) 0.085* (0.005) 0.176* (0.002) -0.013* (0.0005) 0.0002* (0.000008) 39 Sample of dwellings purchased in 12 months preceding survey Estimate (Standard error) (C) 4.726* (0.409) 0.081 (0.007) 0.056* (0.018) -0.008* (0.003) -0.027*** (0.016) 0.0006 (0.0007) -0.031 (0.032) -0.050 0.033 -0.051 (0.036) 0.024 (0.022) -0.0003 (0.002) -0.122** (0.053) 0.070 * (0.020) 0.110 * (0.011) -0.007 * (0.002) 0.0001 * (0.00003) ฀฀฀฀฀฀฀฀฀ 0.030* (0.005) 0.155* (0.008) 0.098* (0.015) -0.0004 (0.0009) -0.008 (0.019) 0.122 * (0.037) 0.076*** (0.042) -0.001 (0.002) Full sample Sample of dwellings purchased in 12 months preceding survey Estimate (Standard error) (C) 0.310* (0.020) 0.289 * (0.024) 0.309 (0.220) -0.001 (0.002) -1.615 * (0.572) 0.006 ** (0.003) -0.486* (0.095) -0.190 (0.205) -0.108 (0.214) 0.152 (0.291) 0.080* (0.023) -0.002* (0.0005) 0.007* (0.002) 0.005** (0.002) -0.021** (0.012) Yes 738 AirConditioner Heating Garden Repairs Table 3 (continue) Estimates of Subjective Valuation Model Variables Bought12months Estimate (Standard error) (B) 0.308* (0.006) 0.597* (0.058) -0.002** (0.0007) -0.966* (0.135) 0.007* (0.0006) -0.693* (0.024) 0.109** (0.049) -0.193* (0.054) -0.599* (0.079) 0.128* (0.006) -0.002* (0.0001) 0.011* (0.001) 0.005* (0.0006) -0.021* (0.003) Yes 21,238 Price dUSD NumTransactCT MaleCT AgeCT Immigrant1990CT ImmEuropeAmericaCT ImmAsiaAfricaCT EthiopiaCT IncomeCT SeaArea SchoolArea RoadArea Road5mArea Fixed effect , years Number of observations 40 ฀฀฀฀฀฀฀฀฀ Adjusted R2 0.70 0.83 *Dependent variable is the natural logarithm of the subjective dwelling value. Standard errors are in parentheses. Significant at: *** 1%. ** 5%. * 10% Table 4 Estimates of Subjective Valuation Bias Model* Variables Intercept Persons Income Mortgage Male Age AgeSq IsraelBorn Immigrant1990 ImmEurope America Married Education Purchased House Rooms BuildingAge BuildingAgeSq AirConditioner Heating Full sample Estimate (Standard error) (A) -0.251* (0.133) 9.910*** (0.002) 9.066*** (0.005) -9.994*** (0.0009) -9.904 (0.006) 9.993*** (0.001) -0.00003** (0.00001) 9.924*** (0.009) -0.075*** (0.011) -0.015* (0.009) 0.0402*** (0.008) 0.0005 (0.0007) -9.089*** (0.011) 0.109*** (0.002) 0.172*** (0.003) -0.007*** (0.0007) 0.0001*** (0.00001) 0.040*** (0.007) 0.056*** (0.010) 41 Estimate (Standard error) (B) -1.076*** (0.352) 0.009*** (0.002) 0.067*** (0.005) -0.003*** (0.001) -0.003 (0.006) 0.003** (0.0011) -0.00002* (0.000010) 0.020** (0.008) -0.052*** (0.010) -0.010 (0.008) 0.045*** (0.007) 0.0009 (0.0007) -0.105*** (0.010) 0.143*** (0.007) 0.196*** (0.003) -0.014*** (0.0007) 0.0001*** (0.00001) 0.050*** (0.007) 0.064*** (0.011) Sample of dwellings purchased in 12 months preceding survey Estimate (Standard error) (C) -1.152** (0.680) 0.023* (0.012) 0.102*** (0.027) -0.008* (0.004) -0.025 (0.025) 0.002 (0.005) -0.00002 (0.00006) -0.5.5 (0.049) -0.055 (0.050) -0.550 (0.055) 0.044 (0.034) -0.004 (0.004) -0.088 (0.085) 0.122*** (0.030) 0.131*** (0.017) -0.004 (0.003) 0.00008* (0.00005) -0.001 (0.029) -0.05. (0.050) ฀฀฀฀฀฀฀฀฀ Garden 0.072*** (0.019) 0.114*** (0.018) -0.030 (0.064) Table 4 (continue) Estimates of Subjective Valuation Bias Model Full sample Sample of dwellings purchased in 12 months preceding survey Estimate (Standard error) (C) -0.004 (0.004) - Estimate (Standard error) (A) -0.001 (0.001) 0.027* (0.015) - Estimate (Standard error) (B) -0.001 (0.001) 0.002 (0.014) - 0.751*** (0.076) -0.007*** (0.001) -0.705*** (0.177) 0.008*** (0.001) 0.281*** (0.029) -0.3.8*** (0.064) -0..8.*** (0.071) 0.7.8*** (0.103) -0.083*** (0.007) -0.0055 (0.0055) 03003*** (03001) 0.002** (0.001) -0.009** (0.004) Yes No 0.712*** (0.073) -0.006*** (0.001) 0.189 (0.249) 0.002 (0.001) 0.217** (0.088) -0.126 (0.137) -0.024 (0.149) 0.169 (0.210) 0.002 (0.015) -0.018 (0.021) 0.0001 (0.002) -0.001 (0.001) 0.003 (0.004) Yes Yes 0.16.*** (0.030) 0.133 (0.335) -0.005** (0.002) -1..88 (0.823) 0.003 (0.004) 0.288** (0.139) -0.580 (0.313) -0.158 (0.326) 1.320*** (0.442) -0.131*** (0.033) -0.001 (0.001) 0.002 (0.003) 0.006 (0.004) -0.026 (0.017) Yes No Number of observations 21,238 20,807 738 Mean dependent variable 0.112 0.112 0.108 Mean bias (pct.) 26.8 26.8 19.3 Variables Repairs Bought12months Price dUSD NumTransactCT MaleCT AgeCT Immigrant1990CT ImmEuropeAmericaCT ImmAsiaAfricaCT EthiopiaCT IncomeCT SeaArea SchoolArea RoadArea Road5mArea Fixed effect , years Fixed effect, census tracts 42 ฀฀฀฀฀฀฀฀฀ Adjusted R2 0.29 0.10 0.33 *Dependent variable is the natural logarithm of the ratio of subjective dwelling value to average sale-transaction price in census tract for properties with the exact same age, the same house/not house type, the same number of rooms, the same air conditioner type and the same heating system type. Standard errors are in parentheses. Significant at: *** 1%. ** 5%. * 10% Table 5 Estimates of Subjective Valuation Bias Model for Different Thresholds of Sample Size in Census Tract* Variables Intercept Persons Income Mortgage Male Age AgeSq IsraelBorn Immigrant1990 ImmEuropeAmerica Married Education Bought12months Purchased House Rooms BuildingAge BuildingAgeSq Threshold: 10 obs. Estimate (Standard error) (A) -0.350** (0.141) 9.011*** (0.002) 9.067*** (0.005) -9.993*** (0.001) 9.003 (0.006) 9.994*** (0.001) -0.00003*** (0.00001) 9.922** (0.009) -0.065*** (0.011) -0.017* (0.009) 0.029*** (0.008) -0.0005 (0.0007) 0.030* (0.016) -9.102*** (0.011) 0.116*** (0.007) 0.170*** (0.003) -0.008*** (0.001) 0.0001*** (0.00001) 43 Threshold: 20 obs. Estimate (Standard error) (B) -0.416** (0.162) 0.010*** (0.003) 0.060*** (0.006) -0.003*** (0.001) 0.005 (0.007) 0.005*** (0.001) -0.00004*** (0.00001) 0.020** (0.010) -0.067*** (0.013) -0.013 (0.010) 0.029*** (0.009) -0.0001 (0.0009) 0.020 (0.018) -0.104*** (0.014) 0.138*** (0.009) 0.173*** (0.004) -0.008*** (0.001) 0.0001*** (0.00001) Threshold: 30 obs. Estimate (Standard error) (C) -0.447* (0.251) 0.008* (0.005) 0.047*** (0.009) -0.002 (0.002) 0.015 (0.002) 0.002 (0.002) -0.00001 (0.00002) 0.023 (0.015) -0.074*** (0.018) 0.002 (0.015) 0.035*** (0.013) 0.001 (0.001) 0.006 (0.027) -0.144*** (0.021) 0.134*** (0.013) 0.195*** (0.006) -0.009*** (0.001) 0.0001*** (0.00002) ฀฀฀฀฀฀฀฀฀ AirConditioner Heating Garden Repairs dUSD 0.047*** (0.007) 0.065*** (0.010) 0.082*** (0.020) -0.001 (0.001) 0.775*** (0.078) 0.048*** (0.008) 0.089*** (0.013) 0.064** (0.025) 0.0003 (0.001) 0.772*** (0.090) 0.049*** (0.012) 0.076*** (0.020) 0.034 (0.041) 0.002 (0.002) 0.909*** (0.131) Table 5 (continue) Estimates of Subjective Valuation Bias Model for Different Thresholds of Sample Size in Census Tract Variables NumTransactCT MaleCT AgeCT Immigrant1990CT ImmEuropeAmericaCT ImmAsiaAfricaCT EthiopiaCT IncomeCT SeaArea SchoolArea RoadArea Road5mArea Fixed effect, years No. of observations Mean dependent variable Mean bias (%) Adjusted R2 Threshold: 10 obs. Estimate (Standard error) (A) -0.006*** (0.001) -0.677*** (0.189) 0.007*** (0.001) 0.284*** (0.030) -0.268*** (0.067) -0.274*** (0.075) 0.653*** (0.108) -0.077*** (0.007) -0.0002 (0.0001) 0.004*** (0.001) 0.002** (0.001) -0.009** (0.004) Yes 19,218 0.110 25.9 0.29 Threshold: 20 obs. Estimate (Standard error) (B) -0.006*** (0.001) -0.496** (0.212) 0.006*** (0.001) 0.307*** (0.036) -0.229*** (0.0798) -0.274*** (0.090) 0.318*** (0.125) -0.074*** (0.009) -0.0004** (0.0002) 0.008*** (0.001) 0.002* (0.001) -0.008* (0.004) Yes 12.959 0.104 23.6 0.31 Threshold: 30 obs. Estimate (Standard error) (C) -0.006*** (0.001) -0.452 (0.292) 0.011*** (0.002) 0.350*** (0.058) -0.505*** (0.123) -0.567*** (0.140) -0.329 (0.221) -0.071*** (0.014) -0.001*** (0.0003) 0.011*** (0.002) -0.001 (0.001) -0.061* (0.034) Yes 5,235 0.099 22.6 0.37 *Dependent variable is the natural logarithm of the ratio of subjective dwelling value to average sale-transaction price in census tract for properties with the exact same age, the same house/not house type, the same number of rooms, the same air conditioner type and the same heating system type. Standard errors are in parentheses. Significant at: *** 1%. ** 5%. * 10% 44 ฀฀฀฀฀฀฀฀฀ Appendix A Correlation between the characteristics that correlated with bias and with differences in asset characteristics from census tract means Name of variable Ln valuation Building age House Rooms Air conditioner Heating system Garden P. Value 0.000 0.000 0.002 0.005 0.013 0.000 0.011 45