Losses of Residential Utility from Budget Constraints on Preferences for Homes

Budget-constrained residential preferences differ from unconstrained residential preferences if residents mentally devalue unaffordable attributes’ levels of available homes in comparison with affordable ones. Budget-constrained and unconstrained utilities of 70 recent-mover respondents in Saskatoon SK in 1987 and 74 inner-city respondents in Windsor ON in 2020 are quantified for 12 generic attributes of homes in conjoint choice experiments. Budget constraints on their utilities for homes’ attributes’ levels are operationalized by superimposing marginal implicit prices from a hedonic housing price model in each city. Residential utilities are then statistically compared both through time and for subsamples within full samples, and losses of utility are predicted. Respondents will experience an approximate one-quarter and onetenth loss of possible utility for a home in Saskatoon and Windsor, respectively, if they cannot afford their unconstrained most preferred attributes’ levels. Losses of utility are predicted even though budget-constrained utilities of subsamples of respondents are higher as hypothesized for affordable levels of four attributes, and lower for unaffordable levels of those attributes. In conclusion, theoretical and practical implications of these predictions of losses of residential utility are discussed for residents, housing providers and policymakers.


Introduction
Recent studies reiterate how a resident's financial constraints may impede them from exercising their preferences when choosing a type of new home (Anders-son, Abramsson, & Malmberg, 2019;De Vos, Van Acker, & Witlox, 2016;Howley, Scott, & Redmond, 2009;Hrast et al., 2019;Li et al., 2020). For example, "lower education degree and income imply they may be less able to act on their preferences and think differently about residential mobility (Jiang, Feng, & Timmermans, 2020: p. 5)." Or, " [residential] preferences are inherently connected to assumptions about what is realistic (in terms of price for instance) (Booi & Boterman, 2020: p. 96)." In other words, when a resident behaves as if they assimilate what they can or cannot afford in their residential preferences, this may justify a choice of a less preferred new home (Sirgy, Grzeskowiak, & Su, 2005). They then may have a measurable loss of utility from an inability to afford their unconstrained socially most preferred home (Kahneman & Thaler, 2006;Niedomysl, 2008). This is the first study to quantify theoretical losses of utility for residents, and to compare them through time, specifically in 1987 and 2020.
This theoretical loss of utility from one home versus another is a quantification of a resident's "residential neighbourhood type dissonance"; this is estimated in another study from commuters' stated preferences for four physical neighbourhood attributes contrasted with their actual location in an urban or suburban community (Schwanen & Mokhtarian, 2004). Residents as well as housing providers and policymakers may benefit from exactly knowing how much this superimposition of budget constraints on residential utilities will constrain most preferred affordable levels below unconstrained most preferred ones. Changes in utility may then be simulated for personal, business, or policymaking purposes: Such as by manipulating local prices of these attributes' levels or amounts of housing wealth necessary for residents' affording more preferred homes (Case, Quigley, & Shiller, 2012;Quigley & Raphael, 2004).
Budget-constrained utilities for attributes' levels may supersede unconstrained utilities as articulations of preferences if a resident habitually inserts the budget constraint into evaluations of those attributes' levels (Verhetsel et al., 2017). This hypothesis supplements the general one of resident having quantifiable preferences for homes' attributes in the form of unconstrained residential utilities (Ben-Akiva, McFadden, & Train, 2019;Karsten, 2007). Budget-constrained utilities differ in theory because they filter out unaffordable preferred homes from the unconstrained utility function. A resident can enact these by superimposing omnipresent personal finances onto utility functions for ordering (im-)practical choices of new homes. They can do this while remaining independent from joint influences of local market conditions and homes' availability (Booi & Boterman, 2020;Desbarats, 1983;Maclennan & Williams, 1979;Timmermans, Molin, & van Noortwijk, 1994).
The research question is therefore about empirical differences between a resident's unconstrained and budget-constrained preferences for attributes of homes if these differences produce losses of utility. It is answered with calculated examples of unconstrained and budget-constrained social utilities for 12 generic attri- A further contribution of calculating budget-constrained utilities at different times is the reassessment of whether residential preferences have changed for some attributes of homes and not others during the past more than 30 years. For example, Canadian residents have changed their preferences between 1987 and 2020 by calculating or interpolating utilities for two of 12 generic attributes of new types of single-detached(-like) homes in their utility functions (Phipps, 2021).
Their preferences for four generic attributes also changed when they evinced indifference between these attributes' levels in 2020, after discriminating between them with high and low social utilities in 1987. The newly tested hypothesis is that subsamples of residents have different unconstrained or budget-constrained utilities for the same attributes' levels, but these are compensatory in aggregate and thus have an appearance of indifference.    (Phipps, 2020(Phipps, , 2021(Phipps, , 2022.

Residential Utility and Price Theory
A resident will retrieve or activate their residential preferences from cognitive values for anticipated attainment of comfort, freedom, family, health, money, happiness, and pleasure in one home or another (Jansen, 2012;Lawton, Murphy, & Redmond, 2013;Lindberg, Gärling, & Montgomery, 1989;Zinas & Mahmud, 2012). These cognitive values for Canadian single-detached(-like) homes are assumed to translate into evaluations of 12 generic attributes. These attributes include three each of the dwelling unit, represented by its type and size (x 1 ), house age and exterior finish (x 2 ), and basement condition and home renovations (x 3 ); the neighbourhood environment, represented by its lot size and garage (x 4 ), neighbourhood's landscaping (x 5 ), and neighbouring homes' types and repair (x 6 ); the neighbours, represented by their ages, ethnic group and education, and mobility (x 7 , x 8 and x 9 ); and a home's accessibilities to work and retail stores, schools, and parks or waterfront (x 10 , x 11 and x 12 ) (Table 1) (Phipps, 1987(Phipps, , 1989(Phipps, , 2021Phipps & Clark, 1988 with respect to work and stores, schools, and the waterfront or parks. Distances and travel times are those in relatively compact urban areas, within which most intra-city travel by private or public vehicle requires one half-hour or less. One operational cognitive scale in the literature for evaluating these attributes is in terms of a home's usefulness or social utility; a second is its assetaccumulation potential realized in a price (Phipps, 1987;Weinberg, Friedman, & Mayo, 1981). These two scales in principle measure a home's commensurate value with different metrics, but a resident may emphasize one or the other when evaluating the same home for a different purpose. Altogether, residents may have different scales of value for a home's social utility and its affordability depending on their gender (Darab, Hartman, & Holdsworth, 2018), income, occupation and race/ethnicity (Boschman, 2018;Clark, 2009;Li et al., 2020), age and family composition (Booi & Boterman, 2020;Jiang, Feng, & Timmermans, 2020), and length of residence and knowledge of the housing market (De Vos, Van Acker, & Witlox, 2016). In other words, unconstrained and budget-constrained utilities, and consequent utility losses may be (dis-)similar for residents who have (in-)comparable ways of evaluating attributes' levels, even while they are not necessarily higher (or lower) income residents with higher (or lower) search prices.
Budget-constrained utilities synthesize two cognitive scales of a home's social utility and price by filtering unaffordable attributes' levels out of a resident's unconstrained utility function. Unaffordable attributes' levels are filtered if their prices are above the resident's indicated search price for affordable homes in the local market. Following Phipps (2022), the n th resident has a budget-constrained utility for a j th level of an i th attribute of a home, p x . A resident who is knowledgeable of prices will assign no utility to unaffordable attributes' levels, or at least lower utility than somebody who can afford them, An observed difference between a resident's unconstrained and budget-constrained utilities for an attribute's levels, an overall cumulative loss of utility is less consequential for results, as interpretation focuses on losses of utility for individual attributes. Magnitudes of differences between a resident's unconstrained and budgetconstrained utilities depend upon not only their social utilities but also the position of their affordable price for homes within the range of prices for an attribute's levels in the market. Following Phipps (2022), each price in theory is their willingness to pay for the j th level of the i th attribute of the home, In reality, they will revise these to conform with prices in the local real estate market after interacting with that market. Prices of attributes' levels of the J th home at time t are marginal implicit prices comprising its overall sale price in the local market, where w i is the contribution of each i th attribute's price to overall price in that market.
In sum, a resident's budget-constrained utilities for an attribute will diverge more from their unconstrained utilities if they can afford some but not all the attribute's levels. Larger losses of utility are therefore predicted for attributes with wide-ranging affordable and unaffordable marginal prices such as those of the house type and size, house age and exterior finish, basement condition and home renovation, and lot size and garage (Malpezzi, 2002). In comparison, attributes of the neighbourhood such as the neighbours' ethnic group and education, ages, and mobility tend not only to be weaker predictors of overall prices but also to have less variability as independent variables in hedonic housing price models (Sirmans, Macpherson, & Zietz, 2005). Similarly, accessibilities to workplaces and stores, schools, and parks or riverbank may have relatively unvarying marginal prices for uniformly short distances in two mid-sized Canadian cities, regardless of their statistical correlation with overall prices (Des Rosiers, Dubé, & Thériault, 2011).
Tested hypotheses in this study are about marginal utilities and prices of attributes' levels rather than overall valuations and prices of homes. This is just in case a resident is not utilizing a linear compensatory form of utility and price functions. That is, they are not behaving as if summing each attribute's social utility for an overall valuation of a J th home at time t, This is after possibly weighting each i th attribute by its w n,i importance for them. Nonlinear noncompensatory functional forms may preclude tradeoffs in an overall evaluation or price of a home between not only more and less preferred attributes' levels, but also affordable and unaffordable ones, respectively. A wise resident will ultimately utilize the linear compensatory form of utility function for evaluating all attributes of a home. They should revert to it after using a nonlinear noncompensatory form for screening a home's attributes such as during an intensive or unfamiliar search process (Phipps, 2018).

Utility, Price and Respondents' Data
As already mentioned, hypothesized differences between budget-constrained and unconstrained utilities for subsamples of residents are tested with three interrelated datasets for Saskatoon SK in 1987 and Windsor ON in 2020. The first dataset includes respondents' utilities for homes' attributes' levels, and the measurement of these is described in the next subsection. The second dataset, described in the subsection following that, has additional data about personal characteristics of respondents and their search prices for a home if they looked for one tomorrow. The third dataset has marginal sale prices of attributes' levels in the local real estate market, and their calculations are described in a subsection preceding the results of hypothesis tests.

Experimental Measurement of Utilities for Homes' Attributes
Social utilities for homes were measured in two similar conjoint choice experiments in Saskatoon SK in late-1986 and early-1987, and Windsor ON in late-2019 and early-2020. The first experiment is part of a human-computer simulation game "played" on a portable personal computer; the second experiment is part of an online surveying project on webpages. Additional images of screen input for the human-computer simulation game and the subsequent online housing survey project are in another study (Phipps, 2021). A respondent in the simulation game or online surveying project rated their desirability or like/ dislike for up to 18 hypothetical homes composed of combinations of 12 generic attributes of homes. Each home is represented in a first screen or tabbed display by levels of three attributes of the dwelling unit; in a second screen or tabbed display by three attributes' levels of the neighbourhood environment; and so on for three attributes' levels of the neighbours and three of the home's accessibilities. Displayed attributes' levels differ slightly between the 1987 and 2020 experiments (Table 1). Also, a Saskatoon home's desirability is rated on a zero-to-100line scale, whereas a Windsor home's like or dislike is rated with between zero and five stars. Also calculated from these overall ratings during each experiment are a respondent's utilities for attributes' levels of homes. These were calculated by means of the non-metric WADDALS conjoint scaling program in the standalone personal computer experiment in 1987 (Takane, Young, & de Leeuw, 1980), and multiple linear regression functions in the online webpage experiment in 2020 (Rosetta Code, 2020). While using dummy independent variables for attributes' displayed levels, utilities were calculated for predicting the desirability or like/dislike of each displayed home; and the prediction was instantaneously displayed next to the observed desirability or like/dislike of it.

Subsamples of Residents
Subsamples of residents are formed from among 70 and 74 respondents who  (Phipps, 2021).
Saskatoon respondents' representativeness of movers or other households was not statistically established at the time of their participation. Respondents' characteristics are fully tabled in another study ( Table 2 in Phipps (2022)).  Potentially interpretable subsamples of respondents are inferred from hierarchical cluster analyses of intercorrelations between individual respondents' unconstrained and budget-constrained utilities for all 12 attributes in each study

Subsamples of respondents in
year (Deurloo, Dieleman, & Clark, 1988;Hrast et al., 2019). Two clusters summarize intercorrelations between unconstrained utilities of Saskatoon respondents, their budget-constrained utilities, and the budget-constrained utilities of Windsor respondents; whereas the latter's unconstrained utilities have three clusters (Table 2). Final clusters are inferred from not only the maximum or second-maximum increments in agglomeration statistics but also numbers of included respondents. Note that agglomeration coefficients, derived from mean distances within clusters, are indices of similarity between clusters formed at each stage. Larger coefficients indicate relatively more heterogeneous clusters with more dissimilar members.
Clusters of Windsorites are more interpretable than Saskatonians' skewed ones. These two clusters of intercorrelated budget-constrained utilities of 50 Windsorites (minus one with a missing classified occupation) are more interpretable from statistically-significant parameter estimates of hierarchical loglinear models at 5% significance level or less (Agresti, 1990;Alba, 1987;Timmermans, Van Der Heyden, & Westerveld, 1984). Budget-constrained respondents in the first cluster are probably wealthier. They are two-and-a-half times more likely to have a managerial or professional occupation, a search price above $200,000 and to be in that cluster than they are in the second cluster with the same base combination (Table 3). Correspondingly more likely in the second cluster than this base combination are budget-constrained respondents who do not have a managerial or professional occupation while having a search price up to $200,000. Note that these odds of a cluster's members being respondents with a particular combination   Managerial or professional occupation * Search price above $200,000 * Unconstrained second cluster 0 are the same four-times more likely in the first cluster as those who do not have a managerial or professional occupation and have a search price up to $200,000, while the latter combination is also three times more likely in the second cluster. Despite this, the combination of cluster membership and two variables of managerial or professional occupation and search price is the sole saturated loglinear model with perfect, zero, goodness of fit statistics (Table 3 and Table 4). In other words, this loglinear model with 1987 or 2020 data performed better than those with alternative characteristics of respondents such as gender, age, tenure class and length of residence.  (Phipps, 1987(Phipps, , 2020. Six attributes' levels constructed from MLS and census data in the city of Saskatoon and inner-city Windsor almost exactly correspond with descriptions in the conjoint choice experiments. These are displayed attributes' levels of house type and size, age of construction (and exterior finish), basement condition and renovations, lot size (and garage), landscaping, and neighbours' mobility. (Windsor's possible new name of an attribute is in parentheses.) Correspondences are more approximate in a second group of five attributes of neighbouring home types (and repair), neighbours' ages, ethnic group and education, and accessibilities to schools and parks in Saskatoon or riverbank in Windsor. The least corresponding attribute of work and stores accessibility is represented by inverse distance to downtown Windsor in kilometres for homes in two relatively compact inner-city neighbourhoods; and by a similar coding to schools' access for near to and far from major workplaces and stores in Saskatoon. Neither multiple regression is the most parsimonious model, owing to entry of independent variables for calculating marginal prices of attributes' levels (cf., Phipps (2020)). Comparisons of attributes are helped by graphing subsamples' mean unconstrained and budget-constrained utilities for four attributes' levels, with their 95% confidence intervals. A graph's single horizontal X-axis has descriptions of an attribute's levels. Its primary vertical Y-axis has mean unconstrained and budget-constrained utilities and 95% confidence intervals of the "wealthier" first cluster of Windsorites in 2020 for an attribute's levels (as blue or purple solid lines, respectively, and same-coloured above and below dashes), as well as those of the "poorer" second cluster (as red or orange solid lines and dashes). The secondary Y-axis has predicted marginal prices of sold homes' attribute's levels in Windsor in 2020 (as a green dashed line).

Budget-Constrained versus Unconstrained Residential Preferences
Mean utilities are also statistically correlated for affirming visual differences between unconstrained and budget-constrained preferences for attributes' levels through time. Three attributes have exceptions to the full samples' almost perfect correlations between their mean budget-constrained and unconstrained utilities. Exceptions in 2020 are the strong but imperfect correlations from 0.78 to 0.89 for attributes' levels of house type and size, house age and exterior finish, and neighbours' ethnic group and education (Table 1). In addition, respondents' subsamples have interpretable higher or lower budget-constrained utilities than unconstrained utilities for the first two of these attributes' levels as well as two additional attributes' levels of basement condition and home renovations, and lot size and garage. Respondents' losses of utility are consequently calculated with their unconstrained and budget-constrained utilities especially for five attributes' levels.
Losses of utility are percentage differences between utilities for unconstrained most preferred attributes' levels and budget-constrained most preferred levels along the full 0/"totally disliked" to 5/"totally liked" utility scale in 2020, or derived −2/"very undesirable" to 2/"very desirable" scale in 1987. They are not calculated with the ranges between a respondent's minimum and maximum utilities for attributes' levels. This is because their minimum or maximum may not equate with an attribute's truly totally disliked or totally liked level, respectively.

Two Attributes' Unaffordable Levels for Some Respondents
Beginning with the full Saskatoon sample, a three-bedroom bungalow with 93 sq•m. or 1050 sq•ft. floor space is the budget-constrained most frequently most preferred attribute's level of house type and size in 1987. This attribute's level is Saskatonians' most frequently most preferred one, that is, by 18 respondents or one-third of those who can afford it (Table 1). They however will experience an average 7% loss of utility if choosing this budget-constrained most preferred house type and size as opposed to their unconstrained most preferred one. A two-and-a-half storey four-and-a-half-bedroom home with 158 sq•m. or 1700 sq•ft. floor space is the unconstrained most frequently most preferred attribute's level by over two-thirds of the full sample. Only 17 respondents however can af- respondents' mean unconstrained utility for it, based on non-overlapping 95% confidence intervals (Figure 3 in Phipps (2022)).
Relatively higher budget-constrained utilities for more preferred attribute's levels, but losses of utility if unable to afford most preferred attribute's levels, are therefore two observed relationships for attribute's levels of house type and size.
These are also relationships in statistically significant differences between two subsamples' mean budget-constrained and unconstrained utilities for this attribute's levels in Windsor in 2020.
Clustered respondents have higher budget-constrained utilities for affordable attribute's levels of house type and size if a wealthier subsample is in the first cluster and a poorer one is in the second cluster. Twelve respondents in the first cluster, or one-half of them, are respondents who most frequently most preferred a two-storey house with three-and-a-half bedrooms ( Figure 3). (Similar tabulated results for clustered Windsor respondents as those in Table 1 for budgetconstrained respondents are available from the author.) Wealthier first-cluster respondents then have lower mean budget-constrained utilities for the most frequently most preferred bungalow or one-and-a-half storey house with two bedrooms by nine respondents in the poorer second cluster, or one-third of them.  In comparison, Windsorites will lose an average 5% in utility if they cannot afford a house such as the most frequently most preferred one less than 5 years old with brick or stucco exterior finish by nine respondents in the first budgetconstrained cluster, or more than one-third of them (Figure 4). This is their average lost utility if they instead choose one such as the most frequently most preferred house more than 30 years old with the same exterior finish by 18 second budget-constrained cluster's respondents, or three-quarters of them. Correspondingly, Saskatonians will lose up to an average 7% in utility if unable to afford a house with unconstrained most preferred young age.

Two Attributes' Differences in Utility between Respondents
Discrepancies between budget-constrained and unconstrained utilities for two attributes' levels of house type and size, and house age and exterior finish, prove the unaffordability of the preferred highest priced attributes' levels for many respondents, and thus predict theoretical losses of utility for them. Moreover, their more discriminating budget-constrained preferences for these two attributes' levels, as well as those of basement condition and home renovations and lot size and garage, contradict the inferred evolution in unconstrained preferences towards indifference for these attributes from 1987 to 2020.   Figure 5). The first cluster's mean utilities for this attribute's two lower-priced levels are not only statistically significantly lower than those of respondents in the second cluster. They are also statistically significantly lower than their own mean utilities for three higher-priced levels.
Altogether, 18 budget-constrained respondents in Windsor, or more than one-   same respondents for six attributes' levels of landscaping, neighbours' ages and mobility, and accessibilities to work and stores, schools, and parks in Saskatoon.

Four Attributes' Differences in Utility Unrelated to Affordability
In short, differences between budget-constrained and unconstrained utilities in both 1987 and 2020 may be nullified by narrow price ranges' exclusions of the same respondents who cannot afford any type of neighbours, neighbourhood, or accessibility.

Discussion
Relatively narrow ranges of predicted marginal prices for six attributes' levels in Saskatoon SK in 1987 and five in Windsor ON in 2020 lead to a violation of one of two conditions under which residents can evaluate homes with budgetconstrained utilities. This first condition is that they can afford some but not all attributes' levels' marginal prices. Some respondents however will have incalculable budget-constrained utilities for all unaffordable attributes' levels, though they may afford them by trading off higher-priced attributes for lower-priced ones of a displayed home. Still, most respondents fulfill the second condition of familiarity with attributes' prices in the local real estate market. For example, majorities of respondents in Saskatoon had recently moved into a new home, and in Windsor knew a neighbour who had recently listed a home or property for sale, or did this themselves. If excluding attributes with narrow ranges of predicted marginal prices, respondents have potentially different budget-constrained utilities than unconstrained utilities for six or seven attributes in 1987 or 2020, respectively. Budgetconstrained utilities are particularly consistent with hypotheses for evaluations A. G. Phipps of three attributes' levels of the dwelling unit of single-detached (-like) homes, plus its lot size, by up to 70 respondents in each of two mid-sized Canadian cities.
Respondents on average have higher utilities for affordable attributes' levels, such as those in wealthier households preferring a more expensive larger house type and size that is a newer home possibly with a brick or stucco finish; with a finished full basement and extensive home renovations; and a large lot possibly with space for double attached or detached front garage. In comparison, respondents who cannot afford those attributes' levels have relatively higher utilities for less expensive attributes' levels: such as a three-bedroom bungalow that is more than 30 years old and has a brick or stucco finish; and has an unfinished or partly finished full basement with some modern features or renovations; and a medium lot with space for a single attached or detached front garage.
Subsamples of respondents who have different affordabilities therefore have compensatory differences between their unconstrained and budget-constrained utilities for four attributes' levels. They are more discriminating between these attributes' levels' utilities than unconstrained respondents in the full sample appeared to be in another study (Phipps, 2021). Consequently, residents have not necessarily become more indifferent about these attributes' levels in 2020 than 1987. Notwithstanding, currently-defined subsamples of respondents are as indifferent or discriminating about remaining attributes' levels as the full samples were. Mean budget-constrained preferences are not statistically significantly different from mean unconstrained preferences for attributes' levels of the neighbouring home types and repair, and the three accessibilities of single-detached (-like) homes in 1987 and 2020. Also, four attributes of the dwelling unit and neighbours have uninterpretable statistically-significant differences in relation to hypotheses.
Hence, residents at least in inner-city Windsor ON can have the same most frequently most preferred levels of eight remaining attributes regardless of whether they are budget-constrained or unconstrained: A single-detached(-like) home in a neighbourhood with very mature landscaping, with lawns, large trees and dense shrubs; and almost all single-detached houses with owner-occupiers and no houses in need of major repair. With neighbours who are middle-aged residents with elementary school-aged children at home; who are skilled and whitecollar workers with high-school or technical-college education, most of whom are from different ethnic groups than them; and few of whom move each year.
With a location within easy driving-or walking-access, up to 10 minutes to major stores and/or work; within 10 minutes walking to a school; and on the Detroit riverbank.

Conclusion
In conclusion, respondents will have a home in Saskatoon in 1987 with an approximate average one-quarter loss of utility, or a one-tenth loss in Windsor attributes of a single-detached(-like) home. A typical resident with a moderate loss of utility will be living in a home with a satisfactory but imperfect combination of attributes' levels. Loss of utility from living in a budget-constrained preferred home, as opposed to the unconstrained most preferred one, may be an "alternative explanation for the low residential satisfaction of rural residents… that these people might have been forced to live in these neighbourhoods due to budget restraints" (De Vos, Van Acker, & Witlox, 2016: p. 855). It also may substantiate whether "this group of families with older children is increasingly made up of households that want to stay in the city, instead of households that had to stay because of limited options on the housing market" (Booi & Boterman, 2020: p. 111). Under these circumstances, a resident's and policymaker's probable question is about the required compensation for affording unconstrained most preferred attributes' levels. Preliminary analyses predict average decreases in attributes' levels' prices or increases in household wealth of $21,000 for Saskatonians and $47,000 for Windsorites as compensating for their loss of utility in 1987 and 2020, respectively. The assessment of these compensatory expenditures is a focus of future research.