Inmoving and outmoving residents as opposed to stayers are sources of most social, economic and environmental changes in a neighbourhood (e.g. [1] [2] [3] [4]). Movers however may sooner or later move again from their current locations, and so explanation of neighbourhood changes during a long study period may be complicated by participation of different (un-)observed individuals in those changes [5] [6]. In comparison, conventional houses remain in the same location long after residents have come and gone. Changes in the same homes’ prices and their attributes of the dwelling unit and neighbourhood will thus be immobile indicators of the changes in a neighbourhood [7] [8]. This is because a home’s sale price, or change in it, is generally hypothesized as a function of attributes of its dwelling unit, neighbourhood and location, and the changes in them; and its time of sale and time of resale if any; as well as the prices and attributes of neighbouring sold homes during the previous few months [9] [10] [11] [12].

In particular, homes’ prices and attributes may get better or worse during occurrences of “local events” that are attributable to individuals’ and organizations’ activities inside or outside a neighbourhood. Impactful events originating outside a neighbourhood include declining employment or housing affordability, and a recessionary state of the economy or not; and those inside a neighbourhood include constructed or planned land use changes [13] [14]. Such events are therefore hypothesized in this study as producing fluctuations in prices of homes through time after controlling for the homes’ attributes of the dwelling unit and neighbourhood [15] [16]. Quigley’s [17] hybrid housing price model is calibrated for testing this hypothesis about changes in homes’ prices in two inner-city neighbourhoods; and so this refines tests with single sales hedonic housing price models or repeat sales models in other studies (e.g. [18] - [23]). The tested data are the prices and the attributes of the dwelling unit and neighbourhood of all approximately 2900 sold homes in two inner-city neighbourhoods in Windsor, Ontario, since 1981 or 1986 depending on when data collection began.

This study therefore not only interprets neighbourhood changes in two inner-city neighbourhoods during long study periods in terms of changes in sold homes’ prices and their attributes of the dwelling unit and neighbourhood. It also correlates predicted neighbourhood changes in houses’ prices with occurrences of local events, hypothesized in the next section as caused by people’s activities inside and outside those neighbourhoods. More precise predictions of changes in prices by a hybrid price model will be advantageous for diagnosing neighbourhood change, as this model is a statistical synthesis of both a single sales hedonic price model and a repeat sales model. In the end, hybrid models empirically predict very modest increases in house prices unless these prices are augmented by changes in sold homes’ attributes of the dwelling unit and neighbourhood. These findings have methodological and practical implications for conclusions about changes in two inner-city neighbourhoods during the past more than 30 years.

Four types of potentially-impactful events for a neighbourhood may be analogous to those hypothesized by Carson and Dastrup [16] as causing changes in the attributes of homes and their prices from one city to another. Hence for an i^th home in an n^th neighbourhood with a predicted change in price Δ p ^   i t at time t:

Δ p ^   i t   = F ( B E n t , E C n t , H C n t , H P n t ) (1).

where the first variable in Equation (1), B E n t , is the surrounding built environment if it has major new buildings and facilities or planned ones inside a neighbourhood that are capitalized in prices of nearby homes—or if outside of it, there are permits for new homes or completions of them in suburbs that siphon off demand for used houses, and decrease their prices [24] [25] [26]. For example, another study [27] speculates that house prices in two study neighbourhoods may have been stabilized by community planners’ residential rehabilitation assistance programs in the early-1980s [28], and community improvement plans during the mid-2000s [29] [30]. Another speculation is the possibly benign effect on house prices of the opening of the so-called temporary casino in 1994 on the border of one neighbourhood, and its closure and replacement with the permanent casino in 1998 on the border of the other neighbourhood (Figure 1) [31]. Operationally, the casinos and the residential rehabilitation assistance programs are coded 1 for their operating years and zero otherwise, especially because the permanent casino has reportedly continuing land use impacts [32].

In comparison, the community improvement plans and four additional major construction or demolition projects near to or in the study neighbourhoods may have created beneficial (in-)accessibilities for a few years for some residents who work in them, play on them, or no longer see them; and so they are coded 1 for their first five years of (in-)existence and zero otherwise. Three constructions are a sculpture park along the Detroit riverbank in 1999 (Figure 2), a downtown corporate headquarters in 2002 (Figure 3), and a suburban sports arena in 2008

instead of a retrofit in one study neighbourhood (Figure 4); and a fourth demolition in 2013 of a hospital closed in 2004 in the other study neighbourhood (Figure 5) [33] [34] [35]. Last, the study neighbourhoods contain few new single-detached and duplex houses, and so metropolitan Windsor’s new residential building permits will be for properties located in far away suburbs. Operationally, monthly numbers of building permits aggregated to calendar years are prorated by metropolitan Windsor’s corresponding annual estimated total population; and then lagged by one year as if used homes’ prices react to a previous year’s new construction [36] [37] [38]

The second variable in Equation (1), E C n t , is the state of the city-wide economy represented by the unemployment rate and presence or absence of an economic

recession [39]. House prices may decline during periods of high adult unemployment when residents are earning and saving less, and possibly moving out [40]. Sales and prices may decline even further during a national economic recession that originates in another economic sector than adult (un-)employment, such as the four just before or during the study period in 1980, 1981-1982, 1990-1992, and 2007-2009 [41] [42] [43] [44], includes graph; operationally, recessionary years are coded 1, and other years, zero. Together, a chronic high unemployment rate after the end of a recession may depress house prices for several more years in an unresilient neighbourhood such as an inner city one [14] [39]. Monthly unemployment rates are available for metropolitan Windsor [45].

The third variable in Equation (1), H C n t , is the ongoing cost of home ownership including requirements and interest rates for mortgages. Decisions about housing purchase and upkeep typically depend on the availability of financing from private financial institutions as well as the ratio of loan to equity that is ultimately related to residents’ savings and earnings [46] [47]. Both components are measured in Canada’s mortgage interest cost index on a monthly basis as a constituent of the consumer price index [48] —although this national index encompasses more expensive housing markets than that of Windsor [49]. Note that this mortgage interest cost index is not correlated with presence or absence of an economic recession in Canada, thereby confirming the effectiveness of banking regulations against subprime mortgages during the 2000s.

The last variable in Equation (1), H P n t , represents the appreciation or depreciation of house prices in the market. This however may be less salient herein than in Carson and Dastrup’s [16] study where it refers to house price changes in a city during the decade until the great recession of 2009. It in any case will be endogenous with changes in prices for a proportion of metropolitan Windsor’s monthly house sales located in two study neighbourhoods (e.g. [50]).

Occurrences of local events will be independent variables in multiple regressions having a hybrid model’s predicted annual percentage changes in homes’ prices in each neighbourhood as the dependent variable. These predictions will have statistically controlled for differences in homes’ times of sale and resale, changes in their attributes of the dwelling and neighbourhood, and compositions of their neighbouring sold homes. Moreover, hybrid models’ predicted changes in prices should provide more precise indicators of change in a neighbourhood from prices and attributes of sold and resold homes through time [17] [51]. This is because a hybrid price model is the statistical synthesis of a single sales hedonic housing price model and a repeat sales model of the same data.

The more frequently-tested hedonic housing price model assumes that a once-sold ( i = 1 , ⋯ , I ) house’s price at a ( t = 1 , ⋯ , T ) time t, p i t , is a function of its ( k = 1 , ⋯ , K ) attributes at that time, { x k , i t } , the composition of its ( m = 1 , ⋯ , M ) neighbouring sold homes up to that time, { λ m , i t } , and the time of sale itself (e.g. year), d i t , equalling 1 for the time of sale and zero otherwise:

LN   p i t = a + β ' x i t + ' A λ i t + ' γ d i t + η i + e i t (2)

where β = { β k } is a K × 1 vector of implicit prices of attributes, and x i t = { x k , i t } is a K × 1 vector of observed attributes of an i^th house at sale time t; similarly A = { α m } is a M × 1 vector of marginal implicit prices, and λ i t = { λ m , i t } is a M × 1 vector of observed correlations with an i^th house’s neighbouring sold homes up to sale time t; γ is the T × 1 vector of price changes through time and d i t is the T × 1 vector of time-dependent dummy variables for this i^th house. And an error term ε i t for this home is decomposed into a time-independent specification error η i and a white noise process e i t .

A single sales hedonic price model does not differentiate between I once-sold homes at time t and J resold homes also indicated as selling at time t when sold either the first time or the second time or more. In comparison, the frequently-tested repeat sales model distinguishes each ( j = 1 , ⋯ , J ) home sold more than once from the I once-sold homes by its t time of original resale and τ later time of resale. A j^th home’s difference in resale price at time τ versus sale price at time t, ( p j τ − p j t ), is a function of its change in each k^th attribute between these times, ( x k , j τ − x k , j t ), the change in its composition of M neighbouring sold homes between those times, ( λ m , j τ − λ m , j t ), and the time between sale and resale, ( d j τ − d j t ), coded (−1) for time of sale, 1 for time of resale, and zero otherwise in a time-dependent dummy variable, δ j τ :

( LN   p j τ − LN   p j t ) = β ( x j τ − x j t ) ' + A ( λ j τ − λ j t ) ' + ' γ δ j τ + e j τ − e j t (3)

where A = { α m } and β = { β k } are now respective M × 1 and K × 1 vectors of marginal implicit price changes; and λ j t = { λ m , j t } and λ j τ = { λ m , j τ } are M × 1 vectors of a j^th house’s correlations with neighbouring sold homes at its sale and resale times, and x j t = { x k , j t } and x j τ = { x k , j τ } are K × 1 vectors of its observed attributes at those times. γ is still the T × 1 vector of price changes through time but δ j τ is the T × 1 vector of time-differenced dummy variables for a j^th house. And the error terms for a j^th house are white noise processes of e j t at time t and e j τ at time τ .

A hybrid price model exploits the inclusion of these repeat sales of the same homes in a dataset for updating the error structure of a single sales hedonic price model by removing unobserved specification errors due to dependencies between repeat sales [52]. The derivation by Jones [53] of these error terms for inclusion in a covariance matrix corresponds with the analysis of the random effects model by Greene [54]. The error variance of a single sales regression in Equation (2) is estimated with the residuals, { ε ^ h } , from the ordinary least squares regression for all ( h = 1 , ⋯ , H ( = I + J ) ) once-sold and resold homes. It also has an adjustment for lost degrees of freedom for K + M coefficients of attributes of homes and their neighbours, T coefficients of their aggregated times of sale, and the constant intercept:

σ ^ ε 2 = ( 1 H − K − M − T − 1 ) ∑ h = 1 H ε ^ h 2 (4)

The error variance of a repeat sales regression in Equation (3) is estimated with the ( j = 1 , ⋯ , J ) residuals, { ξ ^ j } , from this regression, also with an adjustment for lost degrees of freedom for K + M coefficients of attributes of homes and their neighbours, and T coefficients of their aggregated times of sale, but no constant intercept:

σ ^ e 2 = 1 2 ( 1 J − K − M − T ) ∑ j = 1 J ξ ^ j 2 (5)

As explained in another study [52], these estimates of error variances in Equations (4) and (5) are elements of an estimated covariance matrix from which are decomposed values of a p-value matrix for rescaling data of the observed I once-sold homes and J resold homes in a hybrid price model. As a result, this hybrid price model will have lower standard errors of regression coefficients for more precise predictions of house prices than the single sales hedonic model, while also having statistically-similar regression coefficients [17] [20] [52] [55] [56].

Required data for calibrating a hybrid price model are effectively those required by both a single sales hedonic price model and a repeat sales model [57]. A hedonic price model requires time-of-sale data for sold homes’ prices and attributes of their dwelling unit and neighbourhood, and compositions of their neighbouring sold homes. The more onerous required data for a repeat sales model are the changes in prices of the same homes between times of sale and resale, and the corresponding changes in their attributes of the dwelling unit and neighbourhood, and differences in the compositions of neighbouring sold homes.

This study’s data are for all 2,920 inhabitable single-detached and duplex houses sold through the Multiple Listing Service in two inner-city neighbourhoods in Windsor, Ontario. These data were collected from the beginning of January 1981 in one neighbourhood named Glengarry (Figure 6), and from January 1986 in another named Wellington-Crawford (Figure 7), until the end of December 2018 in each neighbourhood. Data from the early-1980s are retained for the former neighbourhood’s study period as these were unusual years for house sales. Addresses of sold houses in each neighbourhood are plotted on online maps available from http://web2.uwindsor.ca/courses/sociology/phipps/agp/gwc/gwcmaps.html.

Nine attributes of the dwelling unit were coded from the MLS listing at each

time of sale, and these are lot size in thousands of square feet; numbers of garages, bedrooms, bathrooms, and storeys; and dummies for exterior brick finish, finished full basement, central air conditioning, and home’s condition coded from a realtor’s summary evaluation as −1 for poor, 0 for normal, and 1 for excellent (Table 1). Eight attributes of the neighbourhood are the median annual income in thousands of dollars for adults in a dissemination area (DA); and percentages in a DA of: dwelling units needing major repairs, households with at least one child at home, owner occupiers, visible minority population, and adults who are blue-collar workers, unattached, or university educated.

Differences between sold homes’ attributes justify distinct analyses of each neighbourhood’s data: Five attributes of the neighbourhood have statistically significant different means in the two study neighbourhoods, as well as four of the dwelling unit based on non-overlapping 95% confidence intervals in the table. Note the attributes of the neighbourhood are from the 2001, 2006, 2011 or 2016 census closest to the time of sale or resale of a home; and they are appended to its data after locating it inside the boundaries of one of 25 DAs in Windsor, Ontario. The year 2001 was the first for subdivision of Canadian census metropolitan areas such as Windsor, Ontario, into DAs with the small-area data used in this study [58]. Theretofore, two study neighbourhoods were covered by four larger census tracts having not only different boundaries but also different variables than subsequent dissemination areas.

Boundaries of the mostly rectangular dissemination areas, approximately one-half kilometre by one-quarter kilometre in size, and aligned with a grid street pattern, may delineate a visual and interactional neighbourhood of homes in this part of the city. However, the neighbourhood of a sold home may have a separate effect from that of its attributes and changes in them if a home’s sale price is correlated with prices of M recently-sold neighbouring homes [59] [60].