Conceptual irregularities in housing affordability definitions.

Earlier attempts by researchers to define HA were characterized by diverse interpretations which focused primarily on the economic dimension; as illustrated in Table 1. For instance, Howenstine’s [17] interpretation of HA as an ‘unreasonable amount’ was faulted by Maclennan and William, [18] whose definition, though clarified the question of ‘unreasonable amount’ but their concept of a ‘given standard of housing’ and ‘unreasonable burden’ was also not comprehensive. Hancock [21] introduced the concept of opportunity cost. This implies trade-offs made by households in order to afford housing cost and whether such trade-offs is reasonable or excessive. The weakness in the concept of opportunity cost is that it created an understanding of HA that does not imply any form of measurement approach.

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Table 1. Selected key definitions of housing affordability based on literature.

https://doi.org/10.1371/journal.pone.0221246.t001

Only a few studies attempted to distinguish the HA concept from its measurement approach. A very clear example is the views of Chapman [26], who opined that HA is the measure of the financial outcome of outright purchase or renting a house. Recently, researchers began to see the need to consider other non-monetary dimensions into the definitions and measurement approaches of housing affordability. For instance, Leishman and Rowley [24] posited that HA is comprised of housing standards and appropriateness, as well as social, neighborhood issues and economic participation. However, Rowley and Ong [27] questioned the extent to which neighborhood quality is addressed when evaluating the appropriateness of affordable housing with regards to cost.

Housing affordability concept–Weaknesses and new understanding.

Indeed, the debates, concerns and opinions about HA concept reflect the different assumptions and priorities of researchers with different orientation. For instance, economists mostly prioritize clarity of concept, utility, and objectivity [28], while sociologists usually focus on social inequality concerns and the research capacity of HA to cover actual experiences of household housing stress [29]. Architects are focused largely on providing savings and cost reductions in both upfront costs and the ongoing cost of occupation [30]. Such diverse academic orientation led to the revelation of the weaknesses in the conventional measurement approaches, and arguments in support of methodologies that better reflect the concept of HA.

However, there are no generally agreed standards by which it is conceived or measured. Thus, international housing policy documents of most countries adopt the 'rule of thumb', advocating that 30 percent or more of household income should be spent on housing for it to be considered affordable [31]. This notion is usually propagated without any recourse to household composition, size, housing quality or neighborhood characteristics, income levels, age groups and location. Therefore, the 30% affordability standard as a qualifying ratio is flawed. But it has remained the reference point for housing policy’s purposes; for instance, in allocating housing vouchers, low-income tax credits, stamp duty concessions and grants.

The most common weakness in the HA concept is its insensitivity to the effect of housing supply; and neglect for people’s heterogeneous behaviors within the same income group. This is consistent with Stone et al., [32] assertion that the HA concept must be founded on the interaction flanked by households and their houses. The authors maintained that affordability is not an innate attribute of the house and its measurement must not depend upon house price and income alone; owning that an affordable house could be different for each individual. Therefore, it suggests that in measuring affordability the approach applied must significantly capture each human variable that describes such relational concept.

Adopting sustainability principles into measurement criteria of HA.

Recent studies are starting to consider wider dimensions of the criteria that induce HA problems and have advocated that HA assessments should address more sustainable and wide ranging criteria such as economic, environmental and social aspects that affect households [6.7]. This implies that a broader range of quantitative and qualitative criteria must be accounted for, towards achieving actual HA. These include, but not limited to, social wellbeing, neighborhood and location issues. In addition to sustainability and health concerns, housing standards and appropriateness, housing market, transportation cost, households and their quality of life as well as political criteria [33,27,34] instead of exclusively focusing on income and housing price as the prime determinants. Congruently, it is essential that both sustainability and affordability issues are tackled simultaneously in the measurement approaches used in HA analysis [7]. These are illustrated in Fig 2, a model for understanding the evolving concept of HA.

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Fig 2. A conceptual model for understanding the HA concept.

(Source: Adapted from [4,6,7].

https://doi.org/10.1371/journal.pone.0221246.g002

Conventional approaches.

There are three kinds of conventional approaches as identified in literature. These are Income ratio method (IRM), residual income method (RIM) and composite method (CM). However, IRM and RIM are generally classified as normative measures. It refers to the certain threshold value of a standard or a limit of HA [11]. This implies that a list of benchmarks are set to determine if a given household income can offset housing cost. Normative measures have been dominant and frequently utilized in housing affordability research.

Income ratio method (IRM)

The IRM designates a threshold value or percentile level of housing cost to income ratio in assessing the housing consumption ability of households [49]. It assumes that no matter the household income, a certain percentage of their income will always be devoted to housing-related expenses. This offers a method that enables researchers, to set a benchmark for HA based on empirical data analysis. The IRM has a long history of development and are of several types such as: housing-expenditure-to-income-ratio, rent-to-income-ratio, ongoing-housing-cost-to-income, house-price-to-income-ratio, housing-loan-repayment-to-income, debt-to-housing-price and mortgage-to-income.

Usually, new IRM is coined to address the weaknesses in an older method. For instance, Wegmann, [9] modified IRM and coined a replacement metric called the subsidy per housing affordability equivalent (SHARE) ratio. Nonetheless, traditional approach of IRM is simply the same as the definition. That is, households suffer HA stress when the ratio of income to housing cost (the affordability ratio) go beyond a given threshold ratio. Mathematically, IRM states that: (1)

The most common of this method is the Price to Income Ratio (PIR) method. It refers to the ratio of median house price and median annual household income. In essence, it measures the number of years that a household needs to accumulate their wealth from their disposable annual incomes in order to purchase an average housing unit:

This model is highly associated with Paldam Macau’s (1970) equilibrium model which states that:

Where, the demand for residential properties (Qd) is a function of price (P), the long-termed income (Yo) and the government policy (Go). The supply of residential properties (Qs) is a function of price (P).

Use of IRM: IRM has often been used due to its relative ease of application. For instance, to determine social housing qualification, and in estimating the size of groups with affordability issue, as well as to assess the prospective borrowers’ ability to service a mortgage. Dong and Zhou, [5] used the ratio of rent to income (RIR), to empirically analyze the impact of HA on the permanent migration will of rural-urban migrants. Similarly, Rowley, et al. [50] examined how the use of ratio measures could give consideration to broader financial stress.

Weaknesses in IRM: IRM suffers multiplicity of weaknesses like the inability to consider quality changes over time of housing stock, and the influence of housing cost appreciation [51]. It designates a small value for a certain cordon of income to housing cost [21] and erroneously assumes that households with different income can afford all non-housing expenditures with 70 percent of their income. IRM is unable to estimate the amount of new households that should have emanated if individuals did not share houses or had remained in their parents’ houses as a result of their inability to afford rental or mortgage payments [52,53,11].

Most prominently, the ratio measures generally do not consider the spatial dimensions of transport cost, irrespective of the enormous effect housing location exerts on household commuting expenditure [14]. Hence, underestimates the number of households over burdened by combined commuting and housing costs. Fundamentally, IRM focuses on the “typical” (median) property and ‘typical’ (median or average) household; hence it neglects the price and property type variations which the first home buyers as well as those low and moderate income households would preferably demand. It can also underestimate the affordability burden of lower-income households and could overestimate such burden for households with higher income. Consequently, its adoption as a measure of HA has always faced criticism.

Residual income method (RIM)

RIM was developed as a better alternative to IRM. It perceives HA from a basic non-housing consumption perspective. Thus, it reveals the interaction between housing cost, income and non-housing expenditure [54]. RIM is hinged on the idea that HA is the ability of households to offset their housing cost, yet retain the capacity to meet non-housing expenditures [11]. Simply put, the income left after housing payment. It is the belief of the protagonists of this method that it makes more sense to evaluate if households posses enough income to meet other none housing expenses after offsetting housing cost, instead of assessing an arbitrary percentage of income consumed by housing [54]. Relying on this notion the “shelter poverty” concept was introduced. It describes as “shelter poor” households whom having paid for decent housing, becomes incapable of meeting other non-housing needs at a minimum socially acceptable standard [29]. A phenomena described as ‘after housing’ poverty, in poverty literature. This implies that RIM cares whether the income left after housing expenses plummet beyond shelter poverty or housing-induced poverty levels [53]. Recently, Luckey [10] introduced a location-sensitive residual income (LSRI) technique, which considers the benefits and impacts of transportation decision on HA. However, mathematically RIM is given generally by: (2)

Hence, RIM posits that expenditure on one item would mean the potential sacrifice of others [11]

RIM = residual income − housing costs

= (Household disposable income–basic non-housing living expenses)–monthly mortgage repayments:

When RIM is less than 0, monthly disposable income of the household after meeting the basic living expenses is not enough for mortgage loan repayment, and vice versa [55].

Use of RIM: Yang, et al., [56] used this method in Beijing to analyze the relationship between affordable housing programs and household accessibility to public services and affordability of decent housing. Revington and Townsend, [57] identified affordable rental housing locations when rapid public transit services are considered using RIM. More recently, Mundt, [58] applied a comprehensive RIM where affordability is at risk to determine household types and market segments.

Weaknesses in RIM: Yip, [59] allergies its confusion with poverty measurement, while Henman and Jones, [60] claim that a separate benchmark is required for each household rather than a uniform percentage, This implies that in solving problems of HA, data requirement transcends housing and labor markets, thus, making it more burdensome. RIM like the IRM is economically focused, and as a result do not assess the non-monetary and qualitative aspects of housing. It problematizes affordability study in the sense that it relies on the minimum housing and non-housing consumption, which is considered subjective and differs among different classes of income, regions and cities, and therefore, should not be used in the analysis of HA on a macro level.

Composite method (CM)

As the debate over the methodological superiority of the RIM over IRM rages, other studies seem to favor CM [61]. Indeed, arguments have been raised by earlier studies that it is not possible to account for all the concerns associated with HA in one simple measurement approach. The protagonists of CM maintain that HA should not be assessed using one approach [62] but combining a number of concepts [63] and developing multiple overlapping measures [64] that can provide better understanding of HA which is more reliable; and reduces the methodological weaknesses in IRM and RIM.

Generally, this method uses the composite regression equation as specified thus: (3)

Where, Y is the Dependent (or Response) variable; θ is the constant or intercept of the regression model, σ² is the variances and covariances of the random term. Hence, the model can be written as: (4)

Such that,

μ = Error associated with the model.

Y is the estimator for affordability while X₁, X₂, and X₃, are identified housing challenges (factors) in the study area; and coefficients of in the model.

Use of Composite Method: Thalmann, [65] combined the three indicators of affordability: rent-to-income ratio, housing consumption and quality based measures. Updating his studies in Thalmann, [22], the author used the RIM rather than the rent-to-income ratio (RIR) and computed it along with housing consumption measure and quality-based measure to quantify and determine over consumption and overpayments of housing services. Ndubueze, [62] refined and updated in Ndubueze, [66] combined the RIM and PIR while adjusting for housing quality to formulate an aggregate measure of HA. Recently, Tang, [64] used RIM (budget and poverty‐line standard), along with RIR in order to complement their weaknesses and optimize their strengths for rental affordability measurement. Similar to Sunega and Lux [67], Sarı and Khurami, [42] assessed HA using a composite of subjective approach, RIM and IRM.

Weaknesses in CM: It considers household income as the only financial source of housing purchase. But other distortion factors such as family savings, housing subsidies and other capital incomes are neglected. CM does not address what gets back to households for what is spent on housing in terms of neighborhood and housing quality [68]. CM produces misleading result when presented as an independent measurement unit since it identifies good or bad policy, but fails to provide how the policy can be improved. In application, the composite is faced with challenges of which indicators should be used to devise the composite in the first place? What should the individual influence of each sub-indicator on the composite be? Are the data sources comparable when measuring the same phenomenon in a cross-country perspective? These weaknesses must be considered before applying the technique.

Scarcely used measurement approaches.

Behavioral approach

The behavioral approach assesses affordability by examining the housing decisions of individual households. It simply reviews the housing consumption behavior of a household. This implies that the behavioral approach focuses on the normal housing decisions while adjusting for what households with certain incomes and compositions confronted by certain prices opt to pay for housing [19]. Behavioral approach deals with understanding the choices households make regarding location, type, tenure, and size of housing. It also deals with the problem of mortgage arrears and repossessions, so as to investigate the household’s affordability based on their decision. Households housing consumption behavior is a veritable tool for HA assessment. However, the outcome of the research performed by Fein, et al., [69] and Maclennan, et al., [70] were inconclusive. Yet, the advocates of behavioral approach believe that when HA problem is assessed as an explicit issue and the empirical data available is sufficient to support an in-depth research, this approach would better reveal households’ spending pattern towards developing indicators of HA [59]. It is also believed that the threshold developed from a behavioral point of view, that is, the point at which the increments in cost of housing indicates a different qualitative model in its interaction with household income, suggests an indication of housing in-affordability, and can be employed as well to validate affordability outcomes of other measurement approaches.

Use of Behavioral Approach: Arguably, the behavioral approach can be integrated into the normative measures in determining the threshold affordability ratios. Using this approach, Wood et al., [71] observed that the behavioral effects of several kinds of housing allowances are insufficiently examined, because housing subsidies could discourage unemployed households from seeking employment opportunities in other locations. Similarly, Grinstein-Weiss, et al., [72] observed that low income households saving behaviors are mainly influenced by the structured opportunities they are offered. Recently, Olanrewaju and Woon, [73] combined both internal and external criteria that influence household decision-making to study homebuyer/homeowner behaviors.

Weaknesses in the Behavioral Approach: The behavioral approach is considered difficult to compute and many a time unable to present a real evidence of the behavioral path of people's housing consumption. However, with the invention of behavioral economics and the perceived weaknesses in normative measures, behavioral approach is believed to have potential for further development.

Subjective approach

Given that both behavioral and normative measures are regarded as objective measurements. Kearns et al., [74] offered a completely different approach, called the subjective approach. Subjective approach summarizes the subjective evaluation of households’ perception of their housing need [75] in relation to housing quality and condition, affordability dilemma and overcrowding. It directly asks respondents if they consider their house affordable or not, as the qualitative and subjective measurements are checked against their financial position and other quantitative criteria. The data generated are used to establish a threshold cordon of their HA with the conviction that households are better positioned to offer the best assessment of their housing situation. This approach rests on the assumption of homo economicus. Following this approach HA is a function of household income. Mathematically, it states that, (5)

Use of Subjective Approach: Subjective indicators are often employed as predictors controlling price of property [75] or as a complement for objective indicators. Stiglitz, et al. [76] noted that obvious difference between objective and subjective indicators which is impossible to explain under human psychology or money illusion could lead to ineffective distribution of public resources and weakening trust in official statistics, in some countries (e.g. the UK). Nevertheless, it is believed that subjective measures can offer other information left out under standard objective measures, and can support cost-benefit analysis and policy evaluation as well as aid the identification of potential policy problems [77]. It is therefore remarkable, that studies in housing have marginally devoted interest in developing alternative HA measures that responds more precisely to subjective perceptions of housing stress [68].

Weaknesses in the Subjective Approach: Subjective indicators easily fluctuate over time more than the objective measures [42]. This approach requires normative assessments of what represents the “living costs”. However, it seems that adopting some sort of normative basis for definition and measurement is unavoidable in any HA analysis [78].

Emerging innovative methodologies.

New methods of measuring housing affordability are emerging as a result of improved understanding of affordability burden, and the fact that the existing HA measures focus mainly on the fiscal dimension while other modified approaches mostly re-emphasized the weaknesses of the methods they tried to amend. Three emerging novel methods (which are essentially adaptations from the distinctive measurement approaches, but with more robust methodologies) were identified in the literature. Examples are; multiple criteria decision making (MCDM); Gini coefficient and mobility probability plot (MPP) methods.

Multiple criteria decision making (MCDM) method

MCDM is a tool involving both qualitative and quantitative factors [79]. It is a set of methods that supports the consideration and aggregation of several criteria, often numerous, mostly at variance, decision criteria [80], which is used to describe, choose, rank or sort, a range of alternatives to support a decision process [79].

Use of MCDM: Several models within the MCDM methodological framework have been suggested [81]. The most commonly used MCDM models include; the Complex Proportional Assessment (COPRAS), Analytical Hierarchy Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) [7]. A novel study by Mulliner, [68] refined and updated in Mulliner, et al., [6] adapted the COPRAS model to assess HA, as an instance on how to apply MCDM for HA analysis. The findings indicate that taking into account additional criteria that clearly consider housing location and community sustainability, housing quality amongst others; against mere economic considerations alone, can significantly impact affordability calculations. Adopting the same method in Sabah, Malaysia Said, et al., [80] assessed the best locations for the development of sustainable affordable housing programs. Mulliner, et al., [7] investigated the applicability of several models within the MCDM methodological framework, for optimal HA assessment. The study revealed that various MCDM models can be applied for sustainable HA assessment, as a result of the model's ability to address the numerous conflicting decision criteria and the multidimensionality of issues found in HA problems. Mathematically put - (6)

For instance, the COPRAS method is represented as (7) where x_ij is the value of the i-th criterion of the j-th alternative, and qi is the weight of the i-th criterion.

Weaknesses in the MCDM: When several models within the MCDM methodological framework are employed to assess same problem, they often generate different results [81]. MCDM is susceptible to manipulation which could alter the degree of result accuracy. Daniel, et al., [82] remarked that though the complex nature of this measure deepens the overall understanding of multiple concerns which breed HA problem, there is a chance that its complexity could weaken the uptake by analysts and researchers.

Gini coefficient method

The Gini coefficient measures the inequality within the income distribution of a given population (by means of a ratio analysis). It captures the influence of income inequality in estimating HA. Various approaches are applicable here, for instance, RIR estimate based on average. However, the method is based on net PIR. Mathematically, Such that the HA at a period t, can be estimated as: (8) where, t is a time period index, GA and GH are net income and housing affordability Gini coefficients, respectively, is the average housing price-to-net income ratio (across all households at time t), CONTROLS is a matrix of macroeconomic variables, including gross domestic product (GDP), unemployment rate (UNEPR), exchange rate (EXR), among others. Meanwhile, β_o to β₂ are parameters, is a vector of parameters and ε_t is a random disturbance term associated with the model.

Use of Gini Coefficient Method: The Gini coefficient method can be applied in the comparison of income distributions across different sub-populations [37]. A novel study by Ben-Shahar and Warszawski, [83] adapted the Gini coefficient method to estimate income inequality in HA, and to evaluate the factors associated with the time-varying inequality measures of HA. More recently Dong, [37] used this method to evaluate the effect of growing income inequality on low income tenant families’ worsening rental affordability.

Weaknesses in Gini Coefficient Method: The Gini coefficient mainly lies on its relative nature; then information on absolute regional and individual income is lost, and fails to consider the causes of inequality [84]. Also, as a measure of inequality and the fact that it only isolates the inequality in the distribution of a particular macroeconomic variable. Thus, it isolates the magnitude of the variable to a relative rather than an absolute degree which implies that a country can witness simultaneously, for instance a rising income inequality and a reduction in absolute poverty [84]. It is also quite possible to have countries of disparate income levels having similar or even in some cases, identical Gini coefficients, which implies a high income country having the same Gini coefficient as a very low income country, or moreover a region with predominantly low income and low quality housing, having the same HA inequality index as a region with higher income and predominantly higher housing quality. Consequently, Gini coefficients should not be used as a stand-alone quantitative measure of a particular variable such as wealth and housing affordability. Instead, it is advisable to augment it with other measures that capture the variable on an absolute scale.

Mobility probability plot (MPP)

MPP was originated by Cheong and Wu [85] for studying regional inequality. It is based on PIR which is obtained by dividing the house price by income [8]. MPP is the transitional dynamics of HA based on Markov transition matrix approach and the stochastic kernel technique. It is however used to analyze the mobility of PIR for cities, thereby measuring city-level trends of HA. MPP is expressed in percentages (ranges between −100 and +100). A positive value of MPP suggests that the city will have a net probability of moving upward in the distribution of PIR, thereby indicating that the PIR of the city will become higher and higher, and the housing price will be more unaffordable. In contrast, a negative value of MPP indicates that the city has a net probability of moving downward in the distribution of PIR which indicates that the city has a high tendency of registering a decline in the PIR.

MPP can be computed by calculating p(x) as: (9)

Where, ∫ is the function of integration, X is an observed value of relative household income at time t; and g_r(z/x) is the transition probability kernel which maps the distribution from time t

Use of MPP: A novel study by Cheong and Li, [8] adopted the MPP to study the transitional dynamics of HA indicators. Li, et al., [40] employed the MPP method to analyze the mobility of housing price growth and impact the enactment and withdrawal of home purchase restrictions (HPR) policy have on changes in housing price.

Weaknesses in MPP: Li, et al., [40] remarked that although the contour maps and three-dimensional plot generated provides much salient information on the distribution dynamics, the interpretation may be very difficult and challenging.