An Analysis of Alignments of District Housing Targets in England

Abstract

Context: It has been claimed that recently, in England, the places with the greatest amount of housing built were the places that least needed them. This is an accusation that has echoes in a number of countries around the globe. The lack of construction leads to greater unaffordability and a lower level of economic activity than could have been achieved if labour, particularly those with high human capital, was not so constrained as to where they could afford to live. The recent National Planning Policy Framework for England imposes mandatory targets on housing planning authorities. As such, the following question is raised: will the targets result in additional residential homes being located in places of greater need than the prevailing pattern? Research Questions: The paper sets out to consider the spatial mismatch between housing additions and national benefit in terms of unaffordability and productivity. Specifically, do the concentrations of high and/or low rates of the prevailing rates of additional dwellings and the target rates of adding dwellings correspond with the clusters of high and/or low unaffordability and productivity? A further question considered is: does the spatial distribution of additional dwellings match the clusters of population growth? Method: The values of the variables are transformed at the first stage into Anselin’s LISA categories. LISA maps can reveal unusually high spatial concentrations of values, or clusters. The second stage entails comparing sets of the transformed data for agreement of the classifications. An agreement coefficient is provided by Fleiss’s kappa. Data: The data used is of additional dwellings, the total number of dwellings, population estimates, gross value added per hour worked (productivity data), and house price–earnings ratios. The period of study covers the eight years prior to 2020 and the two years after, omitting 2020 itself due to the unusual impact on economic activity. All the data is at local authority district level. Findings: The hot and cold spots of additional dwellings do not correspond those of house price–earnings ratios or productivity. However, population growth hot spots show moderate agreement with those of where additional dwellings are concentrated. This is in line with findings from elsewhere, suggesting that population follows housing supply. Concentrations of districts with relatively high targets per unit of existing stocks are found correspond (agree strongly) with clusters of house price–earnings ratios. Links between productivity and housing are much weaker. Conclusions: The strong link between targets and affordability suggests that if the targets are met, the claim that the places that build the most housing are the places that least need them can be challenged. That said, house-price–earnings ratios present a view of unaffordability that will favour greater building in the countryside rather than cities outside of London, which runs against concentrating new housing in urban areas consistent with fostering clusters/agglomerations implicit in the new modern industrial strategy.

1. Introduction

In the Localism Act, 2011, English land-use planning shifted from a ‘top-down’ housebuildingtarget approach to one with local development plans based on local authority estimates of future housing need [1]. Two outcomes from this were that new housing was poorly aligned with local plans, and the districts were too small to establish strategic trade-offs that maximise the benefits and minimise the costs of new housing over a larger area—such as a travel-to-work area [2]. Targets reemerged in 2019 only to be abandoned in 2023, allowing councils the flexibility to set their own goals.

The Institute for Government (IfG) asserts that, following this devolution of authority, the national pattern of new housing has been poorly aligned with where it could deliver the greatest national benefit in terms of tackling the most acute affordability problems, maximising productivity gains in key areas such as England’s second-tier cities, and aligning with national infrastructure plans [2], p. 54. The IfG raised the concern that although targets offer a more strategic approach, can the prioritisation of targets over local objections stand the test of time? It is known that local planning vetoes can skew the distribution of new construction projects away from where they might be needed.

Two strategy documents emerged from the labour administration of 2024 that address these issues, in part. In the green paper of November 2024, the new modern industrial strategy—Invest 20351, the UK government’s 10-year strategy seeks to remove binding constraints on economic performance in its highest potential growth-driving sectors and places. There is an emphasis on clusters, including spatial clusters. It recognises that the UK’s economic performance is skewed towards London and the South East, and it acknowledges that second-tier city-regions, like Greater Manchester, the West Midlands, and Glasgow, are not generating the growth and local prosperity that urban agglomerations of their sizes should. Housing was not mentioned. The IfG has a view on how the new housing could improve the growth prospects of such centres.

In December 2024, the National Planning Policy Framework (NPPF) was published which sets out the housing planning policies for England, including the annual housing target of 370,000 dwellings2. This target is apportioned to local authority districts following a formula. Local targets may be successful in overcoming local vetoes, but do the targets offer a better link between additional residential dwellings and national well-being?

This paper sets out to offer a measure of the similarity of spatial clusters. The variables can be correlated using Kendall’s tau to establish benchmark measures of association. The LISA–kappa process entails two stages. First, each variable’s values are classified into one of five combinations of spatial correlation components using Anselin’s LISA method. This is a means of revealing clusters or concentrations from the data. The extent of agreement between the pairs of variables’ LISA classifications is estimated using Fleiss’s kappa. The utility of the approach in assessing agreement is explored using data from the residential construction industry at a sub-regional level, specifically the recently announced housing targets and the prevailing spatial distribution of additional dwellings. The spatial concentrations are measured for agreement with proxies for socially desirable distributions of additional dwellings based on productivity and affordability. The questions addressed include the following: Do locations of the clusters of high unaffordability and additional dwellings agree? Alternatively, is there a correspondence between the spatial distribution of additional dwellings and clusters of high productivity areas? The same questions are considered with the targets: Does the distribution of the target number of additional dwellings agree with areas of most acute affordability problems? Also, do those areas targeted for greater housing match clusters with high growth potential? In effect, has the opportunity of using targets to overcome local impediments been taken in some form? Elsewhere, due to the varying local management of planning permits, it is found that relatively high housing stock growth is followed by a correspondingly high population growth rate. As such, a further question is considered: do the clusters of additional dwellings spatially align with those of population growth?

The paper is constructed as follows. First, there is a review of housing market areas and the monocentric urban model. The model provides a link between additional dwellings and their location in an unconstrained context, house prices, and productivity. Constrained growth is introduced in the context of planning restrictions. The urban–rural divide is considered, as are locational preferences and different income groups. Next, there is a discussion of productivity and the performances of key parts of England. Poorly performing large centres in the North are highlighted as underperformers by a recent strategy document, which emphasises improving productivity. A link between current thinking on productivity, where locational sorting and clusters feature, is the escalator region.

Factors that affect affordability are reviewed next. These include credit, particularly in a risk-to-lender context. This is followed by discussions of the provision of additional housing with an emphasis on the role of planners, permits and local vetoes. There are many voices calling for some means of overcoming supply bottlenecks. A possible means of constraining local impediments is offered by the recent scheme of mandatory building targets. The algorithm that underpins the targets is outlined.

Section 3 covers the method. Local Indicators of Spatial Autocorrelation (LISA) are outlined, as is the scheme for assessing alignment between the LISA classifications and Fleiss’s kappa. The idea is that, if one were looking to claim that the prevailing provision of housing was distributed to reflect need, as measured by unaffordability, there would be significant overlap between the revealed clusters of house price–earnings ratios and those of additional dwellings.

Results are presented in a graphical and a tabular manner. It is shown that correlation and agreement provide similar inferences. What is actually added to the housing stock is concentrated in areas where there is population growth, which reflects findings elsewhere. The clusters of targets are shown to match house price–earnings ratios, suggesting the new targets are concentrated in areas of need. However, house price–earnings ratios can provide misleading notions of changing in housing need. Lending inserts a wedge between prices and income and those lending policies can vary temporally and spatially, which could result in a different view of what wrong areas for additional dwellings might be.

1.1. House Prices Across Space

Standard theoretical models on industrial location theory focus on the colocation of productive and commercial activities [3] and agglomeration economies. These nodes or urban centres are contrasted against more rural, less densely populated areas. The node attracts workers who collocate with their employment opportunities. A housing market area (HMA), as analysed using the frame of the monocentric urban model (MUM) [4], comprises a central business district (CBD) which benefits from agglomeration economies, which underpins the wage paid to the workers, and hence the average price or rent in the HMA. The more productive the CBD, the greater the wage offered. Assuming a disutility of commuting is common to all agents and dwellings are homogenous, the house price declines with distance from the CBD. The intra-urban house price–earnings ratios (HPERs) duplicate the price decline.

A rise in productivity at the CBD attracts more to the urban area. As there is greater competition for dwellings due to the higher wage offered in the business district, rents rise. In other words, the locational rent premium for existing dwellings rises. In the MUM, construction takes place at the periphery of the city [4], ch10. More commute to the CBD as the higher wage compensates for the longer travel time by those that live at the expanded edge of the city. McCann [3] and Glaeser and Tobio [5] have versions of this with constrained expansion of the city. The HMA or the built-up area of the node will be larger under unconstrained conditions, with a lower average house price. As such, the HPER is higher under constrained conditions. Existing owners have an incentive to restrict the supply of additional dwellings in the locale [4], p. 267 through some control of the planning process in the face of increased productivity. Glaeser and Tobio [5] consider restrictive housing (land) development policies to manage the adverse effects of growth. A city’s population will be greater under unconstrained conditions. In equilibrium, relative to the planner’s optimum, high-productivity locations are settled at dwelling densities that are too low [6].

The homeowners within cities with faster expected growth (in productivity and population), and with otherwise identical features to slower growing nodes, because of expected growth in rental yields, would experience higher house prices [4], p. 49. A negative demand shock is not the inverse of a positive change. With a decline in productivity at a CBD and/or a population contraction and a fall in price, new construction could be suspended until the surplus capacity is removed [4], ch10. In this context, the housing stock is posited to remain static. The durability of housing results in a supply curve being kinked with a vertical portion [7]. A paucity of new dwellings in a locale could be a result of inadequate demand rather than restricted supply.

The MUM has restrictive assumptions that could be relaxed. Where building land is in demand, it could be used more intensively. This could entail demolishing and rebuilding or converting existing dwellings so that there is an increase in the density of population. As such, dwellings close to the CBD are more likely to be high-rise.

Another relaxation is to envisage four income groups that can exercise choice over the size of dwelling [3]. As they are more reliant on public transport networks for commuting, the low-income group would live closer to the CBD than older-rich and middle-income groups that are not so constrained. The rich-younger group prefer being close to the CBD where social facilities are also located, such as shops, theatres, and galleries, whereas the older-rich, who value space and can absorb commuting costs, live further from the CBD in relatively larger dwellings [8]. The middle-income group is posited to slot in between rich-old and low-income groups [3]. A wage compensation hypothesis would posit that there is a non-pecuniary reward for living in a favourable locale, such that the wage is lower than otherwise [3], resulting in a higher HPER.

Rather than solely pecuniary factors affecting utility, locational amenities such as a good school or a historic building [9] would again feature the rich outbidding others to locate in the vicinity. From this it is evident that as the rich outbid others for access to more desirable locations, HPERs may not strongly reflect need.

An HMA is a territory where individual property prices, although diverse, are in a stable intra-urban hierarchy [4]. The comovement is facilitated by migration, commuting or switching house-search behaviour. Price overspill and the ripple effect [10] point to similar, but weaker, forces at work at the inter-urban level. As captured by the spatial equilibrium model [11], agents relocate until their utility cannot be increased. This preserves price level differentials across an urban hierarchy and within a locale. Population shifts are posited to respond to price anomalies.

Depending on the degree of spatial disaggregation used, the complexity of multiple housing market areas can be made evident or averaged out. A spatial unit such as a district could capture an HMA. Alternatively, commuters who live and work across spatial unit boundaries could be seen as a spatial mismatch [12]. The HPER compares the house price with earnings associated with a district. The price of an abode in one district is affected by the productivity or income in another. The most likely case is the rich commuter that works in the city but lives in the country. In this scenario, the prices in both districts will be influenced by the productivity of the city. Thus, this cross-border commuting is part of the mechanism that maintains similarity of house price across borders.

1.2. Relative Productivity and Urban Centres

As discussed in Section 1.1, agglomeration economies underline higher productivity levels and growth rates. However, differences in productivity across cities can in the UK also be explained by locational sorting and place [13]. It has been suggested that UK city performance is an issue of location rather than size [14]. In many countries, large cities can be found among the top and bottom performers. Also, the performance of smaller- and medium-sized cities is highly varied, with some faced with low or even negative growth in population and economic activities [15]. Sluggish growth associated with some larger centres in many northern UK cities is explained by large-scale deindustrialisation [16]. Here, urban areas face a deconcentration of jobs and population. The membership of a place in a broader regional ‘club’ still appears to be an important determinant of its productivity [14].

Enhancing the productivity advantages of larger nodes is locational sorting. The most talented in the labour market are attracted to the productive agglomerations by the returns offered, boosting the advantages of the nodes. Fielding’s escalator region [17] features high productivity in a sorting and regional ‘club’ setting. The featured club in [17] is the South East of England, with London at its heart. The region would

–

Attract to itself many young talented people at the start of their working lives;

–

Provide the context within residents to achieve accelerated upward social mobility through movement within the region’s labour and housing markets;

–

Lose, through outmigration, a significant proportion of those who had experienced this upward social mobility.

Of relevance here is the attraction of the young who benefit from upward mobility in both career and housing schemes. Wages, productivity and house prices would be higher than in non-escalator regions. Consistent with Metcalfe [2], assisting second-order cities [18] to become ‘escalator regions’ would be consistent with the new modern industrial strategy.

Burn-Murdoch [19] claims that the concentration of high-paid jobs in the London area is increasing whilst the weak construction performance of additional dwellings is holding younger, talented workers back. The claim could point to a failure in the provision of housing for the escalator to function. The attraction of talent without a corresponding rise in suitable accommodation could constrain high-productivity cities/escalator regions, lowering national GDP growth by excluding talented workers from the escalators’ housing markets [19,20].

This exclusion of talented workers from primary labour markets may be a filtering mechanism which works to the advantage of large over small cities. More talented individuals stand a higher chance of becoming highly productive entrepreneurs in larger cities, but there is a tougher selection process [21]. The sorting implies the migration of more talented individuals into the larger cities, displacing the less talented workers who move out. Thus, with a static housing stock, output of the city per worker could be larger. This exodus of the not-so-talented can also benefit the productivity of cities elsewhere.

As noted above, rental yields are expected to have a greater locational value in the future in cities with better growth prospects. This expectation can be affected by price dynamics. Over a price cycle, in large cities, prices are consistently higher than the ‘pre-acceleration’ level [22]. It is concluded that the average growth acceleration is a signal of a permanent shift in a location’s economic fundamentals. In small cities, real price gains are not so clear. Indeed, Van Nieuwerburgh and Weill [23] argue that the increase house price dispersion in metropolitan USA over 1975 to 2007 is related to increase productivity differentials. As such, productivity and price should be spatially autocorrelated in a similar manner.

Partridge et al. [24] found that in the decade leading up to 2000, remoteness from a large node in the US urban hierarchy was associated with lower productivity, wage, and housing cost. Yet there was an increase in net-household attractiveness of intermediate-sized areas relative to the largest metropolitan areas. It is suggested that less congestion and leisure activities in smaller urban areas and rural areas were motivating factors in this relocation.

Low productivity levels are also found in coastal and rural areas of England. GVA per head (resident of the principal seaside towns) is around 20% below the national average. This is affected by a large elderly/retired population (23%). In the vast majority of seaside towns, average hourly earnings for both men and women are below the average for the region of which they form a part3 of. Smaller seaside towns are on average 27% below the England GVA/head benchmark4 and have an even higher proportion of elderly individuals (34%). DEFRA [25] observes that in 2020, GVA per job in what are ‘Predominantly Rural’ territories was around 81% of that of England as a whole. In the Drivers of Rural Productivity 2010 to 20155 strategy document, it is noted that the stock of housing is limited in rural areas relative to demand, and house prices are on average 6.7% higher in rural areas than in urban. Given that incomes are lower in rural and coastal areas, such territories have higher HPERs than in urban ones, on average.

1.3. Credit and Affordability

In spatial equilibrium, a well-functioning capital market generates the same returns after adjusting for risk. Mortgage lending across space should be no different [26,27], p. 244. Addison-Smyth et al. [28] posit that in both the UK and Eire, the ability of credit institutions to access funding from abroad, post-2000, has increased average mortgage levels. Prices in 2008, on average, were 30% greater than what they would have been if this alternative source of funding had not been available. That said, an asset price model would predict higher house prices and would be associated with lower interest rates [4]. Post-2008, there was a sustained period of quantitative easing and almost zero interest rates. Macroeconomic policy placed pressures on supply [29] as house prices became dislocated from incomes, separated by larger amounts of debt finance [30].

The distribution of credit is a key cause of price variation. Rae [31] points to deprivation as reducing risk appetite. Housing costs and house prices will be related, in part, by the lenders’ views of risk-in-lending to borrowers in a locale. Areas with declining populations, low wage growth, etc., will be viewed as having poor credit scores, deterring lending there. Szumilo [32] analyses English local authority districts data. He finds a difference between the dispersion of affordability ratios across the least and most dense areas, as the former becomes much more concentrated while the latter sees much more variance. The locational premium in the densest populated areas is, arguably, key to resolving the unaffordability problem. Gray [33] considers district HPER over 1997–2019. On a broad regional basis, consistent with lower productivity [13,14,16], city districts in the North and Midlands are more affordable over the period than the South is.

What is notable in [33] is the divergence of London’s house prices and levels of affordability from the rest of the country. The explanation of the divergence fits an escalator region thesis. The sorting of human capital concentrates those with long-term high earning potential. Despite high prices, mortgage lenders would see the escalator region’s housing market as relatively low risk. Borrowers can repay more over a sustained period, so lenders are flexible on lending criteria. London and the surrounding districts are characterised by higher income plus greater loans for each unit of income. Higher housing equity growth is a feature of an escalator region [17]. Higher equity returns to the owner, that come with high prices, are amortised by moving out of London at the end of their career. Those that are not able or willing to shoulder higher debt before then look at further localities earlier on. Thus, higher London prices extend to neighbouring areas through a variety of routes, including finance and migration [10]. Factors such as lending criteria or risk appetite and interest rates drive affordability rather than need, giving an inflated view of housing need in London and the surrounding areas.

1.4. Building Constraints

Planning permission and monopoly practice have been blamed for an insufficient response to housing signals. In an environment where planning and the regulation of land-use disrupts economic projections, the provision, or lack of it, may inhibit growth. The concern about the inhibiting nature of the planning process at the local level is recognised by [2] and in the National Planning Policy Framework (NPPF). Binding constraints on new construction are found by [34]. They estimate that if the interpretation of planning rules in districts in the South East of England had been the same as in the North East of England, house prices in the south would have been roughly 25% lower in 2008. However, at a more disaggregated level, they conclude that physical supply constraints are genuinely binding in densely developed areas, such as the London borough of Westminster. Regulatory constraints are important in the southeastern city of Reading. In the cities of Newcastle and Darlington in the north of England, supply constraints have little influence on house prices.

Allowing for a heterogeneity of price elasticity of residential dwelling supply, ref. [5] find that the increasing population of the Sunbelt in the US prior to 1970 was driven almost entirely by the increasing association between the amenity of a pleasant climate and economic productivity. In the period after that, the rise of the Sunbelt population would be attributed in equal measure to faster housing supply growth and economic productivity. Wang and Rickman [35] see something similar in mainland China. Land (housing) supply plays a vital a role in determining regional differences in population growth. Shanghai and other major cities in the east of China have the smallest relative growth in land (housing) supply which explains almost all of their faster housing price growth and most of their lower relative population growth. This area is addressed in the English context in Section 4.

The Competition and Markets Authority [36] considers the housing construction market in the main as speculative. Housebuilders bid for land based on the estimation of the value of the homes they can build on it, which is uncertain. Uncertainty, in return, is managed to some extent by restricting the number of new homes released at a time, also known as the build-out rate [36,37], to be consistent with the local absorption rates. New homes are sold at a rate which should not reduce the local price. The CMA does not find this a restrictive practice. Rather, it is a function of the industry and the releasing of land by planners.

There is a poor record of neighbourhoods outside city centres in England adding new houses during the period 2011 to 2019 [38]. This is notable where neighbourhoods are located near commuting infrastructure. This can be attributed to the planning system and the disincentive that planning objections from local actors impose [38,39]. Correspondingly, builders might look to build in areas less likely to be subject to objections. As a result, it is concluded that the planning system acts a gatekeeper to success in the housebuilding industry [37]. Green et al. [40] and Paciorek [41] argue that increasing lags in the permit process adds to the cost of supplying new houses. Green et al. [40] find that increasing either the length of approval timelines or their perceived uncertainty by one standard deviation above average is sufficient to thwart the responsiveness of both the housing supply and demand in desirable neighbourhoods in Canada. Opposition from council and community groups also substantially reduces the housing supply’s ability to respond to growing demand.

The 2024 annual report from Demographia [42], which analyses affordability across the globe, claims that land has been rationed in an effort to curb urban sprawl based on an international planning orthodoxy. The most severe declines in housing affordability for the middle classes are where these artificial restrictions have been imposed on the supply of residential land.

1.5. Target Methodology

Chapter 3.25 of the NPPF offers a link between economic growth and planning, stating that it will be necessary to introduce effective new mechanisms for cross-boundary strategic planning. Chapter 4 of the NPPF proposed planning reforms states that a baseline increase of 0.8% of existing housing stock in each local planning authority should be applied. Chapter 4.12 states that worsening affordability of homes is the best evidence that supply is failing to keep up with demand. The standard method for apportioning the target of adding 1.5 million new homes over 5 years to districts is laid out in Chapter 4. Both the (current) old method introduced in 2018/2020 and the new (2024) method use workplace-based median HPERs to assess affordability. By putting increased weight on the size of the deviations of the local HPER over a ratio of four, the new method puts greater emphasis on housing affordability in assessing needs than the old. The old method added an uplift for districts containing the largest proportion of the population of the top 20 major cities. Overall, the changes resulted in most, but not all, areas seeing an increase in their target. A key exception was London. When analysed by region, London boroughs were required to add 88,000 a year, and when the previous target was linked to the 300,000, it was 99,000 per year. In other words, the proportion of the national target that London had to fulfil was reduced from 33% to 24%. The pressure to meet the national target moved.

How close the targets reflect differences in affordability across space is unknown. The usefulness of HPERs is reviewed in Section 4.

2. Materials and Methods

2.1. Overview

Anselin’s local indicators of spatial association (LISA) [43] statistics reveal the spatial arrangement of variable X, where the adjoining territories have higher [or lower] values of X than is expected by chance, and they are classified as hot or [cold] spots or clusters. Although simple, authors have used such statistics for spatial analysis to reveal Functional Urban Regions (FURs) [44,45], clusters of migrants [46], house price growth [47], and employment centres [48]. FURs have also been exposed by bivariate LISAs [49]. The hinterland districts with high out-commuting (variable Y) are adjacent to a centre or cluster of population (variable X). A software package that supports this statistical treatment, GEODA6, shows the usefulness of ‘linking’ two cluster maps. Once the values for both variables X and Y for each of the territories are transformed into the LISA classification set, they can be compared. Fleiss’s coefficient of agreement (kappa) can be generated for a pair (or more) of variables and for each of the various cluster classifications.

The philosophy behind Kendall’s rank order correlation coefficient (tau) is one of concordance: the rank order between a pair of values in X variable is the same as that in Y. One could see this as a measure of agreement in order. Kendall’s tau has some affinity with the LISA–kappa statistic. They can be seen as measures of association. The former is used as a benchmark for the latter.

2.2. Spatial Autocorrelation

A variable X is spatially random if its distribution follows no discernible spatial pattern: unusually high or low values of X should be dispersed randomly. Spatial autocorrelation implies an absence of this dispersal. Variable X is correlated with the spatial weighted average of itself. Positive spatial autocorrelation is when such unusual values are clustered together beyond what would occur randomly, and negative spatial autocorrelation occurs in cases where such values tend to be dispersed and further apart from each other.

Moran’s I is commonly used to test the null hypothesis of spatial randomness, ranging in value from −1 to +1. Moran’s I does not indicate where these clusters are located. To address this, ref. [43] proposed a LISA, which focuses on the relationships between each observation and what is defined as its surroundings, by the weights matrix. These local Moran’s, when mapped, present five outcomes that are colour-coded for five classifications. High–high (HH) combinations comprise a centre and neighbouring areas with a collection of collocated districts with high values of X. A low–low (LL) combination highlights a cluster of the obverse. There can be one without the other. A high–low (HL) combination entails a district with a high value being surrounded by other districts with low values. If this is a down-market district or declining city, these districts could appear as a doughnut on a map. Alternatively, an up-market district or city in a declining region could be seen as a diamond [-in-the-rough]. A low–high (LH) combination indicates a low value being surrounded by other districts with high values. A LISA can be defined as $I_i=z_i{\sum }_{r=1}^N{w}_{ir}{z}_r$, where $z_i{=x}_i-\overline{x}$, i, r = 1…N districts. LISA inferences are based on conditional permutations. The fifth zone contains the residual random or uninteresting districts, which are not spatially unusual. A similar statistic to LISA, Getis-Ord Gi*, reveals 3 clusters: not interesting (not significant); cold; and hot. These latter two are the equivalents of LL and HH combinations.

The value of I_i depends on how ‘local’ is envisaged and is represented by a weights matrix W. A queen weights matrix defines clusters in terms of contiguous spaces, where w_ir = 1 for a neighbour and 0 for non-neighbour. Islands, having no adjoining spaces, would have weights of zero only, and so cannot be classified as part of a cluster. To address this, the nearest neighbours can be used. In the territory set used here, the Isle of Wight is the only example of an island. The matrix is adapted so that w_ir = 1 corresponds with its two nearest neighbours (New Forest and Gosport). As such, these two districts are treated as the Isle of Wight’s neighbours for assessing clusters.

2.3. Fleiss’s Kappa

Fleiss’s kappa coefficient (κ) measures inter-rater reliability [50]. Kappa is a coefficient of agreement with a range from 0, which is the degree of agreement among the k raters that would be expected by chance to 1, which would be full agreement. It can be negative. Rather than raters, this work uses the LISA classification for variables established at stage 1, where each one has their values classified into one of the (m=) five mutually exclusive LISA categories of HH, LL, LH, HL, and not significant, thus generating Nm (= 308 × 5) = 1540 possibilities. These possibilities are compared for agreement. This offers the scope for generating the degree of agreement between, say, targets and a proxy for need. Additionally, the stability of, say, a measure of need can be assessed for agreement over two or more punctuations of time.

Let n_ij be the number of times the ith district is found in the jth LISA classification. At the extreme, a district is ascribed say to be the hot spot within each of the k variables assessed at one time, and the ith row of the matching matrix would contain the value k in the jth column and zeros elsewhere. This implies full agreement. The proportion of districts to be allocated to the jth category is $p_j={\displaystyle \frac{\sum _{i=1}^N{n}_{ij}}{Nk}}$. If the districts were randomly allocated to a LISA classification, the expected agreement rate across all districts would be $P\left(E\right)={\sum }_{1=j}^m{p}_j^2$. The extent of agreement across k is an average of the proportions across the N districts. The proportion of times the districts are assigned to the same category is P(A). The proportion is calculated as $P\left(A\right)=\left[{\displaystyle \frac{1}{Nk\left(k-1\right)}}\sum _{i=1}^N\sum _{j=1}^m{n}_{ij}^2\right]-{\displaystyle \frac{1}{k-1}}$. The kappa statistic is $\kappa ={\displaystyle \frac{P\left(A\right)-P\left(E\right)}{1-P\left(E\right)}}$. This results in $\kappa =1-\left[{\displaystyle \frac{{Nk}^2-\sum _{i=1}^N\sum _{j=1}^m{n}_{ij}^2}{Nk\left(k-1\right){\sum }_{j=1}^m{p}_j\left({1-p}_j\right)}}\right]$. The variance of kappa is given by ${\displaystyle \frac{2}{Nk\left(k-1\right){\left({\sum }_{j=1}^m{p}_j\left({1-p}_j\right)\right)}^2}}\times \left[{\left({\sum }_{j=1}^m{p}_j\left({1-p}_j\right)\right)}^2-{\sum }_{j=1}^m{p}_j\left({1-p}_j\right){\sum }_{j=1}^m{p}_j\left({1-p}_j\right)\left({1-2p}_j\right)\right]$. The Fleiss method also generates a value κ_j for each LISA category, j. The coefficient is calculated as $1-{\displaystyle \frac{{\sum }_{i=1}^N{n}_{ij}\left({k-n}_{ij}\right)}{{Nk\left(k-1\right)p}_j\left({1-p}_j\right)}}$. The variance of κ_j is given by ${\displaystyle \frac{2}{Nk\left(k-1\right)}}$. The individual kappas are estimated for each of the LISA classifications separately.

Guidance on how to interpret a kappa value is found in [51] and repeated in SPSS Help. Agreement is classified as the following: slight in the range above 0 to 0.20; fair 0.21–0.40; moderate 0.41–0.60; substantial 0.61–0.80; and almost perfect agreement >0.81. Zero is the agreement that would occur by chance, which will be described as non or no agreement. A negative value indicates that agreement is lower than would be expected by chance, which is viewed here as disagreement. Overall, κ will be a weighted average of all κ_j. It is possible for κ_j ≠ 0 ∩ κ = 0 for one of the five.

2.4. Materials

The UK’s Department for Levelling Up, Housing and Communities (DLUHC) reports on additional dwellings7 and on the total number of dwellings by the Local Authority District of England. Population estimates can be drawn from the Office for National Statistics (ONS)8, as can house price–earnings ratios9 and productivity10 data. The electronic map is also supplied by the ONS11.

The house price–earnings ratio is derived by dividing the estimated house price at the median and the earnings at the median for the district concerned. The earnings are workplace-based (where people work) rather than residence-based (where they live). It features only full-time employees on adult rates of pay. The productivity measure deployed here is gross value added per hour worked in the locale. As commuting into London from the surrounding South East is extensive, GVA per hour worked and gross earnings (used to generate the HPER) will vary in size, depending on how it is calculated. The gap between the HPER for London and the South East on a work-based estimate is smaller than if it were residential-based. The former is used here, which is consistent with the methods used to generate the NPPF targets analysed.

Chapter 4 of the NPPF uses a baseline of the existing housing stock in each local planning authority. This standardisation is adopted here across old and new targets as well as the current rate of adding dwellings. The housing stock used is that existing in 2020. The HPER data do not need adapting as they are directly comparable across districts. The population growth rate entails the final year’s population divided by the initial year’s, converted to an annual rate. Productivity for each year, as measured by gross value added per hour worked, is converted to 2020 prices using the consumers price index and averaged over the number of periods. The number of added dwellings is averaged over the number of periods. This average is divided by the number of dwellings in the territory and multiplied by 1000 to generate added dwellings per 1000 dwellings. Excluding the Isles of Scilly which has intermittent data, this covers data across 308 districts. The data runs from 2012/13 to 2022/23. The year 2020 or 2020/21 is omitted due to the unusual impact on economic measures of activity. There are eight periods before and two after.

3. Results

3.1. Productivity and Affordability

DiPasquale and Wheaton, ref. [4] posit that productivity levels drive inter-urban house prices. Greater productivity would attract greater competition of land/housing and result in relatively expensive property. Kendall’s correlation coefficient tau has a value of 0.270.

Stage 1 of the LISA–kappa method entails the classification of all districts into one of five categories. This classification is given a pictorial representation in the form of Figure 1, where the standard colour-coding LISA of coefficients for productivity and affordability are used. The example of GVA/hour worked in Figure 1 displays a hot spot in the south of England focussed in the London area and the east end of the English Silicon Valley around the M4 motorway of Slough, Windsor, Maidenhead, Bracknell, and Newbury. City-regions like Greater Manchester and the West Midlands do not present as spatial clusters. The low productivity clusters found in the north fit with the well-established deindustrialisation narrative of Pike et al. [16] as well as the impact on adjacent areas (or clubs) [14]. The weak rural performance corresponds with DEFRA’s view [25] as well the weak GVA found in villages and coastal towns, such as in the South West (Devon-Cornwall area).

The other cluster map of Figure 1 is of house price–earnings ratios at the median. The concentration of unaffordability is centred, as one would expect, on London. The hot spot has an average HPER of 13.74, more than double the cold spot at 5.73 and over 50% more than the NS districts.

The second stage of the LISA–kappa method entails estimating agreement between the two sets of classifications. The level of agreement between the HPER and productivity classifications is similar to the correlation coefficient of the untransformed data (0.308 vs. 270). Category kappas align with the global value (κ_NS = 0.265, κ_HH = 0.596 and κ_LL = 0.159). In particular, the global value is boosted by the association of the two hot spots. Adopting at 0.5 threshold as a division between weak and strong association (either agreement or correlation), there is perhaps a weaker association than one would expect between the two measures of need. The association is stronger over the productivity hot spot, linked, perhaps, with the escalator region of England, and is in keeping with a finding in the US [23].

3.2. Additional Dwellings

The observed annual average net number of additional dwellings over 2021/22-2023/24 for London was 35,000, much lower than the 88,000 target. But it was not out of line. Weighted by the number of existing dwellings, London added dwellings at the same rate as the three regions of the south of England and the two regions of the Midlands, at around 9.5 per 1000 existing ones. The three regions of the north of England added less, at 7.7. Keeping in line does not of itself indicate there was not a lack of construction. It is asserted that the places that build the most housing as a percentage relative to their existing stock were the places that least need it [2]. As such, it would be useful to see if the extent and spatial pattern of additional dwellings fits market drivers of affordability and productivity.

The cluster map of additions in Figure 2 is based on an 8-year average of district data up to 2019–2020, also known as the COVID-19 period, and weighted by the number of dwellings in 2020. The map of the additional dwellings reveals a large hot spot in an F-shape found over the Midlands/South West/Outer South East area. There is no corresponding large cold spot. There are also diamonds-in-the-rough in the same region as the larger cold spot. The largest area, with 83% of the districts, has no spatial association (NS). These districts have an average additions rate (7.77/1000 dwellings) around that of all districts (8.10). The hot spot’s (12.58) and diamond HL (12.09) rates are above 50% more, and the cold spot (5.64) and doughnut LH (5.25) average rates are 30% less.

If houses are built in areas where they are needed, it is argued that additional dwellings’ hot spots will be collocated with productivity or unaffordability hot spots. The clusters of additional dwellings and productivity appear to overlap slightly. As reported in

Table 1. Tau and Kappa values.

		HPER	GVAphw	Pop Growth	Additional Dwellings
Additional	Tau	0.203	0.175	0.501
Dwellings	Kappa	0.049	0.15	0.347
Old	Tau	0.477	0.276	0.331	0.186
Target	Kappa	0.503	0.194	0.253	0.02
New	Tau	0.883	0.276	0.156	0.184
Target	Kappa	0.833	0.337	0.1	0.049

, the level of agreement is low (0.15) overall. So is the agreement around the hot and cold spots (around 0.21). The corresponding values for additional dwellings and HPERs are lower (0.049, 0.09, 0.135). The agreement is so small, particularly for HPER, that perhaps there is support for claiming a mismatch between where the dwellings are added and where they are needed.

A growing population has been linked with new supply elsewhere [5,35]. The second map in Figure 2 is a cluster map of population growth rates. The hot spots of additional dwelling and population growth overlap. Tau and kappa support this (0.501, 0.347). Agreement over the hot spot location (κ_HH = 0.508 [0.00]) is greater than that of the cold (κ_LL = 0.201 [0.000]) spots’.

The LISA–kappa approach can highlight an association. Drawing on the thesis of Glaeser and Tobio [5] and Wang and Rickman [35], it is the draw of the greater supply of housing that led the rise in population. Breach and Magrini [39] claim that where builders are willing and able to add dwellings, intensity is constrained by planning restrictions. The concentration of new building away from areas of intense unaffordability fits their narrative.

As noted, the distribution of additions is not in agreement with that of HPERs. There is no agreement between clusters of population growth and HPERs (−0.0178 [0.662]) even at category level. Gray [46] tracks the migration of those aged 0–4, 20–24, 25–29 and 30–39, amongst others. The movements of 20–24-year-olds is one of in-migration to London, most likely in the early stage of a career, consistent with the first job within an escalator region. The 30–39-year-olds mirror the migration patterns of infants which have a clear pattern of movement out of London to the Greater Southeast/South Midlands. This is posited to be associated with forming a family unit, the first child, lower density living, and house purchase. It is concluded that the pattern of child movement is not necessarily related to affordability. Rather, back-commuting seems to be the locational driver [46].

3.3. Targets and Clusters

Metcalfe [2] points to a lack of housing density as part of the explanation for why the UK’s second-tier cities are less productive than they could be. Agglomeration economies, including the size of the pool of workers that these cities can access, is smaller than one would think, given their size. Using the Centre for Cities definition of cities or Primary Urban Areas (PUA)12 (similar to FURs), which are a collection of districts that make up the labour/housing market areas of a node in accord with [4], the median district target within a PUA under the old target scheme was 10.6 per 1000 existing dwelling, compared with 9.5 in non-PUA, suggesting something in keeping with concentrating dwellings, and the uplift for the largest 20 cities. Indeed, using a Mann–Whitney test (−2.49 [0.013]) supports the claim of a difference in rates. Once the London PUA is removed from the sample, the uplift is not evident. Indeed, non-PUA districts have slightly higher targets (9 vs. 9.24, MW = −0.410 [0.682]) but not significantly so. The new targets (10.67 vs. 14.39) are higher in non-PUA districts compared with PUA territories (−6.051 [0.000]). To reiterate, if housing and its concentration are a stumbling block to stimulating ‘escalator regions’ centred on second-order cities [2,17], the new targets do not seem to be aligned with that hope.

Figure 3 presents cluster maps of the housing targets. The map for the old targets has a hot spot in the extended London area, and a large cold spot covering much of the north (North East, North West and Yorkshire Humberside regions). There are also diamonds-in-the-rough in the same region as the larger cold spot (Sheffield and York). The largest area with 62% of the districts has no spatial association (NS). On average, these districts have a target of 10.8/1000 dwellings, which is around that of all districts (10.6). The hot spot’s rate is almost double that (20.1) and the cold spot’s average rate is 50% less (4.8). The doughnut LH (9.8) and diamond HL (11.66) rates align with the average rates.

The second map in Figure 3 is a clustering of the district targets announced in December 2024. For districts in the cold spot for the old targets, the new target is 5.51 dwellings/1000 greater than the old at the median. The general increase in the target was 4.3/1000 whilst the hot spot clusters targets were increased by less than that (1.62). With eight of the largest downward adjustments in absolute numbers occurring in London, the spread of targets narrowed. A measure of spread, the coefficient of variation, dropped from 0.57 to 0.362. However, the shift from the old to the new target did not mean that all of London’s boroughs saw a reduction. Six of the largest increases are to be found in London.

There is a strong resemblance between the cluster maps. Both maps have a partial blanket of blue, interspersed with yellow. The yellow flecks are of urban areas. For example, Lincoln (East Midlands region) and Hull (Yorkshire Humberside) are surrounded by rural districts with different [higher] target rates.

3.4. Targeting the Right Places?

From Table 1, both the old and new targets are not duplicating the concentrations found to exist currently. The agreement with the Additional Dwellings classifications is low if tau is used, but very low if kappa is cited.

Both the old and new target classifications are in some agreement with those of productivity, particularly the hot spots. There is better agreement with the new (0.337 > 0.194) than the old targets, likely to be driven by hot spot agreement (0.586 > 0.359), which strongly features the Capital. The cold spots are less well aligned (0.247 > 0.176).

Tau in Table 1 indicates the new targets better reflect HPERs than the old (0.833 > 0.477). Kappa coefficients concur, with the new target’s kappa indicating strong agreement. Category kappas align with the global values (κ_NS = 0.834, κ_HH = 0.901 and κ_LL = 0.812). Agreement with old targets clusters follows a similar pattern (κ = 0.503, κ_NS = 0. 466, κ_HH = 0.694 and κ_LL = 0.499) but with lower values. From this, it suggests that the places with the greatest targets correspond with areas of greatest unaffordability. The new targets align well with both the most and least affordable clusters, showing almost perfect agreement.

3.5. Stable Clusters

The data is split into before and after 2020, the year when much activity ceased due to COVID-19. Tau in

Table 2. Tau and Kappa values for The Same Variables over Time.

		LISA–Kappa Agreement
	Tau	Kappa	κNS	κHH	κLL
Targets	0.523	0.622	0.598	0.679	0.684
Additions	0.419	0.451	0.451	0.608	0.53
PopGrowth	0.273	0.149	0.136	0.375	−0.048
HPER	0.880	0.818	0.795	0.901	0.791

suggests that the variable with the most consistent rank order over time is unaffordability. Figure 4 displays the cluster maps for three variables, including HPER for the post-2020 period, which can be compared with the one shown in Figure 1. The similarity of coverage is picked up by the agreement coefficients. The consistency is most apparent in the hot spot where the category value of 0.9 is of almost complete agreement. If one were looking for a stable indicator, that would be it.

The measures of alignment in population growth (τ = 0.273 and κ = 0.149) in Table 2 indicate that the pattern of population growth changed, particularly the cold spot. London has a ‘blue blanket over it’ whereas before the cold spot covered the north of England. The kappa becomes negative as a result. There is disagreement on the location of the cold spot over time, which fits with COVID-19’s impact on the London area and migration. By contrast, the hot spot is consistent. Lockdown led to a reduction in international migrants to London and a heightened rate of outmigration, particularly among 30–45-year-olds. The Greater South East remained the most popular destination with an emphasis on non-urban locations [52], which also fits with the tendency to relocate at points of life-changing around child rearing [46]. This latter point aligns with the consistency of clusters of Additional Dwellings over time, particularly the hot spot.

4. Discussion

The Institute for Government (IfG), in its framework for building more homes, asserts that the national pattern of new housing has been poorly aligned with where it could deliver the most national benefit in terms of tackling the most acute affordability problems, maximising productivity gains in key areas such as England’s second-tier cities, and aligning with national infrastructure plans [2], p. 54. Both kappa and tau show that there is little agreement between additional dwellings and Productivity or HPERs, supporting the IfG.

There is a concern that building permits and local vetoes could push builders from adding dwellings away from where they are needed [41,42]. This is an international problem [35,40,41]. There is strong agreement between hot spots of actual additions and population growth. The collocation could be a reflection of population following housing supply [5]. It appears to fit a migrational shift out of London [4]. The thesis states that population follows housing supply out of London.

A means of overcoming the local veto problem is to impose targets on the planning authorities. A key finding is that there is strong agreement between targets and HPERs, particularly with the new targets. As such, the distribution of future housing additions is one focused on affordability. This has strengths and weaknesses. On the positive side, HPER clusters are stable, which for a planner, offers the opportunity for looking at the long-term picture. On the negative side, a growing HPER is taken to indicate greater need, and this is resolved by more dwellings. There are several reasons to be cautious. First, as posited by the asset pricing model, lower interest rates which are used for general macroeconomic policy, also boost prices. Second, there is a wedge between price and income filled by lending. In times of excess capital, lax lending boosts prices [28]. House prices, and thus affordability, are strongly affected by the risk appetite of lenders, which means that risk appetite determines targets. The size of this wedge is a function of perceived risk and risk appetite which can vary across space. London, as the escalator region and attractor of those with the greatest human capital, is an atypical housing market area where high lending multiples are the norm. Third, the house price ripple effect exports price inflation to neighbouring areas through a variety of routes, including finance and migration [10]. Long-distance commuting can spread the higher price/greater lending to areas beyond London.

Fourth, HPERs tend to be higher in non-PUA rural areas. One driver of higher rural house prices concerns the locational preferences of the rich and the non-economically active. The more mature buyer with no commuting constraints could bid up the prices of rural and coastal dwellings as they retire to the country. As greater planned supply could threaten the amenity value, locals are likely to challenge local building plans, which is seen by many as a key stumbling block for policy makers [2,34,35,36,37,38,39,40,41,42]. Failure to impose targets here could have negative consequences for their general imposition.

Fifth, the rural house price premium through the assessment of unaffordability will signal that more dwellings could be added in rural areas than perhaps there should be. With lower rural prices, this could encourage too many to leave large nodes, reducing agglomeration effects and lowering national productivity [24].

It is noted that large mature centres can have poor productivity characteristics [15,16]. Both the IfG and the new modern industrial strategy consider second-tier city-regions as underperformers. It is claimed that a concentration of dwellings is needed for greater agglomeration effects to emerge in the second-tier cities [2]. The LISA maps do not reveal productivity or population growth clusters hovering over cities outside of London. The targets favour non-PUA districts, so overall there does not appear to be a focus on the second-tier cities. Perhaps an opportunity missed.

5. Conclusions

This paper aims to offer a means of generating a measure of the similarity of spatial clusters. One could view the maps presented using spatial autocorrelation as ones showing unusually high concentrations, or clusters. When maps of clusters are compared, an evaluation of agreement between these single variable-derived clusters is provided by Fleiss’s kappa. An application of this LISA–kappa approach to assessing agreement is explored using data, primarily from the residential construction industry at a sub-regional level. The data sets include recently announced housing targets and the prevailing spatial distribution of additional dwellings. The spatial concentrations are measured for agreement with proxies for a desirable distribution of additional dwellings based on productivity and affordability.

There is a concern that building permits and local vetoes could push builders from adding dwellings away from where they are needed [38,39,40,41,42]. Burn-Murdoch [19] alleges that insufficient housebuilding has sent rents and prices soaring, resulting in superheated housing markets that force individuals in their twenties and thirties to choose between a broken bank balance and broken dreams. Empirical evidence suggests there is migration out of London to the Greater South East/South Midlands with an emphasis on non-urban locations [51]. It is shown that there is collocation of the hot spots of population growth and additional dwellings, in line with [5,35]. The thesis dictates that population follows housing supply [5], which could fit with a tendency of migrants from London to relocate in their early 30s at key events in their life-cycle [46]. It could be that COVID-19 and unaffordability accelerated this shift [52] but do not alter the locational pattern.

The spatial pattern of targets is found to align strongly with that of house price–earnings ratios, particularly the new targets. As such, one might conclude that the targets are in line with the need to address acute unaffordability. Although this is a widely used indicator of housing distress [42], whether a rising HPER reflects greater need, and whether this is resolved by more dwellings, should be questioned. The targets of the NPPF feature the deviation above a HPER value of four as a measure of need, which can offer a misleading signal of a housing requirement, such as in rural areas or when financial conditions alter.

Second-tier city-regions do not emerge as hot spots with any measure of housing used. The IfG pointed to a greater concentration of dwellings in the HMA of these alternative centres as a means of boosting productivity. As urban HPERs (outside of London) tend to be lower than rural ones, the unaffordability criteria in the new targets would not highlight second cities as in need. Indeed, the new targets favour non-PUA districts. Uplifts were built into the old targets with the enhancement focussed on the inner-city districts. Perhaps the current government should revisit this.

As an area for further research to underpin a housing and industrial policy, it is proposed that the migration of those in their 30s within a multi-district HMA should be a feature. In the new modern industrial strategy, there is an emphasis on clusters, including spatial clusters. A re-examination of how existing PUAs operate with locational sorting is needed. Attracting 20–24-year-olds with high human capital, as London does, is the first stage of locational sorting, which is a platform for high productivity growth [13] in an escalator region framework [17]. The outmigration from London just a few years later implied by Burn-Murdoch [18] is not within the escalator region frame. As a means of boosting productivity of city-regions, the targets on suburbs as a group should be accompanied by conditions on what is built, aimed at attracting and retaining those with high human capital, particularly at the stage when a family is to be started/house bought. This has the merit of featuring locational sorting, directing the concentration of dwellings to underpin agglomeration economies and would apply to second-tier city HMAs.

This proposal requires planning on what to build and where across a multi-district PUA. Sadly, at the lowest level, the IfG raised the issue that any strategic approach requires the prioritisation of policy targets over local objections and a commitment from builders to ‘speed-up’.

The LISA–kappa agreement method is simple. It has the key virtue of assessing the correspondence of hot [or cold] spots between two or more variables, which is unusual. The kappa coefficients tend to be significant at low levels of agreement. Perhaps policy-makers would like to see a stronger link between clusters. In effect, the threshold of agreement at a kappa of 0.5 is applied in this paper as a measure of significant agreement for the key findings.

There are limitations in the analysis undertaken. Two of the five LISA categories were not reported as they regularly had very few cases and generally did not exhibit agreement at a significant level. The Getis-Ord Gi* reveals three clusters: not significant; cold; and hot, so using a different first stage could avoid this problem. The not significant group, because of the relative size compared with the full data set, tends to reflect the median values. This may be a function of using a queen matrix. A distance-based matrix could reveal larger hot and cold clusters.