Abstract
This paper develops a tiered geography of local housing market areas (HMAs) that provides a national framework for spatial planning. It is derived from a theoretical understanding of the economic basis of HMAs. The analysis explores the relationships between the tiers of the HMA geography and local labour market areas. Drawing on this understanding, the empirical research generates sets of different potential geographies of HMAs for England based on an algorithm that applies criteria linked to the degree of closure of migration and/or commuting patterns. A range of theoretically appropriate criteria then enable the different geographies to be assessed. The choice of geography is guided by Chow tests of statistical differences in standardised house prices in neighbouring HMAs derived from hedonic regressions. Finally, conclusions are drawn on the validity of the approach developed. The empirical work is on England and datasets drawn from the Census and Land Registry.
This paper develops a tiered geography of local housing market areas (HMAs) that provides a consistent national framework for spatial planning. It is derived from a theoretical understanding of the economic basis of HMAs. The analysis also explores the relationships between the tiers of the HMA geography and local labour market areas. A prime motivation for this research lies in the growing use of HMAs as planning tools in England and elsewhere, because a valid HMA geography is an essential prerequisite for a full understanding of local housing market dynamics. Underlying this argument is the modifiable areal unit problem (Openshaw and Taylor, 1981) which determines that the results of spatial analyses will depend at least in part on which areas are used for those analyses. As recognised by Briant et al. (2010), the appropriate response is to use areas that are robustly defined with respect to the theoretical basis of the relevant concepts. In the US, the usual response has been to use metropolitan areas whose definitions are rooted in labour market areas. This begs the question of whether housing and labour market areas are necessarily the same, so this paper tackles that question as part of a broader attempt to meet the challenge of creating robust HMA definitions based on the concept of the sub-regional housing market.
The definition of HMAs has often been ignored in empirical studies of local housing markets, following the pioneering analyses of the spatial structure of urban housing sub-markets by Straszheim (1975) and Schnare and Struyk (1976). The subsequent burgeoning literature was reviewed recently by Jones and Watkins (2009), revealing that, although over time there have been refinements such as improved stratification procedures and greater data availability, most studies simply adopt administrative boundaries as a ‘given’ for the overall HMA. Similar issues apply to the measurement of local supply elasticities, as with the use of local authority boundaries by Green et al. (2005) and Pryce (1999). It is clear that the results will be very dependent on the area to which the analysis is applied: for example, a supply elasticity measured on an urban core that excludes its suburbs will be prone to give a biased estimate. Gyourko (2009) in his review of housing supply concludes that an important area for future research is to calculate robust local market supply elasticities, and the argument here is that this in turn requires that such estimates are based on genuine HMAs.
The use of HMAs has become an important element of spatial planning and regional strategies in the UK. Their use was initiated in Scotland where they have been applied in the planning system since the 1980s, with advice on defining HMAs evolving over time. The latest advice (DTZ Peida, 2003) centres on a migration algorithm with a series of stages. The following year, the advice published for England had no clear recommendations (DTZ Peida, 2004). These different approaches are reviewed more fully by Jones et al. (2012) but can incorporate one of three different types of information
— house price levels and/or rates of change;
— household migration and/or search patterns;
— the boundaries of travel-to-work areas (TTWAs) and/or other functional areas.
Based on this highly flexible and pragmatic guidance, the outcome was sets of local HMAs in different regions across England that were not at all comparable with each other and, in some cases, almost arbitrary (Baker et al., 2010). A system of HMAs for Northen Ireland has recently been published based on yet another set of criteria which centres on adapting TTWAs at the margin with migration patterns (Young et al., 2010).
There have been a small number of academic studies that have considered the definition of HMAs, but the motivation for this paper requires a more fundamental review than yet exists in the literature. Studies of the connections between housing market behaviour and the labour market have tended to be limited to work on the linking of residential mobility and job mobility, as for example Pinto (2002). It is necessary here to revisit conceptual issues and to focus on the links between HMAs and labour market areas. The paper seeks to explore the relationships, both theoretical and empirical, between these two basic functional economic geographies (Fox and Kumar, 1965)—i.e. labour and housing market areas. In doing so, it sets out a practical and consistent national geography of HMAs for England, after first showing that there are no easy answers to the construction of such a geography in the face of both theoretical and practical challenges.
The paper begins by comparing previous studies of local labour and housing market areas, noting the dramatic difference in the volume of the two sets of previous academic studies. The following section provides an explanation of the theoretical perspective on the housing market that underpins the case for a tiered view of HMAs. Next, the empirical research generates sets of different potential geographies of HMAs for England based on an algorithm that groups areas and applies a range of criteria derived from the theoretical underpinnings. The next section tests whether there are statistical differences in the results of standardised house price tests between contiguous pairs of individual HMAs in the different geographies. The empirical work draws on data from the population census and the Land Registry. Finally, some general and specific conclusions are outlined.
Defining Labour and Housing Market Areas
Housing and labour markets are unusual in that it is the consumer who moves rather than the product. Studies of the geography of local labour markets are of longer standing than those of HMAs. In the US, it was recognised over 60 years ago that the definition of metropolitan areas should be in terms of labour market areas and this broad approach was more recently extended to cover the whole territory (see for example, Dahmann, 1999, on the question of extending labour market definitions beyond metropolitan areas). Following principles derived from theory by Goodman (1970), labour market areas are almost always defined by analysing commuting patterns to identify localised clusters of journeys to work. The logic of analysing commuting patterns is that these reveal the actual labour market outcome of Cournot’s underlying principle that spatial arbitrage creates a localised market. Thus the labour market area should group areas such that few commuters cross the outer boundary; as a result, most buyers and sellers of labour are interacting within that boundary to establish wage rates (prices).
Coombes et al. (1986) and Tolbert and Killian (1987) exemplify these commuting flow analyses in the UK and US respectively, and the UK approach—which defines the official travel-to-work areas (TTWAs)—has subsequently been used in several countries across the world, such as Spain (Casado-Diaz, 2000). Following the principles of Goodman (1970), the key concern is that the boundaries define relatively self-contained clusters of commuting flows. As a result, it is necessary to select a level of commuting closure to define sub-regional labour market areas. There is no theoretical basis for choosing one level or another (Smart, 1974). For example, the minimum level applied in defining TTWAs has varied through the years; it is currently 66.7 per cent and this produces 140 TTWAs in England.
The parallels between housing and labour markets as sub-regional functional areas suggest that the considerable research on the definition of local labour markets may provide useful ‘pointers’ for the definition of HMAs. In particular, recognising the increasingly complex patterns of mobility in modern economies has fostered a shift away from methods which assume a centre-and-hinterland structure to sub-regional market geography (Cattan, 2001). Methods of definition need to be flexible enough to recognise clustered commuting flows, whether they have one main centre or are polycentric in structure: both types of sub-region are labour market areas if they meet the self-containment threshold set. At the same time, it is clear from this body of research that setting the self-containment level involves empirical experimentation because there is no basis in theory for any particular level of ‘closure’ that all labour market areas must meet.
There are only a few published academic studies that have identified HMA geographies and discussed the relationship with labour market areas. All these studies have been in the UK, with one of the first being an application of the TTWA method of analysis to British migration data (Coombes, 2000). The rationale for analysing migration flows to define HMAs is that the guiding principle of spatial arbitrage implies that the geography of HMAs will be formed through the pattern of movement between where people move to and where they originate from.
The first full academic study taking this approach was Jones (2002): boundaries of HMAs were defined by analysing migration patterns within the owner-occupied sector. The spatial focus of the analysis was the area broadly defined as mainland west central Scotland centred on Glasgow. The migration data were derived from the Land Registry covering the 10-year period 1984 to 1993. The approach was based on the grouping of settlements to establish HMAs by examining migration interaction. These settlements range in size from the city of Glasgow to small villages. The HMAs were based on the notion that each should be defined as a contiguous area comprising a settlement or group of settlements with a high degree of housing market self-containment and where in-migration from outside the immediate HMA was of only minor significance.
The grouping of settlements was undertaken using an iterative algorithm and the self-containment benchmark was 50 per cent internal migration, with any in-migration from an adjacent HMA to be less than 5 per cent of the destination market. These criteria yielded a set of HMAs which were seen to have an embedded relationship with TTWAs and it was this link between housing and labour market area definitions that led Jones (2002) to select these particular criteria after showing how varying the criteria leads to the geography of HMAs changing substantially.
A delineation of HMAs for the North West of England encompassing Manchester and Liverpool was undertaken by Brown and Hincks (2008). Although these HMA definitions were based primarily on migration data, part of the process involved consulting estate agents. Comparison of the HMAs derived on this basis with the TTWAs in the region revealed similarities in most urban areas. There were greater differences between HMA and TTWA boundaries in more rural areas, indicating that the relationship between housing and labour markets may vary by type of area.
Coombes (2009) directly tested the relationship between housing and labour markets by analysing the census migration data with the method used to define TTWAs. The fact that the results varied markedly in different parts of the country prompted the innovation of taking account of non-movers, but the conclusion was that the results were unsatisfactory, even after many variations to the closure levels (i.e. the proportion of migrants ‘allowed’ to cross boundaries of HMAs).
All these studies apply a migration closure approach, although with different algorithms and datasets. Various closure criteria were applied, partly but not entirely because of the different data sources. The studies highlight that there is no a priori theory to guide the choice of the closure criteria for migration flows. None of the empirical results from these studies suggests that housing market areas come close to matching ‘one to one’ with labour market areas across a mix of rural and more urbanised areas; this contradicts the suggestion of labour market areas being close surrogates for housing market areas that featured in policy guidance on the definition of HMAs in England (CLG, 2007).
The conclusions from this brief review are threefold. First, unlike the definition of labour market areas, the most appropriate way of defining HMAs is underresearched. Indeed, their definitions are scarcely an issue for academic debate outside Britain, despite the fact that the areas used will affect the results of any sub-regional analysis of housing finance.
The second conclusion is that there does not yet exist an established approach to defining HMAs. Moreover, the methods which have been tried have shown that there is no ‘natural’ level to set for the key value of closure of migration flows (i.e. the proportion of flows that must not cross the boundary of the HMA if it is to be deemed a sufficiently separate sub-regional market).
The third conclusion is that the existing empirical analyses in Britain do not support the idea that labour and housing market areas are effectively substitutable for each other. Although it is possible to adjust the closure criteria to create similar HMA and labour market area definitions in one type of area (for example, metropolitan regions), doing so can result in the two sets of areas being very different from each other elsewhere (for example, rural areas).
From this starting-point, it is necessary to return to the concept of housing markets and then to develop methods for the empirical definition of HMAs which are rooted in theory.
Theoretical Perspective
This section argues that the system of local housing markets can be seen as series of tiers. It begins by reviewing the theory of urban housing markets that centres on the role of the journey to work as a key influence. It then focuses on the role of spatial arbitrage in moulding the nature of housing markets via household migration. When a household migrates, whether they have a member who is working or not, the process of price bidding occurs and this housing market dynamic offers a basis for determining the boundaries of HMAs.
Before setting out the theoretical arguments, it is useful to observe that there are many studies that contribute to a hierarchical picture of the housing market. There are a range of studies that have identified housing sub-markets at neighbourhood level below HMAs (see Jones and Watkins, 2009, for a review). In addition, the current HMA literature and UK regional planning frameworks derive or are based on HMAs that are spatially smaller than TTWAs. The purpose of the theory in this paper is to integrate these ideas into one framework for the first time that also embraces spatial labour markets as a wider bound. To do this, we begin by considering a uni-nodal model of urban housing markets and then generalise the arguments to the wider polycentric urban landscape.
The essentials of the theory of urban housing markets were developed by Alonso (1964), Muth (1969) and Evans (1973). They develop the concept within an urban area that is characterised by the following key assumptions
— the town or city occupies a featureless plain, so any topographical features that might distort key relationships are ignored;
— employment is concentrated in the city centre, the central business district, and households make a fixed number of work trips a week.
The housing market in this model is assumed to have perfect information and households then make bids for particular locations; through this process, a price surface emerges. In this housing market, the law of one price holds but prices vary with distance or accessibility from the city centre because in deciding the price to bid households take into account the transport cost from any location to the central business district. This basic model assumes that all housing quality (including types) is the same and that there are no neighbourhood preferences within an urban area. Within the model, known as the ‘access-space’ model, the equilibrium price of housing per square metre declines with distance from the city centre.
The model presumes a dominant city or town centre that represents the key point of accessibility and the major locus of urban employment. The urban housing and labour markets are the same. The current pattern of settlements and commuting does not conform to these assumptions. First, the urban systems of modern countries do not comprise a series of independent towns with separate commuting patterns. In addition, within cities, commuting trips are no longer necessarily only from suburbs to city centre because sub-centres increasingly exist within most city-regions (McMillen and Smith, 2003). Persistent increases in personal mobility have meant that, in countries like England with its closely spaced network of towns, there are now many polycentric sub-regions where the key accessibility relationship is linked not to the centre of the town with the largest population but to the point of greatest ‘regional’ accessibility within the interurban road network.
Notwithstanding these differences between the hypothetical and actual urban system and its commuting patterns, empirical price studies consistently find a significant distance decay function from central urban locations (see Jones et al. 2009, for example). This finding implies that the essential dynamic of the access-space model holds under somewhat less restrictive conditions and the journey to work is the key force in shaping local spatial housing markets. The corollary is that the limits to local HMAs are determined by travel to work patterns. In other words, the outer boundaries of HMAs are determined by the distances travelled by the longest-distance commuters in different directions from a dominant accessibility point. Within this perspective, spatial house price arbitrage occurs as households move within this wider labour market area. Thus the labour market area of longer-distance commuters sets the outer bounds for housing market areas, which are here called Framework HMAs.
There are key qualifications to these conclusions. First, the access-space model represents a long-term equilibrium view, so HMAs defined by commuting patterns are best viewed as a framework within which spatial housing market processes operate. Secondly, the simplifying assumptions of the model neglect important dimensions of the housing market and its short-term dynamics—namely, that households have preferences for different house types, neighbourhoods and areas, and that the housing stock is differentiated in terms of housing quality and types and relatively fixed at any particular location. Finally, the assumption of a unitary housing market within an urban area in which the law of one price holds has also been the subject of considerable academic debate through the sub-markets literature beginning with Straszheim (1975) and Schnare and Struyk (1976). Many factors restrict household mobility—the slow response of new house building to price rises. The result is that price differences across different parts of an urban market, which the model assumes will be short term, may in practice persist into the long term. In other words, the extent of spatial arbitrage in the Framework HMA that was defined by commuting is fragmented, implying that several HMAs can co-exist within that wider area.
The heterogeneity of housing, the diversity of neighbourhoods and locations within a sub-region and the short distances often moved by households can thus produce sub-systems or tiers within a Framework HMA due to the differences not being arbitraged away. There have been different approaches to the measurement of these sub-systems. The first approach analyses migration patterns between and within settlements: if an area has a degree of self-containment in the migration flows, then the fluidity of spatial arbitrage within that area will persist alongside a quasi-independence from other parts of the Framework HMA. This is the approach to defining HMAs taken in the British studies already outlined. The second approach considers the outcomes of this quasi-independence, so that the lack of spatial arbitrage should result in differences in the prices of a standardised house in each sub-system. This is tested by using hedonic price analysis and is the basis of many sub-market studies.
The differences between housing markets and sub-markets can be considered by reference to household movement through the family life cycle stages and the range of substitutes and locations households consider when moving home. City-centre or inner-area living, usually in a flat, has become popular for childless households in their 20s and 30s. Later in life, households with children often prefer a home with the use of a garden, or place greater emphasis on neighbourhood factors such as school catchment areas (assuming the work search areas remain unchanged). This spatial movement outward, while not a universal process, is set within the same Local HMA and the associated migration patterns limit spatial arbitrage processes within the Framework HMA.
This spatial perspective can be further disaggregated to recognise neighbourhood or house type sub-markets. The concept of the sub-market implies that the urban housing market may be segmented on both the demand and supply sides of the market. From a demand perspective, households may form distinct ‘consumer groups’ with associated housing preferences and tastes that are in turn linked to stage in the family life cycle, size and composition, and socioeconomic status. These ‘consumer groups’ may also have similar constraints in their search and information costs. In parallel, the housing stock (supply) is also segmented into product groups (Maclennan et al., 1987) that represent relatively homogeneous dwellings and hence close substitutes to the demanders of housing. In the context of the family life cycle movement, young people living in the city centre may collectively create one sub-market, while families with children create another in suburbia within a given school catchment area.
To summarise: the constraints on market adjustment or spatial arbitrage between Local HMAs (and even sub-markets where these exist) means that standardised house prices in different parts of the same Framework HMA can be very different. Spatial arbitrage occurs, but indirectly and with a time lag. Excess demand for particular dwellings (and their close substitutes) will drive prices in a Local HMA upward, but may not affect nearby Local HMAs. The result is that different parts of a Framework HMA may have persistently different house price structures and hence different house price inflation trends and levels of affordability. This also means that building new houses in one part of a Framework HMA may not necessarily address an affordability problem due to supply shortages in an adjacent Local HMA if it does not lead to a redrawing of migration patterns. Hence planners seeking to redress local housing shortages require a sensitive approach to the location of such new housing taking into account transport networks for example and recognising that the Local HMA concerned is embedded within a wider Framework HMA.
This theoretical analysis creates the guidelines for our approach to identifying Framework HMAs and Local HMAs. To restrict the scope of this paper to manageable proportions, we do not define sub-markets as well. There is an evident overlap between the processes that create Local HMAs and sub-markets and hence a potential identification problem that is addressed in Jones et al. (2005). This analysis gives Framework HMAs definitions based on the analysis of commuting, whilst the definitions of Local HMAs derive from migration patterns.
This theory is based on the study of urban economies, with restrictive assumptions then adapted to generalise the processes. When actual data on a complex mix of urban and rural areas are analysed, some divergent patterns are likely to be found. It is possible that the two tiers may partially collapse into a single set of boundaries, or may not closely align with each other where the relationship between migration and commuting ‘on the ground’ conforms less closely to the form of urban region assumed by the original access-space model. One example would be where there are numerous similarly sized settlements without a single dominant urban settlement around which all the flow patterns focus. It is most likely that Framework HMAs will be considerably larger than Local HMAs where long-distance commuting is widespread (for example, around major conurbations). By contrast, Local HMAs could actually be larger than Framework HMAs in some rural areas where many of the migrants are retired and so not part of the local labour market, and where commuting patterns for most workers are localised.
Research Method
The empirical research constructs a tiered HMA geography in stages by applying a grouping algorithm to sets of commuting and migration flows. The final tiered geography is derived by constraining or embedding the boundaries of Local HMAs within those of Framework HMAs. As was mentioned earlier, a key issue is that there is no a priori basis for the degree of closure of commuting and migration which will be required of the tiers of HMAs. It should also be noted that the containment levels of the two flows are not directly comparable because commuting is a daily activity whereas migration is periodic.
The choices of closure levels are based on two criteria. First, the choice can be guided by the theory outlined earlier which argues that in urbanised areas it is likely that Local HMAs will be embedded within Framework HMAs. To achieve this, the analyses examine the interrelationship between the spatial patterns produced using different potential levels for the closure of the commuting/migration flows analysed. Secondly, selected geographies are then compared by testing how many contiguous pairs of individual HMAs have statistical differences in standardised house prices. In particular, standardised house prices in neighbouring HMAs are tested to assess whether they are different, using hedonic multiple regressions and a Chow test to see if they generate statistically different coefficients. This procedure follows the standard sub-market testing first developed by Schnare and Struyk (1976) and also permits a comparison of the reduction in regression variance achieved by the HMA regressions relative to the national equation.
The grouping algorithm applied uses the TTWA definition method (Coombes, 2010) which does not impose any structure (for example, core–periphery) but simply identifies all clusters of flows of any form. In this case, the algorithm groups commuting or migration flows between wards identified in the 2001 census. The algorithm seeks to identify as many as possible separate areas which meet the key criterion of the set level of closure (i.e. the proportion of the flows analysed which both start and end within the same area). It does this by grouping areas in whatever way minimises the number of flows that cross them. The results of applying different levels of migration or commuting closure, within the ranges indicated by theoretical considerations, are examined.
Migration flows in Britain tend to be strongly dominated by the numerous lengthy moves of students, who are not directly relevant to this research. The published census migration data do not cross-tabulate households by either small age-groups or whether the person was a student, so the effect of students on the research has been reduced by the use of a customised dataset of Moving Group Reference Persons (MGRPs) specifically produced by the Office of National Statistics to exclude all people aged under 25. It should be noted here that the definition of MGRPs, who have been classified by the tenure of the dwelling they are in, covers many people who are not heads of households. For example, a 25-year-old returning to the parental home will be a single person moving group and if the parental home is owner-occupied then this 25-year-old will be recorded as an owner-occupying MGRP because the same tenure characteristic applies to all household members. The research presented is based on the dataset covering all 25(+) MGRPs but the results for the owner-occupied sector are very similar in fact (due not only to owner-occupiers being the majority of all migrants, but also because the average length of their moves lies midway between the short distance moves typical of social housing renters and the longer-distance moves of the residual group who are mostly private sector renters).
To test ‘prototype’ HMAs by comparing standardised house prices between the constituent areas requires the estimation of a hedonic regression model (Dale-Johnson, 1982). The details of this estimation are given in the Appendix, but the price equation can broadly be written in algebraic terms as follows
where, P = sale price of house; S = structural attributes; T = market conditions; D = distance to major centre of population; R = residential density of neighbourhood; and M = house type mix of neighbourhood
The choice of variables reflects both the nature of the task (in that it is not concerned with significant local neighbourhood effects) and the practicalities of a nation-wide study. These regression models are inevitably subject to missing variable bias and this is reflected in our interpretation of their results. They are not used to identify the precise boundaries of HMAs but to provide guidance in comparing geographies as a whole.
Constructing a Tiered HMA Geography
The analysis considers different levels of closure for the different housing market tiers. A useful starting-point in the choice of containment criteria is the 66.67 per cent level used for defining TTWAs which are the official labour market areas in the UK. When this level of closure is applied to migration data, the areas produced are fewer—and so larger on average—than TTWAs (which were of course based on commuting data). This does not accord with the theoretical perspective that commuting-based Framework HMAs are either of a similar size to, or larger than, the migration-based Local HMAs. This point is also made by Hincks and Wong (2010). The way forward taken by this analysis is therefore for the definition of Framework HMAs to be based on higher levels of commuting closure than that used for TTWAs. This in fact puts into practice the theoretical principle that sees the Framework HMAs as wider labour market areas, defined to include longer-distance commuters. As a result, lower levels of closure are deemed appropriate for the migration analyses to define Local HMAs.
Framework HMAs Based Solely on Commuting
The grouping analysis of commuting flows applies the same method and data that produced the 140 TTWAs in England but, with the higher 75 per cent closure criterion needed to contain longer-distance commuters, it produces 85 HMAs covering all of England (plus some adjacent parts of Scotland and Wales where there are strong flows across the border). Changing the closure criterion to 77.5 per cent and applying it to all commuters produces 75 HMAs: this indicates that around this level there is only a modest level of sensitivity of the definitions to change in the key closure criterion. Using closure criteria that are around 75 per cent produces large HMAs around metropolitan areas due to longer-distance commuting and this is appropriate for Framework HMAs because they reflect the impact and importance of high-income households and their longer-distance commuting on spatial arbitrage.
Local HMAs Based Solely on Migration
Migration closure defines a Local HMA. Applying the TTWA algorithm with the 66.67 per cent closure criterion generates 86 HMAs. Reducing the migration closure criterion to 60 per cent and 55 per cent leads to increases in the number of HMAs to 152 and 223 respectively, whilst setting the closure level at 50 per cent yields 327 HMAs. This indicates a steep level of sensitivity of the results to the closure criterion. The 50 per cent closure level for Local HMAs produces broadly contiguous areas, increasing its credibility compared with higher closure levels, although at this level the northern conurbations do tend to be broken down into large numbers of areas. There is also a very considerable difference in size between the areas defined in the south and those in the old industrial regions.
A Tiered Approach with Lower-level Areas Based on Migration within Upper-level Areas Based on Commuting
This approach seeks to follow the guidance of tiered HMA theory by defining commuting-based upper-tier areas directly from individual wards and then sub-dividing these areas on the basis of migration self-containment criteria. In this way, both Framework and Local HMAs are established in one system. The algorithm first allows the upper-tier boundaries to be more optimally defined based on the commuting criterion. The second step of the analysis takes each area’s constituent wards individually and then groups them until they meet the migration self-containment criterion without allowing any of these groupings to cross the Framework HMA boundaries which, as a result, then form an upper-tier boundary set.
Reflecting the evidence gathered from the earlier analyses already summarised, the closure criteria applied ranged from 75 per cent to 80 per cent and 50 per cent to 60 per cent commuting and migration respectively. There is a possibility that an upper-tier area may not meet the criterion for lower-tier migration closure. This does in fact occur with three of the smaller upper-tier areas which are defined if the closure rates are set at the lower levels of the ranges (75 per cent commuting and 50 per cent migration): it is notable that these are all rural areas. A summary of the impact of changing the criteria is given in Table 1; ultimately, the selection of the levels of closure is, as already noted, a purely empirical question but guided by the theory set out earlier.
The effect on numbers of Local HMAs of nesting within Framework HMAs
The discussion narrows the choices to a top-tier Framework HMA based on 75 per cent or 77.5 per cent commuting closure and a bottom tier of 50 per cent migration containment. These are preferred as internally and theoretically constant. Figure 1 shows tiered HMAs defined by a 77.5 per cent commuting closure of Framework HMAs (step 1) and a 50 per cent migration closure for Local HMAs (step 2). The map shows where the major cities are through the location of the nine largest urban areas identified for research on the State of the English Cities (Champion, 2006). Many of the more rural upper-tier areas are not divisible at a lower tier, due to factors such as the length of rural migration flows that have already been noted. As a result, a separate lower tier mainly applies to the more metropolitan parts of the country. For example, the Framework HMAs encompassing the provincial cities of Manchester and Liverpool both have 15 Local HMAs embedded within them.

Lower-tier migration-based (50 per cent) within commuting-based upper tier (77.5 per cent).
These geographies are in nested tiers: the lower tier of Local HMAs is bounded by the limits of the upper-tier Framework HMAs. Such a nesting approach can only reduce, not increase, the number which would be produced if the Local HMA geography is defined in an unconstrained way. The significance of this process is shown in Table 1. For example, constraining within the tiered structure reduces 50 per cent Local HMAs from 327 to 280. This constraining effect produces HMA geographies which accord with the theoretical principles.
HMAs and Standardised House Prices
The final stage in the process of choosing the appropriate HMA geographies is guided by hedonic price analyses described in the Appendix. The results of the analyses in general are that most of the prototype HMA geographies pass the pair-wise test that standardised house prices are statistically different. The largest number of similar contiguous pairs which fail this test is found when using the current TTWAs (Table 2).
Comparison of results of hedonic tests of prototype HMA geographies
The number of spatial units do not sum to the totals in Table 1 because island areas have no contiguous areas so cannot be included in these tests.
The differences between the results for the two areas are not significantly different at the 5 per cent level
Reduction in standard error ( percentage) x100/number of spatial units in geography.
The pairs of TTWAs concerned are shown in Figure 2: it is notable that they are all in more peripheral and rural parts of England. This confirms that there is a rurality issue, in the sense referred to earlier, stemming partly from the differences in commuting and migration flows in these areas. TTWAs are smaller because their closure criterion was just 66.67 per cent and in practice this results in a high proportion of TTWAs composed of just smaller towns with traditional market areas around them. Migration flows are often longer in rural areas, especially where there are more retired people, which results in spatial arbitrage operating across the boundaries of such TTWAs.

Contiguous pairs of TTWAs with similar standardised house prices (i.e. not significantly different at the 5 per cent level).
The tests of pairs of prototype HMAs are not very powerful because it is not a fully specified model, partly because of missing variables. The hedonic analysis is therefore utilised not to identify specific boundaries but to compare the efficiency of potential different HMA geographies. The localised nature of the housing market means that spatially disaggregated models should produce better results, compared with a national model. The efficiency of the different geographies can be measured by a reduction in the standard error of the local regression models summed together in comparison of the national regression model. The results are given in Table 2. As expected, the most localised geography considered—352 local authorities—produces the greatest reduction in standard error, 31.4 per cent. The most ‘efficient’ geography considered, defined by an index that looks at the percentage reduction in standard error per area in the geography, is the set of Framework HMAs (Figure 1) derived from the analysis of commuting flows with a 77.5 per cent closure level (see column 5 in Table 2). On this basis, the favoured geography has closure levels of 77.5 per cent and 50 per cent at the top and bottom tiers respectively.
Conclusions and Implications
The research task has been to construct a geography of Local HMAs as a consistent national framework for spatial planning based on strong theoretical foundations. The theoretical perspective develops a layered system for urban areas characterised as follows.
Tier 1: Framework HMAs defined by long-distance commuting flows and the long-term spatial framework with which housing markets operate.
Tier 2: Local HMAs defined by migration patterns that determine the limits of short-term spatial house price arbitrage.
Tier 3: Sub-markets defined in terms of neighbourhood or house type price premiums.
The analysis therefore brings together local labour and housing market markets for the first time. However, this theoretical hierarchy is derived for large urban areas with a dominant employment centre. In rural areas and in sub-regions where there are numerous similarly sized settlements without a single dominant urban settlement, the underlying assumptions may not hold. In these more complex circumstances, the relationship between Local HMAs and Framework HMAs could be blurred and the latter could actually be smaller in some rural areas where many of the migrants are retired, moving long distances.
The empirical analysis constructs only the top two tiers based on a grouping algorithm of commuting and migration respectively that draws heavily on the methods and arguments to identify local labour markets. The key challenge is that there is no a priori basis for the degree of closure of these flows and the analysis considers a range of alternative criteria that are subject to a series of theoretical and technocratic or statistical tests. The favoured geography has Framework HMAs based on 77.5 per cent commuting closure and Local HMAs with 50 per cent migration containment. At these levels of migration/commuting closure, the housing system is revealed in broad terms to be composed of a single tier in rural areas and two tiers in larger city-regions. This finding is consistent with the theoretical arguments, although the broad coincidence between Framework and Local HMAs in rural areas was not predicted.
The spatial patterns revealed shed light on the interaction of spatial functional areas for the first time and suggest that the current rather fuzzy concepts of city-regions and polycentric urban regions may need a rethinking of their theoretical underpinnings. There are also questions too for the definition of TTWAs, the official UK local labour markets, with Framework HMAs comprising more extensive areas.
In the UK, the revocation of UK regional planning in 2010 and the move towards ‘localism’ provides a vacuum and an opportunity for a rethink of HMAs by individual local authorities (Quartermain, 2010). As the tiered framework is untainted by the previous variable approach to HMA definition, it could stimulate local authorities to develop new planning partnership approaches as desired by the Coalition government (HM Government, 2010, para 2.14). As a planning tool, this national tiered HMA geography offers a consistent framework to local planning authorities and, as it can be derived from census (and Land Registry) data and is based on an internationally accepted algorithm, it could be adopted in other countries.
Footnotes
Appendix
The testing procedure assessing differences in local house price structures is in three stages
The purpose of the first stage is to control for property market heterogeneity and define a standardised house type for testing in stage (2). As semi-log is a common form of such a model, we specify the dependent variable as the log of sale price. For the third stage, the implicit price estimates in each HMA are compared with those of the ‘pooled’ models. This final stage involves using a Chow test which is employed to identify whether differential prices are observed for the standardised product in different markets. It is unnecessary to test for ‘parameter stability’ for HMAs that are not physically attached. The tests were applied to 960 000 transactions in 2005 for each different geography considered across England.
Funding Statement
This research was funded by the former National Housing and Planning Advice Unit.
