The preservation of historic districts—is it worth it?

The preservation of historic districts—is it worth it? Abstract I investigate the welfare effect of conservation areas that preserve historic districts by regulating development. Such regulation may improve the quality of life but does so by reducing housing productivity—that is, the efficiency with which inputs (land and non-land) are converted into housing services. Using a unique panel dataset for English cities and an instrumental variable approach, I find that conservation areas lead to higher house prices for given land values and building costs (lower housing productivity) and higher house prices for given wages (higher quality of life). The overall welfare impact is found to be negative. 1. Introduction Conservation areas (CAs) protect historic neighbourhoods by placing restrictions on the aesthetic quality of new development.1 CAs are particularly widespread in England with more than 9600 designations since the legislation came into effect in 1967. Inside a CA, any new development is required to preserve or enhance the existing character of the neighbourhood. Similar policies exist in different forms internationally, for example, as local historic districts in the USA or as Ensembleschutz in Germany. By regulating the subjective quality of new buildings, CAs may reduce the productivity of the housing sector. Historic neighbourhoods are no doubt an important urban amenity; however, their preservation may hinder cities in affordably housing their current and future populations. I estimate the welfare effect of CAs by assembling a unique panel dataset for English cities. The dataset comprises 11 years of CA designations over 1997–2007, as well as house prices, land values, construction costs and other city characteristics. I construct my dataset at the city-level to capture the full costs and benefits of the policy at the level of the housing market. Specifically, I use the Housing Market Area (HMA) definition of urban areas.2 I estimate a net welfare effect composed of quality of life effects (benefits) and housing productivity effects (costs). The quality of life effect is derived from the amenity value that households place on the historic built environment in their city and its conservation. A city-level analysis captures benefits at the neighbourhood level—since residents are more likely to live inside or near a CA if they are widespread in a city—and at the city-level i.e. the value that residents place on the amount of preservation in their urban area as a whole. The costs of conservation are modelled as a housing productivity effect i.e. the effectiveness with which land and non-land inputs are converted into housing services. Underlying this is the assumption that productivity, and not quantity, is the major channel for the supply-side effects of designation.3 Indeed, the purpose of CAs is not to prevent development but to ensure that new buildings preserve the character of a neighbourhood. Such aesthetic restrictions may lower housing productivity in several ways. First, developers wishing to build inside CAs must navigate an extra layer of regulation. Secondly, the planned buildings must meet certain standards, which may not be the most cost-effective way of providing housing services. Thirdly, the extra costs of developing inside CAs may push development out to less favourable sites in a city. For these reasons, cities with lots of CAs will be less productive in the housing sector than other cities. Developers will be able to produce fewer units of housing services for given amounts of land and non-land inputs resulting in higher housing costs. A city-level analysis is required to capture productivity effects that determine prices at the level of the housing market. There is a growing body of literature on the economic effects of CAs. The majority of this literature has focussed on estimating the quality of life effects of CAs by examining property prices. A distinction commonly made in the literature (e.g. by Coulson and Leichenko, 2001) is between (negative) internal effects related to restrictions to property rights and (positive) external effects related to the conservation of neighbourhood character. Quasi-experimental evidence has shown that the overall effect of designating CAs is to increase property prices, which suggests that the positive effects dominate (Koster et al., 2014; Ahlfeldt et al., 2017).4 Furthermore, Koster et al. (2014) find that households with higher incomes have a higher willingness to pay for living inside CAs in the Netherlands. Ahlfeldt et al. (2017) find that the pattern of house price effects in England is consistent with a situation where local planners designate CAs according to the interests of local owners. If local owners who benefit from designation are indeed able to game the planning system to their advantage then it important to know what the effects of designation on housing costs are at the wider market level. There is a current lack of evidence on the supply-side effects of CAs. The only evidence to date is presented by Been et al. (2016), who show that construction is slightly lower inside historic districts in New York City. However, they do not examine quantity effects at the city level or supply-related effects on housing costs. The evidence from other forms of regulation suggests that the costs of development restrictions are significant.5 For example, Hilber and Vermeulen (2016) find that house prices in England would be 35% lower if planning constraints were removed. The available evidence finds that the quality of life benefits associated with planning are smaller than the costs. Glaeser et al. (2005) examine building height restrictions in Manhattan, a policy that is intended to prevent towering developments that block the light and view available to existing structures. They find that the development restrictions led to large increases in house prices that left residents worse off, even after accounting for the policy benefits. This ‘regulatory tax’ finding is repeated in other studies such as Albouy and Ehrlich (2012) and Turner et al. (2014), both for regulatory constraints in the USA, and Cheshire and Sheppard (2002) for land use planning in Reading, England.6 In this article, I investigate the extent to which CAs explain differences in housing productivity across cities and whether there are associated quality of life improvements that compensate. As such, I provide an estimate of the net welfare effect of CAs for the average (owner occupier) household. Evaluation of the welfare effects of CAs in cities is challenging since both quality of life (via demand) and housing productivity (via supply) result in increased house prices. To disentangle these effects, I make use of Albouy and Ehrlich’s (2012) two-step approach. In the first step, I estimate a cost function regressing house prices on input prices (land and non-land) and city characteristics that may shift productivity. Housing productivity is defined as the amount of physical housing that can be produced for given quantities of inputs. The key assumption behind this step is perfect competition. If designation makes building more costly then house prices will be higher for given input prices to maintain zero profits. I find that the average increase in CA designation share at the HMA level over 1997–2007 decreases housing productivity by 4.3%, implying a cost-driven increase in house prices of the same magnitude. In the second step, I construct an expenditure-equivalent quality of life index based on house prices and wages and regress it on the same productivity shifters, including designation. The key assumption here is of household mobility. Spatial equilibrium implies that if designation improves quality of life in a city then house prices must be higher for given wage levels. I find that designation increases quality of life, but not by enough to compensate for the greater expenditure on housing resulting from lower productivity. The results imply that designations in England over 1997–2007 were welfare-decreasing for an average owner-occupier household in these cities. While I make use of the Albouy and Ehrlich (2012) approach, my key contribution is different. I focus on estimating the welfare effect of a particular form of regulation, CAs, rather than of housing regulation in general. CAs are a particularly fitting application for the approach since they are expected to impact on housing productivity less than quantity, specifically. Moreover, focussing on a particular form of regulation allows me to identify a causal impact by employing an instrumental variables approach. Finally, my article distinguishes itself by focussing on England rather than the USA, and by constructing a panel dataset that allows me to control for fixed unobservables. My identification strategy involves an instrumental variables approach. The instrument for designation is a shift-share of the Bartik type (Bartik, 1991). The closest previous approach is Koster and Rouwendal (2017) who use national-level changes in spending on cultural heritage weighted by the local share of listed dwellings as an instrument for local investment in historic amenities. My instrument uses changes in the national-level designation shares for the dwelling stock of particular build periods weighted by the HMA shares of dwellings in those build periods. The national level changes in designation are assumed to reflect changes in the subjective evaluation of the dwelling stock of particular build periods. As such, the instrument is a fairly novel application of the shift-share approach. The identifying assumption is that the instrument is unrelated to unobserved shocks to housing productivity or quality of life, conditional on pre-trends in house prices, trends related to the initial value of the instrument (capturing the initial stock) and trends related to other city characteristics. I support the validity of this assumption by showing that the instrument is not related to gentrification. The key contribution of this article is to estimate both the supply-side costs and demand-side benefits of CAs; evidence that is currently missing from the growing body of literature on the policy. This article also contributes to a literature that investigates the costs and benefits of regulation and planning more generally. I present some of the first causal estimates of the welfare effects of a form of housing regulation. To my knowledge, the only previous paper to examine both the costs and benefits of housing regulation using exogenous policy variation is Turner et al. (2014). I also contribute to a literature on the value of locational amenities, by estimating the quality of life effect of a regulation policy instrumented at the city level.7 Furthermore, my results contribute to the literature on housing production functions by estimating what is, to my knowledge, one of the first housing production functions for the UK. I follow Albouy and Ehrlich (2012) who take the traditional approach of regressing house prices on input prices (e.g. McDonald, 1981; Thorsnes, 1997). A more recent literature attempts to estimate the production function, treating housing as a latent variable (Epple et al., 2010; Ahlfeldt and McMillen, 2014; Combes et al., 2016). According to Combes et al. (2016), the two major challenges with estimating any type of housing production function are data availability and disentangling housing quantity from its price. Data availability is a challenge since the approach usually requires data on both house prices and land values. As discussed, I construct a unique panel dataset of cities that includes house prices and some previously unused data for land values and constructions costs for England. The land value data, depicted in Figure 1 for 2007 play a key role in the production function step and in estimating the productivity impact of designation. Figure 1 View largeDownload slide Residential land values by local authority, 2007. Notes: Valuation Office Agency data. Assessed residential land value for small sites with outline planning permission. Areas are extruded proportionally with land value. Figure 1 View largeDownload slide Residential land values by local authority, 2007. Notes: Valuation Office Agency data. Assessed residential land value for small sites with outline planning permission. Areas are extruded proportionally with land value. The second challenge is disentangling housing quantity from its price, which is difficult due to unobservable property characteristics that impact on price. Having collected a panel dataset, I am able to estimate the cost function using fixed effects, which helps to overcome the problem of unobserved property characteristics. My preferred estimates of the land cost share (0.29) and the elasticity of substitution between land and non-land inputs (0.53) fall within the range in the literature.8 The outline of the rest of the article is as follows. In Section 2, I lay out the theoretical model which demonstrates the potential effects of CAs on quality of life and housing productivity. In Section 3, I go over the data used in empirical analysis. In Section 4, I outline the two-step empirical approach and the identification strategy. In Section 5 I present the results. Section 6 concludes. 2. Model In this section, I describe how CA designation impacts on housing productivity and quality of life in a general equilibrium context. I use the model of Albouy and Ehrlich (2012), which is an intercity spatial equilibrium framework based on work by Roback (1982) and Albouy (2016). Each city j is small relative to the national economy and produces a traded good X and housing Y that is non-traded. The city-specific price of a standard housing unit is pj and the uniform price of the traded good is equal to the numeraire. Households with homogeneous preferences work in either the Y-sector or the X-sector and consume both housing and the traded good. The model involves two important assumptions; that of perfect competition, which gives the zero profit conditions, and that of labour mobility, which gives the spatial equilibrium conditions. 2.1. Housing production under zero profits Since the focus of this article is on the housing sector the derivations for the traded good are relegated to footnotes. The housing good Y represents physical housing services. By ‘physical’, it is meant that the housing services are derived from the characteristics of the physical unit itself. Benefits derived from neighbourhood quality will come in to the individual utility function via a quality of life measure defined later on. Firms produce housing services in each city according to:9 Yj=AjYFY(L,M), (1) where AjY is a city-specific housing productivity shifter, FY is a constant returns to scale (CRS) production function, L is land (price rj in each city) and M is the materials (non-land) input to housing (paid price vj). Materials are conceptualised as all non-land factors to housing production including labour and machinery. The housing productivity shifter represents the efficiency with which developers can convert land and non-land factors into housing services and is a function of city-specific attributes which may include the level of CA designation. Specifically, designation will impact negatively on AjY if the policy makes it more difficult to produce housing services. As discussed in the introduction, I assume that the major supply-side effects of designation come through the productivity rather than the quantity channel. The validity of this assumption has important empirical implications that are discussed in subsection 2.4 below. Changes in AjY are assumed to be factor-neutral productivity shifts i.e. the relative factor productivity remains unchanged. However, I demonstrate robustness to this the factor-neutrality assumption in the empirics. Firms choose between factors to minimise the unit cost at given factor prices cj(rj,vj;Aj)=min⁡L,M{rjL+vjM:FY(L,M;Aj)=1}. Zero profits imply the unit price of housing is equal to this unit cost, i.e. pj=cj(rj,vj;Aj). Log-linearisation and taking deviations around the national average gives the zero profit condition:10 p˜j=φLr˜j+φMv˜j−A˜jY, (2) where for any variable z the tilde notation represents log differences around the national average, i.e. z˜j=ln⁡zj−ln⁡z¯, where z¯ is the national average, φL is the land cost share for housing and φM is the non-land cost share. This condition tells us that for each city the house price is given by the sum of the factors’ prices (weighted by their cost shares) minus productivity. Cities with lower housing productivity must have higher house prices for given factor prices to maintain zero profits. Figure 2 illustrates this point by plotting house prices against land values (holding materials costs constant) in an illustrative diagram. The average productivity curve shows how house prices relate to input prices (land values) for cities of average productivity, such as York and Cambridge. As the input price increases, house prices must also increase to maintain zero profits. The curve is concave since developers can substitute away from land as it becomes more expensive. Cities above the curve, such as Brighton, are considered to have low housing productivity because they have higher house prices for the same input price. Brighton has the same land value as Cambridge but ends up with more expensive housing because it is less effective at converting the inputs into outputs. The productivity difference between two cities such as Brighton and Cambridge can be inferred from the vertical difference between them.11 Figure 2 View largeDownload slide Housing productivity example. Notes: This figure is an adaptation of Figure 1A from Albouy and Ehrlich (2012). Figure 2 View largeDownload slide Housing productivity example. Notes: This figure is an adaptation of Figure 1A from Albouy and Ehrlich (2012). 2.2. Location choice under spatial equilibrium Households with homogeneous preferences have a utility function Uj(x,y;Qj) that is quasi-concave in the traded good x and housing y and increases in city-specific quality of life Qj.12 Quality of life is determined by non-market amenities that are available in each city, such as air quality or employment access. These may also include CA designation. An increase in designation impacts positively on Qj if preservation has amenity value. As the designation share in a city increases it becomes more likely that a representative household lives inside or close to a CA. Furthermore, the general level of preservation in a city may be of amenity value to all residents. Households supply one unit of labour to receive a wage wj, to which a non-wage income I is added to make total household income mj. Households optimally allocate their budget according to the expenditure function e(pj,u;Qj)=min⁡x,y{x+pjy:Uj(x,y;Qj)≥u}. Households are assumed to be perfectly mobile, therefore, spatial equilibrium occurs when all locations offer the same utility level u¯. Perfect mobility is consistent with an extensive empirical literature that shows migration flows follow economic incentives (e.g. Linneman and Graves, 1983; Graves and Waldman, 1991; Gyourko and Tracy, 1991). A more direct test of spatial equilibrium is provided by Greenwood et al. (1991) who find little evidence of disequilibrium pricing in income across cities. Indeed, Notowidigdo (2011) estimates mobility costs finding they are ‘at most modest and are comparable for both high-skill and low-skill workers’ (p. 4). Locations with higher house prices or lower levels of quality of life amenities must therefore be compensated with higher income after tax τ, i.e. e(pj,u¯;Qj)=(1−τ)(wj+I). Log-linearised around national average this spatial equilibrium condition is: Q˜j=syp˜j−(1−τ)sww˜j, (3) where sy is the average share of expenditure on housing, τ is the average marginal income tax rate and sw is the average share of income that comes from wages. The spatial equilibrium condition tells us that in each city the (expenditure-equivalent) quality of life must be equal to the unit house price minus the wage (weighted by expenditure shares). Cities with a higher quality of life must have higher house prices for given wages to compensate. 2.3. The impacts of designation on house prices The two conditions, zero profit and spatial equilibrium, both suggest that CAs may increase house prices but the two channels are entirely separate. It is worth underlining here exactly how these two channels operate since this is the mechanism on which the subsequent empirical approach is based. First, if designation impacts on housing productivity only then house prices must be higher for given input prices to maintain zero profits (Equation (2)). This point is illustrated by the example of Brighton over Cambridge in Figure 2. Since quality of life is left unaffected, higher house prices in cities with designation must be compensated for by higher wages to maintain spatial equilibrium (Equation (3)). In this way, the quality of life index remains unaffected by housing productivity shocks from designation. Secondly, if designation impacts on quality of life only then house prices must be higher for given wage levels to maintain zero spatial equilibrium (Equation (3)). Since housing productivity is unaffected, higher house prices must be associated with higher input prices to maintain zero profits (Equation (2)). Figure 2 does not include wages so quality of life differences cannot be illustrated. However, if wages were held constant then an increase in quality of life could look like a movement from Cambridge to York. Thus, the quality of life effect cannot be confused with the housing productivity effect, and the housing productivity effect cannot be confused with the quality of life effect. 2.4. Quantity effects, preference heterogeneity and sorting So far the costs of designation have been treated as a productivity effect, rather than a quantity effect. This assumption has been motivated by the fact that CAs do not ban development (as in zoning) or specifically restrict the amount of housing (as in height restrictions), but instead impose aesthetic standards that may make building more costly. While there is no specific provision for height restrictions in CA policy, the local planning authority is fairly free to decide which buildings they feel preserve the character of the neighbourhood and which do not. Therefore, it cannot be ruled out that they favour lower-rise buildings, effectively imposing a height restriction. Furthermore, even if CAs do not restrict the amount of housing directly, there may be quantity adjustments resulting from housing productivity reductions. The Albouy and Ehrlich (2012) model neatly sidesteps quantity effects by the assumption of homogeneous individuals. Even if there are quantity effects, this has no impact on city prices because the new marginal resident has the same willingness to pay as the old marginal resident (holding quality of life constant). In a similar model, Albouy and Farahani (2017) introduce a degree of preference heterogeneity which delivers a downward sloping demand curve at the city level. Taking an assumed value for the elasticity of population to housing costs, the model predicts that housing productivity reductions lead to larger increases in prices and smaller decreases in land values, compared with the homogeneous preferences case. The reason for the difference is that the quantity reduction pushes the marginal resident up the demand curve where they have a higher willingness to pay resulting in both higher prices and higher land values, compared with a flat demand curve. The empirical implication of this is that the quality of life step will now capture both (i) quality of life increases due to amenity changes and (ii) quality of life increases of the marginal resident due to quantity rationing. The empirical implication is not an identification problem as such—since the quality of life for the marginal resident continues to be correctly identified—but rather a problem to do with interpreting the quality of life parameter in the welfare calculations. Clearly, using (ii) as a welfare increase misses whatever happens to the residents who would have been living in the city had it not been quantity-rationed. A related problem is that of household sorting. Sorting occurs if CA designation leads to a migration of residents into a city who have a higher willingness to pay for that type of quality of life amenity compared with existing residents. As before, the quality of life effect for the marginal resident will continue to be correctly identified in that empirical step. However, it leaves open the possibility that the quality of life effect has an additional component (iii) a quality of life increase of the marginal resident due to changes in the willingness to pay as a result of sorting. If effects (ii) or (iii) represent a relatively large proportion of the overall quality of life estimate than the model would likely be overestimating the welfare benefits of conservation. The welfare conclusions are justified to the extent that the actual sorting and quantity effects of designation are relatively small over the time period considered. Such effects would be small if price adjustment to the quality of life effects is immediate (since residents value security over the future character of their neighbourhood) but if adjustment through quantities and sorting between cities is limited and occurring over a longer time frame. To somewhat alleviate the concerns related to quantity, I conduct a regression of CAs on the number of dwelling units at both the local and city level. In Table 3, I show that CA designations did not impact on the number of dwelling units in England over 1997–2007, either at the city-level (HMA) or at the very local level (output area).13 However, there remains the possibility that CAs impact on some other measure of housing quantity such as floorspace. Overall then, while the assumption that sorting and quantity effects are limited may be reasonable, the existence of large effects cannot be empirically ruled out and the welfare results are therefore caveated accordingly. 3. Data 3.1. Housing market areas The empirical analysis is conducted at the HMA level. These areas are defined by DCLG (2010) using a grouping algorithm applied to ward-level census data on commuting patterns, house prices and migration flows. The use of commuting patterns makes them similar to the better-known travel-to-work area (TTWA) definition. However, HMAs have a higher commuting self-containment rate of 77.5%, compared with just 66.7% for the TTWAs (DCLG, 2010). For this reason in particular, they are considered a better empirical counterpart to the theoretical j-locations. In addition, HMAs are defined such that similar houses have a similar within-area price (after adjusting for observed characteristics). Furthermore, HMAs have a 50% closure rate for migration flows, implying a good deal of both within- and between-market integration. For much of the data described below, I aggregate from local authorities (LAs) based on the relationship mapped in Figure 3. I use weighted aggregation to address potential spatial mismatch. To improve the precision of the house price index, I drop eight (of 74) HMAs—those with fewer than 100 housing transactions per year.14 Since the greatest period of overlap of the different data is 1997–2007, the final panel dataset has T = 11 and N = 66. While this is a fairly small N, any loss of precision is worth it to ensure self-contained areas prescribed by the theory. The wider costs and benefits of designation may only be fully captured at the market level. As described in the introduction, part of the benefits of conservation may be from living in a city with lots of well-preserved heritage neighbourhoods. On the cost side, designation that lowers productivity in one part of the city will impact on prices elsewhere in the city, since the units offer access to the same labour market and are therefore substitutable. However, in Appendix B in the Online Appendix I demonstrate that the approach is robust to using LAs as the unit of observation. Figure 3 View largeDownload slide Housing markets areas over LAs. Notes: Map P11.4 from Geography of housing market areas by DCLG (2010). Figure 3 View largeDownload slide Housing markets areas over LAs. Notes: Map P11.4 from Geography of housing market areas by DCLG (2010). All variables used in the analysis are expressed as log deviations from the national average in each year, denoted by tilde (e.g. p˜). For each variable, I first log-transform it and then subtract the mean of the log-transformed values across HMAs in each year. For the productivity shifters, I additionally normalise the standard deviation to one. Descriptive statistics for the panel dataset are given in Table 1. Table 1 Descriptive statistics for panel dataset Overall statistics Between-group Within-group Mean SD Min Max SD Min Max SD Min Max Variables (standard)  House price (£000s) 118.2 52.90 41.6 345.9 27.30 76.6 220.2 45.43 7.077 243.8  Land value (£000s/ha) 1486.5 1046.2 183.4 7964.4 740.1 600.1 5197.3 744.5 −1420.7 4253.7  Const. cost index 136.7 26.31 93.1 207.0 7.025 123.2 160.4 25.37 93.20 193.7  Designation share 0.0176 0.0136 0.000004 0.0712 0.0136 0.000004 0.0711 0.00126 0.0103 0.0363  Refusal rate 0.230 0.112 0 0.625 0.0601 0.1 0.389 0.0952 −0.0893 0.588 Variables (normalised)  Price differential −0.000 0.231 −0.573 0.775 0.225 −0.422 0.662 0.055 −0.176 0.164  Land value diff. −0.000 0.483 −1.450 1.458 0.455 −1.012 1.216 0.169 −0.569 0.639  Const. cost diff −0.000 0.054 −0.160 0.192 0.050 −0.101 0.160 0.021 −0.063 0.102  Desig. share (z-value) −0.000 0.993 −4.824 1.765 0.997 −4.798 1.725 0.072 −0.603 1.040  Pred. refusal (z-value) 0.000 0.993 −4.514 2.352 0.910 −2.850 1.942 0.411 −1.879 1.335 Overall statistics Between-group Within-group Mean SD Min Max SD Min Max SD Min Max Variables (standard)  House price (£000s) 118.2 52.90 41.6 345.9 27.30 76.6 220.2 45.43 7.077 243.8  Land value (£000s/ha) 1486.5 1046.2 183.4 7964.4 740.1 600.1 5197.3 744.5 −1420.7 4253.7  Const. cost index 136.7 26.31 93.1 207.0 7.025 123.2 160.4 25.37 93.20 193.7  Designation share 0.0176 0.0136 0.000004 0.0712 0.0136 0.000004 0.0711 0.00126 0.0103 0.0363  Refusal rate 0.230 0.112 0 0.625 0.0601 0.1 0.389 0.0952 −0.0893 0.588 Variables (normalised)  Price differential −0.000 0.231 −0.573 0.775 0.225 −0.422 0.662 0.055 −0.176 0.164  Land value diff. −0.000 0.483 −1.450 1.458 0.455 −1.012 1.216 0.169 −0.569 0.639  Const. cost diff −0.000 0.054 −0.160 0.192 0.050 −0.101 0.160 0.021 −0.063 0.102  Desig. share (z-value) −0.000 0.993 −4.824 1.765 0.997 −4.798 1.725 0.072 −0.603 1.040  Pred. refusal (z-value) 0.000 0.993 −4.514 2.352 0.910 −2.850 1.942 0.411 −1.879 1.335 Notes: Descriptive statistics for panel dataset with 66 cities × 11 years = 726 observations overall. Standard variables are: the price of a house with average characteristics in each HMA (based on predictions from hedonic regression), the residential land value (mean of bulk, small and flats), the construction cost index (100 = UK average in 1996), the share of HMA land that is designated and the planning application refusal rate. The normalised versions of the variables are those used in the empirical analysis after being processed as described in the data section. The ‘diff.’ variables are log differentials (in each year) and hence have a mean of zero. The ‘z-value’ variables are additionally divided by the standard deviation in each year and hence have a between-group standard deviation of approximately one. Table 1 Descriptive statistics for panel dataset Overall statistics Between-group Within-group Mean SD Min Max SD Min Max SD Min Max Variables (standard)  House price (£000s) 118.2 52.90 41.6 345.9 27.30 76.6 220.2 45.43 7.077 243.8  Land value (£000s/ha) 1486.5 1046.2 183.4 7964.4 740.1 600.1 5197.3 744.5 −1420.7 4253.7  Const. cost index 136.7 26.31 93.1 207.0 7.025 123.2 160.4 25.37 93.20 193.7  Designation share 0.0176 0.0136 0.000004 0.0712 0.0136 0.000004 0.0711 0.00126 0.0103 0.0363  Refusal rate 0.230 0.112 0 0.625 0.0601 0.1 0.389 0.0952 −0.0893 0.588 Variables (normalised)  Price differential −0.000 0.231 −0.573 0.775 0.225 −0.422 0.662 0.055 −0.176 0.164  Land value diff. −0.000 0.483 −1.450 1.458 0.455 −1.012 1.216 0.169 −0.569 0.639  Const. cost diff −0.000 0.054 −0.160 0.192 0.050 −0.101 0.160 0.021 −0.063 0.102  Desig. share (z-value) −0.000 0.993 −4.824 1.765 0.997 −4.798 1.725 0.072 −0.603 1.040  Pred. refusal (z-value) 0.000 0.993 −4.514 2.352 0.910 −2.850 1.942 0.411 −1.879 1.335 Overall statistics Between-group Within-group Mean SD Min Max SD Min Max SD Min Max Variables (standard)  House price (£000s) 118.2 52.90 41.6 345.9 27.30 76.6 220.2 45.43 7.077 243.8  Land value (£000s/ha) 1486.5 1046.2 183.4 7964.4 740.1 600.1 5197.3 744.5 −1420.7 4253.7  Const. cost index 136.7 26.31 93.1 207.0 7.025 123.2 160.4 25.37 93.20 193.7  Designation share 0.0176 0.0136 0.000004 0.0712 0.0136 0.000004 0.0711 0.00126 0.0103 0.0363  Refusal rate 0.230 0.112 0 0.625 0.0601 0.1 0.389 0.0952 −0.0893 0.588 Variables (normalised)  Price differential −0.000 0.231 −0.573 0.775 0.225 −0.422 0.662 0.055 −0.176 0.164  Land value diff. −0.000 0.483 −1.450 1.458 0.455 −1.012 1.216 0.169 −0.569 0.639  Const. cost diff −0.000 0.054 −0.160 0.192 0.050 −0.101 0.160 0.021 −0.063 0.102  Desig. share (z-value) −0.000 0.993 −4.824 1.765 0.997 −4.798 1.725 0.072 −0.603 1.040  Pred. refusal (z-value) 0.000 0.993 −4.514 2.352 0.910 −2.850 1.942 0.411 −1.879 1.335 Notes: Descriptive statistics for panel dataset with 66 cities × 11 years = 726 observations overall. Standard variables are: the price of a house with average characteristics in each HMA (based on predictions from hedonic regression), the residential land value (mean of bulk, small and flats), the construction cost index (100 = UK average in 1996), the share of HMA land that is designated and the planning application refusal rate. The normalised versions of the variables are those used in the empirical analysis after being processed as described in the data section. The ‘diff.’ variables are log differentials (in each year) and hence have a mean of zero. The ‘z-value’ variables are additionally divided by the standard deviation in each year and hence have a between-group standard deviation of approximately one. 3.2. House prices The production function relies on the theoretical concept of ‘housing services’, which represents the flow of value derived from physical housing for the occupant. Housing quality and housing quantity are assumed to be entirely substitutable in that each simply delivers a flow of ‘services’ to the occupant. This assumption is a useful simplification since it implies that the unit price of housing services can be estimated from house prices in a hedonic approach that controls for housing quality and quantity. House prices for 1,087,896 transactions in England over the period 1995–2010 come from Nationwide, the largest building society in the UK. All transactions in the Nationwide data are for owner-occupied units.15 In addition to the price paid, the data have property characteristics including postcode location, which is used to identify which HMA the transacted unit belongs to. The house price index is computed by regressing the log of the transaction price p for unit-i in HMA-j and year-t on a vector of property characteristics Xijt and a set of HMA-year indicator variables: pijt=Xijtβ+ϕjt(HMAj×YEARt)+εijt. (4) The house price index is then constructed by taking the predicted HMA-year effects ϕ^jt and subtracting the national average in each year, i.e. p˜jt=ϕ^jt−ϕ^¯t. The result represents log deviations from the national average since house prices are log transformed for the hedonic regression. The results of the hedonic regression and a brief discussion of the coefficients are presented in Appendix A in the Online Appendix. Since the distribution of observed transactions within each HMA-year may differ from the actual distribution of housing stock in the HMA, each observation is weighted by the LA dwellings count in 2003 divided by the LA-year transaction count.16 3.3. Land values Residential land values are obtained from the Valuation Office Agency (VOA). The land values are produced for the Property Market Report which has been released biannually since 1982. Land values for the full set of LAs were, however, not made available until recently (2014). As such, this research is one of the first empirical applications of the full dataset. The assessments are based on a combination of expert opinion and observed values for transactions of land. The values are assessed for small sites (<2 ha), bulk land (>2 ha) and flat sites (for building flats) for vacant land with outline planning permission. To produce an overall land value index I adjust for the price differences by site category using a regression discussed in Appendix A in the Online Appendix. Notably, the regression results show that bulk land is considerably cheaper (by 4.9% to 11.2%) than small plots in every year. It is reassuring that the valuations conform to the well-documented ‘plattage effect’ (by e.g. Colwell and Sirmans, 1993). To validate the valuations, I make use of transaction data in the form of land auctions between 2001 and 2012.17 There is a very high correlation with the valuation data as discussed in Appendix A in the Online Appendix. Land valuations for 1995–1998 are reported using a slightly different LA definition due to a local government reorganisation that occurred over this period. I converted the earlier LA definition to the new definition using the relevant lookup table.18 I then took the mean of the biannually reported land values and aggregated them to the HMA level, again using the distribution of housing stock in 2003 as weights. As a final step, I computed log differentials. 3.4. Construction costs To capture the costs of non-land inputs to construction an index of rebuilding costs was obtained from the Regional Supplement to the Guide to House Rebuilding Cost published by the Royal Institute of Chartered Surveyors (RICS). Rebuilding cost is an approximation of how much it would cost to completely rebuild a standard unit of residential housing had it been entirely destroyed. The index takes into account the cost of construction labour (wages), materials costs, machine hire, etc., and is considered to be an appropriate measure of the price of non-land inputs to housing. The index is also reflective of local build quality.19 The data are based on hedonic regression using observed tender prices for construction projects and the sample size of tenders is given with each factor. I make use of location adjustment factors that are available annually from 1997 to 2008 at the LA-level and take into account the local variations in costs. To my knowledge these data have not been used before in empirical analysis at this level of detail. The location factors were scanned from hard copies and digitised using optical character recognition software. The separate years were then matched to form a panel dataset. Some LAs were missing from the data, especially in the earlier years. However, a higher tier geography (corresponding in most cases with counties) was recorded completely, enabling a simple filling procedure described in Appendix A in the Online Appendix. Finally, the LA level data were aggregated to HMAs weighted by dwelling stock, and then log differenced. 3.5. CA designation A spatial dataset of CAs was obtained from English Heritage. The dataset contains polygons that map the borders of all CAs in England on the British National Grid coordinate system. The full dataset has only been used once before in empirical analysis by Ahlfeldt et al. (2017). The data include the date of designation, which lies between 1966 and 2011. Using this information, I calculated in a geographical information systems (GIS) environment the share of land in each HMA that was covered by CAs in each year over 1997–2007. Figure 4 plots the initial designation share in 1997 against the change in share over the study period. The chart shows variation in both the initial share and the change over the period. Although the changes are small as a proportion of all land, they may still have large productivity or quality of life effects as outlined below. The CA designation share is first computed at the LA level to be aggregated to HMAs weighted by dwelling stock, ensuring all the data are produced comparably. The log land shares are then normalised to have a mean of zero and a standard deviation of one which is achieved by taking log-differences around the national average and then dividing by the standard deviation in each year. Such ‘z-values’ are created for each of the housing productivity factors to ensure the effects on log costs are comparable. Figure 4 View largeDownload slide Initial designation share against change for HMAs. Notes: Blackburn & Burnley HMA is not depicted since the change in designation share over the period is off the chart at 2.6% of the land area. Figure 4 View largeDownload slide Initial designation share against change for HMAs. Notes: Blackburn & Burnley HMA is not depicted since the change in designation share over the period is off the chart at 2.6% of the land area. The designated share of all HMA land is a proxy for the extent to which designation might impact on housing productivity or quality of life. So while the increase in designated land area over the period for the average HMA is relatively small, at 0.13%, the actual effects may be much larger.20 A specific reason for this is that housing productivity effects will depend on the impact of designation on marginal developments which may disproportionately occur in existing residential areas where designations are more common. Moreover, designations might occur specifically to ensure that potential new developments maintain the neighbourhood character. On the benefits side, designations may also have quality of effects outside of the designated areas themselves via spillovers as documented, for example, by Ahlfeldt et al. (2017). 3.6. Planning restrictions and other housing productivity factors To control for the underlying regularity restrictiveness in each city, the share of planning applications that are refused in each year from 1997 to 2007 was obtained. These data were first used by Hilber and Vermeulen (2016) to analyse the effect of planning restrictiveness on housing costs in England. The LA data were aggregated to HMAs weighted by dwelling stock. The variation in refusal rates is volatile over time such that it is unlikely that every fluctuation represents actual changes in planning restrictiveness. The data were, therefore, smoothed to eliminate the short-term noise while keeping the longer-run trends in planning restrictiveness. This smoothing was done by regressing the refusal share on a binomial time trend and using the predicted values. To estimate whether designation effects vary with geographic constraints, I compute the undevelopable share of land within 25 km of each HMA centroid, following Saiz (2010).21 Developable land is defined as land that is flat (<15 degree slope) and dry (solid land covers). To calculate the slopes, I use the OS Terrain 50 topography dataset which is a 50 m grid of the UK with land surface altitudes recorded for the centroid of each grid square. I calculate the slope in the steepest direction for each grid square and if this is greater than 15 degrees then the 50 m grid square is defined as undevelopable. To identify dry land I use the Land Cover Map 2000, which is a 25 m grid for the whole of Great Britain where each square is assigned to one of 26 broad categories of land cover. The grid square is defined as undevelopable if it is water, bog, marsh, etc., following Hilber and Vermeulen (2016). The final undevelopable land share is computed for each HMA as the total land area that is not developable divided by the total area in the 25 km circle. 3.7. Quality of life index I construct a quality of life index according to Equation (3) as follows: QoLjt1=0.31×p˜jt−(1−0.225)×0.64×w˜jt, (5) where 0.31 is the average share of expenditure on housing, which comes from the Expenditure and Food Surveys 2001–2007. In different empirical specifications, I demonstrate robustness to using different values for the housing expenditure share, as well as using shares that vary by average city income. The price differential p˜jt is the same as that used in the cost function step, computed via hedonic regression. The annual wages w˜jt come from the Annual Survey of Hours and Earnings at the local authority level and are aggregated (weighted by the number of jobs) to HMAs before taking log differentials. The average marginal income tax rate of 0.225 was computed using data from the HM Revenue and Customs for 2005–2006 and the average share of income from wages of 0.64 is from the Department for Work and Pensions for 2005–2006. I estimate additional specifications where the marginal income tax rate depends on the average income specific to each HMA-year observation and where the share of income from wages varies across regions. The results are robust to such changes as presented in Appendix B in the Online Appendix suggesting the use of average figures is suitable. A ranking of HMAs according to this quality of life index is presented in Appendix A in the Online Appendix. 4. Empirical strategy and identification My empirical strategy is based on the two-step approach of Albouy and Ehrlich (2012). In the first step I estimate a cost function for housing production. The unit value of housing is regressed on land values, construction prices and productivity shifters, including designation. In the second step, the quality of life index is regressed on housing productivity factors to reveal the overall welfare impact of designation. My identification strategy is based on implementing a panel fixed effects approach and instrumenting for designation with a shift-share. 4.1. First step: cost function Following Albouy and Ehrlich (2012) and Christensen et al. (1973) I first estimate an unrestricted translog cost function: p˜jt=β1r˜jt+β2v˜jt+β3(r˜jt)2+β4(v˜jt)2+β5(r˜jtv˜jt)+πR˜jt+δD˜jt+fj+ujt, (6) where R˜jt is the predicted refusal rate and D˜jt is the CA designation share. The fixed effects fj capture all time-invariant productivity shifters, such as geographic constraints. The parameter δ is an inconsistent estimate of the housing productivity impact of CAs if designation is correlated with the error term. According to the model, quality of life factors are absent from ujt as they are capitalised in land values r˜jt. However, unobserved housing productivity shocks may be correlated with designation as discussed in the identification strategy below. In this panel format, the log-differentials are taken around the national average in each year t. These differentials are equivalent to using year effects in the regression; however, I prefer to stick to the format suggested by the theory.22 Imposing the restrictions of CRS: β1=1−β2; β3=β4=−β5/2 makes this equivalent to a second-order approximation of Equation (2) and imposing the further restrictions of β3=β4=β5=0 makes this a first-order estimation i.e. a Cobb–Douglas cost function (Fuss and McFadden, 1978). Comparing Equation (6) with Equation (2) reveals that housing productivity is given by: A˜jY=−πR˜jt−δD˜jt−fj−ujt. (7) Housing productivity is the (negative of) observed and unobserved city attributes that impact on unit house prices after taking into account input prices. If designation impacts negatively on housing productivity then its coefficient δ is expected to be positive i.e. it will raise house prices above what is predicted by factor prices alone. 4.2. Second step: quality of life Increasing the cost of housing is not the intended effect of designation. Rather, CAs reduce housing productivity to preserve or improve the attractiveness of neighbourhoods. The second step investigates the demand-side effect of CAs by relating the same productivity shifters, including designation, to a measure of quality of life. The regression takes the form: Q˜jt=μ1R˜jt+μ2D˜jt+μ3ujt+gj+εjt, (8) where gj are fixed effects that capture time-invariant quality of life factors. The parameter μ3 gives the relationship between designation and quality of life. According to the model, productivity factors are absent from εjt, despite the fact that house prices go into the quality of life index. They are absent because higher wages will compensate for higher prices from productivity factors to maintain spatial equilibrium. However, unobserved quality of life factors may lead to a bias of μ2, as discussed in the identification strategy below. If CAs increase quality of life then μ2 will be positive. The coefficient gives the quality of life impact expressed as a share of expenditure. Combining this with the estimate from the first step gives the total welfare as μ2−(0.31×δ), since 0.31 is the housing expenditure share. 4.3. Identification There are two features to the identification strategy. First, I make use of the panel nature of the data by estimating a fixed effects model. Secondly, I combine fixed effects with a time-varying instrument for designation based on the Bartik (1991) shift-share. It is worth noting that identification here focusses only on the impacts of designation. Consistent estimates of the land cost share are obtained by instrumenting land values in an alternative specification outlined in subsection 4.5, but this step is neither necessary nor desirable for consistent estimation of the impacts of designation, as explained in that subsection. Fixed effects estimation alone provides a major improvement over pooled OLS estimation by controlling for time-invariant housing productivity factors or quality of life factors. For example, on the cost function side, a time-invariant factor such as soil type may both affect housing productivity and be correlated with today’s CAs (if it drove the location of historical settlements). Likewise on the quality of life side, many urban amenities such as job accessibility, natural factors and cultural amenities are relatively fixed over the period of one decade. Furthermore, the fixed effects models remove any effect from unobservable housing characteristics that biased the house price index in the hedonic regression stage. Thus, they help to deal with a common problem with estimating housing production functions (Combes et al., 2016). I additionally include individual HMA trends to capture the effect of unobservable trends in housing productivity and quality of life factors that may be related to designation. A relationship in trends could come about if, for example, trends in unobservable housing productivity or quality of life factors and trends in designation are both related to the initial heritage endowment of a city. In terms of the theoretical model, estimation of a fixed effects model assumes spatial equilibrium in each year.23 The fixed effects strategy does not help when unobservables are time-variant. To illustrate, consider the example of a city with ongoing transport improvements that increase housing productivity and/or quality of life. Such improvements may also be the result of (or may result in) gentrification, which itself has been empirically demonstrated to lead to designation (Ahlfeldt et al., 2017). In general, changes in city attributes that impact on housing productivity or quality of life will likely be interlinked with gentrification and, therefore, designation. To address this I employ an instrumental variable approach similar in spirit to a Bartik instrument (Bartik, 1991). The instrument provides HMA-level ‘shocks’ that are a weighted average of the national level designation share of buildings in different build date categories. The weights used for a given HMA are the share of its dwelling stock in each build date band. Specifically, the instrument is computed as: Zjt=∑b=114Dj−1,btHjb0, (9) where Zjt is the counterfactual designation share in HMA-j and year t, Dj−1,bt is the designation share in each age band b for all HMAs other than HMA-j and Hjb0 is the initial share of dwelling stock in HMA-j in age band. The national level designation share in each of the age bands are based on the Nationwide transactions data and are described in Appendix A in the Online Appendix. The counterfactual designation share is expected to be a relevant predictor of HMA designation even conditional on fixed effects and trend controls. National changes in the designation share for buildings of certain build periods capture shifts in preferences for heritage. If an HMA has a high proportion of buildings in those build periods then the chances of designation are increased. Relevance is confirmed by the F-stats in Table 4 and Table 6 for the cost function and quality of life regressions, respectively. Furthermore, the instruments are significant and (mostly) have the expected signs in the first-stage regressions in tables presented in Appendix A in the Online Appendix. The charts in Figure 5 illustrate the counterfactual designation share and the actual designation share conditional on HMA fixed effects and trend interactions for a selection of cities.24 Figure 5 View largeDownload slide Actual designation against counterfactual designation for selected HMAs. Notes: Designation (z-scores) have been adjusted for HMA fixed effects giving them a zero mean across years for each HMA. The shares are also conditional on trend interactions. Figure 5 View largeDownload slide Actual designation against counterfactual designation for selected HMAs. Notes: Designation (z-scores) have been adjusted for HMA fixed effects giving them a zero mean across years for each HMA. The shares are also conditional on trend interactions. To be a valid instrument, the counterfactual designation share must be orthogonal to the error terms ujt and εjt. The argument for exogeneity is that changes in the national level designation share are unrelated to anything going on at the individual city level, like gentrification. To capture general trends in unobservables that might be correlated with the initial stock, I include a trend variable interacted with the initial value (in 1997) for the instrument. To capture further possible trends I include interactions of a trend variable with city characteristics: the initial designation share, the initial refusal rate, the city population, protected land share and undevelopable land share.25 Therefore, the identifying assumption is that the instrument is unrelated to unobserved shocks to housing productivity or quality of life, conditional on controlling for trends related to the initial stock (as captured in the initial value of the instrument) and trends related to other city characteristics. The exclusionary restriction requires that the instrument not lead directly to changes in the outcome variable. The exclusionary restriction could be violated if national-level changes in preferences for buildings of an HMA lead to the gentrification of that HMA, which in turns impacts on housing productivity or quality of life. I argue, however, that such a correlation is unlikely to continue conditional on HMA fixed effects and trend controls. Gentrification is a complex process that depends on many more factors than the build date of the dwelling stock. In Table 2 I present evidence to support this argument. Here, the designation share and the counterfactual designation share are regressed on a measure of the share of residents who hold a degree certificate. This dependent variable comes from the UK census and proxies gentrification of a city. The positive and significant relationship with designation in the pooled OLS model implies that gentrification and designation are indeed interlinked. The size of this coefficient decreases as fixed effects and trends are introduced. However, for the instrument there is no relationship at all in either of the models. Given that gentrification is the most likely source of unobserved shocks, it is reassuring that it is not related to the instrument. Table 2 Degree share regression (1) (2) (3) (4) OLS OLS FE & Trends FE & Trends Designation share 0.010* −0.002 (0.005) (0.002) Counterfactual designation 0.001 −0.062 (0.005) (0.043) F-stat 3.619 0.029 0.965 2.069 R2 0.068 0.000 0.002 0.023 AIC −543.0 −532.7 −1239.3 −1242.4 Numbers of HMAs 74 74 74 74 Observations 148 148 148 148 (1) (2) (3) (4) OLS OLS FE & Trends FE & Trends Designation share 0.010* −0.002 (0.005) (0.002) Counterfactual designation 0.001 −0.062 (0.005) (0.043) F-stat 3.619 0.029 0.965 2.069 R2 0.068 0.000 0.002 0.023 AIC −543.0 −532.7 −1239.3 −1242.4 Numbers of HMAs 74 74 74 74 Observations 148 148 148 148 Notes: The dependent variable is degree share (differential) in 2001 and 2011. Fixed effects and trends are implemented by demeaning and detrending the variables beforehand. This pre-step was carried out using two separate samples: (i) annual data over 1997–2007 for the designation shares and (ii) Census data for 1991, 2001 and 2011 for the degree share. The data were then merged for 2 years, 2001 and 2011. The designation shares for 2007 were used for 2011 as this is the closest possible match. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. Table 2 Degree share regression (1) (2) (3) (4) OLS OLS FE & Trends FE & Trends Designation share 0.010* −0.002 (0.005) (0.002) Counterfactual designation 0.001 −0.062 (0.005) (0.043) F-stat 3.619 0.029 0.965 2.069 R2 0.068 0.000 0.002 0.023 AIC −543.0 −532.7 −1239.3 −1242.4 Numbers of HMAs 74 74 74 74 Observations 148 148 148 148 (1) (2) (3) (4) OLS OLS FE & Trends FE & Trends Designation share 0.010* −0.002 (0.005) (0.002) Counterfactual designation 0.001 −0.062 (0.005) (0.043) F-stat 3.619 0.029 0.965 2.069 R2 0.068 0.000 0.002 0.023 AIC −543.0 −532.7 −1239.3 −1242.4 Numbers of HMAs 74 74 74 74 Observations 148 148 148 148 Notes: The dependent variable is degree share (differential) in 2001 and 2011. Fixed effects and trends are implemented by demeaning and detrending the variables beforehand. This pre-step was carried out using two separate samples: (i) annual data over 1997–2007 for the designation shares and (ii) Census data for 1991, 2001 and 2011 for the degree share. The data were then merged for 2 years, 2001 and 2011. The designation shares for 2007 were used for 2011 as this is the closest possible match. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. Another potential violation of the exclusionary restriction is if the instrument captures increased valuations placed on specific property characteristics. As it stands, these are not controlled for in the hedonic regression. To deal with this, for the IV models only, I re-estimate the hedonic regression with interactions between year effects and the build date categories. In a robustness check in Appendix B in the Online Appendix, I demonstrate that the results are not sensitive to this change. 4.4. Alternative specifications I estimate three alternative specifications. First, I investigate whether the effects of designation depend on the quantity of available land around a city. If there is an abundance of land, designation may have less effect on productivity as developers can easily build outside the city. To test this idea I create two dummy variables, one for HMAs that are above-average on the Saiz index and one for those below average. I interact the designation variable with each of these dummies and include the interactions in the two regression steps in place of the uninteracted version of the designation variable. These separate dummy interactions give the effect on housing productivity or quality of life in HMAs that have a scarcity of land or an abundance of land. Secondly, I investigate whether the benefits/costs of designation take time to materialise. I create a cumulative version of the designation share that is the sum of the designation share across periods, i.e. Cjt=∑t=1TDjt. If this is significant in either step it may indicate that the productivity or quality of life effects build up over time. Thirdly, I investigate whether designation is associated with factor non-neutral productivity shifts. I follow Albouy and Ehrlich (2012) by interacting the designation share with the factor price difference. This interaction captures whether designation impacts on the productivity of land more than it does on the productivity of non-land. 4.5. Consistent estimation of the land cost share Since the land cost share is of independent interest it should be estimated consistently. The land cost share will be inconsistent if there are unobserved housing productivity factors in the error term of Equation (6) since according to the model these capitalise in land values. The theory provides guidance as to a potential instrument since both quality of life and non-housing productivity factors will also capitalise into land values. If any of these factors are unrelated to housing productivity then they could serve as suitable instruments. I create such an instrument based on the original Bartik (1991) shift-share where initial local employment shares across industries act as weights on national level changes in gross value added in those industries. This instrument predicts local changes in productivity (which capitalise into land values) that arise from national-level shocks that are unrelated to local-level housing productivity factors (conditional on city-level fixed effects and trends). The initial local employment shares come from the 1991 UK Census (Office of Population Censuses and Surveys, 1991). This Census is a number of years before the panel begins to remain as exogenous as possible. The annual national level GVA over 1997–2007 comes from Cambridge Econometrics (2013). Both are available for some 30 different industries. Instrumentation of land values is kept to a separate specification because such instrumentation prevents the cost function of Equation (6) from properly disentangling the housing productivity from quality of life effects. If land values are predicted by an exogenous factor then they do not include variation as a result of capitalised quality of life effects from CA designation. These effects will therefore instead be captured in δ, making it a mixture of quality of life and housing productivity effects, and difficult to interpret. In effect, for the cost function to work as desired, land values are required to be endogenous. 5. Results 5.1. Housing cost function Figure 6 plots mean house price differentials ( p˜¯j) against mean land value differentials ( r˜¯j) and serves as an introduction to the regression results. The slope of the linear trend suggests a land cost share of φL=β1=0.436 and the binomial slope suggests convexity ( β3=0.076) and an elasticity of substitution less than one. Holding all else constant the HMAs above (below) these lines have lower (higher) than average housing productivity. However, some of the price differences will be explained by construction costs. Furthermore, construction costs are correlated with land values, therefore, the land cost share itself is biased. Figure 6 View largeDownload slide House prices vs land values for English Housing Market Areas. Notes: These trend lines depict predicted values from simplified versions of Equation (7). The linear version of the simple regression is: p˜¯j=β1v˜¯j+β3(r˜¯j)2 where the bar accent signifies the average across years for each HMA. Figure 6 View largeDownload slide House prices vs land values for English Housing Market Areas. Notes: These trend lines depict predicted values from simplified versions of Equation (7). The linear version of the simple regression is: p˜¯j=β1v˜¯j+β3(r˜¯j)2 where the bar accent signifies the average across years for each HMA. Table 4 presents the results from the panel fixed effects and IV estimation of Equation (7). I estimate the Cobb–Douglas and translog production functions with and without CRS restrictions. The key parameter is CA designation, and this is positive and significant across all specifications, implying that CAs lead to higher house prices by reducing housing productivity. A standard deviation increase (an increase of 0.013) in designation is associated with a 0.159–0.169 house price effect in the fixed effects models and a 0.433–0.600 effect in the instrumented models. Since the fixed effects results are inconsistent under the existence of time-variant unobservables and since the first stage F-stats indicate the instrument is not weak, the IV estimates are the preferred results. The estimates imply that designation over 1997–2007 would have increased house prices (via reduced productivity) by 4.3–6.0% for the average HMA.26 The instrumented estimates are significantly larger than their uninstrumented versions, implying that unobservables that are positively related to designation (such as gentrification) are positively related to housing productivity (i.e. reduce house prices for given input prices). As discussed in the empirical strategy this could be the case if gentrification is associated with, for example, transport improvements at the city level that increase productivity in the housing sector.27 Table 3 Housing quantity regression Output Area HMA Dep. Var.: Log Dwelling count OLS (1) FE (2) OLS (3) FE (4) IV (5) CA land share 0.022*** 0.001 0.003* −0.000 −0.001 (0.001) (0.002) (0.002) (0.000) (0.001) R2 0.010 0.872 0.085 1.000 1.000 Number of areas 165665 165663 74 74 74 Observations 1655727 1655725 740 740 740 Output Area HMA Dep. Var.: Log Dwelling count OLS (1) FE (2) OLS (3) FE (4) IV (5) CA land share 0.022*** 0.001 0.003* −0.000 −0.001 (0.001) (0.002) (0.002) (0.000) (0.001) R2 0.010 0.872 0.085 1.000 1.000 Number of areas 165665 165663 74 74 74 Observations 1655727 1655725 740 740 740 Notes: Regressions of logged dwelling count on CA land share at the city (HMA) and very local (Output Area, OA) levels. CA land share has been scaled to give the effect of an average-sized designation for each geography. The fixed effects specification includes HMA trends, and the IV specification includes a trend variable interacted with the initial value of the instrument and designation share. The regressions demonstrate that designation does not significantly decrease housing quantity. The pooled OLS specifications in columns (1) and (3) demonstrate a significant positive relationship most likely due to unobservables. However, there is no effect once fixed effects have been included in columns (2) and (4) and when instrumenting in column (5) for HMAs with the counterfactual designation share used for the main specifications in this paper. Standard errors in parentheses are clustered on the geographical units. *p < 0.1, **p < 0.05, ***p < 0.01. Table 3 Housing quantity regression Output Area HMA Dep. Var.: Log Dwelling count OLS (1) FE (2) OLS (3) FE (4) IV (5) CA land share 0.022*** 0.001 0.003* −0.000 −0.001 (0.001) (0.002) (0.002) (0.000) (0.001) R2 0.010 0.872 0.085 1.000 1.000 Number of areas 165665 165663 74 74 74 Observations 1655727 1655725 740 740 740 Output Area HMA Dep. Var.: Log Dwelling count OLS (1) FE (2) OLS (3) FE (4) IV (5) CA land share 0.022*** 0.001 0.003* −0.000 −0.001 (0.001) (0.002) (0.002) (0.000) (0.001) R2 0.010 0.872 0.085 1.000 1.000 Number of areas 165665 165663 74 74 74 Observations 1655727 1655725 740 740 740 Notes: Regressions of logged dwelling count on CA land share at the city (HMA) and very local (Output Area, OA) levels. CA land share has been scaled to give the effect of an average-sized designation for each geography. The fixed effects specification includes HMA trends, and the IV specification includes a trend variable interacted with the initial value of the instrument and designation share. The regressions demonstrate that designation does not significantly decrease housing quantity. The pooled OLS specifications in columns (1) and (3) demonstrate a significant positive relationship most likely due to unobservables. However, there is no effect once fixed effects have been included in columns (2) and (4) and when instrumenting in column (5) for HMAs with the counterfactual designation share used for the main specifications in this paper. Standard errors in parentheses are clustered on the geographical units. *p < 0.1, **p < 0.05, ***p < 0.01. Table 4 Cost function Panel fixed effects Instrumental variable Cobb–Douglas Translog Cobb–Douglas Translog Unrestr. (1) Restrict. (2) Unrestr. (3) Restrict. (4) Unrestr. (5) Restrict. (6) Unrestr. (7) Restrict. (8) Land value differential 0.178*** 0.172*** 0.180*** 0.175*** 0.176*** 0.173*** 0.185*** 0.181*** (0.022) (0.022) (0.021) (0.021) (0.013) (0.014) (0.012) (0.012) Constr. cost differential 0.553*** 0.828*** 0.527*** 0.825*** 0.635*** 0.827*** 0.544*** 0.819*** (0.138) (0.022) (0.123) (0.021) (0.119) (0.014) (0.110) (0.012) CA land 0.159*** 0.158*** 0.169*** 0.165*** 0.480*** 0.600*** 0.496*** 0.433*** share (z-value) (0.036) (0.036) (0.038) (0.037) (0.131) (0.117) (0.123) (0.087) Predicted refusal rate 0.099*** 0.092*** 0.101*** 0.087*** 0.027*** 0.030*** 0.034*** 0.026*** (z-value) (0.021) (0.019) (0.022) (0.019) (0.008) (0.009) (0.008) (0.007) Land value differential 0.021 0.018 0.074*** 0.058*** squared (0.026) (0.020) (0.013) (0.011) Constr. cost differential −1.409 0.018 −0.261 0.058*** squared (1.249) (0.020) (1.257) (0.011) Land value differential −0.101 −0.035 −0.717*** −0.117*** × Constr. cost diff. (0.262) (0.041) (0.234) (0.022) R2 0.975 0.975 0.976 0.975 0.950 0.940 0.951 0.954 AIC −2488.9 −2480.9 −2491.1 −2482.2 −2348.7 −2381.4 −2363.0 −2363.0 Number of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.048 0.095 0.105 0.001 p-value for CD 0.595 0.098 0.000 0.000 p-value for all restrictions 0.169 0.000 Elasticity of substitution 1.000 1.000 0.755 1.000 1.000 0.213 F-stat of instruments 33.73 33.73 38.08 38.08 Panel fixed effects Instrumental variable Cobb–Douglas Translog Cobb–Douglas Translog Unrestr. (1) Restrict. (2) Unrestr. (3) Restrict. (4) Unrestr. (5) Restrict. (6) Unrestr. (7) Restrict. (8) Land value differential 0.178*** 0.172*** 0.180*** 0.175*** 0.176*** 0.173*** 0.185*** 0.181*** (0.022) (0.022) (0.021) (0.021) (0.013) (0.014) (0.012) (0.012) Constr. cost differential 0.553*** 0.828*** 0.527*** 0.825*** 0.635*** 0.827*** 0.544*** 0.819*** (0.138) (0.022) (0.123) (0.021) (0.119) (0.014) (0.110) (0.012) CA land 0.159*** 0.158*** 0.169*** 0.165*** 0.480*** 0.600*** 0.496*** 0.433*** share (z-value) (0.036) (0.036) (0.038) (0.037) (0.131) (0.117) (0.123) (0.087) Predicted refusal rate 0.099*** 0.092*** 0.101*** 0.087*** 0.027*** 0.030*** 0.034*** 0.026*** (z-value) (0.021) (0.019) (0.022) (0.019) (0.008) (0.009) (0.008) (0.007) Land value differential 0.021 0.018 0.074*** 0.058*** squared (0.026) (0.020) (0.013) (0.011) Constr. cost differential −1.409 0.018 −0.261 0.058*** squared (1.249) (0.020) (1.257) (0.011) Land value differential −0.101 −0.035 −0.717*** −0.117*** × Constr. cost diff. (0.262) (0.041) (0.234) (0.022) R2 0.975 0.975 0.976 0.975 0.950 0.940 0.951 0.954 AIC −2488.9 −2480.9 −2491.1 −2482.2 −2348.7 −2381.4 −2363.0 −2363.0 Number of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.048 0.095 0.105 0.001 p-value for CD 0.595 0.098 0.000 0.000 p-value for all restrictions 0.169 0.000 Elasticity of substitution 1.000 1.000 0.755 1.000 1.000 0.213 F-stat of instruments 33.73 33.73 38.08 38.08 Notes: Fixed effects and IV regressions of Equation (7). The dependent variable is the house price differential. All columns include HMA fixed effects. Fixed effects models include individual HMA trends. IV models include a trend variable interacted with the initial value (in 1997) for the instrument, and with other city characteristics. The instrument is the counterfactual designation share given by Equation (9) and first stages for the restricted translog model are reported in Appendix B in the Online Appendix. The elasticity of substitution is computed as σY=1−2β3/[β1(1−β1)]. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. Table 4 Cost function Panel fixed effects Instrumental variable Cobb–Douglas Translog Cobb–Douglas Translog Unrestr. (1) Restrict. (2) Unrestr. (3) Restrict. (4) Unrestr. (5) Restrict. (6) Unrestr. (7) Restrict. (8) Land value differential 0.178*** 0.172*** 0.180*** 0.175*** 0.176*** 0.173*** 0.185*** 0.181*** (0.022) (0.022) (0.021) (0.021) (0.013) (0.014) (0.012) (0.012) Constr. cost differential 0.553*** 0.828*** 0.527*** 0.825*** 0.635*** 0.827*** 0.544*** 0.819*** (0.138) (0.022) (0.123) (0.021) (0.119) (0.014) (0.110) (0.012) CA land 0.159*** 0.158*** 0.169*** 0.165*** 0.480*** 0.600*** 0.496*** 0.433*** share (z-value) (0.036) (0.036) (0.038) (0.037) (0.131) (0.117) (0.123) (0.087) Predicted refusal rate 0.099*** 0.092*** 0.101*** 0.087*** 0.027*** 0.030*** 0.034*** 0.026*** (z-value) (0.021) (0.019) (0.022) (0.019) (0.008) (0.009) (0.008) (0.007) Land value differential 0.021 0.018 0.074*** 0.058*** squared (0.026) (0.020) (0.013) (0.011) Constr. cost differential −1.409 0.018 −0.261 0.058*** squared (1.249) (0.020) (1.257) (0.011) Land value differential −0.101 −0.035 −0.717*** −0.117*** × Constr. cost diff. (0.262) (0.041) (0.234) (0.022) R2 0.975 0.975 0.976 0.975 0.950 0.940 0.951 0.954 AIC −2488.9 −2480.9 −2491.1 −2482.2 −2348.7 −2381.4 −2363.0 −2363.0 Number of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.048 0.095 0.105 0.001 p-value for CD 0.595 0.098 0.000 0.000 p-value for all restrictions 0.169 0.000 Elasticity of substitution 1.000 1.000 0.755 1.000 1.000 0.213 F-stat of instruments 33.73 33.73 38.08 38.08 Panel fixed effects Instrumental variable Cobb–Douglas Translog Cobb–Douglas Translog Unrestr. (1) Restrict. (2) Unrestr. (3) Restrict. (4) Unrestr. (5) Restrict. (6) Unrestr. (7) Restrict. (8) Land value differential 0.178*** 0.172*** 0.180*** 0.175*** 0.176*** 0.173*** 0.185*** 0.181*** (0.022) (0.022) (0.021) (0.021) (0.013) (0.014) (0.012) (0.012) Constr. cost differential 0.553*** 0.828*** 0.527*** 0.825*** 0.635*** 0.827*** 0.544*** 0.819*** (0.138) (0.022) (0.123) (0.021) (0.119) (0.014) (0.110) (0.012) CA land 0.159*** 0.158*** 0.169*** 0.165*** 0.480*** 0.600*** 0.496*** 0.433*** share (z-value) (0.036) (0.036) (0.038) (0.037) (0.131) (0.117) (0.123) (0.087) Predicted refusal rate 0.099*** 0.092*** 0.101*** 0.087*** 0.027*** 0.030*** 0.034*** 0.026*** (z-value) (0.021) (0.019) (0.022) (0.019) (0.008) (0.009) (0.008) (0.007) Land value differential 0.021 0.018 0.074*** 0.058*** squared (0.026) (0.020) (0.013) (0.011) Constr. cost differential −1.409 0.018 −0.261 0.058*** squared (1.249) (0.020) (1.257) (0.011) Land value differential −0.101 −0.035 −0.717*** −0.117*** × Constr. cost diff. (0.262) (0.041) (0.234) (0.022) R2 0.975 0.975 0.976 0.975 0.950 0.940 0.951 0.954 AIC −2488.9 −2480.9 −2491.1 −2482.2 −2348.7 −2381.4 −2363.0 −2363.0 Number of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.048 0.095 0.105 0.001 p-value for CD 0.595 0.098 0.000 0.000 p-value for all restrictions 0.169 0.000 Elasticity of substitution 1.000 1.000 0.755 1.000 1.000 0.213 F-stat of instruments 33.73 33.73 38.08 38.08 Notes: Fixed effects and IV regressions of Equation (7). The dependent variable is the house price differential. All columns include HMA fixed effects. Fixed effects models include individual HMA trends. IV models include a trend variable interacted with the initial value (in 1997) for the instrument, and with other city characteristics. The instrument is the counterfactual designation share given by Equation (9) and first stages for the restricted translog model are reported in Appendix B in the Online Appendix. The elasticity of substitution is computed as σY=1−2β3/[β1(1−β1)]. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. The refusal rate control is also positive and significant in all models, implying planning restrictiveness decreases housing productivity. Here, the magnitude of the coefficient in the instrumented models suggests an increase in house prices of 6.0–7.8% over the period.28 However, the refusals data has been smoothed making the coefficients unreliable. Furthermore, only the designation variable has been instrumented. The land cost share is around 0.17-0.18 in all columns, which compares with a land cost share of 0.35–0.37 when estimating a housing cost function for the US (Albouy and Ehrlich, 2012). However, as outlined in Appendix B in the Online Appendix my preferred estimate of the land cost share is 0.29 after instrumenting for land values. The elasticity of substitution is 0.755 in the (restricted translog) panel fixed effects model and 0.213 in the instrumented model (compared with 0.367 for the US in Albouy and Ehrlich (2012)). The parameter from the instrumented model falls at the lower end of the range of estimates in the literature, however, a robustness check in Appendix B in the Online Appendix using only new properties finds it increases to 0.402 which is the preferred estimate of the elasticity of substitution since new properties will not be subject to a depreciation of the capital component of the cost of housing, as argued by Ahlfeldt and McMillen (2014). In terms of model selection, I focus on the tests of the restrictions in the instrumented models. The Cobb–Douglas restrictions are easily rejected in columns (5) and (6). The CRS restrictions are not rejected in column (6) but are rejected in column (8). Although CRS is rejected in column (8) I choose to proceed with the restricted translog model assumed in the theory. This decision is also justifiable given the results of interest do not differ greatly between restricted and unrestricted models. 5.2. Alternative specifications Table 5 presents the alternative specifications of the restricted translog cost function. The baseline fixed effects and instrumented models are repeated in columns (1) and (5) for comparison. The first stages in Appendix B in the Online Appendix indicate that the instrumental variable approach encounters varying degrees of success across these alternative specifications. Therefore, in cases where the instrument appears to fail, evidence from the ‘second-best’ fixed effects model will be drawn upon to form tentative findings. Table 5 Alternative specifications for cost function Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share (z-value) 0.165*** 0.164*** 0.433*** 0.947*** (0.037) (0.038) (0.087) (0.235) CA land share × above-average 0.189*** 0.327*** undev. share (0.034) (0.119) CA land share × below-average 0.052 −3.437*** undev. share (0.117) (0.995) CA land share × (land value −0.008 0.238*** diff. – construction cost diff.) (0.027) (0.088) Cumulative CA 0.767 1.368*** designation ( z-value) (0.510) (0.270) R2 0.975 0.975 0.975 0.975 0.954 0.886 0.893 0.946 AIC −2482.2 −2745.5 −2743.3 −2481.9 −2363.0 −2385.7 −2381.4 −2370.3 Numbers of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.095 0.093 0.075 0.108 0.001 0.521 0.401 0.013 Elasticity of substitution 0.755 0.740 0.724 0.740 0.213 −0.022 2.535 0.350 F-stat of instruments 38.08 6.45 3.60 48.98 Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share (z-value) 0.165*** 0.164*** 0.433*** 0.947*** (0.037) (0.038) (0.087) (0.235) CA land share × above-average 0.189*** 0.327*** undev. share (0.034) (0.119) CA land share × below-average 0.052 −3.437*** undev. share (0.117) (0.995) CA land share × (land value −0.008 0.238*** diff. – construction cost diff.) (0.027) (0.088) Cumulative CA 0.767 1.368*** designation ( z-value) (0.510) (0.270) R2 0.975 0.975 0.975 0.975 0.954 0.886 0.893 0.946 AIC −2482.2 −2745.5 −2743.3 −2481.9 −2363.0 −2385.7 −2381.4 −2370.3 Numbers of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.095 0.093 0.075 0.108 0.001 0.521 0.401 0.013 Elasticity of substitution 0.755 0.740 0.724 0.740 0.213 −0.022 2.535 0.350 F-stat of instruments 38.08 6.45 3.60 48.98 Notes: Alternative regressions of the restricted translog cost function. Columns (1)–(4) are variants of fixed effects model from Table 4, column (4) and columns (5)–(8) of the IV model from Table 4, column (8). The dependent variable is the house price differential. Only CA variables differ from baseline specification and to save space the other variables are not presented in this table. The instrument is the counterfactual designation share given by Equation (9) and first stages are reported in Appendix B in the Online Appendix. The reported F-stat of instruments is the Cragg-Donald statistic in columns (6) and (7) where there is more than one instrument. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. Table 5 Alternative specifications for cost function Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share (z-value) 0.165*** 0.164*** 0.433*** 0.947*** (0.037) (0.038) (0.087) (0.235) CA land share × above-average 0.189*** 0.327*** undev. share (0.034) (0.119) CA land share × below-average 0.052 −3.437*** undev. share (0.117) (0.995) CA land share × (land value −0.008 0.238*** diff. – construction cost diff.) (0.027) (0.088) Cumulative CA 0.767 1.368*** designation ( z-value) (0.510) (0.270) R2 0.975 0.975 0.975 0.975 0.954 0.886 0.893 0.946 AIC −2482.2 −2745.5 −2743.3 −2481.9 −2363.0 −2385.7 −2381.4 −2370.3 Numbers of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.095 0.093 0.075 0.108 0.001 0.521 0.401 0.013 Elasticity of substitution 0.755 0.740 0.724 0.740 0.213 −0.022 2.535 0.350 F-stat of instruments 38.08 6.45 3.60 48.98 Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share (z-value) 0.165*** 0.164*** 0.433*** 0.947*** (0.037) (0.038) (0.087) (0.235) CA land share × above-average 0.189*** 0.327*** undev. share (0.034) (0.119) CA land share × below-average 0.052 −3.437*** undev. share (0.117) (0.995) CA land share × (land value −0.008 0.238*** diff. – construction cost diff.) (0.027) (0.088) Cumulative CA 0.767 1.368*** designation ( z-value) (0.510) (0.270) R2 0.975 0.975 0.975 0.975 0.954 0.886 0.893 0.946 AIC −2482.2 −2745.5 −2743.3 −2481.9 −2363.0 −2385.7 −2381.4 −2370.3 Numbers of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.095 0.093 0.075 0.108 0.001 0.521 0.401 0.013 Elasticity of substitution 0.755 0.740 0.724 0.740 0.213 −0.022 2.535 0.350 F-stat of instruments 38.08 6.45 3.60 48.98 Notes: Alternative regressions of the restricted translog cost function. Columns (1)–(4) are variants of fixed effects model from Table 4, column (4) and columns (5)–(8) of the IV model from Table 4, column (8). The dependent variable is the house price differential. Only CA variables differ from baseline specification and to save space the other variables are not presented in this table. The instrument is the counterfactual designation share given by Equation (9) and first stages are reported in Appendix B in the Online Appendix. The reported F-stat of instruments is the Cragg-Donald statistic in columns (6) and (7) where there is more than one instrument. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. Columns (2) and (6) report the results for designation interacted with dummy variables for the Saiz undevelopable land index. In the instrumented model, there is a surprising negative effect for the land-abundant HMAs. However, the instrument has an unexpected sign for the subsample of land-abundant HMAs, suggesting this result may be disregarded. Instead, I focus on the fixed effects results where the productivity effect of designation in land constrained HMAs is larger than the baseline effect. For HMAs with plenty of land, however, the effect is far smaller and is statistically insignificant. Therefore, the results from the fixed effects model imply there is a greater effect of designation on housing productivity where there is a lack of land availability. This result conforms to expectations, since regulating development in CAs should have a smaller impact on productivity if there is an abundance of land elsewhere in the city. Columns (3) and (7) report the factor non-neutral specification. Again, the first-stage coefficient of the instrument has the wrong sign for the non-neutral variable, suggesting that instrumentation is not successful in this model. In the fixed effects model, however, the designation parameter is unaffected by the inclusion of the interaction with the factor price difference. The interacted variable itself is insignificant, implying factor neutrality is a reasonable assumption. This result is in line with that found by Albouy and Ehrlich (2012) for regulation across US MSAs. Finally, columns (4) and (8) report the effect of the cumulative version of the designation variable. The variable is insignificant in the fixed effects specification but significant in the instrumented model. Since the instrument is strong, the instrumented version is preferred, suggesting that the housing productivity effects of designation may increase over time. The alternative specifications support the main result of the cost function step that designation increases housing costs by reducing housing productivity. The additional specification suggest that the effect may decrease with land availability and may be cumulative with time. The results also support the assumption of a factor neutral housing productivity impact. 5.3. Quality of life and CAs Table 6 presents the estimates from the quality of life regression of Equation (8). The same productivity shifters are used as in the respective first step cost functions. Columns (1)–(4) use the fixed effects model in both the cost function and quality of life steps and columns (5)–(8) use the instrumented model in both steps. In general, the parameters for the designation variables are positive and significant, implying designation increases quality of life. In the baseline fixed effects model of column (1), a one-point decrease in designation is associated with a 0.077 point increase in quality of life expressed as a share of expenditure. Instrumenting designation in column (5) reveals a similar quality of life effect of 0.071. A similar estimate makes sense if designation was associated with trends in both positive and negative quality of life factors. Table 6 Quality of life regressions Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share 0.077*** 0.074*** 0.071** 0.163*** (z-value) (0.019) (0.020) (0.033) (0.045) CA land share × Above-average 0.088*** 0.046* undev. share (0.025) (0.028) CA land share × Below-average 0.024 -0.845*** undev. share (0.032) (0.234) CA land share × (land value −0.008 0.029*** diff. – construction cost diff.) (0.009) (0.008) Cumulative CA 0.294*** 0.388*** designation ( z-value) (0.074) (0.087) Predicted refusal rate (z-value) 0.040*** 0.040*** 0.042*** 0.041*** 0.002 0.005* 0.006** −0.000 (0.010) (0.010) (0.009) (0.010) (0.002) (0.003) (0.003) (0.002) Residuals 0.266*** 0.266*** 0.266*** 0.266*** 0.245*** 0.256*** 0.190*** 0.291*** (0.026) (0.026) (0.024) (0.026) (0.024) (0.046) (0.031) (0.026) 1st step specification Table 4, Col. (4) Table 5, Col. (2) Table 5, Col. (3) Table 5, Col. (4) Table 4, Col. (8) Table 5, Col. (6) Table 5, Col. (7) Table 5, Col. (8) R2 0.955 0.955 0.955 0.954 0.934 0.934 0.928 0.937 AIC −4121.2 −4120.1 −4259.9 −4247.5 −3836.5 −3829.3 −3769.5 −3864.8 Observations 726 726 726 726 726 726 726 726 F-stat of instruments 63.62 18.51 32.21 70.04 Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share 0.077*** 0.074*** 0.071** 0.163*** (z-value) (0.019) (0.020) (0.033) (0.045) CA land share × Above-average 0.088*** 0.046* undev. share (0.025) (0.028) CA land share × Below-average 0.024 -0.845*** undev. share (0.032) (0.234) CA land share × (land value −0.008 0.029*** diff. – construction cost diff.) (0.009) (0.008) Cumulative CA 0.294*** 0.388*** designation ( z-value) (0.074) (0.087) Predicted refusal rate (z-value) 0.040*** 0.040*** 0.042*** 0.041*** 0.002 0.005* 0.006** −0.000 (0.010) (0.010) (0.009) (0.010) (0.002) (0.003) (0.003) (0.002) Residuals 0.266*** 0.266*** 0.266*** 0.266*** 0.245*** 0.256*** 0.190*** 0.291*** (0.026) (0.026) (0.024) (0.026) (0.024) (0.046) (0.031) (0.026) 1st step specification Table 4, Col. (4) Table 5, Col. (2) Table 5, Col. (3) Table 5, Col. (4) Table 4, Col. (8) Table 5, Col. (6) Table 5, Col. (7) Table 5, Col. (8) R2 0.955 0.955 0.955 0.954 0.934 0.934 0.928 0.937 AIC −4121.2 −4120.1 −4259.9 −4247.5 −3836.5 −3829.3 −3769.5 −3864.8 Observations 726 726 726 726 726 726 726 726 F-stat of instruments 63.62 18.51 32.21 70.04 Notes: Fixed effects and IV regressions of Equation (8). Dependent variable is a quality of life index computed according to Equation (5). All columns include HMA fixed effects. Fixed effects models include individual HMA trends. IV models include a trend variable interacted with the initial value (in 1997) for the instrument, and with other city characteristics. The instrument in columns (5)–(8) is the counterfactual designation share given by Equation (9) and first stages are reported in Appendix B in the Online Appendix. The reported F-stat of instruments is the Cragg-Donald statistic in columns (6) and (7) where there is more than one instrument. The welfare impact can be computed as the coefficients here minus the share of expenditure on housing times the coefficients from the first step specification. For example, for column (5) a one-point increase in designation results in a 0.071 − (0.31*0.433) = −0.063 decrease in welfare expressed as a share of expenditure. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. Table 6 Quality of life regressions Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share 0.077*** 0.074*** 0.071** 0.163*** (z-value) (0.019) (0.020) (0.033) (0.045) CA land share × Above-average 0.088*** 0.046* undev. share (0.025) (0.028) CA land share × Below-average 0.024 -0.845*** undev. share (0.032) (0.234) CA land share × (land value −0.008 0.029*** diff. – construction cost diff.) (0.009) (0.008) Cumulative CA 0.294*** 0.388*** designation ( z-value) (0.074) (0.087) Predicted refusal rate (z-value) 0.040*** 0.040*** 0.042*** 0.041*** 0.002 0.005* 0.006** −0.000 (0.010) (0.010) (0.009) (0.010) (0.002) (0.003) (0.003) (0.002) Residuals 0.266*** 0.266*** 0.266*** 0.266*** 0.245*** 0.256*** 0.190*** 0.291*** (0.026) (0.026) (0.024) (0.026) (0.024) (0.046) (0.031) (0.026) 1st step specification Table 4, Col. (4) Table 5, Col. (2) Table 5, Col. (3) Table 5, Col. (4) Table 4, Col. (8) Table 5, Col. (6) Table 5, Col. (7) Table 5, Col. (8) R2 0.955 0.955 0.955 0.954 0.934 0.934 0.928 0.937 AIC −4121.2 −4120.1 −4259.9 −4247.5 −3836.5 −3829.3 −3769.5 −3864.8 Observations 726 726 726 726 726 726 726 726 F-stat of instruments 63.62 18.51 32.21 70.04 Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share 0.077*** 0.074*** 0.071** 0.163*** (z-value) (0.019) (0.020) (0.033) (0.045) CA land share × Above-average 0.088*** 0.046* undev. share (0.025) (0.028) CA land share × Below-average 0.024 -0.845*** undev. share (0.032) (0.234) CA land share × (land value −0.008 0.029*** diff. – construction cost diff.) (0.009) (0.008) Cumulative CA 0.294*** 0.388*** designation ( z-value) (0.074) (0.087) Predicted refusal rate (z-value) 0.040*** 0.040*** 0.042*** 0.041*** 0.002 0.005* 0.006** −0.000 (0.010) (0.010) (0.009) (0.010) (0.002) (0.003) (0.003) (0.002) Residuals 0.266*** 0.266*** 0.266*** 0.266*** 0.245*** 0.256*** 0.190*** 0.291*** (0.026) (0.026) (0.024) (0.026) (0.024) (0.046) (0.031) (0.026) 1st step specification Table 4, Col. (4) Table 5, Col. (2) Table 5, Col. (3) Table 5, Col. (4) Table 4, Col. (8) Table 5, Col. (6) Table 5, Col. (7) Table 5, Col. (8) R2 0.955 0.955 0.955 0.954 0.934 0.934 0.928 0.937 AIC −4121.2 −4120.1 −4259.9 −4247.5 −3836.5 −3829.3 −3769.5 −3864.8 Observations 726 726 726 726 726 726 726 726 F-stat of instruments 63.62 18.51 32.21 70.04 Notes: Fixed effects and IV regressions of Equation (8). Dependent variable is a quality of life index computed according to Equation (5). All columns include HMA fixed effects. Fixed effects models include individual HMA trends. IV models include a trend variable interacted with the initial value (in 1997) for the instrument, and with other city characteristics. The instrument in columns (5)–(8) is the counterfactual designation share given by Equation (9) and first stages are reported in Appendix B in the Online Appendix. The reported F-stat of instruments is the Cragg-Donald statistic in columns (6) and (7) where there is more than one instrument. The welfare impact can be computed as the coefficients here minus the share of expenditure on housing times the coefficients from the first step specification. For example, for column (5) a one-point increase in designation results in a 0.071 − (0.31*0.433) = −0.063 decrease in welfare expressed as a share of expenditure. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. As stated, the overall welfare effect is computed as the quality of life effect minus the housing expenditure share times the housing productivity effect. Using the baseline fixed effects specification results in a welfare effect of 0.077−(0.31×0.159)=0.028 and using the baseline instrumental variables specification results in a welfare effect of 0.071−(0.31×0.433)=−0.063. The fixed effects model suggests that designations are welfare-improving, whereas the instrumented model suggests designation worsens welfare. Since the fixed effects results are inconsistent under the presence of time-variant unobservables, and since the F-stats indicate the instrument is strong, the instrumented model is preferred. The average HMA increased its designation share by 1/10 points over the period, suggesting an effect on welfare of −0.63% of expenditure.29 Given the mean income of £22,800 in 2004–2005 this is equivalent to an income reduction of about £1500 over the study period. As discussed in the theory, the validity of the welfare effect relies on there being relatively little quantity adjustments or sorting. In the case where such effects are large, the welfare benefits of designation are overestimated, implying that the welfare loss from designation is an underestimate. Further, it should be noted that I have computed the overall welfare effect using point estimates. To obtain confidence intervals in another specification I estimate both steps together using seemingly unrelated regressions (SUR). This approach allows for computation of the welfare effect as a linear combination of coefficients across models. Following this approach implies a 90% confidence interval with a lower bound of −0.005 and an upper bound −0.126. Essentially, the welfare loss could range from almost zero to around double the point estimate. For planning refusals, the quality of life effects are very small in the instrumented specification. Given that the housing productivity effects were negative, this suggests that planning refusals are welfare-decreasing. However, since the planning variable is volatile and is not instrumented, this should not be taken at face value. Columns (2) and (6) examine the quality of life effects when interacting the designation variable with the Saiz index dummies. As in the cost function step, the first stage for land abundant cities has an unexpected sign, suggesting that instrumentation was unsuccessful and that the fixed effects results are preferred. The fixed effects model shows a significant positive impact on quality of life for areas with land scarcity but an insignificant effect in areas with a land abundance. The coefficient for land scarce areas implies slightly larger quality of life effects than in the baseline specification. Together with the first step, these results imply designations will have both larger housing productivity and larger quality of life effects in cities with a scarcity of developable land. This result makes sense since it is unlikely that designation will have quality of life effects without impacting on housing productivity. Columns (3) and (7) investigate the quality of life effects allowing for non-factor-neutral productivity shifts from designation. As with the first step, the instrumentation appears to fail when predicting the non-neutral designation variable. I therefore concentrate on the fixed effect results where the substantive conclusions are unchanged from the baseline specification. This result supports the evidence from the cost function step that indicated that factor neutrality was a reasonable assumption. Finally, columns (4) and (8) investigate the quality of life effects for the cumulative version of the designation variable. The cumulative designation effects in the instrumented specification are larger than the baseline effects, but the overall welfare effect remains negative (although smaller in magnitude). 5.4. Robustness checks To check the sensitivity of these results, I estimate a number of robustness checks in Appendix B in the Online Appendix. These checks are (i) unweighted aggregation of the data to the HMA-level, (ii) using only new properties (<5 years old),30 (iii) using the full sample of 74 HMAs (not excluding the eight with few transactions), (iv) using a quality of life measure that uses regional variation in the marginal tax rate and the share of wages in income, (v) using a quality of life measure with a high expenditure share on housing, (vi) using a quality of life measure with a low expenditure share on housing, (vii) using a quality of life measure where the expenditure share varies according to city income and (viii) repeating the IV specification using prices from the hedonic model without date bands interacted with year effects. As discussed in Appendix B, the broad results are robust to these changes. In Appendix B, I also demonstrate that the approach is robust to using LAs as the unit of observation. 6. Conclusion This article provides evidence of the effects of CA designation on economic welfare. I constructed a unique panel dataset for English housing market areas (HMAs) that resemble city regions. In the first step of the empirical strategy, I estimated the housing productivity effect of designation using a cost function approach. Here, I regressed house prices on factor prices (land and construction costs) and productivity shifters (including designation). In the second step, I estimated the quality of life benefits and the overall welfare impact of designation. I regressed a quality of life index on housing productivity factors used in the first step. I implemented both stages using panel fixed effects and IV approaches. The main results imply that CA designations (in England, 1997–2007) are associated with both negative housing productivity effects and positive quality of life effects. In the cost function step, increases in designation share lead to higher house prices (compared with land values) indicating a negative shift in housing productivity. The second step reveals that designation leads to increases in quality of life. However, the overall welfare effect is negative in the instrumented and preferred specification. This result is in line with previous evidence that suggests housing regulation is welfare-decreasing. The negative welfare impact of designation over 1997–2007 makes sense if there are concave returns to designation. The areas most worthy of protection may have been designated in the policy’s first 30 years of operation (1966–1996). More recent designations then would be of a less distinctive heritage character, and perhaps only of local significance. Designation has continued despite large costs incurred at the housing market level, since, as argued by Ahlfeldt et al. (2017), designation status is largely determined by local homeowners who stand to gain from the localised benefits of the policy. Nevertheless, though, there may be significant heterogeneity in the quality of CAs over the studied period and the results of this article do not suggest that all of these CAs reduced welfare. Furthermore, there may be significant heterogeneity across individuals, for example, the designation would be more welfare-improving for individuals with a greater than average preference for heritage or with a less than average expenditure share on housing. Overall, though, the results suggest that the average household would have been better off without the average CA being designated in the period between 1997 and 2007 in England. This overall welfare improvement of these designation not being made would have been equivalent to about £1500 per household. Supplementary material Supplementary data for this article are available at Journal of Economic Geography online. Footnotes 1 CAs protect groups of buildings within certain boundaries. Single buildings are usually protected by different legislation, e.g. ‘listed buildings’ status in England. 2 HMAs are defined to capture individual housing markets, based on evidence from patterns of commuting, migration and house prices (DCLG, 2010). As such, they are characterised by a high level of self-containment—77.5% of working residents of an HMA have their workplace inside the HMA—and typically approximate recognisable city regions. 3 I provide some empirical support for this assumption by showing that CA designations do not impact negatively on dwelling stock in England over 2001–2010. 4 Other studies that examine the impact of CAs on property prices include Asabere et al. (1989); Asabere and Huffman (1994); Asabere et al. (1994); Coulson and Lahr (2005); Leichenko et al. (2001); Noonan (2007); Noonan and Krupka (2011); Schaeffer and Millerick (1991). 5 See Gyourko and Molloy (2015) for a good overview of the evidence. 6 Further studies find that planning policies have damaging effects on the retail sector (Cheshire and Hilber, 2008; Cheshire et al., 2011). 7 The amenities literature is large, but a few examples are Albouy (2016); Bayer et al. (2007); Brueckner et al. (1999); Chay and Greenstone (2005); Cheshire and Sheppard (1995); Gibbons et al. (2011); Glaeser et al. (2001); Moeller (2018). 8 For example, Albouy and Ehrlich (2012) find a land cost share of about one third and an elasticity of substitution of 0.5 for the USA. 9 The traded good is produced from land, labour and capital according to Xj=AjXFX(L,NX,K) where AjX is traded good productivity, NX is traded good labour (paid wages wjX) and K is mobile capital paid a price i everywhere. 10 Zero profits in the traded good sector is given by A˜jX=θLr˜j+θNwX where θL and θN are the land and labour cost shares, respectively, for the traded good. 11 To complete the firm-side of the model, the non-land input is produced using labour and capital Mj=FM(NY,K) and the equivalent zero profit condition gives v˜j=αw˜Y, where α is the labour cost share of the non-land input. 12 There are two types of worker: housing sector and traded good sector. They may each receive a different wage and may be attracted to different amenities. The condition for only one type of worker is presented here for simplicity. 13 Output areas (OAs) are the smallest geographical units available for most UK data. They cover 0.78 km2 on average, which is only three times the size of the average CA (0.26 km2). In comparison, HMAs cover 1762 km2, on average. 14 This is an arbitrary cut-off point. Results for the full dataset are presented in robustness checks in Appendix B in the Online Appendix. 15 This implies that the quality of life index will reflect homeowner spatial equilibrium only. However, during the time period considered, private renters represented only around 10% of households, whereas homeowners represented nearly 70%. The small share of private renters and the fact that rents are likely to be closely related to house prices means that a homeowner spatial equilibrium is likely to be broadly representative. 16 Further detail on the weighting procedure and regressions without weights are reported in Appendix B in the Online Appendix. The main results without weights are similar. 17 It is not possible to use these transactions as the main source of data for land values since in many of the smaller cities there are not enough observations. 18 Most LAs were unaffected. Of the original 36,621 were merged into nine new areas, making the new total 354 LAs. 19 This is beneficial since otherwise unobserved build quality would lead to designation being associated with higher house prices for given construction costs. Note that time-invariant build quality differences are captured by fixed effects in the cost function. 20 In fact, the average increase of 0.13% in designated land share already looks much larger when looking at the proportion of designated buildings, according to the Nationwide transaction dataset—this is three and a half times larger at 0.45%. 21 Saiz (2010) uses 50 km circles around US MSA centroids—whereas I define 25 km circles to adjust for the smaller size of English HMAs. The average area of a US MSA is about 7000 km2, which corresponds to the area of a circle with a radius of around 50 km and is perhaps the reasoning behind Saiz’s choice of radius. Since the average HMA in England is about 1800 km2, an appropriately sized circle would have a radius of about 25 km. 22 Taking differentials is necessary in certain parts of the model, e.g. to eliminate the interest rate i or reservation utility u. 23 This will be the case if prices adjust quickly to quality of life changes. This assumption seems reasonable since consumers will immediately be willing to pay more for locations with improved amenity value. Theoretically, all prices (house prices, land values and construction costs) will immediately reflect changes to housing productivity and quality of life due to market competition. For example, developers buying land will pay a price that takes into account the latest information on what their buildings will sell for. The available evidence shows that house prices do respond quickly to amenity changes. For example, Gibbons and Machin (2005) show house prices in 2000 and 2001 adjusting to rail improvements from 1999. 24 The designation share in these figures may appear to have a slight tendency towards a downward trend; however, this is just due to the selection of cities. The average trend is in fact zero after conditioning on trend interactions. 25 Note that individual HMA trends are not used to ensure the instrument is relevant in the first stages. 26 The average HMA increased its designation share by about one tenth of the (between-group) standard deviation over the period 1997–2007. One tenth is multiplied by the coefficients to arrive at the average effect on prices. As argued in the data section, the increase in designation of 0.13% of all HMA land may produce large productivity effects if it disproportionately affects marginal developments. Therefore, the estimated effect sizes are plausible. 27 Transport is also a likely quality of life amenity that would increase house prices via the quality of life route. However, it would also increase land values and therefore be captured in the land cost share of the cost function step. 28 The effect implied by the coefficients of 2.6–3.4% multiplied by the average increase in refusals of 2.3 (between-group) standard deviations. 29 This effect refers to an average homeowner in a city, and there may be a distribution of effects depending on whether the household lives inside or nearby a CA. 30 Using only new properties follows Ahlfeldt and McMillen (2014) who argue that accurate estimates of the land cost share and elasticity of substitution will be biased by a depreciation of the capital component for older housing stock. Acknowledgements The author thanks seminar participants at the London School of Economics and the Humboldt University of Berlin, and especially Gabriel Ahlfeldt, Paul Cheshire, Oliver Falck, Steve Gibbons, Christian Hilber, Kristoffer Moeller, Henry Overman, Olmo Silva, Daniel Sturm, Felix Weinhardt and Nicolai Wendland for helpful comments and suggestions. This work has been supported by English Heritage in terms of data provision. The housing transactions dataset was provided by the Nationwide Building Society. The author thanks Christian Hilber and Wouter Vermeulen for supplying the data on planning refusals. All errors are the sole responsibility of the author. Funding English Heritage provided funding for an earlier project that this work stemmed from. References Ahlfeldt G. , McMillen D. ( 2014 ) New estimates of the elasticity of substitution of land for capital. (ersa14p108), November 2014. Available online at: http://ideas.repec.org/p/wiw/wiwrsa/ersa14p108.html. Ahlfeldt G. M. , Moeller K. , Waights S. , Wendland N. ( 2017 ) Game of zones: the political economy of conservation areas . The Economic Journal , 127 : F421 – F445 . Google Scholar CrossRef Search ADS Albouy D. ( 2016 ) What are cities worth? Land rents, local productivity, and the total value of amenities . Review of Economics and Statistics , 98 : 477 – 487 . Google Scholar CrossRef Search ADS Albouy D. , Ehrlich G. ( 2012 ) Metropolitan land values and housing productivity. National Bureau of Economic Research Working Paper Series, No. 18110. Available online at: http://www.nber.org/papers/w18110. Albouy D. , Farahani A. ( 2017 ) Valuing public goods more generally: the case of infrastructure. Upjohn Institute Working Paper. Asabere P. K. , Huffman F. E. ( 1994 ) Historic designation and residential market values . Appraisal Journal , 62 : 396 . Asabere P. K. , Hachey G. , Grubaugh S. ( 1989 ) Architecture, historic zoning, and the value of homes . Journal of Real Estate Finance and Economics , 2 : 181 – 195 . Google Scholar CrossRef Search ADS Asabere P. K. , Huffman F. E. , Mehdian S. ( 1994 ) The adverse impacts of local historic designation: the case of small apartment buildings in philadelphia . Journal of Real Estate Finance & Economics , 8 : 225 – 234 . Google Scholar CrossRef Search ADS Bartik T. J. ( 1991 ) Who Benefits from State and Local Economic Development Policies ? Kalamazoo, MI: W.E. Upjohn Institute for Employment Research. Google Scholar CrossRef Search ADS Bayer P. , Ferreira F. , McMillan R. ( 2007 ) A unified framework for measuring preferences for schools and neighborhoods . Journal of Political Economy , 115 : 588 – 638 . Google Scholar CrossRef Search ADS Been V. , Ellen I. G. , Gedal M. , Glaeser E. , McCabe B. J. ( 2016 ) Preserving history or restricting development? The heterogeneous effects of historic districts on local housing markets in new york city . Journal of Urban Economics , 92 : 16 – 30 . Google Scholar CrossRef Search ADS Brueckner J. K. , Thisse J.-F. , Zenou Y. ( 1999 ) Why is central paris rich and downtown detroit poor? An amenity-based theory . European Economic Review , 43 : 91 – 107 . Google Scholar CrossRef Search ADS Cambridge Econometrics. Uk Regional Data. February 2013. Chay K. Y. , Greenstone M. ( 2005 ) Does air quality matter? Evidence from the housing market . Journal of Political Economy , 113 : 376 – 424 . Google Scholar CrossRef Search ADS Cheshire P. , Sheppard S. ( 2002 ) The welfare economics of land use planning . Journal of Urban Economics , 52 : 242 – 269 . Google Scholar CrossRef Search ADS Cheshire P. C. , Hilber C. A. L. ( 2008 ) Office space supply restrictions in Britain: the political economy of market revenge . The Economic Journal , 118 : F185 – F221 . Google Scholar CrossRef Search ADS Cheshire P. , Sheppard S. ( 1995 ) On the price of land and the value of amenities . Economica , 62 : 247 – 267 . Google Scholar CrossRef Search ADS Cheshire P. , Hilber C. A. L. , Kaplanis I. ( 2011 ) Evaluating the effects of planning policies on the retail sector: or do town centre first policies deliver the goods? SERC Discussion Papers , 66 : 1 – 34 . Christensen L. R. , Jorgensen D. W. , Lau L. J. ( 1973 ) The Translog Function and the Substitution of Equipment, Structures, and Labor in US Manufacturing 1929-68 . Social Systems Research Institute, University of Wisconsin-Madison . Colwell P. F. , Sirmans C. F. ( 1993 ) A comment on zoning, returns to scale, and the value of undeveloped land . The Review of Economics and Statistics , 783 – 786 . Combes P.-P. , Duranton G. , Gobillon L. ( 2016 ) The production function for housing: evidence from France. Working Paper. Coulson N. E. , Lahr M. L. ( 2005 ) Gracing the land of elvis and beale street: historic designation and property values in memphis . Real Estate Economics , 33 : 487 – 507 . Google Scholar CrossRef Search ADS Coulson N. E. , Leichenko R. M. ( 2001 ) The internal and external impact of historical designation on property values . Journal of Real Estate Finance & Economics , 23 : 113 – 124 . Google Scholar CrossRef Search ADS DCLG ( 2010 ) Geography of housing market areas: final report. GOV.UK Publications. Available online at: https://www.gov.uk/government/publications/housing-market-areas. Epple D. , Gordon B. , Sieg H. ( 2010 ) A new approach to estimating the production function for housing . The American Economic Review , 100 : 905 – 924 . Google Scholar CrossRef Search ADS Fuss M. , McFadden D. ( 1978 ) Production Economics: A Dual Approach to Theory and Applications . North-Holland . Gibbons S. , Machin S. ( 2005 ) Valuing rail access using transport innovations . Journal of Urban Economics , 57 : 148 – 169 . Google Scholar CrossRef Search ADS Gibbons S. , Overman H. G. , Resende G. ( 2011 ) Real earnings disparities in Britain. SERC Discussion Papers, 0065. Glaeser E. L. , Kolko J. , Saiz A. ( 2001 ) Consumer city . Journal of Economic Geography , 1 : 27 – 50 . Google Scholar CrossRef Search ADS Glaeser E. L. , Gyourko J. , Saks R. ( 2005 ) Why is Manhattan so expensive? Regulation and the rise in housing prices . The Journal of Law and Economics , 48 : 331 – 369 . Google Scholar CrossRef Search ADS Graves P. E. , Waldman D. M. ( 1991 ) Multimarket amenity compensation and the behavior of the elderly . The American Economic Review , 81 : 1374 – 1381 . Greenwood M. J. , Hunt G. L. , Rickman D. S. , Treyz G. I. ( 1991 ) Migration, regional equilibrium, and the estimation of compensating differentials . The American Economic Review , 81 : 1382 – 1390 . Gyourko J. , Molloy R. ( 2015 ) Regulation and housing supply . Handbook of Regional and Urban Economics , 5 : 1289 – 1337 . Google Scholar CrossRef Search ADS Gyourko J. , Tracy J. ( 1991 ) The structure of local public finance and the quality of life . Journal of Political Economy , 99 : 774 – 806 . Google Scholar CrossRef Search ADS Hilber C. A. L. , Vermeulen W. ( 2016 ) The impact of supply constraints on house prices in England . The Economic Journal , 126 : 358 – 405 . Google Scholar CrossRef Search ADS Koster H. R. A. , Rouwendal J. ( 2017 ) Historic amenities and housing externalities: evidence from the Netherlands . The Economic Journal , 127 : F396 – F420 . Google Scholar CrossRef Search ADS Koster H. R. A. , van Ommeren J. N. , Rietveld P. ( 2014 ) Historic amenities, income and sorting of households . Journal of Economic Geography , 16 : 203 – 236 . Google Scholar CrossRef Search ADS Leichenko R. M. , Coulson N. E. , Listokin D. ( 2001 ) Historic preservation and residential property values: an analysis of Texas cities . Urban Studies , 38 : 1973 – 1987 . Google Scholar CrossRef Search ADS Linneman P. , Graves P. E. ( 1983 ) Migration and job change: a multinomial logit approach . Journal of Urban Economics , 14 : 263 – 279 . Google Scholar CrossRef Search ADS PubMed McDonald J. F. ( 1981 ) Capital-land substitution in urban housing: a survey of empirical estimates . Journal of Urban Economics , 9 : 190 – 211 . Google Scholar CrossRef Search ADS Moeller K. ( 2018 ) Culturally clustered or in the cloud? Location of internet start-ups in Berlin . Forthcoming in Journal of Regional Science . Noonan D. S. ( 2007 ) Finding an impact of preservation policies: price effects of historic landmarks on attached homes in Chicago, 1990-1999 . Economic Development Quarterly , 21 : 17 – 33 . Google Scholar CrossRef Search ADS Noonan D. S. , Krupka D. J. ( 2011 ) Making-or picking-winners: evidence of internal and external price effects in historic preservation policies . Real Estate Economics , 39 : 379 – 407 . Google Scholar CrossRef Search ADS Notowidigdo M. J. ( 2011 ) The incidence of local labor demand shocks. National Bureau of Economic Research Working Paper Series, No. 17167. URL http://www.nber.org/papers/w17167. Office of Population Censuses and Surveys ( 1991 ) 1991 census: Special workplace statistics (Great Britain). URL https://www.nomisweb.co.uk/. Roback J. ( 1982 ) Wages, rents, and the quality of life . The Journal of Political Economy , 1257 – 1278 . Saiz A. ( 2010 ) The geographic determinants of housing supply . The Quarterly Journal of Economics , 125 : 1253 – 1296 . Google Scholar CrossRef Search ADS Schaeffer P. V. , Millerick C. A. ( 1991 ) The impact of historic district designation on property values: an empirical study . Economic Development Quarterly , 5 : 301 – 312 . Google Scholar CrossRef Search ADS Thorsnes P. ( 1997 ) Consistent estimates of the elasticity of substitution between land and non-land inputs in the production of housing . Journal of Urban Economics , 42 : 98 – 108 . Google Scholar CrossRef Search ADS Turner M. A. , Haughwout A. , Van Der Klaauw W. ( 2014 ) Land use regulation and welfare . Econometrica , 82 : 1341 – 1403 . Google Scholar CrossRef Search ADS © The Author(s) (2018). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Economic Geography Oxford University Press

The preservation of historic districts—is it worth it?

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Abstract

Abstract I investigate the welfare effect of conservation areas that preserve historic districts by regulating development. Such regulation may improve the quality of life but does so by reducing housing productivity—that is, the efficiency with which inputs (land and non-land) are converted into housing services. Using a unique panel dataset for English cities and an instrumental variable approach, I find that conservation areas lead to higher house prices for given land values and building costs (lower housing productivity) and higher house prices for given wages (higher quality of life). The overall welfare impact is found to be negative. 1. Introduction Conservation areas (CAs) protect historic neighbourhoods by placing restrictions on the aesthetic quality of new development.1 CAs are particularly widespread in England with more than 9600 designations since the legislation came into effect in 1967. Inside a CA, any new development is required to preserve or enhance the existing character of the neighbourhood. Similar policies exist in different forms internationally, for example, as local historic districts in the USA or as Ensembleschutz in Germany. By regulating the subjective quality of new buildings, CAs may reduce the productivity of the housing sector. Historic neighbourhoods are no doubt an important urban amenity; however, their preservation may hinder cities in affordably housing their current and future populations. I estimate the welfare effect of CAs by assembling a unique panel dataset for English cities. The dataset comprises 11 years of CA designations over 1997–2007, as well as house prices, land values, construction costs and other city characteristics. I construct my dataset at the city-level to capture the full costs and benefits of the policy at the level of the housing market. Specifically, I use the Housing Market Area (HMA) definition of urban areas.2 I estimate a net welfare effect composed of quality of life effects (benefits) and housing productivity effects (costs). The quality of life effect is derived from the amenity value that households place on the historic built environment in their city and its conservation. A city-level analysis captures benefits at the neighbourhood level—since residents are more likely to live inside or near a CA if they are widespread in a city—and at the city-level i.e. the value that residents place on the amount of preservation in their urban area as a whole. The costs of conservation are modelled as a housing productivity effect i.e. the effectiveness with which land and non-land inputs are converted into housing services. Underlying this is the assumption that productivity, and not quantity, is the major channel for the supply-side effects of designation.3 Indeed, the purpose of CAs is not to prevent development but to ensure that new buildings preserve the character of a neighbourhood. Such aesthetic restrictions may lower housing productivity in several ways. First, developers wishing to build inside CAs must navigate an extra layer of regulation. Secondly, the planned buildings must meet certain standards, which may not be the most cost-effective way of providing housing services. Thirdly, the extra costs of developing inside CAs may push development out to less favourable sites in a city. For these reasons, cities with lots of CAs will be less productive in the housing sector than other cities. Developers will be able to produce fewer units of housing services for given amounts of land and non-land inputs resulting in higher housing costs. A city-level analysis is required to capture productivity effects that determine prices at the level of the housing market. There is a growing body of literature on the economic effects of CAs. The majority of this literature has focussed on estimating the quality of life effects of CAs by examining property prices. A distinction commonly made in the literature (e.g. by Coulson and Leichenko, 2001) is between (negative) internal effects related to restrictions to property rights and (positive) external effects related to the conservation of neighbourhood character. Quasi-experimental evidence has shown that the overall effect of designating CAs is to increase property prices, which suggests that the positive effects dominate (Koster et al., 2014; Ahlfeldt et al., 2017).4 Furthermore, Koster et al. (2014) find that households with higher incomes have a higher willingness to pay for living inside CAs in the Netherlands. Ahlfeldt et al. (2017) find that the pattern of house price effects in England is consistent with a situation where local planners designate CAs according to the interests of local owners. If local owners who benefit from designation are indeed able to game the planning system to their advantage then it important to know what the effects of designation on housing costs are at the wider market level. There is a current lack of evidence on the supply-side effects of CAs. The only evidence to date is presented by Been et al. (2016), who show that construction is slightly lower inside historic districts in New York City. However, they do not examine quantity effects at the city level or supply-related effects on housing costs. The evidence from other forms of regulation suggests that the costs of development restrictions are significant.5 For example, Hilber and Vermeulen (2016) find that house prices in England would be 35% lower if planning constraints were removed. The available evidence finds that the quality of life benefits associated with planning are smaller than the costs. Glaeser et al. (2005) examine building height restrictions in Manhattan, a policy that is intended to prevent towering developments that block the light and view available to existing structures. They find that the development restrictions led to large increases in house prices that left residents worse off, even after accounting for the policy benefits. This ‘regulatory tax’ finding is repeated in other studies such as Albouy and Ehrlich (2012) and Turner et al. (2014), both for regulatory constraints in the USA, and Cheshire and Sheppard (2002) for land use planning in Reading, England.6 In this article, I investigate the extent to which CAs explain differences in housing productivity across cities and whether there are associated quality of life improvements that compensate. As such, I provide an estimate of the net welfare effect of CAs for the average (owner occupier) household. Evaluation of the welfare effects of CAs in cities is challenging since both quality of life (via demand) and housing productivity (via supply) result in increased house prices. To disentangle these effects, I make use of Albouy and Ehrlich’s (2012) two-step approach. In the first step, I estimate a cost function regressing house prices on input prices (land and non-land) and city characteristics that may shift productivity. Housing productivity is defined as the amount of physical housing that can be produced for given quantities of inputs. The key assumption behind this step is perfect competition. If designation makes building more costly then house prices will be higher for given input prices to maintain zero profits. I find that the average increase in CA designation share at the HMA level over 1997–2007 decreases housing productivity by 4.3%, implying a cost-driven increase in house prices of the same magnitude. In the second step, I construct an expenditure-equivalent quality of life index based on house prices and wages and regress it on the same productivity shifters, including designation. The key assumption here is of household mobility. Spatial equilibrium implies that if designation improves quality of life in a city then house prices must be higher for given wage levels. I find that designation increases quality of life, but not by enough to compensate for the greater expenditure on housing resulting from lower productivity. The results imply that designations in England over 1997–2007 were welfare-decreasing for an average owner-occupier household in these cities. While I make use of the Albouy and Ehrlich (2012) approach, my key contribution is different. I focus on estimating the welfare effect of a particular form of regulation, CAs, rather than of housing regulation in general. CAs are a particularly fitting application for the approach since they are expected to impact on housing productivity less than quantity, specifically. Moreover, focussing on a particular form of regulation allows me to identify a causal impact by employing an instrumental variables approach. Finally, my article distinguishes itself by focussing on England rather than the USA, and by constructing a panel dataset that allows me to control for fixed unobservables. My identification strategy involves an instrumental variables approach. The instrument for designation is a shift-share of the Bartik type (Bartik, 1991). The closest previous approach is Koster and Rouwendal (2017) who use national-level changes in spending on cultural heritage weighted by the local share of listed dwellings as an instrument for local investment in historic amenities. My instrument uses changes in the national-level designation shares for the dwelling stock of particular build periods weighted by the HMA shares of dwellings in those build periods. The national level changes in designation are assumed to reflect changes in the subjective evaluation of the dwelling stock of particular build periods. As such, the instrument is a fairly novel application of the shift-share approach. The identifying assumption is that the instrument is unrelated to unobserved shocks to housing productivity or quality of life, conditional on pre-trends in house prices, trends related to the initial value of the instrument (capturing the initial stock) and trends related to other city characteristics. I support the validity of this assumption by showing that the instrument is not related to gentrification. The key contribution of this article is to estimate both the supply-side costs and demand-side benefits of CAs; evidence that is currently missing from the growing body of literature on the policy. This article also contributes to a literature that investigates the costs and benefits of regulation and planning more generally. I present some of the first causal estimates of the welfare effects of a form of housing regulation. To my knowledge, the only previous paper to examine both the costs and benefits of housing regulation using exogenous policy variation is Turner et al. (2014). I also contribute to a literature on the value of locational amenities, by estimating the quality of life effect of a regulation policy instrumented at the city level.7 Furthermore, my results contribute to the literature on housing production functions by estimating what is, to my knowledge, one of the first housing production functions for the UK. I follow Albouy and Ehrlich (2012) who take the traditional approach of regressing house prices on input prices (e.g. McDonald, 1981; Thorsnes, 1997). A more recent literature attempts to estimate the production function, treating housing as a latent variable (Epple et al., 2010; Ahlfeldt and McMillen, 2014; Combes et al., 2016). According to Combes et al. (2016), the two major challenges with estimating any type of housing production function are data availability and disentangling housing quantity from its price. Data availability is a challenge since the approach usually requires data on both house prices and land values. As discussed, I construct a unique panel dataset of cities that includes house prices and some previously unused data for land values and constructions costs for England. The land value data, depicted in Figure 1 for 2007 play a key role in the production function step and in estimating the productivity impact of designation. Figure 1 View largeDownload slide Residential land values by local authority, 2007. Notes: Valuation Office Agency data. Assessed residential land value for small sites with outline planning permission. Areas are extruded proportionally with land value. Figure 1 View largeDownload slide Residential land values by local authority, 2007. Notes: Valuation Office Agency data. Assessed residential land value for small sites with outline planning permission. Areas are extruded proportionally with land value. The second challenge is disentangling housing quantity from its price, which is difficult due to unobservable property characteristics that impact on price. Having collected a panel dataset, I am able to estimate the cost function using fixed effects, which helps to overcome the problem of unobserved property characteristics. My preferred estimates of the land cost share (0.29) and the elasticity of substitution between land and non-land inputs (0.53) fall within the range in the literature.8 The outline of the rest of the article is as follows. In Section 2, I lay out the theoretical model which demonstrates the potential effects of CAs on quality of life and housing productivity. In Section 3, I go over the data used in empirical analysis. In Section 4, I outline the two-step empirical approach and the identification strategy. In Section 5 I present the results. Section 6 concludes. 2. Model In this section, I describe how CA designation impacts on housing productivity and quality of life in a general equilibrium context. I use the model of Albouy and Ehrlich (2012), which is an intercity spatial equilibrium framework based on work by Roback (1982) and Albouy (2016). Each city j is small relative to the national economy and produces a traded good X and housing Y that is non-traded. The city-specific price of a standard housing unit is pj and the uniform price of the traded good is equal to the numeraire. Households with homogeneous preferences work in either the Y-sector or the X-sector and consume both housing and the traded good. The model involves two important assumptions; that of perfect competition, which gives the zero profit conditions, and that of labour mobility, which gives the spatial equilibrium conditions. 2.1. Housing production under zero profits Since the focus of this article is on the housing sector the derivations for the traded good are relegated to footnotes. The housing good Y represents physical housing services. By ‘physical’, it is meant that the housing services are derived from the characteristics of the physical unit itself. Benefits derived from neighbourhood quality will come in to the individual utility function via a quality of life measure defined later on. Firms produce housing services in each city according to:9 Yj=AjYFY(L,M), (1) where AjY is a city-specific housing productivity shifter, FY is a constant returns to scale (CRS) production function, L is land (price rj in each city) and M is the materials (non-land) input to housing (paid price vj). Materials are conceptualised as all non-land factors to housing production including labour and machinery. The housing productivity shifter represents the efficiency with which developers can convert land and non-land factors into housing services and is a function of city-specific attributes which may include the level of CA designation. Specifically, designation will impact negatively on AjY if the policy makes it more difficult to produce housing services. As discussed in the introduction, I assume that the major supply-side effects of designation come through the productivity rather than the quantity channel. The validity of this assumption has important empirical implications that are discussed in subsection 2.4 below. Changes in AjY are assumed to be factor-neutral productivity shifts i.e. the relative factor productivity remains unchanged. However, I demonstrate robustness to this the factor-neutrality assumption in the empirics. Firms choose between factors to minimise the unit cost at given factor prices cj(rj,vj;Aj)=min⁡L,M{rjL+vjM:FY(L,M;Aj)=1}. Zero profits imply the unit price of housing is equal to this unit cost, i.e. pj=cj(rj,vj;Aj). Log-linearisation and taking deviations around the national average gives the zero profit condition:10 p˜j=φLr˜j+φMv˜j−A˜jY, (2) where for any variable z the tilde notation represents log differences around the national average, i.e. z˜j=ln⁡zj−ln⁡z¯, where z¯ is the national average, φL is the land cost share for housing and φM is the non-land cost share. This condition tells us that for each city the house price is given by the sum of the factors’ prices (weighted by their cost shares) minus productivity. Cities with lower housing productivity must have higher house prices for given factor prices to maintain zero profits. Figure 2 illustrates this point by plotting house prices against land values (holding materials costs constant) in an illustrative diagram. The average productivity curve shows how house prices relate to input prices (land values) for cities of average productivity, such as York and Cambridge. As the input price increases, house prices must also increase to maintain zero profits. The curve is concave since developers can substitute away from land as it becomes more expensive. Cities above the curve, such as Brighton, are considered to have low housing productivity because they have higher house prices for the same input price. Brighton has the same land value as Cambridge but ends up with more expensive housing because it is less effective at converting the inputs into outputs. The productivity difference between two cities such as Brighton and Cambridge can be inferred from the vertical difference between them.11 Figure 2 View largeDownload slide Housing productivity example. Notes: This figure is an adaptation of Figure 1A from Albouy and Ehrlich (2012). Figure 2 View largeDownload slide Housing productivity example. Notes: This figure is an adaptation of Figure 1A from Albouy and Ehrlich (2012). 2.2. Location choice under spatial equilibrium Households with homogeneous preferences have a utility function Uj(x,y;Qj) that is quasi-concave in the traded good x and housing y and increases in city-specific quality of life Qj.12 Quality of life is determined by non-market amenities that are available in each city, such as air quality or employment access. These may also include CA designation. An increase in designation impacts positively on Qj if preservation has amenity value. As the designation share in a city increases it becomes more likely that a representative household lives inside or close to a CA. Furthermore, the general level of preservation in a city may be of amenity value to all residents. Households supply one unit of labour to receive a wage wj, to which a non-wage income I is added to make total household income mj. Households optimally allocate their budget according to the expenditure function e(pj,u;Qj)=min⁡x,y{x+pjy:Uj(x,y;Qj)≥u}. Households are assumed to be perfectly mobile, therefore, spatial equilibrium occurs when all locations offer the same utility level u¯. Perfect mobility is consistent with an extensive empirical literature that shows migration flows follow economic incentives (e.g. Linneman and Graves, 1983; Graves and Waldman, 1991; Gyourko and Tracy, 1991). A more direct test of spatial equilibrium is provided by Greenwood et al. (1991) who find little evidence of disequilibrium pricing in income across cities. Indeed, Notowidigdo (2011) estimates mobility costs finding they are ‘at most modest and are comparable for both high-skill and low-skill workers’ (p. 4). Locations with higher house prices or lower levels of quality of life amenities must therefore be compensated with higher income after tax τ, i.e. e(pj,u¯;Qj)=(1−τ)(wj+I). Log-linearised around national average this spatial equilibrium condition is: Q˜j=syp˜j−(1−τ)sww˜j, (3) where sy is the average share of expenditure on housing, τ is the average marginal income tax rate and sw is the average share of income that comes from wages. The spatial equilibrium condition tells us that in each city the (expenditure-equivalent) quality of life must be equal to the unit house price minus the wage (weighted by expenditure shares). Cities with a higher quality of life must have higher house prices for given wages to compensate. 2.3. The impacts of designation on house prices The two conditions, zero profit and spatial equilibrium, both suggest that CAs may increase house prices but the two channels are entirely separate. It is worth underlining here exactly how these two channels operate since this is the mechanism on which the subsequent empirical approach is based. First, if designation impacts on housing productivity only then house prices must be higher for given input prices to maintain zero profits (Equation (2)). This point is illustrated by the example of Brighton over Cambridge in Figure 2. Since quality of life is left unaffected, higher house prices in cities with designation must be compensated for by higher wages to maintain spatial equilibrium (Equation (3)). In this way, the quality of life index remains unaffected by housing productivity shocks from designation. Secondly, if designation impacts on quality of life only then house prices must be higher for given wage levels to maintain zero spatial equilibrium (Equation (3)). Since housing productivity is unaffected, higher house prices must be associated with higher input prices to maintain zero profits (Equation (2)). Figure 2 does not include wages so quality of life differences cannot be illustrated. However, if wages were held constant then an increase in quality of life could look like a movement from Cambridge to York. Thus, the quality of life effect cannot be confused with the housing productivity effect, and the housing productivity effect cannot be confused with the quality of life effect. 2.4. Quantity effects, preference heterogeneity and sorting So far the costs of designation have been treated as a productivity effect, rather than a quantity effect. This assumption has been motivated by the fact that CAs do not ban development (as in zoning) or specifically restrict the amount of housing (as in height restrictions), but instead impose aesthetic standards that may make building more costly. While there is no specific provision for height restrictions in CA policy, the local planning authority is fairly free to decide which buildings they feel preserve the character of the neighbourhood and which do not. Therefore, it cannot be ruled out that they favour lower-rise buildings, effectively imposing a height restriction. Furthermore, even if CAs do not restrict the amount of housing directly, there may be quantity adjustments resulting from housing productivity reductions. The Albouy and Ehrlich (2012) model neatly sidesteps quantity effects by the assumption of homogeneous individuals. Even if there are quantity effects, this has no impact on city prices because the new marginal resident has the same willingness to pay as the old marginal resident (holding quality of life constant). In a similar model, Albouy and Farahani (2017) introduce a degree of preference heterogeneity which delivers a downward sloping demand curve at the city level. Taking an assumed value for the elasticity of population to housing costs, the model predicts that housing productivity reductions lead to larger increases in prices and smaller decreases in land values, compared with the homogeneous preferences case. The reason for the difference is that the quantity reduction pushes the marginal resident up the demand curve where they have a higher willingness to pay resulting in both higher prices and higher land values, compared with a flat demand curve. The empirical implication of this is that the quality of life step will now capture both (i) quality of life increases due to amenity changes and (ii) quality of life increases of the marginal resident due to quantity rationing. The empirical implication is not an identification problem as such—since the quality of life for the marginal resident continues to be correctly identified—but rather a problem to do with interpreting the quality of life parameter in the welfare calculations. Clearly, using (ii) as a welfare increase misses whatever happens to the residents who would have been living in the city had it not been quantity-rationed. A related problem is that of household sorting. Sorting occurs if CA designation leads to a migration of residents into a city who have a higher willingness to pay for that type of quality of life amenity compared with existing residents. As before, the quality of life effect for the marginal resident will continue to be correctly identified in that empirical step. However, it leaves open the possibility that the quality of life effect has an additional component (iii) a quality of life increase of the marginal resident due to changes in the willingness to pay as a result of sorting. If effects (ii) or (iii) represent a relatively large proportion of the overall quality of life estimate than the model would likely be overestimating the welfare benefits of conservation. The welfare conclusions are justified to the extent that the actual sorting and quantity effects of designation are relatively small over the time period considered. Such effects would be small if price adjustment to the quality of life effects is immediate (since residents value security over the future character of their neighbourhood) but if adjustment through quantities and sorting between cities is limited and occurring over a longer time frame. To somewhat alleviate the concerns related to quantity, I conduct a regression of CAs on the number of dwelling units at both the local and city level. In Table 3, I show that CA designations did not impact on the number of dwelling units in England over 1997–2007, either at the city-level (HMA) or at the very local level (output area).13 However, there remains the possibility that CAs impact on some other measure of housing quantity such as floorspace. Overall then, while the assumption that sorting and quantity effects are limited may be reasonable, the existence of large effects cannot be empirically ruled out and the welfare results are therefore caveated accordingly. 3. Data 3.1. Housing market areas The empirical analysis is conducted at the HMA level. These areas are defined by DCLG (2010) using a grouping algorithm applied to ward-level census data on commuting patterns, house prices and migration flows. The use of commuting patterns makes them similar to the better-known travel-to-work area (TTWA) definition. However, HMAs have a higher commuting self-containment rate of 77.5%, compared with just 66.7% for the TTWAs (DCLG, 2010). For this reason in particular, they are considered a better empirical counterpart to the theoretical j-locations. In addition, HMAs are defined such that similar houses have a similar within-area price (after adjusting for observed characteristics). Furthermore, HMAs have a 50% closure rate for migration flows, implying a good deal of both within- and between-market integration. For much of the data described below, I aggregate from local authorities (LAs) based on the relationship mapped in Figure 3. I use weighted aggregation to address potential spatial mismatch. To improve the precision of the house price index, I drop eight (of 74) HMAs—those with fewer than 100 housing transactions per year.14 Since the greatest period of overlap of the different data is 1997–2007, the final panel dataset has T = 11 and N = 66. While this is a fairly small N, any loss of precision is worth it to ensure self-contained areas prescribed by the theory. The wider costs and benefits of designation may only be fully captured at the market level. As described in the introduction, part of the benefits of conservation may be from living in a city with lots of well-preserved heritage neighbourhoods. On the cost side, designation that lowers productivity in one part of the city will impact on prices elsewhere in the city, since the units offer access to the same labour market and are therefore substitutable. However, in Appendix B in the Online Appendix I demonstrate that the approach is robust to using LAs as the unit of observation. Figure 3 View largeDownload slide Housing markets areas over LAs. Notes: Map P11.4 from Geography of housing market areas by DCLG (2010). Figure 3 View largeDownload slide Housing markets areas over LAs. Notes: Map P11.4 from Geography of housing market areas by DCLG (2010). All variables used in the analysis are expressed as log deviations from the national average in each year, denoted by tilde (e.g. p˜). For each variable, I first log-transform it and then subtract the mean of the log-transformed values across HMAs in each year. For the productivity shifters, I additionally normalise the standard deviation to one. Descriptive statistics for the panel dataset are given in Table 1. Table 1 Descriptive statistics for panel dataset Overall statistics Between-group Within-group Mean SD Min Max SD Min Max SD Min Max Variables (standard)  House price (£000s) 118.2 52.90 41.6 345.9 27.30 76.6 220.2 45.43 7.077 243.8  Land value (£000s/ha) 1486.5 1046.2 183.4 7964.4 740.1 600.1 5197.3 744.5 −1420.7 4253.7  Const. cost index 136.7 26.31 93.1 207.0 7.025 123.2 160.4 25.37 93.20 193.7  Designation share 0.0176 0.0136 0.000004 0.0712 0.0136 0.000004 0.0711 0.00126 0.0103 0.0363  Refusal rate 0.230 0.112 0 0.625 0.0601 0.1 0.389 0.0952 −0.0893 0.588 Variables (normalised)  Price differential −0.000 0.231 −0.573 0.775 0.225 −0.422 0.662 0.055 −0.176 0.164  Land value diff. −0.000 0.483 −1.450 1.458 0.455 −1.012 1.216 0.169 −0.569 0.639  Const. cost diff −0.000 0.054 −0.160 0.192 0.050 −0.101 0.160 0.021 −0.063 0.102  Desig. share (z-value) −0.000 0.993 −4.824 1.765 0.997 −4.798 1.725 0.072 −0.603 1.040  Pred. refusal (z-value) 0.000 0.993 −4.514 2.352 0.910 −2.850 1.942 0.411 −1.879 1.335 Overall statistics Between-group Within-group Mean SD Min Max SD Min Max SD Min Max Variables (standard)  House price (£000s) 118.2 52.90 41.6 345.9 27.30 76.6 220.2 45.43 7.077 243.8  Land value (£000s/ha) 1486.5 1046.2 183.4 7964.4 740.1 600.1 5197.3 744.5 −1420.7 4253.7  Const. cost index 136.7 26.31 93.1 207.0 7.025 123.2 160.4 25.37 93.20 193.7  Designation share 0.0176 0.0136 0.000004 0.0712 0.0136 0.000004 0.0711 0.00126 0.0103 0.0363  Refusal rate 0.230 0.112 0 0.625 0.0601 0.1 0.389 0.0952 −0.0893 0.588 Variables (normalised)  Price differential −0.000 0.231 −0.573 0.775 0.225 −0.422 0.662 0.055 −0.176 0.164  Land value diff. −0.000 0.483 −1.450 1.458 0.455 −1.012 1.216 0.169 −0.569 0.639  Const. cost diff −0.000 0.054 −0.160 0.192 0.050 −0.101 0.160 0.021 −0.063 0.102  Desig. share (z-value) −0.000 0.993 −4.824 1.765 0.997 −4.798 1.725 0.072 −0.603 1.040  Pred. refusal (z-value) 0.000 0.993 −4.514 2.352 0.910 −2.850 1.942 0.411 −1.879 1.335 Notes: Descriptive statistics for panel dataset with 66 cities × 11 years = 726 observations overall. Standard variables are: the price of a house with average characteristics in each HMA (based on predictions from hedonic regression), the residential land value (mean of bulk, small and flats), the construction cost index (100 = UK average in 1996), the share of HMA land that is designated and the planning application refusal rate. The normalised versions of the variables are those used in the empirical analysis after being processed as described in the data section. The ‘diff.’ variables are log differentials (in each year) and hence have a mean of zero. The ‘z-value’ variables are additionally divided by the standard deviation in each year and hence have a between-group standard deviation of approximately one. Table 1 Descriptive statistics for panel dataset Overall statistics Between-group Within-group Mean SD Min Max SD Min Max SD Min Max Variables (standard)  House price (£000s) 118.2 52.90 41.6 345.9 27.30 76.6 220.2 45.43 7.077 243.8  Land value (£000s/ha) 1486.5 1046.2 183.4 7964.4 740.1 600.1 5197.3 744.5 −1420.7 4253.7  Const. cost index 136.7 26.31 93.1 207.0 7.025 123.2 160.4 25.37 93.20 193.7  Designation share 0.0176 0.0136 0.000004 0.0712 0.0136 0.000004 0.0711 0.00126 0.0103 0.0363  Refusal rate 0.230 0.112 0 0.625 0.0601 0.1 0.389 0.0952 −0.0893 0.588 Variables (normalised)  Price differential −0.000 0.231 −0.573 0.775 0.225 −0.422 0.662 0.055 −0.176 0.164  Land value diff. −0.000 0.483 −1.450 1.458 0.455 −1.012 1.216 0.169 −0.569 0.639  Const. cost diff −0.000 0.054 −0.160 0.192 0.050 −0.101 0.160 0.021 −0.063 0.102  Desig. share (z-value) −0.000 0.993 −4.824 1.765 0.997 −4.798 1.725 0.072 −0.603 1.040  Pred. refusal (z-value) 0.000 0.993 −4.514 2.352 0.910 −2.850 1.942 0.411 −1.879 1.335 Overall statistics Between-group Within-group Mean SD Min Max SD Min Max SD Min Max Variables (standard)  House price (£000s) 118.2 52.90 41.6 345.9 27.30 76.6 220.2 45.43 7.077 243.8  Land value (£000s/ha) 1486.5 1046.2 183.4 7964.4 740.1 600.1 5197.3 744.5 −1420.7 4253.7  Const. cost index 136.7 26.31 93.1 207.0 7.025 123.2 160.4 25.37 93.20 193.7  Designation share 0.0176 0.0136 0.000004 0.0712 0.0136 0.000004 0.0711 0.00126 0.0103 0.0363  Refusal rate 0.230 0.112 0 0.625 0.0601 0.1 0.389 0.0952 −0.0893 0.588 Variables (normalised)  Price differential −0.000 0.231 −0.573 0.775 0.225 −0.422 0.662 0.055 −0.176 0.164  Land value diff. −0.000 0.483 −1.450 1.458 0.455 −1.012 1.216 0.169 −0.569 0.639  Const. cost diff −0.000 0.054 −0.160 0.192 0.050 −0.101 0.160 0.021 −0.063 0.102  Desig. share (z-value) −0.000 0.993 −4.824 1.765 0.997 −4.798 1.725 0.072 −0.603 1.040  Pred. refusal (z-value) 0.000 0.993 −4.514 2.352 0.910 −2.850 1.942 0.411 −1.879 1.335 Notes: Descriptive statistics for panel dataset with 66 cities × 11 years = 726 observations overall. Standard variables are: the price of a house with average characteristics in each HMA (based on predictions from hedonic regression), the residential land value (mean of bulk, small and flats), the construction cost index (100 = UK average in 1996), the share of HMA land that is designated and the planning application refusal rate. The normalised versions of the variables are those used in the empirical analysis after being processed as described in the data section. The ‘diff.’ variables are log differentials (in each year) and hence have a mean of zero. The ‘z-value’ variables are additionally divided by the standard deviation in each year and hence have a between-group standard deviation of approximately one. 3.2. House prices The production function relies on the theoretical concept of ‘housing services’, which represents the flow of value derived from physical housing for the occupant. Housing quality and housing quantity are assumed to be entirely substitutable in that each simply delivers a flow of ‘services’ to the occupant. This assumption is a useful simplification since it implies that the unit price of housing services can be estimated from house prices in a hedonic approach that controls for housing quality and quantity. House prices for 1,087,896 transactions in England over the period 1995–2010 come from Nationwide, the largest building society in the UK. All transactions in the Nationwide data are for owner-occupied units.15 In addition to the price paid, the data have property characteristics including postcode location, which is used to identify which HMA the transacted unit belongs to. The house price index is computed by regressing the log of the transaction price p for unit-i in HMA-j and year-t on a vector of property characteristics Xijt and a set of HMA-year indicator variables: pijt=Xijtβ+ϕjt(HMAj×YEARt)+εijt. (4) The house price index is then constructed by taking the predicted HMA-year effects ϕ^jt and subtracting the national average in each year, i.e. p˜jt=ϕ^jt−ϕ^¯t. The result represents log deviations from the national average since house prices are log transformed for the hedonic regression. The results of the hedonic regression and a brief discussion of the coefficients are presented in Appendix A in the Online Appendix. Since the distribution of observed transactions within each HMA-year may differ from the actual distribution of housing stock in the HMA, each observation is weighted by the LA dwellings count in 2003 divided by the LA-year transaction count.16 3.3. Land values Residential land values are obtained from the Valuation Office Agency (VOA). The land values are produced for the Property Market Report which has been released biannually since 1982. Land values for the full set of LAs were, however, not made available until recently (2014). As such, this research is one of the first empirical applications of the full dataset. The assessments are based on a combination of expert opinion and observed values for transactions of land. The values are assessed for small sites (<2 ha), bulk land (>2 ha) and flat sites (for building flats) for vacant land with outline planning permission. To produce an overall land value index I adjust for the price differences by site category using a regression discussed in Appendix A in the Online Appendix. Notably, the regression results show that bulk land is considerably cheaper (by 4.9% to 11.2%) than small plots in every year. It is reassuring that the valuations conform to the well-documented ‘plattage effect’ (by e.g. Colwell and Sirmans, 1993). To validate the valuations, I make use of transaction data in the form of land auctions between 2001 and 2012.17 There is a very high correlation with the valuation data as discussed in Appendix A in the Online Appendix. Land valuations for 1995–1998 are reported using a slightly different LA definition due to a local government reorganisation that occurred over this period. I converted the earlier LA definition to the new definition using the relevant lookup table.18 I then took the mean of the biannually reported land values and aggregated them to the HMA level, again using the distribution of housing stock in 2003 as weights. As a final step, I computed log differentials. 3.4. Construction costs To capture the costs of non-land inputs to construction an index of rebuilding costs was obtained from the Regional Supplement to the Guide to House Rebuilding Cost published by the Royal Institute of Chartered Surveyors (RICS). Rebuilding cost is an approximation of how much it would cost to completely rebuild a standard unit of residential housing had it been entirely destroyed. The index takes into account the cost of construction labour (wages), materials costs, machine hire, etc., and is considered to be an appropriate measure of the price of non-land inputs to housing. The index is also reflective of local build quality.19 The data are based on hedonic regression using observed tender prices for construction projects and the sample size of tenders is given with each factor. I make use of location adjustment factors that are available annually from 1997 to 2008 at the LA-level and take into account the local variations in costs. To my knowledge these data have not been used before in empirical analysis at this level of detail. The location factors were scanned from hard copies and digitised using optical character recognition software. The separate years were then matched to form a panel dataset. Some LAs were missing from the data, especially in the earlier years. However, a higher tier geography (corresponding in most cases with counties) was recorded completely, enabling a simple filling procedure described in Appendix A in the Online Appendix. Finally, the LA level data were aggregated to HMAs weighted by dwelling stock, and then log differenced. 3.5. CA designation A spatial dataset of CAs was obtained from English Heritage. The dataset contains polygons that map the borders of all CAs in England on the British National Grid coordinate system. The full dataset has only been used once before in empirical analysis by Ahlfeldt et al. (2017). The data include the date of designation, which lies between 1966 and 2011. Using this information, I calculated in a geographical information systems (GIS) environment the share of land in each HMA that was covered by CAs in each year over 1997–2007. Figure 4 plots the initial designation share in 1997 against the change in share over the study period. The chart shows variation in both the initial share and the change over the period. Although the changes are small as a proportion of all land, they may still have large productivity or quality of life effects as outlined below. The CA designation share is first computed at the LA level to be aggregated to HMAs weighted by dwelling stock, ensuring all the data are produced comparably. The log land shares are then normalised to have a mean of zero and a standard deviation of one which is achieved by taking log-differences around the national average and then dividing by the standard deviation in each year. Such ‘z-values’ are created for each of the housing productivity factors to ensure the effects on log costs are comparable. Figure 4 View largeDownload slide Initial designation share against change for HMAs. Notes: Blackburn & Burnley HMA is not depicted since the change in designation share over the period is off the chart at 2.6% of the land area. Figure 4 View largeDownload slide Initial designation share against change for HMAs. Notes: Blackburn & Burnley HMA is not depicted since the change in designation share over the period is off the chart at 2.6% of the land area. The designated share of all HMA land is a proxy for the extent to which designation might impact on housing productivity or quality of life. So while the increase in designated land area over the period for the average HMA is relatively small, at 0.13%, the actual effects may be much larger.20 A specific reason for this is that housing productivity effects will depend on the impact of designation on marginal developments which may disproportionately occur in existing residential areas where designations are more common. Moreover, designations might occur specifically to ensure that potential new developments maintain the neighbourhood character. On the benefits side, designations may also have quality of effects outside of the designated areas themselves via spillovers as documented, for example, by Ahlfeldt et al. (2017). 3.6. Planning restrictions and other housing productivity factors To control for the underlying regularity restrictiveness in each city, the share of planning applications that are refused in each year from 1997 to 2007 was obtained. These data were first used by Hilber and Vermeulen (2016) to analyse the effect of planning restrictiveness on housing costs in England. The LA data were aggregated to HMAs weighted by dwelling stock. The variation in refusal rates is volatile over time such that it is unlikely that every fluctuation represents actual changes in planning restrictiveness. The data were, therefore, smoothed to eliminate the short-term noise while keeping the longer-run trends in planning restrictiveness. This smoothing was done by regressing the refusal share on a binomial time trend and using the predicted values. To estimate whether designation effects vary with geographic constraints, I compute the undevelopable share of land within 25 km of each HMA centroid, following Saiz (2010).21 Developable land is defined as land that is flat (<15 degree slope) and dry (solid land covers). To calculate the slopes, I use the OS Terrain 50 topography dataset which is a 50 m grid of the UK with land surface altitudes recorded for the centroid of each grid square. I calculate the slope in the steepest direction for each grid square and if this is greater than 15 degrees then the 50 m grid square is defined as undevelopable. To identify dry land I use the Land Cover Map 2000, which is a 25 m grid for the whole of Great Britain where each square is assigned to one of 26 broad categories of land cover. The grid square is defined as undevelopable if it is water, bog, marsh, etc., following Hilber and Vermeulen (2016). The final undevelopable land share is computed for each HMA as the total land area that is not developable divided by the total area in the 25 km circle. 3.7. Quality of life index I construct a quality of life index according to Equation (3) as follows: QoLjt1=0.31×p˜jt−(1−0.225)×0.64×w˜jt, (5) where 0.31 is the average share of expenditure on housing, which comes from the Expenditure and Food Surveys 2001–2007. In different empirical specifications, I demonstrate robustness to using different values for the housing expenditure share, as well as using shares that vary by average city income. The price differential p˜jt is the same as that used in the cost function step, computed via hedonic regression. The annual wages w˜jt come from the Annual Survey of Hours and Earnings at the local authority level and are aggregated (weighted by the number of jobs) to HMAs before taking log differentials. The average marginal income tax rate of 0.225 was computed using data from the HM Revenue and Customs for 2005–2006 and the average share of income from wages of 0.64 is from the Department for Work and Pensions for 2005–2006. I estimate additional specifications where the marginal income tax rate depends on the average income specific to each HMA-year observation and where the share of income from wages varies across regions. The results are robust to such changes as presented in Appendix B in the Online Appendix suggesting the use of average figures is suitable. A ranking of HMAs according to this quality of life index is presented in Appendix A in the Online Appendix. 4. Empirical strategy and identification My empirical strategy is based on the two-step approach of Albouy and Ehrlich (2012). In the first step I estimate a cost function for housing production. The unit value of housing is regressed on land values, construction prices and productivity shifters, including designation. In the second step, the quality of life index is regressed on housing productivity factors to reveal the overall welfare impact of designation. My identification strategy is based on implementing a panel fixed effects approach and instrumenting for designation with a shift-share. 4.1. First step: cost function Following Albouy and Ehrlich (2012) and Christensen et al. (1973) I first estimate an unrestricted translog cost function: p˜jt=β1r˜jt+β2v˜jt+β3(r˜jt)2+β4(v˜jt)2+β5(r˜jtv˜jt)+πR˜jt+δD˜jt+fj+ujt, (6) where R˜jt is the predicted refusal rate and D˜jt is the CA designation share. The fixed effects fj capture all time-invariant productivity shifters, such as geographic constraints. The parameter δ is an inconsistent estimate of the housing productivity impact of CAs if designation is correlated with the error term. According to the model, quality of life factors are absent from ujt as they are capitalised in land values r˜jt. However, unobserved housing productivity shocks may be correlated with designation as discussed in the identification strategy below. In this panel format, the log-differentials are taken around the national average in each year t. These differentials are equivalent to using year effects in the regression; however, I prefer to stick to the format suggested by the theory.22 Imposing the restrictions of CRS: β1=1−β2; β3=β4=−β5/2 makes this equivalent to a second-order approximation of Equation (2) and imposing the further restrictions of β3=β4=β5=0 makes this a first-order estimation i.e. a Cobb–Douglas cost function (Fuss and McFadden, 1978). Comparing Equation (6) with Equation (2) reveals that housing productivity is given by: A˜jY=−πR˜jt−δD˜jt−fj−ujt. (7) Housing productivity is the (negative of) observed and unobserved city attributes that impact on unit house prices after taking into account input prices. If designation impacts negatively on housing productivity then its coefficient δ is expected to be positive i.e. it will raise house prices above what is predicted by factor prices alone. 4.2. Second step: quality of life Increasing the cost of housing is not the intended effect of designation. Rather, CAs reduce housing productivity to preserve or improve the attractiveness of neighbourhoods. The second step investigates the demand-side effect of CAs by relating the same productivity shifters, including designation, to a measure of quality of life. The regression takes the form: Q˜jt=μ1R˜jt+μ2D˜jt+μ3ujt+gj+εjt, (8) where gj are fixed effects that capture time-invariant quality of life factors. The parameter μ3 gives the relationship between designation and quality of life. According to the model, productivity factors are absent from εjt, despite the fact that house prices go into the quality of life index. They are absent because higher wages will compensate for higher prices from productivity factors to maintain spatial equilibrium. However, unobserved quality of life factors may lead to a bias of μ2, as discussed in the identification strategy below. If CAs increase quality of life then μ2 will be positive. The coefficient gives the quality of life impact expressed as a share of expenditure. Combining this with the estimate from the first step gives the total welfare as μ2−(0.31×δ), since 0.31 is the housing expenditure share. 4.3. Identification There are two features to the identification strategy. First, I make use of the panel nature of the data by estimating a fixed effects model. Secondly, I combine fixed effects with a time-varying instrument for designation based on the Bartik (1991) shift-share. It is worth noting that identification here focusses only on the impacts of designation. Consistent estimates of the land cost share are obtained by instrumenting land values in an alternative specification outlined in subsection 4.5, but this step is neither necessary nor desirable for consistent estimation of the impacts of designation, as explained in that subsection. Fixed effects estimation alone provides a major improvement over pooled OLS estimation by controlling for time-invariant housing productivity factors or quality of life factors. For example, on the cost function side, a time-invariant factor such as soil type may both affect housing productivity and be correlated with today’s CAs (if it drove the location of historical settlements). Likewise on the quality of life side, many urban amenities such as job accessibility, natural factors and cultural amenities are relatively fixed over the period of one decade. Furthermore, the fixed effects models remove any effect from unobservable housing characteristics that biased the house price index in the hedonic regression stage. Thus, they help to deal with a common problem with estimating housing production functions (Combes et al., 2016). I additionally include individual HMA trends to capture the effect of unobservable trends in housing productivity and quality of life factors that may be related to designation. A relationship in trends could come about if, for example, trends in unobservable housing productivity or quality of life factors and trends in designation are both related to the initial heritage endowment of a city. In terms of the theoretical model, estimation of a fixed effects model assumes spatial equilibrium in each year.23 The fixed effects strategy does not help when unobservables are time-variant. To illustrate, consider the example of a city with ongoing transport improvements that increase housing productivity and/or quality of life. Such improvements may also be the result of (or may result in) gentrification, which itself has been empirically demonstrated to lead to designation (Ahlfeldt et al., 2017). In general, changes in city attributes that impact on housing productivity or quality of life will likely be interlinked with gentrification and, therefore, designation. To address this I employ an instrumental variable approach similar in spirit to a Bartik instrument (Bartik, 1991). The instrument provides HMA-level ‘shocks’ that are a weighted average of the national level designation share of buildings in different build date categories. The weights used for a given HMA are the share of its dwelling stock in each build date band. Specifically, the instrument is computed as: Zjt=∑b=114Dj−1,btHjb0, (9) where Zjt is the counterfactual designation share in HMA-j and year t, Dj−1,bt is the designation share in each age band b for all HMAs other than HMA-j and Hjb0 is the initial share of dwelling stock in HMA-j in age band. The national level designation share in each of the age bands are based on the Nationwide transactions data and are described in Appendix A in the Online Appendix. The counterfactual designation share is expected to be a relevant predictor of HMA designation even conditional on fixed effects and trend controls. National changes in the designation share for buildings of certain build periods capture shifts in preferences for heritage. If an HMA has a high proportion of buildings in those build periods then the chances of designation are increased. Relevance is confirmed by the F-stats in Table 4 and Table 6 for the cost function and quality of life regressions, respectively. Furthermore, the instruments are significant and (mostly) have the expected signs in the first-stage regressions in tables presented in Appendix A in the Online Appendix. The charts in Figure 5 illustrate the counterfactual designation share and the actual designation share conditional on HMA fixed effects and trend interactions for a selection of cities.24 Figure 5 View largeDownload slide Actual designation against counterfactual designation for selected HMAs. Notes: Designation (z-scores) have been adjusted for HMA fixed effects giving them a zero mean across years for each HMA. The shares are also conditional on trend interactions. Figure 5 View largeDownload slide Actual designation against counterfactual designation for selected HMAs. Notes: Designation (z-scores) have been adjusted for HMA fixed effects giving them a zero mean across years for each HMA. The shares are also conditional on trend interactions. To be a valid instrument, the counterfactual designation share must be orthogonal to the error terms ujt and εjt. The argument for exogeneity is that changes in the national level designation share are unrelated to anything going on at the individual city level, like gentrification. To capture general trends in unobservables that might be correlated with the initial stock, I include a trend variable interacted with the initial value (in 1997) for the instrument. To capture further possible trends I include interactions of a trend variable with city characteristics: the initial designation share, the initial refusal rate, the city population, protected land share and undevelopable land share.25 Therefore, the identifying assumption is that the instrument is unrelated to unobserved shocks to housing productivity or quality of life, conditional on controlling for trends related to the initial stock (as captured in the initial value of the instrument) and trends related to other city characteristics. The exclusionary restriction requires that the instrument not lead directly to changes in the outcome variable. The exclusionary restriction could be violated if national-level changes in preferences for buildings of an HMA lead to the gentrification of that HMA, which in turns impacts on housing productivity or quality of life. I argue, however, that such a correlation is unlikely to continue conditional on HMA fixed effects and trend controls. Gentrification is a complex process that depends on many more factors than the build date of the dwelling stock. In Table 2 I present evidence to support this argument. Here, the designation share and the counterfactual designation share are regressed on a measure of the share of residents who hold a degree certificate. This dependent variable comes from the UK census and proxies gentrification of a city. The positive and significant relationship with designation in the pooled OLS model implies that gentrification and designation are indeed interlinked. The size of this coefficient decreases as fixed effects and trends are introduced. However, for the instrument there is no relationship at all in either of the models. Given that gentrification is the most likely source of unobserved shocks, it is reassuring that it is not related to the instrument. Table 2 Degree share regression (1) (2) (3) (4) OLS OLS FE & Trends FE & Trends Designation share 0.010* −0.002 (0.005) (0.002) Counterfactual designation 0.001 −0.062 (0.005) (0.043) F-stat 3.619 0.029 0.965 2.069 R2 0.068 0.000 0.002 0.023 AIC −543.0 −532.7 −1239.3 −1242.4 Numbers of HMAs 74 74 74 74 Observations 148 148 148 148 (1) (2) (3) (4) OLS OLS FE & Trends FE & Trends Designation share 0.010* −0.002 (0.005) (0.002) Counterfactual designation 0.001 −0.062 (0.005) (0.043) F-stat 3.619 0.029 0.965 2.069 R2 0.068 0.000 0.002 0.023 AIC −543.0 −532.7 −1239.3 −1242.4 Numbers of HMAs 74 74 74 74 Observations 148 148 148 148 Notes: The dependent variable is degree share (differential) in 2001 and 2011. Fixed effects and trends are implemented by demeaning and detrending the variables beforehand. This pre-step was carried out using two separate samples: (i) annual data over 1997–2007 for the designation shares and (ii) Census data for 1991, 2001 and 2011 for the degree share. The data were then merged for 2 years, 2001 and 2011. The designation shares for 2007 were used for 2011 as this is the closest possible match. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. Table 2 Degree share regression (1) (2) (3) (4) OLS OLS FE & Trends FE & Trends Designation share 0.010* −0.002 (0.005) (0.002) Counterfactual designation 0.001 −0.062 (0.005) (0.043) F-stat 3.619 0.029 0.965 2.069 R2 0.068 0.000 0.002 0.023 AIC −543.0 −532.7 −1239.3 −1242.4 Numbers of HMAs 74 74 74 74 Observations 148 148 148 148 (1) (2) (3) (4) OLS OLS FE & Trends FE & Trends Designation share 0.010* −0.002 (0.005) (0.002) Counterfactual designation 0.001 −0.062 (0.005) (0.043) F-stat 3.619 0.029 0.965 2.069 R2 0.068 0.000 0.002 0.023 AIC −543.0 −532.7 −1239.3 −1242.4 Numbers of HMAs 74 74 74 74 Observations 148 148 148 148 Notes: The dependent variable is degree share (differential) in 2001 and 2011. Fixed effects and trends are implemented by demeaning and detrending the variables beforehand. This pre-step was carried out using two separate samples: (i) annual data over 1997–2007 for the designation shares and (ii) Census data for 1991, 2001 and 2011 for the degree share. The data were then merged for 2 years, 2001 and 2011. The designation shares for 2007 were used for 2011 as this is the closest possible match. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. Another potential violation of the exclusionary restriction is if the instrument captures increased valuations placed on specific property characteristics. As it stands, these are not controlled for in the hedonic regression. To deal with this, for the IV models only, I re-estimate the hedonic regression with interactions between year effects and the build date categories. In a robustness check in Appendix B in the Online Appendix, I demonstrate that the results are not sensitive to this change. 4.4. Alternative specifications I estimate three alternative specifications. First, I investigate whether the effects of designation depend on the quantity of available land around a city. If there is an abundance of land, designation may have less effect on productivity as developers can easily build outside the city. To test this idea I create two dummy variables, one for HMAs that are above-average on the Saiz index and one for those below average. I interact the designation variable with each of these dummies and include the interactions in the two regression steps in place of the uninteracted version of the designation variable. These separate dummy interactions give the effect on housing productivity or quality of life in HMAs that have a scarcity of land or an abundance of land. Secondly, I investigate whether the benefits/costs of designation take time to materialise. I create a cumulative version of the designation share that is the sum of the designation share across periods, i.e. Cjt=∑t=1TDjt. If this is significant in either step it may indicate that the productivity or quality of life effects build up over time. Thirdly, I investigate whether designation is associated with factor non-neutral productivity shifts. I follow Albouy and Ehrlich (2012) by interacting the designation share with the factor price difference. This interaction captures whether designation impacts on the productivity of land more than it does on the productivity of non-land. 4.5. Consistent estimation of the land cost share Since the land cost share is of independent interest it should be estimated consistently. The land cost share will be inconsistent if there are unobserved housing productivity factors in the error term of Equation (6) since according to the model these capitalise in land values. The theory provides guidance as to a potential instrument since both quality of life and non-housing productivity factors will also capitalise into land values. If any of these factors are unrelated to housing productivity then they could serve as suitable instruments. I create such an instrument based on the original Bartik (1991) shift-share where initial local employment shares across industries act as weights on national level changes in gross value added in those industries. This instrument predicts local changes in productivity (which capitalise into land values) that arise from national-level shocks that are unrelated to local-level housing productivity factors (conditional on city-level fixed effects and trends). The initial local employment shares come from the 1991 UK Census (Office of Population Censuses and Surveys, 1991). This Census is a number of years before the panel begins to remain as exogenous as possible. The annual national level GVA over 1997–2007 comes from Cambridge Econometrics (2013). Both are available for some 30 different industries. Instrumentation of land values is kept to a separate specification because such instrumentation prevents the cost function of Equation (6) from properly disentangling the housing productivity from quality of life effects. If land values are predicted by an exogenous factor then they do not include variation as a result of capitalised quality of life effects from CA designation. These effects will therefore instead be captured in δ, making it a mixture of quality of life and housing productivity effects, and difficult to interpret. In effect, for the cost function to work as desired, land values are required to be endogenous. 5. Results 5.1. Housing cost function Figure 6 plots mean house price differentials ( p˜¯j) against mean land value differentials ( r˜¯j) and serves as an introduction to the regression results. The slope of the linear trend suggests a land cost share of φL=β1=0.436 and the binomial slope suggests convexity ( β3=0.076) and an elasticity of substitution less than one. Holding all else constant the HMAs above (below) these lines have lower (higher) than average housing productivity. However, some of the price differences will be explained by construction costs. Furthermore, construction costs are correlated with land values, therefore, the land cost share itself is biased. Figure 6 View largeDownload slide House prices vs land values for English Housing Market Areas. Notes: These trend lines depict predicted values from simplified versions of Equation (7). The linear version of the simple regression is: p˜¯j=β1v˜¯j+β3(r˜¯j)2 where the bar accent signifies the average across years for each HMA. Figure 6 View largeDownload slide House prices vs land values for English Housing Market Areas. Notes: These trend lines depict predicted values from simplified versions of Equation (7). The linear version of the simple regression is: p˜¯j=β1v˜¯j+β3(r˜¯j)2 where the bar accent signifies the average across years for each HMA. Table 4 presents the results from the panel fixed effects and IV estimation of Equation (7). I estimate the Cobb–Douglas and translog production functions with and without CRS restrictions. The key parameter is CA designation, and this is positive and significant across all specifications, implying that CAs lead to higher house prices by reducing housing productivity. A standard deviation increase (an increase of 0.013) in designation is associated with a 0.159–0.169 house price effect in the fixed effects models and a 0.433–0.600 effect in the instrumented models. Since the fixed effects results are inconsistent under the existence of time-variant unobservables and since the first stage F-stats indicate the instrument is not weak, the IV estimates are the preferred results. The estimates imply that designation over 1997–2007 would have increased house prices (via reduced productivity) by 4.3–6.0% for the average HMA.26 The instrumented estimates are significantly larger than their uninstrumented versions, implying that unobservables that are positively related to designation (such as gentrification) are positively related to housing productivity (i.e. reduce house prices for given input prices). As discussed in the empirical strategy this could be the case if gentrification is associated with, for example, transport improvements at the city level that increase productivity in the housing sector.27 Table 3 Housing quantity regression Output Area HMA Dep. Var.: Log Dwelling count OLS (1) FE (2) OLS (3) FE (4) IV (5) CA land share 0.022*** 0.001 0.003* −0.000 −0.001 (0.001) (0.002) (0.002) (0.000) (0.001) R2 0.010 0.872 0.085 1.000 1.000 Number of areas 165665 165663 74 74 74 Observations 1655727 1655725 740 740 740 Output Area HMA Dep. Var.: Log Dwelling count OLS (1) FE (2) OLS (3) FE (4) IV (5) CA land share 0.022*** 0.001 0.003* −0.000 −0.001 (0.001) (0.002) (0.002) (0.000) (0.001) R2 0.010 0.872 0.085 1.000 1.000 Number of areas 165665 165663 74 74 74 Observations 1655727 1655725 740 740 740 Notes: Regressions of logged dwelling count on CA land share at the city (HMA) and very local (Output Area, OA) levels. CA land share has been scaled to give the effect of an average-sized designation for each geography. The fixed effects specification includes HMA trends, and the IV specification includes a trend variable interacted with the initial value of the instrument and designation share. The regressions demonstrate that designation does not significantly decrease housing quantity. The pooled OLS specifications in columns (1) and (3) demonstrate a significant positive relationship most likely due to unobservables. However, there is no effect once fixed effects have been included in columns (2) and (4) and when instrumenting in column (5) for HMAs with the counterfactual designation share used for the main specifications in this paper. Standard errors in parentheses are clustered on the geographical units. *p < 0.1, **p < 0.05, ***p < 0.01. Table 3 Housing quantity regression Output Area HMA Dep. Var.: Log Dwelling count OLS (1) FE (2) OLS (3) FE (4) IV (5) CA land share 0.022*** 0.001 0.003* −0.000 −0.001 (0.001) (0.002) (0.002) (0.000) (0.001) R2 0.010 0.872 0.085 1.000 1.000 Number of areas 165665 165663 74 74 74 Observations 1655727 1655725 740 740 740 Output Area HMA Dep. Var.: Log Dwelling count OLS (1) FE (2) OLS (3) FE (4) IV (5) CA land share 0.022*** 0.001 0.003* −0.000 −0.001 (0.001) (0.002) (0.002) (0.000) (0.001) R2 0.010 0.872 0.085 1.000 1.000 Number of areas 165665 165663 74 74 74 Observations 1655727 1655725 740 740 740 Notes: Regressions of logged dwelling count on CA land share at the city (HMA) and very local (Output Area, OA) levels. CA land share has been scaled to give the effect of an average-sized designation for each geography. The fixed effects specification includes HMA trends, and the IV specification includes a trend variable interacted with the initial value of the instrument and designation share. The regressions demonstrate that designation does not significantly decrease housing quantity. The pooled OLS specifications in columns (1) and (3) demonstrate a significant positive relationship most likely due to unobservables. However, there is no effect once fixed effects have been included in columns (2) and (4) and when instrumenting in column (5) for HMAs with the counterfactual designation share used for the main specifications in this paper. Standard errors in parentheses are clustered on the geographical units. *p < 0.1, **p < 0.05, ***p < 0.01. Table 4 Cost function Panel fixed effects Instrumental variable Cobb–Douglas Translog Cobb–Douglas Translog Unrestr. (1) Restrict. (2) Unrestr. (3) Restrict. (4) Unrestr. (5) Restrict. (6) Unrestr. (7) Restrict. (8) Land value differential 0.178*** 0.172*** 0.180*** 0.175*** 0.176*** 0.173*** 0.185*** 0.181*** (0.022) (0.022) (0.021) (0.021) (0.013) (0.014) (0.012) (0.012) Constr. cost differential 0.553*** 0.828*** 0.527*** 0.825*** 0.635*** 0.827*** 0.544*** 0.819*** (0.138) (0.022) (0.123) (0.021) (0.119) (0.014) (0.110) (0.012) CA land 0.159*** 0.158*** 0.169*** 0.165*** 0.480*** 0.600*** 0.496*** 0.433*** share (z-value) (0.036) (0.036) (0.038) (0.037) (0.131) (0.117) (0.123) (0.087) Predicted refusal rate 0.099*** 0.092*** 0.101*** 0.087*** 0.027*** 0.030*** 0.034*** 0.026*** (z-value) (0.021) (0.019) (0.022) (0.019) (0.008) (0.009) (0.008) (0.007) Land value differential 0.021 0.018 0.074*** 0.058*** squared (0.026) (0.020) (0.013) (0.011) Constr. cost differential −1.409 0.018 −0.261 0.058*** squared (1.249) (0.020) (1.257) (0.011) Land value differential −0.101 −0.035 −0.717*** −0.117*** × Constr. cost diff. (0.262) (0.041) (0.234) (0.022) R2 0.975 0.975 0.976 0.975 0.950 0.940 0.951 0.954 AIC −2488.9 −2480.9 −2491.1 −2482.2 −2348.7 −2381.4 −2363.0 −2363.0 Number of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.048 0.095 0.105 0.001 p-value for CD 0.595 0.098 0.000 0.000 p-value for all restrictions 0.169 0.000 Elasticity of substitution 1.000 1.000 0.755 1.000 1.000 0.213 F-stat of instruments 33.73 33.73 38.08 38.08 Panel fixed effects Instrumental variable Cobb–Douglas Translog Cobb–Douglas Translog Unrestr. (1) Restrict. (2) Unrestr. (3) Restrict. (4) Unrestr. (5) Restrict. (6) Unrestr. (7) Restrict. (8) Land value differential 0.178*** 0.172*** 0.180*** 0.175*** 0.176*** 0.173*** 0.185*** 0.181*** (0.022) (0.022) (0.021) (0.021) (0.013) (0.014) (0.012) (0.012) Constr. cost differential 0.553*** 0.828*** 0.527*** 0.825*** 0.635*** 0.827*** 0.544*** 0.819*** (0.138) (0.022) (0.123) (0.021) (0.119) (0.014) (0.110) (0.012) CA land 0.159*** 0.158*** 0.169*** 0.165*** 0.480*** 0.600*** 0.496*** 0.433*** share (z-value) (0.036) (0.036) (0.038) (0.037) (0.131) (0.117) (0.123) (0.087) Predicted refusal rate 0.099*** 0.092*** 0.101*** 0.087*** 0.027*** 0.030*** 0.034*** 0.026*** (z-value) (0.021) (0.019) (0.022) (0.019) (0.008) (0.009) (0.008) (0.007) Land value differential 0.021 0.018 0.074*** 0.058*** squared (0.026) (0.020) (0.013) (0.011) Constr. cost differential −1.409 0.018 −0.261 0.058*** squared (1.249) (0.020) (1.257) (0.011) Land value differential −0.101 −0.035 −0.717*** −0.117*** × Constr. cost diff. (0.262) (0.041) (0.234) (0.022) R2 0.975 0.975 0.976 0.975 0.950 0.940 0.951 0.954 AIC −2488.9 −2480.9 −2491.1 −2482.2 −2348.7 −2381.4 −2363.0 −2363.0 Number of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.048 0.095 0.105 0.001 p-value for CD 0.595 0.098 0.000 0.000 p-value for all restrictions 0.169 0.000 Elasticity of substitution 1.000 1.000 0.755 1.000 1.000 0.213 F-stat of instruments 33.73 33.73 38.08 38.08 Notes: Fixed effects and IV regressions of Equation (7). The dependent variable is the house price differential. All columns include HMA fixed effects. Fixed effects models include individual HMA trends. IV models include a trend variable interacted with the initial value (in 1997) for the instrument, and with other city characteristics. The instrument is the counterfactual designation share given by Equation (9) and first stages for the restricted translog model are reported in Appendix B in the Online Appendix. The elasticity of substitution is computed as σY=1−2β3/[β1(1−β1)]. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. Table 4 Cost function Panel fixed effects Instrumental variable Cobb–Douglas Translog Cobb–Douglas Translog Unrestr. (1) Restrict. (2) Unrestr. (3) Restrict. (4) Unrestr. (5) Restrict. (6) Unrestr. (7) Restrict. (8) Land value differential 0.178*** 0.172*** 0.180*** 0.175*** 0.176*** 0.173*** 0.185*** 0.181*** (0.022) (0.022) (0.021) (0.021) (0.013) (0.014) (0.012) (0.012) Constr. cost differential 0.553*** 0.828*** 0.527*** 0.825*** 0.635*** 0.827*** 0.544*** 0.819*** (0.138) (0.022) (0.123) (0.021) (0.119) (0.014) (0.110) (0.012) CA land 0.159*** 0.158*** 0.169*** 0.165*** 0.480*** 0.600*** 0.496*** 0.433*** share (z-value) (0.036) (0.036) (0.038) (0.037) (0.131) (0.117) (0.123) (0.087) Predicted refusal rate 0.099*** 0.092*** 0.101*** 0.087*** 0.027*** 0.030*** 0.034*** 0.026*** (z-value) (0.021) (0.019) (0.022) (0.019) (0.008) (0.009) (0.008) (0.007) Land value differential 0.021 0.018 0.074*** 0.058*** squared (0.026) (0.020) (0.013) (0.011) Constr. cost differential −1.409 0.018 −0.261 0.058*** squared (1.249) (0.020) (1.257) (0.011) Land value differential −0.101 −0.035 −0.717*** −0.117*** × Constr. cost diff. (0.262) (0.041) (0.234) (0.022) R2 0.975 0.975 0.976 0.975 0.950 0.940 0.951 0.954 AIC −2488.9 −2480.9 −2491.1 −2482.2 −2348.7 −2381.4 −2363.0 −2363.0 Number of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.048 0.095 0.105 0.001 p-value for CD 0.595 0.098 0.000 0.000 p-value for all restrictions 0.169 0.000 Elasticity of substitution 1.000 1.000 0.755 1.000 1.000 0.213 F-stat of instruments 33.73 33.73 38.08 38.08 Panel fixed effects Instrumental variable Cobb–Douglas Translog Cobb–Douglas Translog Unrestr. (1) Restrict. (2) Unrestr. (3) Restrict. (4) Unrestr. (5) Restrict. (6) Unrestr. (7) Restrict. (8) Land value differential 0.178*** 0.172*** 0.180*** 0.175*** 0.176*** 0.173*** 0.185*** 0.181*** (0.022) (0.022) (0.021) (0.021) (0.013) (0.014) (0.012) (0.012) Constr. cost differential 0.553*** 0.828*** 0.527*** 0.825*** 0.635*** 0.827*** 0.544*** 0.819*** (0.138) (0.022) (0.123) (0.021) (0.119) (0.014) (0.110) (0.012) CA land 0.159*** 0.158*** 0.169*** 0.165*** 0.480*** 0.600*** 0.496*** 0.433*** share (z-value) (0.036) (0.036) (0.038) (0.037) (0.131) (0.117) (0.123) (0.087) Predicted refusal rate 0.099*** 0.092*** 0.101*** 0.087*** 0.027*** 0.030*** 0.034*** 0.026*** (z-value) (0.021) (0.019) (0.022) (0.019) (0.008) (0.009) (0.008) (0.007) Land value differential 0.021 0.018 0.074*** 0.058*** squared (0.026) (0.020) (0.013) (0.011) Constr. cost differential −1.409 0.018 −0.261 0.058*** squared (1.249) (0.020) (1.257) (0.011) Land value differential −0.101 −0.035 −0.717*** −0.117*** × Constr. cost diff. (0.262) (0.041) (0.234) (0.022) R2 0.975 0.975 0.976 0.975 0.950 0.940 0.951 0.954 AIC −2488.9 −2480.9 −2491.1 −2482.2 −2348.7 −2381.4 −2363.0 −2363.0 Number of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.048 0.095 0.105 0.001 p-value for CD 0.595 0.098 0.000 0.000 p-value for all restrictions 0.169 0.000 Elasticity of substitution 1.000 1.000 0.755 1.000 1.000 0.213 F-stat of instruments 33.73 33.73 38.08 38.08 Notes: Fixed effects and IV regressions of Equation (7). The dependent variable is the house price differential. All columns include HMA fixed effects. Fixed effects models include individual HMA trends. IV models include a trend variable interacted with the initial value (in 1997) for the instrument, and with other city characteristics. The instrument is the counterfactual designation share given by Equation (9) and first stages for the restricted translog model are reported in Appendix B in the Online Appendix. The elasticity of substitution is computed as σY=1−2β3/[β1(1−β1)]. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. The refusal rate control is also positive and significant in all models, implying planning restrictiveness decreases housing productivity. Here, the magnitude of the coefficient in the instrumented models suggests an increase in house prices of 6.0–7.8% over the period.28 However, the refusals data has been smoothed making the coefficients unreliable. Furthermore, only the designation variable has been instrumented. The land cost share is around 0.17-0.18 in all columns, which compares with a land cost share of 0.35–0.37 when estimating a housing cost function for the US (Albouy and Ehrlich, 2012). However, as outlined in Appendix B in the Online Appendix my preferred estimate of the land cost share is 0.29 after instrumenting for land values. The elasticity of substitution is 0.755 in the (restricted translog) panel fixed effects model and 0.213 in the instrumented model (compared with 0.367 for the US in Albouy and Ehrlich (2012)). The parameter from the instrumented model falls at the lower end of the range of estimates in the literature, however, a robustness check in Appendix B in the Online Appendix using only new properties finds it increases to 0.402 which is the preferred estimate of the elasticity of substitution since new properties will not be subject to a depreciation of the capital component of the cost of housing, as argued by Ahlfeldt and McMillen (2014). In terms of model selection, I focus on the tests of the restrictions in the instrumented models. The Cobb–Douglas restrictions are easily rejected in columns (5) and (6). The CRS restrictions are not rejected in column (6) but are rejected in column (8). Although CRS is rejected in column (8) I choose to proceed with the restricted translog model assumed in the theory. This decision is also justifiable given the results of interest do not differ greatly between restricted and unrestricted models. 5.2. Alternative specifications Table 5 presents the alternative specifications of the restricted translog cost function. The baseline fixed effects and instrumented models are repeated in columns (1) and (5) for comparison. The first stages in Appendix B in the Online Appendix indicate that the instrumental variable approach encounters varying degrees of success across these alternative specifications. Therefore, in cases where the instrument appears to fail, evidence from the ‘second-best’ fixed effects model will be drawn upon to form tentative findings. Table 5 Alternative specifications for cost function Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share (z-value) 0.165*** 0.164*** 0.433*** 0.947*** (0.037) (0.038) (0.087) (0.235) CA land share × above-average 0.189*** 0.327*** undev. share (0.034) (0.119) CA land share × below-average 0.052 −3.437*** undev. share (0.117) (0.995) CA land share × (land value −0.008 0.238*** diff. – construction cost diff.) (0.027) (0.088) Cumulative CA 0.767 1.368*** designation ( z-value) (0.510) (0.270) R2 0.975 0.975 0.975 0.975 0.954 0.886 0.893 0.946 AIC −2482.2 −2745.5 −2743.3 −2481.9 −2363.0 −2385.7 −2381.4 −2370.3 Numbers of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.095 0.093 0.075 0.108 0.001 0.521 0.401 0.013 Elasticity of substitution 0.755 0.740 0.724 0.740 0.213 −0.022 2.535 0.350 F-stat of instruments 38.08 6.45 3.60 48.98 Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share (z-value) 0.165*** 0.164*** 0.433*** 0.947*** (0.037) (0.038) (0.087) (0.235) CA land share × above-average 0.189*** 0.327*** undev. share (0.034) (0.119) CA land share × below-average 0.052 −3.437*** undev. share (0.117) (0.995) CA land share × (land value −0.008 0.238*** diff. – construction cost diff.) (0.027) (0.088) Cumulative CA 0.767 1.368*** designation ( z-value) (0.510) (0.270) R2 0.975 0.975 0.975 0.975 0.954 0.886 0.893 0.946 AIC −2482.2 −2745.5 −2743.3 −2481.9 −2363.0 −2385.7 −2381.4 −2370.3 Numbers of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.095 0.093 0.075 0.108 0.001 0.521 0.401 0.013 Elasticity of substitution 0.755 0.740 0.724 0.740 0.213 −0.022 2.535 0.350 F-stat of instruments 38.08 6.45 3.60 48.98 Notes: Alternative regressions of the restricted translog cost function. Columns (1)–(4) are variants of fixed effects model from Table 4, column (4) and columns (5)–(8) of the IV model from Table 4, column (8). The dependent variable is the house price differential. Only CA variables differ from baseline specification and to save space the other variables are not presented in this table. The instrument is the counterfactual designation share given by Equation (9) and first stages are reported in Appendix B in the Online Appendix. The reported F-stat of instruments is the Cragg-Donald statistic in columns (6) and (7) where there is more than one instrument. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. Table 5 Alternative specifications for cost function Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share (z-value) 0.165*** 0.164*** 0.433*** 0.947*** (0.037) (0.038) (0.087) (0.235) CA land share × above-average 0.189*** 0.327*** undev. share (0.034) (0.119) CA land share × below-average 0.052 −3.437*** undev. share (0.117) (0.995) CA land share × (land value −0.008 0.238*** diff. – construction cost diff.) (0.027) (0.088) Cumulative CA 0.767 1.368*** designation ( z-value) (0.510) (0.270) R2 0.975 0.975 0.975 0.975 0.954 0.886 0.893 0.946 AIC −2482.2 −2745.5 −2743.3 −2481.9 −2363.0 −2385.7 −2381.4 −2370.3 Numbers of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.095 0.093 0.075 0.108 0.001 0.521 0.401 0.013 Elasticity of substitution 0.755 0.740 0.724 0.740 0.213 −0.022 2.535 0.350 F-stat of instruments 38.08 6.45 3.60 48.98 Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share (z-value) 0.165*** 0.164*** 0.433*** 0.947*** (0.037) (0.038) (0.087) (0.235) CA land share × above-average 0.189*** 0.327*** undev. share (0.034) (0.119) CA land share × below-average 0.052 −3.437*** undev. share (0.117) (0.995) CA land share × (land value −0.008 0.238*** diff. – construction cost diff.) (0.027) (0.088) Cumulative CA 0.767 1.368*** designation ( z-value) (0.510) (0.270) R2 0.975 0.975 0.975 0.975 0.954 0.886 0.893 0.946 AIC −2482.2 −2745.5 −2743.3 −2481.9 −2363.0 −2385.7 −2381.4 −2370.3 Numbers of HMAs 66 66 66 66 66 66 66 66 Observations 726 726 726 726 726 726 726 726 p-value for CRS 0.095 0.093 0.075 0.108 0.001 0.521 0.401 0.013 Elasticity of substitution 0.755 0.740 0.724 0.740 0.213 −0.022 2.535 0.350 F-stat of instruments 38.08 6.45 3.60 48.98 Notes: Alternative regressions of the restricted translog cost function. Columns (1)–(4) are variants of fixed effects model from Table 4, column (4) and columns (5)–(8) of the IV model from Table 4, column (8). The dependent variable is the house price differential. Only CA variables differ from baseline specification and to save space the other variables are not presented in this table. The instrument is the counterfactual designation share given by Equation (9) and first stages are reported in Appendix B in the Online Appendix. The reported F-stat of instruments is the Cragg-Donald statistic in columns (6) and (7) where there is more than one instrument. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. Columns (2) and (6) report the results for designation interacted with dummy variables for the Saiz undevelopable land index. In the instrumented model, there is a surprising negative effect for the land-abundant HMAs. However, the instrument has an unexpected sign for the subsample of land-abundant HMAs, suggesting this result may be disregarded. Instead, I focus on the fixed effects results where the productivity effect of designation in land constrained HMAs is larger than the baseline effect. For HMAs with plenty of land, however, the effect is far smaller and is statistically insignificant. Therefore, the results from the fixed effects model imply there is a greater effect of designation on housing productivity where there is a lack of land availability. This result conforms to expectations, since regulating development in CAs should have a smaller impact on productivity if there is an abundance of land elsewhere in the city. Columns (3) and (7) report the factor non-neutral specification. Again, the first-stage coefficient of the instrument has the wrong sign for the non-neutral variable, suggesting that instrumentation is not successful in this model. In the fixed effects model, however, the designation parameter is unaffected by the inclusion of the interaction with the factor price difference. The interacted variable itself is insignificant, implying factor neutrality is a reasonable assumption. This result is in line with that found by Albouy and Ehrlich (2012) for regulation across US MSAs. Finally, columns (4) and (8) report the effect of the cumulative version of the designation variable. The variable is insignificant in the fixed effects specification but significant in the instrumented model. Since the instrument is strong, the instrumented version is preferred, suggesting that the housing productivity effects of designation may increase over time. The alternative specifications support the main result of the cost function step that designation increases housing costs by reducing housing productivity. The additional specification suggest that the effect may decrease with land availability and may be cumulative with time. The results also support the assumption of a factor neutral housing productivity impact. 5.3. Quality of life and CAs Table 6 presents the estimates from the quality of life regression of Equation (8). The same productivity shifters are used as in the respective first step cost functions. Columns (1)–(4) use the fixed effects model in both the cost function and quality of life steps and columns (5)–(8) use the instrumented model in both steps. In general, the parameters for the designation variables are positive and significant, implying designation increases quality of life. In the baseline fixed effects model of column (1), a one-point decrease in designation is associated with a 0.077 point increase in quality of life expressed as a share of expenditure. Instrumenting designation in column (5) reveals a similar quality of life effect of 0.071. A similar estimate makes sense if designation was associated with trends in both positive and negative quality of life factors. Table 6 Quality of life regressions Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share 0.077*** 0.074*** 0.071** 0.163*** (z-value) (0.019) (0.020) (0.033) (0.045) CA land share × Above-average 0.088*** 0.046* undev. share (0.025) (0.028) CA land share × Below-average 0.024 -0.845*** undev. share (0.032) (0.234) CA land share × (land value −0.008 0.029*** diff. – construction cost diff.) (0.009) (0.008) Cumulative CA 0.294*** 0.388*** designation ( z-value) (0.074) (0.087) Predicted refusal rate (z-value) 0.040*** 0.040*** 0.042*** 0.041*** 0.002 0.005* 0.006** −0.000 (0.010) (0.010) (0.009) (0.010) (0.002) (0.003) (0.003) (0.002) Residuals 0.266*** 0.266*** 0.266*** 0.266*** 0.245*** 0.256*** 0.190*** 0.291*** (0.026) (0.026) (0.024) (0.026) (0.024) (0.046) (0.031) (0.026) 1st step specification Table 4, Col. (4) Table 5, Col. (2) Table 5, Col. (3) Table 5, Col. (4) Table 4, Col. (8) Table 5, Col. (6) Table 5, Col. (7) Table 5, Col. (8) R2 0.955 0.955 0.955 0.954 0.934 0.934 0.928 0.937 AIC −4121.2 −4120.1 −4259.9 −4247.5 −3836.5 −3829.3 −3769.5 −3864.8 Observations 726 726 726 726 726 726 726 726 F-stat of instruments 63.62 18.51 32.21 70.04 Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share 0.077*** 0.074*** 0.071** 0.163*** (z-value) (0.019) (0.020) (0.033) (0.045) CA land share × Above-average 0.088*** 0.046* undev. share (0.025) (0.028) CA land share × Below-average 0.024 -0.845*** undev. share (0.032) (0.234) CA land share × (land value −0.008 0.029*** diff. – construction cost diff.) (0.009) (0.008) Cumulative CA 0.294*** 0.388*** designation ( z-value) (0.074) (0.087) Predicted refusal rate (z-value) 0.040*** 0.040*** 0.042*** 0.041*** 0.002 0.005* 0.006** −0.000 (0.010) (0.010) (0.009) (0.010) (0.002) (0.003) (0.003) (0.002) Residuals 0.266*** 0.266*** 0.266*** 0.266*** 0.245*** 0.256*** 0.190*** 0.291*** (0.026) (0.026) (0.024) (0.026) (0.024) (0.046) (0.031) (0.026) 1st step specification Table 4, Col. (4) Table 5, Col. (2) Table 5, Col. (3) Table 5, Col. (4) Table 4, Col. (8) Table 5, Col. (6) Table 5, Col. (7) Table 5, Col. (8) R2 0.955 0.955 0.955 0.954 0.934 0.934 0.928 0.937 AIC −4121.2 −4120.1 −4259.9 −4247.5 −3836.5 −3829.3 −3769.5 −3864.8 Observations 726 726 726 726 726 726 726 726 F-stat of instruments 63.62 18.51 32.21 70.04 Notes: Fixed effects and IV regressions of Equation (8). Dependent variable is a quality of life index computed according to Equation (5). All columns include HMA fixed effects. Fixed effects models include individual HMA trends. IV models include a trend variable interacted with the initial value (in 1997) for the instrument, and with other city characteristics. The instrument in columns (5)–(8) is the counterfactual designation share given by Equation (9) and first stages are reported in Appendix B in the Online Appendix. The reported F-stat of instruments is the Cragg-Donald statistic in columns (6) and (7) where there is more than one instrument. The welfare impact can be computed as the coefficients here minus the share of expenditure on housing times the coefficients from the first step specification. For example, for column (5) a one-point increase in designation results in a 0.071 − (0.31*0.433) = −0.063 decrease in welfare expressed as a share of expenditure. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. Table 6 Quality of life regressions Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share 0.077*** 0.074*** 0.071** 0.163*** (z-value) (0.019) (0.020) (0.033) (0.045) CA land share × Above-average 0.088*** 0.046* undev. share (0.025) (0.028) CA land share × Below-average 0.024 -0.845*** undev. share (0.032) (0.234) CA land share × (land value −0.008 0.029*** diff. – construction cost diff.) (0.009) (0.008) Cumulative CA 0.294*** 0.388*** designation ( z-value) (0.074) (0.087) Predicted refusal rate (z-value) 0.040*** 0.040*** 0.042*** 0.041*** 0.002 0.005* 0.006** −0.000 (0.010) (0.010) (0.009) (0.010) (0.002) (0.003) (0.003) (0.002) Residuals 0.266*** 0.266*** 0.266*** 0.266*** 0.245*** 0.256*** 0.190*** 0.291*** (0.026) (0.026) (0.024) (0.026) (0.024) (0.046) (0.031) (0.026) 1st step specification Table 4, Col. (4) Table 5, Col. (2) Table 5, Col. (3) Table 5, Col. (4) Table 4, Col. (8) Table 5, Col. (6) Table 5, Col. (7) Table 5, Col. (8) R2 0.955 0.955 0.955 0.954 0.934 0.934 0.928 0.937 AIC −4121.2 −4120.1 −4259.9 −4247.5 −3836.5 −3829.3 −3769.5 −3864.8 Observations 726 726 726 726 726 726 726 726 F-stat of instruments 63.62 18.51 32.21 70.04 Panel fixed effects Instrumental variable (1) (2) (3) (4) (5) (6) (7) (8) Baseline model Undev. interact Factor non-neut. Cumulat. desigat. Baseline model Undev. interact Factor non-neut. Cumulat. designat. CA land share 0.077*** 0.074*** 0.071** 0.163*** (z-value) (0.019) (0.020) (0.033) (0.045) CA land share × Above-average 0.088*** 0.046* undev. share (0.025) (0.028) CA land share × Below-average 0.024 -0.845*** undev. share (0.032) (0.234) CA land share × (land value −0.008 0.029*** diff. – construction cost diff.) (0.009) (0.008) Cumulative CA 0.294*** 0.388*** designation ( z-value) (0.074) (0.087) Predicted refusal rate (z-value) 0.040*** 0.040*** 0.042*** 0.041*** 0.002 0.005* 0.006** −0.000 (0.010) (0.010) (0.009) (0.010) (0.002) (0.003) (0.003) (0.002) Residuals 0.266*** 0.266*** 0.266*** 0.266*** 0.245*** 0.256*** 0.190*** 0.291*** (0.026) (0.026) (0.024) (0.026) (0.024) (0.046) (0.031) (0.026) 1st step specification Table 4, Col. (4) Table 5, Col. (2) Table 5, Col. (3) Table 5, Col. (4) Table 4, Col. (8) Table 5, Col. (6) Table 5, Col. (7) Table 5, Col. (8) R2 0.955 0.955 0.955 0.954 0.934 0.934 0.928 0.937 AIC −4121.2 −4120.1 −4259.9 −4247.5 −3836.5 −3829.3 −3769.5 −3864.8 Observations 726 726 726 726 726 726 726 726 F-stat of instruments 63.62 18.51 32.21 70.04 Notes: Fixed effects and IV regressions of Equation (8). Dependent variable is a quality of life index computed according to Equation (5). All columns include HMA fixed effects. Fixed effects models include individual HMA trends. IV models include a trend variable interacted with the initial value (in 1997) for the instrument, and with other city characteristics. The instrument in columns (5)–(8) is the counterfactual designation share given by Equation (9) and first stages are reported in Appendix B in the Online Appendix. The reported F-stat of instruments is the Cragg-Donald statistic in columns (6) and (7) where there is more than one instrument. The welfare impact can be computed as the coefficients here minus the share of expenditure on housing times the coefficients from the first step specification. For example, for column (5) a one-point increase in designation results in a 0.071 − (0.31*0.433) = −0.063 decrease in welfare expressed as a share of expenditure. Standard errors in parentheses are clustered on HMAs. *p < 0.1, **p < 0.05, ***p < 0.01. As stated, the overall welfare effect is computed as the quality of life effect minus the housing expenditure share times the housing productivity effect. Using the baseline fixed effects specification results in a welfare effect of 0.077−(0.31×0.159)=0.028 and using the baseline instrumental variables specification results in a welfare effect of 0.071−(0.31×0.433)=−0.063. The fixed effects model suggests that designations are welfare-improving, whereas the instrumented model suggests designation worsens welfare. Since the fixed effects results are inconsistent under the presence of time-variant unobservables, and since the F-stats indicate the instrument is strong, the instrumented model is preferred. The average HMA increased its designation share by 1/10 points over the period, suggesting an effect on welfare of −0.63% of expenditure.29 Given the mean income of £22,800 in 2004–2005 this is equivalent to an income reduction of about £1500 over the study period. As discussed in the theory, the validity of the welfare effect relies on there being relatively little quantity adjustments or sorting. In the case where such effects are large, the welfare benefits of designation are overestimated, implying that the welfare loss from designation is an underestimate. Further, it should be noted that I have computed the overall welfare effect using point estimates. To obtain confidence intervals in another specification I estimate both steps together using seemingly unrelated regressions (SUR). This approach allows for computation of the welfare effect as a linear combination of coefficients across models. Following this approach implies a 90% confidence interval with a lower bound of −0.005 and an upper bound −0.126. Essentially, the welfare loss could range from almost zero to around double the point estimate. For planning refusals, the quality of life effects are very small in the instrumented specification. Given that the housing productivity effects were negative, this suggests that planning refusals are welfare-decreasing. However, since the planning variable is volatile and is not instrumented, this should not be taken at face value. Columns (2) and (6) examine the quality of life effects when interacting the designation variable with the Saiz index dummies. As in the cost function step, the first stage for land abundant cities has an unexpected sign, suggesting that instrumentation was unsuccessful and that the fixed effects results are preferred. The fixed effects model shows a significant positive impact on quality of life for areas with land scarcity but an insignificant effect in areas with a land abundance. The coefficient for land scarce areas implies slightly larger quality of life effects than in the baseline specification. Together with the first step, these results imply designations will have both larger housing productivity and larger quality of life effects in cities with a scarcity of developable land. This result makes sense since it is unlikely that designation will have quality of life effects without impacting on housing productivity. Columns (3) and (7) investigate the quality of life effects allowing for non-factor-neutral productivity shifts from designation. As with the first step, the instrumentation appears to fail when predicting the non-neutral designation variable. I therefore concentrate on the fixed effect results where the substantive conclusions are unchanged from the baseline specification. This result supports the evidence from the cost function step that indicated that factor neutrality was a reasonable assumption. Finally, columns (4) and (8) investigate the quality of life effects for the cumulative version of the designation variable. The cumulative designation effects in the instrumented specification are larger than the baseline effects, but the overall welfare effect remains negative (although smaller in magnitude). 5.4. Robustness checks To check the sensitivity of these results, I estimate a number of robustness checks in Appendix B in the Online Appendix. These checks are (i) unweighted aggregation of the data to the HMA-level, (ii) using only new properties (<5 years old),30 (iii) using the full sample of 74 HMAs (not excluding the eight with few transactions), (iv) using a quality of life measure that uses regional variation in the marginal tax rate and the share of wages in income, (v) using a quality of life measure with a high expenditure share on housing, (vi) using a quality of life measure with a low expenditure share on housing, (vii) using a quality of life measure where the expenditure share varies according to city income and (viii) repeating the IV specification using prices from the hedonic model without date bands interacted with year effects. As discussed in Appendix B, the broad results are robust to these changes. In Appendix B, I also demonstrate that the approach is robust to using LAs as the unit of observation. 6. Conclusion This article provides evidence of the effects of CA designation on economic welfare. I constructed a unique panel dataset for English housing market areas (HMAs) that resemble city regions. In the first step of the empirical strategy, I estimated the housing productivity effect of designation using a cost function approach. Here, I regressed house prices on factor prices (land and construction costs) and productivity shifters (including designation). In the second step, I estimated the quality of life benefits and the overall welfare impact of designation. I regressed a quality of life index on housing productivity factors used in the first step. I implemented both stages using panel fixed effects and IV approaches. The main results imply that CA designations (in England, 1997–2007) are associated with both negative housing productivity effects and positive quality of life effects. In the cost function step, increases in designation share lead to higher house prices (compared with land values) indicating a negative shift in housing productivity. The second step reveals that designation leads to increases in quality of life. However, the overall welfare effect is negative in the instrumented and preferred specification. This result is in line with previous evidence that suggests housing regulation is welfare-decreasing. The negative welfare impact of designation over 1997–2007 makes sense if there are concave returns to designation. The areas most worthy of protection may have been designated in the policy’s first 30 years of operation (1966–1996). More recent designations then would be of a less distinctive heritage character, and perhaps only of local significance. Designation has continued despite large costs incurred at the housing market level, since, as argued by Ahlfeldt et al. (2017), designation status is largely determined by local homeowners who stand to gain from the localised benefits of the policy. Nevertheless, though, there may be significant heterogeneity in the quality of CAs over the studied period and the results of this article do not suggest that all of these CAs reduced welfare. Furthermore, there may be significant heterogeneity across individuals, for example, the designation would be more welfare-improving for individuals with a greater than average preference for heritage or with a less than average expenditure share on housing. Overall, though, the results suggest that the average household would have been better off without the average CA being designated in the period between 1997 and 2007 in England. This overall welfare improvement of these designation not being made would have been equivalent to about £1500 per household. Supplementary material Supplementary data for this article are available at Journal of Economic Geography online. Footnotes 1 CAs protect groups of buildings within certain boundaries. Single buildings are usually protected by different legislation, e.g. ‘listed buildings’ status in England. 2 HMAs are defined to capture individual housing markets, based on evidence from patterns of commuting, migration and house prices (DCLG, 2010). As such, they are characterised by a high level of self-containment—77.5% of working residents of an HMA have their workplace inside the HMA—and typically approximate recognisable city regions. 3 I provide some empirical support for this assumption by showing that CA designations do not impact negatively on dwelling stock in England over 2001–2010. 4 Other studies that examine the impact of CAs on property prices include Asabere et al. (1989); Asabere and Huffman (1994); Asabere et al. (1994); Coulson and Lahr (2005); Leichenko et al. (2001); Noonan (2007); Noonan and Krupka (2011); Schaeffer and Millerick (1991). 5 See Gyourko and Molloy (2015) for a good overview of the evidence. 6 Further studies find that planning policies have damaging effects on the retail sector (Cheshire and Hilber, 2008; Cheshire et al., 2011). 7 The amenities literature is large, but a few examples are Albouy (2016); Bayer et al. (2007); Brueckner et al. (1999); Chay and Greenstone (2005); Cheshire and Sheppard (1995); Gibbons et al. (2011); Glaeser et al. (2001); Moeller (2018). 8 For example, Albouy and Ehrlich (2012) find a land cost share of about one third and an elasticity of substitution of 0.5 for the USA. 9 The traded good is produced from land, labour and capital according to Xj=AjXFX(L,NX,K) where AjX is traded good productivity, NX is traded good labour (paid wages wjX) and K is mobile capital paid a price i everywhere. 10 Zero profits in the traded good sector is given by A˜jX=θLr˜j+θNwX where θL and θN are the land and labour cost shares, respectively, for the traded good. 11 To complete the firm-side of the model, the non-land input is produced using labour and capital Mj=FM(NY,K) and the equivalent zero profit condition gives v˜j=αw˜Y, where α is the labour cost share of the non-land input. 12 There are two types of worker: housing sector and traded good sector. They may each receive a different wage and may be attracted to different amenities. The condition for only one type of worker is presented here for simplicity. 13 Output areas (OAs) are the smallest geographical units available for most UK data. They cover 0.78 km2 on average, which is only three times the size of the average CA (0.26 km2). In comparison, HMAs cover 1762 km2, on average. 14 This is an arbitrary cut-off point. Results for the full dataset are presented in robustness checks in Appendix B in the Online Appendix. 15 This implies that the quality of life index will reflect homeowner spatial equilibrium only. However, during the time period considered, private renters represented only around 10% of households, whereas homeowners represented nearly 70%. The small share of private renters and the fact that rents are likely to be closely related to house prices means that a homeowner spatial equilibrium is likely to be broadly representative. 16 Further detail on the weighting procedure and regressions without weights are reported in Appendix B in the Online Appendix. The main results without weights are similar. 17 It is not possible to use these transactions as the main source of data for land values since in many of the smaller cities there are not enough observations. 18 Most LAs were unaffected. Of the original 36,621 were merged into nine new areas, making the new total 354 LAs. 19 This is beneficial since otherwise unobserved build quality would lead to designation being associated with higher house prices for given construction costs. Note that time-invariant build quality differences are captured by fixed effects in the cost function. 20 In fact, the average increase of 0.13% in designated land share already looks much larger when looking at the proportion of designated buildings, according to the Nationwide transaction dataset—this is three and a half times larger at 0.45%. 21 Saiz (2010) uses 50 km circles around US MSA centroids—whereas I define 25 km circles to adjust for the smaller size of English HMAs. The average area of a US MSA is about 7000 km2, which corresponds to the area of a circle with a radius of around 50 km and is perhaps the reasoning behind Saiz’s choice of radius. Since the average HMA in England is about 1800 km2, an appropriately sized circle would have a radius of about 25 km. 22 Taking differentials is necessary in certain parts of the model, e.g. to eliminate the interest rate i or reservation utility u. 23 This will be the case if prices adjust quickly to quality of life changes. This assumption seems reasonable since consumers will immediately be willing to pay more for locations with improved amenity value. Theoretically, all prices (house prices, land values and construction costs) will immediately reflect changes to housing productivity and quality of life due to market competition. For example, developers buying land will pay a price that takes into account the latest information on what their buildings will sell for. The available evidence shows that house prices do respond quickly to amenity changes. For example, Gibbons and Machin (2005) show house prices in 2000 and 2001 adjusting to rail improvements from 1999. 24 The designation share in these figures may appear to have a slight tendency towards a downward trend; however, this is just due to the selection of cities. The average trend is in fact zero after conditioning on trend interactions. 25 Note that individual HMA trends are not used to ensure the instrument is relevant in the first stages. 26 The average HMA increased its designation share by about one tenth of the (between-group) standard deviation over the period 1997–2007. One tenth is multiplied by the coefficients to arrive at the average effect on prices. As argued in the data section, the increase in designation of 0.13% of all HMA land may produce large productivity effects if it disproportionately affects marginal developments. Therefore, the estimated effect sizes are plausible. 27 Transport is also a likely quality of life amenity that would increase house prices via the quality of life route. However, it would also increase land values and therefore be captured in the land cost share of the cost function step. 28 The effect implied by the coefficients of 2.6–3.4% multiplied by the average increase in refusals of 2.3 (between-group) standard deviations. 29 This effect refers to an average homeowner in a city, and there may be a distribution of effects depending on whether the household lives inside or nearby a CA. 30 Using only new properties follows Ahlfeldt and McMillen (2014) who argue that accurate estimates of the land cost share and elasticity of substitution will be biased by a depreciation of the capital component for older housing stock. Acknowledgements The author thanks seminar participants at the London School of Economics and the Humboldt University of Berlin, and especially Gabriel Ahlfeldt, Paul Cheshire, Oliver Falck, Steve Gibbons, Christian Hilber, Kristoffer Moeller, Henry Overman, Olmo Silva, Daniel Sturm, Felix Weinhardt and Nicolai Wendland for helpful comments and suggestions. This work has been supported by English Heritage in terms of data provision. The housing transactions dataset was provided by the Nationwide Building Society. The author thanks Christian Hilber and Wouter Vermeulen for supplying the data on planning refusals. All errors are the sole responsibility of the author. Funding English Heritage provided funding for an earlier project that this work stemmed from. References Ahlfeldt G. , McMillen D. ( 2014 ) New estimates of the elasticity of substitution of land for capital. (ersa14p108), November 2014. Available online at: http://ideas.repec.org/p/wiw/wiwrsa/ersa14p108.html. Ahlfeldt G. M. , Moeller K. , Waights S. , Wendland N. ( 2017 ) Game of zones: the political economy of conservation areas . The Economic Journal , 127 : F421 – F445 . Google Scholar CrossRef Search ADS Albouy D. ( 2016 ) What are cities worth? Land rents, local productivity, and the total value of amenities . Review of Economics and Statistics , 98 : 477 – 487 . Google Scholar CrossRef Search ADS Albouy D. , Ehrlich G. ( 2012 ) Metropolitan land values and housing productivity. National Bureau of Economic Research Working Paper Series, No. 18110. Available online at: http://www.nber.org/papers/w18110. Albouy D. , Farahani A. ( 2017 ) Valuing public goods more generally: the case of infrastructure. Upjohn Institute Working Paper. Asabere P. K. , Huffman F. E. ( 1994 ) Historic designation and residential market values . Appraisal Journal , 62 : 396 . Asabere P. K. , Hachey G. , Grubaugh S. ( 1989 ) Architecture, historic zoning, and the value of homes . Journal of Real Estate Finance and Economics , 2 : 181 – 195 . Google Scholar CrossRef Search ADS Asabere P. K. , Huffman F. E. , Mehdian S. ( 1994 ) The adverse impacts of local historic designation: the case of small apartment buildings in philadelphia . Journal of Real Estate Finance & Economics , 8 : 225 – 234 . Google Scholar CrossRef Search ADS Bartik T. J. ( 1991 ) Who Benefits from State and Local Economic Development Policies ? Kalamazoo, MI: W.E. Upjohn Institute for Employment Research. Google Scholar CrossRef Search ADS Bayer P. , Ferreira F. , McMillan R. ( 2007 ) A unified framework for measuring preferences for schools and neighborhoods . Journal of Political Economy , 115 : 588 – 638 . Google Scholar CrossRef Search ADS Been V. , Ellen I. G. , Gedal M. , Glaeser E. , McCabe B. J. ( 2016 ) Preserving history or restricting development? The heterogeneous effects of historic districts on local housing markets in new york city . Journal of Urban Economics , 92 : 16 – 30 . Google Scholar CrossRef Search ADS Brueckner J. K. , Thisse J.-F. , Zenou Y. ( 1999 ) Why is central paris rich and downtown detroit poor? An amenity-based theory . European Economic Review , 43 : 91 – 107 . Google Scholar CrossRef Search ADS Cambridge Econometrics. Uk Regional Data. February 2013. Chay K. Y. , Greenstone M. ( 2005 ) Does air quality matter? Evidence from the housing market . Journal of Political Economy , 113 : 376 – 424 . Google Scholar CrossRef Search ADS Cheshire P. , Sheppard S. ( 2002 ) The welfare economics of land use planning . Journal of Urban Economics , 52 : 242 – 269 . Google Scholar CrossRef Search ADS Cheshire P. C. , Hilber C. A. L. ( 2008 ) Office space supply restrictions in Britain: the political economy of market revenge . The Economic Journal , 118 : F185 – F221 . Google Scholar CrossRef Search ADS Cheshire P. , Sheppard S. ( 1995 ) On the price of land and the value of amenities . Economica , 62 : 247 – 267 . Google Scholar CrossRef Search ADS Cheshire P. , Hilber C. A. L. , Kaplanis I. ( 2011 ) Evaluating the effects of planning policies on the retail sector: or do town centre first policies deliver the goods? SERC Discussion Papers , 66 : 1 – 34 . Christensen L. R. , Jorgensen D. W. , Lau L. J. ( 1973 ) The Translog Function and the Substitution of Equipment, Structures, and Labor in US Manufacturing 1929-68 . Social Systems Research Institute, University of Wisconsin-Madison . Colwell P. F. , Sirmans C. F. ( 1993 ) A comment on zoning, returns to scale, and the value of undeveloped land . The Review of Economics and Statistics , 783 – 786 . Combes P.-P. , Duranton G. , Gobillon L. ( 2016 ) The production function for housing: evidence from France. Working Paper. Coulson N. E. , Lahr M. L. ( 2005 ) Gracing the land of elvis and beale street: historic designation and property values in memphis . Real Estate Economics , 33 : 487 – 507 . Google Scholar CrossRef Search ADS Coulson N. E. , Leichenko R. M. ( 2001 ) The internal and external impact of historical designation on property values . Journal of Real Estate Finance & Economics , 23 : 113 – 124 . Google Scholar CrossRef Search ADS DCLG ( 2010 ) Geography of housing market areas: final report. GOV.UK Publications. Available online at: https://www.gov.uk/government/publications/housing-market-areas. Epple D. , Gordon B. , Sieg H. ( 2010 ) A new approach to estimating the production function for housing . The American Economic Review , 100 : 905 – 924 . Google Scholar CrossRef Search ADS Fuss M. , McFadden D. ( 1978 ) Production Economics: A Dual Approach to Theory and Applications . North-Holland . Gibbons S. , Machin S. ( 2005 ) Valuing rail access using transport innovations . Journal of Urban Economics , 57 : 148 – 169 . Google Scholar CrossRef Search ADS Gibbons S. , Overman H. G. , Resende G. ( 2011 ) Real earnings disparities in Britain. SERC Discussion Papers, 0065. Glaeser E. L. , Kolko J. , Saiz A. ( 2001 ) Consumer city . Journal of Economic Geography , 1 : 27 – 50 . Google Scholar CrossRef Search ADS Glaeser E. L. , Gyourko J. , Saks R. ( 2005 ) Why is Manhattan so expensive? Regulation and the rise in housing prices . The Journal of Law and Economics , 48 : 331 – 369 . Google Scholar CrossRef Search ADS Graves P. E. , Waldman D. M. ( 1991 ) Multimarket amenity compensation and the behavior of the elderly . The American Economic Review , 81 : 1374 – 1381 . Greenwood M. J. , Hunt G. L. , Rickman D. S. , Treyz G. I. ( 1991 ) Migration, regional equilibrium, and the estimation of compensating differentials . The American Economic Review , 81 : 1382 – 1390 . Gyourko J. , Molloy R. ( 2015 ) Regulation and housing supply . Handbook of Regional and Urban Economics , 5 : 1289 – 1337 . Google Scholar CrossRef Search ADS Gyourko J. , Tracy J. ( 1991 ) The structure of local public finance and the quality of life . Journal of Political Economy , 99 : 774 – 806 . Google Scholar CrossRef Search ADS Hilber C. A. L. , Vermeulen W. ( 2016 ) The impact of supply constraints on house prices in England . The Economic Journal , 126 : 358 – 405 . Google Scholar CrossRef Search ADS Koster H. R. A. , Rouwendal J. ( 2017 ) Historic amenities and housing externalities: evidence from the Netherlands . The Economic Journal , 127 : F396 – F420 . Google Scholar CrossRef Search ADS Koster H. R. A. , van Ommeren J. N. , Rietveld P. ( 2014 ) Historic amenities, income and sorting of households . Journal of Economic Geography , 16 : 203 – 236 . Google Scholar CrossRef Search ADS Leichenko R. M. , Coulson N. E. , Listokin D. ( 2001 ) Historic preservation and residential property values: an analysis of Texas cities . Urban Studies , 38 : 1973 – 1987 . Google Scholar CrossRef Search ADS Linneman P. , Graves P. E. ( 1983 ) Migration and job change: a multinomial logit approach . Journal of Urban Economics , 14 : 263 – 279 . Google Scholar CrossRef Search ADS PubMed McDonald J. F. ( 1981 ) Capital-land substitution in urban housing: a survey of empirical estimates . Journal of Urban Economics , 9 : 190 – 211 . Google Scholar CrossRef Search ADS Moeller K. ( 2018 ) Culturally clustered or in the cloud? Location of internet start-ups in Berlin . Forthcoming in Journal of Regional Science . Noonan D. S. ( 2007 ) Finding an impact of preservation policies: price effects of historic landmarks on attached homes in Chicago, 1990-1999 . Economic Development Quarterly , 21 : 17 – 33 . Google Scholar CrossRef Search ADS Noonan D. S. , Krupka D. J. ( 2011 ) Making-or picking-winners: evidence of internal and external price effects in historic preservation policies . Real Estate Economics , 39 : 379 – 407 . Google Scholar CrossRef Search ADS Notowidigdo M. J. ( 2011 ) The incidence of local labor demand shocks. National Bureau of Economic Research Working Paper Series, No. 17167. URL http://www.nber.org/papers/w17167. Office of Population Censuses and Surveys ( 1991 ) 1991 census: Special workplace statistics (Great Britain). URL https://www.nomisweb.co.uk/. Roback J. ( 1982 ) Wages, rents, and the quality of life . The Journal of Political Economy , 1257 – 1278 . Saiz A. ( 2010 ) The geographic determinants of housing supply . The Quarterly Journal of Economics , 125 : 1253 – 1296 . Google Scholar CrossRef Search ADS Schaeffer P. V. , Millerick C. A. ( 1991 ) The impact of historic district designation on property values: an empirical study . Economic Development Quarterly , 5 : 301 – 312 . Google Scholar CrossRef Search ADS Thorsnes P. ( 1997 ) Consistent estimates of the elasticity of substitution between land and non-land inputs in the production of housing . Journal of Urban Economics , 42 : 98 – 108 . Google Scholar CrossRef Search ADS Turner M. A. , Haughwout A. , Van Der Klaauw W. ( 2014 ) Land use regulation and welfare . Econometrica , 82 : 1341 – 1403 . Google Scholar CrossRef Search ADS © The Author(s) (2018). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com

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Journal of Economic GeographyOxford University Press

Published: Feb 5, 2018

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