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2013 50: 3205 originally published online 16 May 2013Urban StudMarco Brambilla, Alessandra Michelangeli and Eugenio Peluso

Equity in the City: On Measuring Urban (Ine)quality of Life

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Equity in the City: On Measuring Urban(Ine)quality of Life

Marco Brambilla, Alessandra Michelangeli and Eugenio Peluso

[Paper first received, August 2011; in final form, January 2013]

Abstract

In economic literature, the quality of life (QoL) in a city is usually assessed throughthe standard revealed-preference approach, which defines a QoL index as the mone-tary value of urban amenities. This paper proposes an innovative methodology tomeasure urban QoL when equity concerns arise. The standard approach is extendedby introducing preferences for even accessibility to amenities throughout the cityinto the QoL assessment. The QoL index is then reformulated to account for theunequal availability of amenities across neighbourhoods. The more unbalanced thedistribution of amenities across neighbourhoods, the lower the assessment based onthe new index. This methodology is applied to derive a QoL index for the city ofMilan. The results show that the unequal distribution of amenities across neighbour-hoods significantly affects the assessment of QoL for that city.

1. Introduction

The economic approach to measuringurban quality of life (QoL) is based on thework of Rosen (1979) and Roback (1982)who, rather than assessing overall well-being or happiness of households, measureQoL indirectly, in terms of the monetaryvalue of local amenities. They define a QoLindex as the monetary value of a set of

amenities, where the amenities are location-specific characteristics with positive or neg-ative effects on individual’s utility (Bartikand Smith, 1987; Blomquist, 2006).

This paper focuses on a single city andextends the previous methodology by pro-viding a new measure to assess urban QoLby explicitly taking into account equity

Marco Brambilla is in the DEFAP, Catholic University of Milan, Piazza Buonarroti 30, Milan,20100, Italy. Email: [email protected].

Alessandra Michelangeli (corresponding author) is in the Department of Economics, Managementand Statistics (DEMS), University of Milan-Bicocca, Piazza dell’Ateneo Nuovo 1, Building U6,Milan, 20126, Italy. Email: [email protected].

Eugenio Peluso is in the Department of Economics, University of Verona, Vicolo Campofiore 4,Verona, 37129, Italy. Email: [email protected].

Urban Studies at 50

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concerns. Our methodology relies on thehypothesis that a more equal distributionof resources in the city is beneficial to over-all QoL. As we will see later, there are sev-eral arguments for equity in the city, someof them used as a starting-point for devel-oping a branch of planning and economicliterature. Regardless of the perspectiveadopted for studying the effect of equity onQoL, or more generally well-being, every-one agrees that the opposite of equity—i.e.inequality—is detrimental to quality of life.The concentration of poor or disadvan-taged people in some areas of the city cangenerate negative externalities and fuelsocial discontent, eventually leading toslums, delinquency, drugs, and other symp-toms of social and economic marginalisa-tion (see Glaeser et al., 2008). In ourframework, the priority for equity is cap-tured by the mathematical properties of anexplicit evaluation function. The specificform of the evaluation function can embedeither citizens’ preferences for equity(where useful, investigated by suitable sur-veys) or the ethical judgment of a city plan-ner. The main assumption is that anunequal availability of amenities within thecity has a negative impact on the evaluationfunction; in the same way as incomeinequality generates a loss in social welfareaccording to Atkinson’s (1970) approach toinequality measurement. Under thisassumption, a new QoL index is obtainedby discounting the Roback (1982) indexthrough a multiplicative correction term.The more unbalanced the distribution ofamenities across neighbourhoods, the lowerthe correction term. More precisely, thecorrection term is obtained as the sum ofunidimensional inequality indices, account-ing for the dispersion of each amenitywithin the city, plus a residual term sum-marising any correlation among the distri-bution of amenities. This formulation canbe used to disentangle the contribution of

the dispersion of each amenity to the over-all index from the joint effect of the ame-nities. The correction term depends on asmany parameters as the number of ame-nities under examination. Each parameterregisters the aversion to the unequal avail-ability of the corresponding amenity withinthe city. The model is therefore sufficientlyflexible to allow for a specific degree ofaversion to the unequal availability of eachamenity.

One point requires further explanation.Our analysis is based on two different com-ponents: the Roback (1982) spatial modeland an evaluation function expressing thepreferences for equity. In the former, therepresentative agent looks for the most con-venient location given the distribution ofamenities across neighbourhoods. The dif-ferent amenities available at the equilibriumare capitalised in housing prices and therepresentative agent’s utility is equalisedwithin the city. This outcome is logicallyindependent of the fact that it might bepossible to increase or re-allocate someamenities within the city, improving thewell-being of the representative citizen. Thiseffect is captured by the correction termdepending on the evaluation function. Forexample, in the short run, agent locationdecisions depend on the current availabilityof green areas within the city, which alsoaffects his well-being at the equilibrium.However, if new green areas are developed,especially in neighbourhoods where theyare lacking, overall well-being in the cityincreases. These points of view are recon-ciled by first computing a Roback QoLindex based on the citizens’ evaluation ofamenities, then adjusted via the correctionterm sensitive to their unequal availability.

The suggested methodology is illustratedusing data for the city of Milan over theperiod 2004–08 regarding the availability ofeducation, green areas, recreational activi-ties, commercial facilities, public transport

3206 MARCO BRAMBILLA ET AL.

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and socio-demographic characteristics. Bytaking into account the uneven availabilityof amenities within the city, the Robackindex is reduced by 28 per cent.

The methodology is shown in section 2.Section 3 presents the empirical applicationto Milan with a discussion of the data andvariables and a descriptive analysis of thecity neighbourhoods. The econometric spe-cification of the hedonic function is alsodiscussed and the results are illustrated interms of amenity prices and QoL assess-ment. Section 4 concludes and suggestssome potential extensions of our approach,paving the way for future research.

2. Theoretical Framework

This section first reviews the Roback (1982)index, then shows how to measure the avail-ability of amenities within the city and,thirdly, shows how to obtain a new QoLindex accounting for the unequal availabil-ity of amenities across neighbourhoods.

2.1 The Roback (1982) QoL Index

Let a 2 <k+ be the vector of the average

quantities of k amenities in a given city.The index developed by Rosen (1979) andRoback (1982) consists of the weightedsum of the values of the k amenities of thecity, where the weights are the implicitprices associated with the amenities

QoL =Xk

j = 1

pjaj ð1Þ

The implicit price pj for j = 1, ., k is esti-mated through housing and wage hedonicregressions. Actually the coefficients in theestimated hedonic regression do not onlyreflect consumer preferences, but also factorsthat determine production. However, in thecase of a fixed supplied amenity, the hedonic

price reflects the preferences of the marginalperson just indifferent between buying ahouse with and without amenity. For ame-nities that vary more continuously through-out a city, a hedonic regression is likely tocapture something much closer to mean pre-ferences (Bayer and McMillan, 2008, p. 229).The implicit price is the sum of the housingprice differential and the negative of thewage differential. In other words, the eco-nomic value of a local amenity is determinedby the housing price individuals are willingto pay and the wage they are willing to acceptto locate in a given city. The idea underlyingthis approach is that people will accept lowerwages and/or greater housing prices in anarea with desirable amenities, but requiregreater wages and/or lower housing prices inan area with less attractive amenities. AsRoback acknowledges

associating the implicit marginal price with

mean quantity of the amenity provides an

approximated value of the amenities because

the prices of infra-marginal units are differ-

ent from the marginal prices. Such an expen-

diture computation in (1) merely shows the

order of magnitude of the expenditure in the

average budget (Roback, 1982, p. 1274).

In what follows, the focus is on a singlecity,1 computing a QoL index for the wholecity that accounts for the uneven availabil-ity of amenities across its neighbourhoods.Focusing on a single city has three mainconsequences.

First, the implicit prices of amenities in(1) are derived solely from the hedonichousing price equation. Wages are ignoredsince they are assumed to be determined forthe city’s labour market as a whole withoutvariation within the city. Actually, severalstudies carried out on American cities showthat wages may vary slightly within a city.According to Bartik and Eberts (2006), forexample, the wages of identical workers

EQUITY IN THE CITY 3207



decline about 1 per cent for each additionalmile the job is located from the central busi-ness district (CBD). Even supposing thatwages can vary within a city, it is not easy tomeasure such a phenomenon, since theneighbourhood where individuals live is notnecessarily where they work. In addition,the lack of data on employment precludes aconsideration of city-wide wage variations.

Secondly, only the prices of amenitiesthat vary within the city can be identified.We ignore several variables usually consid-ered in intercity analysis (for example, cli-mate, altitude).

A third potential problem with intracityanalysis relates to spatial sorting on unob-servables (Gyourko et al., 1999). This occurswhen high-quality housing units are locatedin the best city neighbourhoods and the fac-tors determining the high quality of housesare unobservable. The value of QoL will beoverestimated in the nice neighbourhoods.This point will be returned to in section 4.

The conventional approach is nowextended to quantify the availability ofamenities for city inhabitants living in dif-ferent neighbourhoods.

2.2 Amenities and Their Availability

Let us consider a city exogenously parti-tioned into n neighbourhoods. Each neigh-bourhood i = 1, . . . , n is described by avector ai containing the values of the k ame-nities. The element aij 2 <+ indicates thelevel of the amenity j in the neighbourhoodi. The information on the distribution ofamenities in the city is then summarised bya n x k matrix, where each line correspondsto a neighbourhood and each column to anamenity

A =a11. . .a1k

an1. . .ank

24

35

Suppose that an individual lives in a neigh-bourhood with few amenities or none at all.He can benefit from amenities located in thesurrounding neighbourhoods. Therefore,the overall quantity of the amenities avail-able is the sum of the amenities where theindividual dwells, plus a term indicatingtheir presence in the surroundings, whoseaccessibility is a function of the distancebetween the neighbourhood we are consid-ering and its adjacent neighbourhoods (seeFigure 1).

In formal terms, starting from A, a fur-ther n x k matrix Z is obtained, whose gen-eric term zij indicates the overall availabilityof amenity j for individuals of neighbour-hood i. The element zij is obtained by addingto aij the availability of the amenity j in theneighbourhoods bordering i. Defining S(i)the set of neighbourhoods adjacent to i(with i 2 S(i)), we obtain

zij =X

s2S(i)ais � f (dis) ð2Þ

where, asj is the value of amenity j in theneighbourhood s bordering i; f disð Þ is thevalue of a continuous and non increasingfunction f : <+ ! 0, 1½ � defined on the dis-tance dis between the neighbourhoods i ands.2

Let �zj denote the average level of amenityj in the city and �z = �z1, ::, �zk½ � the vector con-taining the means of the k amenities in thecity. We reformulate the Roback (1982)index as follows

ild

Figure 1. Distance between district centroids.




QoL =Xk

j = 1pj�zj ð3Þ

where, the vector of the average quantities ais replaced by �z.

We call this index the QoL index adjustedfor the available amenities. A procedure tocorrect this index accounting for inequalityis now presented.

2.3 The Equity-adjusted QoL Index

The idea of ‘just city’ is enshrined in bothplanning and economic literature. Theequity approach developed in planning lit-erature requires that urban amenities andpublic services must be evenly available in away such that

everyone receives the same public benefit,

regardless of socioeconomic status, willing-

ness or ability to pay, or other criteria; resi-

dents receive either equal input or equal

benefit (Talen, 1998, p. 24).

An alternative approach (needs-based), fol-lows a ‘compensatory’ criterion that subor-dinates the distribution of facilities andservices to the different needs of the popu-lation living in different neighbourhoods ofthe city.3

In urban economics literature, aiming atevenly available amenities within the city isrecommended by Berliant et al. (2006),who determine the optimum number andlocation of public facilities through a gen-eral equilibrium analysis. They prove theexistence of an equilibrium characterisedby a dispersed and homogeneous distribu-tion of public facilities across locations.They also argue that an equal treatmentidentical-provision optimum may be justi-fied by the equal protection clause of theUS Constitution, federal law or by stateconstitutions. On the efficiency side,Benabou (1993) shows that stratification

can create ghettos and can even bringabout the complete collapse of the city’sproductive capacity. Finally, from a socialwelfare perspective, the equal availability oflocal facilities mitigates well-being inequal-ity (Aaberge et al., 2010) and promotesequality of opportunities in the sense ofRoemer (1998) and van de Gaer (1993).Moving from these different equity con-cerns to an analysis of QoL, a measure ofQoL is now derived. This measure is ableto disentangle the different relevance, ifany, given to the unequal availability ofeach amenity. For example, the unequalavailability of shopping facilities can have ahigher impact in lowering QoL than theidentically unequal availability of culturalsites. Let W(Z) be the function evaluatingthe distribution of the k amenities betweenthe n city neighbourhoods.4 The functionW is assumed as additive

W(Z) =1

n

Xn

i = 1w(zi) ð4Þ

where, w(zi) is the value taken by theincreasing and concave functionw : <k

+ ! < summarising the assessmentof the QoL in the neighbourhood i,endowed with the vector of amenities zi.

It is well known (see Weymark, 2006)that, under inequality aversion, the valueW(Z) is less than or equal to the value guar-anteed by an even availability of the sameamount of amenities across neighbour-hoods. If ~W = W(Z)is the evaluation of thecurrent distribution, due to continuity, it ispossible to define a scalar q 2 0, 1½ � depend-ing on Z and W, such that

~W = W(Z) =1

n

Xn

i = 1w(zi) = W(q � �z) ð5Þ

In the same spirit as Atkinson (1970), theelements of the vector q�z are called ‘equallydistributed equivalent amenities’ (EDEAs).




This equation (5) means that, if the propor-tion q of the average amount of amenities isuniformly available across neighbourhoods,the evaluation function W(q � �z) reaches thesame value W(Z) associated with the actualdistribution.

Accounting for inequality, the indexadjusted for the available amenities (3) isthen modified as follows

Definition 1. For any Z, the equity-adjustedurban quality of life index QoLq(Z; W) is

QoLq(Z; W) = qXk

j = 1

pj�zj ð6Þ

where, pj is the implicit price of the amenity jand the ‘equally-distributed equivalent ame-nities’ vector q�z is implicitly defined by (5).

Instead of assessing the value of �z repre-senting the average quantity of amenitiesavailable in the city as in (3), the equity-adjusted QoL index (6) corrects it througha multiplicative factor q. The vector q�zconsists in the multidimensional extension(Tsui, 1995; Weymark, 2006) of the ‘equallydistributed equivalent income’ used ininequality literature (Atkinson, 1970) andof the ‘certainty equivalent’ used in risktheory (Pratt, 1964). The more unbalancedthe distribution of amenities, the lower thecorrection term q. In the Appendix, weshow how to derive q from the evaluationfunction (5). The proposed methodologycan be used to disentangle the contributionof each amenity to the value of q and thento the overall QoL index. The correctionterm q is derived through a parametricinequality index embedding preferences foran equal availability of the k amenitieswithin the city. The k parameters measurethe level of inequality aversion of either citi-zens or a city planner on each dimension.Identifying the origin of the aversion toinequality is beyond the aim of this paper.

Our aim is to show how preferences forequity can be introduced in QoL assess-ment, without recommending a specificequity perspective. In this respect, ourattempt offers a pioneering contribution toboth urban and inequality literature.5 Toproceed with the empirical investigation, apragmatic procedure is adopted to calibrateinequality aversion, exploiting the availableinformation on the willingness to pay foreach amenity, estimated through a hedonicmodel referred to the housing market. Thek parameters indicating aversion to theunequal availability of the different ame-nities will be set equal to their respectiveweight on the city’s monetary assessment ofquality of life.

3. Empirical Application

In this section, we employ the previousmodel to assess QoL in Milan, the largestcity in Italy after Rome.6 In addition tobeing the biggest industrial city in Italy, it isalso a historical city with a significant assort-ment of churches, buildings and monu-ments mainly inside the Mura Spagnole, thecity walls that border the historical citycentre. Despite all these positive aspects,other factors do not positively impact onquality of life. Some neighbourhoods haveexperienced a gradual process of urbandecay and more and more Italian residentshave abandoned these areas. Housing priceshave decreased and these neighbourhoodshave frequently attracted newcomers toMilan. The next section describes the infor-mation we have collected to capture thesephenomena and, more generally, the mainvariables affecting the quality of life in thedifferent neighbourhoods of Milan.

3.1 Data and Variables

As we showed in relation to the Roback(1982) QoL index in (1), overall QoL




depends on the set of amenities consideredwhen implementing the analysis. For thepurpose of this study, several data sourcesare combined into a single dataset that con-tains detailed information on housing andcity characteristics. Data on residentialhousing transactions were taken from theOsservatorio del Mercato Immobiliare(OMI) managed by a public agency (theAgenzia del Territorio). Transactions referto 55 neighbourhoods identified by theOMI for a period of 5 years, from January2004 to December 2008.7 Each neighbour-hood is internally homogeneous in terms ofsocioeconomic and urban characteristics,making it likely that prices of houses locatedwithin a neighbourhood move together. Inaddition to the housing market value, thedataset provides a detailed description ofstructural attributes, such as total floorspace, age of the building in the year of sale,number of bathrooms, whether the housingunit needs to be renovated, whether thehousing unit has independent heating, thefloor above street level, presence of an eleva-tor or a garage, and build quality.

Neighborhood-level data on amenitiesand socioeconomic conditions were takenfrom public authority records. They includeinformation on six important aspects ofquality of life: environmental characteris-tics, public transport, education, shoppingfacilities, recreational activities, and socioe-conomic characteristics. Table A2 in theAppendix sets out a full list of variablesused in our analysis with their sources. Ofcourse, other variables that cannot be soreadily observed may contribute to thequality of life as presented in this paper. Inaddition, depending on the revealed prefer-ences of residents over a limited bundle ofamenities, our QoL index could not prop-erly account for the preferences of those res-idents who give priority to other (omitted)amenities. However, this paper aims toshow the potential of our methodology,

carrying out an empirical analysis which isas rigorous as possible.

The environmental dimension is proxiedby the green areas relative to the area of theneighbourhood (Green); public transport isrepresented by the number of metro stations(Transport); shopping facilities (Shoppingfacilities) are proxied by the number ofsupermarkets, discount stores and malls per10 000 inhabitants; the recreational dimen-sion (Cultural) is proxied by the number ofcinemas, theatres, museums, art galleries,academies of music and libraries per 10 000inhabitants.

The socioeconomic dimension (Ethnic)is based on the ratio of Italian/foreign resi-dents. More precisely, the Ethnic variablefor the neighbourhood i is constructed as

Ethnici =ItiP

s2S(i)Imms

~d2is

where, Iti is the number of Italians living inthe neighbourhood i. In the denominator,we add to the immigrants living in theneighbourhood, Immi, those living in thesurrounding neighbourhoods. The weightassociated with immigrants of each adjacentneighbourhood s 2 S(i) is set to be equal to1~d2

is

, with ~d2is = max(1, dis) and roughly approx-

imates the probability that Italian residentsin neighbourhood i interact with foreignersin neighbourhood s. In this case, ourassumption of preference for equity corre-sponds to aversion to residential segregation.The resulting unidimensional index for thevariable Ethnic can be safely interpreted interms of a segregation index of the exposureclass (see Reardon and O’Sullivan, 2004). Inthis spirit, we consider as foreign residents(Imm) the ethnic groups most often subjectto discrimination, such as African, SouthAmerican and some Asian communities.Other immigrants—from, for example,North America or western Europe—have




become ‘invisible’ in Italy8 and are includedwith Italian residents.

Education is proxied by the proximity tothe nearest university (Proximity_University).Unfortunately, we do not have informationon other variables for the quality of educa-tion, such as the percentage of pupils movingup to a higher class or parameters for class-room and/or building facilities.9 We do haveinformation on the degree of availability ofdifferent educational levels, such as thenumber of primary and secondary schools,both public and private, in the neighbour-hood. We also have data on early years ofeducation—i.e. the number of nurseryschools and pre-schools. We tried alternativespecifications including these variables butnone of these turned out to be statisticallysignificant. There are at least two reasons forthis result. First, the number of schools avail-able in the neighbourhood is a rough proxyof education services and is unable to capturethe quality of education services. Secondly,the variability of some of these covariates isquite modest across neighbourhoods.

In addition to these amenities, theEuclidean proximity of each neighbour-hood to the city centre is included, in orderto handle the problem of the spatial sortingon unobservables described in section 2.1.Furthermore, the Euclidean proximity tothe city centre enables verification of thehypothesis of a monocentric structure ofthe urban area modelled by Alonso (1965)and Muth (1969). The urban pattern ofMilan is clearly identifiable by the old innerring of inland waterways (Navigli) designedby Leonardo da Vinci. Outside the former,a second ring comprises the Mura Spagnole.The most important historical monuments(Duomo, Castello Sforzesco, Royal Palace,etc.) and historical buildings of residentialuse are located within the two rings, beyondwhich, as far as the confines of the munici-pal territory, large neighbourhoods spreadout.10

Descriptive statistics are set out in Table 1.Amenity statistics enshrine the availability ofamenities in the bordering zones, calculatedby using the distance function f disð Þ= 1

~d2is

.

Following Marans (2003), the distance isexpressed in miles: amenities located in sur-rounding neighbourhoods at a distance lessthan or equal to a mile are added to that ofthe initial neighbourhood entirely, whilethose further than a mile are divided by d2

is.The specification of f can be motivated inthis case by the current practice adopted ingravitation models (White, 1983; Batten andBoyce, 1986; Wong, 1993).

The average value of the 2592 propertiessold over the 2004–08 period was e403 288.The average property had 95.72 squaremetres of total floor space and was 48 yearsold at the time of sale. Each neighbourhoodhad on average 12 per cent of greenery in theurban area, but with substantial differences—from 1 per cent in the Ronchetto ChiaravalleRipamonti neighbourhood in the south-westto 25 per cent in the off-centre neighbour-hood of Monza Precotto Gorla in the north.The number of metro stations also variesgreatly: from 0 to 13 stations. Each neigh-bourhood had on average 9.44 shoppingareas and five cultural sites per 10 000 inha-bitants. Finally, the average ratio of foreign toItalian residents in the neighbourhood was 9per cent, the minimum percentage being 3.22and the maximum 21.26.

3.2 Estimated Implicit Prices

To obtain the full implicit prices of location-specific amenities given in (6), we estimate areduced form of the housing price hedonicequation

ln phit = b0 + b1Xhit + b2Ait + hhit ð7Þ

where, ln phit is the price of housing unit h inneighbourhood i at time t; Xhit is a vector ofhousing characteristics; Ait is a vector of




available amenities in neighbourhood i; hhit~N(0, s2

n):The structural characteristics in Xhit

are listed in Table A2. In addition to thesecharacteristics, the proximity of each neigh-bourhood to the city centre and year dummiesare included in Xhitto account for unobserva-ble factors and time fixed effects respectively.

3.3 Results

Table 2 presents the results obtained fromestimating (7) by OLS. Robust standard

errors are used with clustering at neighbour-hood level in order to allow for within-neighborhood correlation. All in all, thehousing variables used in the model accountfor about 87 per cent of the variance of thelogarithm of price. The stability of theregression model was verified using pairwiseChow tests on adjacent sub-periods. Thehypothesis of no structural change is notrejected with the exception of the sub-period 2006–07. Therefore our modelappears to be sufficiently stable. The amenity

Table 1. Summary statistics for the variables

Variable Mean S.D. Minimum Maximum Unit

Housing value 403 288 409 900 80 000 7 000 000 EuroMarket_p 0.304 0.460 0 1 DummyOffer_p 0.446 0.496 0 1 DummyEstimated_p 0.251 0.434 0 1 Dummy

AmenitiesTransports 4.36 3.31 0 12.90 ContinuousProximity_university 4.61 1.62 0 6.60 KmGreen 12.04 5.24 1 25 PercentageCultural 5.00 10.74 0.06 70.43 ContinuousShopping_facilities 9.44 4.96 1.34 21.64 ContinuousEthnic 9.14 3.75 3.22 21.26 Percentage

Housing characteristicsTotal floor area 95.72 46.01 19.00 452 Square metresNumber of bathrooms 1.36 0.63 1 6 DiscreteTo be renovated 0.042 0.200 0 1 DummyHeating 0.124 0.330 0 1 Dummy2nd floor (or higher) 0.817 0.386 0 1 DummyLow_cost 0.538 0.498 0 1 DummyMedium_cost 0.428 0.494 0 1 DummyLuxury 0.032 0.178 0 1 DummyParking 0.019 0.067 0 1 DummyElevator 0.819 0.384 0 1 DummyAge 48.20 21.90 1 205 Discrete

Control variablesCity centre 0.15 0.35 0 1 DummyProximity_city centre 4.50 2.20 0.1 9.3 KmYear 2004 (ref.) 0.14 0.35 0 1 DummyYear 2005 0.23 0.42 0 1 DummyYear 2006 0.19 0.39 0 1 DummyYear 2007 0.21 0.41 0 1 DummyYear 2008 0.20 0.40 0 1 Dummy




coefficients are statistically significant; toquantify their relative importance in ourspecification, standardised beta coefficientsare set out in column 3.11 According to thiscriterion, the most important amenity isGreen since an increase by one standarddeviation in this variable implies an increaseof 0.161 standard deviation in the value of

the housing unit. One possible explanationof the statistical relevance of this variable isthat it measures not only the size of the avail-able green areas, but also the facilities whichare often located within gardens and parks(playgrounds for children, bicycle lanes andsports centres). The next amenity in terms ofimportance is Cultural (0.156). In this case,

Table 2. Hedonic regression

Variable Coefficient t Standard b coefficient

Intercept 10.600 273.90 —Offer_p 0.062 4.51 0.048Estimated_p �0.007 �0.51 0.005

AmenitiesTransport 0.007 4.21 0.041Proximity_university 0.004 1.05 0.011Green 0.001 2.02 0.161Cultural 0.009 11.72 0.155Shopping_facilities 0.003 2.31 0.025Ethnic 0.008 5.84 0.048

Housing chacteristicsln(size) 0.940 67.07 0.662Second bathroom 0.048 3.65 0.035Third bathroom 0.093 3.49 0.027To be renewed �0.110 �4.85 �0.035Heating 0.012 0.86 0.0062nf floor (or higher) 0.017 1.53 0.010Medium cost 0.029 2.73 0.023Luxury 0.116 4.21 0.032Parking 0.154 3.33 0.023Elevator 0.068 5.41 0.041ln(age) �0.006 �1.51 �0.018proximity 0.0003 3.48 0.123proximity squared 0.0001 1.83 0.077

Control variablesCity centre 0.104 4.16 0.059Year 2005 0.040 2.72 0.027Year 2006 0.108 7.08 0.068Year 2007 0.101 6.09 0.663Year 2008 0.104 6.03 0.067

Number of observations 2592F(26; 2565) 672.8400Prob . F 0.0000R2 0.8721Adjusted R2 0.8708




the importance could be explained by thelocation of specific theatres and museums inancient buildings where individuals appreci-ate aesthetic and artistic value. For example,the Museum of Ancient Art is in the CastelloSforzesco, probably the most famous build-ing in Milan, together with the Duomo andLa Scala Opera House. The other standar-dised beta coefficients are 0.048 for Ethnic,0.042 for Transport, 0.025 for Shopping facil-ities and 0.011 for the proximity to the near-est university (Proximity_university).

Full implicit prices for each amenity areshown in Table 3, with Cultural, Ethnic andTransport showing the highest prices inabsolute value. The hedonic price for anadditional cultural site per 10 000 inhabi-tants in the areal unit is e2839; increasingthe Italian/foreign ratio by one leads to anincrease of e2500 in the value of the aver-age housing unit and an additional metrostation provides a benefit of e2470. Weincluded distance from the nearest univer-sity and it turns out that reducing the dis-tance by 1 km increases housing unit valueby e1377. The estimated implicit price foran additional shopping facility per 10 000inhabitants is e1051 and the hedonic pricefor public green areas is e 612 for one morepercentage point.

Column 2 in Table 3 sets out the values ofe, given by (A6), which corresponds to thecontribution of each amenity to the determi-nation of the overall QoL index adjusted bythe availability of the amenities defined byequation (3). These values are represented inthe pie chart in Figure 2 where it is evidentthat variables related to social dimension(Ethnic) and leisure (Cultural) play the mostimportant role.

According to the model presented in sec-tion 3 and detailed in the Appendix, theweights s = s1, ::, skð Þ assigned to the setof amenities are calculated using the esti-mated implicit prices and the average quan-tities of amenities in the city according toequations (A5) and (A6). The third columnin Table 3 shows that these weights arefairly similar and that the lowest is assignedto the socioeconomic amenity Ethnic. Thisimplies that aversion to the unequal distri-bution of immigrants across neighbour-hoods will be higher than to the unequaldistribution of the other amenities.

The last column in Table 3 shows thevalues of the equally distributed equivalentshare gj associated with each amenity j. Asstated earlier, it corresponds to the share ofthe city-wide average value of the amenity jso that, if equally distributed throughout all

Table 3. Hedonic prices and QoL indexes

Variable pj (e) ej =pj��zjPk

l = 1pl��zl

[A6] sj =1�ej

k�1 [A5] lj = 1�zj

1n

Pni = 1 z

sj

ij

h i 1sj [A2]

Transport (e/station) 2 475 0.151 0.1698 0.5418Prox_univ (e/km) 1 377 0.089 0.1822 0.8608Green (e/ + 1%) 612 0.103 0.1794 0.5683Cultural (e/unit) 2 839 0.198 0.1603 0.3339Shop_fac (e/unit) 1 051 0.139 0.1722 0.8671Ethnic (e/unit) 2 500 0.320 0.1360 0.9300

QoL index (equation (3)) 71 473Correlation term k 1.0909Correction term u 0.72Equity-adjusted index QoLu 51 460




neighbourhoods, it would provide the samevalue of the evaluation function (4) assessedwith the actual distribution of j, as claimedby equation (5). Its value depends both onthe degree of aversion to the unequal distri-bution of amenity j and its actual distribu-tion across neighbourhoods. The highestvalue of gj is for Ethnic (0.93), which showsa limited degree of residential segregationin Milan, followed by Shopping facilities(0.86) and Proximity to university (0.86).The lower gj found for Cultural (0.33)Transport (0.54) and Green (0.56) roughlyindicate an unequal availability of theseamenities across city neighbourhoods.Finally, the interaction term k is calculatedto be slightly bigger than 1 (1.09),12 imply-ing that the joint effect of amenity distribu-tions positively contributes to the overallequity-adjusted QoL index.

The last step backward defines the extentof the reduction of the QoL index adjustedfor the amenity availability shown in (3).This value amounts to e71 473. The calcu-lations carried out show that the overallcorrection term q amounts to 0.72 andtherefore the QoL index accounting forequity is equal to e51 460. This result doesnot differ so much from the benchmarkcase where ej is 1/6 for all j and inequality

aversion is the same for each amenity. Thecorrection term q reduces from 0.28 to0.26 and the adjusted QoL value rises toe52 246.

3.4 Discussion

This result implies that the uneven availabil-ity of amenities within the city reduces theindex adjusted for the availability of ame-nities (3) by 28 per cent. Increasing the levelof amenities improves quality of life buttheir even availability also matters. Figure 3shows the level of QoL by neighbourhoodcomputed according to (3).13 This mapconfirms the monocentric shape of Milanwhere QoL levels are much higher in thecity centre and decrease as the distance fromthe centre increases. All neighbourhoods inthe city centre have a QoL value near to orfar exceeding e100 000, with the exceptionof neighbourhood 6—Castello, Melzi d’Eril,Sarpi with a value of e74 775. This lowervalue is due to the numerous settlement inthe past 10 years of wholesalers trading inclothing and leather goods, essentially com-prising a Chinese community. Moreover, inthe district there is friction between resi-dents and wholesalers because of the

Figure 2. Contribution of amenities to the overall QoL index adjusted for the availability ofamenities.




continuous loading and unloading ofgoods, causing traffic problems and endan-gering pedestrians. The lowest value(e30 096) is for neighbourhood 55—Quarto Oggiaro, Roserio, Amoretti—whichsprang up in the 1950s to house workersfrom southern Italy. In the course of time,this neighbourhood developed a reputationfor organised crime, dilapidated housingand a high percentage of illegal immigrants(of the 4000 apartments made available bypublic housing, 700 are occupied illegally).

The relationship between the value ofQoL and income across neighbourhoods isexamined. The Pearson correlation coeffi-cient is 0.846 implying that QoL is stronglypositively related to income. This result is inline with the study of Brueckner et al. (1999)regarding the importance of amenities indriving the location choice of rich individu-als towards the best-endowed neighbour-hoods, rises rapidly with income.

We conclude this section with a concernabout whether these empirical results wouldstill be meaningful if the needs-based criter-ion of equity in the city, cited in section 2.3,was adopted. Suppose for instance thathouseholds comprising people of over 65years of age are concentrated in a few cityneighbourhoods. In this case, it would bereasonable to concentrate amenities such ashealthcare services in these neighbour-hoods. To investigate this point, we lookedat the distribution of two kinds of house-holds with specific traits able to shape theirpreferences (households with children andpeople over 65) in Milan. It turns out thatthese households are evenly distributedacross city neighbourhoods (their Gini con-centration index is respectively 0.056 and0.068) so we can conclude that our resultshold up against the preference heterogeneityinduced by the demographic compositionof households.

0 - 40 000

40 000 - 75 000

> 75 000

52 4849

4647

50

5153

2325

5526

24

27

30

2829

3231

3335

3421

2036

373819

39

4042

4154

43

44

45 181716 10 9

15

135

1412

11 22

6 7

432

1 8

1 km

Figure 3. QoL across Milan neighbourhoods. Key: see Table A1 for key to names ofneighbourhoods.




4. Concluding Remarks

This paper is an original attempt to bridgethe gap between the urban economics andinequality measurement literature. Startingfrom the premise that these two fields ofeconomics share a multidimensional viewof QoL, we propose an innovative metho-dology to assess urban QoL when equityconcerns arise. Without recommending anyspecific equity perspective, we show howpreferences for equity can be introducedinto QoL assessment through a simple listof parameters which generate a correctionterm for the Roback QoL index adjustedfor amenity availability. Our empiricalinvestigation for Milan indicates the quitesignificant impact of inequality on the QoLindex for the whole city. To disentanglethis result, we assessed QoL across neigh-bourhoods, showing significant differences.Milan has a monocentric shape like othermajor European cities both in terms ofincome and QoL values. These two vari-ables are strongly positively related acrossMilan’s neighbourhoods. Better-endoweddistricts attract wealthier households. It fol-lows that to decrease stratification in thecity, improving efficiency and equalisingopportunities and life-chances in the spiritof Massey and Denton (1996), policiesfavouring a more even availability of ame-nities should be promoted. In this perspec-tive, our methodology has a wide range ofapplications, from simulating the effects ofchanges in the provision of public goods onQoL, to the analysis of poverty and stratifi-cation at the urban level. It can also beused to assess the effects of gentrification(Helms, 2003; Lees, 2008) or urban renova-tion policies (Barthelemy et al., 2007).Finally, our approach could be extended onthe basis that certain groups might bebetter clustered for equity reasons (i.e. theelderly or families with children). In thiscase, the correction term applied to the

QoL indicator should account for thedegree of association between the distribu-tion of these categories of people and thespatial provision of specific amenities. Thisconstitutes a promising avenue for futureresearch.

Notes

1. A large number of studies have used datafor a single city focusing in particular onenvironmental issues (air or water pollu-tion, proximity to noxious sites, etc.). See,for example, Kohlhase (1991); Michaels andSmith (1990).

2. In our application, for the sake of simpli-city, we use the Euclidean distance betweenthe centroids of the neighbourhoods. Ofcourse a more refined technique would beto use commuting time and mobility costs,where these data are available.

3. At the end of the empirical section, weshow that the results for Milan also proveto be robust in the light of this second per-spective. See Lucy (1981) for a taxonomy ofequity criteria in urban planning and Rusk(2003) for a long-term analysis of US cities.

4. To simplify the presentation, in what fol-lows we simply call ‘amenities’ the ame-nities adjusted for their availability.

5. Indeed, in the body of literature oninequality and welfare measurement, thetraditional approach based on the prefer-ences of a social planner has only recentlybeen questioned by alternative approachesbased on individual preferences (seeFleurbaey and Maniquet, 2011).

6. The total population was 1 295 339 inhabi-tants in 2008, within an area of about 183square km.

7. See Table A1 in the Appendix for the list ofdistricts with their population size.

8. As in other Western countries; see forexample Pan Ke Shon (2010) for France.

9. By classroom facilities we mean, for exam-ple, modern teaching aids, air conditionedrooms, spacious rooms and neat and cleanclassrooms. The building facilities are, forexample, recreation and gym facilities,




high-speed Internet access, an extensivelibrary and computer lab facilities.

10. Michelangeli and Zanardi (2009) provideempirical evidence for a monocentric shapeof the residential housing market in Milan.Gonzales (2009, sec. 3) describes the histor-ical and political roots of the monocentricstructure of Milan. More recently Veneri(2013) accounts for the transformation intoan increasingly polycentric space of theMilan metropolitan area. Extending ouranalysis to such a larger area would requirean alternative empirical specification of thehedonic equation (7).

11. The standardised beta coefficient quantifieshow many standard deviations change thevalue of a house when each control variableis increased by one standard deviation.

12. If k were equal to 1 there would be no jointeffect of amenity distributions on QoL index.

13. To compute the QoL index adjusted for theavailable amenities for neighbourhood i,with i = 1, ., n, equation (3) is modifiedas follows

QoLi =Xk

j = 1pjzij

14. We do not explore these properties andinvite the reader interested in axiomatics toconsult Tsui (1995).

15. The reader will note that 1� lj is exactlythe famous Atkinson (1970) inequalityindex: so lj approaches 1 when the amenityj is evenly available within the city; while lj

approaches 0 when inhabitants of only fewneighbourhoods are neatly advantaged.

16. See also Brambilla and Peluso (2010).17. This issue is usually solved in multidimen-

sional inequality literature by resorting tosensitivity analysis—i.e. by showing how theresults stand up to different numeric valuesfor the parameters.

18. See www.lisdatacentre.org/data-access/key-figures/download-key-figures/.

Acknowledgements

We gratefully acknowledge the Osservatorio delMercato Immobiliare for data on housing trans-actions; the Statistics Bureau of the Municipality

of Milan joint with the Department of Statisticsof the University of Milano-Bicocca for data onincome and demographic variables; Luca Stancafor data on public transportation. We would liketo thank the editors for their time and valuableremarks. We thank also Rolf Aaberge, FrancescoAndreoli, Michel Le Breton and Vito Peragine foruseful discussions. The usual disclaimer applies.

Funding

Financial support by the Italian Ministry ofUniversity and Research and the Institute forEconomic Research on Firms in Vicenza is grate-fully acknowledged.

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Appendix. Derivation of theCorrection Term q in theEquity-adjusted QoL Index

To derive the correction term q in (5), weassume a Cobb-Douglas specification for theevaluation function w:

w(zi) =Yk

j = 1z

sj

ij ðA1Þ

This specification has several advantages

(1) From the theoretical point of view, theCobb–Douglas form gives a multidimen-sional index q that generalises the Atkinson(1970) index and is supported by solidaxiomatics.14

(2) From the computational point of view, theCobb–Douglas allows one to obtain q byaggregating k univariate inequality indexesof the Atkinson type (computed for eachamenity separately) and a residual termaccounting for the interaction among thedistribution of amenities within the city.

(3) The value of q depends on a list of k para-meters sj, with j = 1, :: , k, with a clear inter-pretation: each parameter sj indicates thelevel of aversion to the unequal distributionof the amenity zj associated with it.The aggregation property for q and the ‘cali-bration’ of parameters—that is the choice of

numerical values for the parameters—arenow illustrated. To get q, k unidimensionalindices of the Atkinson type must becomputed

lj =1

�zj

1

n

Xn

i = 1z

sj

ij

� � 1sj

with j = 1, :: , k ðA2Þ

These indices are interesting in themselvesbecause they reflect the unequal availability ofthe different amenities across city districts.15

Moreover, one can delve into the contribu-tion of the distribution of each amenity to thecorrection term q, by exploiting the following

Proposition 2: (Abul Naga and Geoffard, 2006)If w(zi) =

Qkj = 1 z

sj

ij , andPk

j = 1 sj\1; :::, the cor-rection term q can be decomposed as follows

Xk

j = 1sj

� �ln q =

Xk

j = 1sj ln lj + ln k ðA3Þ

where, lj are the univariate indices of theAtkinson class defined in (A2) and k is an inter-action term equal to16

k =nk�1

Pni = 1

Qkj = 1 z

sj

ij

� �Qk

j = 1

Pni = 1 z

sj

ij

� � ðA4Þ

Moving on now to the calibration problem,notice that equations (A2), (A3) and (A4) dependon the vector of parameters s = s1, :: , skð Þ. In(A2), they enter as parameters of the univariateindices of the Atkinson type. The higher sj, for j= 1, ., k, the lower aversion to an unequal distri-bution of the amenity j within the city. A numeri-cal value must be assigned to sj with j = 1, ., kto carry out the empirical analysis.17 We first nor-malise s = s1, ., skð Þ as follows

sj =1� ej

k� 1ðA5Þ

where,Pk

j = 1 ej = 1. The normalisation gives adouble advantage: the sum of the k values of sj is1 and—more importantly—because of the isoe-lastic form of (A2), the normalisation allowsexpressing the Pratt (1964) coefficient of relativerisk (inequality) aversion over the distribution of




amenity j, that is 1� sj, as an affine function ofej (1� sj coincides with ej for k = 2). In this way,each ej represents specific preferences vis-a-visinequality. In the benchmark case of an identicaldegree of inequality aversion for each amenity,1� sj approaches 1 if the number of amenitiesgoes to infinite, while it is equal to ½ if k = 2.Notice that ½ and 1 are the two parameters usu-ally chosen by the Luxembourg Income Studyfor the Atkinson index.18 In our analysis, thedegree of inequality aversion is allowed to varywith amenities. Since implicit prices truly cap-ture the assessment of each amenity by the city’srepresentative citizen, we pragmatically assumethat the higher the contribution of an amenity indetermining the QoL value in the city, the moreintense is the aversion for its uneven distributionwithin the city. This is enshrined in the followingassumption

Assumption: The relative inequality aversion coef-ficient ej, with j = 1, ., k, is set to be equal to

ej =pj � �zjPk

l = 1 pl � �zl

ðA6Þ

Each parameter ej is set to be equal to the ratiobetween the estimated value of the average

quantity of the amenity j and the value of allamenities which are on average available in thecity. In other terms, ej corresponds to the relativecontribution of amenity j to the overall QoLindex.

All in all, the methodology can be summarisedin the following steps

(1) The available amenities zij are computedusing expression (2).

(2) The implicit prices of the k available ame-nities are estimated through the hedonicregression (7).

These two steps are sufficient to compute theQoL index adjusted for the availability of theamenities (4). To compute the equity-adjustedQoL index (5) the procedure also includes thefollowing three steps

(1) The coefficients ej, with j=1,..,k, are com-puted from equation (A6).

(2) Vectors s = s1, . . . , skð Þ and l =l1, . . . , lkð Þ are computed using expres-

sions (A5) and (A2) respectively.(3) The correction term q is obtained from

equation (A3) and QoLq(Z; W) is finallydetermined.




Table A1. List of neighbourhoods in Milan

Zone Neighbourhood name Inhabitants Average income (e)S QoL (e)

Centre1 Scala, Manzoni, Vittorio Emanuele, S. Babila 3 265 60 257 263 4532 Brera, Duomo, Cordusio, Torino 7 712 61 387 146 5533 Missori, Italia, Vetra, Sant’Eufemia 6 134 45 529 161 9744 Diaz, Fontana, Europa 4 448 51 638 179 8335 Cadorna, Monti, Boccaccio 6 493 57 335 130 1766 Castello, Melzi d’Eril, Sarpi 24 478 30 850 74 7757 Turati, Moscova, Repubblica 7 975 41 599 138 5168 Venezia, Majno, Monforte 2 658 76 556 194 8099 Mascagni, Porta Vittoria, Porta Romana 16 355 49 959 99 89110 Porta Ticinese, Porta Genova, Magenta 18 958 33 647 103 477

Mid centre11 Cenisio, Procaccini, Firenze 26 088 20 024 52.74912 Fiera, Giulio Cesare, Sempione 19 756 28 289 77.18313 Amendola, Monte Rosa, Buonarroti 17 566 32 762 74.48314 Pagano, Monti, Wagner 8 448 44 901 107.13015 Piemonte, Washington, Cimarosa 32 651 28 928 90.53916 Solari, Napoli, Savona 10 757 23 921 101.28317 Naviglio Grande, Argelati, San Gottardo 13 353 18 715 68.72418 Tabacchi, Sarfatti, Crema 31 802 21 618 65.10019 Libia, XXII Marzo, Indipendenza 52 173 22 264 56.48220 Regina Giovanna, Pisacane, Castel Morrone 22 410 26 847 90.67021 Abruzzi, Eustachi, Plinio 22 906 26 321 106.41522 Stazione Centrale, Gioia, Zara 50 087 22 457 82.059

Outlying23 Musocco, Varesina, Certosa 36 200 14 740 35 25124 Bovisa, Bausan, Imbonati 32 519 14 595 42 88425 Largo Boccioni, Aldini, Lopez 15 514 11 887 35 84826 Bovisasca, Affori, P. Rossi 43 240 14 335 40 67927 Niguarda, Ornato 25 397 14 411 51 49028 Fulvio Testi, Bicocca, Ca’ Granda 26 694 15 885 62 74929 Monza, Precotto, Gorla 30 814 15 458 50 08630 Zara, Istria, Murat 14 361 16 034 52 88331 Loreto, Turro, Padova 51 457 16 813 69 69332 Parco Lambro, Feltre, Udine 56 571 14 993 47 34633 Aspromonte, Porpora, Teodosio 26 259 19 721 67 78934 Leonardo da Vinci, Gorini 19 303 20 247 65 14935 Lambrate, Rubattino, Folli 6 768 16 518 42 87836 Argonne, Viale Corsica 27 318 20 777 59 49637 Forlanini, Mecenate, Rogoredo 32 255 14 540 34 69738 Ortomercato, Molise, Piranesi 12 071 18 783 50 89639 Boncompagni, Toffetti, Bacchiglione 11 933 17 235 41 15940 Omero, Gabriele Rosa, Brenta 20 996 13 447 34 28341 Ronchetto, Chiaravalle, Ripamonti 12 158 17 404 37 38942 Montegani, Cermenate, Vigentino 45 664 16 991 49 032

(continued)




Table A1. (Continued)

Zone Neighbourhood name Inhabitants Average income (e)S QoL (e)

43 Barona, Famagosta, Faenza 46 458 14 761 50 40144 San Cristoforo, Ronchetto, Ludovico il Moro 22 260 12 360 55 36745 Giambellino, Tirana, Frattini 27 723 16 396 45 90346 Siena, Tripoli, Brasilia 42 150 19 313 66 70647 Lorenteggio, Inganni, Bisceglie 41 657 14 848 50 97248 Novara, San Carlo, Amati 9 704 14 729 47 38349 Segesta, Capecelatro, Aretusa 29 543 16 204 46 15450 Ippodromo, Caprilli, Monte Stella 5 070 27 664 91 34051 Cagnola, Achille, Papa, Tiro Segno 5 826 19 907 52 780

Suburbs52 Baggio, Quinto Romano, Quarto Cagnino 45 757 14 107 36 11553 Gallaratese, Lampugnano, Figino 44 020 18 652 66 15454 Missaglia, Chiesa Rossa, Gratosoglio 20 624 12 595 40 79255 Quarto Oggiaro, Roserio, Amoretti 17 894 11 791 30 096

Table A2. Description of variables

Variable Definition Source

Market_p 1 if the housing value is a market price (ref.) OMIOffer_p 1 if the housing value is an offer price OMIEstimated_p 1 if the housing value estimated by OMI OMIPrivate characteristics

ln(size) logarithm of the total floor surface area OMISecond bathroom 1 if the unit has a second bathroom, or more OMIThird bathroom 1 if the unit has a third bathroom, or more OMITo be renewed 1 if the unit needs to be renewed OMIHeating 1 if the unit has gas central heating OMI2nd floor (or higher) 1 if the unit is on second floor, or higher OMILow cost 1 if the unit is in a low-cost building (ref.) OMIMedium cost 1 if the unit is in a medium-cost building OMILuxury 1 if the unit is in a luxury building OMIParking 1 if the unit has at least one parking space OMIElevator 1 if the unit is in a building with an elevator OMIln(age) logarithm of the age of building OMIDistance distance of the unit to the centre Authors’ computationCity centre 1 if the unit is one of the zones in the centre OMI

AmenitiesTransport number of metro stations Milan Transport AgencyProximity_university proximity to the nearest university Authors’ computationGreen percentage of public green areas Milan MunicipalityCultural cultural placesa per 10 000 inhabitants Yellow PagesShopping_facilities commercial facilitiesb per 10 000 inhabitants Authors’ computationEthnic Italian/foreign Milan Municipality

aCinemas, theatres, museums, art galleries, academies of music and libraries.bSupermarkets, discount stores and malls.




Urban Stud 2013 Brambilla 3205 24

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