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

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1 Equity in the City On Measuring Urban (Ine)Quality of Life Marco G. Brambilla 1, Alessandra Michelangeli 2, Eugenio Peluso 3 July 7, Defap-Catholic University of Milan. 2 DSGE, University of Milan-Bicocca. 3 Department of Economics, University of Verona. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

2 The standard approach in the economics literature Rosen (1979) and Roback (1982) spatial equilibrium model: Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

3 The standard approach in the economics literature Rosen (1979) and Roback (1982) spatial equilibrium model: Urban quality of Life: monetary assessment of city amenities by a representative individual free to move among several cities. QOL = k j=1 p j a j Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

4 The standard approach in the economics literature Rosen (1979) and Roback (1982) spatial equilibrium model: Urban quality of Life: monetary assessment of city amenities by a representative individual free to move among several cities. QOL = k j=1 p j a j a = (a 1,..., a k ) vector of the average quantities of k amenities in the city. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

5 The standard approach in the economics literature Rosen (1979) and Roback (1982) spatial equilibrium model: Urban quality of Life: monetary assessment of city amenities by a representative individual free to move among several cities. QOL = k j=1 p j a j a = (a 1,..., a k ) vector of the average quantities of k amenities in the city. Prices p j, for j = 1,.., k estimated through housing and wage hedonic regressions. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

6 Our contribution New methodology: analyzing a single city, we merge contributions from NUE and inequality measurement to obtain a novel QOL index. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

7 Our contribution New methodology: analyzing a single city, we merge contributions from NUE and inequality measurement to obtain a novel QOL index. We take the normative point of view of a city-planner in favor of an even accessibility to amenities throughout the city. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

8 Our contribution New methodology: analyzing a single city, we merge contributions from NUE and inequality measurement to obtain a novel QOL index. We take the normative point of view of a city-planner in favor of an even accessibility to amenities throughout the city. An unequal availability of the amenities within the city has a negative impact on the evaluation function of the city planner as income inequality generates a loss in social welfare according to Atkinson (1970), Kolm (1969), Sen (1973) in their approach to inequality measurement. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

9 Amenities and their availability The city is partitioned in n zones. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

10 Amenities and their availability The city is partitioned in n zones. Each zone i is described by a vector a i containing the average values of k relevant amenities. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

11 Amenities and their availability The city is partitioned in n zones. Each zone i is described by a vector a i containing the average values of k relevant amenities. Distribution of amenities within the city: n k matrix A, 2 A = 6 4 a a 1k... a ij a n a nk (1) Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

12 d il Figure 1: Distance between neighborhood centroids. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

13 d il Figure 1: Distance between neighborhood centroids. S(i) set of neighborhood adjacent to i (with i 2 S(i)) Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

14 d il Figure 1: Distance between neighborhood centroids. S(i) set of neighborhood adjacent to i (with i 2 S(i)) z ij = a lj f (d il ) 8j = 1,..., k l2s(i) Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

15 a lj is the value of the amenity j in the areal units l bordering with i; Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

16 a lj is the value of the amenity j in the areal units l bordering with i; f (d il ) nonincreasing function f : R +! R + de ned on the distance d il between the centroids of any two areal units belonging to S(i). Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

17 a lj is the value of the amenity j in the areal units l bordering with i; f (d il ) nonincreasing function f : R +! R + de ned on the distance d il between the centroids of any two areal units belonging to S(i). 2 Z= 6 4 z z 1k... z ij z n z nk Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

18 Evaluation function of the city planner We assume that urban amenities should be available in a way such that everyone receives the same public bene t, regardless of socioeconomic status, willingness or ability to pay, or other criteria: residents receive either equal input or equal bene t (Talen 1998, p. 24). Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

19 Evaluation function of the city planner We assume that urban amenities should be available in a way such that everyone receives the same public bene t, regardless of socioeconomic status, willingness or ability to pay, or other criteria: residents receive either equal input or equal bene t (Talen 1998, p. 24). For any Z 2D n, let W (Z) be the additive evaluation function of the city planner: W (Z) = 1 n n i=1 w (z i ), w (z i ) summarizes the city planner assessment about the QOL in the neighborhood i with characteristics z i. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

20 Equally-distributed equivalent amenities Let z = [ z 1,... z k ] the k- dimensional vector containing the means of the k amenities in the city. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

21 Equally-distributed equivalent amenities Let z = [ z 1,... z k ] the k- dimensional vector containing the means of the k amenities in the city. If W = W (Z) is the evaluation of the city-planner of the actual distribution, there exists a scalar ϑ (Z), ϑ 2 [0, 1], such that: W = W (Z) = 1 n n i=1 w (z i ) = W (ϑ z). (2) Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

22 Equally-distributed equivalent amenities Let z = [ z 1,... z k ] the k- dimensional vector containing the means of the k amenities in the city. If W = W (Z) is the evaluation of the city-planner of the actual distribution, there exists a scalar ϑ (Z), ϑ 2 [0, 1], such that: W = W (Z) = 1 n n i=1 w (z i ) = W (ϑ z). (2) In the same spirit of Atkinson (1970) and Tsui (1995), we call the elements of the vector ϑ z "equally-distributed equivalent amenities". Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

23 Equally-distributed equivalent amenities Let z = [ z 1,... z k ] the k- dimensional vector containing the means of the k amenities in the city. If W = W (Z) is the evaluation of the city-planner of the actual distribution, there exists a scalar ϑ (Z), ϑ 2 [0, 1], such that: W = W (Z) = 1 n n i=1 w (z i ) = W (ϑ z). (2) In the same spirit of Atkinson (1970) and Tsui (1995), we call the elements of the vector ϑ z "equally-distributed equivalent amenities". ϑ 2 [0, 1] expresses the willingness of the city planner to renounce the share 1 ϑ of the amount of the amenities, against their even distribution within the city. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

24 The equity-adjusted QOL index De nition For any Z, we de ne the equity-adjusted Quality of Life index QOL ϑ as " the value of the multidimensional certainty equivalent" of the vector of amenities within the city QOL ϑ = k j=1 p zj ϑz j, (3) We replace in the Rosen-Roback index the "equally-distributed equivalent amenities" ϑz j. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

25 Decomposition of the correction term Proposition If w (z i ) = Π k z σ j j=1 ij,with σ j > 0 8j, the equivalent share ϑ can be decomposed as follows:! k k σ j j=1 ln ϑ = j=1 σ j ln γ j + ln κ (4) where γ 1,.., γ k are Atkinson univariate indices and κ 1 is an interaction term equal to: a κ = n k kπ 1 n i=1 j=1 zσ j ij k Π n z σ j j=1 ij i=1. (5) Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

26 An adjusted QOL index (cont.) The weight σ j associated with each amenity j is: σ j = 1 ε j (6) k 1 where ε j is the Pratt (1964) coe cient of relative risk (inequality) aversion over the dimension j. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

27 An adjusted QOL index (cont.) The weight σ j associated with each amenity j is: σ j = 1 ε j (6) k 1 where ε j is the Pratt (1964) coe cient of relative risk (inequality) aversion over the dimension j. The Pratt coe cient ε j is set to be equal to the relative incidence of the attribute j on the QOL index. The higher ε j, the higher the loss in the planner evaluation function due to the unequal distribution of the amenity j, ε j = p j z j. (7) k p zj z j j=1 Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

28 Empirical application Milan Fig. A.2: QOL across neighborhoods Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

29 QOL Index Amenities 1 Environment: green area (pct.) Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

30 QOL Index Amenities 1 Environment: green area (pct.) 2 Transport: number of metro stations Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

31 QOL Index Amenities 1 Environment: green area (pct.) 2 Transport: number of metro stations 3 Education: proximity to the nearest university Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

32 QOL Index Amenities 1 Environment: green area (pct.) 2 Transport: number of metro stations 3 Education: proximity to the nearest university 4 Shopping facilities: number of supermarkets, discount stores and malls for 10,000 inhabitants Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

33 QOL Index Amenities 1 Environment: green area (pct.) 2 Transport: number of metro stations 3 Education: proximity to the nearest university 4 Shopping facilities: number of supermarkets, discount stores and malls for 10,000 inhabitants 5 Recreational amenities: number of cinemas, theatres, museums, art galleries, academies of music, libraries per 10,000 inhabitants. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

34 QOL Index Amenities 1 Environment: green area (pct.) 2 Transport: number of metro stations 3 Education: proximity to the nearest university 4 Shopping facilities: number of supermarkets, discount stores and malls for 10,000 inhabitants 5 Recreational amenities: number of cinemas, theatres, museums, art galleries, academies of music, libraries per 10,000 inhabitants. 6 Concentration of immigrants: ratio Italian/foreign residents. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

35 Estimated implicit prices p hit = β 0 + β 1 X ht + β 2 Z it + ε hit Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

36 Estimated implicit prices p hit = β 0 + β 1 X ht + β 2 Z it + ε hit Source: Real Estate Observatory of the Agenzia del Territorio. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

37 Estimated implicit prices p hit = β 0 + β 1 X ht + β 2 Z it + ε hit Source: Real Estate Observatory of the Agenzia del Territorio individual house transactions in Milan districts from 2004 to Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

38 Estimated implicit prices p hit = β 0 + β 1 X ht + β 2 Z it + ε hit Source: Real Estate Observatory of the Agenzia del Territorio individual house transactions in Milan districts from 2004 to Each transaction reports sale price and a detailed description of the housing characteristics. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

39 Results 1 By taking into account the uneven availability of amenities within the city, the Roback index is reduced by 28%. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

40 Results 1 By taking into account the uneven availability of amenities within the city, the Roback index is reduced by 28%. 2 Green, Transport and Recreational amenities have lower equally distributed equivalent shares while Ethnic, Shopping facilities and Education have highest values. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

41 Results 1 By taking into account the uneven availability of amenities within the city, the Roback index is reduced by 28%. 2 Green, Transport and Recreational amenities have lower equally distributed equivalent shares while Ethnic, Shopping facilities and Education have highest values. 3 The interaction term is bigger than 1 implying that the joint e ect of amenity distributions positively contributes to the overall QOL index. Brambilla Michelangeli Peluso () Equity in the City On Measuring Urban (Ine)Quality of Life July 7, / 15

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