Introduction: Equivalence scales (ES) Definition Principle: ‘Income needed for a family with given composition to be "as well off" as some reference family’ In practice (US Census Bureau, 2014): Single, no child: poverty threshold at $12,316 Couple, no child: $15,853 Single, 1 child: $16,317 Couple, 2 children: $24,000 Single, 3 children: $24,091 Note the non linearities. Why? → capture different aspects ‘differences in need’ (e.g.: children eat less than adults, but may have specific needs) domestic production technology: economies of scale Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 3 / 30
Introduction: Equivalence scales (ES) Definition Principle: ‘Income needed for a family with given composition to be "as well off" as some reference family’ In practice (US Census Bureau, 2014): Single, no child: poverty threshold at $12,316 Couple, no child: $15,853 Single, 1 child: $16,317 Couple, 2 children: $24,000 Single, 3 children: $24,091 Note the non linearities. Why? → capture different aspects ‘differences in need’ (e.g.: children eat less than adults, but may have specific needs) domestic production technology: economies of scale public goods, etc. Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 3 / 30
Introduction: Equivalence scales (ES) Implementation Two main approaches Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 4 / 30
Introduction: Equivalence scales (ES) Implementation Two main approaches Engel: share of food expenditures → Prais-Houthakker, Barten: Engel curves for different goods → however, may depend on the source of income (Attanasio Lechene 2013) Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 4 / 30
Introduction: Equivalence scales (ES) Implementation Two main approaches Engel: share of food expenditures → Prais-Houthakker, Barten: Engel curves for different goods → however, may depend on the source of income (Attanasio Lechene 2013) Rothbarth: consumption of ‘adult goods’ Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 4 / 30
Introduction: Equivalence scales (ES) Implementation Two main approaches Engel: share of food expenditures → Prais-Houthakker, Barten: Engel curves for different goods → however, may depend on the source of income (Attanasio Lechene 2013) Rothbarth: consumption of ‘adult goods’ In practice (US Census Bureau) Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 4 / 30
Introduction: Equivalence scales (ES) Implementation Two main approaches Engel: share of food expenditures → Prais-Houthakker, Barten: Engel curves for different goods → however, may depend on the source of income (Attanasio Lechene 2013) Rothbarth: consumption of ‘adult goods’ In practice (US Census Bureau) defines the poverty line for a typical household as three times the cost of a nutritionally adequate diet, Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 4 / 30
Introduction: Equivalence scales (ES) Implementation Two main approaches Engel: share of food expenditures → Prais-Houthakker, Barten: Engel curves for different goods → however, may depend on the source of income (Attanasio Lechene 2013) Rothbarth: consumption of ‘adult goods’ In practice (US Census Bureau) defines the poverty line for a typical household as three times the cost of a nutritionally adequate diet, then uses Engel scales to extend to households of different compositions Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 4 / 30
Introduction: Equivalence scales (ES) Implementation Two main approaches Engel: share of food expenditures → Prais-Houthakker, Barten: Engel curves for different goods → however, may depend on the source of income (Attanasio Lechene 2013) Rothbarth: consumption of ‘adult goods’ In practice (US Census Bureau) defines the poverty line for a typical household as three times the cost of a nutritionally adequate diet, then uses Engel scales to extend to households of different compositions adjusts by the consumer price index. Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 4 / 30
Introduction: Equivalence scales (ES) Implementation Two main approaches Engel: share of food expenditures → Prais-Houthakker, Barten: Engel curves for different goods → however, may depend on the source of income (Attanasio Lechene 2013) Rothbarth: consumption of ‘adult goods’ In practice (US Census Bureau) defines the poverty line for a typical household as three times the cost of a nutritionally adequate diet, then uses Engel scales to extend to households of different compositions adjusts by the consumer price index. See Fisher 1997 and Lewbel-Pendakur 2006 Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 4 / 30
Roadmap 1. Problems with Equivalent Scales 1.1 Theory and empirical estimation 1.2 Normative issues 2. Indifference Scales 2.1 Definition 2.2 Benchmark case: private goods only 2.3 Public and private goods Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 5 / 30
Roadmap 1. Problems with Equivalent Scales 1.1 Theory and empirical estimation 1.2 Normative issues 2. Indifference Scales 2.1 Definition 2.2 Benchmark case: private goods only 2.3 Public and private goods Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 6 / 30
Introduction: Equivalence scales (ES) Problems with ES ES raises specific issues at various levels: conceptual, normative, empirical Conceptual issues: Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 7 / 30
Introduction: Equivalence scales (ES) Problems with ES ES raises specific issues at various levels: conceptual, normative, empirical Conceptual issues: Interpersonal comparison of utilities → central, although highly debatable → compounded, since we are comparing families of different compositions Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 7 / 30
Introduction: Equivalence scales (ES) Problems with ES ES raises specific issues at various levels: conceptual, normative, empirical Conceptual issues: Interpersonal comparison of utilities → central, although highly debatable → compounded, since we are comparing families of different compositions Utility implicitly defined at the family level → methodological individualism: utility defined at the individual level → ‘utility of the family’ must be defined by reference to individual utilities → various solutions (Lewbel 89, Blackorby Donaldson 93): Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 7 / 30
Introduction: Equivalence scales (ES) Problems with ES ES raises specific issues at various levels: conceptual, normative, empirical Conceptual issues: Interpersonal comparison of utilities → central, although highly debatable → compounded, since we are comparing families of different compositions Utility implicitly defined at the family level → methodological individualism: utility defined at the individual level → ‘utility of the family’ must be defined by reference to individual utilities → various solutions (Lewbel 89, Blackorby Donaldson 93): � U 1 , ..., U n � Samuelson’s welfare index W Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 7 / 30
Introduction: Equivalence scales (ES) Problems with ES ES raises specific issues at various levels: conceptual, normative, empirical Conceptual issues: Interpersonal comparison of utilities → central, although highly debatable → compounded, since we are comparing families of different compositions Utility implicitly defined at the family level → methodological individualism: utility defined at the individual level → ‘utility of the family’ must be defined by reference to individual utilities → various solutions (Lewbel 89, Blackorby Donaldson 93): � U 1 , ..., U n � Samuelson’s welfare index W � U 1 , ..., U n � → ‘all agents have the same utility’ Even min Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 7 / 30
Introduction: Equivalence scales (ES) Problems with ES ES raises specific issues at various levels: conceptual, normative, empirical Conceptual issues: Interpersonal comparison of utilities → central, although highly debatable → compounded, since we are comparing families of different compositions Utility implicitly defined at the family level → methodological individualism: utility defined at the individual level → ‘utility of the family’ must be defined by reference to individual utilities → various solutions (Lewbel 89, Blackorby Donaldson 93): � U 1 , ..., U n � Samuelson’s welfare index W � U 1 , ..., U n � → ‘all agents have the same utility’ Even min Note, however, that this assumption is unsupported and even undefined Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 7 / 30
Introduction: Equivalence scales (ES) Problems with ES ES raises specific issues at various levels: conceptual, normative, empirical Conceptual issues: Interpersonal comparison of utilities → central, although highly debatable → compounded, since we are comparing families of different compositions Utility implicitly defined at the family level → methodological individualism: utility defined at the individual level → ‘utility of the family’ must be defined by reference to individual utilities → various solutions (Lewbel 89, Blackorby Donaldson 93): � U 1 , ..., U n � Samuelson’s welfare index W � U 1 , ..., U n � → ‘all agents have the same utility’ Even min Note, however, that this assumption is unsupported and even undefined ‘Reduced form’ approach: the exact nature of the gains (ES, public goods,...) not explicitly described (household as a black box) Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 7 / 30
Introduction: Equivalence scales (ES) Problems with ES (cont.) Empirical problems Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 8 / 30
Introduction: Equivalence scales (ES) Problems with ES (cont.) Empirical problems Serious identification problems (Blundell Lewbel 1991). Basically: Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 8 / 30
Introduction: Equivalence scales (ES) Problems with ES (cont.) Empirical problems Serious identification problems (Blundell Lewbel 1991). Basically: Behavior driven by expenditure functions e ( p , u , a ) where a denotes family composition Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 8 / 30
Introduction: Equivalence scales (ES) Problems with ES (cont.) Empirical problems Serious identification problems (Blundell Lewbel 1991). Basically: Behavior driven by expenditure functions e ( p , u , a ) where a denotes family composition However, ordinal representation → cannot distinguish e ( p , u , a ) and e ( p , f ( u , a ) , a ) (at least from demand/labor supply) ... although this distinction is crucial for the measure of ES Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 8 / 30
Introduction: Equivalence scales (ES) Problems with ES (cont.) Empirical problems Serious identification problems (Blundell Lewbel 1991). Basically: Behavior driven by expenditure functions e ( p , u , a ) where a denotes family composition However, ordinal representation → cannot distinguish e ( p , u , a ) and e ( p , f ( u , a ) , a ) (at least from demand/labor supply) ... although this distinction is crucial for the measure of ES In practice: changes are identified, but not levels (Blundell Lewbel 91) Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 8 / 30
Introduction: Equivalence scales (ES) Problems with ES (cont.) Empirical problems Serious identification problems (Blundell Lewbel 1991). Basically: Behavior driven by expenditure functions e ( p , u , a ) where a denotes family composition However, ordinal representation → cannot distinguish e ( p , u , a ) and e ( p , f ( u , a ) , a ) (at least from demand/labor supply) ... although this distinction is crucial for the measure of ES In practice: changes are identified, but not levels (Blundell Lewbel 91) Standard solution: independence of base (IB) - preferences are such that the ES are independent of income (or utility) Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 8 / 30
Introduction: Equivalence scales (ES) Problems with ES (cont.) Empirical problems Serious identification problems (Blundell Lewbel 1991). Basically: Behavior driven by expenditure functions e ( p , u , a ) where a denotes family composition However, ordinal representation → cannot distinguish e ( p , u , a ) and e ( p , f ( u , a ) , a ) (at least from demand/labor supply) ... although this distinction is crucial for the measure of ES In practice: changes are identified, but not levels (Blundell Lewbel 91) Standard solution: independence of base (IB) - preferences are such that the ES are independent of income (or utility) But IB requires specific properties for individual utilities → limitation of the ‘reduced-form’ vision: the nature of the gains (economies of scale, public goods,..), which are not explicitly modelled, may contradict the required properties. Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 8 / 30
Introduction: Equivalence scales (ES) Problems with ES (cont.) Empirical problems Serious identification problems (Blundell Lewbel 1991). Basically: Behavior driven by expenditure functions e ( p , u , a ) where a denotes family composition However, ordinal representation → cannot distinguish e ( p , u , a ) and e ( p , f ( u , a ) , a ) (at least from demand/labor supply) ... although this distinction is crucial for the measure of ES In practice: changes are identified, but not levels (Blundell Lewbel 91) Standard solution: independence of base (IB) - preferences are such that the ES are independent of income (or utility) But IB requires specific properties for individual utilities → limitation of the ‘reduced-form’ vision: the nature of the gains (economies of scale, public goods,..), which are not explicitly modelled, may contradict the required properties. On the normative front: Intra family allocation and inequality → what if some members are extremely well-off and others are miserable? Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 8 / 30
Benchmark framework: private consumptions, no economies of scale ES in the benchmark framework Definition of ES: compare the expenditure function of a family a , e ( p , u , a ) , to that of a reference family, ¯ e ( p , u ) D ( p , u ) = e ( p , u , a ) e ( p , u ) ¯ Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 9 / 30
Benchmark framework: private consumptions, no economies of scale ES in the benchmark framework Definition of ES: compare the expenditure function of a family a , e ( p , u , a ) , to that of a reference family, ¯ e ( p , u ) D ( p , u ) = e ( p , u , a ) e ( p , u ) ¯ ‘ Independence of base’ (Lewbel 89), ‘equivalence-scale exactness’ (Blackorby, Donaldson 93) : ∂ D ( p , u ) = 0 ⇒ e ( p , u , a ) = φ ( p , a ) ¯ e ( p , u ) ∂ u � � y V ( p , y , a ) = ¯ ⇒ V p , φ ( p , a ) Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 9 / 30
Benchmark framework: private consumptions, no economies of scale ES in the benchmark framework Definition of ES: compare the expenditure function of a family a , e ( p , u , a ) , to that of a reference family, ¯ e ( p , u ) D ( p , u ) = e ( p , u , a ) e ( p , u ) ¯ ‘ Independence of base’ (Lewbel 89), ‘equivalence-scale exactness’ (Blackorby, Donaldson 93) : ∂ D ( p , u ) = 0 ⇒ e ( p , u , a ) = φ ( p , a ) ¯ e ( p , u ) ∂ u � � y V ( p , y , a ) = ¯ ⇒ V p , φ ( p , a ) Problem: is it compatible with economies of scale, public goods,...? Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 9 / 30
Economies of scale Basic idea: ‘Consumption technology’ → relationship between commodities consumed, x i k , and commodities purchased, z k : � � x i ∑ z = F i Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 10 / 30
Economies of scale Basic idea: ‘Consumption technology’ → relationship between commodities consumed, x i k , and commodities purchased, z k : � � x i ∑ z = F i In practice, affine (Gorman 76): z = Λ · ∑ x i − ∆ i Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 10 / 30
Economies of scale Basic idea: ‘Consumption technology’ → relationship between commodities consumed, x i k , and commodities purchased, z k : � � x i ∑ z = F i In practice, affine (Gorman 76): z = Λ · ∑ x i − ∆ i ... and moreover Λ diagonal (‘Barten scales’): x i z k = λ k ∑ k − δ k i Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 10 / 30
Economies of scale Basic idea: ‘Consumption technology’ → relationship between commodities consumed, x i k , and commodities purchased, z k : � � x i ∑ z = F i In practice, affine (Gorman 76): z = Λ · ∑ x i − ∆ i ... and moreover Λ diagonal (‘Barten scales’): x i z k = λ k ∑ k − δ k i GE perspective → impact on prices : p replaced with π , where: λ k p k π k = 1 + 1 y ∑ j δ j p j Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 10 / 30
Economies of scale (cont.) Independence of base with economies of scale: Assume preferences satisfy IB in the absence of economies of scale. Can we expect the same property to hold with (arbitrary) economies of scale? Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 11 / 30
Economies of scale (cont.) Independence of base with economies of scale: Assume preferences satisfy IB in the absence of economies of scale. Can we expect the same property to hold with (arbitrary) economies of scale? Translation: can it be the case that � � y V ( π , y , a ) = ¯ V p , for all ( p , y ) ? φ ( p , a ) Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 11 / 30
Economies of scale (cont.) Independence of base with economies of scale: Assume preferences satisfy IB in the absence of economies of scale. Can we expect the same property to hold with (arbitrary) economies of scale? Translation: can it be the case that � � y V ( π , y , a ) = ¯ V p , for all ( p , y ) ? φ ( p , a ) Answer: No in general (need δ j = 0 ∀ j , λ k = λ ∀ k ) Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 11 / 30
Economies of scale (cont.) Independence of base with economies of scale: Assume preferences satisfy IB in the absence of economies of scale. Can we expect the same property to hold with (arbitrary) economies of scale? Translation: can it be the case that � � y V ( π , y , a ) = ¯ V p , for all ( p , y ) ? φ ( p , a ) Answer: No in general (need δ j = 0 ∀ j , λ k = λ ∀ k ) Plus: what about public goods? Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 11 / 30
Economies of scale (cont.) Independence of base with economies of scale: Assume preferences satisfy IB in the absence of economies of scale. Can we expect the same property to hold with (arbitrary) economies of scale? Translation: can it be the case that � � y V ( π , y , a ) = ¯ V p , for all ( p , y ) ? φ ( p , a ) Answer: No in general (need δ j = 0 ∀ j , λ k = λ ∀ k ) Plus: what about public goods? Same issue: shifting from singles to couples (or changing family size) impact (Lindahl) prices ... Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 11 / 30
Economies of scale (cont.) Independence of base with economies of scale: Assume preferences satisfy IB in the absence of economies of scale. Can we expect the same property to hold with (arbitrary) economies of scale? Translation: can it be the case that � � y V ( π , y , a ) = ¯ V p , for all ( p , y ) ? φ ( p , a ) Answer: No in general (need δ j = 0 ∀ j , λ k = λ ∀ k ) Plus: what about public goods? Same issue: shifting from singles to couples (or changing family size) impact (Lindahl) prices ... ... with the additional twist that prices are now personal and endogenous! Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 11 / 30
Roadmap 1. Problems with Equivalent Scales 1.1 Theory and empirical estimation 1.2 Normative issues 2. Indifference Scales 2.1 Definition 2.2 Benchmark case: private goods only 2.3 Public and private goods Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 12 / 30
Normative issues Notions of compensating variation: Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 13 / 30
Normative issues Notions of compensating variation: Reform that changes the price vector from p to p � . Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 13 / 30
Normative issues Notions of compensating variation: Reform that changes the price vector from p to p � . Single agent, initial income x : � � − x p � , v ( p , x ) CV = e Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 13 / 30
Normative issues Notions of compensating variation: Reform that changes the price vector from p to p � . Single agent, initial income x : � � − x p � , v ( p , x ) CV = e Two different notions (Chiappori 2005, Chiappori Meghir 2014): Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 13 / 30
Normative issues Notions of compensating variation: Reform that changes the price vector from p to p � . Single agent, initial income x : � � − x p � , v ( p , x ) CV = e Two different notions (Chiappori 2005, Chiappori Meghir 2014): Definition Potentially compensating variation: amount such that agents could both reach the same utility level as before the reform Actually compensating variation: amount such that agents will both reach at least the same utility level as before the reform Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 13 / 30
Normative issues Notions of compensating variation: Reform that changes the price vector from p to p � . Single agent, initial income x : � � − x p � , v ( p , x ) CV = e Two different notions (Chiappori 2005, Chiappori Meghir 2014): Definition Potentially compensating variation: amount such that agents could both reach the same utility level as before the reform Actually compensating variation: amount such that agents will both reach at least the same utility level as before the reform Underlying intuition: potential discrepancy between actual and optimal intrahousehold allocations → what if some members are well-off and others are miserable? Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 13 / 30
U h U w Pareto frontier: initial
U h U w Pareto frontier: initial
U h U w Pareto frontier: post reform, pre compensation
U h U w Pareto frontier: potentially compensating variation
U h U w Pareto frontier: potentially compensating variation
U h U w Pareto frontier: actually compensating variation
Roadmap 1. Problems with Equivalent Scales 1.1 Theory and empirical estimation 1.2 Normative issues 2. Indifference Scales 2.1 Definition 2.2 Benchmark case: private goods only 2.3 Public and private goods Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 16 / 30
‘Indifference scales’ Hahn’s legacy: Theory should be taken seriously Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 17 / 30
‘Indifference scales’ Hahn’s legacy: Theory should be taken seriously Indifference scales (IS) as an alternative, and (we think) much better way of addressing the same issues Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 17 / 30
‘Indifference scales’ Hahn’s legacy: Theory should be taken seriously Indifference scales (IS) as an alternative, and (we think) much better way of addressing the same issues Crucial idea: Comparing utility of the same person in different family contexts Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 17 / 30
‘Indifference scales’ Hahn’s legacy: Theory should be taken seriously Indifference scales (IS) as an alternative, and (we think) much better way of addressing the same issues Crucial idea: Comparing utility of the same person in different family contexts Reference: Browning, Chiappori, Lewbel REStud 2013; Dunbar, Lewbel, Pendakur 2013; Lewbel, Pendakur 2014,... Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 17 / 30
‘Indifference scales’ Hahn’s legacy: Theory should be taken seriously Indifference scales (IS) as an alternative, and (we think) much better way of addressing the same issues Crucial idea: Comparing utility of the same person in different family contexts Reference: Browning, Chiappori, Lewbel REStud 2013; Dunbar, Lewbel, Pendakur 2013; Lewbel, Pendakur 2014,... Research still in progress Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 17 / 30
Indifference scales Intuition: the appropriate question to ask is: “ How much income would an individual living alone need to attain the same indifference curve over goods that the individual attains as a member of the household? ” Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 18 / 30
Indifference scales Intuition: the appropriate question to ask is: “ How much income would an individual living alone need to attain the same indifference curve over goods that the individual attains as a member of the household? ” Note that this question: Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 18 / 30
Indifference scales Intuition: the appropriate question to ask is: “ How much income would an individual living alone need to attain the same indifference curve over goods that the individual attains as a member of the household? ” Note that this question: avoids issues of interpersonal comparability Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 18 / 30
Indifference scales Intuition: the appropriate question to ask is: “ How much income would an individual living alone need to attain the same indifference curve over goods that the individual attains as a member of the household? ” Note that this question: avoids issues of interpersonal comparability does not depend on the utility level assigned to an indifference curve → only depends on ordinal preferences Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 18 / 30
Indifference scales Intuition: the appropriate question to ask is: “ How much income would an individual living alone need to attain the same indifference curve over goods that the individual attains as a member of the household? ” Note that this question: avoids issues of interpersonal comparability does not depend on the utility level assigned to an indifference curve → only depends on ordinal preferences therefore is (in principle) answerable from revealed preference data. Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 18 / 30
Indifference scales Intuition: the appropriate question to ask is: “ How much income would an individual living alone need to attain the same indifference curve over goods that the individual attains as a member of the household? ” Note that this question: avoids issues of interpersonal comparability does not depend on the utility level assigned to an indifference curve → only depends on ordinal preferences therefore is (in principle) answerable from revealed preference data. Note the relationship with wrongful death: distinction between ‘economic gain/losses’ and ‘pain and suffering’ Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 18 / 30
Indifference scales Intuition: the appropriate question to ask is: “ How much income would an individual living alone need to attain the same indifference curve over goods that the individual attains as a member of the household? ” Note that this question: avoids issues of interpersonal comparability does not depend on the utility level assigned to an indifference curve → only depends on ordinal preferences therefore is (in principle) answerable from revealed preference data. Note the relationship with wrongful death: distinction between ‘economic gain/losses’ and ‘pain and suffering’ In particular, our framework: Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 18 / 30
Indifference scales Intuition: the appropriate question to ask is: “ How much income would an individual living alone need to attain the same indifference curve over goods that the individual attains as a member of the household? ” Note that this question: avoids issues of interpersonal comparability does not depend on the utility level assigned to an indifference curve → only depends on ordinal preferences therefore is (in principle) answerable from revealed preference data. Note the relationship with wrongful death: distinction between ‘economic gain/losses’ and ‘pain and suffering’ In particular, our framework: does not assume the existence of a unique household utility function Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 18 / 30
Indifference scales Intuition: the appropriate question to ask is: “ How much income would an individual living alone need to attain the same indifference curve over goods that the individual attains as a member of the household? ” Note that this question: avoids issues of interpersonal comparability does not depend on the utility level assigned to an indifference curve → only depends on ordinal preferences therefore is (in principle) answerable from revealed preference data. Note the relationship with wrongful death: distinction between ‘economic gain/losses’ and ‘pain and suffering’ In particular, our framework: does not assume the existence of a unique household utility function does not require comparability of utility between individuals Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 18 / 30
Summary: assumptions and issues for ES Assumptions ES Existence of a househod utility (unitary framework) X Interpersonal comparison of utility X Restrictions on preferences X Issues Intrafamily inequality not considered X Identification: requires IB X Is IB compatible with economies of scale? X Is IB compatible with public goods? X Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 19 / 30
Summary: assumptions and issues for IS Assumptions ES IS Existence of a househod utility (unitary framework) X O Interpersonal comparison of utility X O Restrictions on preferences X O Issues Intrafamily inequality not considered X O Identification: requires IB X O Is IB compatible with economies of scale? X O Is IB compatible with public goods? X O Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 20 / 30
Conceptual Framework: Collective Model Commodities: 1 K -person household; N public goods Q = ( Q 1 , ..., Q N ) ; n private goods � � Q , q a with ∑ a q a Member a ( a = 1 , ..., K ) consumes i = q i . � Q , q 1 , ..., q K � i An allocation is a N + Kn -vector ; market prices: N -vector P , n -vector p Plus: household production Preferences: 2 egoistic U a ( Q , q a ) - but could be caring W a � , ..., U K � Q , q K �� U 1 � Q , q 1 � ordinally defined; may depend on marital status � µ 1 , ..., µ K � with ∑ a µ a = 1 Decision process: efficiency → ∃ µ = 3 such that household solves µ a u a ( Q , q a ) ( Q , q 1 ,..., q K ) ∑ max a → unitary model as a particular (and not too interesting) case Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 21 / 30
Indifference scales Definition: The equivalent expenditure is the total expenditure level y i ∗ required by i, if purchasing goods privately, to be on the same indifference curve as while living in a reference household with joint income y. Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 22 / 30
Indifference scales Definition: The equivalent expenditure is the total expenditure level y i ∗ required by i, if purchasing goods privately, to be on the same indifference curve as while living in a reference household with joint income y. In practice: Chiappori (Columbia University) Equivalence vs indifference scales Manchester, March 2015 22 / 30
Recommend
More recommend
