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Royal Economic Society

Royal Economic Society

Royal Economic Society

The RES Prize

Presented by Morton Ravn

Royal Economic Society

The RES Prize Michele PELLIZZARI and Giacomo DE GIORGIO

Royal Economic Society

Royal Economic Society

The Hahn Lecture Pierre-André Chiappori

Equivalence Scales versus Indifference Scales Chair: Sir Richard Blundell

Royal Economic Society

Royal Economic Society

Equivalence scales versus indifference scales

Franck Hahn Lecture Royal Economic Society Conference 2015 Pierre-André Chiappori

Columbia University

Manchester, March 2015

Introduction: Equivalence scales (ES)

What are they used for?

Basic goal: define income thresholds for families of different compositions. Applications: Poverty

Introduction: Equivalence scales (ES)

What are they used for?

Basic goal: define income thresholds for families of different compositions. Applications: Poverty

‘A four-person family with two adults and two children is poor with annual cash income below $24,000’ (US Census Bureau, 2014)

Introduction: Equivalence scales (ES)

What are they used for?

Basic goal: define income thresholds for families of different compositions. Applications: Poverty

‘A four-person family with two adults and two children is poor with annual cash income below $24,000’ (US Census Bureau, 2014) → what about couples without children? Single parents with one child? ...

Introduction: Equivalence scales (ES)

What are they used for?

Basic goal: define income thresholds for families of different compositions. Applications: Poverty

‘A four-person family with two adults and two children is poor with annual cash income below $24,000’ (US Census Bureau, 2014) → what about couples without children? Single parents with one child? ...

Means-tested benefits

Introduction: Equivalence scales (ES)

What are they used for?

Basic goal: define income thresholds for families of different compositions. Applications: Poverty

‘A four-person family with two adults and two children is poor with annual cash income below $24,000’ (US Census Bureau, 2014) → what about couples without children? Single parents with one child? ...

Means-tested benefits Inequality

Introduction: Equivalence scales (ES)

What are they used for?

Basic goal: define income thresholds for families of different compositions. Applications: Poverty

‘A four-person family with two adults and two children is poor with annual cash income below $24,000’ (US Census Bureau, 2014) → what about couples without children? Single parents with one child? ...

Means-tested benefits Inequality

Usually measured across households (which raises some problems)

Introduction: Equivalence scales (ES)

What are they used for?

Basic goal: define income thresholds for families of different compositions. Applications: Poverty

‘A four-person family with two adults and two children is poor with annual cash income below $24,000’ (US Census Bureau, 2014) → what about couples without children? Single parents with one child? ...

Means-tested benefits Inequality

Usually measured across households (which raises some problems) How do we compare households with different compositions?

Introduction: Equivalence scales (ES)

What are they used for?

Basic goal: define income thresholds for families of different compositions. Applications: Poverty

‘A four-person family with two adults and two children is poor with annual cash income below $24,000’ (US Census Bureau, 2014) → what about couples without children? Single parents with one child? ...

Means-tested benefits Inequality

Usually measured across households (which raises some problems) How do we compare households with different compositions?

Compensation for wrongful death (Lewbel 2003)

Introduction: Equivalence scales (ES)

What are they used for?

Basic goal: define income thresholds for families of different compositions. Applications: Poverty

‘A four-person family with two adults and two children is poor with annual cash income below $24,000’ (US Census Bureau, 2014) → what about couples without children? Single parents with one child? ...

Means-tested benefits Inequality

Usually measured across households (which raises some problems) How do we compare households with different compositions?

Compensation for wrongful death (Lewbel 2003) → ES widely used - but their theoretical foundations are weak!

Introduction: Equivalence scales (ES)

Definition

Principle: ‘Income needed for a family with given composition to be "as well

• ff" as some reference family’

Introduction: Equivalence scales (ES)

Definition

Principle: ‘Income needed for a family with given composition to be "as well

• ff" as some reference family’

In practice (US Census Bureau, 2014):

Introduction: Equivalence scales (ES)

Definition

Principle: ‘Income needed for a family with given composition to be "as well

• ff" as some reference family’

In practice (US Census Bureau, 2014):

Single, no child: poverty threshold at $12,316

Introduction: Equivalence scales (ES)

Definition

Principle: ‘Income needed for a family with given composition to be "as well

• ff" as some reference family’

In practice (US Census Bureau, 2014):

Single, no child: poverty threshold at $12,316 Couple, no child: $15,853

Introduction: Equivalence scales (ES)

Definition

Principle: ‘Income needed for a family with given composition to be "as well

• ff" 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

Introduction: Equivalence scales (ES)

Definition

Principle: ‘Income needed for a family with given composition to be "as well

• ff" 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

Introduction: Equivalence scales (ES)

Definition

Principle: ‘Income needed for a family with given composition to be "as well

• ff" 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

Introduction: Equivalence scales (ES)

Definition

Principle: ‘Income needed for a family with given composition to be "as well

• ff" 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

Introduction: Equivalence scales (ES)

Definition

Principle: ‘Income needed for a family with given composition to be "as well

• ff" 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)

Introduction: Equivalence scales (ES)

Definition

Principle: ‘Income needed for a family with given composition to be "as well

• ff" 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

Introduction: Equivalence scales (ES)

Definition

Principle: ‘Income needed for a family with given composition to be "as well

• ff" 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.

Introduction: Equivalence scales (ES)

Implementation

Two main approaches

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)

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’

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)

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

• f a nutritionally adequate diet,

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

• f a nutritionally adequate diet,

then uses Engel scales to extend to households of different compositions

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

• f a nutritionally adequate diet,

then uses Engel scales to extend to households of different compositions adjusts by the consumer price index.

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

• f 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

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

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

Introduction: Equivalence scales (ES)

Problems with ES

ES raises specific issues at various levels: conceptual, normative, empirical Conceptual issues:

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

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):

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):

Samuelson’s welfare index W

• U1, ..., Un

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):

Samuelson’s welfare index W

• U1, ..., Un

Even min

• U1, ..., Un → ‘all agents have the same utility’

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):

Samuelson’s welfare index W

• U1, ..., Un

Even min

• U1, ..., Un → ‘all agents have the same utility’

Note, however, that this assumption is unsupported and even undefined

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):

Samuelson’s welfare index W

• U1, ..., Un

Even min

• U1, ..., Un → ‘all agents have the same utility’

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)

Introduction: Equivalence scales (ES)

Problems with ES (cont.)

Empirical problems

Introduction: Equivalence scales (ES)

Problems with ES (cont.)

Empirical problems

Serious identification problems (Blundell Lewbel 1991). Basically:

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

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

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)

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)

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

• f the ‘reduced-form’ vision: the nature of the gains (economies of

scale, public goods,..), which are not explicitly modelled, may contradict the required properties.

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

• f 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?

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)

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) ∂u = 0 ⇒ e (p, u, a) = φ (p, a) ¯ e (p, u) ⇒ V (p, y, a) = ¯ V

• p,

y φ (p, a)

• Chiappori

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) ∂u = 0 ⇒ e (p, u, a) = φ (p, a) ¯ e (p, u) ⇒ V (p, y, a) = ¯ V

• p,

y φ (p, a)

• Problem: is it compatible with economies of scale, public goods,...?

Economies of scale

Basic idea: ‘Consumption technology’ → relationship between commodities consumed, xi

k, and commodities purchased, zk:

z = F

• ∑

i

xi

• Chiappori

Economies of scale

Basic idea: ‘Consumption technology’ → relationship between commodities consumed, xi

k, and commodities purchased, zk:

z = F

• ∑

i

xi

• In practice, affine (Gorman 76):

z = Λ · ∑

i

xi − ∆

Economies of scale

Basic idea: ‘Consumption technology’ → relationship between commodities consumed, xi

k, and commodities purchased, zk:

z = F

• ∑

i

xi

• In practice, affine (Gorman 76):

z = Λ · ∑

i

xi − ∆ ... and moreover Λ diagonal (‘Barten scales’): zk = λk ∑

i

xi

k − δk

Economies of scale

Basic idea: ‘Consumption technology’ → relationship between commodities consumed, xi

k, and commodities purchased, zk:

z = F

• ∑

i

xi

• In practice, affine (Gorman 76):

z = Λ · ∑

i

xi − ∆ ... and moreover Λ diagonal (‘Barten scales’): zk = λk ∑

i

xi

k − δk

GE perspective → impact on prices: p replaced with π, where: πk = λkpk 1 + 1

y ∑j δjpj

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

• f scale?

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

• f scale?

Translation: can it be the case that V (π, y, a) = ¯ V

• p,

y φ (p, a)

• for all (p, y) ?

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

• f scale?

Translation: can it be the case that V (π, y, a) = ¯ V

• p,

y φ (p, a)

• for all (p, y) ?

Answer: No in general (need δj = 0 ∀j, λk = λ ∀k)

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

• f scale?

Translation: can it be the case that V (π, y, a) = ¯ V

• p,

y φ (p, a)

• for all (p, y) ?

Answer: No in general (need δj = 0 ∀j, λk = λ ∀k) Plus: what about public goods?

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

• f scale?

Translation: can it be the case that V (π, y, a) = ¯ V

• p,

y φ (p, a)

• for all (p, y) ?

Answer: No in general (need δj = 0 ∀j, λk = λ ∀k) Plus: what about public goods?

Same issue: shifting from singles to couples (or changing family size) impact (Lindahl) prices ...

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

• f scale?

Translation: can it be the case that V (π, y, a) = ¯ V

• p,

y φ (p, a)

• for all (p, y) ?

Answer: No in general (need δj = 0 ∀j, λk = 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!

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

Normative issues

Notions of compensating variation:

Normative issues

Notions of compensating variation:

Reform that changes the price vector from p to p.

Normative issues

Notions of compensating variation:

Reform that changes the price vector from p to p. Single agent, initial income x: CV = e

• p, v (p, x)

− x

Normative issues

Notions of compensating variation:

Reform that changes the price vector from p to p. Single agent, initial income x: CV = e

• p, v (p, x)

− x

Two different notions (Chiappori 2005, Chiappori Meghir 2014):

Normative issues

Notions of compensating variation:

Reform that changes the price vector from p to p. Single agent, initial income x: CV = e

• p, v (p, x)

− x

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

Normative issues

Notions of compensating variation:

Reform that changes the price vector from p to p. Single agent, initial income x: CV = e

• p, v (p, x)

− x

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

• ptimal intrahousehold allocations

→ what if some members are well-off and others are miserable?

Uw Uh Pareto frontier: initial

Uw Uh Pareto frontier: initial

Uw Uh Pareto frontier: post reform, pre compensation

Uw Uh Pareto frontier: potentially compensating variation

Uw Uh Pareto frontier: potentially compensating variation

Uw Uh 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

‘Indifference scales’

Hahn’s legacy: Theory should be taken seriously

‘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

‘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

‘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,...

‘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

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?”

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:

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

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

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.

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’

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:

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

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

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

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

Conceptual Framework: Collective Model

Commodities:

K-person household; N public goods Q = (Q1, ..., QN ) ; n private goods Member a (a = 1, ..., K) consumes

• Q, qa

i

• with ∑a qa

i = qi.

An allocation is a N + Kn-vector

• Q, q1, ..., qK

; market prices: N-vector P, n-vector p Plus: household production

Preferences:

egoistic Ua (Q, qa)- but could be caring W a U1 Q, q1 , ..., UK Q, qK

• rdinally defined; may depend on marital status

Decision process: efficiency → ∃ µ =

• µ1, ..., µK

with ∑a µa = 1 such that household solves max

(Q,q1,...,qK )∑ a

µaua (Q, qa) → unitary model as a particular (and not too interesting) case

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.

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:

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:

Consider the Indifference Curve of person i in a given household

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:

Consider the Indifference Curve of person i in a given household Let ui denote the utility corresponding to that IC if i was single

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:

Consider the Indifference Curve of person i in a given household Let ui denote the utility corresponding to that IC if i was single Define y∗i = ei p, P, ui

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:

Consider the Indifference Curve of person i in a given household Let ui denote the utility corresponding to that IC if i was single Define y∗i = ei p, P, ui Individual i’s "indifference scale" is Si = yi∗/y

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:

Consider the Indifference Curve of person i in a given household Let ui denote the utility corresponding to that IC if i was single Define y∗i = ei p, P, ui Individual i’s "indifference scale" is Si = yi∗/y

Note that Si depends on technology and intrahousehold allocation

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:

Consider the Indifference Curve of person i in a given household Let ui denote the utility corresponding to that IC if i was single Define y∗i = ei p, P, ui Individual i’s "indifference scale" is Si = yi∗/y

Note that Si depends on technology and intrahousehold allocation Basic question: identifiability?

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

Private goods only: theory

Assume all goods are private, then: Efficiency equivalent to the existence of a sharing rule: ρ =

• ρ1, ..., ρK

with ∑k ρk = y, such that xk solves max uk xk s.t. ∑

i

pkxi

k = ρi

Private goods only: theory

Assume all goods are private, then: Efficiency equivalent to the existence of a sharing rule: ρ =

• ρ1, ..., ρK

with ∑k ρk = y, such that xk solves max uk xk s.t. ∑

i

pkxi

k = ρi

The sharing rule fully describes intrahousehold allocation of welfare

Private goods only: theory

Assume all goods are private, then: Efficiency equivalent to the existence of a sharing rule: ρ =

• ρ1, ..., ρK

with ∑k ρk = y, such that xk solves max uk xk s.t. ∑

i

pkxi

k = ρi

The sharing rule fully describes intrahousehold allocation of welfare With domestic production, xk solves max uk xk s.t. ∑

i

πkxi

k = ρi

Private goods only: identification

1. Without domestic production/technology:

Private goods only: identification

1. Without domestic production/technology:

Need one exclusion restriction per agent

Private goods only: identification

1. Without domestic production/technology:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive prices

Private goods only: identification

1. Without domestic production/technology:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive prices Global restrictions → bounds (L4, 14) and sometimes full identification

Private goods only: identification

1. Without domestic production/technology:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive prices Global restrictions → bounds (L4, 14) and sometimes full identification

2. With domestic production/technology: use singles

Private goods only: identification

1. Without domestic production/technology:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive prices Global restrictions → bounds (L4, 14) and sometimes full identification

2. With domestic production/technology: use singles

Old idea (→ ex: labor supply: Bargain et al 2006, Lise and Seitz 2011)

Private goods only: identification

1. Without domestic production/technology:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive prices Global restrictions → bounds (L4, 14) and sometimes full identification

2. With domestic production/technology: use singles

Old idea (→ ex: labor supply: Bargain et al 2006, Lise and Seitz 2011) With intrahousehold production function (Browning, Chiappori, Lewbel 2013):

Private goods only: identification

1. Without domestic production/technology:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive prices Global restrictions → bounds (L4, 14) and sometimes full identification

2. With domestic production/technology: use singles

Old idea (→ ex: labor supply: Bargain et al 2006, Lise and Seitz 2011) With intrahousehold production function (Browning, Chiappori, Lewbel 2013):

Basic insight: same preferences when single or married, but different production technology

Private goods only: identification

1. Without domestic production/technology:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive prices Global restrictions → bounds (L4, 14) and sometimes full identification

2. With domestic production/technology: use singles

Old idea (→ ex: labor supply: Bargain et al 2006, Lise and Seitz 2011) With intrahousehold production function (Browning, Chiappori, Lewbel 2013):

Basic insight: same preferences when single or married, but different production technology In practice: consumes x, buys z = F (x) → in particular, internal prices!

Private goods only: identification

1. Without domestic production/technology:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive prices Global restrictions → bounds (L4, 14) and sometimes full identification

2. With domestic production/technology: use singles

Old idea (→ ex: labor supply: Bargain et al 2006, Lise and Seitz 2011) With intrahousehold production function (Browning, Chiappori, Lewbel 2013):

Basic insight: same preferences when single or married, but different production technology In practice: consumes x, buys z = F (x) → in particular, internal prices! Basic result: generic identification

Private goods only: identification

1. Without domestic production/technology:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive prices Global restrictions → bounds (L4, 14) and sometimes full identification

2. With domestic production/technology: use singles

Old idea (→ ex: labor supply: Bargain et al 2006, Lise and Seitz 2011) With intrahousehold production function (Browning, Chiappori, Lewbel 2013):

Basic insight: same preferences when single or married, but different production technology In practice: consumes x, buys z = F (x) → in particular, internal prices! Basic result: generic identification

But requires:

Private goods only: identification

1. Without domestic production/technology:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive prices Global restrictions → bounds (L4, 14) and sometimes full identification

2. With domestic production/technology: use singles

Old idea (→ ex: labor supply: Bargain et al 2006, Lise and Seitz 2011) With intrahousehold production function (Browning, Chiappori, Lewbel 2013):

Basic insight: same preferences when single or married, but different production technology In practice: consumes x, buys z = F (x) → in particular, internal prices! Basic result: generic identification

But requires:

price variations

Private goods only: identification

1. Without domestic production/technology:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive prices Global restrictions → bounds (L4, 14) and sometimes full identification

2. With domestic production/technology: use singles

Old idea (→ ex: labor supply: Bargain et al 2006, Lise and Seitz 2011) With intrahousehold production function (Browning, Chiappori, Lewbel 2013):

Basic insight: same preferences when single or married, but different production technology In practice: consumes x, buys z = F (x) → in particular, internal prices! Basic result: generic identification

But requires:

price variations

• bservation of singles

Private goods only: identification

1. Without domestic production/technology:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive prices Global restrictions → bounds (L4, 14) and sometimes full identification

2. With domestic production/technology: use singles

Old idea (→ ex: labor supply: Bargain et al 2006, Lise and Seitz 2011) With intrahousehold production function (Browning, Chiappori, Lewbel 2013):

Basic insight: same preferences when single or married, but different production technology In practice: consumes x, buys z = F (x) → in particular, internal prices! Basic result: generic identification

But requires:

price variations

• bservation of singles

plus: selection bias, etc.

Identification: private goods only (cont.)

3. Recent developments: Scale independent production functions (Dunbar Lewbel Pendakur 2013)

Identification: private goods only (cont.)

3. Recent developments: Scale independent production functions (Dunbar Lewbel Pendakur 2013)

Insight: relax the previous assumptions → replaced with:

Identification: private goods only (cont.)

3. Recent developments: Scale independent production functions (Dunbar Lewbel Pendakur 2013)

Insight: relax the previous assumptions → replaced with:

Preference restrictions: adults’ MRS between goods does not depend on number of children

Identification: private goods only (cont.)

3. Recent developments: Scale independent production functions (Dunbar Lewbel Pendakur 2013)

Insight: relax the previous assumptions → replaced with:

Preference restrictions: adults’ MRS between goods does not depend on number of children Scale independence: the fraction of expenditures going to each member independent of income, at least for low income levels

Identification: private goods only (cont.)

3. Recent developments: Scale independent production functions (Dunbar Lewbel Pendakur 2013)

Insight: relax the previous assumptions → replaced with:

Preference restrictions: adults’ MRS between goods does not depend on number of children Scale independence: the fraction of expenditures going to each member independent of income, at least for low income levels

Outcome: identification of economies of scale and the sharing rule

Identification: private goods only (cont.)

3. Recent developments: Scale independent production functions (Dunbar Lewbel Pendakur 2013)

Insight: relax the previous assumptions → replaced with:

Preference restrictions: adults’ MRS between goods does not depend on number of children Scale independence: the fraction of expenditures going to each member independent of income, at least for low income levels

Outcome: identification of economies of scale and the sharing rule

4. Also, if assignable good and distribution factor: no preference restriction (Lewbel, Pendakur 2014)

Example: Dunbar Lewbel Pendakur 2013

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

Public and private goods: identification

Without domestic production:

Public and private goods: identification

Without domestic production:

Need one exclusion restriction per agent

Public and private goods: identification

Without domestic production:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive private prices (Chiappori-Ekeland 2009; L4 2014)

Public and private goods: identification

Without domestic production:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive private prices (Chiappori-Ekeland 2009; L4 2014) Welfare-relevant concepts identified

Public and private goods: identification

Without domestic production:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive private prices (Chiappori-Ekeland 2009; L4 2014) Welfare-relevant concepts identified

With domestic production and economies of scale for private goods:

Public and private goods: identification

Without domestic production:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive private prices (Chiappori-Ekeland 2009; L4 2014) Welfare-relevant concepts identified

With domestic production and economies of scale for private goods:

Open problem...

Public and private goods: identification

Without domestic production:

Need one exclusion restriction per agent Then model locally identified up to an additive function of non exclusive private prices (Chiappori-Ekeland 2009; L4 2014) Welfare-relevant concepts identified

With domestic production and economies of scale for private goods:

Open problem... ... but encouraging results

Conclusion

Need a tool to scale income between households of different compositions

Conclusion

Need a tool to scale income between households of different compositions

Equivalence scales: comparing welfare across individuals (and even accross households)

Conclusion

Need a tool to scale income between households of different compositions

Equivalence scales: comparing welfare across individuals (and even accross households)

weak theoretical foundations

Conclusion

Need a tool to scale income between households of different compositions

Equivalence scales: comparing welfare across individuals (and even accross households)

weak theoretical foundations unsatisfactory, ‘reduced form’ logic

Conclusion

Need a tool to scale income between households of different compositions

Equivalence scales: comparing welfare across individuals (and even accross households)

weak theoretical foundations unsatisfactory, ‘reduced form’ logic serious identification problem

Conclusion

Need a tool to scale income between households of different compositions

Equivalence scales: comparing welfare across individuals (and even accross households)

weak theoretical foundations unsatisfactory, ‘reduced form’ logic serious identification problem We believe these issues are closely related

Conclusion

Need a tool to scale income between households of different compositions

Equivalence scales: comparing welfare across individuals (and even accross households)

weak theoretical foundations unsatisfactory, ‘reduced form’ logic serious identification problem We believe these issues are closely related

Indifference scales: comparing a person’s welfare in different situations

Conclusion

Need a tool to scale income between households of different compositions

Equivalence scales: comparing welfare across individuals (and even accross households)

weak theoretical foundations unsatisfactory, ‘reduced form’ logic serious identification problem We believe these issues are closely related

Indifference scales: comparing a person’s welfare in different situations

much sounder foundations

Conclusion

Need a tool to scale income between households of different compositions

Equivalence scales: comparing welfare across individuals (and even accross households)

weak theoretical foundations unsatisfactory, ‘reduced form’ logic serious identification problem We believe these issues are closely related

Indifference scales: comparing a person’s welfare in different situations

much sounder foundations theory readily available (collective model)

Conclusion

Need a tool to scale income between households of different compositions

Equivalence scales: comparing welfare across individuals (and even accross households)

weak theoretical foundations unsatisfactory, ‘reduced form’ logic serious identification problem We believe these issues are closely related

Indifference scales: comparing a person’s welfare in different situations

much sounder foundations theory readily available (collective model) strong identification results

Conclusion

Need a tool to scale income between households of different compositions

Equivalence scales: comparing welfare across individuals (and even accross households)

weak theoretical foundations unsatisfactory, ‘reduced form’ logic serious identification problem We believe these issues are closely related

Indifference scales: comparing a person’s welfare in different situations

much sounder foundations theory readily available (collective model) strong identification results work in progress

Conclusion

Need a tool to scale income between households of different compositions

Equivalence scales: comparing welfare across individuals (and even accross households)

weak theoretical foundations unsatisfactory, ‘reduced form’ logic serious identification problem We believe these issues are closely related

Indifference scales: comparing a person’s welfare in different situations

much sounder foundations theory readily available (collective model) strong identification results work in progress

In any case, complex welfare issues are unavoidable ... but should be considered upfront!

Royal Economic Society