Measuring Intra-household Inequality KCP Project: Intra-Household - PowerPoint PPT Presentation

Cooperative Approach: the Collective Model Basic assumption: e¢ciency Translation: max U a + µ U b , where µ Pareto weight ! µ as summarizing power : Power matters In general, µ may be a function of: Incomes (and wages, prices,...) explains violations of income pooling income shocks: renegotiation versus insurance ‘Distribution factors’, including: household-speci…c characteristics (e.g. individual incomes, wealth, networks, etc.) (although exogeneity may be an issue) the environment (e.g., divorce laws: CFL 2002, Voena 2015; the marriage market; global policies;...) In particular, recovering µ Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 3 / 17

Cooperative Approach: the Collective Model Basic assumption: e¢ciency Translation: max U a + µ U b , where µ Pareto weight ! µ as summarizing power : Power matters In general, µ may be a function of: Incomes (and wages, prices,...) explains violations of income pooling income shocks: renegotiation versus insurance ‘Distribution factors’, including: household-speci…c characteristics (e.g. individual incomes, wealth, networks, etc.) (although exogeneity may be an issue) the environment (e.g., divorce laws: CFL 2002, Voena 2015; the marriage market; global policies;...) In particular, recovering µ directly addresses intra-household inequality Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 3 / 17

Cooperative Approach: the Collective Model Basic assumption: e¢ciency Translation: max U a + µ U b , where µ Pareto weight ! µ as summarizing power : Power matters In general, µ may be a function of: Incomes (and wages, prices,...) explains violations of income pooling income shocks: renegotiation versus insurance ‘Distribution factors’, including: household-speci…c characteristics (e.g. individual incomes, wealth, networks, etc.) (although exogeneity may be an issue) the environment (e.g., divorce laws: CFL 2002, Voena 2015; the marriage market; global policies;...) In particular, recovering µ directly addresses intra-household inequality leads to policies (targeting) Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 3 / 17

The Collective Model with private goods Simple translation: e¢ciency equivalent to the existence of a ’sharing rule’ ! two stage process Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 4 / 17

The Collective Model with private goods Simple translation: e¢ciency equivalent to the existence of a ’sharing rule’ ! two stage process Stage 1: individuals (cooperatively) allocate income ( ! sharing rule) Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 4 / 17

The Collective Model with private goods Simple translation: e¢ciency equivalent to the existence of a ’sharing rule’ ! two stage process Stage 1: individuals (cooperatively) allocate income ( ! sharing rule) Stage 2: individuals each choose their consumption vector under BC Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 4 / 17

The Collective Model with private goods Simple translation: e¢ciency equivalent to the existence of a ’sharing rule’ ! two stage process Stage 1: individuals (cooperatively) allocate income ( ! sharing rule) Stage 2: individuals each choose their consumption vector under BC Note that this is simply the …rst and second welfare theorems Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 4 / 17

The Collective Model with private goods Simple translation: e¢ciency equivalent to the existence of a ’sharing rule’ ! two stage process Stage 1: individuals (cooperatively) allocate income ( ! sharing rule) Stage 2: individuals each choose their consumption vector under BC Note that this is simply the …rst and second welfare theorems Sharing rule: ‘in dollars’ ! easier interpretation than a Pareto weight (which is an ordinal concept) ! but price to pay: no public good (although conditional demands)! Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 4 / 17

The Collective Model with private goods Simple translation: e¢ciency equivalent to the existence of a ’sharing rule’ ! two stage process Stage 1: individuals (cooperatively) allocate income ( ! sharing rule) Stage 2: individuals each choose their consumption vector under BC Note that this is simply the …rst and second welfare theorems Sharing rule: ‘in dollars’ ! easier interpretation than a Pareto weight (which is an ordinal concept) ! but price to pay: no public good (although conditional demands)! Identifying intra-household inequality amounts to recovering the sharing rule! Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 4 / 17

The Collective Model with private goods Simple translation: e¢ciency equivalent to the existence of a ’sharing rule’ ! two stage process Stage 1: individuals (cooperatively) allocate income ( ! sharing rule) Stage 2: individuals each choose their consumption vector under BC Note that this is simply the …rst and second welfare theorems Sharing rule: ‘in dollars’ ! easier interpretation than a Pareto weight (which is an ordinal concept) ! but price to pay: no public good (although conditional demands)! Identifying intra-household inequality amounts to recovering the sharing rule! ! Basic question: what do we need to identify the sharing rule? Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 4 / 17

The Collective Model with private goods Simple translation: e¢ciency equivalent to the existence of a ’sharing rule’ ! two stage process Stage 1: individuals (cooperatively) allocate income ( ! sharing rule) Stage 2: individuals each choose their consumption vector under BC Note that this is simply the …rst and second welfare theorems Sharing rule: ‘in dollars’ ! easier interpretation than a Pareto weight (which is an ordinal concept) ! but price to pay: no public good (although conditional demands)! Identifying intra-household inequality amounts to recovering the sharing rule! ! Basic question: what do we need to identify the sharing rule? Obviously identi…ed if all individual, private consumptions are observed Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 4 / 17

The Collective Model with private goods Simple translation: e¢ciency equivalent to the existence of a ’sharing rule’ ! two stage process Stage 1: individuals (cooperatively) allocate income ( ! sharing rule) Stage 2: individuals each choose their consumption vector under BC Note that this is simply the …rst and second welfare theorems Sharing rule: ‘in dollars’ ! easier interpretation than a Pareto weight (which is an ordinal concept) ! but price to pay: no public good (although conditional demands)! Identifying intra-household inequality amounts to recovering the sharing rule! ! Basic question: what do we need to identify the sharing rule? Obviously identi…ed if all individual, private consumptions are observed Theory shows that one observed private consumption per person is su¢cient Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 4 / 17

The Collective Model with private goods Simple translation: e¢ciency equivalent to the existence of a ’sharing rule’ ! two stage process Stage 1: individuals (cooperatively) allocate income ( ! sharing rule) Stage 2: individuals each choose their consumption vector under BC Note that this is simply the …rst and second welfare theorems Sharing rule: ‘in dollars’ ! easier interpretation than a Pareto weight (which is an ordinal concept) ! but price to pay: no public good (although conditional demands)! Identifying intra-household inequality amounts to recovering the sharing rule! ! Basic question: what do we need to identify the sharing rule? Obviously identi…ed if all individual, private consumptions are observed Theory shows that one observed private consumption per person is su¢cient Pragmatic view: ‘the more the better’ Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 4 / 17

Collective model: Testability Main message: the collective model is testable With price variations: two main approaches Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 5 / 17

Collective model: Testability Main message: the collective model is testable With price variations: two main approaches ‘Di¤erentiable’ approach: general tests Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 5 / 17

Collective model: Testability Main message: the collective model is testable With price variations: two main approaches ‘Di¤erentiable’ approach: general tests Demand function ! Slutsky matrix: SNR1 (Browning Chiappori 98) Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 5 / 17

Collective model: Testability Main message: the collective model is testable With price variations: two main approaches ‘Di¤erentiable’ approach: general tests Demand function ! Slutsky matrix: SNR1 (Browning Chiappori 98) Distribution factors proportionality Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 5 / 17

Collective model: Testability Main message: the collective model is testable With price variations: two main approaches ‘Di¤erentiable’ approach: general tests Demand function ! Slutsky matrix: SNR1 (Browning Chiappori 98) Distribution factors proportionality Links between the two Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 5 / 17

Collective model: Testability Main message: the collective model is testable With price variations: two main approaches ‘Di¤erentiable’ approach: general tests Demand function ! Slutsky matrix: SNR1 (Browning Chiappori 98) Distribution factors proportionality Links between the two Revealed preferences: general tests (L3+ complete works) Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 5 / 17

Collective model: Testability Main message: the collective model is testable With price variations: two main approaches ‘Di¤erentiable’ approach: general tests Demand function ! Slutsky matrix: SNR1 (Browning Chiappori 98) Distribution factors proportionality Links between the two Revealed preferences: general tests (L3+ complete works) Engel curves (no price variation): Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 5 / 17

Collective model: Testability Main message: the collective model is testable With price variations: two main approaches ‘Di¤erentiable’ approach: general tests Demand function ! Slutsky matrix: SNR1 (Browning Chiappori 98) Distribution factors proportionality Links between the two Revealed preferences: general tests (L3+ complete works) Engel curves (no price variation): Need 2 DF at least Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 5 / 17

Collective model: Testability Main message: the collective model is testable With price variations: two main approaches ‘Di¤erentiable’ approach: general tests Demand function ! Slutsky matrix: SNR1 (Browning Chiappori 98) Distribution factors proportionality Links between the two Revealed preferences: general tests (L3+ complete works) Engel curves (no price variation): Need 2 DF at least Then DF proportionality (or z -conditional demands) Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 5 / 17

Collective model: Testability Main message: the collective model is testable With price variations: two main approaches ‘Di¤erentiable’ approach: general tests Demand function ! Slutsky matrix: SNR1 (Browning Chiappori 98) Distribution factors proportionality Links between the two Revealed preferences: general tests (L3+ complete works) Engel curves (no price variation): Need 2 DF at least Then DF proportionality (or z -conditional demands) With private consumptions only: additional conditions Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 5 / 17

Collective model: Testability Main message: the collective model is testable With price variations: two main approaches ‘Di¤erentiable’ approach: general tests Demand function ! Slutsky matrix: SNR1 (Browning Chiappori 98) Distribution factors proportionality Links between the two Revealed preferences: general tests (L3+ complete works) Engel curves (no price variation): Need 2 DF at least Then DF proportionality (or z -conditional demands) With private consumptions only: additional conditions Labor supply (in particular when leisure is private) ! strong restrictions, with or without DF Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 5 / 17

Collective model: empirical testing Main conclusions: Unitary model generally rejected for couples, but not for singles ! Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 6 / 17

Collective model: empirical testing Main conclusions: Unitary model generally rejected for couples, but not for singles ! Interpretation: Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 6 / 17

Collective model: empirical testing Main conclusions: Unitary model generally rejected for couples, but not for singles ! Interpretation: ‘Power matters’ ... Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 6 / 17

Collective model: empirical testing Main conclusions: Unitary model generally rejected for couples, but not for singles ! Interpretation: ‘Power matters’ ... ... and powers are a¤ected by the economic environment Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 6 / 17

Collective model: empirical testing Main conclusions: Unitary model generally rejected for couples, but not for singles ! Interpretation: ‘Power matters’ ... ... and powers are a¤ected by the economic environment ! policy may aim at ‘empowering’ speci…c subpopulations ... Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 6 / 17

Collective model: empirical testing Main conclusions: Unitary model generally rejected for couples, but not for singles ! Interpretation: ‘Power matters’ ... ... and powers are a¤ected by the economic environment ! policy may aim at ‘empowering’ speci…c subpopulations ... ... and at reducing intra-household inequality Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 6 / 17

Collective model: empirical testing Main conclusions: Unitary model generally rejected for couples, but not for singles ! Interpretation: ‘Power matters’ ... ... and powers are a¤ected by the economic environment ! policy may aim at ‘empowering’ speci…c subpopulations ... ... and at reducing intra-household inequality Collective model often performs well Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 6 / 17

Collective model: empirical testing Main conclusions: Unitary model generally rejected for couples, but not for singles ! Interpretation: ‘Power matters’ ... ... and powers are a¤ected by the economic environment ! policy may aim at ‘empowering’ speci…c subpopulations ... ... and at reducing intra-household inequality Collective model often performs well for consumption (BBCL , BC , AL ,...) Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 6 / 17

Collective model: empirical testing Main conclusions: Unitary model generally rejected for couples, but not for singles ! Interpretation: ‘Power matters’ ... ... and powers are a¤ected by the economic environment ! policy may aim at ‘empowering’ speci…c subpopulations ... ... and at reducing intra-household inequality Collective model often performs well for consumption (BBCL , BC , AL ,...) for production: Udry (1996), agricultural production in Burkina Faso ! social norms may harm e¢ciency; but Rangel & Thomas (2019): not clear after controling for (unobservable) land quality Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 6 / 17

Collective model: empirical testing Main conclusions: Unitary model generally rejected for couples, but not for singles ! Interpretation: ‘Power matters’ ... ... and powers are a¤ected by the economic environment ! policy may aim at ‘empowering’ speci…c subpopulations ... ... and at reducing intra-household inequality Collective model often performs well for consumption (BBCL , BC , AL ,...) for production: Udry (1996), agricultural production in Burkina Faso ! social norms may harm e¢ciency; but Rangel & Thomas (2019): not clear after controling for (unobservable) land quality Rough estimates of ‘sharing rules’, broadly consistent across studies; therefore of intra-household elasticities, etc. Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 6 / 17

Collective model: empirical testing Main conclusions: Unitary model generally rejected for couples, but not for singles ! Interpretation: ‘Power matters’ ... ... and powers are a¤ected by the economic environment ! policy may aim at ‘empowering’ speci…c subpopulations ... ... and at reducing intra-household inequality Collective model often performs well for consumption (BBCL , BC , AL ,...) for production: Udry (1996), agricultural production in Burkina Faso ! social norms may harm e¢ciency; but Rangel & Thomas (2019): not clear after controling for (unobservable) land quality Rough estimates of ‘sharing rules’, broadly consistent across studies; therefore of intra-household elasticities, etc. Strong policy implications Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 6 / 17

Collective model: empirical testing Main conclusions: Unitary model generally rejected for couples, but not for singles ! Interpretation: ‘Power matters’ ... ... and powers are a¤ected by the economic environment ! policy may aim at ‘empowering’ speci…c subpopulations ... ... and at reducing intra-household inequality Collective model often performs well for consumption (BBCL , BC , AL ,...) for production: Udry (1996), agricultural production in Burkina Faso ! social norms may harm e¢ciency; but Rangel & Thomas (2019): not clear after controling for (unobservable) land quality Rough estimates of ‘sharing rules’, broadly consistent across studies; therefore of intra-household elasticities, etc. Strong policy implications In all cases, opens to a ‘metatheory’ of Pareto weights determination Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 6 / 17

Collective model: identi…ability from couples’ behavior only Di¤erent approaches: With price variations (CE 09) Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 7 / 17

Collective model: identi…ability from couples’ behavior only Di¤erent approaches: With price variations (CE 09) ! generic identi…ability if one exclusion restriction per person Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 7 / 17

Collective model: identi…ability from couples’ behavior only Di¤erent approaches: With price variations (CE 09) ! generic identi…ability if one exclusion restriction per person more robust if DF Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 7 / 17

Collective model: identi…ability from couples’ behavior only Di¤erent approaches: With price variations (CE 09) ! generic identi…ability if one exclusion restriction per person more robust if DF But: identi…cation ‘up to’ Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 7 / 17

Collective model: identi…ability from couples’ behavior only Di¤erent approaches: With price variations (CE 09) ! generic identi…ability if one exclusion restriction per person more robust if DF But: identi…cation ‘up to’ Revealed Preferences: bounds, which can be narrow Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 7 / 17

Collective model: identi…ability from couples’ behavior only Di¤erent approaches: With price variations (CE 09) ! generic identi…ability if one exclusion restriction per person more robust if DF But: identi…cation ‘up to’ Revealed Preferences: bounds, which can be narrow Cross-sectional data: demand as function of income (or total expenditures) and a DF Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 7 / 17

Collective model: identi…ability from couples’ behavior only Di¤erent approaches: With price variations (CE 09) ! generic identi…ability if one exclusion restriction per person more robust if DF But: identi…cation ‘up to’ Revealed Preferences: bounds, which can be narrow Cross-sectional data: demand as function of income (or total expenditures) and a DF If one exclusive (or assignable) good per person: robust identi…cation Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 7 / 17

Collective model: identi…ability from couples’ behavior only Di¤erent approaches: With price variations (CE 09) ! generic identi…ability if one exclusion restriction per person more robust if DF But: identi…cation ‘up to’ Revealed Preferences: bounds, which can be narrow Cross-sectional data: demand as function of income (or total expenditures) and a DF If one exclusive (or assignable) good per person: robust identi…cation Identi…cation obtains even without assignable goods (less robust) Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 7 / 17

Collective model: identi…ability from couples’ behavior only Di¤erent approaches: With price variations (CE 09) ! generic identi…ability if one exclusion restriction per person more robust if DF But: identi…cation ‘up to’ Revealed Preferences: bounds, which can be narrow Cross-sectional data: demand as function of income (or total expenditures) and a DF If one exclusive (or assignable) good per person: robust identi…cation Identi…cation obtains even without assignable goods (less robust) In all cases: sharing rule identi…ed up to an additive constant Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 7 / 17

Collective model: identi…ability from couples’ behavior only Di¤erent approaches: With price variations (CE 09) ! generic identi…ability if one exclusion restriction per person more robust if DF But: identi…cation ‘up to’ Revealed Preferences: bounds, which can be narrow Cross-sectional data: demand as function of income (or total expenditures) and a DF If one exclusive (or assignable) good per person: robust identi…cation Identi…cation obtains even without assignable goods (less robust) In all cases: sharing rule identi…ed up to an additive constant Note that the additive constant is welfare irrelevant (but matters for inequality) ! ‘welfare paradox’ Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 7 / 17

Collective model: identi…ability from couples’ behavior only Di¤erent approaches: With price variations (CE 09) ! generic identi…ability if one exclusion restriction per person more robust if DF But: identi…cation ‘up to’ Revealed Preferences: bounds, which can be narrow Cross-sectional data: demand as function of income (or total expenditures) and a DF If one exclusive (or assignable) good per person: robust identi…cation Identi…cation obtains even without assignable goods (less robust) In all cases: sharing rule identi…ed up to an additive constant Note that the additive constant is welfare irrelevant (but matters for inequality) ! ‘welfare paradox’ ... and could be pinned down by ‘out of sample’ global restrictions (e.g., y = 0 ) ρ = 0) Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 7 / 17

Collective model: identi…ability with additional assumptions Using singles Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 8 / 17

Collective model: identi…ability with additional assumptions Using singles Old idea (e.g. Laisney et all 2006, Myck et al. 2006): recovering ‘part of’ individual utilities from singles’ behavior Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 8 / 17

Collective model: identi…ability with additional assumptions Using singles Old idea (e.g. Laisney et all 2006, Myck et al. 2006): recovering ‘part of’ individual utilities from singles’ behavior Requires assumptions: Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 8 / 17

Collective model: identi…ability with additional assumptions Using singles Old idea (e.g. Laisney et all 2006, Myck et al. 2006): recovering ‘part of’ individual utilities from singles’ behavior Requires assumptions: selection Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 8 / 17

Collective model: identi…ability with additional assumptions Using singles Old idea (e.g. Laisney et all 2006, Myck et al. 2006): recovering ‘part of’ individual utilities from singles’ behavior Requires assumptions: selection changes in preferences after marriage, ... Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 8 / 17

Collective model: identi…ability with additional assumptions Using singles Old idea (e.g. Laisney et all 2006, Myck et al. 2006): recovering ‘part of’ individual utilities from singles’ behavior Requires assumptions: selection changes in preferences after marriage, ... More generally: comparing families with di¤erent compositions ! notion of ‘household technology’ Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 8 / 17

Collective model: identi…ability with additional assumptions Household technology (Becker): distinction between Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 9 / 17

Collective model: identi…ability with additional assumptions Household technology (Becker): distinction between commodities consumed ! vector q Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 9 / 17

Collective model: identi…ability with additional assumptions Household technology (Becker): distinction between commodities consumed ! vector q commodities purchased ! vector r Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 9 / 17

Collective model: identi…ability with additional assumptions Household technology (Becker): distinction between commodities consumed ! vector q commodities purchased ! vector r production technology: p i r i = y r = A ( q 1 + q 2 ) with ∑ i Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 9 / 17

Collective model: identi…ability with additional assumptions Household technology (Becker): distinction between commodities consumed ! vector q commodities purchased ! vector r production technology: p i r i = y r = A ( q 1 + q 2 ) with ∑ i Main intuition: preferences do not change with marriage (or with family composition); only the technology changes Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 9 / 17

Collective model: identi…ability with additional assumptions Household technology (Becker): distinction between commodities consumed ! vector q commodities purchased ! vector r production technology: p i r i = y r = A ( q 1 + q 2 ) with ∑ i Main intuition: preferences do not change with marriage (or with family composition); only the technology changes Consumption goods only and A diagonal ! Barten scales: � � r i = A ii q i 1 + q i 2 (and A ii < 1 for economies of scale)... Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 9 / 17

Collective model: identi…ability with additional assumptions Household technology (Becker): distinction between commodities consumed ! vector q commodities purchased ! vector r production technology: p i r i = y r = A ( q 1 + q 2 ) with ∑ i Main intuition: preferences do not change with marriage (or with family composition); only the technology changes Consumption goods only and A diagonal ! Barten scales: � � r i = A ii q i 1 + q i 2 (and A ii < 1 for economies of scale)... ... but with the addition of intrahousehold allocation (and inequality) ! Indi¤erence scales Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 9 / 17

Indi¤erence scales Old problem: compare income across families with di¤erent compositions; e.g., couple with income Y with a single ! which income y would the single need? Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 10 / 17

Indi¤erence scales Old problem: compare income across families with di¤erent compositions; e.g., couple with income Y with a single ! which income y would the single need? Standard solution: equivalence scale Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 10 / 17

Indi¤erence scales Old problem: compare income across families with di¤erent compositions; e.g., couple with income Y with a single ! which income y would the single need? Standard solution: equivalence scale De…nition: ‘y is such that the couple, endowed with Y , is as well o¤ as the single with y’ Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 10 / 17

Indi¤erence scales Old problem: compare income across families with di¤erent compositions; e.g., couple with income Y with a single ! which income y would the single need? Standard solution: equivalence scale De…nition: ‘y is such that the couple, endowed with Y , is as well o¤ as the single with y’ Problems with that de…nition: Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 10 / 17

Indi¤erence scales Old problem: compare income across families with di¤erent compositions; e.g., couple with income Y with a single ! which income y would the single need? Standard solution: equivalence scale De…nition: ‘y is such that the couple, endowed with Y , is as well o¤ as the single with y’ Problems with that de…nition: requires interpersonal comparison of utility Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 10 / 17

Indi¤erence scales Old problem: compare income across families with di¤erent compositions; e.g., couple with income Y with a single ! which income y would the single need? Standard solution: equivalence scale De…nition: ‘y is such that the couple, endowed with Y , is as well o¤ as the single with y’ Problems with that de…nition: requires interpersonal comparison of utility (worse) requires comparing utility of single with that of couple Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 10 / 17

Indi¤erence scales Old problem: compare income across families with di¤erent compositions; e.g., couple with income Y with a single ! which income y would the single need? Standard solution: equivalence scale De…nition: ‘y is such that the couple, endowed with Y , is as well o¤ as the single with y’ Problems with that de…nition: requires interpersonal comparison of utility (worse) requires comparing utility of single with that of couple (even worse) requires the notion of ‘utility of a couple’ Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 10 / 17

Indi¤erence scales Old problem: compare income across families with di¤erent compositions; e.g., couple with income Y with a single ! which income y would the single need? Standard solution: equivalence scale De…nition: ‘y is such that the couple, endowed with Y , is as well o¤ as the single with y’ Problems with that de…nition: requires interpersonal comparison of utility (worse) requires comparing utility of single with that of couple (even worse) requires the notion of ‘utility of a couple’ (worst of all) not identi…ed in a deep sense (Blundell - Lewbel) Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 10 / 17

Indi¤erence scales (cont.) New notion: indi¤erence scale ! question: ‘y is such that the person, when single , is as well o¤ as she was when married’ Note that: No interpersonal comparison (compare utility of the same person in di¤erent situations) ... ... although requires utility to be comparable across marital status No ’utility of the couple’ - instead, utility of each spouse Moreover, (non parametrically) identi…ed ! revival of household technology! Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 11 / 17

Indi¤erence scales (cont.) In practice: Couple: new prices (Barten!) π = A 0 p and sharing rule ( ρ 1 , ρ 2 ) ; i solves max U i ( q i ) π 0 q i = ρ i ! indirect utility V i ( π , ρ i ) Single: max U i ( q i ) p 0 q i = y i ! indirect utility V i ( p , y i ) , estimated from singles’ demand IS based on ¯ y i such that V i ( π , ρ i ) = V i ( p , ¯ y i ) Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 12 / 17

Indi¤erence scales: identi…cation Browning-Chiappori-Lewbel (2013) ! Main result: exact identi…cation Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 13 / 17

Indi¤erence scales: identi…cation Browning-Chiappori-Lewbel (2013) ! Main result: exact identi…cation But requires: Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 13 / 17

Indi¤erence scales: identi…cation Browning-Chiappori-Lewbel (2013) ! Main result: exact identi…cation But requires: singles’s demand observable ( ! problematic for children!) Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 13 / 17

Indi¤erence scales: identi…cation Browning-Chiappori-Lewbel (2013) ! Main result: exact identi…cation But requires: singles’s demand observable ( ! problematic for children!) price variations + complex estimation techniques Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 13 / 17

Indi¤erence scales: identi…cation Browning-Chiappori-Lewbel (2013) ! Main result: exact identi…cation But requires: singles’s demand observable ( ! problematic for children!) price variations + complex estimation techniques Simpler version: Dunbar-Lewbel-Pendakur (2011), Bargain-Donni (2012) Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 13 / 17

Indi¤erence scales: identi…cation Browning-Chiappori-Lewbel (2013) ! Main result: exact identi…cation But requires: singles’s demand observable ( ! problematic for children!) price variations + complex estimation techniques Simpler version: Dunbar-Lewbel-Pendakur (2011), Bargain-Donni (2012) Basic assumption: ‘ scale invariance ’ (sharing rule proportional to income) ... Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 13 / 17

Indi¤erence scales: identi…cation Browning-Chiappori-Lewbel (2013) ! Main result: exact identi…cation But requires: singles’s demand observable ( ! problematic for children!) price variations + complex estimation techniques Simpler version: Dunbar-Lewbel-Pendakur (2011), Bargain-Donni (2012) Basic assumption: ‘ scale invariance ’ (sharing rule proportional to income) ... ... and a milder restrictions (parents’ preferences independent of the # of children) Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 13 / 17

Indi¤erence scales: identi…cation Browning-Chiappori-Lewbel (2013) ! Main result: exact identi…cation But requires: singles’s demand observable ( ! problematic for children!) price variations + complex estimation techniques Simpler version: Dunbar-Lewbel-Pendakur (2011), Bargain-Donni (2012) Basic assumption: ‘ scale invariance ’ (sharing rule proportional to income) ... ... and a milder restrictions (parents’ preferences independent of the # of children) Then simple and robust identi…cation (from Engel curves) ... Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 13 / 17

Indi¤erence scales: identi…cation Browning-Chiappori-Lewbel (2013) ! Main result: exact identi…cation But requires: singles’s demand observable ( ! problematic for children!) price variations + complex estimation techniques Simpler version: Dunbar-Lewbel-Pendakur (2011), Bargain-Donni (2012) Basic assumption: ‘ scale invariance ’ (sharing rule proportional to income) ... ... and a milder restrictions (parents’ preferences independent of the # of children) Then simple and robust identi…cation (from Engel curves) ... ... even for children, despite no observable demand Chiappori (Columbia University) Measuring Intra-household Inequality World Bank HQ, Nov. 2019 13 / 17