Measuring individual poverty with OLS and off-the-shelf household - PowerPoint PPT Presentation

Measuring individual poverty with OLS and off-the-shelf household budget surveys Valérie Lechene UCL and IFS , Krishna Pendakur SFU , Alex Wolf IFS KCP Project: Intra-Household Allocation of and Gender Differences in Consumption Poverty, with Theophiline Bose-Ducker, Isis Gaddis and Talip Kilic - Dissemination Workshop Nov 5. 2019, World Bank HQ, Washington DC

What we do and why: We develop a method to measure the share of household consumption that go to each individual in a household. Individual resource shares are not directly observable The method is simple, theory consistent, easy to implement. Poverty is experienced at the individual level, as there might exist inequality within households. Any interest in poverty requires its measurement. Effective and cost effective policy designed to alleviate poverty should target individuals.

Dream data Table 1a: Dream Data Man Woman Child Total Food 400 300 200 900 Clothing 50 75 25 150 Shelter 200 200 200 600 Transport 125 63 63 250 Other 45 37 37 120 Total 820 675 525 2020 As a share of the household total expenditure, the amounts in green are resource shares. Poverty line: $1.90 per day, ie $694 per year per person. The woman and the child are poor but the man is not. Dream data: Cherchye, Demuynck, De Rock and Vermeulen (2017); Brown, Ravallion and van de Walle (2019); Bargain, Lacroix and Tiberti (2019)

Dream data Table 1a: Dream Data Man Woman Child Total Food 400 300 200 900 Clothing 50 75 25 150 Shelter 200 200 200 600 Transport 125 63 63 250 Other 45 37 37 120 Total 820 675 525 2020 As a share of the household total expenditure, the amounts in green are resource shares. Poverty line: $1.90 per day, ie $694 per year per person. The woman and the child are poor but the man is not. Dream data: Cherchye, Demuynck, De Rock and Vermeulen (2017); Brown, Ravallion and van de Walle (2019); Bargain, Lacroix and Tiberti (2019)

Dream data Table 1a: Dream Data Man Woman Child Total Food 400 300 200 900 Clothing 50 75 25 150 Shelter 200 200 200 600 Transport 125 63 63 250 Other 45 37 37 120 Total 820 675 525 2020 As a share of the household total expenditure, the amounts in green are resource shares. Poverty line: $1.90 per day, ie $694 per year per person. The woman and the child are poor but the man is not. Dream data: Cherchye, Demuynck, De Rock and Vermeulen (2017); Brown, Ravallion and van de Walle (2019); Bargain, Lacroix and Tiberti (2019)

Dream data Table 1a: Dream Data Man Woman Child Total Food 400 300 200 900 Clothing 50 75 25 150 Shelter 200 200 200 600 Transport 125 63 63 250 Other 45 37 37 120 Total 820 675 525 2020 As a share of the household total expenditure, the amounts in green are resource shares. Poverty line: $1.90 per day, ie $694 per year per person. The woman and the child are poor but the man is not. Dream data: Cherchye, Demuynck, De Rock and Vermeulen (2017); Brown, Ravallion and van de Walle (2019); Bargain, Lacroix and Tiberti (2019)

Real Data Real Data Man Woman Child Total Food 900 Clothing 50 75 25 150 Shelter 600 Transport 250 Other 120 Total 2020 Poverty line: still $1.90 per person per day, or $694 per person per year, or $2080 for this household per year. The household is poor, hence we conclude that all members of the household are poor.

Real Data Real Data Man Woman Child Total Food 900 Clothing 50 75 25 150 Shelter 600 Transport 250 Other 120 Total 2020 Poverty line: still $1.90 per person per day, or $694 per person per year, or $2080 for this household per year. The household is poor, hence we conclude that all members of the household are poor.

Real Data Real Data Man Woman Child Total Food 900 Clothing 50 75 25 150 Shelter 600 Transport 250 Other 120 Total 2020 Poverty line: still $1.90 per person per day, or $694 per person per year, or $2080 for this household per year. The household is poor, hence we conclude that all members of the household are poor.

Dream data vs real data Real Data Man Woman Child Total Food 400 300 200 900 Clothing 50 75 25 150 Shelter 200 200 200 600 Transport 125 63 63 250 Other 45 37 37 120 Total 820 675 525 2020 With the same poverty line: With dream data, we observe that there is intra-household inequality, and we conclude that the woman and the child are poor, while the man is not poor. With real data, we assume that there is no intra-household inequality, and we conclude that the man, the woman and the child are poor. With real data, we need to fill in the blanks with a model.

What has been done before In practice: ◮ Measure consumption at the household level, divide by the number of household members and compare against a per-capita poverty line (1.90$ per person per day) In theory: ◮ Chiappori (1988, 1991, ...) Collective model ◮ Browning, Chiappori and Lewbel (BCL, 2013) ◮ Dunbar, Lewbel and Pendakur (DLP, 2013) Practice very far from theoretical results: ◮ BCL is demanding in terms of data and hard to implement. ◮ DLP tried to make it easier in both dimensions, but still not trivial to estimate.

What we do We develop a linear method, L-DLP, to estimate individual resource shares as in DLP: ◮ Theory consistent ◮ Allows for multiple men and women ◮ Recover structural parameters from OLS estimation We develop a pre-test to check whether the methods will work. We implement our method on the LSMS data. We find that there is gender inequality inside households in some places.

Notations and definitions (BCL) h = 1 ,..., H households, containing individuals of types t . A household consists of N t h individuals of each type t ; let N h = ∑ t N t h y h denotes the observed household budget. Market price vector p , shadow price vector Ap where diagonal A ≤ 1. A characterises scale economies . We allow for them, but don’t estimate them. Efficient collective households: collections of people (with utility functions) living together, who reach the Pareto frontier. Decentralisation : The household problem reduces to a set of individual problems. ◮ It is as if each type gets a shadow budget ; denoted � y t h , spent at prices Ap . ◮ The household purchases enough to satisfy everyone. Resource share , denoted η t h , is the fraction of the household budget going to type t . ◮ ∑ t η t h = 1. ◮ a type’s shadow budget is � y t h = η t h y h ; a person’s shadow budget is η t h y h / N t h .

Notations and definitions (BCL) h = 1 ,..., H households, containing individuals of types t . A household consists of N t h individuals of each type t ; let N h = ∑ t N t h y h denotes the observed household budget. Market price vector p , shadow price vector Ap where diagonal A ≤ 1. A characterises scale economies . We allow for them, but don’t estimate them. Efficient collective households: collections of people (with utility functions) living together, who reach the Pareto frontier. Decentralisation : The household problem reduces to a set of individual problems. ◮ It is as if each type gets a shadow budget ; denoted � y t h , spent at prices Ap . ◮ The household purchases enough to satisfy everyone. Resource share , denoted η t h , is the fraction of the household budget going to type t . ◮ ∑ t η t h = 1. ◮ a type’s shadow budget is � y t h = η t h y h ; a person’s shadow budget is η t h y h / N t h .

Notations and definitions (BCL) h = 1 ,..., H households, containing individuals of types t . A household consists of N t h individuals of each type t ; let N h = ∑ t N t h y h denotes the observed household budget. Market price vector p , shadow price vector Ap where diagonal A ≤ 1. A characterises scale economies . We allow for them, but don’t estimate them. Efficient collective households: collections of people (with utility functions) living together, who reach the Pareto frontier. Decentralisation : The household problem reduces to a set of individual problems. ◮ It is as if each type gets a shadow budget ; denoted � y t h , spent at prices Ap . ◮ The household purchases enough to satisfy everyone. Resource share , denoted η t h , is the fraction of the household budget going to type t . ◮ ∑ t η t h = 1. ◮ a type’s shadow budget is � y t h = η t h y h ; a person’s shadow budget is η t h y h / N t h .

Assignable goods Assignable goods : Private goods consumed only by one type of individual in the household. E.g., clothing. W t ( y ) denotes the observed household Engel curve function for type t ’s assignable good: the fraction of household expenditure commanded by that good at prices p and household budget y . w t ( � y t ) denotes the unobserved individual Engel curve function for type t : the fraction of expenditure commanded by the assignable good y t . for type t at shadow prices Ap and shadow budget � Key to identification in BCL and DLP and here: The household-level Engel curves at market price are equal to the product of the resource share of type t by the Engel curve at shadow price and shadow budget: W t ( y h ) = η t ( y h ) w t � � � y t h