Parallel Session IARIW 2014

1. • “An equivalence scale is a measure of the cost of living
of a household of a given size and demographic
composition, relative to the cost of living of a reference
household (usually a single adult), when both households
attain the same level of utility or standard of living”.
• New Palgrave Dictionary of Economics, 2nd edition
• Arthur Lewbel and Krishna Pendakur (Dec. 2006)
• Folbre/Close: what about children?
• Johnson/Jantti: can we compare over time & across
countries?

2. Public Social Expenditure on Family in % of
GDP - Day Care / Home-help Services
2000 2005 2009
Canada 0.2 0.2 0.2
United States 0.3 0.3 0.3
Finland 1 1 1.1
France 1.2 1.2 1.3
Iceland 0.9 1.2 1.7
Netherlands 0.8 1.1 0.9
OECD - Total 0.5 0.6 0.7

3. UNPAID WORK, UNPRICED SERVICES,
AND EQUIVALENCE SCALES
NANCY FOLBRE & MARTA MURRAY CLOSE
33rd General IARIW conference – Rotterdam,
Session 2B: Equivalence Scales over Time and Space
August 25, 2014
Presentation by: Lars Osberg
Dalhousie University

4. Market Work + Household Production =
Household Income
• Non-Market Household Production
• Large % of $ GDP
• Varies hugely across households
• Families with children necessarily have to purchase &/or provide care
• In practice, home production is a gendered task
• Sure to affect measurement of poverty & inequality
• How should household production be valued?
• Modern Industrialized societies; ↓ infrastructure & ↓ skills => limited range (e.g.
meal preparation, child care, laundry, shopping, cleaning ..)
• Time Use Surveys => Hours; Replacement cost => Wage rate
• BUT: children need both direct care & supervision
• “they need you around so that they can ignore you”
• secondary activities often poorly captured in time use data

5. Why do household economies of scale
depend on locus of production?
• Food
• Purchased meal portions – zero economies of scale
• Home cooked meals: declining average cost of production
• Shopping + preparation time = fixed cost; portion cost = variable cost
• Child supervision:
• Purchased – nil economies of scale
• Home produced – on average, it’s easier as numbers increase !
• Children play with each other + older siblings can supervise
• Time costs ≈ 62% - 65% of total costs of 2 children

6. Adding Home Production into income?
• Ye = Y / N ᶿ
• Y= household market income
• N = Number of household members
• Ye = equivalent income per person
• [ LO: surprising that no mention of importance of “equal sharing” assumption]
• ϴ = economies of scale parameter (ϴ = 0.5 commonly used)
• ϴ = 1 implies “per capita” income; ϴ = 0 implies household income;
• Yee = [Y + NpH] / N ϴ
• Np = number of “productive” members; H = average home production
• Yee = equivalent extended income per person
• BUT market income and household production not perfectly fungible

7. Unequal economies of scale: ϴ m ≠ ϴ h?
• Yee = Yme + Yhe = Y/N ϴm + NpH / N ϴh
• DO CHILDREN NEED LESS ?
• Replace N = (Na + λ Nk) ϴ
• Yee = Y/ (Na + λm Nk) ϴ m + NpH / (Na + λh Nk) ϴ h
• Two differences for market income & non-market production
• Children count differently as adult equivalent units
• Economies of scale different for market income & household production

8. Empirical Illustrations
• Note: U.S. focus, assumes no public child care provision
• Families with kids < 6:
• Added household production value of non-employed adult ≈ $6,880
• But this does not imply increased adult consumption
• Comparable to cost of FT daycare ($3,900(Miss) - $11,700 (Mass) for 4 year old)
• Young children – very time intensive; more “expensive” than adults
• Varies with child age & supervision/direct care needs
• Economies of scale depend on whether purchase or home produce
• Recommendation: combine time use and consumption surveys
• Estimate substitutability of market & home produced goods, for children &
for adults

9. SEARCHING FOR A
CONSISTENT EQUIVALENCE
SCALE ACROSS COUNTRIES
M. JANTTI & D.S. JOHNSON
33rd General IARIW conference – Rotterdam,
Session 2B: Equivalence Scales over Time and Space
August 25, 2014
Presentation by: Lars Osberg
Dalhousie University

10. Questions asked:
• Is there one consistent equivalence scale to use for all
countries?
• NO
• LO: Important issue for international comparisons poverty & inequality
• Can one use the same scale over time for one country?
• YES
• LO: Important result for domestic policy debates
• Can we choose the scale that minimizes inequality?
• MAYBE
• LO: why would we want to do this?
• How can we choose the “best” scale?
• DON’T KNOW

11. What are Equivalence Scales?
• They represent the cost ratio required to equate the well-
being or utility for households with different sizes and
compositions.
• Key is U0 = max U(x,A,K)
subject to px ≤ T
• That is, U0 solves T = E(p,U0,A, K).
• This will only hold for U0 and is not a “general”
equivalence scale. And scale could be different for
different levels of U0.
   
   KAS
KAUpE
KAUpE
KAUpS
RRo
o
o ,
,;,
,;,
,;, 

12. Equivalence scales could impact the growth in GDP 0r
Disposable Personal Income
0.5
1
1.5
2
2.5
DPI per capita
DPI per equivalent adult
DPI per Household
12
BEA, Real Disposable Personal Income (in $2009)

13. Equivalence scales affect measured poverty
rates
13

14. Methodology: test sensitivity by varying
parametric equivalence scales
• One-parameter scale
• (M)d = (M)0.5
M = household size
• Two-parameter scale
• (A+gK)d = (A+0.7K)0.7
A = number of adults, K = number of children

15. Scale parameters affect measurement of inequality (and
poverty) in a predictable manner
• For the Mean log deviation
𝐼0 =
1
𝑁
𝑖
ln(
𝑦
𝑦𝑖
)
• y = x/(Md) M = household size
•
𝜕𝐼0
𝜕𝛿
= −
𝑐𝑜𝑣 𝑦,log 𝑚
𝜇 𝑦
=
• −
𝑐𝑜𝑣 𝑥,log 𝑚
𝜇 𝑥
+ 𝛿 ∙ 𝑣𝑎𝑟 log 𝑚
• Coulter, Cowell and Jenkins show U-shape relationship between
d and measured inequality (and relative poverty)
• 𝑎𝑡 𝑡ℎ𝑒 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝛿:
𝑐𝑜𝑣(𝑥,log 𝑚 )
𝜇(𝑥)
= 𝛿 ∙ 𝑣𝑎𝑟(log 𝑚 )
• LO: connection with utility of household member which is equal to that of
representative single individual is ???????
15

16. Countries show U-shaped relationship, with no crossings.
16

17. Countries show U-shape for child parameter, too Inequality falls for Finland; rises for US
For most countries, the ranking does not change
17

18. 18
For most countries, the ranking does not change

19. Countries show uniform increases in inequality over time
19

20. The “Inequality Minimizing” δ and ϒ ??
• Actual Inequality is unchanged by measurement choices
but indices of measured inequality will vary with:
• assumed δ (economies of scale)
• assumed ϒ (child adult equivalence)
• The “Inequality Minimizing” δ*, ϒ* vary by country
• Will leave it to the authors to explain why this matters

21. Can we go on as before & use EA=N0.5 ?
• Cross country inequality rankings stable – robust to scale
parameter choices
• Within country Inequality year rankings also robust
• Some cross-country poverty rankings may be more sensitive to
assumed δ and ϒ
• not examined: sensitivity of within country distribution of poverty to
assumed δ and ϒ
• E.g. is elderly poverty greater / less than child poverty?
• Does anybody really care that:
• Scale parameters matter for the calculated level of inequality & poverty ?
• Inequality minimizing δ*, ϒ* vary by country ?
• EA=N0.5 is probably still safe

22. Osberg Comments: (1)
• Large families are now
quite rare in most rich
nations
+ economies of scale for N>5 is
only an issue for families with
children
BUT 2 person & 1 person
households are common
among the elderly
• So why not show readers
explicitly what the distribution
of household size looks like &
which parts of distribution are
affected by scale choice?
0
1
2
3
4
5
6
Scalerelativetosingle
Per-capita
House
Square root
Official
Census Povert
Two-parameter

23. (2) Equivalence scales & Calorie-counter
poverty lines in sub-Saharan Africa
• Food only – composition diet =
average of poor half families
• Equivalent Adult <= daily food
intake = 2200 calories
• No economies household size
• No allowance for activity
• Male 30, 63 Kilo, 168 cm
• 2291 if “Rarely” physically active
• 3200 if active > 1 hour a day
• US National Academy of Sciences
• Note: Equal sharing per
Equivalent Adult is a
necessary assumption
Equivalence Scales - Tanzania
Sex
Age groups Male Female
0-2 0.4 0.4
3 to 4 0.4 0.48
5 to 6 0.56 0.56
7 to 8 0.64 0.64
9 to 10 0.76 0.76
11 to 12 0.8 0.88
13 to 14 1 1
15 to 18 1.2 1
19 to 59 1 0.88
60+ 0.8 0.72
2014-08-28 23

24. (3) Compare to Subjective Well-being ?
• Estimate U* = F(x) would enable far richer set of controls
• E.g. Age of children, disability status
(4) Public Services Matter for Poverty
and Inequality Measurement
Public day care, elder care services and health care are
hugely important for economies of scale in household well-
being – but not now recognized in equivalence scales