Session 2 b daley et_al_-_equivalence_scales_over_time_and_space

Background/Context
Methods and Results
Possible Extensions
Summary
Cross-National Comparisons of Changes in
Expenditure Patterns over Time
Session 2B: Equivalence Scales over Time and Space
A. Daley,1 T. Garner,2 S. Phipps,1 E. Sierminska,3 and P.
Ruggles4
1Dalhousie University, Halifax, Nova Scotia
2U.S. Bureau of Labor Statistics
3CEPS/INSTEAD
4NORC, University of Chicago
33rd IARIW General Conference, Rotterdam, 2014
A. Daley, T. Garner, S. Phipps, E. Sierminska, and P. Ruggles Equivalence Scales

Background/Context
Methods and Results
Possible Extensions
Summary
Outline
1 Background/Context
Equivalence Scales, Poverty and Inequality
2 Methods and Results
Econometric Speciﬁcations
Data and Results
3 Possible Extensions
Application and Inference

Background/Context
Methods and Results
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Outline
Data and Results

Background/Context
Methods and Results
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Summary
Equivalence Scales
Equivalence scales are employed to compare economic
wellbeing across households of different sizes.
When economies of scale exist within a household, larger
households will have higher wellbeing for a given income level.
Example: a household of two individuals on $50,000 will be
better off than a sole individual on $25,000.
This is due to the effective sharing of fixed costs (e.g. rent,
food, transport).

Background/Context
Methods and Results
Possible Extensions
Summary
Equivalence Scales
Scales are estimated from consumption data.
What are the income levels required to offset differentials in
consumption across different households?
A large literature on this topic.
OECD scale: First adult +1, subsequent adults +0.5, +0.3
for each child.
Square-root scale: Total household income divided by the
square root of the number of occupants.

Background/Context
Methods and Results
Possible Extensions
Summary
Equivalence Scales
In practice it is common to apply a single scale over time or
over a cross-section.
However the underlying rationale for that scale may no longer
exist.
For example there may be more/less effective sharing in some
countries, or in earlier/latter time periods.
This will affect poverty and inequality measures.
Goal of the paper is to see how equivalence scales differ over
time and across countries.

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Methods and Results
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Determining the Scales
Poor spend a greater share on food than the rich (Engel’s
Law).
Larger households spend relatively more on food for a given
income level.
The proportion of the budget devoted to food can be used as
a measure of wellbeing.
More recent literature has considered baskets of necessities
rather than just food.
These can include clothing, shelter and health care costs.

Background/Context
Methods and Results
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Summary
Data and Results
Outline
Data and Results

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Data and Results
Estimations
The authors consider two forms of estimation.
First is based upon Engel methodology with a ﬂexible
functional form (dummies) for household size.
Second is a single parameter scale that follows the LIS
methodology.
All sets of estimates use multiple deﬁnitions of necessary
expenditure.
Food, food clothing and shelter, food clothing, shelter and
healthcare.

Background/Context
Methods and Results
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Summary
Data and Results
Engel Speciﬁcation
Estimating equation
ln (x) = β0 + β1 ln (y) +
N
n=2
γnHn + ε
Hn =
1 household size = n
0 otherwise
Relative expenditure
yn
y1
= exp
γn
1 − β1

Background/Context
Methods and Results
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Data and Results
Single-Parameter Speciﬁcation
Estimating equation
ln (x) = β0 + β1 ln (y) + β1 ln (n) + ε
Relative expenditure
yn
y1
= n
β2
β1−1

Background/Context
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Data and Results
Data
Harmonized expenditure and income data mostly taken from
LIS.
Necessity bundles as before.
11 Countries: Canada, France, Hungary, Israel, Mexico,
Poland, Russia, South Africa, Taiwan, Switzerland and the
United States.
Earliest observations in 1998 - latest in 2012. Most data in
the 2000s.

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Data and Results
Results
Most emphasis on US Canada comparison.
Equivalence scales behave as expected.
Increase with household size in all cases. Generally concave.
Economies of scale depend upon the necessity bundle.
Smaller scales when only food is used. The choice of
consumption bundle matters.
Interesting diﬀerences across countries. E.g. more sharing
within Canadian households relative to US on food (opposite
for other variables).

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Data and Results
Results
Other countries are compared with the single parameter scale.
Tend to vary a lot from country to country.
Smaller estimates indicate more economies of scale.
LIS scale is an exponent of 0.5.
These authors ﬁnd slightly smaller estimates (generally
0.3-0.5).
Why do these diﬀer from the LIS estimates? One answer is
that economies of scale may have changed.
Time-series estimates show declining scales in US and Canada.

Background/Context
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Outline
Data and Results

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Data and Application
Could the results be extended to panel data?
U.S. Post-govt income is available from PSID - TAXSIM
algorithm (Feenberg and Coutts).
Could this be used for these data?
Could inequality or poverty trends be calculated using the
alternative scales such that their eﬀects can be observed?

Background/Context
Methods and Results
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Application
Why do estimates vary so much across countries?
Diﬀerences in data? Prices? Culture? Could be interesting to
speculate.
Modeling could be responsible. Are there semiparametric
methods that could be used instead of log function?
Could pooled estimation (perhaps with dummies for
countries) provide a single summary measure?

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Inference
May be desirable to test for diﬀerences in scales across time or
location.
Two simple computational methods spring to mind (are there
analytic SEs for equiv scales?)
Bootstrap
Simulation

Background/Context
Methods and Results
Possible Extensions
Summary
Bootstrap
Take two data sets (e.g. US and Canada) with sizes tUS and
tCA.
Calculate key ratios and take diﬀerence D =
ˆβ2US
ˆβ1US −1
−
ˆβ2CA
ˆβ1CA−1
(or similar).
Pool data sets.
Draw (with replacement) from pooled data two random
samples of sizes t∗
US and t∗
CA.
Calculate D∗ =
ˆβ∗
A2
ˆβ∗
A1
−1
−
ˆβ∗
B2
ˆβ∗
B1
−1
a large number (e.g. 999
times).
Compare D to distribution of D∗.

Background/Context
Methods and Results
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Simulation
Again consider key ratios γn
1−β1
and β2
β1−1 .
Take ﬁrst case
ˆγn
ˆβ1
∼ N
γn
β1
,
σ2
1 σ2
21
σ2
12 σ2
2
Draw randomly from bivariate normal with these parameters.
Simulate distribution of scales this way.
How much does sampling variation in the estimation of ES
aﬀect inequality or poverty?

Background/Context
Methods and Results
Possible Extensions
Summary
Summary
High quality work on the estimation of equivalence scales.
Scales seem to vary substantially across countries, and with
diﬀering choices of necessity bundle.
Should we use estimated scales, or stick with something
constant?

Session 2 b daley et_al_-_equivalence_scales_over_time_and_space

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Session 2 b daley et_al_-_equivalence_scales_over_time_and_space