Using Efficiency Analysis to
Measure Individual Well-Being
with an illustration for Catalonia
Xavi Ramos
UAB & IZA
1
Outline
 Explain how distance functions can be
adapted to measure multidimensional wellbeing, and thus poverty (Lovell et al. 1994)
 Apply the methodology to data for
Catalonia, 2000.
 Draw some policy implications and
conclude.
2
Distance Functions and Well-Being
 Distance functions measure the distance between a
given (output or input) vector and a benchmark
vector as the (inverse) of the factor by which the
vector has to be scaled (up or down) to be on the
benchmark vector.
 To measure well-being the benchmark is taken to be
the individual with highest/lowest well-being.
 Then, the distance function measures by how much
individual’s attributes have to be expanded or
contracted to have the same level of well-being as
the benchmark. This is our measure of well-being.
3
Output Distance Functions
Measure the extent to which the output vector may be
proportionally expanded with the input vector held fixed.
y2
B
y2B
y2A
max. amount output (y) achievable
with given input set, x
A
PPF(x)
P(x)
0
y1A
y1B
Dout(A) = (0A/0B) < 1; Dout(B) = 1
y1
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Output Distance Functions
Dout(x,y) = min {:(y/)  P(x)}
Properties




Non-decreasing, linearly homogeneous in y
Decreasing in x
Dout(x,y) ≤ 1 if y  P(x)
Dout(x,y) = 1 if y  PPF(x)
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Input Distance Functions
Measure the extent to which the input vector may be
proportionally contracted given an output vector.
x2
A
x2A
L(y)
x2B
min. amount inputs (x) required to
produce given output set, y
B
IQ(y)
0
x1B
x1A
Din(A) = (0A/0B) > 1; Din(B) = 1
x1
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Input Distance Functions
Din(x,y) = max {:(x/)  L(y)}
Properties




Non-decreasing, linearly homogeneous in x
Decreasing in y
Dout(x,y) ≥ 1 if y  L(y)
Dout(x,y) = 1 if y  IQ(y)
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Two stage method
Assume well-being stems from achievement
in many dimensions of life, which in turn
may be captured by a set of indicators.
Indicators
Dimensions
Input DF
Output DF
Dimensions
Well-Being
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Level of Achievement in a Dimension
• Empirical Problem: Din(∙) depends on y
 Suppose all individuals have the same
minimum level of achievement, i.e. one unit.
 Reference set becomes IQ(e), bounds input
vector from below.
 Individuals with input vector on IQ(e) share
the lowest level of achievement (=1)
 The radially farther away from IQ(e) the
higher the level of achievement (> 1)
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Level of Achievement in a Dimension
Estimation procedure:
 Normalize using one of the inputs, xN,
 use a trans-log for the resource frontier, and
 estimate by COLS: Din(xi,e) = exp{max(ε)- εi} ≥ 1,
 which guarantees that all input vectors lie on or
above the resource frontier IQ(e)
 Warning: if Din(∙) is not homothetic in inputs,
results will depend on normalising variable, i.e. xN.
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Overall Level of Well-Being
Empirical Problem: WB(∙) depends on x
 Suppose all individuals have the same
minimum level of inputs, i.e. one unit.
 Reference set becomes PPF(e), bounds
achievement vector from above.
 Individuals with achievement vector on
PPF(e) share the highest level of well-being
(=1)
 The radially farther away from PPF(e) the
lower the level of achievement (< 1)
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Overall Level of Well-Being
Estimation procedure:
As before. Now,
 OLS: ln(1/ yM) = TL(e,y/yM,β)+ ε
 Then, Dout(e,yi) = exp{min(ε)- εi} ≤ 1
 Which guarantees that all dimension vectors lie on or
below the achievement frontier PPF(e)
 Warning: if Dout(∙) is not homothetic in outputs, results will
depend on normalising variable, i.e. yM.
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The Data: PaD 2000
6 dimensions of Well-being
 Health related
 Provide Good Education
 Work-Life Balance
 Housing Conditions
 Social Life and Network
 Economic Status
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Correlations
 Not doing well in any one dimensions does not
imply doing bad in another one [r(dmi,dmj) = low]
 More economic resources do not necessarily lead
to higher achievement levels in a dimensions
[r(dm,y) = low & expected sign]
 Any Well-being analysis should take its many
dimensions into account –not only income
[r(wb,y) = low]
 Very low levels of inequality !!
[G(wb) = 0.06; 0.02 ≤ G(dmi) ≤ 0.15]
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Multivariate analysis: Main findings
POSITIVE effect
 Age up to 41
 Education
 Retired
 Living near relatives
NEGATIVE effect
 Age from 41
 Female
 Renting flat
 Life shaking event
 National Identity: Catalan
NO effect
 Marital status
 Labour mkt relation
 # employed in HH
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Poverty estimates: Head Count
0.50
Head Count
0.40
0.30
0.20
0.10
0.00
50
60
70
80
90
100
Poverty Line (% median)
Well-being
Equivalent Income
 Exponential relationship btw. Head Count & Poverty Line
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Well-Being and Income Poverty
WB-poor if belongs to the bottom 18.4% of the
WB distribution
 Only 5% are Well-Being and Income poor
 Two thirds of income poor manage to escape
well-being poverty
 Logit estimates on Well-Being poverty in line with
OLS results. But two differences:
 Gender does not condition poverty risk
 Divorced face higher well-being poverty
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Policy Implications and Conclusions
 Our analysis vindicates the necessity to
take due account of as many of the many
dimensions of well-being as possible.
 Well-Being cannot be proxied by happiness
or life satisfaction questions
 Multivariate analysis seems to indicate that
our multidimensional well-being index
makes sense ...
… but suffers from one major drawback …18
Policy Implications and Conclusions
 Derived indices display exceedingly equal
distributions and very low levels of poverty
… probably due to (i) qualitative data
(ii) two aggregating stages employed to
estimate the overall index of Well-Being.
 This should be further investigated if
distance function based multidimensional
indices are to become widely employed.
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Using Efficiency Analysis to
Measure Individual Well-Being
with an illustration for Catalonia
Xavi Ramos
UAB & IZA
20
Health Related




Health hinders certain activities
Physical disability
Psychological disability
Self-assessed health status
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Provide Good Education
 Satisfaction with children’s education
 Good neighbourhood to bring up children?
 School discarded because of its cost?
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Work-Life Balance
 Had to quit job to care for relatives
 Satisfaction with amount of leisure time
 Satisfaction with amount of time spent with
children
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Housing Conditions
 Crowding index (m2/equivalence scale)
 Housing deficiencies which cannot afford
repairing
 Live in desired dwelling
 Reside in desired neighbourhood
 Can afford living in a comfortable house?
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Social Life and Network
 Satisfaction with social life
 Is there someone who can help if personal
problems?
 Is there someone who can help if financial
problems?
 Anyone to help if in need to care for
relatives or sick?
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Economic Status




Possibility of making ends meet
Financial difficulties
Amount saved last year
Deprivation index
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Level of Achievement in a Dimension
Estimation procedure:
 By homogeneity: Din(x/xN,e) = Din(x,e)/xN
 Since Din(x,e) ≥ 1, then (1/ xN) ≤ Din(x/xN,e)
 Then (1/ xN) = Din(x/xN,e)∙exp(ε), ε ≤ 0
 Assume ln[Din(x/xN,e)] has a TL(x/xN,e,β).
 OLS: ln(1/ xN) = TL(x/xN,e,β)+ ε
 Finally, Din(xi,e) = exp{max(ε)- εi} ≥ 1
 Which guarantees that all input vectors lie on or above the resource
frontier IQ(e)
 Warning: if Din(∙) is not homothetic in inputs, results will depend on
normalising variable, i.e. xN.
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