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Transcript of 1 Using Efficiency Analysis to Measure Individual Well-Being Using Efficiency Analysis to Measure...
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Using Efficiency Analysis to Using Efficiency Analysis to Measure Individual Well-BeingMeasure Individual Well-Beingwith an illustration for Catalonia
Xavi Ramos
UAB & IZA
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Outline
Explain how distance functions can be adapted to measure multidimensional well-being, and thus poverty (Lovell et al. 1994)
Apply the methodology to data for Catalonia, 2000.
Draw some policy implications and conclude.
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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.
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Output Distance Functions
Dout(A) = (0A/0B) < 1; Dout(B) = 1
B
A
y2B
y1B0
P(x)
PPF(x)
y2
y1
y2A
y1A
max. amount output (y) achievable with given input set, x
Measure the extent to which the output vector may be proportionally expanded with the input vector held fixed.
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Output Distance Functions
Dout(x,y) = min {:(y/) P(x)}
PropertiesProperties 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
Din(A) = (0A/0B) > 1; Din(B) = 1
A
B
x2A
x1A0
L(y)
IQ(y)
x2
x1
x2B
x1B
min. amount inputs (x) required to produce given output set, y
Measure the extent to which the input vector may be proportionally contracted given an output vector.
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Input Distance Functions
Din(x,y) = max {:(x/) L(y)}
PropertiesProperties 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-beingwell-being stems from achievement in many dimensionsdimensions of life, which in turn may be captured by a set of indicatorsindicators.
Indicators Dimensions
Dimensions Well-Being
Input DF
Output DF
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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)
WarningWarning: 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)
WarningWarning: 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-being6 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
POSITIVEPOSITIVE effect
Age up to 41
Education
Retired
Living near relatives
National Identity: Catalan
NEGATIVENEGATIVE effect Age from 41 Female Renting flat Life shaking event
NONO effect Marital status Labour mkt relation # employed in HH
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Poverty estimates: Head Count
Exponential relationship btw. Head Count & Poverty Line
0.00
0.10
0.20
0.30
0.40
0.50
50 60 70 80 90 100
Poverty Line (% median)
He
ad
Co
un
t
Well-being Equivalent I ncome
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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 …
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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 Using Efficiency Analysis to Measure Individual Well-BeingMeasure Individual Well-Beingwith an illustration for Catalonia
Xavi Ramos
UAB & IZA
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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)
WarningWarning: if Din(∙) is not homothetic in inputs, results will depend on
normalising variable, i.e. xN.