1 Using Efficiency Analysis to Measure Individual Well-Being Using Efficiency Analysis to Measure Individual Well-Being with an illustration for Catalonia.

1

Using Efficiency Analysis to Using Efficiency Analysis to Measure Individual Well-BeingMeasure Individual Well-Beingwith an illustration for Catalonia

Xavi Ramos

UAB & IZA

2

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.

3

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.

4

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.

5

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)

6

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.

7

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)

8

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

9

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)

10

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.

11

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)

12

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.

13

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

14

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]

15

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

16

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

17

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

18

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 …

19

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.

20

Using Efficiency Analysis to Using Efficiency Analysis to Measure Individual Well-BeingMeasure Individual Well-Beingwith an illustration for Catalonia

Xavi Ramos

UAB & IZA

21

Health Related

Health hinders certain activities Physical disability Psychological disability Self-assessed health status

22

Provide Good Education

Satisfaction with children’s education Good neighbourhood to bring up children? School discarded because of its cost?

23

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

24

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?

25

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?

26

Economic Status

Possibility of making ends meet Financial difficulties Amount saved last year Deprivation index

27

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.