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

1. Using Efficiency Analysis to Measure 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 Measure the extent to which the output vector may be proportionally expanded with the input vector held fixed. Dout(A) = (0A/0B) < 1; Dout(B) = 1 y2 B y2B max. amount output (y) achievable with given input set, x A y2A PPF(x) P(x) y1A y1B y1 0

5. 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)

6. x2 A x2A L(y) min. amount inputs (x) required to produce given output set, y x2B B IQ(y) x1 x1B x1A 0 Input Distance Functions Measure the extent to which the input vector may be proportionally contracted given an output vector. Din(A) = (0A/0B) > 1; Din(B) = 1

7. 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)

8. 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 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) • Warning: 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) • Warning: 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-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. POSITIVE effect Age up to 41 Education Retired Living near relatives National Identity: Catalan NEGATIVE effect Age from 41 Female Renting flat Life shaking event NO effect Marital status Labour mkt relation # employed in HH Multivariate analysis: Main findings

16. Poverty estimates: Head Count • Exponential relationship btw. Head Count & Poverty Line

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 Measure 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) • Warning: if Din(∙) is not homothetic in inputs, results will depend on normalising variable, i.e. xN.