1. Social Evaluation of Alternative Basic Income Schemes in Italy R. Aaberge (Statistics Norway, Oslo) U. Colombino (Department of Economics, Torino) S. Strøm (Department of Economics, Oslo)

2. We develop a model of labor supply which features: simultaneous treatment of spouses’ decisions exact representation of complex tax rules quantity constraints on the choice of hours of work choice among jobs that differ with respect to hours, wage rate and other characteristics

3. Traditional approach max U(C, h) s.t. C=f(wh, I) h  0,T] where: C = net income h = hours of work w = wage rate I = other income T = total available time f( ) = tax rule

4. Our approach max U(C, h, j) s.t. C=f(wh, I) (h, w, j)  B where: j = other job characteristics B = opportunity set

5. The approach we use is different from the traditional approach Traditional model: max U(C, h) s.t. C = f(wh, I) h  0,T] Our model: max U(C, h, j) s.t. C = f(wh,I) (h, w, j)  B

6. The opportunity set in the traditional approach h w T 0

7. The Flat Tax 0 Gross Income Net Income 45 o FT

8. The Negative Income Tax 0 Gross Income Net Income 45 o NIT G

9. The Workfare Scheme 0 Gross Income Net Income 45 o WF G H min

10. The opportunity set in our model (the numbers represent hypothetical densities or relative frequencies of alternatives in the corresponding “spot”) 0.1 0.3 0.025 h w 0 0.2 0.01 0.1 0.15 0.015

11. Jobs differ not only w.r.t. wage (w) and hours (h) but also other characteristics (  ) h w  w0w0 h0h0 00 (w 0, h 0,  0 ) - +

12. The opportunity set contains different number of jobs with different characteristics This is taken into account by specifying a frequency or density function: p(h,w) = density of jobs with hours and wage (h,w).

13. Basic assumptions U(C, h, j) = V(C, h)  (h,w,j) =V(f(wh,I), h)  (h,w,j) V(f(wh,I), h) is the systematic component  (h,w,j) is the stochastic component Prob(  < u) = exp(-1/u)

14. Choice probability Given the assumptions, the probability (density) that the household chooses a job (h,w) is given by:

15. Imputation of the choice set The choice set B is in principle infinite In the estimation and simulation, B is replaced by a subset A  B Subset A contains 200 elements (jobs) sampled according to a procedure (“importance” sampling) suggested by McFadden (1978)

16. Importance Sampling of the Sub-Set A Estimate an empirical density q(h,w) If A must contain M elements, sample M-1 points from q(h,w) Add the chosen job to make a set A containing M elements

17. The choice density, given choice-set A, then becomes:

18. The key differences with respect to other discrete choice models of labour supply are: Our discrete model is an estimation device for an underlying continuous model In other discrete choice model of labour supply the choice set is typically fixed a-priori an equal for every one In our model we estimate the composition of the choice set (i.e. p(h,w)), which can differ from household to household

19. Model Estimation By specifying parametric forms for V( ) and p( ) we can estimate the parameters of the utility function V( ) and of the opportunity density p( ) by Maximul Likelihood

20. Model Specification V(C, h) is a Box-Cox form p(h,w) = g 1 (h)g 2 (w)g 0 p(0,0) = 1-g 0 g 1 (h) is uniform with a “peak”for full time g 2 (w) is log-normal g 0 is a logistic function [0,1] of personal characteristics

21. The data We use the Bank of Italy’s Survey of Household Income and Wealth 1993 We exclude single person households Both partners must belong to the age group 18-54 Retired and self-employed are excluded The selected sample contains 2160 households

22. Policy Simulation A policy is a change in the opportunity set B and/or in the tax rule f( ) Let B be the new opportunity set and f the new tax rule In order to simulate household behavior we solve the new problem: max U(C, h, j) s.t. C = f( wh, I) (h,w,j)  B

23. We simulate the effects of three tax reforms: A flat tax (FT) A negative income tax, with a guaranteed income equal to 3/4 the poverty level (NIT) A workfare system with a guaranteed income equal to 3/4 the poverty level, provided that the household works at least 1000 hours (WF)

24. It turns out that you can generate the same tax revenue either with: The 1993 tax rule A 18.4% FT A NIT that supports income up to 3/4 the poverty level and then applies a 28,4% tax rate A WF that requires 1000 hours worked, supports income up to 3/4 the poverty level and then applies a 27,3% tax rate

25. Wife’s participation rate under alternative tax rules

26. Wife’s hours of work (if employed) under alternative tax rules

27. Husband’s hours of work (if employed) under alternative tax rules

28. Household gross (Y) and net (C) income under alternative tax rules (000000 ITL)

29. Gini coefficients for the distribution of disposable household income

30. Disposable income variations under alternative tax reforms, by 1993 disposable income decile

31. Measurement of Utility V i (m i, w i, f k ) = utility reached by household i when endowed with exogenous income m i and wages w i, under tax regime f k

32. Measurement of Utility Equivalent Income y ik : (King 1983) V i (m i, w i, f k ) = V R (y ik, w R, f * )

33. The Efficiency Effect is the percentage variation of average utility (as measured by equivalent income)

34. The equality effect is based on Atkinson’s Index in the case of SW ak and on Aaberge (1992) in the case of SW bk

35. The percentage variations of both S ak and S bk can be decomposed into an Efficiency Effect and an Equality Effect

36. Social Welfare King (1983): SW ak =  i (y ik ) 1-a /(1-a) a = inequality aversion parameter Aaberge (1992): SW bk =  i y ik (1-F(y ik ) b-1 )b/(b-1) b = inverse inequality aversion parameter where F is the distribution function of y under tax regime k.

37. Welfare Gain of Household i from the reform (f 0 to f 1 ) WG i (0,1) = y i1 - y i0

38. Percentage of “welfare-winners” under alternative tax reforms

39. Percentage of “welfare-winners” under alternative tax reforms, by 1993 welfare level (equivalent income) decile

40. Percentage of “welfare-winners” under alternative tax reforms, by 1993 household income decile

42. Percentage of “welfare-winners” under alternative tax reforms, by 1993 welfare (equivalent income) decile

43. Wefare Gains (King, 1983) of a WF Reform by welfare decile. Mean CWG = 1724 (000 ITL)

44. Wefare Gains (King, 1983) of a NIT Reform by welfare decile. Mean CWG = 1643 (000 ITL)

45. Wefare Gains (King, 1983) of a FT Reform by welfare decile. Mean CWG = 3105 (000 ITL)

46. Percentage variations of Social Welfare and its components (Efficiency and Equality) a = 0

47. Percentage variations of Social Welfare and its components (Efficiency and Equality) a = 1

48. Percentage variations of Social Welfare and its components (Efficiency and Equality) a = 2