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)

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

Traditional approach

max U(C, h)

s.t.

C=f(wh, I)

h0,T]

where:

C = net income

h = hours of work

w = wage rate

I = other income

T = total available time

f( ) = tax rule

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

The approach we use is different from the

traditional approach

• Traditional model:

max U(C, h)

s.t.

C = f(wh, I)

h0,T]

• Our

model:

max U(C, h, j)

s.t.

C = f(wh,I)

(h, w, j) B

The opportunity set in the traditional approach

h

w

T0

The Flat Tax

0

Gross Income

Net Income

45o

FT

The Negative Income Tax

0

Gross Income

Net Income

45o

NIT

G

The Workfare Scheme

0

Gross Income

Net Income

45o

WF

G

Hmin

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

0.20.01

0.1

0.15

0.015

Jobs differ not only w.r.t. wage (w) and

hours (h) but also other characteristics ()

h

w

w0

h0

0

(w0 , h0 , 0 )

-

+

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).

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)

Choice probability

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

B y xdxdy y x p h I yx f V

h)p(h,w) V(f(wh,I),w h

) , () , ( ) ), , ( (

) , (

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)

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

The choice density, given choice-set A, then

becomes:

]),(/[)],(/[

)\,(

)(

Ax,yyxqp(x,y)x)V(f(yx,I),

whqp(h,w)h)V(f(wh,I),Awh

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

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

Model Specification

• V(C, h) is a Box-Cox form

• p(h,w) = g1(h)g2(w)g0

• p(0,0) = 1-g0

• g1(h) is uniform with a “peak”for full time

• g2(w) is log-normal

• g0 is a logistic function [0,1] of personal characteristics

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

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

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)

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

Wife’s participation rate under alternative tax rules

40

40,5

41

41,5

42

42,5

43

43,5

44

44,5

45

part. 43,7 45 41,9 42,5

Basis(93) FT NIT WF

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

rules

1570

1580

1590

1600

1610

1620

1630

hours 1590 1623 1589 1597

Basis(93) FT NIT WF

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

rules

1940

1950

1960

1970

1980

1990

2000

2010

2020

2030

2040

hours 1972 2036 1976 2001

Basis(93) FT NIT WF

Household gross (Y) and net (C) income under alternative tax rules

(000000 ITL)

0

10

20

30

40

50

60

70

Basis(93)FTNITWF

Basis(93) 54,5 43,2

FT 60,2 49,1

NIT 55,9 44,8

WF 56,7 45,7

Y C

Gini coefficients for the distribution of disposable

household income

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

Basis(93)FTNITWF

Basis(93) 0,323 0,282

FT 0,332 0,332

NIT 0,343 0,298

WF 0,336 0,301

Y C

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

0

2

4

6

8

10

12

14

16

I 4 3,8 3,2

II 3,6 1,4 2,1

III-VIII 5 1 2

IX 8 1,7 2,9

X 14,3 3,9 5,5

FT NIT WF

Measurement of Utility

Vi(mi, wi, fk) =

utility reached by household i when endowed with exogenous income mi

and wages wi, under tax regime fk

Measurement of Utility

Equivalent Income yik:

(King 1983)

Vi(mi, wi, fk) = VR(yik, wR, f*)

The Efficiency Effect is the percentage variation

of average utility (as measured by equivalent

income)

The equality effect is based on Atkinson’s Index in the case of

SWak and on Aaberge (1992) in the case of

SWbk

The percentage variations of both Sak

and Sbk can be decomposed into an

Efficiency Effect and an Equality Effect

Social Welfare

King (1983):

SWak= i(yik)1-a /(1-a)a = inequality aversion parameter

Aaberge (1992):

SWbk = iyik(1-F(yik)b-1 )b/(b-1)b = inverse inequality aversion parameter

where F is the distribution function of y under tax regime k.

Welfare Gain of Household i from the reform (f0 to f1)

WGi(0,1) = yi1 - yi0

Percentage of “welfare-winners” under alternative tax reforms

49

50

51

52

53

54

55

56

% 51,8 55 55,6

FT NIT WF

Percentage of “welfare-winners” under alternative tax reforms, by 1993 welfare level (equivalent

income) decile

0

10

20

30

40

50

60

70

I 41,5 65,3 64,8

II 43,5 59,2 59,3

III-VIII 52 54,6 55,4

IX 60,1 51,4 52,6

X 60,9 46,2 47,6

FT NIT WF

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

0

20

40

60

80

100

I 14,1 74,1 66,7

II 19 43,7 45,8

III-VIII 51,3 44,8 50,9

IX 86,5 51,1 60,4

X 90,6 64,9 71,5

FT NIT WF

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

0

10

20

30

40

50

60

70

80

90

100

I II III-VIII IX X

FTNITWF

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

decile

0

10

20

30

40

50

60

70

I II III-VIII IX X

FTNITWF

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

-10000

-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

10000

Losers -2656 -2773 -3958 -5551 -9668

All 2750 2165 1835 1793 -478

Winners 5732 5540 6531 8459 9776

I IIIII-VIII

IX X

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

-10000

-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

10000

Losers -2620 -2762 -3998 -5595 -9719

All 3039 2208 1736 1573 -808

Winners 6082 5634 6526 8408 9726

I IIIII-VIII

IX X

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

-10000

-5000

0

5000

10000

15000

20000

Losers -5528 -5641 -6029 -6607 -8299

All -122 457 2848 6307 7325

Winners 7051 8310 1105 1492 1746

I IIIII-VIII

IX X

Percentage variations of Social Welfare and its components

(Efficiency and Equality)a = 0

0

0,5

1

1,5

2

2,5

Efficiency 2,1 0,8 1,1

Soc. Wel 2,1 0,8 1,1

Equality 0 0 0

FT NIT WF

Percentage variations of Social Welfare and its components

(Efficiency and Equality)a = 1

-1

-0,5

0

0,5

1

1,5

2

2,5

Efficiency 2,1 0,8 1,1

Soc. Wel 1,4 1,3 1,4

Equality -0,69 0,49 0,3

FT NIT WF

Percentage variations of Social Welfare and its components

(Efficiency and Equality)a = 2

-2

-1,5

-1

-0,5

0

0,5

1

1,5

2

2,5

Efficiency 2,1 0,8 1,1

Soc. Wel 0,5 1,9 1,8

Equality -1,57 1,09 0,69

FT NIT WF