Chapter 2 Behavioral micro-simulation models: the case of labor supply François Bourguignon Paris School of Economics M2-PPD, M2-APE, 2009-10 1
Outline 1. The case of labor supply a) The problem of the non-linear budget constraint b) Simple linear approaches c) Continuous non-linear rational models d) Discrete non-linear models e) Example: the WFTC in UK 2. The case of child labor and the demand for schooling in developing countries Example: the Bolsa Familia program in Brazil 3. Other types of behavior 2
d) Using discrete labor choice models • Present models use a discrete choice formulation (Van Soest, 1995; Hoynes, 1996; Blundell and MaCurdy, 1999) • More flexibility can be obtained when individuals are supposed to choose from a finite set of working times (including zero) D j . • Conventional multi-logit model: = + − γ j C y w D TB y w D D z ( , , ; ; ) i oi i j oi i j j i = = + ≥ = + ≠ j j j j k k k k L D U u(z ; C ; β ) ε U u(z ; C ; β ε k j if ) for all i j i i i i i i i i where ε distributed as independent double exponential and u( ) an unrestricted quadratic function of its (z, C) arguments. 3
Using discrete labor choice models (2) ) β • Estimates j of coefficients of quadratic form obtained from multinomial logit model. Likelihood of an observation: [ ] { } * β * j j Exp u z C ( ; i ; i ) = = = + − k L D i i C y w D TB Pr ; ( ) ∑ i i i i k β * k k 0 j Exp u z C [ ( ; ; ] i i i k j where is the (observed) duration of work by agent i * i ) ε j • "Pseudo-residuals" obtained from drawing randomly in the i double exponential law under conditions ) ) ) ) + ≥ + ≠ = j j j k k k u(z ; C ; β ) ε u(z ; C ; β ε k j with D L ) for all i i i i i i j i 4
Using discrete labor choice models (3) • Simulation of modifying the tax-benefit system to TB*(…, γ * ) : obtained by solving numerically the utility maximizing problem: = ≥ ≠ s js ˆ j j ks ˆ k k L D such that u(z ; C ; β , ε ) u(z ; C ; β , ε ) for all k j ˆ ˆ i j i i i i i i = + − γ js C y w D TB y w D D z * ( , , ; ; *) i oi i j oi i j j i Disposable income is given by: = + − γ s C y w D TB y w D D z * ( , , ; ; *) i oi i j oi i j j i 5
Example: Effect of the Working Family Tax Credit in UK (Blundell et al. 2000) 6
Budget constraint example for lone parent with childcare costs C 400 300 200 100 L w 10 20 30 50 7
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Final remarks on labor supply models • The issue of participation and non-observed wages (Heckman, 1974, 1979) • The role of labor demand – Are unemployed "unemployable" or voluntarily inactive? Identifying through specification of the distribution of heterogeneity (Laroque and Salanié, 1999) ? • Households vs. Individuals – Options = duration of work for both members of a couple, easily modeled with discrete choice model (Aaberge et al., 1998) – Intensive (hours) vs. extensive (participation) labor supply elasticity (Saez, 2002) • Identifying behavioral response to reform with cross-sectional income-wage variations 11
2. The case of child labor and the demand for schooling in developing countries • Bolsa Escola = Conditional cash transfer (CCT) program to alleviate poverty and incentivize schooling: – Eligible: poor households with school age kids – Cash transfer for each kid at school age attending school • Can we think of a simple econometric model that permits simulating ex-ante this program? • Ex-ante model by Bourguignon, Ferreira and Leite (2004) • Note: Bolsa Escola transformed into Bolsa Familia 12
The Bolsa Escola Programme • Means-test : income per capita less than R$90 (50 per cent of the minimum wage) • Conditionality : 6-15 year-olds must attend school. • Transfer : R$15 per child in school • Limit : R$45 per household • Monitoring at the local and federal levels (1 US $ ~ 2 reais) 13
A minimal schooling and child labor supply model • Child’s occupational choice Choose the alternative with maximum utility among: (0) Not going to school (paid or unpaid work); (1) Going to school and paid work; (2) Going to school and no paid work . γ 0 + α 0 U i (0) = Z i .(Y -i + y i0 ) + v i0 . γ 1 + α 1 U i (1) = Z i .(Y -i + y i1 ) + v i1 . γ 2 + α 2 U i (2) = Z i .(Y -i + y i2 ) + v i2 Z i = characteristics of household i, Y -i = income without child' work, y ij = income of the child in alternative j 14
… model (ctd.) • Child i’s Contribution to Household Income in alternatives j = 0, 1 or 2: y i0 = w i ; y i1 = Mw i ; y i2 = Dw i (not observed) with w i = ("full time") market earnings: . δ Log y i0 = X i + u i . δ Log y i1 = X i + m*Ind(S i =1) +u i and M = Exp(m) = "part-time" wage reduction coefficient 15
full model: (y i0 = w i ; y i1 = Mw i ; y i2 = Dw i ) Household (kid ?) i chooses the alternative j that yields the highest utility U i (j): . γ 0 + α 0 + β 0 U i (0) = Z i .Y -i .w i + v i0 . γ 1 α 1 + β 1 U i (1) = Z i + .Y -i .w i + v i1 . γ 2 + α 2 + β 2 U i (2) = Z i .Y -i .w i + v i2 β 0 = α 0 ; β 1 = α 1 M; β 2 = α 2 with D 16
Estimating the model V ij = double exponential leading to multi-logit: [ ] γ + α + β Exp Z Y w { } . . . − i i i j * j * j * ≥ ≠ = Likelihood U j U k k j * * i i i Pr ( ) ( ), [ ] ∑ i i i i γ + α + β Exp Z Y w . . . − i k i k i k = k 0 , 1 , 2 β = α β = α β = α M D With 0 0 1 1 2 2 It is possible to identify all parameters (rather than only the differences between two alternatives). Then necessary to draw random values for v's consistent with observed choice (see above) 17
The simulation framework Introducing the Cash Conditional Transfer: = γ + α + β + ˆ U Z Y w v ˆ ˆ ˆ ( 0 ) . − i i i i i 0 0 0 0 = γ + α + + α + + ≤ ° ˆ ˆ U Z Y T M w v if Y M w Y ˆ ˆ ˆ ˆ ( 1 ) . ( ) − − i i i i i i i 1 1 1 1 = γ + α + α + + > ° ˆ ˆ U Z Y M w v if Y M w Y ˆ ˆ ˆ ˆ ( 1 ) . − − i i i i i i i 1 1 1 1 = γ + α + + α + ≤ ° ˆ U Z Y T D w v if Y Y ˆ ˆ ˆ ˆ ( 2 ) . ( ) − − i i i i i i 2 2 2 2 = γ + α + α + > ° ˆ U Z Y D w v if Y Y ˆ ˆ ˆ ˆ ( 2 ) . − − i i i i i i 2 2 2 2 α j , β j , γ j Easily evaluated when , v ij are known. 18
Descriptive Statistics and Estimation Results 19
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Simulation Results. AFTER REFORM MODEL BY AGE Before reform Not going to school Going to school and working Going to school and not working Total Not going to school 65,7% 10,2% 24,1% 5,8% Going to school and working 0,0% 99,8% 0,2% 16,9% Going to school and not working 0,0% 0,0% 100,0% 77,3% Total 3,8% 17,4% 78,8% 100,0% Poor Households Not going to school Going to school and working Going to school and not working Total Not going to school 52,2% 14,2% 33,6% 9,1% Going to school and working 0,0% 99,6% 0,4% 23,7% Going to school and not working 0,0% - 100,0% 67,2% Total 4,7% 24,9% 70,3% 100,0% 23
Simulation of Alternative Programme Designs 1. Transfer doubled from R$15 to R$30. 2. Age Progressive Transfer (R$10 to R$35). 3. Means-Test raised to R$120. 4. Transfer doubled & Means-Test raised. 5. Age Progressive Transfer & Means-Test raised. 6. No conditionality. 24
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Table 7. Simulated distributional effects of alternative specifications of the conditional cash transfer program Original Bolsa escola's program Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 Scenario 6 Mean Income per capita 253.9 255.0 256.1 255.8 255.2 256.5 256.3 255.1 Inequality measures Gini coefficient 0.594 0.589 0.584 0.585 0.588 0.583 0.584 0.589 Mean logarithmic deviation 0.704 0.670 0.647 0.652 0.669 0.644 0.649 0.668 Theil index 0.710 0.700 0.690 0.692 0.699 0.687 0.689 0.699 Generalized Entropy (2) 1.605 1.589 1.572 1.575 1.585 1.565 1.569 1.587 Poverty measures Poverty headcount 30.5% 29.5% 28.2% 28.5% 29.5% 28.2% 28.5% 29.4% Poverty gap 13.5% 12.4% 11.2% 11.5% 12.4% 11.2% 11.5% 12.3% Total square deviation from poverty line 8.1% 7.1% 6.2% 6.4% 7.1% 6.2% 6.4% 7.0% Annual cost of the program (million Reais) 1,668 3,228 3,000 1,944 3,984 3,720 1,668 Source: PNAD/IBGE 1999 and author's calculation 26
Conclusions 1. Bolsa Escola’s conditionality is mildly effective: likely to send to school one third of 10-15 year- olds currently not attending (and up to one-half among the poor). 2. Likely to INCREASE number of children studying and working. (Time at school?) 3. The program’s impact on overall poverty and inequality is modest, due largely to low transfer amounts. 27
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