Amaresh K Tiwari University of Tartu

1. Panel Data Binary Response Model in a Triangular
System with Unobserved Heterogeneity
Amaresh K Tiwari
University of Tartu
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2. Introduction
Binary Choice Model with Strictly Exogeneous Regressors
Consider a Static Binary Choice model for Panel Data:
yit = 1{y∗
it = xxx′
itϕϕϕ + θi + ζit > 0} = H(xxxit,θi,ζit;ϕϕϕ) (1)
y∗
it is the latent variable underlying yit (eg, decision to participate in workforce)
θi: Unobserved Individual Specific Effect/Heterogeneity
ζit: Idiosyncratic Errors
If xxxit is Strictly Exogenous (θi,ζit ⊥ Xi), where Xi = {xxx′
1t,...,xxx′
iT }, then
E(y∗
it|xxxit) = xxx′
itϕϕϕ
Policy Parameter: Average Structural Function (ASF) is given by
G(xxxit) = Pr(yit = 1|xxxit) = Eθ,ζ [H(xxxit,θi,ζit ;ϕϕϕ)|xxxit].
Result: ϕϕϕ and ASF are identified, even Nonparametrically
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3. Model Specification
The Setup when Regressors are Endogenous
Structural Equation: Consider a Binary Outcome yit that takes value 1 and 0
yit = 1{y∗
it = (www′
it,xxx′
it)ϕϕϕ +θi +ζit > 0} = H(xxxit,θi,ζit ;ϕϕϕ) (1)
xit: Continuous Endogenous Variables θi,ζit ⊥ xxxit
Most papers assume that ζit ⊥ xxxit|θi: Point Identification only when ζit is logit (Chamberlain, 2010,
ECA )
Dimension of xit is ‘m’, the dimension of the exogenous variables, wwwit, is ‘r’.
The system of ‘m’ Treatment Choice Equations/Reduced Form for xit is estimated.
xit = πzzzit +αααi +εεεit, (2)
zzzit = (www′
it,˜zzz′
it)′, where ˜zzzit are additional ‘Instruments’ with dimension greater that or equal to ‘m’.
Time Invariant Individual Effect: αααi = (αααi1,...,αααm)′
Idiosyncratic Component: εεεit = (εεε1it,...,εεεmit)′.
zzzit are Exogenous Variables: εεεit ⊥ zzzit,ααα.
To ease notation, wwwit in (1) is suppressed in the rest of the slides.
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4. Objectives
Objectives
Develope a Control Function Method to Estimate consistently when xxxit is Endogenous:
θi,ζit ⊥ xxxit ( Papke and Wooldridge, 2008 (JoE); Hoderlein and White, 2012 (JoE) ).
Point Identification & Estimation of ϕϕϕ
Point Identification & Estimation of Average Structural Function (ASF): (Blumdell and
Powel, 2004, REStd)
G(xxxit) = Eθ,ζ [H(xxxit,θi,ζit;ϕϕϕ)]
It is the counterfactual conditional probability that yit = 1 given xxxit = ¯xxx as if xxxit were
exogenous, i.e., if the conditional distribution of θi,ζit given xxxit = ¯xxx were assumed to be
identical to their true marginal distribution.
Point Identification & Estimation of Average Partial Effect (APE) of w
∂G(xxxit)
∂w
where w ∈ xxxit.
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5. Objectives
Objectives
Allow for Discrete Instruments, ˜zzz
Torgovitsky (2015), ECA; D’Haultfœuille and Février (2015), ECA:
(Non-separable, Nonparametric, Triangular but Scalar Heterogeneity)
Allow for Limited Multidimensional Heterogeneity in the Structural (θi,ζit)
& Treatment Choice equation (αααi,εεεit)
θi and αααi could random effects or random coefficients. I only present the model
with random effects.
Many nonparametric, non-separable models in a triangular setup allow the
dimension of Heterogeneity in Structural Equation to be arbitrary but Scalar
Heterogeneity in the Treatment Choice equation.
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6. Identification Strategy
Identification with Control Functions
The “control function” approach is a method for correcting inconsistency that
arise due to endogeneity of covariates.
The idea is to model the dependence between unobserved variables (θi,ζit) on the
observables (Xi,Zi) in a way that allows us to construct functions, C(Xi,Zi), such
that, conditional on the functions, the endogeneity problem disappears.
If
θi,ζit|xxxit,C(Xi,Zi) ∼ θi,ζit|C(Xi,Zi)
where Zi = (zzz′
i1,...,zzz′
iT )′, Xi = (x′
i1,...,x′
iT )′, then
E(yit|xxxit,C(Xi,Zi)) = Pr[xxx′
itϕϕϕ > −(θi + ζit)|xxxit,C(Xi,Zi)]
= F(xxx′
itϕϕϕ,C(Xi,Zi)),
where F(xxx′
itϕϕϕ,C(Xi,Zi)) is the conditional c.d.f. of −(θi + ζit) given C(Xi,Zi).
Then we can estimate ϕϕϕ and ASF consistently.
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7. Identification Strategy
How can we model the dependence between unobserved errors (θi,ζit) on the
observables (Xi,Zi)?
The identification strategy that allows us to construct control functions is based on
the following conditional distribution restriction:
Assumption 1: ζζζi,θi ⊥ Zi|αααi,εεεi and εεεi ⊥ Zi,αααi, where Zi = (zzz′
i1,...,zzz′
iT )′,
ζζζi = {ζi1,...,ζiT }′ , and εεεi = {εεε′
i1,...,εεε′
iT }′.
Assumption 1 is weaker. In traditional control function method it is assumed that
ζit,θi ⊥ Zi|υυυit = αααi +εεεit; that is, heterogeneity is scalar.
Assumption 1 implies that
θi,ζit|Xi,Zi,αααi ∼ θi,ζit|Xi − E(Xi|Zi,αααi),Zi,αααi
∼ θi,ζit|εεεi,Zi,αααi
∼ θi,ζit|εεεi,αααi.
According to Assumption 1, the dependence of the structural error term θi and ζit on
the regressors Xi, Zi, and αααi is completely characterized by the reduced form error εεεit
and αααi.
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8. Identification Strategy
If the conditional expectation of θi + ζit is
E(θi + ζit|Xi,Zi,αααi) = E(θi + ζit|αααi,εεεi) = ρρρααααi +ρρρεεεεit,
where ρρρα and ρρρε respectively are vectors of population regression coefficients of
θi + ζit on αααi and εεεit.
Then
E(y∗
it|Xi,Zi,αααi) = E(y∗
it|αααi,εεεi) = xxx′
itϕϕϕ +ρρρααααi +ρρρεεεεit.
In standard Control function method the control function,
υυυit = αααi +εεεit = xxxit − πzzzit, is identified.
In our model, εεεit = xit − πzzzit −αααi and αααi are not identified because αααi is
unobserved.
What we can do is that we can integrate out αααi
E(y∗
it|Xi,Zi) = E(y∗
it|Xi,Zi,αααi)f(αααi|Xi,Zi) = xxx′
itϕϕϕ +ρρρα ˆαααi(Xi,Zi)+ρρρε ˆεεεit(Xi,Zi),
where ˆααα(Xi,Zi) ≡ E(αααi|Xi,Zi) and ˆεεεit(Xi,Zi) ≡ E(εεεit|Xi,Zi)
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9. Identification Strategy
Estimation of Treatment Choice Equations (First Stage)
xit = πzzzit +αααi +εεεit, (2)
Since αααi and Zi are correlated, to consistently estimate (2), we assume the conditional distribution
of αααi:
Assumption 2: αααi|Zi ∼ N E(αααi|Zi),Λαα ,
so that the tail, aaai = αααi −E(αααi|Zi) is distributed normally with mean zero and variance Λαα ,
and where E(αααi|Zi) = ¯π¯zzz is a Chamberlain (1984) or Mundlak (1978) type specification for
correlated random effects.
Then we have
xxxit = πzzzit + ¯π¯zzzi +aaai
αααi
+εεεit, which, with a slight abuse of notation, we write as
xxxit = πzzzit +aaai +εεεit. (2)
where
Assumption 3: εεεit ∼ N 0,Σεε .
The parameters Θ1 = {π,Σεε ,Λαα } of (2) is estimated using Biorn’s (2004) step-wise ML method.
When xit is scalar, there are estimators that allow for non-spherical error components.
Parameterization of reduced form easily gives conditional distribution of αααi given Xi and Zi.
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10. Identification Strategy
It turns out that
ˆαααi(Xi,Zi,Θ1) = ¯π¯zzzi + ˆaaai(Xi,Zi,Θ1)
= ¯π¯zzzi +[TΣ−1
εε +Λ−1
αα ]−1
Σ−1
εε
T
∑
t=1
(xxxit −πzzzit).
ˆaaai(Xi,Zi,Θ1) is the Expected a Posteriori value of aaai.
ˆεεεit(Xi,Zi,Θ1) = xxxit −πzzzit − ˆaaai(Xi,Zi,Θ1)
If the population parameters, Θ1, were known we could write y∗
t in error form as
y∗
it = E(y∗
it|Xi,Zi)+ ˜ζit = xxx′
itϕϕϕ +ρρρα ˆαααi +ρρρε ˆεεεit + ˜ζit
= X′
itΘ2 + ˜ζit,
where ˜ζit is distributed independently of Xi and Zi.
Equation (1) then is written as
yit = 1{X′
it Θ2 + ˜ζit > 0}. (3)
The identification conditions for Θ2 when the distribution of ˜ζit is known:
1 ˜ζit be distributed independently of Xit
2 rank(E(XitX′
it)) = 3m
Lemma 2 of the paper shows that rank(E(XitX′
it)) = 3m if
1 rank(E(xxxitxxx′
it)) = m
2 rank(πm×k) = m
3 rank(E(zzzitzzz′
it)) = k
4 Σεε & Λαα are positive definite
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11. Identification Strategy
Semiparametric Identification of the Structural Model
We propose ˆεεεit and ˆαααi to be used as control functions for semiparametric estimation.
In semiparametric method we do not have to specify
E(yit|xxxit, ˆεεεit, ˆαααi) = Pr[xxx′
itϕϕϕ > −(θi +ζit)|xxxit, ˆεεεit, ˆαααi]
= F(xxx′
itϕϕϕ; ˆεεεit, ˆαααi)
where F(xxx′
itϕϕϕ; ˆεεεit, ˆαααi) is the conditional c.d.f. of −(θi +ζit) given ˆεεεit and ˆαααi.
Standard control function: the key identifying assumptions is ζit +θi ⊥ xxxit|υυυit where
υυυit = αααi +εεεit = xxxit −πzzzit
Instead assume that ζit,θi ⊥ xxxit|ˆεεεit, ˆαααi, which is weaker:
Given that ˆεεεit = υυυit − ˆαααi, there is one-to-one mapping between (ˆεεεit, ˆαααi) and (υυυit, ˆαααi).
Therefore the conditioning σ-algebra, σ(ˆεεεit, ˆαααi), is same as the σ-algebra, σ(υυυit, ˆαααi).
Conditioning on ˆεεεit and ˆαααi is equivalent to conditioning on υυυt and additional individual specific
information as summarized by ˆαααi (Accounting for heterogeneity).
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12. Identification Strategy
Semiparametric Identification: When is ζit,θi ⊥ xxxit|ˆεεεit, ˆαααi.
When is ζit,θi ⊥ xxxit|ˆεεεit, ˆαααi.
It does not follow from the maintained assumptions.
V ≡ {υυυ′
1,... ,υυυ′
T }′ is identified.
ˆεεεit and ˆαααi are functions of υυυt’s.
Let E(αααi|Zi) = 0. For an individual i:
AS 1: ζit,θi|Xi,Zi ∼ ζit,θi|Zi,Xi −E(Xi|Zi) = Vi
∼ ζit,θi|Vi.
Further assume that
AS 2: ζit,θi|Vi ≡ {υυυ′
i1,...,υυυ′
iT }′
∼ ζit,θi|υυυit, ¯υυυi,
where ¯υυυi = ∑T
s=1 υυυis; that is, if we assume that conditional on sum or average of υυυit’s, υυυi,−t is
independent of ζit,θi, then
ζit,θi|υυυit, ¯υυυi ∼ ζit,θi|υυυit, ˆαααi ∼ ζit,θi|ˆεεεit, ˆαααi,
The first equality in distribution follows because Σ = [TΣ−1
εε +Λ−1
αα ]−1Σ−1
εε is a positive definite
matrix, hence ¯υυυi = ∑T
s=1 υυυis → ∑T
s=1 Συυυis = ˆαααi is a one-to-one mapping.
The second follows again because of one-to-one mapping between (ˆεεεit, ˆαααi) and (υυυit, ˆαααi).
If E(αααi|Zi) = 0, the required condition is AS 3: ζit,θi|Vi ≡ {υυυ′
i1,...,υυυ′
iT }′ ∼ ζit,θi|υυυit, ˆαααi.
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13. Identification Strategy
Identification and Estimation of Average Structural
Function
The Average Structural Function (ASF), G(xxxit), can be obtained by averaging
over ˆααα and ˆεεεt.
G(xxxit) = Pr(yit = 1|xxxit) = F(xxx′
itϕϕϕ; ˆαααi, ˆεεεit)dF( ˆαααi, ˆεεεit). (4)
The above requires that the support of ˆαααi and ˆεεεit be independent of xxxit.
Lemma 3: The support of the conditional distribution of ˆαααi(Xi,Zi,Θ1) and
ˆεεεit(Xi,Zi,Θ1), conditional on xxxit = ¯xxx, is same as the support of their marginal
distribution.
Intuition: Because ˆαααi is a continuous and unbounded functions of xxxit ∀t, and because
xxxis, s = t, which is unrestricted, has an unbounded support, the support of the
conditional distribution – conditional on ¯xxxit – of ˆαααi and ˆεεεit = xxxit −πππzzzit − ˆαααi are
unbounded too.
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14. Identification Strategy
Identification and Estimation of Average Structural
Function
If ˜ζit in yit = 1{X′
itΘ2 + ˜ζit > 0} is normally distributed,
Average Structural Function (ASF)
G(xxxit) = Pr(yit = 1|xxxit, ˆαααi, ˆεεεit)dFˆαααi,ˆεεεit
= Φ xxx′
itϕϕϕ +ρρρα ˆαααi +ρρρε ˆεεεit dFˆαααi,ˆεεεit
Sample Analog: G(xxxit) =
1
NT
N
∑
i=1
T
∑
t=1
Φ xxx′
it ˆϕϕϕ + ˆρρρα
ˆˆαααi + ˆρρρε
ˆˆεεεit ,
where Φ is the cumulative distribution function of a standard normal.
The Average Partial Effect (APE) of wt is given by
∂G(xxxit)
∂w
=
∂ Pr(yit = 1|xxxit)
∂w
= ϕwφ xxx′
itϕϕϕ +ρρρα ˆαααi +ρρρε ˆεεεit dFˆεεεit , ˆαααi
Sample Analog:
∂G(xxxit)
∂w
=
1
NT
N
∑
i=1
T
∑
t=1
ˆϕwφ xxx′
it ˆϕϕϕ + ˆρρρα
ˆˆαααi + ˆρρρε
ˆˆεεεit ,
where φ is the density function of a standard normal and ϕw is the coefficient of w.
Amaresh K Tiwari Binar Response Model 14 / 29

15. Estimation
Accounting for Heteroscedasticity and Serial Correlation in
the Estimation Of Probit Conditional Mean Function
To obtain consistent estimates of the structural parameters of interest,
Θ2 = {ϕϕϕ′,ρρρ′
α,ρρρ′
ε }′, one can employ Nonlinear Least Squares by pooling the
data.
However, since Var(yit|Xi,Zi) will most likely be heteroscedastic and since there
will be serial correlation across time in the joint distribution,
F(yi0,...,yiT |Xi,Zi), the estimates, though consistent, will be estimated
inefficiently resulting in biased standard errors.
Modeling F(yi0,...,yiT |Xi,Zi) and applying MLE methods, while possible, is
not trivial. Moreover, if the model for F(yi0,...,yiT |Xi,Zi) is misspecified but
E(yit|Xi,Zi) is correctly specified, the MLE will be inconsistent for the
conditional mean parameter, Θ2, and resulting APEs.
To account for heteroscedasticity and serial dependence we employ
Multivariate Weighted Nonlinear Least Squares (MWNLS) to obtain
efficient estimates of Θ2.
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16. Household Income and Wealth Effect on Child Labor
Motivation
Most incidence of Child Labor takes place in Rural Areas of Developing Countries.
While Poverty is held to be the main cause of Child Labor, it has been found
that the amount a Child Work increases with the amount of Land the
household own. Basu et al. (2010), Dumas (2007), Bhalotra and Heady (2003)
Since land is usually strongly correlated with a household’s income, this finding
challenges the presumption that child labor involves the poorest households.
What is the Cause for this Phenomena?
• Negative Wealth Effect of large Landholding or any Asset Reduces
Child Labor.
• Labor and Land market Imperfections Increase Child Labor as
Landholding Increases.
=⇒ Incentive for child labor due to labor and market imperfections dominates the
wealth effect of landholding.
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17. Household Income and Wealth Effect on Child Labor
Research Question
How does Income, Landholding and Productive Farm Assets affect Child Labor?
Income
• Major component of household income is non-agriculture
income. Also tests the Poverty Hypothesis
Landholding
• Economic Development, Economic Reforms, and
Commercialization may reduce Labor and Land market
imperfection. The kind of relationship between landholding and
child labor therefore is an empirical issue.
Productive Farm Assets
• Productive Farm Assets may have different implication for child
labor, because they may not be operated by children.
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18. Household Income and Wealth Effect on Child Labor
Data
Data from Young Lives Study (YLS). Collected by Oxford University
A panel study from six districts of the state of Andhra Pradesh
We consider two rounds 2006-07 and 2009-2010
Children in the age group of 5 to 14 years in the base year
Information on 2458 children in each year
Table: Work Status of Children
Work
Not Working Working Total
2007 68.13 31.87 100.00
2010 46.23 53.77 100.00
The figures are in percentage.
Total number of children/observations in each period: 2458
Work defined as domestic + paid employment
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19. Household Income and Wealth Effect on Child Labor
Empirical Model
Structural Model
yit = 1{y∗
it = (www′
it,xxx′
it)′
ϕϕϕ + θi + ζit > 0} (1)
Decision Variable yit = 1 if the child i works, 0 otherwise
Endogenous Regressors: xxx = {IN,LN,AS}
IN: Total Income (in thousands) of the household
LN: Size of the Landholding: Distribution of Landholding has changed over
the years, can’t be Exogenous
AS: Index of number of Productive Farm Assets (Principal Component
Analysis)
Exogenous Regressors: www
Treatment Choice Equation (Estimated in the First Stage)
xxxit = πzzz′
it +αααi +εεεit (2)
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20. Household Income and Wealth Effect on Child Labor
Instruments for Endogenous Regressors
For the endogenous regressors: x = {IN,LN,AS} we need instruments ˜zit
Funds sanctioned through National Rural Employment Guarantee Scheme
(NREGS) at the Regional level
• Fund sanctioned at the beginning of the financial year can not be affected by
current demand for work
• More funds sanctioned → more work opportunity in NREGS → positive effect
on household income (IN)
CASTE, Discrete Variable:
1 for Scheduled Castes and Tribes (SC/ST),
2 for Other Backward Classes (OBC),
3 for Others (OT)
• Wealth and Income are distributed along Caste Lines
• Child labor & Schooling not affected by the Caste
Dummy Variables Capturing Infrastructure Development
• Households in Regions where infrastructure development is high are expected to
possess more Productive Assets
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21. Household Income and Wealth Effect on Child Labor
Modified Structural Equations
yt = 1{(www′
it,xxx′
it)′
ϕϕϕ +ρρρα ˆαααi +ρρρε ˆεεεit + ˜ζit > 0}, (3)
where ˜ζit is normally distributed with variances σζ (Heteroscedastic)
=⇒ Control Function: ˆαααi and ˆεεεit
ρρρε ˆεεεt = ρεIN
ˆεtIN + ρεLN
ˆεtLN + ρεAS
ˆεtAS and
ρρρα ˆααα = ραIN
ˆαIN + ραLN
ˆαLN + ραAS
ˆαAS
For Example, Income :
ραIN and ρεIN : Test of exogeneity of “Income" (IN) with respect to θ and ζ
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22. Household Income and Wealth Effect on Child Labor
Table: Household Income and Wealth Effect on Child’s Decision to
Work
Panel Probit† EAP Control Functions
Coefficients Coefficients APEs
Income 0.00326∗∗∗ -0.0234∗∗∗ -0.0054∗∗∗
(0.0009) (0.0028) (0.0008)
Landholding 0.002 0.031∗∗∗ 0.0071∗∗∗
(0.002) (0.007) (0.0017)
Farm Asset Index -0.012 -0.976∗∗∗ -0.226∗∗∗
(0.0296) (0.169) (0.0302)
Age 2.288∗∗∗ 0.402∗∗∗ 0.093∗∗∗
(0.102) (0.057) (0.009)
Sex 0.731∗∗∗ 0.394∗∗∗ 0.0908∗∗∗
(0.053) (0.0473) (0.0129)
ln(σ2
θ )‡ -1.302∗∗∗
(0.239) Control Functions
ˆαINCOME 0.005∗
(0.00302)
ˆαLAND -0.015∗∗
(0.0065)
ˆαASSET 1.512∗∗∗
(0.129)
ˆεINCOME 0.0275∗∗∗
(0.003)
ˆεLAND -0.031∗∗∗
(0.0075)
ˆεASSET 0.882∗∗∗
(0.185)
Total number of children: 2458
Total number of observations: 4916. Total number of observations with positive outcome: 2128
† Panel Probit is the Chamberlain’s (1984) method with Correlated Random Effects.
‡ σθ is the panel-level standard deviation (see STATA command ‘xtprobit’).
All the specifications include time dummy, district dummies, and the interaction of the two.
Standard errors (SE) in parentheses
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23. Household Income and Wealth Effect on Child Labor
Effect of Midday Meal Scheme on Child Labor
Figure: Children having midday meal at schools.
The Midday Meal Scheme is the world’s largest school feeding programme.
It aims at providing nutrition to children
Encourage poor children of the disadvantaged sections to attend school more
regularly, so that enrollment, retention and attendance rates increase.
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24. Household Income and Wealth Effect on Child Labor
Effect of Midday Meal Scheme on Child Labor
Baland & Robinson, 2000, (JPE) show that child labor, which hampers human
capital accumulation, can be socially inefficient.
The family cannot be expected to solve this source of inefficiency on its own.
Ban on child labor, or, more generally, government policies that seek to alleviate
child labor could be welfare enhancing.
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25. Household Income and Wealth Effect on Child Labor
Effect of Midday Meal Scheme on Child Labor & Schooling
Table: Effect of household income, wealth, and availability of free midday-meal
at school on decision to work and attend school for Index children.
Work School
Coefficients APEs Coefficients APEs
Income -0.0232∗∗∗ -0.0041∗∗∗ 0.0128∗ 0.0016∗∗
(0.00446) (0.0011) (0.00692) (0.0007)
Landholding 0.0442∗∗∗ 0.0078∗∗∗ -0.00629 -0.0008
(0.0109) (0.002) (0.0195) (0.0024)
Farm Asset Index -1.284∗∗∗ -0.2268∗∗∗ 1.559∗∗∗ 0.1906∗∗∗
(0.289) (0.0403) (0.327) (0.0588)
Age 0.757∗∗∗ 0.1337∗∗∗ -0.797∗∗∗ -0.0974∗∗∗
(0.121) (0.0104) (0.182) (0.0362)
Sex 0.308∗∗∗ 0.0543∗∗∗ -0.00963 -0.0012
(0.0757) (0.0153) (0.121) (0.0147)
Midday Meal -0.180∗∗ -0.0317∗∗ 2.003∗∗∗ 0.2355∗∗∗
(0.0701) (0.0136) (0.248) (0.0326)
ˆαINCOME 0.00582 -0.0151∗∗
(0.00504) (0.00722)
ˆαLAND -0.00977 0.0126
(0.00897) (0.0138)
ˆαASSET 1.757∗∗∗ -1.541∗∗∗
(0.214) (0.332)
ˆεINCOME 0.0283∗∗∗ 0.00219
(0.00476) (0.00672)
ˆεLAND -0.0451∗∗∗ -0.0247∗
(0.0111) (0.0147)
ˆεASSET 1.146∗∗∗ -1.432∗∗∗
(0.323) (0.324)
Total number of Index children: 1265; Total number of observations: 2530
Total number of observations with DWORK=1: 884
Total number of observations with DSCHOOL=1: 2350
All the specifications include time dummy, district dummies, and the interaction of time and district dummies.
Standard errors are in parentheses.
Significance levels : ∗ : 10% ∗∗ : 5% ∗∗∗ : 1%
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26. Household Income and Wealth Effect on Child Labor
Effect of Midday Meal Scheme on Child Labor & Schooling
Table: APE’s of Income, Wealth & Midday Meal on Child’s Decision to Work
and Attend School for different Social Groups
Work
Scheduled Caste/Tribe Other Backward Class Others
Income -0.004∗∗∗ -0.0042∗∗∗ -0.0035∗∗∗
(0.0012) (.0011) (0.0006)
Landholding 0.0075∗∗∗ 0.008∗∗∗ 0.0066∗∗∗
(0.0021) (.002) (0.0016)
Farm Asset Index -0.2191∗∗∗ -0.2316∗∗∗ -0.1908∗∗∗
(0.0379) (.0426) (0.0392)
Midday Meal -0.0306∗∗ -0.0324∗∗ -0.0265∗∗∗
(0.0137) (.0138) (0.01)
School
Scheduled Caste/Tribe Other Backward Class Others
Income 0.0019∗∗ 0.0015∗∗ 0.001∗∗
(0.0009) (0.0006) (0.0005)
Landholding -0.0009 -0.0007 -0.0005
(0.0029) (0.0022) (0.0016)
Farm Asset Index 0.2329∗∗∗ 0.1787∗∗∗ 0.1243∗∗∗
(0.0665) (0.0578) (0.0362)
Midday Meal 0.299∗∗∗ 0.2216∗∗∗ 0.1288∗∗∗
(0.0346) (0.0337) (0.0201)
Standard errors in parentheses
Significance levels : ∗ : 10% ∗∗ : 5% ∗∗∗ : 1%
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27. Household Income and Wealth Effect on Child Labor
Summary of Results
Probability of child labor decreases with Household Income and Productive
Farm Assets
Probability of child labor Increases with Land Ownership
Boys more likely to work
Older children more likely to work
Child labor, Income, Landholding and Productive Farm Assets are determined
simultaneously
Provision of free midday meal at school, reduces child labor and increases
school attendance.
The Control Function estimator performs better than Standard Binary Choice
For Panel Data
Amaresh K Tiwari Binar Response Model 27 / 29

28. Conclusion & Direction for Future Research
Conclusion & Direction for Future Research
The method allows for
Continuous Endogenous Covariates
Limited multidimensional heterogeneity
General Instruments in the estimation of ASF and APE
No assumption about the Serial Dependence in the response outcomes and
provides an estimation strategy to account for it.
Future Research
Semi or Non-parametric estimation of the Control Functions
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29. Conclusion & Direction for Future Research
Thank You!
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