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Panel Data Binary Response Model in a Triangular System with Unobserved Heterogeneity

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Amaresh K Tiwari
University of Tartu

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Panel Data Binary Response Model in a Triangular System with Unobserved Heterogeneity

  1. 1. Panel Data Binary Response Model in a Triangular System with Unobserved Heterogeneity Amaresh K Tiwari University of Tartu Amaresh K Tiwari Binar Response Model 1 / 29
  2. 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 Amaresh K Tiwari Binar Response Model 2 / 29
  3. 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. Amaresh K Tiwari Binar Response Model 3 / 29
  4. 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. Amaresh K Tiwari Binar Response Model 4 / 29
  5. 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. Amaresh K Tiwari Binar Response Model 5 / 29
  6. 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. Amaresh K Tiwari Binar Response Model 6 / 29
  7. 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. Amaresh K Tiwari Binar Response Model 7 / 29
  8. 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) Amaresh K Tiwari Binar Response Model 8 / 29
  9. 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. Amaresh K Tiwari Binar Response Model 9 / 29
  10. 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 Amaresh K Tiwari Binar Response Model 10 / 29
  11. 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). Amaresh K Tiwari Binar Response Model 11 / 29
  12. 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. Amaresh K Tiwari Binar Response Model 12 / 29
  13. 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. Amaresh K Tiwari Binar Response Model 13 / 29
  14. 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. 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. Amaresh K Tiwari Binar Response Model 15 / 29
  16. 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. Amaresh K Tiwari Binar Response Model 16 / 29
  17. 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. Amaresh K Tiwari Binar Response Model 17 / 29
  18. 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 Amaresh K Tiwari Binar Response Model 18 / 29
  19. 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) Amaresh K Tiwari Binar Response Model 19 / 29
  20. 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 Amaresh K Tiwari Binar Response Model 20 / 29
  21. 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 Amaresh K Tiwari Binar Response Model 21 / 29
  22. 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 Amaresh K Tiwari Binar Response Model 22 / 29
  23. 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. Amaresh K Tiwari Binar Response Model 23 / 29
  24. 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. Amaresh K Tiwari Binar Response Model 24 / 29
  25. 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% Amaresh K Tiwari Binar Response Model 25 / 29
  26. 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% Amaresh K Tiwari Binar Response Model 26 / 29
  27. 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. 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 Amaresh K Tiwari Binar Response Model 28 / 29
  29. 29. Conclusion & Direction for Future Research Thank You! Amaresh K Tiwari Binar Response Model 29 / 29

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