25 September, 2018

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\[ \def\indep{\perp\!\!\!\perp} \def\Er{\mathrm{E}} \def\R{\mathbb{R}} \def\En{{\mathbb{E}_n}} \def\Pr{\mathrm{P}} \newcommand{\norm}[1]{\left\Vert {#1} \right\Vert} \newcommand{\abs}[1]{\left\vert {#1} \right\vert} \DeclareMathOperator*{\argmax}{arg\,max} \DeclareMathOperator*{\argmin}{arg\,min} \]

Introduction

Background

  • Program Keluarga Harapan : pilot conditional cash transfer program in Indonesia
    • Alatas et al. (2011), Triyana (2016)

  • Conditional cash transfer: receive cash if

    • Expectant women: 4 prenatal visits, iron supplement, delivery by doctor or midwife, 2 postnatal visits

    • Children under 5: weighed monthly, vaccinated, vitamin A

  • Quarterly transfer of 600,000-2,200,000 rupiah ($60 - $220) depending on household composition (15-20% of quaterly consumption)

  • Randomized at subdistrict level : want to capture supply side effects that would occur if policy implemented everywhere

Baseline characteristics

Main results

Delivery attendant usage

ITT estimates
Dependent variable:
Doctor Midwife Traditional
(1) (2) (3)
pkh_kec_ever 0.043*** 0.094*** -0.090***
(0.012) (0.017) (0.016)
Observations 6,629 6,629 6,629

Delivery attendant usage

IV effect of program participation
Dependent variable:
Doctor Midwife Traditional
(1) (2) (3)
pkh_ever(fit) 0.091*** 0.198*** -0.189***
(0.025) (0.036) (0.035)
Observations 6,629 6,629 6,629

Health outcomes

ITT estimates
Dependent variable:
Infant mortality Birthweight Low birthweight
(1) (2) (3)
pkh_kec_ever 0.005 -5.559 0.017
(0.004) (23.805) (0.012)
Observations 8,303 4,988 4,988

Health outcomes

IV effect of program participation
Dependent variable:
Infant mortality Birthweight Lowbirthweigt
(1) (2) (3)
pkh_ever(fit) 0.011 -12.674 0.039
(0.008) (54.269) (0.026)
Observations 8,303 4,988 4,988

Exploring heterogeneity

Machine learning as proxy

  • Generic machine learning approach of Chernozhukov et al. (2018)

  • Estimate machine learning proxies for \(B(x) = \Er[y(0)|x]\) and \(S(x) = \Er[y(1) - y(0) |x]\)

  • Use proxies to :

    • Estimate best linear projection on true \(\Er[y(1) - y(0)|x]\)

    • Estimate \(\Er[y(1) - y(0) | groups]\)

Heterogeneity in CATE for Birthweight

Best linear projection of CATE

  • Randomly partition sample into auxillary and main samples

  • Use any method on auxillary sample to estimate \[S(x) = \widehat{\Er[y(1) - y(0) | x]}\] and \[B(x) = \widehat{\Er[y(0)|x]}\]

  • Use main sample to regress with weights \((P(x)(1-P(X)))^{-1}\) \[ y = \alpha_0 + \alpha_1 B(x) + \beta_0 (d-P(x)) + \beta_1 (d-P(x))(S(x) - \Er[S(x)]) + \epsilon \]

  • \(\hat{\beta}_0, \hat{\beta}_1 \to_p \argmin_{b_0,b_1} \Er[(s_0(x) - b_0 - b_1 (S(x)-E[S(x)]))^2]\)

  • \(\Lambda = \beta_1^2 Var(S(x)) = corr(s_0(x),S(X))^2 Var(s_0(x))\)

Machine learning proxies as BLP of CATE on Birthweight
Lasso Regression forest Neural network
ATE=b0 -3.325 -12.390 -9.003
se 33.095 32.024 31.416
b1 0.169 0.435 0.114
se 0.480 0.653 0.118
Lambda 562.187 574.082 403.610

Group average treatment effects

  • Define \(G_k = 1\{\ell_{k-1} \leq S(x) \leq \ell_k\}\) with \(\ell_k = k/5\) quantile of \(S(x)\)

  • Use main sample to regress with weights \((P(x)(1-P(X)))^{-1}\) \[ y = \alpha_0 + \alpha_1 B(x) + \sum_k \gamma_k (d-P(X)) 1(G_k) + \epsilon \]

  • \(\hat{\gamma}_k \to_p \Er[y(1) - y(0) | G_k]\)

  • \(\bar{\Lambda} = \frac{1}{K} \sum_k \gamma_k^2\)

GATE on Birthweight
Lasso Regression forest Neural network
GATE 1 -16.413 -28.554 -14.990
se 71.836 72.023 62.556
GATE 2 44.850 -39.772 -30.630
se 67.828 64.132 67.542
GATE 3 -41.362 -1.857 -5.024
se 71.415 63.443 68.606
GATE 4 -25.154 -28.400 0.072
se 69.296 65.399 70.607
GATE 5 12.703 54.117 84.213
se 72.644 76.440 71.837
Lambda 2850.894 6524.788 3937.901

Heterogeneity in CATE on Midwife utilization

Machine learning proxies as BLP of CATE on Midwife Use
Lasso Regression forest Neural network
ATE=b0 0.057 0.058 0.056
se 0.024 0.024 0.025
b1 0.368 0.606 0.150
se 0.167 0.263 0.088
Lambda 0.003 0.003 0.002

GATE on Midwife Use
Lasso Regression forest Neural network
GATE 1 0.012 0.000 0.036
se 0.049 0.054 0.057
GATE 2 -0.023 -0.024 0.030
se 0.052 0.051 0.058
GATE 3 0.022 0.021 0.044
se 0.052 0.050 0.047
GATE 4 0.056 0.058 0.034
se 0.056 0.050 0.053
GATE 5 0.169 0.178 0.137
se 0.053 0.053 0.052
Lambda 0.008 0.009 0.009

Covariate means by group

References

Alatas, Vivi, Nur Cahyadi, Elisabeth Ekasari, Sarah Harmoun, Budi Hidayat, Edgar Janz, Jon Jellema, H Tuhiman, and M Wai-Poi. 2011. “Program Keluarga Harapan : Impact Evaluation of Indonesia’s Pilot Household Conditional Cash Transfer Program.” World Bank. http://documents.worldbank.org/curated/en/589171468266179965/Program-Keluarga-Harapan-impact-evaluation-of-Indonesias-Pilot-Household-Conditional-Cash-Transfer-Program.

Chernozhukov, Victor, Mert Demirer, Esther Duflo, and Iván Fernández-Val. 2018. “Generic Machine Learning Inference on Heterogenous Treatment Effects in Randomized Experimentsxo.” Working Paper 24678. Working Paper Series. National Bureau of Economic Research. https://doi.org/10.3386/w24678.

Triyana, Margaret. 2016. “Do Health Care Providers Respond to Demand-Side Incentives? Evidence from Indonesia.” American Economic Journal: Economic Policy 8 (4): 255–88. https://doi.org/10.1257/pol.20140048.