Do Financial Incentives Induce Unequal Parental Investment ......conditional cash transfers to...

Do Financial Incentives Induce Unequal Parental Investment Across Siblings? Evidence from a Field Experiment

Amanda Chuan, John List, and Anya Samek

October 31, 2017

Abstract

Human capital is crucially affected by parental investment in early childhood. One way to induce parents to invest in children is to decrease the shadow price of investment by providing financial incentives. Yet, incentivizing investment in one child may have negative consequences for allocation of time to other children in the household. We take advantage of a novel field experiment in which low-income parents of 3-5 year-olds were exposed to a year-long parenting intervention and were randomized to either receive immediate or delayed incentives to invest in the targeted child. We surveyed parents regarding the time they spent with their targeted child and with the child’s siblings. As predicted, we found that parents spent more time with targeted children when they received immediate rewards relative to delayed rewards. Importantly, we found statistically significantly lower time investment in siblings of families treated with the immediate versus the delayed incentive. Our findings point to the importance of considering negative spillover effects of incentivizing parental investment, and are consistent with a model of intra-household resource allocation. Keywords: family economics, intrahousehold allocation, early childhood education JEL Classifications: D13, I21, I24, I26, J13, J24

I. Introduction Early childhood is a crucial time in which the returns to human capital investment

are considered highest (see Almond and Currie, 2011; Cunha and Heckman, 2007;

Heckman, 2006; Heckman and Masterov, 2007; Heckman, 2008; Sacerdote, 2007; Juhn

et al., 2015). A great deal of work has focused on the role of early childhood

interventions, particularly preschool programs, on decreasing the achievement gap

between high and low socio-economic status children (Rolnick and Grunewald, 2003;

Schweinhart et al., 2005; Belfield et al., 2006; Anderson, 2008; Barnett and Masse, 2007;

Heckman and Masterov, 2007; Knudsen et al., 2008; Heckman et al., 2009; Garcia et al.,

2016).

Human capital is affected both by schooling and parental investment decisions in

early childhood. Any changes to parental investment during this period could have large

impacts that propagate throughout the child’s lifetime. In low-income families, parents

must make especially difficult allocation decisions when it comes to their monetary

resources and their time, and may therefore be under-investing in the human capital of

their children (Coleman, 1966; Raudenbush, 2004; Heckman, 2006) These challenges are

exacerbated in low-income families with multiple children, since parents may also be

forced to make hard trade-offs in investments across children.

In cases where parents experience different marginal returns from investing in

each child, the most efficient allocation of parental inputs could lead to unequal amounts

of human capital investment across children (Becker and Tomes, 1976). In this study, we

explore how parental investment changes when we vary key factors that change the

shadow price of investing in some children within the household. Recent research has

demonstrated a potential for a policy of conditional cash transfers to increase parental

investment in and academic outcomes of low SES children (Schultz, 2004; de Janvry et

al., 2006; Baez and Camacho, 2011; Barrera-Osorio et al., 2006, 2011; Baird et al., 2011;

Angrist et al., 2006; Ferreira et al., 2009). Yet, while conditional cash transfers have been

studied relative to the impact on the targeted child, there is mixed evidence about their

impact on non-targeted siblings. Moreover, all research in this area has focused on

children in a developing context, which is uniquely different from a developed country

context.

We take advantage of the Chicago Heights Early Childhood Center (CHECC)

intervention, a unique randomized controlled trial designed to increase parental

investment in their preschool-aged children. A main finding of CHECC was that an

incentivized, year-long parenting intervention (called “Parent Academy”) increases the

academic achievement of treated children relative to a control group (Fryer et al., 2015).

In this paper, we focus on the parental resource allocation problem associated with Parent

Academy treatments that incentivized parents to invest in children. Specifically, we

administered surveys to CHECC parents to determine whether parents increase time

investments toward their preschool-aged children and shift investments away from their

non-preschool-aged children as a result of the incentives provided as part of the

interventions.

The CHECC Parent Academy program provided parents with a bi-monthly class

during which parents learned how to teach to their child at home and earned financial

incentives for investing in their preschool-aged child (the “CHECC child”). Parents could

earn almost $7,000 each year for participation in the parenting classes, completion of

homework with their preschool-aged child, and improvements in their preschool-aged

child’s academic performance. Children in the Parent Academy did not receive any

additional educational interventions. The financial incentive effectively decreased the

shadow price of investment in the CHECC child while holding constant the price of

investment for other children in the household (for simplicity, we will call other children

in the household who are not directly targeted by the CHECC program “siblings”). Since

the net-of-cost marginal return for the CHECC child increased substantially relative to

that of the child’s siblings, our first prediction is that parents will invest less in siblings

that were not targeted by the program relative to the CHECC child.

Two treatment groups of Parent Academy were implemented: both

included the same course-work and examinations, but differed in the incentives provided

to the parents. In one treatment group, financial incentives were paid out immediately in

cash. In the other group, the majority of financial incentives were directly deposited into

a bank account and could only be accessible once the CHECC child enrolled in post-

secondary education years later. We therefore specifically compare between these two

treatment groups and show that substitution patterns differ when parents are given

immediate versus delayed incentives. We find that the difference in the two treatments

led to significant differences in parents’ investment strategies. Parents in the immediate

payment group appeared to shift significantly more investment away from siblings than

parents in the delayed payment group.

Our results are consistent with a model of intra-household resource reallocation.

We present a simple model in which households must allocate parental time and money

to investment in the CHECC child and siblings. We show that the shadow price of

investing in the CHECC child, relative to the siblings, is much lower when parents are

paid their financial incentives immediately relative to with a delay. Therefore, parents

randomized to the Cash treatment will trade off a greater amount of sibling investment to

obtain the same increase in CHECC child investment relative to parents randomized to

the College treatment.

The aim of the Parent Academy was to improve parents’ teaching abilities and

make parents more motivated to teach to their children, which could in turn generate

positive spillover effects to children not directly targeted by the program. These positive

spillover effects should not differ between the immediate and the delayed incentive

payments, since parents in both groups attended the same parenting classes, completed

the same homework assignments, and brought their CHECC children to the same

assessments during the same time period. The experimental design therefore allows us to

isolate the effect of the immediate versus delayed financial incentive payments on

substitution of parental time across children.

Our study connects three streams of literature: the literature that explores the

quantity-quality trade-off in children (see Willis, 1973; Becker and Lewis, 1973; Becker

and Tomes, 1976; Angrist et al., 2010; Black et al., 2005, 2008, 2011, 2017; Juhn et al.,

2015; Rosenzweig and Zhang, 2009; Sacerdote, 2007), the literature on early childhood

development (see Cunha et al., 2006; Heckman, 2006; Heckman and Masterov, 2007;

Knudsen et al., 2006; Rolnick and Grunewald, 2003; Schweinhart et al., 2005; Cunha and

Heckman, 2008), and the literature on conditional cash transfers (see Behrman et al.,

2005; Parker and Skoufias, 2000; Schultz, 2004; Schultz, 2004; de Janvry et al., 2006;

Todd and Wolpin, 2006; Baez and Camacho, 2011; Barrera-Osorio et al., 2006, 2011;

Baird et al., 2011; Ferreira et al., 2009; Parker and Todd, 2017). We explore the quantity-

quality trade-off in children in resource-constrained families by providing a financial

incentive for parents to invest in their CHECC children. Specifically, we show that

households shift parental time away from siblings not targeted by the program when the

price of investing in preschool-aged children becomes relatively cheaper. We

demonstrate the existence of trade-offs in human capital investment across children, and

show that financial incentive programs that do not sufficiently address these trade-offs

can have unanticipated negative consequences.

Previous research examined programs that rewarded households for the school

enrollment or attendance of their children. These studies rarely focused on academic

achievement. Here, we directly incentivize parents based on time spent with targeted

children and improvements in the academic performance of targeted children. Much of

the financial reward is on the latter, which parents cannot directly control. In spite of this,

the intervention led to sizable changes in parental investment. Our results show that

households’ human capital investment decisions respond to financial incentives that

condition on academic performance, even if parents experience uncertainty in how their

investment maps onto their children’s academic outcomes.

The majority of the previous work on financial incentives and parental investment

occurs in a developing country context where parents must choose between sending their

children to school or having their children work to earn money for the household. Such a

context may hold little relevance for a developed country seeking to use similar

conditional cash transfers to reduce academic achievement gaps of the rich and poor.

Most of this work found that giving households conditional cash transfers led parents to

assign more work and less schooling to children not targeted by the cash transfer

program. In the United States and in other developed countries, parents do not face the

same harsh tradeoffs between sending children to work and sending them to school.

However, parents do face a tradeoff between how much time to invest in each child,

which is a different dimension of the household resource allocation problem. We directly

examine parental investment decisions using data collected from a survey that we

designed and administered to parents. We measure parental investment as the time

parents spend teaching or reading to each child living in the household. Our program is

designed to elicit a more subtle type of behavior change: greater parental time input,

which could be more difficult to observe from the administrative or school attendance

data typically used by prior work. Our results show that parental time, a crucial input in

the human capital production function, experiences substitution patterns in the face of

external incentives.

II. Background

A large body of work has demonstrated a negative relationship between the

number of children in a household and the human capital of each child (Becker and

Lewis, 1973; Conley and Glauber, 2006; Rosenzweig and Zhang, 2009; Caceres-

Delpiano, 2006; Sacerdote, 2007; Rosenzweig and Wolpin, 1980; Stafford, 1987;

Behrman, Pollak, and Taubman, 1989; Lu and Treiman, 2005; Conley, 2000; Black,

Devereux, and Salvanes, 2005; Ponczek and Souza, 2007; Manacorda, 2006; Rosenzweig

and Zhang, 2009; Juhn et al., 2015). Juhn et al. (2015) find that the arrival of a younger

sibling negatively impacts the formation of cognitive and non-cognitive skills in older

siblings, and that decreases in parental time is the key input that drove these changes.

Based on their results, constraints on parental time might be an important factor behind

under-investment in children among low-income households with multiple children.

Becker and Tomes (1976) considers the implications of differential costs of

investment across siblings within a household. Their model argues that if the costs of

human capital investments differed among children within a household, price effects

would induce parents to shift investment toward children with lower investment costs and

away from children with higher investment costs. Experimental research exploring this

hypothesis is sparse. Studies of financial incentives on parental investment have largely

ignored spillover effects on siblings’ human capital, in spite of the large literature on

financial incentives and child investment. Conditional cash transfer programs have been

shown to increase the years of education of targeted children (Skoufias and Parker, 2001;

Skoufias et al., 2001; Behrman et al., 2005; Todd and Wolpin, 2006; Schultz, 2004;

Coady and Parker, 2004; Barrera-Osorio et al., 2008; Ferreira, Filmer, and Schady, 2009;

Bobonis and Finan, 2009; Angelucci et al., 2010; Behrman, Parker, and Todd 2009a,

Bobonis and Finan, 2009; Lalive and Cattaneo, 2009; de Brauw and Hoddinott, 2011;

Behrman et al., 2012; Behrman, Parker, and Todd, 2011; Dubois, de Janvry, and Sadoulet

2012; Baez and Camacho, 2011; Edmonds and Shrestha, 2015), the grades of targeted

children (Behrman, Parker, and Todd 2009a; Behrman et al., 2012; Baird et al., 2011;

Edmonds and Shrestha, 2015), the health of targeted children (Parker and Todd, 2017;

Gertler, 2004; Rivera et al., 2004; Behrman and Hoddinott, 2005; Fernald, Gertler, and

Neufeld, 2008; Fernald and Gunnar, 2009; Fernald, Gertler, and Neufeld, 2009; Ozer et

al., 2009; Barham, 2011; Andalon, 2011), and parents’ aspirations for their targeted

children (Attanasio and Kaufman, 2014; Chiapa, Garrido, and Prina, 2012).

The few studies that have examined the impact of financial incentives on non-

targeted siblings were conducted in a developing country context. This literature reports

mixed results, potentially due to differences in implementation or context. Some studies

found that using financial incentives increased the enrollment of targeted children, but

decreased the educational attainment of non-targeted siblings (Barrera-Osorio et al.,

2011; Shrestha and Palaniswamy, 2017). A conditional cash transfer program in

Nicaragua increased school enrollment rates for both targeted children and for older

siblings who were not directly targeted themselves, since the transfers gave families the

income needed to send older children back to school (Bustelo, 2011; Takamatsu, 2011).

One study reports no significant spillover impacts of a conditional cash transfer on

siblings (Ferreira, Filmer, and Schady, 2009).

Both context and program structure heavily influenced the spillover effects of the

previous interventions, and more work is required to clearly identify the specific program

components that most significantly influenced outcomes for non-targeted siblings. In the

United States, children must attend school until high school, so the intra-household

resource reallocation observed in prior studies may not occur in our context. Would this

resource reallocation still occur in a developed country? Families do not have to make the

same tradeoff between sending some children to school and sending others to work, but

time is nevertheless a valuable resource that parents need to allocate between children.

III. Experimental Background and Data

A. Experimental Description

The Chicago Heights Early Childhood Center (CHECC) was established in 2010.

An early paper on the impact of the program focused on the academic achievement of

children targeted by a Parent Academy intervention and demonstrated clear gains for

Whites and Hispanics, but not Blacks (Fryer et al., 2015). Chicago Heights is a low-

income area south of the city of Chicago, with Blacks and Hispanics comprising 80% of

the population and a per capita income of $17,546 (Fryer et al., 2015).

Households who register for the CHECC lottery are randomly chosen to

participate in one of several treatment groups, including two treatment arms of the Parent

Academy called “Parent Academy Cash” and “Parent Academy College”. Both the

Parent Academy Cash and Parent Academy College groups were assigned the same

course-work and examinations, and both groups received their earnings for attending

classes immediately in cash. However, financial incentives for performance on

homework, evaluations, and assessments were paid out differently by group. Families

randomized to the Parent Academy Cash group received their earnings for homework,

evaluations, and assessments immediately in cash, while families randomized to the

Parent Academy College group had their earnings for homework, evaluations, and

assessments deposited into a bank account that could only be accessible once the CHECC

child enrolled in post-secondary education in the future.

Over each school year, there were 18 parent academy sessions, 17 homework

assignments, three parent-child evaluations, and three child assessments. Parents had the

opportunity to earn up to $6,900 from the CHECC program. Households participated in

the program for either 1 or 2 years, depending on the age of the child at enrollment and

the year of enrollment. Children enrolled at the age of 4 participated for 1 year, while

children enrolled at the age of 3 could participate for 1 or 2 years, depending on date of

enrollment. Since Parent Academy was implemented in 2010-2011 and 2011-2012, 3-

year-olds enrolled in 2010 could participate for 2 years while 3-year-olds enrolled in

2011 could only participate for only one year.

The Parent Academy classes were held once every two weeks over nine months

during each school year. Parents earned $100 for attending each session, and free onsite

child care services were provided to facilitate attendance. Parents who arrived between 5

to 30 minutes late received $50 instead of $100, and parents who arrived more than 30

minutes late were not paid. Parents were also paid for turning in homework that they

completed with their CHECC child. They received $100 for an A grade, $60 for a B

grade, $30 for a C grade, and $0 for an incomplete grade.

Parent Academy also held three evaluations per year, where parents brought their

CHECC child and interacted with their CHECC child to answer questions administered

by an assessor. Depending on the CHECC child’s absolute performance on these

evaluations, parents could earn up to $600 for each evaluation. If the child got 80-100%

of the evaluation correct, the family earned $600. If the child received 60-79% of the

evaluation correct, the family earned $360. If the child got 40-59% of the evaluation

correct, the family earned $180. If the child got less than 40% of the evaluation correct,

the family earned nothing.

Finally, parents could also earn money based on improvements in their CHECC

child’s academic performance, using CHECC assessments of cognitive and non-cognitive

skills. CHECC administered assessments at the beginning, middle, and end of each

school year. Assessments held at the beginning of the year were not financially

incentivized, but families were required to participate in the assessments in order to enroll

in the CHECC program. Parents could earn up to $800 each during the mid-year and the

end-of-year assessments. In these assessments, parents did not interact with their CHECC

child – rather, a professional assessor privately administered a battery of questions to the

CHECC child on a one-on-one basis. Earnings were determined on a household basis,

since financial incentives were based on the CHECC child’s improvements in academic

performance relative to his or her baseline performance at the beginning of the year.

This paper focuses on the effect of immediate versus delayed cash incentives on

substitution patterns in parental investment, so we directly compare between Parent

Academy Cash and Parent Academy College. In the immediate payment group, the net

marginal return of investing in the CHECC child grew immediately and substantially

relative to the marginal return of investing in other children in the household. In the

delayed payment group, the gain in investing in the CHECC child could only be realized

far into the future, provided that the CHECC child enrolled in some form of post-

secondary education.

B. Data Description

For parental investment data, we use both administrative and survey data.

Administrative data are used to measure parental investment in the CHECC child, while

survey data are used to measure parental investment in both the CHECC child and in

siblings.

The Parent Academy administrative data include information on each family’s

class attendance, homework grades, earnings from evaluations, and earnings from

assessments. These data include all families that were randomized to the Parent Academy

program. To measure parental investment, we examine average number of classes

attended, the overall grades from homework, the total number of homework assignments

that received an “A” grade, the total number of homework assignments that received an

“incomplete” grade, earnings from evaluations, and earnings from assessments.

CHECC also administered a series of surveys throughout the course of the school

year. The parent investment surveys were administered in the middle of the 2010-2011

school year and the 2011-2012 school year. The surveys ask parents about the number of

hours spent teaching to each child in their household per weekday (which includes tasks

such as helping children with homework, teaching children math, and reading to the

child), whether older siblings taught younger siblings in the household, and whether

parents taught multiple children at the same time. The amount of time parents spent

teaching to teach child in the household is the primary measure parental investment in

siblings that were not targeted by CHECC.5

In addition to the parental investment survey, the demographic survey was

administered in May prior to the beginning of the school year. This occurred before the

CHECC lottery, since the randomization blocked on key demographic characteristics. We 5 Parents may teach to multiple children at once, or have their older children teach their younger children. Such behavior may distort our ability to cleanly measure how their time investment decisions respond to financial incentives to invest in the CHECC child. In the appendix, we control for whether older siblings taught younger siblings and whether parents taught multiple children at the same time; we find that our main results are robust to these alternative specifications.

include demographic characteristics in our analysis to control for potential confounding

effects that were not addressed by the block randomization. Our regressions controlled

for the gender of the CHECC child, the age of the CHECC child, the age of the siblings,

household income, the mother’s education, race, the number of adults in the household,

the number of children in the household, the year of the program, and the total number of

years that a family had participated in CHECC.

All analysis was conducted at the household level. All standard errors are

clustered at the household level, which is the level of randomization. We use the number

of Parent Academy classes that parents attended, parents’ grades on Parent Academy

homework, CHECC children’s performance on Parent Academy evaluations, and

CHECC children’s performance on CHECC assessments as the primary measures of

investment in the CHECC child. We use the average number of hours a parent spent

teaching to siblings on a weekday as the primary measure of investment in siblings.

Following Fryer et al. (2015), we only include families with exactly one CHECC

child in our analysis sample. Our sample consists of 186 families with one CHECC child

in Parent Academy (84 in 2010-2011 school year, 135 in 2011-2012 school year, and 33

in both school years). 115 families out of the 186 have one CHECC child and at least one

sibling (31 in the 2010-2011 school year, 94 in the 2011-2012 school year, and 18 in both

school years), so we use this sample to test for substitution effects in parental time.

Table 1 describes summary statistics for the 186 families. Note that some families

are represented twice, since 18 total families were in the program for two years. Table 1

shows summary statistics for the 186 families during the first year of program

participation. Columns (1) and (2) describe the mean and standard error for each variable

for families in the Parent Academy College and Parent Academy Cash groups,

respectively. Other than sibling age, all characteristics were measured at the beginning of

the school year (prior to treatment).

In both conditions, girls consist of 42-46% of the CHECC children sample.

CHECC children are about 4 years old on average, while siblings are 7-8 years old on

average. Black families constitute 38-40% of the sample, Hispanic families consist of 45-

49% of the sample, and the rest comprise of white families. Median mother’s education is

“Some College (but No Degree)” in both conditions. Median household income is

$16,000-25,000 in Parent Academy Cash and $26,000-35,000 in Parent Academy

College; the difference in median household income is not statistically significant. About

52-57% of CHECC children have at least one sibling, and the number of children in each

condition average to 2.5 per household. On average, there are 2.2 adults per household in

each condition. Finally, about 55% of the sample belong in the 2011-2012 school year

and families have spent 1.2 years in the CHECC program at the time of data collection.6

The third column in table 1 provides the difference in means and the associated

standard error. The fourth column lists the t-statistic of a two-sample t-test, and the last

column lists the associated p-value. For all measures, there appear to be no significant

differences in family characteristics, which suggests that the experimental randomization

procedure was successful in balancing observed characteristics that might affect parental

investment across the two conditions.

There are 10 more families in Parent Academy Cash than in Parent Academy

College, making selective attrition a concern in this sample. In appendix table A.1, we

run probit regressions of the probability of participating in the program on randomized

assignment to each condition. We find that randomized assignment has no significant

impact on the likelihood of participating in the program. Equal participation between the

two groups is consistent with one important feature of the experimental design: families

in both Parent Academy Cash and Parent Academy College received their attendance

payments (of up to $100 for each class) in cash.

Table 1: Summary Statistics

VARIABLES PA College PA Cash Difference T-statistic P-value CHECC child is female 0.463

(0.061) 0.418

(0.056) 0.045

(0.083) 0.542 0.588

CHECC child age 4.122 (0.108)

4.019 (0.087)

0.104 (0.138)

0.752 0.454

Sibling age 6.525 (0.595)

7.584 (0.518)

-1.06 (0.790)

-1.34 0.183

Black 0.375 0.398 -0.023 -0.319 0.750

6 For the 2011-2012 school year, we placed greater effort on recruiting families than in the 2010-2011 school year. We therefore had a slightly larger sample for the 2011-2012 school year than the 2010-2011 school year.

(0.052) (0.050) (0.72) Hispanic 0.489

(0.054) 0.449

(0.051) 0.040

(0.074) 0.539 0.591

Mother's education 6.257 (0.354)

6.307 (0.260)

-0.050 (0.430)

-0.116 0.908

Adults in household 2.178 (0.111)

2.207 (0.108)

-0.0284 (0.156)

-0.182 0.856

Children in household 2.466 (0.156)

2.473 (0.142)

-0.007 (0.211)

-0.032 0.974

Household income 4.197 (0.273)

3.900 (0.254

0.297 (0.374)

0.793 0.429

CHECC child has siblings 0.568 (0.053)

0.520 (0.051)

0.048 (0.073)

0.650 0.516

Years in CHECC 1.148 (0.038)

1.204 (0.041)

-0.056 (0.045)

-1.00 0.318

Year = 2011 0.557 (0.053)

0.541 (0.051)

0.016 (0.073)

0.218 0.828

Observations 88 98 186 186 186

Standard errors in parentheses. Sibling age data were collected from the sibling survey, which was administered after the treatment began. All other data were collected prior to each family’s participation in the program. Years in CHECC and year of CHECC variables were collected from the program’s administrative data. All other variables were collected from the demographic survey, administered at the beginning of the school year. The child and sibling investment measures represent program effects; all other variables represent baseline measures and are used as controls in the regression analysis.

IV. Model

To formalize the predictions of our experiment, we present a simple model of the

parental investment allocation decision that draws from the model in Becker and Tomes

(1976). From our model, we extract a set of hypotheses that we then test in the

experimental data. Since our research question focuses on household resource allocations

within the family, for simplicity we abstract away from intra-household bargaining

between parents and focus on a single-agent model.

The parent experiences utility over the following goods: investment in the CHECC

child 𝑋! , investment in the siblings 𝑋!, and aggregate other consumption 𝑍. She has 𝑛

children, where one is the CHECC child and the others are siblings who are not targeted

by the program. She can purchase each good on the market or use her own time to

produce each good in the household. Her income is comprised of wages, earnings from

investing in the CHECC child, and earnings from the CHECC child’s academic

performance. She can use this income to purchase investment in her children (e.g.,

tutoring, extra classes) and aggregate other consumption. Equation (1) formalizes the

budget constraint.

𝑤𝑡! + 𝑡!𝑋!𝑀! + 𝑋!𝑀! = 𝑝!𝑋! + (𝑛 − 1)𝑝!𝑋! + 𝑝!𝑍 (1)

where 𝑡! is time spent at work at wage rate 𝑤, 𝑡! is amount of hours the parent spends

on household production for a unit increase in 𝑋! , 𝑀! is the amount the parent can earn

from each hour spent teaching to the CHECC child, and 𝑀! is the amount the parent can

earn for improvements in the CHECC child’s assessment performance. 𝑝! is the market

price of investing in the human capital of the CHECC child, 𝑝! is the market price of

investing in the human capital of the siblings, and 𝑝! is the market price of all other

aggregate goods 𝑍. For simplicity, we assume that the market price of investing in the

human capital of the siblings 𝑝! is the same across all siblings. Relaxing this assumption

does not change our results. The parent can allocate her total time 𝑇 towards working 𝑡!, investing in her

CHECC child 𝑡! , investing in her sibling 𝑡!, and aggregate other consumption 𝑡!. The

time constraint is given in equation (2).

𝑇 = 𝑡! + 𝑡! + (𝑛 − 1)𝑡! + 𝑡! (2)

Substituting 𝑡! from equation (2) into equation (1) yields the constraint

𝑤𝑇 = (𝑝! + 𝑤𝑡! − 𝑡!𝑀! −𝑀!)!!

𝑋! + (𝑛 − 1) (𝑝! + 𝑤𝑡!)𝑋!!!

+ (𝑝! + 𝑤𝑡!)!!

𝑍

(3)

where 𝜋! , 𝜋!, and 𝜋! are the respective shadow prices of human capital for the CHECC

child, human capital for the sibling, and aggregate other consumption. Equating the

marginal rate of substitution of CHECC child investment and sibling investment with the

ratio of shadow prices yields equation (4)

|𝑀𝑅𝑆| =

𝜕𝑈 𝑋! ,𝑋!,𝑍𝜕𝑋!

𝜕𝑈 𝑋! ,𝑋!,𝑍𝜕𝑋!

=𝑝! + 𝑤𝑡! − 𝑡!𝑀! −𝑀!

𝑝! + 𝑤𝑡!

(4)

Let 𝐾! denote the constant amount parents in Parent Academy can earn from attending

Parent Academy classes and doing homework with their CHECC child. 𝐾! denotes the

amount parents can earn from improvements in their CHECC child’s academic

performance. In Parent Academy Cash, where parents are immediately paid their

earnings, 𝑀!!"#! = 𝐾! and 𝑀!

!"#! = 𝐾!. In Parent Academy College, where parents could

access their earnings after their CHECC child enrolled in college, 𝑀!!"##$%$ = 𝛿!𝜆𝐾! and

𝑀!!"##$%$ = 𝛿!𝜆𝐾! , where 𝛿 ∈ 0,1 is the parent’s discount factor, 𝑞 ∈ ℤ! is the

expected number of years between the program and when the CHECC child enrolls in

college, and 𝜆 ∈ [0,1] is the probability that the CHECC child will enroll in college. The

ratio of the marginal rates of substitution in Parent Academy Cash and Parent Academy

College is therefore

𝑀𝑅𝑆!"#!

𝑀𝑅𝑆!"##$%$ =𝑝! + 𝑤𝑡! − 𝑡!𝐾! − 𝐾!

𝑝! + 𝑤𝑡! − 𝑡!𝛿!𝜆𝐾! − 𝛿!𝜆𝐾!< 1

(4)

Figure 1 summarizes the prediction of equation (4). The marginal rate of substitution

between investment in CHECC children and investment in siblings is steeper in Parent

Academy College than in Parent Academy Cash – for a given increase in investment in

CHECC children, parents are willing to trade-off more investment in siblings when they

receive their incentive payments right away than when they have to wait. In other words,

the model predicts that parents are willing to sacrifice more investment in siblings for the

same gain in CHECC child investment when they are randomized to the Cash treatment

rather than the College treatment.

Figure 1: Marginal Rate of Substitution between CHECC Child and Sibling

IV. Results

A. Investment in CHECC Children

We first present the analysis regarding parental investment in CHECC children. As

predicted, the immediate financial incentive led parents to exert greater effort in Parent

Academy relative to the delayed financial incentive. Parents randomized to the Cash

condition had higher grades on homework, since they scored a greater number of As and

a fewer number of incompletes than parents randomized to the College condition.

Parents in the Cash condition also had CHECC children who performed better on

evaluations and showed greater improvement on assessments than parents in the College

condition.

We first examine whether the difference in incentive payments led to differences

in attendance at Parent Academy classes. Table 2 reports the negative binomial

regression results of the proportion of classes attended by parents in the Cash compared

to the College condition. All regressions are clustered at the household level. The first

column controls for the year of the CHECC intervention and whether the family was in

their first or second year of CHECC. The coefficient on being randomized to Cash

relative to College is positive but insignificant (coefficient = 0.101, p=0.111). Column (2)

adds controls for the CHECC child’s gender, the CHECC child’s age, whether the family

is black, whether the family is Hispanic, and the number of hours spent teaching to the

CHECC child per weekday prior to program participation. These additional demographic

controls do not substantially change the coefficient estimate, which remains insignificant

(coefficient = 0.099, p=0.141). Lastly, column (3) adds controls for the average age of

any siblings in the household, the mother’s age, and the CHECC child’s cognitive and

non-cognitive performance measures taken prior to program participation. Again, adding

these additional controls do not substantially change the coefficient estimate, which

remains positive but insignificant (coefficient = 0.061, p=0.413). Overall, it appears that

randomization to Cash compared to College does not significantly affect the number of

classes that parents attend. This is consistent with the experimental design of Parent

Academy, which pays all parents in cash for attending classes, independent of whether

the parents were randomized to the Cash or the College condition.

Table 2: Negative Binomial Regression of Parent Academy Class Attendance on Treatment

(1) (2) (3)

VARIABLES Classes

Attended Classes

Attended Classes

Attended

Parent Academy Cash 0.101 0.0988 0.0614

(0.0632) (0.0672) (0.0751)

Constant 2.041*** 1.597*** 2.212***

(0.131) (0.412) (0.526)

Observations 327 327 327

Mean 12.83 12.83 12.83

(0.379) (0.379) (0.379)

Demographic controls

YES YES

Additional Controls

YES Note: Regressions of parent outcomes on assignment to Cash or College treatment. All regressions control for school year and total years in program. Demographic controls: child's gender; child's age; black; hispanic; hours spent teaching to child per weekday prior to program participation. Additional controls: sibling’s age, mother’s age, baseline cognitive score, baseline non-cognitive score. Dummies for missing variables suppressed. Standard errors clustered at family level. Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1

For all other features of Parent Academy, financial incentives differ by condition.

Parents in the Cash condition receive their incentives right away, while parents in the

College condition must wait until their CHECC child is ready for postsecondary

education before accessing their earnings. Tables 3 demonstrates that parents in the Cash

condition exhibit better performance on homework assignments than parents in the

College condition. Table 3 shows that relative to the College condition, parents in the

Cash condition have significantly higher homework GPAs. Appendix tables A.2-A.5

show that the higher homework GPA stems from parents in the Cash condition having

more As and fewer incompletes than parents in the College condition.

Table 3 presents the OLS regression results of GPA on treatment status. Average

GPA for homework is 2.13 (standard error = 0.08), which is equivalent to a C. Most of

this difference is driven by parents failing to complete their homework with their CHECC

child; conditional on completing homework, most parents receive an A, as shown by

appendix tables A.1-A.4. The first column controls only for year of the CHECC program

and the number of years the family has been in the CHECC program. Receiving the

financial incentive immediately leads parents to score nearly half a point higher in their

homework GPA relative to receiving the financial incentive with a delay (coefficient =

0.415, p<0.05). Adding demographic controls for gender, age, race, and parental

investment in the CHECC child at baseline does not change the estimates substantially.

As shown by column (2), the coefficient is still at around 0.4 of a GPA point, and this

effect is still significant at the p<0.05 level. Lastly, adding controls for mother’s age, the

average age of any siblings, the CHECC child’s cognitive score at baseline, and the

CHECC child’s non-cognitive score at baseline decreases the coefficient estimate to

0.318 of a GPA point, but the effect is still significant at the p<0.05 level. Overall, the

immediate financial incentive payment leads parents’ homework grades to increase by

about one third to one half of a GPA point, which is a substantial effect.

Table 3: OLS Regressions of Homework GPA on Treatment

(1) (2) (3)

VARIABLES Homework

GPA Homework

GPA Homework

GPA Parent Academy Cash 0.415** 0.396** 0.318**

(0.163) (0.164) (0.160)

Constant 0.697*** 0.337 1.022

(0.261) (0.810) (1.025)

Observations 327 327 327 Mean 2.134 2.134 2.134

(0.0790) (0.0790) (0.0790)


YES YES Additional Controls

YES

R2 0.117 0.150 0.303 Note: Regressions of parent outcomes on assignment to Cash or College treatment. All regressions control for school year and total years in program. Demographic controls: child's gender; child's age; black; hispanic; hours spent teaching to child per weekday prior to program participation. Additional controls: sibling’s age, mother’s age, baseline cognitive score, baseline non-cognitive score. Dummies for missing variables suppressed. Standard errors clustered at family level. Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1

In addition, we use the data on earnings from evaluations and assessments to

determine whether Cash compared to the College condition led to changes in parental

investment, as measured by CHECC children’s performance. Table 4 demonstrates the

OLS regression estimates of evaluation earnings on treatment. Overall, families

randomized to the Cash condition have CHECC children that perform significantly better

than families randomized to the College condition. Column (1), which includes only

controls for the year of the CHECC program and the family’s years in CHECC, shows

that families in the Cash condition earn over $175 more in total earnings than families in

the College condition on evaluations (where families can earn up to $1,800). This

relationship is significant at the p<0.01 level. Column (2) shows that including

demographic controls for child’s gender, age, race, and baseline parental investment

decreases the point estimate slightly to about $165 (p<0.05). Finally, including mother’s

age, the average age of siblings in the household, and baseline cognitive and non-

cognitive scores decreases the point estimate to $130, as shown by column (3) (p<0.10).

Table 4: OLS Regression of Earnings from Evaluations on Treatment

(1) (2) (3)

VARIABLES

Total Earnings from

Evaluations

Total Earnings from

Evaluations

Total Earnings from

Evaluations Parent Academy Cash 176.8*** 164.6** 130.3*

(67.59) (67.03) (66.39)

Constant 388.6*** -356.2 438.7

(114.1) (316.9) (405.0)


(33.39) (33.39) (33.39)



YES


Table 5 paints a similar picture by summarizing the results from a regression of

earnings from assessments on treatment. Overall, families randomized to the Cash

condition had CHECC children that exhibited greater improvements in academic

performance than families randomized to the College condition. Column (1) only

controls for the year of the program and the years that the family has participated in

CHECC. Families randomized to the Cash condition earn about $95 more than families

randomized to the College condition (p<0.05). Column (2) demonstrates that the

inclusion of demographic controls does not substantially change point estimates. Column

(3) adds controls for baseline cognitive and non-cognitive scores, siblings’ average age,

and mother’s age. The estimated effect decreases to about $75 but remains significant at

p<0.10.

Table 5: OLS Regression of Total Earnings from Assessments on Treatment

(1) (2) (3)

VARIABLES

Total Earnings from

Assessments

Total Earnings from

Assessments

Total Earnings from

Assessments Parent Academy Cash 95.63** 93.22** 76.56*

(45.36) (45.71) (43.03)

Constant 249.0*** 344.8 1,091***

(76.11) (213.9) (255.4)


(21.58) (21.58) (21.58)



YES


Overall, the evidence indicates that the immediate financial incentive is more

effective than the delayed financial incentive in encouraging parents to invest more time

with the CHECC child on doing homework and other activities that improve academic

performance. How might this impact how much parental time is invested in siblings, who

were not directly targeted by the CHECC program?

B. Investment in Siblings

In this section, we present results regarding parental investment in siblings of children

who were targeted by the CHECC program. The model presented in Section IV predicts

that parental time investments for siblings would be lower in the Cash condition relative

to the College condition. Empirically, however, prior research has demonstrated mixed

results, with sibling investment increasing in some cases (Bustelo, 2011; Takamatsu,

2011), decreasing in others (Barrera-Osorio et al., 2011; Shrestha and Palaniswamy,

2017), or remaining unchanged (Ferreira, Filmer, and Schady, 2009). We use the parent

investment survey data to determine whether the immediate relative to the delayed

financial incentive led to changes in parents’ time spent with siblings.

The investment survey asks parents how much time they spent teaching to each

child on a typical weekday. Parents were asked to select from one of the following

answers: “None”, “0-1 hour”, “1-2 hours”, “2-3 hours”, “3-5 hours”, or “5 or more

hours”. We conduct an ordered probit regression of the effect of treatment on these

responses for both investment in the CHECC child and investment in the siblings. Figure

2 plots the predicted probabilities of reported investment at each available interval. The

blue bars represent invest in the CHECC child, while the pink bars represent investment

in the sibling. The ordered probit regressions control the year of the program, the number

of years the family has spent in CHECC, the CHECC child’s gender, the CHECC child’s

age, whether the family is black, whether the family is Hispanic, the average age of

siblings, the mother’s age, and baseline cognitive and non-cognitive scores of the

CHECC child, which were obtained prior to program participation.

Figure 2: Ordered Probit Estimates of Treatment Effect on Parental Investment

Prior analysis shows that parents in the Cash condition appeared to spend more

time with their CHECC child on Parent Academy homework assignments, and that they

taught their CHECC children to perform better on evaluations and assessments. The

survey measure of parental investment, time spent teaching to the CHECC child, shows

evidence consistent with these results. Directionally, parents in the Cash condition are

less likely to report that they spent no time, 0-1 hours, or 1-2 hours of time spent teaching

to the CHECC child on a typical weekday compared to parents in the College condition.

Relative to the College condition group, the Cash condition group is more likely to report

spending 2-3, 3-5, or more than 5 hours spent teaching to the CHECC child on a typical

weekday.

The survey data present strong evidence that parents shift time investments away

from siblings in the household when the financial incentives to invest in the CHECC

child are immediate compared to delayed. Compared to the College condition, parents in

the Cash condition are 4.5 percentage points more likely to report spending no time at all

teaching to siblings on a typical weekday (p<0.05) and 13 percentage points more likely

to report spending only 1-2 hours teaching to siblings on a typical weekday (p<0.05).

They are 7.1 percentage points less likely to report spending 2-3 hours teaching to

siblings (p<0.10), and 3.2 percentage points less likely to report spending 3-5 hours

teaching to siblings (p<0.10). Appendix figure A.1 plot the coefficient estimates

controlling for whether parents teach to multiple children at the same time and whether

older siblings teach to younger siblings in the household. The estimated coefficients

remain robust to this alternative specification and support the story that parents

randomized to the Cash condition spend more time completing Parent Academy tasks

with their CHECC child, and that this time would have otherwise been spent teaching to

other siblings in the household.

V. Conclusion

We use a field experiment called the Chicago Heights Early Childhood Center (CHECC)

to determine how immediate financial rewards affect parental investment in children

relative to delayed financial rewards. We separately explore the effect on children

targeted by the program (“CHECC children”) and siblings not directly targeted by the

program (“siblings”). First, we develop a simple Beckerian model of parental investment

in the human capital of children to assess how parents in the Cash condition, who receive

their financial incentives immediately in cash, will differ in their time allocation relative

to parents in the College condition, who receive their financial incentives deposited in a

bank account that can only be accessible once the CHECC child enrolls in postsecondary

education. Using a set of minimal assumptions, the model predicts that parents in the

Cash condition will be more willing to sacrifice investment in siblings for the same

marginal gain in human capital investment in the CHECC child.

Our results corroborate these predictions. First, we demonstrate that parents in the

Cash condition invest more in their CHECC child than parents in the College condition,

using a series of measures from administrative data. Although attendance does not

significantly differ between parents in the Cash or College conditions, parents in the Cash

condition perform better on homework that they must complete with the CHECC child.

They turn in more assignments that earn As and have fewer assignments marked

incomplete relative to parents in the College condition. Parents in the Cash condition

have CHECC children that exhibit better absolute performance on Parent Academy

evaluations than CHECC children in the College condition. Finally, CHECC children in

the Cash condition exhibit greater improvements on mid-year and end-of-year

assessments than CHECC children in the College condition. Overall, the administrative

data from the experiment presents consistent evidence that immediate incentives had a

greater positive effect on parental investment in CHECC children than delayed

incentives.

How does this influence parental investment in siblings, who were not targeted by

the program? We use survey data administered throughout the year, which asked parents

about the amount of time they spent teaching to each child in their household. We find

that relative to the College condition, parents in the Cash condition were significantly

more likely to report low amounts of investment, namely no time or 0-1 hours spent

teaching to each sibling on a typical weekday. Relative to the College condition, parents

in the Cash condition were significantly less likely to report high amounts of investment,

namely 2-3 hours spent teaching to each sibling per weekday.

Overall, the results support an intra-household resource reallocation story, where

the resource being reallocated is parental time. When parents receive a large financial

incentive to invest in one child in the household, the shadow price of investment for that

child plummets relative to the shadow price of investment for all other children in the

household. Parents therefore substitute time away from teaching other children in the

household and spend more time attending classes to teach the CHECC child, completing

homework with the CHECC child, and preparing the CHECC child for evaluations and

assessments. This has large implications for policy, since parental time is among the most

important assets in the human capital production of children, and siblings who suffer a

loss in parental time may face large disadvantages in their human capital formation

process (Juhn et al., 2015).

Our results speak to the importance of considering spillover effects on financial

incentives, especially high-powered financial incentives designed to impact parental time

and childhood skill formation. Unforeseen negative consequences may result from these

spillover effects, since low-income parents, who are already heavily resource-constrained

in terms of both time and money, may respond to conditional cash transfers by making

difficult and irreversible decisions that benefit some children but harm other children in

the household. Thus, interventions designed to narrow socioeconomic disparities between

families may perversely exacerbate inequalities within families. Our work informs the

design of financial incentives to narrow socioeconomic disparities, as well as policies to

promote early childhood education. Our paper also highlights the importance of future

work to examine spillover impacts of financial incentives within families, communities,

and social networks.

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Baird, S., C. McIntosh and B. Ozler (2011). Cash or Condition? Evidence From a Cash Transfer Experiment. Quarterly Journal of Economics Barrera-Osorio, F., M. Bertrand, L.L. Linden, and F. Perez-Calle (2011). “Improving the Design of Conditional Transfer Programs: Evidence from a Randomized Education Experiment in Colombia.” American Economic Journal: Applied Economics 3(2): 167-195. Becker, G.S. and H.G. Lewis (1973). “Interaction between Quantity and Quality of Children.” The Journal of Political Economy 81(2) Part 2: S279-S288. Becker, G.S. and N. Tomes (1976). “Child Endowments and the Quantity and Quality of Children.” The Journal of Political Economy 84(4): Essays in Labor Economics in Honor of H. Gregg Lewis S143-S162. Behrman, J.R., R.A. Pollak, and P. Taubman (1989). “Financial Resources, Family Size, and Access to Financing for College Education.” Journal of Political Economy 97(2): 398-419. Black, S.E., P.J. Devereux, and K. Salvanes (2005). “The More the Merrier? The Effect of Family Size and Birth Order on Children’s Education.” Quarterly Journal of Economics 120(2): 669-700. Bustelo, M., (2011). “Three Essays on Investments in Children’s Human Capital.” Doctoral Dissertation, University of Illinois at Urbana-Champaign. Caceres-Delpiano, J. (2006). “The Impacts of Family Size on Investment in Child Quality.” Journal of Human Resources 41(4): 738-754. Conley, D. (2000). “Sibship Sex Composition: Effects on Educational Attainment.” Social Science Research 29(3): 441-457. Conley, D. and R. Glauber (2006). “Parental Educational Investment and Children’s Academic Risk.” Journal of Human Resources 41(4): 722-737. Cunha, F. and J.J. Heckman (2007). “The Technology of Skill Formation.” American Economic Review 97(2): 31-47. De Janvry, A., F. Finan, E. Sadoulet, and V. Renos (2006). Can Conditional Cash Transfer Programs Serve as Safety Nets in Keeping Children at School and from Working When Exposed to Shocks? Journal of Development Economics 79(2): 349-373. Ferreira, Francisco H.G., Deon Filmer, and Norbert Schady. (2009). "Own and Sibling Effects of Conditional Cash Transfer Programs: Theory and Evidence from Cambodia." World Bank Policy Research Working Paper 5001.

Fryer, R., Levitt, S., List, J., (2015). Parental Incentives and Early Childhood Achievement: A Field Experiment in Chicago Heights. NBER Working Paper 21477. Heckman, J.J. (2006). “Skill Formation and the Economics of Investing in Disadvantaged Children.” Science 312(5782): 1900-1902. Heckman, J.J. (2008). “Schools, Skills, and Synapses.” Economic Inquiry 46(3): 289-324. Heckman, J.J. and D.V. Masterov (2007). “The Productivity Argument for Investing in Young Children.” Review of Agricultural Economics 29(3): 446-493. Juhn, C., Rubinstein, Y., Zuppann, C., 2015. The Quantity-Quality Trade-off and the Formation of Cognitive and Non-Cognitive Skills. NBER Working Paper 21824. Knudsen, E., Heckman, J., Cameron, J., Shonkoff, J., (2006). Economic, neurobiological, and behavioral perspectives on building America’s future workforce. Proceedings of the National Academy of Sciences 103(27): 10155–10162.

Lu, Y. and D. Treiman (2005). “The Effect of Sibship Size on Educational Attainment in China: Cohort Variations.” California Center for Population Research On-Line Working Paper Series CCPR 052-05. Manacorda, M. (2006). “Child Labor and the Labor Supply of Other Household Members: Evidence from 1920 America.” American Economic Review 96(5): 1788-1801. Ponczek, V. and A.P. Souza (2007). “The Causal Effect of Family Size on Child Labor and School Progression.” Rosenzweig, M.R. and K.I. Wolpin (1980). “Testing the Quantity-Quality Fertility Model: The Use of Twins as a Natural Experiment.” Econometrica 48(1): 227-240. Rosenzweig, M.R., Zhang, J., (2009). “Do Population Control Policies Induce More Human Capital Investment? Twins, Birth Weight and China’s “One-Child” Policy.” Review of Economic Studies 76(3), 1149-1174. Sacerdote, B., 2007. How Large Are the Effects from Changes in Family Environment? A Study of Korean American Adoptees. Schultz, P.T. (2004). School Subsidies for the Poor: Evaluating the Mexican Progresa Poverty Program. Journal of Development Economics 74(1): 199-250. Shrestha, S.A. (2011). "Sibling Rivalry in Education: Estimation of Intra-household Trade-offs in Human Capital Investment."

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Appendix

Figure A.1: Ordered Probit Estimates of Treatment Effect on Parental Investment (Controls for whether parent teaches to multiple children in household,

whether older siblings teach to younger siblings in household)

Table A.1: Probit Regressions on Participation in Survey

(1) (2) (3) (4)

VARIABLES Participate in Child Investment

Survey Participate in Sibling

Investment Survey Parent Academy Cash 0.225 0.244 0.195 0.170

(0.151) (0.157) (0.151) (0.153)

Constant -0.539** -0.570 -0.891*** -0.985

(0.251) (0.761) (0.252) (0.775)

Observations 329 327 329 327 Demographic controls

YES

YES

Note: Regressions of participation in investment survey on assignment to Cash or College treatment. All regressions control for school year and total years in program. Demographic controls: child's gender; child's age; black; Hispanic. Dummies for missing variables suppressed. Standard errors clustered at family level, shown in parentheses. *** p<0.01, ** p<0.05, * p<0.1

Table A.2: Negative Binomial Regression of Total As on Homework on Treatment

(1) (2) (3) VARIABLES Total As Total As Total As Parent Academy Cash 0.252*** 0.256*** 0.194**

(0.0917) (0.0945) (0.0906)

Constant 1.122*** 0.522 1.125*

(0.177) (0.529) (0.649)


0.331 0.331 0.331



YES

Note: Regressions of parent outcomes on assignment to Cash or College treatment. All regressions control for school year and total years in program. Demographic controls: child's gender; child's age; black; hispanic; hours spent teaching to child per weekday prior to program participation. Additional controls: sibling’s age, mother’s age, baseline cognitive score, baseline non-cognitive score. Dummies for missing variables suppressed. Standard errors clustered at family level, presented in parentheses. *** p<0.01, ** p<0.05, * p<0.1

Table A.3: Negative Binomial Regression of Total Bs on Homework on Treatment

(1) (2) (3) VARIABLES Total Bs Total Bs Total Bs Parent Academy Cash -0.104 -0.0926 -0.140

(0.157) (0.152) (0.163)

Constant 0.0684 -1.268 -0.271

(0.279) (0.872) (1.001)


0.0840 0.0840 0.0840



YES


Table A.4: Negative Binomial Regression of Total Cs on Homework on Treatment

(1) (2) (3) VARIABLES Total Cs Total Cs Total Cs Parent Academy Cash -0.0813 -0.0416 -0.0864

(0.210) (0.205) (0.207)

Constant -0.510 0.816 2.058

(0.344) (1.174) (1.326)


0.0560 0.0560 0.0560



YES


Table A.5: Negative Binomial Regression of Total Incompletes on Homework on Treatment

(1) (2) (3)

VARIABLES Total

Incompletes Total

Incompletes Total

Incompletes Parent Academy Cash -0.245** -0.230** -0.155

(0.105) (0.107) (0.105)

Constant 2.722*** 2.620*** 2.532***

(0.165) (0.503) (0.708)


0.334 0.334 0.334



YES


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