Appendices: The Expanded Child Tax Credit and Economic Wellbeing of Low-Income Families
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Appendices to The Expanded Child Tax Credit and Economic Wellbeing of Low-Income Families by Natasha V. Pilkauskas, Katherine Michelmore, Nicole Kovski, and H. Luke Shaefer. Appendix 1, Additional Information on Measures and Data, states that after the passage of the American Rescue Plan Act in March 2021 the authors partnered with Propel, the makers of the Providers application, and describes measures of material hardship including food insecurity, medical hardship, severe housing hardship and bill hardship. Appendix 2, Reweighting Procedures, describes the reweighting procedures used. The text also includes regression tables whose note states that coefficients represent the effect of a $100 increase in the CTC, that estimates are intent-to-treat with local average treatment effects obtained by instrumenting for CTC receipt, and that N is 19,154.
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APPENDICES: THE EXPANDED CHILD TAX CREDIT AND ECONOMIC
WELLBEING OF LOW-INCOME FAMILIES
Natasha V. Pilkauskas, Katherine Michelmore, Nicole Kovski, and H. Luke Shaefer
APPENDIX 1 – ADDITIONAL INFORMATION ON MEASURES AND DATA
This appendix provides additional information on the coding and selection of the measures of
economic wellbeing.
Shortly after the passage of the American Rescue Plan Act in March 2021, we partnered with
Propel, the makers of the Providers application. Propel runs a monthly survey with Providers users
to better understand the needs of their users. When we partnered with them they allowed us to
include a few additional measures on their monthly survey, but in the interest of minimizing
respondent burdens we tried to keep the new questions to a minimum. Additionally, because Propel
tracks measures over time, we did not want to change any questions they regularly asked their
users. Thus, the questions we included in this study of economic wellbeing were a mix of new
questions we added to their survey (like the 2-item food insecurity scale) and questions they were
already asking their users. We aimed to select (or add) measures of material hardship that mirror
those used in other studies (e.g., the Survey of Income and Program Participation). The additional
measures of economic wellbeing and of labor supply were questions Propel was already asking
their users on a regular basis.
Measures of Material Hardship
Food Insecurity
Our measure of food insecurity relies on four items. First is the 2-item food insecurity scale (Hager
et al., 2010) that is a well-validated instrument that is derived from the 18-item USDA food
insecurity scale. Referring to the last 30 days, we asked respondents if they “worried whether your
food would run out before you got money to buy more” and if “the food you bought just didn’t
last and you didn’t have money to get more”. Second, respondents were asked if they had “skipped
meals” or “eaten less” in the last 30 days. Because these questions did not specify that these
behaviors were undertaken as a result of a lack of money, we were unsure if we should include
them in our index. To explore this issue we examined the Cronbach’s alpha of the 2-item food
insecurity scale (=0.62) and compared it to the alpha that included the two additional food related
items. We found that including the additional two food items increased the alpha to =0.71. Thus,
we decided to keep all 4 items in our measure of food insecurity. Items were summed and then
standardized (M=0, SD=1). In extensions we tested the robustness of our findings to just using the
2-item food insecurity index and found they were robust.
Medical Hardship
Medical hardship is assessed with two questions that are commonly assessed in the material
hardship literature: whether in the last 30 days the respond had “Not visited the doctor when you
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CTC and Economic Wellbeing Pilkauskas et al.
needed to because of the cost” or “Not visited the dentist when you needed because of the cost”
(=0.64). These measures were selected as they are frequently used in the material hardship
literature (e.g., Rodems & Shaefer, 2020; Pilkauskas et al., 2017). Items are summed and then
standardized.
Severe Housing Hardship
Inability to pay rent or mortgage is a common measure of material hardship. Unfortunately the
available survey questions asking about rent, do not allow us to create a good measure of rental
hardship. We do, however, have four good indicators of more severe housing hardships. The first
measure is whether the respondent was evicted by a landlord or court order in the last 30 days, the
second assesses shelter use – “have you slept or stayed in a shelter at least one night in the past
month”. A third indicator relies on a question that asks respondents about their current living
situation that gets at homelessness. If a respondent says they do not currently have a home, we
code them as homeless. The final measure asks respondents “Do you currently live in a house,
apartment or other stable housing? Answer “no” if you currently live in a motel, car or shelter.”
We code respondents as not having stable housing if they say no to this question. These indicators
of severe housing hardships are frequently included in studies of material hardship (e.g.,
Pilkauskas et al., Forthcoming). We create an index summing across these four measures (=0.64)
and then we standardize the measure.
Bill Hardship
Another common measure of material hardship is of bill hardships. For this measure we include
three questions, two focused on utility bills and one on general bill paying. These measures often
vary across studies. Some consider all bills (like rent), while others separately consider utilities.
The two utility hardship questions are: “In the last 30 days, did you pay the full amount of your
utility bills (e.g., water, gas, oil, electric)?” and the second question asks if the respondent had their
utilities shut off in the last 30 days. We also include a single bill hardship item, “Did you decide
not to pay a bill”. This item is somewhat unusual as deciding not to pay is distinct from not actually
paying. Unfortunately, we cannot distinguish these two concepts with this measure. We sum the
three measures (= 0.39) and standardize the measure (M=0, SD=1). We included these items as
an index, similar to other research (e.g., Iceland, 2021), but recognize that this scale has a very low
alpha. (None of the three items ever attain statistical significance individually in any of our
specifications).
Transportation hardship
Lastly, we examine a single item measure of transportation hardship with a question that was
adapted from the Transportation Security Index (Murphy et al., 2021). This question asks
respondents (about the last 30 days) if they “missed an appointment, skipped going somewhere,
or missed work because you didn’t have a way to get there”. Transportation hardship is rarely
included in measures of material hardship but new work suggests that 24% of adults experience
transportation insecurity, with rates that are closer to 50% among lower income households
(Murphy et al., 2022); thus, we added this measure to our suite of hardship indicators. However,
Appendix 1 2
CTC and Economic Wellbeing Pilkauskas et al.
we note, this one-item measure likely does not fully capture the likelihood of experiencing
transportation insecurity.
Material Hardship Scale
Finally, we construct an index using all 14 indicators of material hardship (=0.71). This measure
is summed and standardized (M=0, SD=1).
Additional Measures of Economic Wellbeing
Have Needs Met
To assess how well families were doing economically, we used a measure that Propel created to
consider whether families were able to meet their basic needs: “Do you have everything you
typically need in your home right now? Like food, household products, and cleaning supplies”.
Respondents can indicate 1) they have everything, 2) most things, 3) some things, 4) running low
on most things, or 5) they do not have most things they need. We create a binary indicator taking
on the value of one if the respondent reports having everything or most things; all others are coded
as zero.
Cash on Hand
To assess whether the CTC changed the amount of cash families had on hand, we used a question
that asked “About how much money do you have in total right now (not including food stamps)?
This question was asked as a categorical question with responses ranging from $25 to $1,000 or
more. To make this variable into a continuous measure we coded them with mid-points, with the
top code being $1,000.
How Long Will Cash Last?
After asking respondents how much cash they had on hand, a follow up question asked about how
long that money might last. The six-item responses ranged from 1-2 days to two weeks or more.
We converted the weeks into days and assigned respondents the mid-point (e.g., 1.5 days for 1-2
days). The top code was 14 days for those who reported two or more weeks.
Hardship Avoidance
Rely on Friends and Family for Food
One way in which families might avoid experiencing food insecurity is through relying on friends
and family for food. This measure was a single item question that asked respondents if they had to
rely on friends or family for meals in the last 30 days. We coded this as a dummy variable (yes/no).
Food Pantry Use
Respondents were asked if they had visited a food pantry in the last 30 days. We consider this a
hardship avoidance technique as those who got food from a food pantry may have been less likely
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CTC and Economic Wellbeing Pilkauskas et al.
to experience food insecurity – or may have been able to put some of their money towards other
living expenses. We create a dummy variable where 1= yes the respondent went to a food pantry.
Borrow Money from Friends/Family
Our final measure of hardship avoidance is relying on friends and family for money. This measure
was derived from two variables, first was a question that asked respondents if they “borrowed
money or used credit to cover their expenses? This could be from family, friends, churches,
GoFundMe, etc.” If respondents said they had gotten money, they were then asked “How did you
borrow or use credit?” and respondents could say “friend/family” as well as a number of additional
options. If respondents said friends/family then they were coded as one on this variable.
Labor Force Participation
We rely on a measure that asked respondents about their current labor force from a question that
asked “How would you describe your employment status currently?”. Respondents could answer
that they worked full-time, part-time, not working but looking for work, not working and not
looking for work, not able to work, or retired. We categorized respondents who were working full-
time or part-time or looking for work as those who were in the labor force and the rest were
considered out of the labor force. Those who were not working but looking for work were
considered unemployed.
REFERENCES
Iceland, J. (2021). Hardship among immigrants and the native-born in the United
States. Demography, 58(2), 655-684.
Murphy, A. K., Gould-Werth, A. & Griffin, J. (2021). Validating the sixteen-item transportation
security index in a nationally representative sample: A confirmatory factor analysis. Survey
Practice 14 (1). https://doi.org/10.29115/SP-2021-0011.
Murphy, A., McDonald-Lopez, K., Pilkauskas, N.V. & Gould-Werth, A. (2022). The prevalence
of transportation insecurity. Socius, 8, 23780231221121060.
Pilkauskas, N. V., Campbell, C., & Wimer, C. (2017). Giving unto others: Private financial
transfers and hardship among families with children. Journal of Marriage and Family, 79(3), 705-
722.
Pilkauskas, N. V., Jacob, B. A., Rhodes, E., Richard, K., & Shaefer, H. L. (Forthcoming). The
COVID Cash Transfer Study: The Impacts of a One‐Time Unconditional Cash Transfer on the
Well‐Being of Families Receiving SNAP in Twelve States. Journal of Policy Analysis and
Management. https://doi.org/10.1002/pam.22464
Rodems, R., & Shaefer, H. L. (2020). Many of the kids are not alright: Material hardship among
children in the United States. Children and Youth Services Review, 112, 104767.
Appendix 1 4
CTC and Economic Wellbeing Pilkauskas et al.
APPENDIX 2 – REWEIGHTING PROCEDURES
This appendix describes the reweighting procedures used in the robustness section of the paper
(results shown in appendix tables 10 and 11). Although the Providers data are an excellent data
source of families living in, or near, poverty, one potential concern is the extent to which the these
data represent the overall population of families with children participating in SNAP as those who
use an application to track their benefits may differ from other SNAP families.
As described in more detail in the manuscript, we compared the similarity of respondents’
sociodemographic characteristics to those in three independent, nationally-representative surveys
that include large samples of SNAP participants -- the 2019 American Community Survey (ACS),
the 2019 Current Population Survey (CPS), and the 2019 SNAP Quality Control Data (SNAP QC).
This evaluation revealed that the demographic profiles of Providers respondents resembled those
of participants in other nationally representative samples (see Table 1). To further ensure
representativeness of our estimates, we also constructed a series of weights that align Providers
respondents to observable characteristics in each of the three benchmark samples.
Weights are constructed in two steps. First, in an effort to align the ACS, CPS, and SNAP
QC samples with our the population of interest, we restrict each sample to households with at least
one coresident child under the age of 18. We then further restrict the ACS and CPS samples to
individuals who report having received SNAP benefits in the last 12 months and who are
designated the household reference person. For the SNAP QC data, we further restrict the sample
to household heads deemed eligible for the SNAP case under review.
Second, we calculate the ratio of the weighted proportion of a particular subgroup among
the total sample of respondents in each benchmark sample (the ACS, CPS, and SNAP QC sample)
relative to the corresponding proportion of that subgroup in Providers sample.1 To form subgroups
for this exercise, we use every combination of sociodemographic covariate available to us across
both the Propel and benchmark datasets. These characteristics include age (18-24 years, 25-34
years, 35-44 years, 45-54 years, or 55+ years), race/ethnicity (Black non-Hispanic, white non-
Hispanic, Hispanic, or other non-Hispanic) highest level of education (less than high school, high
school, some college, or college or more), sex (male or female), and partner status (whether the
respondent has a partner/spouse; however, this variable is not available in the SNAP QC sample).
Following this second step, we obtain three sets of weights (one for each ratio based on
different pairings of the Providers sample and ACS, CPS, and SNAP QC benchmark samples).
The logic of this reweighting technique is that a weight greater than 1 indicates that a demographic
subgroup is underrepresented in the Providers sample relative to the benchmark sample.
Conversely, a weight less than 1 indicates that a demographic subgroup is overrepresented in the
Providers sample. Our reweighting approach allows us to adjust for differences in the distributions
of observed individuals characteristics between the Providers and benchmark samples by either
up-weighting or down-weighting specific subgroups. This weighting technique is similar to that
implemented by Schneider and Harknet (2022) in their prior research based on non-probability
samples recruited through Facebook. Appendix Table 10 shows that applying the weights
successfully balance observable characteristics of Providers respondents to resemble each of the
benchmark samples.
1
To produce weighted proportions for each of the benchmark samples, we use, respectively, the ACS, CPS, and
SNAP QC provided weights, which allow for nationally-representative estimates.
Appendix 2 1
Appendix Table 1: Sample Descriptive Statistics, Households with Children, Before
and After the CTC Expansion
Average Pre-CTC Post-CTC
Age
18-24 0.07 0.07 0.07
25-34 0.40 0.38 0.41
35-44 0.35 0.36 0.35
45-54 0.12 0.13 0.11
55+ 0.05 0.07 0.05
Race/ethnicity
Black 0.35 0.31 0.37
White 0.35 0.38 0.34
Hispanic 0.21 0.22 0.21
Other 0.09 0.10 0.09
Education
Less than High School 0.23 0.22 0.24
High School 0.39 0.37 0.40
Some College 0.27 0.28 0.26
Associate Degree + 0.10 0.12 0.10
Female 0.94 0.94 0.94
Urbanicity
Urban 0.46 0.44 0.47
Rural 0.32 0.32 0.32
Suburban 0.22 0.24 0.21
Household structure
Partner/spouse 0.30 0.33 0.29
Household size 4.30 4.26 4.32
(SD) 1.64 1.65 1.64
Number of kids
1 0.25 0.26 0.24
2 0.31 0.32 0.31
3 0.21 0.21 0.21
4 0.12 0.12 0.13
5+ 0.10 0.09 0.11
Receive food stamps 0.85 0.85 0.85
N 20,545 5,265 15,280
Note: Data come from the providers study, June 2021- January 2022. Sample is
restricted to households with at least one child under the age of 18.
Appendix Table 2: Association between own Child Tax Credit Receipt and Amount and Material Hardship
Self-reported CTC receipt (0/1) Self-reported CTC $$ (in $100's)
(1) (2) (3) (4)
Hardship index (14-item scale) -0.098 *** -0.096 *** -0.019 *** -0.018 ***
(0.018) (0.018) (0.003) (0.003)
Food hardship (4-item scale) -0.085 *** -0.08 *** -0.019 *** -0.016 ***
(0.018) (0.018) (0.003) (0.003)
Medical hardship (2-item scale) -0.022 -0.02 -0.005 ** -0.004
(0.017) (0.017) (0.003) (0.003)
Severe housing hardship (4-item scale) -0.148 *** -0.149 *** -0.021 *** -0.023 ***
(0.017) (0.017) (0.003) (0.003)
Transportation hardship -0.036 *** -0.036 *** -0.005 *** -0.005 ***
(0.008) (0.008) (0.001) (0.001)
Bill hardship (3-item scale) 0.016 0.013 0.000 -0.001
(0.018) (0.018) (0.001) (0.003)
Household size fixed effects Yes No Yes No
Number of children fixed effects No Yes No Yes
N 19,154
Note: Standard errors in parentheses. Scales are in standard deviation units (M=0; SD=1). Sample is restricted
to households with at least one child under the age of 18. All models include all demographic controls (age,
gender, education, race/ethnicity, partnered, urbanicity), state fixed effects, month fixed effects, and contextual
(SNAP/PEBT/UI) controls. Models in columns 1 and 3 include household size fixed effects. Models in
columns 2 and 4 include number of children fixed effects. Regressions for severe housing hardship have
20,545 observations.
*p <0 .10;**p 0< .05; ***p < 0.01
Appendix Table 3: Effect of the Child Tax Credit on Material Hardship, by Race/Ethnicity, Intent to Treat Estimates
Black White Hispanic
(1) (2) (3) (4) (5) (6)
Hardship index (14-item scale) -0.012 *** -0.016 *** -0.010 * -0.005 -0.002 0.003
(0.004) (0.006) (0.005) (0.007) (0.004) (0.006)
Food hardship (4-item scale) -0.013 *** -0.015 ** -0.019 *** -0.007 -0.009 ** -0.001
(0.004) (0.006) (0.005) (0.008) (0.004) (0.006)
Medical hardship (2-item scale) -0.008 ** -0.006 -0.003 -0.002 -0.008 * -0.002
(0.004) (0.006) (0.005) (0.007) (0.005) (0.007)
Severe housing hardship (4-item scale) -0.003 -0.010 -0.007 -0.003 0.011 *** 0.008
(0.005) (0.007) (0.005) (0.007) (0.004) (0.006)
Transportation hardship 0.001 0.001 -0.001 0.002 0.002 0.003
(0.002) (0.003) (0.002) (0.003) (0.002) (0.003)
Bill hardship (3-item scale) -0.006 -0.012 * 0.008 -0.001 0.005 0.002
(0.004) (0.006) (0.005) (0.007) (0.002) (0.003)
Household size fixed effects Yes No Yes No Yes No
Number of children fixed effects No Yes No Yes No Yes
N
Note: Coefficients represent the effect of a $100 increase in the CTC. Intent-to-treat (ITT) estimates. Standard errors in parentheses.
Scales are in standard deviation units (M=0; SD=1). Sample restricted to households with at least one child under the age of 18. All
models include all demographic controls (age, gender, education, partnered, urbanicity), state fixed effects, month fixed effects, and
contextual (SNAP/PEBT/UI) controls. Models in columns 1, 3 and 5 include household size fixed effects. Models in columns 2, 4
and 6 include number of children fixed effects.
*p <0 .10;**p 0< .05; ***p < 0.01
Appendix Table 4: The Effects of the Child Tax Credit on Basic Needs, Cash on Hand, Hardship Avoidance, and Employment, by Race/Ethnicity
Black White Hispanic
ITT LATE ITT LATE ITT LATE
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)
Needs/Cash on hand
Have needs met 0.004 * 0.005 * 0.020 * 0.028 * 0.002 -0.003 0.007 -0.010 -0.002 -0.001 -0.012 -0.013
(0.002) (0.003) (0.010) (0.017) (0.003) (0.003) (0.008) (0.011) (0.002) (0.003) (0.017) (0.043)
Total $ on hand ($) 0.881 1.096 4.732 6.595 1.328 -3.383 4.074 -11.118 ** 1.687 1.693 12.483 21.133
(0.844) (1.212) (4.531) (7.291) (1.106) (1.517) (3.388) (5.053) (1.099) (1.608) (8.167) (20.461)
Time $ will last (days) 0.004 0.021 0.022 0.125 0.012 -0.033 0.036 -0.108 0.005 0.029 0.034 0.366
(0.015) (0.021) (0.078) (0.126) (0.019) (0.025) (0.057) (0.084) (0.018) (0.026) (0.131) (0.332)
Hardship avoidance
Relied on friends/family for food -0.005 *** -0.001 -0.025 *** -0.008 -0.005 ** 0.001 -0.016 *** 0.004 -0.004 *** -0.002 -0.032 *** -0.031
(0.002) (0.002) (0.009) (0.014) (0.002) (0.003) (0.006) (0.009) (0.002) (0.002) (0.012) (0.029)
Visited food pantry 0.000 0.000 -0.002 0.002 0.001 0.001 0.004 0.002 0.000 -0.002 -0.004 -0.019
(0.002) (0.002) (0.008) (0.013) (0.002) (0.003) (0.007) (0.01) (0.002) (0.003) (0.013) (0.033)
Borrow from friends or family 0.002 0.004 0.011 0.022 -0.003 0.000 -0.010 0.000 -0.003 0.002 -0.024 0.029
(0.002) (0.003) (0.011) (0.018) (0.003) (0.004) (0.008) (0.012) (0.002) (0.004) (0.018) (0.045)
Employment
Any employment -0.003 -0.002 -0.018 -0.013 -0.002 -0.003 -0.007 -0.011 -0.003 -0.001 -0.019 -0.016
(0.002) (0.003) (0.011) (0.018) (0.002) (0.003) (0.008) (0.011) (0.002) (0.004) (0.018) (0.044)
Full-time work -0.002 -0.002 -0.010 -0.015 0.001 -0.003 0.002 -0.010 -0.002 -0.005 -0.018 -0.058
(0.002) (0.002) (0.009) (0.015) (0.002) (0.003) (0.006) (0.009) (0.002) (0.003) (0.014) (0.039)
Part-time work -0.002 0.000 -0.008 0.002 -0.003 0.000 -0.010 0.000 0.000 0.003 -0.001 0.042
(0.002) (0.002) (0.009) (0.014) (0.002) (0.003) (0.006) (0.009) (0.002) (0.003) (0.015) (0.039)
Labor force participation -0.004 ** -0.004 * -0.022 ** -0.026 * -0.003 -0.001 -0.010 -0.004 0.003 0.005 0.019 0.057
(0.002) (0.002) (0.010) (0.015) (0.002) (0.003) (0.008) (0.011) (0.002) (0.003) (0.016) (0.04)
F-statistic - - 305.3 *** 119.2 *** - - 661.4 *** 305.9 *** - - 117.3 *** 19.3 ***
First stage coefficient - - 18.6 ** 16.6 *** - - 32.6 *** 30.4 *** - - 13.5 *** 8.0 ***
Household size fixed effects Yes No Yes No Yes No Yes No Yes No Yes No
Number of children fixed effects No Yes No Yes No Yes No Yes No Yes No Yes
6430 6146 3985
Note: Coefficients represent the effect of a $100 increase in the CTC. Intent-to-treat (ITT) estimates. Local average treatment effects (LATE) obtained by instrumenting for CTC receipt as reported by the
respondent.Standard errors in parentheses. Scales are in standard deviation units (M=0; SD=1). Sample restricted to households with at least one child under the age of 18. All models include all
demographic controls (age, gender, partnered, education, urbanicity), state fixed effects, month fixed effects, and contextual (SNAP/PEBT/UI) controls. Odd numbered columns are models with
household size fixed effects; Even numbered columns are models with number of children fixed effects.
*p <0 .10;**p 0< .05; ***p < 0.01
Appendix 5: Effect of the Child Tax Credit on Material Hardship, by Monthly Earnings, Intent-to-
Treat Estimates
Earn less than $500 Earn more than $500
(1) (2) (3) (4)
Hardship index (14-item scale) -0.006 -0.008 -0.009 *** -0.008 *
(0.004) (0.006) (0.003) (0.005)
Food hardship (4-item scale) -0.011 *** -0.010 * -0.016 *** -0.012 **
(0.004) (0.006) (0.003) (0.005)
Medical hardship (2-item scale) -0.005 -0.002 -0.007 ** -0.003
(0.004) (0.005) (0.004) (0.005)
Severe housing hardship (4-item scale) 0.001 -0.005 0.000 -0.003
(0.005) (0.007) (0.003) (0.004)
Transportation hardship 0.001 -0.001 0.001 0.002
(0.002) (0.003) (0.001) (0.002)
Bill hardship (3-item scale) 0.001 -0.003 0.003 -0.003
(0.004) (0.006) (0.004) (0.005)
Household size fixed effects Yes No Yes No
Number of children fixed effects No Yes No Yes
N 7,040 10,390
Note: Coefficients represent the effect of a $100 increase in the CTC. Intent-to-treat (ITT)
estimates. Standard errors are in parentheses. Scales are in standard deviation units (M=0;
SD=1). Sample restricted to households with at least one child under the age of 18. All models
include all demographic controls (age, gender, education, partnered, urbanicity), state fixed
effects, month fixed effects, and contextual (SNAP/PEBT/UI) controls. Models in columns 1
and 3 include household size fixed effects. Models in columns 2 and 4 include number of
children fixed effects.
*p <0 .10;**p 0< .05; ***p < 0.01
Appendix Table 6: Effect of the Child Tax Credit on Basic Needs, Cash on Hand, Hardship Avoidance, and Employment, by Monthly Earnings
Earn less than $500 Earn more than $500
ITT LATE ITT LATE
(1) (2) (3) (4) (5) (6) (7) (8)
Needs/Cash on hand
Have needs met -0.003 0.000 -0.018 -0.001 0.004 ** 0.001 0.016 ** 0.003
(0.002) (0.003) (0.012) (0.019) (0.002) (0.002) (0.007) (0.01)
Total $ on hand ($) 0.464 -0.485 3.2135 -3.652 1.649 ** -0.016 6.304 ** -0.068
(0.703) (1.022) (4.752) (7.711) (0.820) (1.130) (3.129) (4.82)
Time $ will last (days) -0.011 -0.003 -0.077 -0.024 0.012 0.003 0.046 0.014
(0.013) (0.019) (0.090) (0.145) (0.013) (0.018) (0.049) (0.076)
Hardship avoidance
Relied on friends/family for food -0.006 *** -0.003 -0.043 *** -0.026 -0.003 ** 0.000 -0.011 ** 0.001
(0.002) (0.002) (0.011) (0.017) (0.001) (0.002) (0.005) (0.007)
Visited food pantry 0.001 -0.001 0.007 -0.006 -0.002 -0.001 -0.007 -0.004
(0.002) (0.002) (0.011) (0.017) (0.001) (0.002) (0.005) (0.008)
Borrow from friends or family 0.001 0.002 0.003 0.012 -0.001 0.003 -0.004 0.014
(0.002) (0.003) (0.013) (0.021) (0.002) (0.002) (0.007) (0.01)
Employment
Any employment -0.001 0.001 -0.007 0.008 -0.003 -0.002 -0.010 -0.011
(0.001) (0.002) (0.010) (0.016) (0.002) (0.002) (0.007) (0.010)
Full-time work 0.000 0.000 -0.003 0.002 -0.001 -0.004 + -0.006 -0.018 *
(0.001) (0.001) (0.006) (0.009) (0.002) (0.002) (0.006) (0.010)
Part-time work 0.000 0.001 -0.003 0.007 -0.001 0.002 -0.004 0.008
(0.001) (0.002) (0.009) (0.014) (0.002) (0.002) (0.006) (0.009)
Labor force participation 0.001 0.003 0.006 0.023 -0.002 -0.001 -0.006 -0.005
(0.002) (0.003) (0.012) (0.020) (0.001) (0.002) (0.006) (0.009)
F-statistic - - 234.2 *** 89.7 *** - - 867.3 *** 366.6 ***
First stage coefficient - - 14.8 *** 13.3 *** - - 26.3 *** 23.4 ***
Household size fixed effects Yes No Yes No Yes No Yes No
Number of children fixed effects No Yes No Yes No Yes No Yes
N 7,040 10,390
Note: Coefficients represent the effect of a $100 increase in the CTC. Intent-to-treat (ITT) estimates.Standard errors in parentheses. Local average
treatment effects (LATE) obtained by instrumenting for CTC receipt as reported by the respondent. Scales are in standard deviation units (M=0;
SD=1). Sample restricted to households with at least one child under the age of 18. All models include all demographic controls (age, gender,
education, race/ethnicity, partnered, urbanicity), state fixed effects, month fixed effects, and contextual (SNAP/PEBT/UI) controls. Odd numbered
columns are models with household size fixed effects; Even numbered columns are models with number of children fixed effects.
*p <0 .10;**p 0< .05; ***p < 0.01
Appendix Table 7: Pre-Post Parameterized Difference-in-Differences - Households without Children as the
Comparison Group, Effects on Material Hardship
ITT LATE
(1) (2) (3) (4)
Hardship index (14-item scale) -0.002 -0.001 -0.007 -0.006
(0.002) (0.003) (0.008) (0.012)
Food hardship (4-item scale) -0.007 *** -0.005 * -0.028 *** -0.019 *
(0.002) (0.003) (0.008) (0.012)
Medical hardship (2-item scale) -0.001 0.000 -0.004 -0.002
(0.002) (0.003) (0.008) (0.012)
Severe housing hardship (4-item scale) -0.005 ** 0.001 -0.022 ** 0.005
(0.002) (0.003) (0.008) (0.012)
Transportation hardship 0.004 *** 0.003 *** 0.014 *** 0.014 ***
(0.001) (0.001) (0.003) (0.005)
Bill hardship (3-item scale) 0.007 *** -0.001 0.026 *** -0.003
(0.002) (0.003) (0.008) (0.012)
F-statistic - - 3792 *** 1725 ***
First stage coefficient - - 25.3 *** 24.5 ***
Household size fixed effects Yes No Yes No
Number of children fixed effects No Yes No Yes
N 30,265
Note: Standard errors in parentheses. Scales are in standard deviation units (M=0; SD=1). Sample includes
households with and without children (excludes individuals who live alone). All models include all demographic
controls (age, gender, education, race/ethnicity, partnered, urbanicity), state fixed effects, month fixed effects,
and contextual (SNAP/PEBT/UI) controls. Models in columns 1 and 3 include household size fixed effects.
Models in columns 2 and 4 include number of children fixed effects. Regressions for severe housing hardship
have 32,615 observations.
*p <0 .10;**p 0< .05; ***p < 0.01
Appendix Table 8: Effect of the Child Tax Credit on Economic Wellbeing Outcomes, Local Average Treatment Effects, in $100;
Testing Time Periods
Excluding August Excluding January Controlling for the date
(1) (2) (3) (4) (5) (6)
Hardship index (14-item scale) -0.035 *** -0.041 ** -0.033 ** -0.037 -0.033 *** -0.043 **
(0.012) (0.019) (0.013) (0.020) (0.012) (0.019)
Food hardship (4-item scale) -0.067 *** -0.055 *** -0.068 *** -0.051 ** -0.065 *** -0.055 ***
(0.013) (0.019) (0.013) (0.020) (0.012) (0.019)
Medical hardship (2-item scale) -0.031 ** -0.018 -0.031 ** -0.020 -0.031 *** -0.020
(0.012) (0.019) (0.013) (0.019) (0.012) (0.019)
Severe housing hardship (4-item scale) 0.014 -0.001 0.017 0.003 0.015 0.002
(0.012) (0.019) (0.013) (0.020) (0.012) (0.019)
Transportation hardship 0.009 0.007 0.009 0.005 0.009 * 0.005
(0.005) (0.008) (0.006) (0.009) (0.005) (0.009)
Bill hardship (3-item scale) 0.009 -0.014 0.014 -0.014 0.011 -0.024
(0.012) (0.020) (0.013) (0.020) (0.012) (0.019)
F-statistic 1036.1 442.5 971.5 414.5 1078.8 413.7
First stage coefficient 33.2 30.6 33.0 30.3 33.3 30.1
Household size fixed effects Yes No Yes No Yes No
Number of children fixed effects No Yes No Yes No Yes
N 17,414 17,411 19,154
Note: Coefficients represent the effect of a $100 increase in the CTC. Local average treatment effects (LATE) obtained by
instrumenting for CTC receipt as reported by the respondent.Standard errors in parentheses. Scales are in standard deviation units
(M=0; SD=1). Sample restricted to households with at least one child under the age of 18. All models include all demographic
controls (age, gender, education, race/ethnicity, partnered, urbanicity), state fixed effects, month fixed effects, and contextual
(SNAP/PEBT/UI) controls. Models in columns 1, 3 and 5 include household size fixed effects. Models in columns 2, 4 and 6
include number of children fixed effects. Regressions for severe housing hardship have the following observations: Excluding
August: N=18709; Excluding January: N=18674; Date control: N=20545.
*p <0 .10;**p 0< .05; ***p < 0.01
Appendix Table 9: Testing the Addition of Controls, Material Hardship, Local Average Treatment Effects
LATE
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
Hardship index (14-item scale) -0.007 -0.007 -0.007 -0.033 *** -0.042 ** -0.040 ** -0.011 -0.011 -0.043 ** -0.031 *** -0.038 **
(0.008) (0.008) (0.008) (0.012) (0.019) (0.019) (0.015) (0.016) (0.019) (0.018) (0.019)
Food hardship (4-item scale) -0.054 *** -0.054 *** -0.054 *** -0.065 *** -0.055 *** -0.054 *** -0.028 *** -0.027 *** -0.055 *** -0.040 ** -0.054 ***
(0.008) (0.008) (0.008) (0.012) (0.019) (0.019) (0.015) (0.015) (0.019) (0.018) (0.019)
Medical hardship (2-item scale) -0.011 -0.011 -0.011 -0.031 *** -0.019 -0.017 -0.006 -0.004 -0.020 -0.015 -0.013
(0.008) (0.008) (0.008) (0.012) (0.019) (0.019) (0.015) (0.015) (0.019) (0.018) (0.018)
Severe housing hardship (4-item scale) 0.009 0.009 0.009 0.014 0.002 0.001 -0.006 -0.005 0.001 -0.002 0.002
(0.008) (0.008) (0.008) (0.012) (0.019) (0.019) (0.015) (0.015) (0.019) (0.019) (0.019)
Transportation hardship 0.013 *** 0.013 *** 0.013 *** 0.008 0.005 0.005 0.013 *** 0.009 0.005 0.005 0.004
(0.004) (0.004) (0.004) (0.005) (0.009) (0.008) (0.007) (0.007) (0.008) (0.008) (0.008)
Bill hardship (3-item scale) 0.047 *** 0.047 *** 0.047 *** 0.011 -0.023 -0.020 0.006 0.006 -0.023 -0.015 -0.016
(0.008) (0.008) (0.008) (0.012) (0.019) (0.019) (0.015) (0.016) (0.019) (0.018) (0.018)
F-statistic 2339.6 *** 2338.9 *** 2339.6 *** 1078.8 *** 415.0 *** 420.4 *** 658.9 *** 629.4 *** 417.6 *** 455.9 *** 458.4 ***
First stage coefficient 23.7 *** 23.7 *** 23.7 *** 19.5 *** 17.6 *** 17.7 *** 25.2 *** 23.9 *** 17.6 *** 18.4 *** 18.5 ***
Demographic controls (age, gender,
race/ethnicity, education, partnered,
Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
urbanicity), month fixed effects + state fixed
effects
Contextual controls (SNAP/PEBT/UI) No Yes Yes Yes Yes Yes Yes Yes Yes Yes No
Controlling for COVID-19 rates No No Yes No No No No No No No No
Household size fixed effects No No No Yes No Yes No Yes No No No
Number of children fixed effects No No No No Yes Yes Yes Yes Yes Yes Yes
Number of children under 6 years fixed
No No No No No No Yes Yes No No No
effects
Indicator for "doubled-up" household
No No No No No No No No Yes No No
(additional adults)
Indicator for any children under 6 years No No No No No No No No No Yes No
Number of children fixed effects x
No No No No No No No No No No Yes
demographic controls
N 19,154
Note: Coefficients represent the effect of a $100 increase in the CTC. Local average treatment effects (LATE) obtained by instrumenting for CTC receipt as reported by the respondent. Standard errors in
parentheses. Scales are in standard deviation units (M=0; SD=1). Sample restricted to households with at least one child under the age of 18. Regressions for severe housing hardship have 20,545 observations.
*p <0 .10;**p 0< .05; ***p < 0.01
Appendix Table 10: Weighting Providers Data to Match the ACS, CPS and SNAP QC Data
Providers data
Weighted to the Weighted to Weighted to the CPS ASEC SNAP
Original 2019 ACS the 2019 CPS 2019 SNAP QC ACS 2019 2019 QC 2019
Age
18-24 7 6 8 9 6 8 9
25-34 40 37 37 40 38 38 41
35-44 35 37 34 30 38 35 32
45-54 12 15 15 13 15 15 12
55+ 5 5 5 6 3 5 5
Household structure
Household size 4.30 4.43 4.43 4.27 4.19 4.11 3.56
Number of kids 2.53 2.50 2.49 2.48 2.31 2.18 2.03
Partner/spouse 30 45 47 32 47 50
Race/ethnicity
Black 35 27 28 33 27 27 31
White 35 37 38 43 37 37 41
Hispanic 21 28 26 16 29 27 22
Other 9 7 9 7 7 9 7
Education
<High school 23 18 23 21 18 23 25
High school 39 45 37 59 45 37 55
Some college 27 27 31 15 27 31 15
College or more 10 9 10 6 9 10 5
Female 94 75 75 89 72 73 89
Receive food stamps 85 84 84 86 100 100
Notes: All samples are restricted to households with at least one coresident child under the age of 18. Weighting procedure
described in more detail in Appendix 2.
Data: ACS= American Community Survey 2019. CPS = Current Population Survey ASEC 2019. SNAP QC = SNAP
Quality Control data 2019.
Appendix Table 11: Regression results after reweighting Providers data to the ACS, CPS and SNAP QC benchmarks
ITT LATE
ACS CPS SNAP QC ACS CPS SNAP QC
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)
Material Hardship
Hardship index (14-item scale) -0.014 *** -0.010 -0.012 *** -0.007 -0.009 *** -0.009 ** -0.072 *** -0.070 -0.063 *** -0.050 -0.046 *** -0.054 **
(0.005) (0.006) (0.004) (0.006) (0.003) (0.004) (0.026) (0.048) (0.022) (0.039) (0.014) (0.023)
Food hardship (4-item scale) -0.017 *** -0.007 -0.016 *** -0.006 -0.013 *** -0.005 -0.087 *** -0.046 -0.081 *** -0.043 -0.062 *** -0.031
(0.004) (0.006) (0.004) (0.006) (0.003) (0.004) (0.023) (0.042) (0.021) (0.039) (0.014) (0.023)
Medical hardship (2-item scale) -0.018 *** -0.010 * -0.017 *** -0.008 * -0.009 *** -0.007 * -0.092 *** -0.066 -0.086 *** -0.054 -0.046 *** -0.039 *
(0.004) (0.005) (0.004) (0.005) (0.003) (0.004) (0.023) (0.041) (0.021) (0.035) (0.014) (0.022)
Severe housing hardship (4-item scale) 0.003 0.000 0.005 0.001 0.000 -0.004 0.017 -0.002 0.025 0.006 0.001 -0.024
(0.003) (0.004) (0.004) (0.005) (0.003) (0.003) (0.017) (0.029) (0.019) (0.033) (0.013) (0.020)
Transportation hardship 0.000 -0.003 0.000 -0.001 0.000 0.000 -0.002 -0.018 0.000 -0.006 0.002 -0.002
(0.002) (0.002) (0.002) (0.002) (0.001) (0.002) (0.010) (0.018) (0.009) (0.015) (0.006) (0.010)
Bill hardship (3-item scale) -0.001 -0.006 0.000 -0.004 0.000 -0.009 + -0.006 -0.044 0.000 -0.025 0.002 -0.049 *
(0.005) (0.008) (0.005) (0.008) (0.003) (0.005) (0.028) (0.056) (0.026) (0.052) (0.017) (0.029)
F-statistic 76.2 *** 28.6 *** 89.7 *** 36.4 *** 291.3 *** 141.7 ***
First stage coefficient 19.0 *** 14.1 *** 19.3 *** 14.6 *** 19.9 *** 16.8 ***
Household size fixed effects Yes No Yes No Yes No Yes No Yes No Yes No
Number of children fixed effects No Yes No Yes No Yes No Yes No Yes No Yes
N 19,154
Note: Coefficients represent the effect of a $100 increase in the CTC. Intent-to-treat (ITT) estimates.Standard errors in parentheses. Local average treatment effects (LATE) obtained by instrumenting for CTC
receipt as reported by the respondent. Scales are in standard deviation units (M=0; SD=1). Sample restricted to households with at least one child under the age of 18. All models include all demographic
controls (age, gender, education, race/ethnicity, partnered, urbanicity), state fixed effects, month fixed effects, and contextual (SNAP/PEBT/UI) controls. Odd numbered columns are models with household
size fixed effects; Even numbered columns are models with number of children fixed effects. Models are weighted to the demographic characteritics of the ACS, CPS, or SNAP QC benchmarks. Weighting
procedure described in more detail in Appendix 2. Regressions for severe housing hardship have 20,545 observations.
Data: ACS= American Community Survey 2019. CPS = Current Population Survey ASEC 2019. SNAP QC = SNAP Quality Control data 2019.
*p <0 .10; **p 0< .05; ***p < 0.01
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