The Effects of the Child Tax Credit

on Labor Supply

Kye Lippold1

Office of Tax Analysis, U.S. Treasury

FCSM Conference

October 2022

1. Email: Kye.Lippold@treasury.gov. Opinions and conclusions expressed are

those of the author and do not necessarily represent the views or policies of the

U.S. Department of the Treasury.
Introduction Background Method Results Conclusion

Motivation

• Tax credits subsidizing work, such as the Earned Income Tax

Credit (EITC) and Child Tax Credit (CTC) attract bipartisan

policy interest

• EITC has positive effects on labor supply, health and education

(Meyer and Rosenbaum 2001; Dahl and Lochner 2012; Hoynes,

Miller, and Simon 2015)

• Most EITC research based on expansions in early 1990s

• Recent work has questioned labor supply findings (Kleven 2021)

• Evidence that labor supply elasticities have declined since 1990s

• What does this imply for future credit expansions, like changes

to the CTC in the American Rescue Plan?

• The CTC provides a new source of evidence on low-income tax

credits

• Little studied (Hoynes and Rothstein 2016)

• Offers new identification strategy with discontinuity at age 17

1 / 22
Introduction Background Method Results Conclusion

CTC and EITC for Single Parent with Two Children, 2016

0 2000 4000 6000

Credit ($)

0 50k 100k 150k

Earnings (2016$)

Earned Income Credit Child Tax Credit Source: Author’s calculations using Taxsim. Calculations assume no unearned income or itemized deductions.

2 / 22
Introduction Background Method Results Conclusion

This Study

• Determine the labor supply impacts of the CTC

• Focusing on extensive margin (strongest EITC effects)

• Approach: difference in regression discontinuities (DiRD)

• Families claim the CTC until their child turns 17

• The EITC, dependent exemption, going to college (etc.)

change when children turn 18 or 19

• Counterfactual:

• Children who are born on January 1st, 1994 give their parents a

full CTC for 2010

• Children who are born on December 31st, 1993 give no CTC

for 2010

• Method controls for preexisting seasonal differences

3 / 22
Introduction Background Method Results Conclusion

Preview of Main SIPP Results (DiRD)

-.2 -.15 -.1 -.05 0 .05 .1 .15 .2

Diff. in Residual for Percent with Employed Parent

Jun

May

Apr

Mar

Feb

Jan

DecNov

Oct

SepAug

Jul

Child Month of Birth

With Controls

Parent Employed

-.2 -.15 -.1 -.05 0 .05 .1 .15 .2

Diff. in Residual for Percent with Parent in Labor Force

Jun

May

Apr

Mar

Feb

Jan

DecNov

Oct

SepAug

Jul

Child Month of Birth

With Controls

Parent in Labor Force

Notes: Estimated with local linear regressions, uniform kernels, 6-month bandwidths, on residuals of control variables.

Shaded areas are 90 percent confidence intervals.

4 / 22
Introduction Background Method Results Conclusion

Contribution

• Inform recent debate on earlier EITC literature (Kleven 2021)

• CTC provides alternative identification strategy to test

robustness

• Estimates of intertemporal substitution elasticity of labor

supply

• No wealth effects in this setting, only price effects (anticipated,

temporary variation)

• (in paper) Develop model to compare responses to temporary

versus permanent tax changes

• Inform policy for new credit expansions

• CTC expanded as part of Tax Cuts and Jobs Act (TCJA)

• California young child CTC (July 2019)

• Strength of labor supply effects for fully refundable CTC (Acs

and Werner 2021; Goldin, Maag, and Michelmore 2022; Corinth

et al. 2022)

5 / 22
Introduction Background Method Results Conclusion

Expenditures on the CTC and EITC over Time

CTC Created Bush Tax Cuts EESA ARRA

0 20 40 60 80

Credits Claimed (2016$, billions)

199019911992199319941995199619971998199920002001200220032004200520062007200820092010

2011

20122013201420152016

Year

EITC Total CTC: One-Time Nonrefundable Refundable Source: Author’s calculations from IRS Statistics of Income data.

6 / 22
Introduction Background Method Results Conclusion

Value of the CTC Over Time

1998

0 500 1000 1500 2000 2500 3000

Value of CTC (2016$)

0 50k 100k 150k 200k

Earnings (2016$) Source: Author’s calculations using Taxsim. Figures are for single parent with two children, no unearned income, and

no itemized deductions.

7 / 22
Introduction Background Method Results Conclusion

Value of the CTC Over Time

1998

1999

0 500 1000 1500 2000 2500 3000

Value of CTC (2016$)

0 50k 100k 150k 200k

Earnings (2016$) Source: Author’s calculations using Taxsim. Figures are for single parent with two children, no unearned income, and

no itemized deductions.

7 / 22
Introduction Background Method Results Conclusion

Value of the CTC Over Time

1998

1999

2001

0 500 1000 1500 2000 2500 3000

Value of CTC (2016$)

0 50k 100k 150k 200k

Earnings (2016$) Source: Author’s calculations using Taxsim. Figures are for single parent with two children, no unearned income, and

no itemized deductions.

7 / 22
Introduction Background Method Results Conclusion

Value of the CTC Over Time

1998

1999

2001

2003

0 500 1000 1500 2000 2500 3000

Value of CTC (2016$)

0 50k 100k 150k 200k

Earnings (2016$) Source: Author’s calculations using Taxsim. Figures are for single parent with two children, no unearned income, and

no itemized deductions.

7 / 22
Introduction Background Method Results Conclusion

Value of the CTC Over Time

1998

1999

2001

2003

2004

0 500 1000 1500 2000 2500 3000

Value of CTC (2016$)

0 50k 100k 150k 200k

Earnings (2016$) Source: Author’s calculations using Taxsim. Figures are for single parent with two children, no unearned income, and

no itemized deductions.

7 / 22
Introduction Background Method Results Conclusion

Value of the CTC Over Time

1998

1999

2001

2003

2004

2008

0 500 1000 1500 2000 2500 3000

Value of CTC (2016$)

0 50k 100k 150k 200k

Earnings (2016$) Source: Author’s calculations using Taxsim. Figures are for single parent with two children, no unearned income, and

no itemized deductions.

7 / 22
Introduction Background Method Results Conclusion

Value of the CTC Over Time

1998

1999

2001

2003

2004

2008

2009

0 500 1000 1500 2000 2500 3000

Value of CTC (2016$)

0 50k 100k 150k 200k

Earnings (2016$) Source: Author’s calculations using Taxsim. Figures are for single parent with two children, no unearned income, and

no itemized deductions.

7 / 22
Introduction Background Method Results Conclusion

Value of the CTC Over Time

1998

1999

2001

2003

2004

2008

2009

2016

0 500 1000 1500 2000 2500 3000

Value of CTC (2016$)

0 50k 100k 150k 200k

Earnings (2016$) Source: Author’s calculations using Taxsim. Figures are for single parent with two children, no unearned income, and

no itemized deductions.

7 / 22
Introduction Background Method Results Conclusion

Value of the CTC Over Time

1998

1999

2001

2003

2004

2008

2009

2016

0 500 1000 1500 2000 2500 3000

Value of CTC (2016$)

0 20k 50k 100k 150k 200k

Earnings (2016$) Source: Author’s calculations using Taxsim. Figures are for single parent with two children, no unearned income, and

no itemized deductions.

7 / 22
Introduction Background Method Results Conclusion

Literature - CTC and December Discontinuities

• Several papers use similar identification strategy (e.g. Nichols,

Sorensen, and Lippold (2012))

• Feldman, Katuščák, and Kawano (2016): Loss of CTC for

middle-income households, where credit is lump sum

• Intensive margin elasticity of 0.3 in year after age 17

(misperception), no age 17 effect

• Looks at higher income group and different margin of response

• Looney and Singhal (2006): Children aging out of dependent

status

• Intensive intertemporal substitution elasticity of 0.75

• Dependency endogenous with college enrollment

• Wingender and LaLumia (2017): Extra tax benefits from

December births lead new mothers to work less

• Looks at unanticipated variation in income, rather than

anticipated variation in wages

• This study looks at future effects of birth timing decision

8 / 22
Introduction Background Method Results Conclusion

Data

• Survey of Income and Program Participation (1984-2014

panels)

• Panel data for 3-5 years; focus on 2001-2016, before TCJA

• Detailed information on demographics, income, family structure,

and birth month

• Tax information from Taxsim (Feenberg and Coutts 1993)

• Sample: Children ages 13.5-17.5 in the survey at end of year,

prior year AGI of $20,000 or below

• Child’s age (in months) provides running variable

• Standardize ages, exclude imputed values

• Limit to children linked to parents in tax unit, observed for 8+

months in current and prior year

• Impute incomes for partial years following Looney and Singhal

(2006)

9 / 22
Introduction Background Method Results Conclusion

Identification

• Compare children born just above age 17 cutoff to just below

cutoff

• Birthday one day before cutoff removes entire credit for the year

• Other programs do not typically change at the cutoff

• Dependent exemption and EITC end at age 19 (or age 24 if the

child is a full-time student)

• Child care credit and child care subsidies end at age 13

• Children receive special treatment under SSI and SNAP until

age 18

• TANF rules change at age 16, 18 or 19 depending on the state

and child’s student status

• Medicaid and CHIP end at age 19

• WIC benefits end at age 5

• (All parameters taken from Urban Institute (2019))

10 / 22
Introduction Background Method Results Conclusion

Identification

• Caveats: birth timing and seasonality

• Long literature that some parents time births to gain eligibility

for credits (Dickert-Conlin and Chandra 1999; Gans and Leigh

2009; Schulkind and Shapiro 2014)

• My cutoff is affected by retiming, but 17 years later

• LaLumia, Sallee, and Turner (2015) finds shifts are small (about

1% of births moved)

• Seasonal trends in outcomes (Buckles and Hungerman 2013;

Schulkind and Shapiro 2014; Bound and Jaeger 1996)

• December and January parents differ on observables

• Exacerbated because my SIPP birthdate data is at monthly

level

11 / 22
Introduction Background Method Results Conclusion

Trends in Seasonality

-.15 -.1 -.05 0 .05 .1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Age Cutoff around End of Year

Discontinuities in Parental Employment by Age Cutoff

-.1 -.05 0 .05 .1 .15

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Age Cutoff around End of Year

Discontinuities in Parental Labor Force Participation by Age Cutoff

Notes: Estimated with local linear regressions, uniform kernels, 6-month bandwidths, on residuals of control variables.

Dashed lines are 90 percent confidence intervals.

12 / 22
Introduction Background Method Results Conclusion

Difference-in-Regression Discontinuities (DiRD)

• Hybrid of DiD and RD designs (Grembi, Nannicini, and Troiano

2016)

• Approach to deal with seasonality

• Difference out December / January differences at earlier ages

• Identifying assumptions:

• Seasonal differences are constant over time

• The effect of the CTC does not depend on seasonality (that is,

parents with children born in different months respond similarly

to the incentives)

13 / 22
Introduction Background Method Results Conclusion

Model

• Linear probability model

yit = α + δDit + φ1AitDit + φ2Ait (1 − Dit)

+ (γ + βDit + φ3AitDit + φ4Ait (1 − Dit))Tit

+ θXit + εit

• yit is indicator of parental work for child i in year t

• Ait is the age of the child (in months relative to December of

that year)

• Dit is a discontinuity (Ait ≥ 0)

• Tit indicates the age 17 cutoff (as opposed to earlier ages)

• Xit are controls

• Using December weights, clustered by panel / variance strata

14 / 22
Introduction Background Method Results Conclusion

First Stage

0 .5 1 1.5 2 2.5 3

Parent's Maximum Eligible CTC ($1000s)

Jun

May

Apr

Mar

Feb

Jan

DecNov

Oct

SepAug

Jul

Child Month of Birth

Age 14-16 Cutoff

0 .5 1 1.5 2 2.5 3

Parent's Maximum Eligible CTC ($1000s)

Jun

May

Apr

Mar

Feb

Jan

DecNov

Oct

SepAug

Jul

Child Month of Birth

Age 17 Cutoff

15 / 22
Introduction Background Method Results Conclusion

RDs for Parental Employment

-.2 -.15 -.1 -.05 0 .05 .1 .15 .2

Residual for Percent with Employed Parent

Jun

May

Apr

Mar

Feb

Jan

DecNov

Oct

SepAug

Jul

Child Month of Birth

Age 14-16 Cutoff

-.2 -.15 -.1 -.05 0 .05 .1 .15 .2

Residual for Percent with Employed Parent

Jun

May

Apr

Mar

Feb

Jan

DecNov

Oct

SepAug

Jul

Child Month of Birth

Age 17 Cutoff

Notes: Estimated with local linear regressions, uniform kernels, 6-month bandwidths, on residuals of control variables.

Shaded areas are 90 percent confidence intervals. Raw All Ages

16 / 22
Introduction Background Method Results Conclusion

DiRD for Parental Employment

-.2 -.15 -.1 -.05 0 .05 .1 .15 .2

Difference in Percent with Employed Parent

Jun

May

Apr

Mar

Feb

Jan

DecNov

Oct

SepAug

Jul

Child Month of Birth

No Controls

Difference, Age 17 Minus Age 14-16

-.2 -.15 -.1 -.05 0 .05 .1 .15 .2

Diff. in Residual for Percent with Employed Parent

Jun

May

Apr

Mar

Feb

Jan

DecNov

Oct

SepAug

Jul

Child Month of Birth

With Controls

Difference, Age 17 Minus Age 14-16

Notes: Estimated with local linear regressions, uniform kernels, 6-month bandwidths, on residuals of control variables.

Shaded areas are 90 percent confidence intervals.

17 / 22
Introduction Background Method Results Conclusion

DiRD Results for Primary Sample

Parent Employed Parent in Labor Force

(1) (2) (3) (4) (5) (6)

Diff in Disc. -0.097∗ -0.087∗ -0.084∗∗ -0.107∗∗ -0.091∗∗ -0.096∗∗

(0.054) (0.044) (0.042) (0.048) (0.040) (0.039)

Age 16.5+ (Post) 0.091∗∗ 0.067∗ 0.076∗∗ 0.086∗∗ 0.067∗∗ 0.076∗∗

(0.044) (0.038) (0.035) (0.039) (0.034) (0.032)

December Disc. -0.007 0.021 0.026 0.025 0.034∗ 0.042∗∗

(0.036) (0.021) (0.021) (0.034) (0.018) (0.019)

Lagged DV Yes Yes Yes Yes

Controls Yes Yes

N 9,443 9,443 9,443 9,443 9,443 9,443

Clusters 1,034 1,034 1,034 1,034 1,034 1,034

Notes: ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. Standard errors (clustered by variance strata) in parentheses.

Discontinuities are estimated with local linear regressions, uniform kernels, in 6-month windows centered around the

December age cutoff. Estimated in window of 13.5 to 17.5 year old children in tax units with prior year AGI below

$20,000. Controls are year and state fixed effects and parental characteristics (race, education, max age [quadratic],

marriage, metro residence, number of dependents, and indicators for current and lagged months observed).

18 / 22
Introduction Background Method Results Conclusion

Fuzzy RD and Elasticity Estimates

(1) (2)

Employed In Labor Force

(A) Parent Employed / In LF

Diff in Disc. -0.084∗∗ -0.096∗∗

(0.042) (0.038)

(B) Maximum Eligible CTC ($1,000s)

Diff in Disc. -1.049∗∗∗ -1.048∗∗∗

(0.065) (0.065)

(C) Percent Working / LFP (lag)

Mean 0.608∗∗∗ 0.723∗∗∗

(0.009) (0.009)

(D) Return to Work / LFP (lag, $1,000s)

Mean 7.928∗∗∗ 4.683∗∗∗

(0.396) (0.437)

ITT Estimate 0.080∗ 0.091∗∗

(= A/B) (0.041) (0.038)

Elasticity at Average 1.040∗ 0.591∗∗

(= (A/C)/(B/D)) (0.539) (0.251)

N 9,443 9,443

Clusters 1,034 1,034

Notes: ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. Standard errors (clustered by variance strata) in parentheses.

Discontinuities are estimated with local linear regressions, uniform kernels, in 6-month windows centered around the

December age cutoff. Estimated in window of 13.5 to 17.5 year old children in tax units with prior year AGI below

$20,000. Return to work is computed as difference in post-tax income between working and non-working parents

(and likewise for LFP). Fuzzy RD and elasticity standard errors are computed using the delta method. Controls are

year and state fixed effects and parental characteristics (see text). 19 / 22
Introduction Background Method Results Conclusion

Elasticity at Steady State

• Use equation from dynamic model

εI ≈





1 −

γWt

1−st



1 −

2α

1+rt

+

(2+rt )α

2

(1+rt )

2



1 −

γWt

1−st





εS

calibrated based on other literature.

• Yields estimates of extensive margin steady-state labor supply

elasticity:

• 0.43 for employment

• 0.47 for labor force participation

• Close to estimates from EITC literature (e.g. 0.43 in Meyer

and Rosenbaum (2001), as calculated by Chetty (2012))

20 / 22
Introduction Background Method Results Conclusion

Results by Entry or Exit Status

Employed In Labor Force

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

Entry Exit Entry Exit

Diff in Disc. -0.108 -0.046 -0.182∗∗ -0.060∗

(0.080) (0.041) (0.090) (0.034)

Age 16.5+ (Post) 0.117∗ 0.037 0.164∗∗ 0.037

(0.066) (0.033) (0.070) (0.028)

December Disc. 0.026 0.005 0.060 0.022

(0.042) (0.022) (0.045) (0.019)

Controls Yes Yes Yes Yes

N 3,695 5,748 2,609 6,834

Clusters 810 931 696 971

Notes: ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. Standard errors (clustered by variance strata) in parentheses.

Discontinuities are estimated with local linear regressions, uniform kernels, in 6-month windows centered around the

December age cutoff. Estimated in window of 13.5 to 17.5 year old children in tax units with prior year AGI below

$20,000. Controls are year and state fixed effects and parental characteristics (race, education, max age [quadratic],

marriage, metro residence, number of dependents, and indicators for current and lagged months observed).

21 / 22
Introduction Background Method Results Conclusion

Conclusion

• Extensive margin response to the CTC equal to or above the

EITC

• Relies on DiRD assumptions of constant seasonality, but

strongest in the subgroups where expected

• Reinforces earlier literature

• Elasticity is higher given temporary tax change

• Provides evidence of timing response (similar to capital gains

realizations)

• Tax credits can still have strong labor supply effects

• Future work

• Replicate with higher precision datasets (SIPP Gold Standard

files, CDW data)

• Investigate responses to new expansions

22 / 22
References Robustness Checks Model Details

References

Acs, Gregory, and Kevin Werner. 2021. How a Permanent Expansion of the Child Tax

Credit Could Affect Poverty. Washington, DC: Urban Institute.

https://www.urban.org/research/publication/how-permanent-expansionchild-tax-credit-could-affect-poverty.

Bound, John, and David Jaeger. 1996. “On the Validity of Season of Birth as an

Instrument in Wage Equations: A Comment on Angrist and Krueger’s ‘Does

compulsory school attendance affect schooling and earnings?’” NBER Working

Paper, no. 5835, https://doi.org/10.3386/w5835.

Buckles, Kasey S., and Daniel M. Hungerman. 2013. “Season of Birth and Later

Outcomes: Old Questions, New Answers.” The Review of Economics and

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Chetty, Raj. 2006. “A New Method of Estimating Risk Aversion.” American Economic

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. 2012. “Bounds on Elasticities With Optimization Frictions: A Synthesis of

Micro and Macro Evidence on Labor Supply.” Econometrica 80 (3): 969–1018.

https://doi.org/10.3982/ECTA9043.

1 / 22
References Robustness Checks Model Details

References

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Anti-Poverty, Targeting, and Labor Supply Effects of Replacing a Child Tax Credit

with a Child Allowance.” NBER Working Paper, no. 29366,

https://doi.org/10.3386/w29366.

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Four Tax Reforms in the United States: Labor Supply and Welfare Effects for

Single Mothers.” Journal of Public Economics 92:795–816.

https://doi.org/10.1016/j.jpubeco.2007.08.005.

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References Robustness Checks Model Details

References

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807–835. https://doi.org/10.1257/aer.20131189.

Gans, Joshua S., and Andrew Leigh. 2009. “Born on the First of July: An (Un)Natural

Experiment in Birth Timing.” Journal of Public Economics 93 (1-2): 246–263.

https://doi.org/10.1016/j.jpubeco.2008.07.004.

Goldin, Jacob, Elaine Maag, and Katherine Michelmore. 2022. “Estimating the Net

Fiscal Cost of a Child Tax Credit Expansion.” Tax Policy and the Economy

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Matter?” American Economic Journal: Applied Economics 8 (3): 1–30.

https://doi.org/10.1257/app.20150076.

Hoynes, Hilary Williamson, Douglas L. Miller, and David Simon. 2015. “Income, the

Earned Income Tax Credit, and Infant Health.” American Economic Journal:

Economic Policy 7 (1): 172–211. https://doi.org/10.1257/pol.20120179.

Hoynes, Hilary Williamson, and Jesse Rothstein. 2016. “Tax Policy Toward Low-Income

Families.” NBER Working Paper, no. 22080, https://doi.org/10.3386/w22080.

3 / 22
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References

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of Consumer Spending to Rebates During an Expansion: Evidence from the 2003

Child Tax Credit.” Working Paper. http://finance.wharton.upenn.edu/%7B~%7

Dsouleles/research/papers/JPSChildTaxCreditApril2009.pdf.

Kleven, Henrik Jacobsen. 2021. “The EITC and the Extensive Margin: A Reappraisal.”

NBER Working Paper, no. 26405, https://doi.org/10.3386/W26405.

LaLumia, Sara, James M. Sallee, and Nicholas Turner. 2015. “New Evidence on Taxes

and the Timing of Birth.” American Economic Journal: Economic Policy 7 (2):

258–293. https://doi.org/10.1257/pol.20130243.

Looney, Adam, and Monica Singhal. 2006. “The Effect of Anticipated Tax Changes on

Intertemporal Labor Supply and the Realization of Taxable Income.” NBER

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References

Meyer, Bruce D, and Dan T Rosenbaum. 2001. “Welfare, the Earned Income Tax

Credit, and the Labor Supply of Single Mothers.” The Quarterly Journal of

Economics 116 (3): 1063–1114. https://doi.org/10.1162/00335530152466313.

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Saez, Emmanuel, and Gabriel Zucman. 2016. “Wealth Inequality in the United States

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References Robustness Checks Model Details

References

Wingender, Philippe, and Sara LaLumia. 2017. “Income Effects on Maternal Labor

Supply: Evidence from Child-Related Tax Benefits.” National Tax Journal 70 (1):

11–52. https://doi.org/10.17310/ntj.2017.1.01.

6 / 22
References Robustness Checks Model Details

Robustness Checks

• Alternative specifications: Link

• No demographic differences: Link

• Smooth density: Link

• Varying age window: Link

• Different local polynomial methods: Link

• Placebo tests: Link

7 / 22
References Robustness Checks Model Details

Alternate Specifications

Parent Employed Parent in Labor Force

(1) (2) (3) (4) (5) (6) (7)

Base

Single

Low Educ.

Leave

School

̸= 17

LFP

Measure Base

Single

Low Educ.

Leave

School

̸= 17

Diff in Disc. -0.084∗∗ -0.055 -0.091∗ -0.075∗ -0.096∗∗ -0.041 -0.107∗∗

(0.042) (0.040) (0.047) (0.042) (0.039) (0.035) (0.044)

Age 16.5+ 0.076∗∗ 0.072∗∗ 0.069∗ 0.057 0.076∗∗ 0.047∗ 0.062∗

(0.035) (0.031) (0.038) (0.036) (0.032) (0.027) (0.036)

Dec. Disc. 0.026 0.008 0.034 0.025 0.042∗∗ 0.008 0.050∗∗

(0.021) (0.020) (0.023) (0.020) (0.019) (0.019) (0.021)

Lagged DV Yes Yes Yes Yes Yes Yes Yes

Controls Yes Yes Yes Yes Yes Yes Yes

N 9,443 6,420 7,659 9,443 9,443 6,420 7,659

Clusters 1,034 943 963 1,034 1,034 943 963

Notes: ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. Standard errors (clustered by variance strata) in parentheses.

Discontinuities are estimated with local linear regressions, uniform kernels, in 6-month windows centered around the

December age cutoff. Estimated in window of 13.5 to 17.5 year old children in tax units with prior year AGI below

$20,000. Controls are year and state fixed effects and parental characteristics (race, education, max age [quadratic],

marriage, metro residence, number of dependents, and indicators for current and lagged months observed).

Back

8 / 22
References Robustness Checks Model Details

Demographics (Parents)

(1) (2) (3) (4) (5) (6) (7) (8)

Educ

(Coll+)

Race (NonWhite) Married

Age

(max)

Num

Dep.

Lag

Emp.

Lag

LFP Index

Diff in Disc. -0.041 -0.087 0.042 -0.723 -0.153 -0.016 -0.023 -0.071

(0.048) (0.055) (0.050) (0.970) (0.152) (0.056) (0.053) (0.132)

Age 16.5+ 0.042 0.054 -0.077∗ 2.062∗∗ -0.174 0.035 0.028 0.064

(0.044) (0.046) (0.042) (0.803) (0.130) (0.045) (0.043) (0.123)

Dec. Disc. -0.016 0.039 -0.024 0.834 -0.034 -0.042 -0.013 -0.137∗

(0.023) (0.038) (0.034) (0.692) (0.109) (0.036) (0.033) (0.072)

N 9,443 9,443 9,443 9,443 9,443 9,443 9,443 9,443

Clusters 1,034 1,034 1,034 1,034 1,034 1,034 1,034 1,034

Mean DV 0.08 0.61 0.27 44.27 2.55 0.61 0.72 0.41

χ

2

p-value 0.32

Notes: ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. Standard errors (clustered by variance strata) in parentheses.

Discontinuities are estimated with local linear regressions, uniform kernels, in 6-month windows centered around the

December age cutoff. Estimated in window of 13.5 to 17.5 year old children in tax units with prior year AGI below $20,000.

Index refers to standardized index of all other columns. χ

2

p-value is for test of first 7 columns being jointly different

from zero in seemingly unrelated regression.

Back

9 / 22
References Robustness Checks Model Details

Demographics (Children)

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

Enrolled

in School

Highest Grade

Completed Attrition

Future

Months Obs.

Diff in Disc. 0.026 -0.015 -0.004 -0.210

(0.024) (0.110) (0.050) (0.589)

Age 16.5+ (Post) -0.041∗∗ 0.805∗∗∗ 0.015 0.220

(0.018) (0.091) (0.038) (0.456)

December Disc. -0.022 -0.086 -0.008 -0.155

(0.017) (0.089) (0.025) (0.307)

N 4,691 4,686 7,167 7,167

Clusters 938 937 997 997

Mean DV 0.96 9.56 0.13 8.80

Notes: ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. Standard errors (clustered by variance strata) in parentheses.

Discontinuities are estimated with local linear regressions, uniform kernels, in 6-month windows centered around the

December age cutoff. Estimated in window of 13.5 to 17.5 year old children in tax units with prior year AGI below

$20,000. (Except columns 1 and 2 are estimated in window of 15.5 to 17.5 year old children).

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References Robustness Checks Model Details

Receipt of Income

(1) (2) (3) (4) (5) (6)

Dividends Property Pensions Soc. Sec. Transfers UI

Diff in Disc. -0.001 0.005 -0.006 -0.031 0.015 -0.001

(0.011) (0.010) (0.017) (0.029) (0.032) (0.022)

Age 16.5+ -0.000 -0.004 0.001 0.005 0.011 -0.012

(0.010) (0.009) (0.014) (0.023) (0.023) (0.016)

Dec. Disc. -0.010 -0.005 -0.000 0.033∗∗ -0.018 0.006

(0.007) (0.005) (0.008) (0.014) (0.017) (0.011)

Lagged DV Yes Yes Yes Yes Yes Yes

Controls Yes Yes Yes Yes Yes Yes

N 9,443 9,443 9,443 9,443 9,443 9,443

Clusters 1,034 1,034 1,034 1,034 1,034 1,034

Notes: ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. Standard errors (clustered by variance strata) in parentheses.

Discontinuities are estimated with local linear regressions, uniform kernels, in 6-month windows centered around the

December age cutoff. Estimated in window of 13.5 to 17.5 year old children in tax units with prior year AGI below

$20,000. Controls are year and state fixed effects and parental characteristics (race, education, max age [quadratic],

marriage, metro residence, number of dependents, and indicators for current and lagged months observed).

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11 / 22
References Robustness Checks Model Details

Density Test

200 300 400 500 600

Weighted Observations

Jun

May

Apr

Mar

Feb

Jan

DecNov

Oct

SepAug

Jul

Child Month of Birth

Age 14-16

200 300 400 500 600

Weighted Observations

Jun

May

Apr

Mar

Feb

Jan

DecNov

Oct

SepAug

Jul

Child Month of Birth

Age 17

Notes: Each point in the figures represents the weighted sum of observations by month of birth for children around

each age cutoff. Back

12 / 22
References Robustness Checks Model Details

Varying Pre-Period Age Window

-.15 -.1 -.05 0

0 5 10 15

Minimum Age in Window

DiRD Estimates for Employment, with Controls

-.15 -.1 -.05 0 .05

0 5 10 15

Minimum Age in Window

DiRD Estimates for LFP, with Controls

Notes: Estimated with local linear regressions, uniform kernels, 6-month bandwidths, on residuals of control variables.

Shaded areas are 90 percent confidence intervals. Back

13 / 22
References Robustness Checks Model Details

Varying Calculation Method

Employment LFP

(1) (2) (3) (4) (5) (6) (7) (8)

Diff in Disc. -0.084∗∗ -0.049 -0.007 -0.037 -0.096∗∗ -0.062 -0.009 -0.050∗∗

(0.042) (0.048) (0.075) (0.026) (0.039) (0.043) (0.066) (0.025)

Age 16.5+ (Post) 0.076∗∗ 0.073∗ 0.064 0.043∗∗ 0.076∗∗ 0.063∗ 0.032 0.052∗∗∗

(0.035) (0.041) (0.071) (0.020) (0.032) (0.037) (0.062) (0.018)

December Disc. 0.026 0.022 0.023 0.009 0.042∗∗ 0.035∗ 0.024 0.018

(0.021) (0.023) (0.034) (0.014) (0.019) (0.021) (0.031) (0.012)

Lagged DV Yes Yes Yes Yes Yes Yes Yes Yes

Controls Yes Yes Yes Yes Yes Yes Yes Yes

N 9,443 9,443 9,443 4,840 9,443 9,443 9,443 4,840

Clusters 1,034 1,034 1,034 899 1,034 1,034 1,034 899

Degree 1 1 2 0 1 1 2 0

Kernel Uni Tri Uni Uni Uni Tri Uni Uni

Bandwidth 6 6 6 3 6 6 6 3

Notes: ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. Standard errors (clustered by variance strata) in parentheses. Estimated

in window of 13.5 to 17.5 year old children in tax units with prior year AGI below $20,000. Results are estimated for

varying degree local linear regresions with uniform or triangular kernels. Controls are year and state fixed effects and parental

characteristics (race, education, max age [quadratic], marriage, metro residence, number of dependents, and indicators for

current and lagged months observed).

Back

14 / 22
References Robustness Checks Model Details

Sensitivity to Bandwidth

-.2 -.1 0 .1

1 2 3 4 5 6

Bandwidth in Months

DiRD Estimates for Employment, with Controls

-.2 -.1 0 .1 .2

1 2 3 4 5 6

Bandwidth in Months

DiRD Estimates for LFP, with Controls

Notes: Estimated with local linear regressions, uniform kernels, varying bandwidths, on residuals of control variables.

Shaded areas are 90 percent confidence intervals. Back

15 / 22
References Robustness Checks Model Details

Placebo DiRD for Period Before CTC was Refundable

1984-1999 1990-1999

(1) (2) (3) (4) (5) (6) (7) (8)

Emp. Emp. LFP LFP Emp. Emp. LFP LFP

Diff in Disc. 0.074 0.044 -0.011 0.010 0.075 0.044 -0.011 0.010

(0.086) (0.065) (0.078) (0.063) (0.086) (0.065) (0.079) (0.063)

Age 16.5+ -0.069 -0.092∗ -0.001 -0.043 -0.069 -0.092∗ -0.001 -0.043

(0.066) (0.053) (0.064) (0.053) (0.066) (0.053) (0.064) (0.053)

Dec. Disc. -0.053 -0.043 -0.005 -0.012 -0.053 -0.043 -0.005 -0.012

(0.061) (0.031) (0.058) (0.030) (0.061) (0.031) (0.058) (0.030)

Lagged DV Yes Yes Yes Yes

Controls Yes Yes Yes Yes

N 7,467 7,466 7,467 7,466 5,830 5,830 5,830 5,830

Clusters 1,396 1,395 1,396 1,395 826 826 826 826

Notes: ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. Standard errors (clustered by variance strata) in parentheses.

Discontinuities are estimated with local linear regressions, uniform kernels, in 6-month windows centered around the

December age cutoff. Estimated in window of 13.5 to 17.5 year old children in tax units with prior year AGI below

$20,000. Controls are year and state fixed effects and parental characteristics (race, education, max age [quadratic],

marriage, metro residence, number of dependents, and indicators for current and lagged months observed). Note that

full-year data for 2000 is not included in SIPP data. "Emp." is employment, "LFP" is labor force participation.

Back

16 / 22
References Robustness Checks Model Details

Placebo Tests Shifting Cutoff to Earlier Ages

Parent Employed Parent in Labor Force

(1) (2) (3) (4) (5) (6)

Age 16 Age 15 Age 14 Age 16 Age 15 Age 14

Diff in Disc. 0.017 0.010 0.044 -0.059∗ 0.018 0.059∗

(0.039) (0.040) (0.039) (0.033) (0.037) (0.034)

Age ≥ Cutoff - 0.5 (Post) -0.017 -0.018 -0.006 0.029 -0.018 -0.043

(0.030) (0.031) (0.031) (0.024) (0.028) (0.028)

December Disc. 0.004 0.011 -0.018 0.050∗∗∗ 0.036∗ 0.016

(0.021) (0.019) (0.020) (0.019) (0.019) (0.017)

Lagged DV Yes Yes Yes Yes Yes Yes

Controls Yes Yes Yes Yes Yes Yes

N 9,487 9,562 9,641 9,487 9,562 9,641

Clusters 1,040 1,052 1,045 1,040 1,052 1,045

Notes: ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01. Standard errors (clustered by variance strata) in parentheses.

Discontinuities are estimated with local linear regressions, uniform kernels, in 6-month windows centered around the

December age cutoff. Estimated in age windows of 3.5 years to left and 0.5 years to right of placebo cutoff, in primary

sample. Controls are year and state fixed effects and parental characteristics (race, education, max age [quadratic],

marriage, metro residence, number of dependents, and indicators for current and lagged months observed).

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17 / 22
References Robustness Checks Model Details

Dynamic Model

• Following Macurdy (1981), adding fixed costs as in Eissa,

Kleven, and Kreiner (2008)

• Continuum of households living τ periods maximizes

Vt[At, θt] = max

pt,At+1

U [Ct] − Fpt + βEt[Vt+1 [At+1, θt+1]]

s.t. At+1 = (1 + rt) (At + Yt − Ct)

Yt = Nt + (1 − pt) Gt + wtpt − T [wt, νt] pt

• Key elements:

• Abstract from hours of work; extensive margin only

• Fixed cost F drawn from CDF φ {F} (once at t = 0)

• Creates binary participation decision pt

• Can borrow and save assets At across periods

• Could reflect paying down debt in low-income context

18 / 22
References Robustness Checks Model Details

Dynamic Model - Definitions

• Parameter definitions:

• Consumption Ct

, discount rate β

• Exogenous wages wt and interest rate rt

• Income Yt

includes non-labor income Nt, transfer income Gt,

and subtracts taxes T [wt, νt]

• G = −T [0, Nt

, νt] is the value of transfers when not working.

• Average tax rate at = at

[wt, Gt, Nt, νt] = T[wt, Nt, νt]+Gt

wt

• θt = {wt

, Gt, Nt, νt,rt} includes exogenous state variables

• Assumes indivisible labor, additive intertemporal separability of

utility, additive separability of fixed costs, complete capital

markets (to borrow and save), rational expectations, and

unitary household decision-making

19 / 22
References Robustness Checks Model Details

Dynamic Model Solution

• Take small deviations around steady state (Taylor expansions)

• Standard Euler equation pins down A

∗

t+1

in each participation

state

• Solve problem of dependence of optimal savings on past and

future work decisions by setting savings as linear function of

marginal propensity to save α:

∆A

∗

t+1 = α∆Yt

• Work decision in each period based on cutoff condition

∆V

∗ = ∆U + βEt

[∆Vt+1] ≥ F

• Probability of participation is Pt = E [pt

] = φ [∆V

∗

]

20 / 22
References Robustness Checks Model Details

Dynamic Model Solution, Cont.

• Simplify with Taylor expansion (to second order) to find

εI =

∂Pt

∂ (1 − at)

·

1 − at

Pt

≈

φ

′

[∆V

∗

]

φ [∆V∗]

λ

0wt (1 − at)

∗

 

1 +

λ

0

c

λ0

wt (1 − at)

 

1 −

2α

1 + rt

+

(2 + rt) α

2

(1 + rt)

2

!!

• Solve in case with α = 0 (steady state) and take ratio, then

cancel terms and substitute, to get:

εI ≈





1 −

γWt

1−st



1 −

2α

1+rt

+

(2+rt )α

2

(1+rt )

2



1 −

γWt

1−st





εS

21 / 22
References Robustness Checks Model Details

Calibration

To calibrate the model, I set:

• γ = 1 (following Chetty (2006))

• α = 0.75 (following Johnson, Parker, and Souleles (2009), who

find μ = 0.25 in a study based on a response to the Child Tax

Credit)

• rt = 0.073, st = −0.02 (using Saez and Zucman (2016))

• Wt = 0.80 for employment and Wt = 0.41 for labor force

participation

• computed based on the mean changes in post-tax income when

working in my sample, computed for the prior year

Back

22 / 22