NATIONAL CENTER FOR POLICY ANALYSIS HOME / DONATE / ONE LEVEL UP / ABOUT NCPA / CONTACT Child Care Tax Credits: A Supply-Side Success Story
TECHNICAL APPENDIX by David R. Henderson and John C. Goodman In this appendix we use the Blau and Robins estimate 38 of the elasticity of employment with respect to child care costs, along with other information, to estimate the revenue effects of the child care tax credit. 39 Assume that (1) W = aPb where, W = the percent of mothers who are working; a = a constant term; P = the expenditure for child care; and b = the elasticity of work with respect to P. With a child care tax credit, (2) P = P^(1-r) where, P^ = the market price of child care; and r = the percent of tax credit From Blau and Robins, we know that the elasticity, b, is -0.38. Under current law, the tax credit, r, is equal to 30 percent of allowable expenses for families with an annual income up to $10,000. Beyond that, the tax credit drops by one percentage point for each additional $2,000 of taxable income, reaching 20 percent for a family with an income of $28,000 or higher. Thus, (1- r) is equal to 0.7 for a family with an income of $10,000 and 0.8 for a family with an income of $28,000. Currently, the average weekly price of child care in a day-care facility is $66. There is considerable variation among cities around the country, however, with the average weekly price ranging from $104 in New York City to $39 in Ogden, Utah 40. In addition, families may also purchase child care by hiring a sitter to come to their own home or by placing their children in day-care in someone else's home. These options cause even greater variation in price. A survey by Louis Harris and Associates found that, on the average, families spend $2,280 per year per child for child care -- or $43.85 per week based on a 50-week workyear. This number varied considerably with family income, family structure, location and other factors. 41 In 1986, the latest year for which statistics are available, about 62 percent of women with children under age 18 were employed. The 62 percent figure is a national average, with the percent being lower for women with younger children and higher for women with older children. This number also undoubtedly varies with other differences among families. Any global estimate of the effects of the child care tax credit on the decision of women to enter the labor market must ignore the many important differences among women and among families. In Table A-1, however, we present the results of sensitivity analysis -- using different values for P^ and W. Note that under a broad range of assumptions, the effect of the child care tax credit on the labor market participation of mothers is quite high. TABLE A-1 PERCENT OF WOMEN WHO WORK BECAUSE OF THE CHILD CARE TAX CREDIT* (Sensitivity Analysis) Tax P^ =$66 P^ =$66 P^ =$66 P^ =$44 P^ =$44 P^ =$44 Credit W=.62 W=.50 W=.70 W=.62 W=.50 W=.70 30% 8.8% 6.3% 8.9% 8.8% 6.3% 8.9% 28% 7.3% 5.9% 8.2% 7.3% 5.9% 8.2% 26% 6.7% 5.4% 7.6% 6.7% 5.4% 7.6% 24% 6.1% 5.0% 6.9% 6.1% 5.0% 6.9% 22% 5.6% 4.5% 6.3% 5.6% 4.5% 6.3% 20% 5.0% 4.1% 5.7% 5.0% 4.1% 5.7% *Entries are expressed as a percent of all women with children. Because the federal government has created the dependent child care credit, it loses revenue. On the other hand, because the credit induces women at the margin to enter the labor market and earn taxable income, governments at all levels gain additional income. We can express these revenue losses and gains as follows. (3) Static Revenue Loss = W x N x P^ x r From the Tax Credit (4) Dynamic Revenue Gain = ~W x N x Y x MTR From the Tax Credit where N is the number of women with children, ~W is the change in the percent of women with children who work because of the tax credit, Y is the average weekly wage and MTR is the marginal tax rate. Note that all working women who are eligible receive the tax credit, whereas there is a supply-side offset to this revenue loss only to the extent that the credit induces women who would not otherwise have done so to earn taxable income. If we assume that national averages apply, then the work week is 33 hours and the wage is $7.00 per hour. Thus, the average weekly wage is $231, and the average annual wage is $11,550 based on a 50-week workyear. In addition, 62 percent of women with children work and their average weekly child care expense is $44. Under these assumptions we can calculate the additional earnings (addition to GNP) due to the tax credit for different levels of gross family income -- i.e., for different values of r. If we further assume a payroll tax rate of 15 percent, and state and local marginal income tax rates of 4 percent and 6 percent (for federal income tax brackets of 15 and 28 percent respectively), 42 we can calculate the additional government revenue due to the tax credit for different levels of family income. For low-income families who receive the full 30 percent credit, government receives about 77 cents back in new work-related taxes for each dollar of the tax credit. For families in the 28 percent federal income tax bracket, government receives $1.04 in new revenue for each dollar of tax credit. For families in the 33 percent bracket, government receives $1.14 in new taxes for each dollar of tax credit. In a similar way, we can calculate a supply-side return for different tax credits, such as those depicted in the first column of Table A-II. TABLE A-II ADDITIONAL GOVERNMENT REVENUE PER DOLLAR OF TAX CREDIT (Sensitivity Analysis) Tax P^ =$44 P^ =$66 P^ =$66 P^=$44 P^ =$44 P^ =$33 Credit Y=$231 Y=$231 Y=$347 Y=$347 Y=$116 Y=$116 30% $ .77 $ .51 $ .77 $1.15 $ .38 $ .51 28% .75 .50 .75 1.13 .38 .50 26% .74 .49 .74 1.10 .37 .49 24% .74 .49 .74 1.10 .37 .49 22% .74 .49 .74 1.10 .37 .49 20% 1.04 .69 1.04 1.55 .52 .69 Table A-II also presents results for other values of the weekly wage and day-care cost. These other values may be important because national averages may obscure important differences among the groups entitled to different percentage tax credits. Thus the table contains an average weekly wage equal to one-half the national average, and one that is 50 percent greater than the national average. Similarly, the table contains the average weekly price of child care in a day-care center ($66) and child care costs of one-half that amount ($33). For the parameters selected, the return to government ranges from a low of 37 cents for each dollar of tax credit to a high of $1.55. We can place limits on these values, however, by making some reasonable assumptions. Assume that women in families in the 28 percent income tax bracket either match the national average or pay higher-than-average child care costs. If they earn above the national average, they definitely pay higher-than-average child care costs 43. Assume the reverse is true for families in the 15 percent income tax bracket. Women in these families either match the national average or pay lower-than-average child care costs. If they earn lower-than-average wages, they definitely pay lower-than-average child care costs. These assumptions allow us to place a lower and an upper bound on the range of values for families in different income groups as depicted in Table A-III. Note that in the last column of Table A-III, the high estimate for the return to government on each dollar of tax credit obtained by assuming that all women match the national average in terms of wages and child care costs. The low estimate is obtained by assuming that women in the 28 percent income tax bracket pay higher-than-average child care costs, while women in the 15 percent bracket pay below-average costs. TABLE A-III TAX CREDIT BY FAMILY INCOME Additional Taxes Family Average Marginal Paid Per Dollar Income Tax Credit Tax Rate of Credit 0 - $12,000 30% 34% .51 - .77 $12,000 - $20,700 26% 34% .49 - .74 $20,700 - $32,050 22% 34% .49 - .74 $32,050 + 20% 49% .69 - 1.04 For reasons discussed in the text, not all working mothers take advantage of the child care tax credit. Table A-IV, for example, presents the Urban Institute's estimate on the distribution of tax credits under the current system. Although the 30 percent of families with incomes of $12,000 or less receive the most generous tax credit, they claim only 3.3 percent of total tax credit dollars. TABLE A-IV DISTRIBUTION OF THE CURRENT TAX CREDIT Percent of Family Income Total Credit Dollars 0 - $12,000 3.3% $12,000 - $20,700 20.3% $20,700 - $32,050 27.1% $32,050 + 49.3% Using the Urban Institute's estimate of where child care tax dollars currently go, and combining this estimate with the results presented in Table A-III, we can derive an economy-wide approximation of the effects of the credit. For example, based on the distribution of credit dollars shown in Table A-IV, the weighted average revenue return to government for each dollar of tax credit is between 59 and 89 cents. Thus with $4 billion of tax credits, government revenues increase by between $2.36 and $3.54 billion. Given a weighted average marginal tax rate of 42 percent, this implies a net addition to GNP of $5.6 to $8.4 billion. Given an average annual wage of $11,550, this implies that the tax credit has led to between 485 and 730 thousand new jobs. These results are depicted in Table A-V. It is important to note that the upper bound of these estimates is more consistent with the results of Table A-I. If 730 thousand women are induced to enter the labor market because of the child care tax credit, this represents a little more than 8 percent of the families who claim the credit. This is within the range that the results of Table A-I would lead us to expect. TABLE A-V AN APPROXIMATION OF THE EFFECTS OF THE CHILD CARE TAX CREDIT ON THE ECONOMY Total Tax Credit Dollars: $4 billion Increase in GNP: $5.6 - $8.4 billion Increase in Government Revenues: $2.4 - $3.5 billion Increase in Jobs: 485 - 730 thousand Estimates Using a Different Approach The above results are based on Blau and Robins' estimate of the elasticity of married women's employment with respect to the cost of child care. Our confidence in these results would be increased if they were confirmed by other methods. Fortunately, another straightforward method of computing the child care tax credit's effect on tax revenues is available. Instead of using the elasticity of women's employment with respect to the cost of child care, one can use the elasticity of women's employment with respect to the wage. 44 With this approach, the child care tax credit is treated as an increase in the net wage. The method of computing the effect of the tax credit on work and therefore on tax revenues is as follows. The working woman's annual gross pay is $11,550. 45 Her marginal and average federal income tax rate is about 0.15, the marginal and average Social Security tax rate is 0.075, 46 and the marginal and average state income tax rate is about 0.04, for a total marginal and average tax rate on labor income of 0.265. Therefore the net pay is (1 - 0.265) x $11,550, or $8,489. But, assuming the woman pays for child care for only one child, the tax credit reduces the cost of day-care by 30% of $2400, or by $720. Thus the additional after-tax income from the woman's choice to work is $8,489 + $720, or $9,209. Removing the tax credit would reduce the after-tax income by 7.8 percent. If the relevant labor supply elasticity is 1.0, removing the tax credit would cause a 7.8 percent decrease in the number of women working. Thus the number of women working would fall to 54.2 percent. In general, the revenue gains and losses from the tax credit are as follows: (5) Static Revenue Loss = W x N x $2,400 x r From the Tax Credit (6) Dynamic Revenue Gain = ~W x N x $11,550 x MTR From the Tax Credit Using equations (5) and (6) we can compute the percent of the revenue loss from the child care tax credit recaptured by taxes on increased earnings -- for different elasticity estimates for both low-income and middle-income working mothers. These estimates are reproduced in Table A-VI. TABLE A-VI GOVERNMENT REVENUE GAIN PER DOLLAR OF TAX CREDIT Elasticity Low-Income Middle-Income 0.4 26 % 38 % 1.0 44 % 76 % 1.5 62 % 114 % For an elasticity of 1.0, the estimates of the percent of the tax credit that is recaptured is close to the lower-bound estimate done with the first method. For an elasticity of 1.5, the estimates are close to the upper bound estimated by the previous method. The estimates in Table A-VI are more consistent with the previous findings for middle-income women, than for low-income women, however. At least for middle-income women, the range of estimates made with the first method fall well within the range of estimates in Table A-VI. For low-income families, government gets 26 to 62 cents in additional tax revenue for every $1 the federal government loses through the child care tax credit for working parents. For middle-income families, governments get 38 to 114 cents per dollar lost. In short, at least one quarter and possibly all of the revenue "loss" typically estimated from the child tax-care credit is a phantom loss. It is gained back because more mothers are motivated to work.