Isabel Sawhill and Emily Cuddy have written two new posts for the Brookings Institution against expanding the tax credit for children.

They make three arguments against it. Argument No. 1 is that the expansion, at least as proposed by Senators Lee and Rubio, will benefit “very few if any lower-income families with children.” The child credit is designed to reduce tax liability: It offsets taxes paid, including the income tax and the payroll tax. It counts the “employer’s share” of the payroll tax as a tax paid by employees, which is what economists generally think it is. This means that it offers considerable tax relief to low-income people if they have tax liabilities to reduce; but does not if they do not.

The Tax Foundation estimates that the expanded child credit would increase adjusted gross income by 3.3 percent for the bottom 10 percent of tax filers. The next 10 percent of filers would see their AGI increase by 6.2 percent, and the ten percent after that (those in the twentieth to thirtieth percentiles of income) by 7.3 percent. Thereafter the percentage increase starts declining: If you’re in the eightieth to ninetieth percentiles of income, for example, the child credit will increase your AGI by 1 percent. (These estimates do not, by the way, reflect any controversial “dynamic scoring.”)

So the argument seems both beside the point (since the goal of this policy is to reduce parents’ tax liability, rather than simply increase the incomes of the poor) and overstated (since lower-income families would see real gains from the policy).

Argument No. 2 kindly refers to my argument about how the structure of old-age entitlements results in overtaxation of parents, who contribute to those entitlements both by paying taxes and by making the financial sacrifices entailed by raising children. Sawhill and Cuddy rebut this point thus: “But motivation matters here. Parents do not see these costs as a penalty they are being forced to pay in order to keep Medicare and Social Security solvent. Instead, children are valued for their own sake, with the understanding that the joy of parenthood comes with explicit commitments of both time and money.”

I think this whole way of looking at the issue is wrongheaded. First, a tax penalty can exist even if those paying it are not aware of it. It must be the case that many couples who are paying a marriage penalty because of the way the tax code and benefit programs are structured are unaware they are paying it. Yet nobody treats discussions of a “marriage penalty” and proposals to reduce or end it as mistaken because of this lack of awareness.

Second, the argument is neither that government policy should make raising children costless nor that the costs of raising children are a penalty imposed by the government. It’s that the government should provide tax relief that reflects the extent to which those costs are contributions to the future of entitlement programs. An analogy to state laws that provide tax credits for people who donate to scholarship funds may illuminate the point. One argument for such credits is that the donors are relieving the government of a financial obligation, and differ from non-donors in that respect. That argument does not imply that the donors are unhappy to be making their contribution.

Argument No. 3 is that governments spend money on children, notably through public education. If entitlements make free riders out of adults with few or no children whose retirements are subsidized by adults with several children, then does education spending make free riders out of the latter group? And do these effects cancel each other out?

No. Consider, first, a hypothetical situation where for generation after generation couples have two kids each but, in one generation, birthrates spike to four and then fall back to two. Hold taxes constant, and the generation with more kids gets to have retirement benefits twice as large. When the kids retire, they go back to having the same benefit level as their grandparents—but not a lower level. Raising extra kids creates a long-run surplus for the old-age retirement system. (Hold benefits constant, and we can let the generation of kids from large families pay a lower tax rate and then have taxes snap back up in the next generation. Same point.)*

What happens to education in this scenario? Costs temporarily go up as the big families send their kids to school. Later costs go down and revenues temporarily go up as those kids leave school and start to pay taxes. Then education costs and revenues go back to where they started. Having extra kids doesn’t generate any net loss over the long run.

Another way to look at it: People benefit (in theory!) from public education as kids whether or not any of them go on to have kids of their own. They don’t benefit from old-age entitlements unless some people go on to have kids of their own. The situations aren’t equivalent, and Sawhill and Cuddy are wrong to treat them as such.

* I wouldn’t get too hung up on the fact that new entrants to Social Security are projected to pay more than they take in, which would seem to strengthen the case for the credits, or that the reverse is true of new entrants to Medicare, which would seem to weaken the case. These programs require reforms, but the needed reforms and the expansion of the child credit are not substitutes for each other. What matters in the argument above is that additional children increase the benefits that can be financed at any given tax rate, and reduce the taxes that have to be paid at any given benefit level, and that this gain persists over time.