David Rea and Tony Burton write:

The Heckman Curve describes the rate of return to public investments in human capital for the disadvantaged as rapidly diminishing with age. Investments early in the life course are characterised as providing significantly higher rates of return compared to investments targeted at young people and adults. This paper uses the Washington State Institute for Public Policy dataset of program benefit cost ratios to assess if there is a Heckman Curve relationship between program rates of return and recipient age. The data does not support the claim that social policy programs targeted early in the life course have the largest returns, or that the benefits of adult programs are less than the cost of intervention.

Here’s the conceptual version of the curve, from a paper published by economist Heckman in 2006:

This graph looks pretty authoritative but of course it’s not directly data-based.

As Rea and Burton explain, the curve makes some sense:

Underpinning the Heckman Curve is a comprehensive theory of skills that encompass all forms of human capability including physical and mental health . . . • skills represent human capabilities that are able to generate outcomes for the individual and society; • skills are multiple in nature and cover not only intelligence, but also non cognitive skills, and health (Heckman and Corbin, 2016); • non cognitive skills or behavioural attributes such as conscientiousness, openness to experience, extraversion, agreeableness and emotional stability are particularly influential on a range of outcomes, and many of these are acquired in early childhood; • early skill formation provides a platform for further subsequent skill accumulation . . . • families and individuals invest in the costly process of building skills; and • disadvantaged families do not invest sufficiently in their children because of information problems rather than limited economic resources or capital constraints (Heckman, 2007; Cunha et al., 2010; Heckman and Mosso, 2015). Early intervention creates higher returns because of a longer payoff over which to generate returns.

But the evidence is not so clear. Rea and Burton write:

The original papers that introduced the Heckman Curve cited evidence on the relative return of human capital interventions across early childhood education, schooling, programs for at-risk youth, university and active employment and training programs (Heckman, 1999).

I’m concerned about these all being massive overestimates because of the statistical significance filter (see for example section 2.1 here or my earlier post here). The researchers have every motivation to exaggerate the effects of these interventions, and they’re using statistical methods that produce exaggerated estimates. Bad combination.

Rea and Burton continue:

A more recent review by Heckman and colleagues is contained in an OECD report Fostering and Measuring Skills: Improving Cognitive and Non-Cognitive Skills to Promote Lifetime Success (Kautz et al., 2014). . . . Overall 27 different interventions were reviewed . . . twelve had benefit cost ratios reported . . . Consistent with the Heckman Curve, programs targeted to children under five have an average benefit cost ratio of around 7, while those targeted at older ages have an average benefit cost ratio of just under 2.

But:

This result is however heavily influenced by the inclusion of the Perry Preschool programme and the Abecedarian Project. These studies are somewhat controversial in the wider literature . . . Many researchers argue that the Perry Preschool programme and the Abecedarian Project do not provide a reliable guide to the likely impacts of early childhood education in a modern context . . .

Also the statistical significance filter. A defender of those studies might argue that these biases don’t matter because they could be occurring for all studies, not just early childhood interventions. But these biases can be huge, and in general it’s a mistake to ignore huge biases in the vague hope that they may be canceling out.

And:

The data on programs targeted at older ages do not appear to be entirely consistent with the Heckman Curve. In particular the National Guard Challenge program and the Canadian Self-Sufficiency Project provide examples of interventions targeted at older age groups which have returns that are larger than the cost of funds. Overall the programs in the OECD report represent only a small sample of the human capital interventions with well measured program returns . . . many rigorously studied and well known interventions are not included.

So Rea and Burton decide to perform a meta-analysis:

In order to assess the Heckman Curve we analyse a large dataset of program benefit cost ratios developed by the Washington State Institute for Public Policy. Since the 1980s the Washington State Institute for Public Policy has focused on evidence-based policies and programs with the aim of providing state policymakers with advice about how to make best use of taxpayer funds. The Institute’s database covers programs in a wide range of areas including child welfare, mental health, juvenile and adult justice, substance abuse, healthcare, higher education and the labour market. . . . The August 2017 update provides estimates of the benefit cost ratios for 314 interventions. . . . The programs also span the life course with 10% of the interventions being aimed at children 5 years and under.

And here’s what they find:

Wow, that’s one ugly graph! Can’t you do better than that? I also don’t really know what to do with these numbers. Benefit-cost ratios of 90! That’s the kind of thing you see with, what, a plan to hire more IRS auditors? I guess what I’m saying is that I don’t know which of these dots I can really trust, which is a problem with a lot of meta-analyses (see for example here).

To put it another way: Given what I see in Rea and Burton’s paper, I’m prepared to agree with their claim that the data don’t support the diminishing-returns “Heckman curve”: The graph from that 2006 paper, reproduced at the top of this post, is just a story that’s not backed up by what is known. At that same time, I don’t know how seriously to take the above scatterplot, as many or even most of the dots there could be terrible estimates. I just don’t know.

In their conclusion, Rea and Burton say that their results do not “call into question the more general theory of human capital and skills advanced by Heckman and colleagues.” They express the view that:

Heckman’s insights about the nature of human capital are essentially correct. Early child development is a critical stage of human development, partly because it provides a foundation for the future acquisition of health, cognitive and non-cognitive skills. Moreover the impact of an effective intervention in childhood has a longer period of time over which any benefits can accumulate.

Why, then, do the diminishing returns of interventions not show up in the data? Rea and Burton write:

The importance of early child development and the nature of human capital are not the only factors that influence the rate of return for any particular intervention. Overall the extent to which a social policy investment gives a good rate of return depends on the assumed discount rate, the cost of the intervention, the interventions ability to impact on outcomes, the time profile of impacts over the life course, and the value of the impacts. Some interventions may be low cost which will make even modest impacts cost effective. The extent of targeting and the deadweight loss of the intervention are also important. Some interventions may be well targeted to those who need the intervention and hence offer a good rate of return. Other interventions may be less well targeted and require investment in those who do not require the intervention. A potential example of this might be interventions aimed at reducing youth offending. While early prevention programs may be effective at reducing offending, they are not necessarily more cost effective than later interventions if they require considerable investment in those who are not at risk. Another consideration is the proximity of an intervention to the time where there are the largest potential benefits. . . . Another factor is that the technology or active ingredients of interventions differ, and it is not clear that those targeted to younger ages will always be more effective. . . . In general there are many circumstances where interventions to deliver ‘cures’ can be as cost effective as ‘prevention’. Many aspects of life have a degree of unpredictability and interventions targeted as those who experience an adverse event (such as healthcare in response to a car accident) can plausibly be as cost effective as prevention efforts.

These are all interesting points.

P.S. I sent Rea some of these comments, and he wrote: