The 'Heckman Curve' takes some heat

The 'Heckman Curve' is the idea that investments in educational interventions have lower net value among older target populations than among younger populations. At least, that is the implication of this curve, taken from the Heckman paper published in the journal Science in 2006:

I refer to the Heckman curve in passing in the topic on the economics of education in my ECONS102 class. But, I hadn't realised until recently that I had the curve wrong (more on that later in the post). It was actually reading this recent article by David Rea (Victoria University of Wellington) and Tony Burton (Auckland University of Technology), published in the Journal of Economic Surveys (open access), that drew my attention to my error. Rea and Burton present a strong critique of the Heckman Curve, based on cost-benefit data on 339 interventions collated by the Washington State Institute for Public Policy. Looking at how benefit-cost ratios vary across the age of the target population of interventions, Rea and Burton find that:

...there does not appear to be any clear relationship between the age of the treatment group and program cost effectiveness.

Indeed, here's Figure 3 from the Rea and Burton paper, showing the lack of a relationship bearing any resemblance to the figure at the top of this post:

To be fair to Heckman, most of the data that Rea and Burton use doesn't actually pertain to educational interventions. However, when they limit their sample to the 110 educational programmes, the key results hold. There is no Heckman Curve in this data.

That wasn't to be the end of this story though, as Andrew Gelman reported back in August (based on an email from David Rea), James Heckman had written a response to Rea and Burton's critique, which was to be published in the Journal of Economic Surveys. Rea and Burton had written a rejoinder to the reply, also to be published. Then, Heckman inexplicably withdrew his reply, but not before the rejoinder had appeared on the JES website as an early view. It's not there now, but you can read it in its entirety in Gelman's post. We are left to wonder what it is that Heckman said in his reply - I guess we may never know. It is disappointing that the debate will not be available in its entirety in the published record.

Anyway, coming back to my error. I've always interpreted the 'Heckman Curve' not as having age on the x-axis, but prior education. I've been interpreting it as a manifestation of diminishing marginal returns to education, regardless of the age at which that education occurs. So, basic literacy and numeracy programmes have large positive effects when enacted at young children, but also when enacted among adults. When you look at the types of programmes that are included in the dataset that Rea and Burton use, it is clear that the adult education programmes are targeted at low-education adults, or at least at adults whose first experience of education probably didn't lead to the best outcomes. So, it is of no surprise to me that the observed benefit-cost ratios have no apparent relationship with age. The programmes at young ages are often much less targeted, and if you re-scaled the x-axis to follow prior education (or prior effective education, appropriately defined), you may well see the declining curve that Heckman envisaged. Of course, that doesn't allow you to tell quite as compelling a story as this, from the Heckman paper in Science:

Early interventions targeted toward disadvantaged children have much higher returns than later interventions such as reduced pupil-teacher ratios, public job training, convict rehabilitation programs, tuition subsidies, or expenditure on police. At current levels of resources, society overinvests in remedial skill investments at later ages and underinvests in the early years.

[HT for the Gelman post: Marginal Revolution]