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]

Ethnic segregation in Sao Paulo schools, and its relationship with employment and wages

Following Thursday's post about ethnic segregation and spatial inequality in Europe, I was interested to dig out this 2017 article from my to-be-read pile, by Gustavo Fernandes (Fundacao Getulio Vargas, Brazil), published in the journal World Development (sorry, I don't see an ungated version online). Fernandes used data from the 2005 School Census and the 2010 Population Census for the city of Sao Paulo, and looked at the association between segregation within public and private schools, and employment and wages for those aged 18-35. As motivation, he notes that:

The belief that Brazil has benefitted from an absence of racial and ethnic problems has been widely accepted over the last century. Brazil has often been described as a racial democracy.

Part of the motivation, then, is to debunk this 'myth'. I'm not quite sure that this counts as debunking though:

...our results show that Sao Paulo is not a city with a high degree of segregation, especially when compared to the U.S. In the city, approximately 21.29% of students would have to change schools to a new institution in order to achieve an equal composition of students by color among the entire student population of the city.

That's a fairly low level of segregation, compared not just with the U.S., but with many other countries (for instance, there's a lot of concern about segregation in the New Zealand school system). But is segregation related to inequality? Fernandes finds that, for Sao Paulo:

...segregation is correlated with the level of development in the region, which positively affects the expected returns of brancos and amarelos and negatively affects those of pretos e pardos. This result appears to be explained by the predominance of brancos and amarelos in private schools, despite the fact that most of the population of white students attends public schools. However, the effect of segregation becomes negligible when analyzing only the outcomes of students within the public school system.

The predominance of whites in private schools may be the main reason for the deep economic inequality found in Sao Paulo among races. Those schools provide a higher quality of education in comparison to public schools. They may also offer access to social networks that lead to better jobs. Both factors can exponentially increase the average income of the entire white population, resulting in large disparities between the wages of whites and the wages of pardos and pretos.

The brancos and amarelos (whites and Asians, respectively) tend to make up the majority of the class in private schools, and it is private school segregation (and not public school segregation) that is most associated with young adult employment and wages.

Ultimately, this paper demonstrates a result that is the opposite of the paper I discussed last Thursday, where greater segregation was associated with lower spatial inequality. It is impossible to reconcile the results given the wide difference in methods (not least the difference between cross-country analysis at the regional level, and small-area analysis of neighbourhoods within a single city in Brazil). However, this does demonstrate that more research on this topic is needed.

Ethnic segregation and spatial inequality

For the last few years one of my PhD students, Mohana Mondal, has been looking into ethnic segregation in Auckland (see this earlier post on some of her work). I've also maintained an interest in income inequality. So, I was really interested to read this 2017 article by Roberto Ezcurra (Universidad Publica de Navarra) and Andres Rodriguez-Pose (London School of Economics), published in the Journal of Economic Geography (ungated earlier version here), which links those two ideas. Specifically, Ezcurra and Rodriguez-Pose look at whether ethnic segregation (the concentrate of different ethnic groups within a country) matters for spatial inequality (income inequality between regions or areas of a country).

They use data on a cross-section of 71 countries where they have regional-level data on ethnic groups and region-level GDP per capita. After controlling for various factors known to affect spatial inequality such as the average size of regions, the degree of ethnic fractionalisation of the population (which is basically a measure of how many different ethnic groups there are in a country), the stage of economic development, trade openness, country size and whether a country is a transition country, they find that:

The coefficient of the index of ethnic segregation... is in all cases positive and statistically significant at the 1% level. This implies that more ethnically segregated countries have on average higher levels of spatial inequality...

This holds both for a basic regression specification, but also for an instrumental variables regression, where they attempt to demonstrate a causal effect of ethnic segregation on spatial inequality (as an instrument, they use segregation predicted using the ethnic composition of neighbouring countries). They also show that their results are robust to using alternative measures of segregation and inequality.

Ezcurra and Rodriguez-Pose then go on to investigate potential transmission channels that might explain this relationship. They find that:

...once political decentralisation and government quality are controlled for, the coefficient of the index of ethnic segregation still remains positive, but its effect on spatial inequality is statistically significant only at the 10% level... While not conclusive, these findings suggest the possibility that political decentralisation and government quality could be possible transmission channels linking ethnic segregation and spatial inequality.

The argument is that countries with more ethnic segregation are more likely to decentralise authority to their regions, which increases inequality between the regions.

This is a nice paper, but there are a couple of aspects of the research where some further work is needed. First, this research was based only on cross-sectional data. I would like to see some analysis that included a time dimension before I would conclude definitively that this relationship is causal. Second, the instrumental variables analysis seems fine on the surface, but only until you read this bit:

...the instrument used in the article predicts zero segregation for island countries...

It's pretty difficult to defend an instrument that results in such a wildly off-the-mark prediction. Certainly, you wouldn't want to predict zero ethnic segregation in New Zealand or Australia. I wouldn't expect an alternative conception of the instrument to change the results by a lot, but I think it is worth exploring. So, while this article is interesting, there is definitely more research required in this area.

 

Nobel Prize for Paul Milgrom and Robert Wilson

Last night, the 2020 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (aka Nobel Prize in Economics) was announced as being awarded to Paul Milgrom and Robert Wilson (both Stanford), "for improvements to auction theory and inventions of new auction formats". Based on some informal conversations today, I wasn't the one in my corridor to raise an eyebrow and wonder whether Milgrom didn't already have a Nobel Prize. Needless to say then, the award is well deserved and probably overdue.

This prize is just the latest in a long run of awards for advances in game theory and related work, but this time at the intersection of theoretical and applied economics. Auction theory, as developed by Wilson and Milgrom, is the basis for allocating radio spectrum (for mobile phone signals, for example), for electricity spot markets, and for advertising on Google. It was interesting to note Wilson's original work on the "winner's curse", which is something I have blogged on before (see for example here and here).

Marginal Revolution has good coverage on their broader research, with separate posts for Milgrom and Wilson, pointing to their key contributions. A Fine Theorem also has an excellent post on the topic. The Nobel Committee's website also has a good overall summary.

Milgrom was Wilson's PhD student, but it is worth noting that Wilson was also the PhD advisor for two other earlier Nobel Prize winners, Bengt Holmstrom (2016 winner) and Alvin Roth (2012 winner). That is quite some achievement!