So let's start where they should start: what is "enrichment" to the authors?
> Our definition of enrichment intends to capture the kinds of activities that are typically considered to be investments in children’s skills. Therefore, our baseline measure includes only those activities that are unambiguously related to skill development over and above class time in school.
> we aggregate the 300+primitive time-use categories into eight categories: enrichment activities, other enrichment activities, play and social activities, passive leisure, duties/chores, class time, sleep, and other
They go on to show (on page 8) that (1) 3% of children's time is "Enrichment" and 2% is "Other Enrichment" (...), which is all in all a whopping 5% (70 minutes) in the day, and (2) that 66% of that time is homework.
Seems to me like they have a beef with kids having 45 minutes of homework per day. The title of this paper is attractive and the conclusions broad, but really they could have said "let's compare children doing homework to children doing no homework and measure cognitive abilities", and they'd have something more substantial.
But what is cognitive skill vs non-cognitive skill then? Well it's not explained in the paper, but they say that they use the Child Development Supplement (CDS) to aggregate that information, and that the CDS is three "waves" that they look at together. All of those "waves" correspond to years, respectively 1997, 2002 and 2007. I'd like to argue that these last 13 years have seen a wee-bit of change in the world (remember when youtube and twitter were one-year olds?), but whatever. It takes a text-search to finally find the data, on page 44. Cognitive skills include (and are limited to) Letter Word (?!), Applied Problems, and Passage Comprehension (?!).
So... ok. Let's just say they were really trying to research homework, in which case those only-three-existing-cognitive-skills would mean something (although the jury's out on what Letter Word means). The NON COGNITIVE SKILLS include things like "Curious and exploring, likes new experiences", "Does neat, careful work", "Tries things for himself/herself", "Thinks before acting, not impulsive".
At this point I throw my hands up in the air, I forget that I spent far too much time reading this "paper", and I move on.
They say that since time is finite, the benefit from music lessons seems to be canceled out by lost opportunities of doing other things. It’s totally reasonable to think that, in fact if enrichment was positive in net then that would actually mean kids are doing too little.
Perhaps music lessons have some second-order effect on "does neat, careful work", but it doesn't seem impossible that might have opposing effects on other so-called skills too: "too fearful or anxious" for stage fright, "disobedient" for not practicing when told.
This is more "chess won't make you smarter." I'm assuming what does is related to family environment, genes, and quality of primary education.
The "non-cognitive skills" come from a factor analysis of a hodgepodge of behavioral ratings ("Cheats or tells lies", "Too dependent on others"), none of which seem similar to what I'd call a skill. It is not clear to me why the loadings on these factors vary across years: if you think that not depending on others is a non-cognitive skill, surely it's the same skill in 1997 and 2002.
Did you read the paper? That’s not what they say at all. In fact they say that we would expect no real difference from a few minutes and 0 but because we do find differences we can use that to control for other factors.
First, they are looking at a very wide range of activities and calling them enrichment. They include tutoring, music lessons, reading, and other "extracurricular activities" as an "enrichment activity." That seems like too wide of a net, as many extracurricular activities and homework likely are a waste of time, therefore diluting the extracurricular activities with positive effects.
Second, if I understand their methodology, they are checking students with no enrichment activities to children with a few minutes a week of enrichment time. Skill acquisition takes more than a few minutes a week, so of course those children would not be receiving benefit.
Third, the results seem absurd. They are saying there are no cognitive benefits to taking music lessons, but I guarantee that the children who took a music lesson is much better at playing an instrument than a student who didn't.
Fourth, there's already a lot of statistical and neurological evidence that reading is good for your thinking and your brain, and I don't think this study overcomes that evidence.