"The positive effects were seen only in older siblings, not in younger ones."
So the headline is false.
Your "kids" won't be smarter.
But maybe the older one will be.
Then the rest of the article just fills space.
It's linkbait, which is my expectation with anything from Freakonomics.
My problem is that their headlines are disseminated as gospel and repeated verbatim thousands or millions of times, until that headline becomes a truth.
And winds up in a parenting book.
And causes somebody to make a decision based on false data.
Maybe I have too active an imagination, but this just gets under my skin.
"Study: Oldest children test scores higher when 2+ years older"
Personally, I find all of the focus on doing things to make one's children "smart" to be kind of creepy.
Go shopping for infant toys sometime, you will see what I mean.