I have been curious about this question for over a decade.
Minimum age laws/rules/policies are all around us. Think of voting, driving, drinking, and military service. The U.S. Constitution even has minimum age rules for certain political offices - 25 for the House of Representatives, 30 for the Senate, and 35 for Presidency. Minimum age rules are also plentiful in sports, of course.
Dan Stone and I recently published an economics-based analysis of minimum age rules in women's professional tennis in the Journal of Labor Research. The published version can be found here. The SSRN version can be found here. We provide some background in the paper's introduction (AR = age rule):
ARs are often controversial, and understanding their effects is clearly important to policy-makers. However, analyzing AR effects is generally a challenge empirically. In most nonsport contexts, the ARs have been in place for a substantial period of time. Women’s professional tennis provides a unique environment to analyze the effects of ARs on labor market outcomes, as the major change in the sports’ age rule was made fairly recently, in 1995. This allows a meaningful comparison to be made between the groups of players that had to comply with the restriction and those that did not. Moreover, consistent with the observation by Rosen and Sanderson (2001) regarding sports labor market research in general, the availability of player-specific records and the relatively static nature of other rules of the game over the past few decades make women’s tennis an excellent context for such an investigation.
We use regression analysis (OLS and probit) to test both the short-run and long-run effects of the age eligibility rule. With our data set comprised of year-level ordinal rankings, we were also able to use panel data methods, which allowed us to control for year and age effects more precisely. We tested whether players subject to the age rule (adopted in 1995) had longer and/or stronger careers. Our study found null results. We concluded as follows:
We find very limited evidence that the AR has had any systematic beneficial effect on players’ career longevity or success. Our results suggest that sport governing bodies should (re-)evaluate the efficacy and necessity of “one size fits all” age eligibility rules.
I have been working on a couple related studies (using different methods) pertaining to NBA basketball and women's gymnastics this summer. Given the "before and after" quality of minimum age rules and a plethora of metrics to track labor market outcomes, sports is a near-ideal environment to test whether such age eligibility rules "work."