THE BOOK--Playing The Percentages In Baseball

I haven’t RTA, but maybe it’s because married players tend to be older than single players.

Dave: I sure hope they controlled for age and/or free agency status.

I actually had my first econometrics class with Naomi (she was the prof) and saw her present this in the fall.  She was pretty exhaustive with the parameters of the model, though I’m still a bit skeptical of what’s going on.  I suspect that being married is simply correlated with likeability.  Considering this is a team sport with very large investment, it seems reasonable that the married guys are more likeable/less likely to have character issues, and therefore get paid slightly more.

And I’m not on board with Martin’s criticism.  Page length is usually extremely limited in the publishing world and citing an entire debate on the usefulness of the statistics is not all that useful in the paper.  I can vouch from hearing it presented that she considered plenty of statistics coming from sabermetric websites (including WAR).  The topic of interest is marriage premiums, and the measurement issue is a stepping stone to getting there.  What articles should have reasonably been cited regarding OPS?

Correlation is not causation…

maybe woman are more attracted to guys who make more

I would not be surprised if it is simply that single guys (with no families to support) are not more satisfied with slightly smaller salaries on the average.  That would not surprise me at all.  Certainly, motivation to make big money is, subconsciously at least, part of the negotiating process.  Not to mention the fact that single guysare probably less mature and savvy…

Married guys certainly don’t get to KEEP more of their money.  I can vouch for that.

It might be the same reason why insurance is cheaper for married man. They take less risk?

I concur that being married is an incentive to seek as high an income as possible.

I think Brian’s theory (#4) is more likely to be the key factor.  I only skimmed the paper, but it didn’t seem they even considered the possibility that women are more likely to marry a man who is on the cusp of earning many millions of dollars (or who has just signed a large contract).  Millsy can correct me if I missed that.

More generally, there is just no conceivable way that MLB players get a 20% marriage premium if you control for everything else that affects salary.  I’m quite prepared to believe this premium occurs at lower levels, especially in smaller firms, where an employer may feel he should pay a guy a few thousand more because he’s supporting a family (and maybe married guys negotiate more aggressively, as MGL suggests).  But MLB teams throw an extra $2M at a player just because he’s married?  Not a chance.  When you get a result like that, it’s time to revise your model, not time to publish.

Guy,

I was thinking something similar to your ‘cusp of earning’ after thinking about it some more yesterday.  I’m curious what the lag is after getting married in terms of the next contract.  Perhaps women are forward looking.  I think they attempted to check as best they could for this spousal attracting selection bias.  If you go to Page 28, they attempt to address this issue to some extent:

“...we are interested in whether players after their third or sixth years are more likely to marry given that wages tend to sharply increase after these milestone years. The results show that players are no more likely to marry. We subsequently include the lagged value of wages (column 2), their growth rate (column 3) and lagged productivity growth rates (column
4). None of the specifications show that lags of wages or productivity are statistically significant predictors of future marital status, suggesting that our main findings are not driven by reverse causality.”

I did not buy one of the authors’ explanations when I saw her present.  In general, her theory was that players with wives have someone to take care of other life tasks (including standard traditional roles stuff as well as taking care of ensuring his image is better by heading up foundations, marketing, etc.).  I’m sure there is some of that going on with respect to allowing the player to focus on baseball (or hell, just not going out every night) but I think the wife’s ‘marketing and lobbying’ for the player applies to a select few, rather than the large majority of married baseball players even at the top tier of players where they find the effect (they don’t find it for the lower two-thirds of the population of players).

But the authors do state that the marriage itself may not be directly causal but more of a signal in a number of ways about things that they do not include in the model.

The authors measure a nonzero marriage premium for major-league hitters.  In the absence of controls, this premium was statistically significant (*) (p<0.10).  After controlling for other factors, the premium was no longer statistically significant, even under their loose standards.

Factors controlled for included: race, team, position, ballpark, manager, age, age-squared, league, handedness (**), and rookie height and weight.

(*) It strikes me as silly that p~0.05 is considered statistically significant, especially knowing the difficulty of purging spurious positive results from the discussion.  What strikes me as even sillier is that in many fields, it is acceptable to choose a significance level after conducting the analysis.
(**) Handedness was handled poorly.  There were non-exclusive variables for left- and right-handedness.  It is unclear whether only hitting was included or (irrelevant to the hitting analysis) throwing was included.  What is clear is that switch-hitters were treated as the sum of left- and right-handed effects rather than as a separate category.

After finding that the results were not statistically significant, the authors attempted to measure the source of the marriage premium, attempting to distinguish between five hypotheses:
(1) Marriage is correlated to intangibles (e.g. leadership) that employers value.
(2) Married men are more likely to forego non-pecuniary compensation in favor of wages (dismissed as irrelevant to the case of MLB players).
(3) Reverse causation: Higher earners have more marriage options.
(4) Marriage causes increased productivity.  (Addressing this point is the core of their analysis.)
(5) Employers discriminate in favor of married men.

Most of the things that have been thought of on this page were discussed by the authors.  Since they are trying to explain something that is statistically consistent with zero, we can expect a lot of hand-waving.

I have not read the paper yet, but the conclusion is not all that surprising given what I know about the economics of marriage. It’s not discrimination-- it’s mostly the issues discussed in this thread probably, but married men do tend to earn more than single men after controlling for other quantifiable factors. On the other hand, a lot of the reasons for this trend may be relevant for baseball players, so the article could be illuminating, assuming the specification is good.

One of the more interesting things I remember is that the rate of changing jobs is lower for married men. In most fields, this is very important because of the issue of benefiting from your own investment in a worker. If he’s less likely to leave, the firm will invest more in increasing his human capital, since they’re more likely to recoup this investment. (This is probably one of the reasons for wage discrimination against women-- they tend to leave their jobs more often for family reasons and firms invest less in their future earnings expecting more of them will leave, which leaves lower investment in the women that stay.)

Baseball is an interesting example because contracts bind players to teams, and they lack an alternative profession with comparable salaries if they leave. But apparently, they still probably have higher salaries when they’re married.

Interesting check: what does the aging curve look like for married and single men?  Given that married men live longer than single men, perhaps teams are investing in a belief that married men will keep up their productivity longer?  I’ll need to read the paper.

@11: The list of controls that you gave is incomplete. The inclusion of player fixed effects means that the authors also controlled for unobserved time constant factors specific to each player (disposition, appearance, and anything else that is plausibly time invariant). Ditto for the other fixed effects in the model (park, manager, etc.).

Before discussing *why* this effect might pop up I think we should note what Jeremy pointed out in #11.  Once controls were in place no statistically significance effect of marriage was found.  I think they might have buried the lead but they do say:

It appears, thus, that marital status does not significantly impact wages once taking into
account variables such as age, experience, race, etc.

From table 7, the effect of marriage (OLD post-1975 with controls) is -0.7% with a standard error of 3.4%.  Put another way, the effect of marriage on salary is (95% confidence interval) likely somewhere between -7.4% and +6.0%.

I think most of us would have said pretty confidently that marriage doesn’t effect salary by more than 5% in either direction before reading this study and that entire range is included in their confidence interval.  So, in terms of the effect of marriage on salary (controlling for age, ability etc) we have no new
information. 

Note: I would consider even a 2% increase in salary due to marriage *significant* (not used in the statistical sense) so this article didn’t rule out the possibility of what I’d consider a large marriage effect.

Married guys are likely more mature and keep a more stable and consistent schedule:

single guys are mire likely to have their minds going in a few directions and are likely more vulnerable to distractions.

To joke, married guys only stay out until 2, single guys until 4-5 AM.

There is also a change in perspective, on all things really, when you’re married and/or start a family.

For myself, I would be an absolute mess as a single athlete, with some money, on the road, and being able to follow every impulse or desire that popped into my mind.

Whether it’s statistically significant in performance or not is another issue. But there are a few reasons why some managers strongly prefer veteran players, and it’s not solely about on field things.

@14: If I understand correctly, the “player fixed effects” is really only a control in the latter part of the analysis (when they are looking for the source of the difference).  But there is one big control I did leave out—MLB experience.  The authors look at bins that roughly correspond to pre-arb, arb, and free-agent groupings (although it looks like they measure in calendar years rather than service time).

J. Cross/15:  Wouldn’t you say it’s worse than just “burying their lead?” Despite having found no significant relationship overall when controlling for all the relevant factors they could, the authors say (abstract):  “Our results show that the marriage premium also holds for baseball players, where married players earn up to 20% more than those who are not married, even after controlling for selection. The results are generally robust only for players in the top third of the ability distribution and post 1975 when changes in the rules that govern wage contracts allowed for players to be valued closer to their true market price.”

Maybe I’m misreading this—and I didn’t read the paper carefully—but it seems to me they sliced and diced the data until they found a sub-population with the desired relationship, and then decided to report that this confirms a marriage premium.  Seems highly questionable to me.  Especially since they only find an apparent relationship among the best players.  For those players, how you handle multi-year salaries becomes extremely important.  If you average total salary over life of contract, for example, you will invariably find that older players are “overpaid,” and they will of course be more likely to be married.  Not to mention the small sample size they are now dealing with (there are not a lot of single superstars in their free-agent years). 

If they were reporting that marriage is a predictor of superior future performance (rather than an independent influence on salary), I could believe that.  But they say “Nonetheless, there do not appear to be clear differences in productivity between married and nonmarried players.” So they really are claiming there is a marriage premium per se, and that seems like a conclusion they were determined to reach, rather than one based on a fair reading of their own data. 

Am I missing something?