Given the attention, it seemed useful to apply a little QR to the topic to gain a deeper understanding. If you click the link above, you will quickly learn that the gender gap is 23%. But who is in the sample? It takes a little digging, but you eventually find the answer: "full-time, year-round workers." That's a start, but a student armed with 10 Foundational Quantitative Reasoning Questions would know to press further by wondering how the concept of "full-time" is defined. The answer turns out to be anyone working over 35 hours is employed full-time. That well-prepared student might then wonder what is controlled for in this analysis. The answer is nothing other than full time status–not even hours worked.
A recent Labor Department study reports that the wage gap shrinks by 71% (to around 5%) after controlling for well-documented income-altering factors other than sex like hours worked, age, number of children, marital status, union representation, race, education, and fraction of women working in the person's industry and occupation. In other words, the gender pay gap is largely explained by choices.
So, does that mean that we can largely ignore complaints of discrimination? Clearly not. That women and men on the same career path earn the same income does not rule out discrimination that limits work choices. Are there barriers in the education system or in hiring that make it harder for women to end up in higher-paying positions? Does society push women into lower paying life paths? These are hypotheses that cannot be ruled out by the data.
But the tools of QR can help us focus in on the real explanations for an important observation.
But now the internet is also creating its own potentially useful data. "Google it!" Forecasting the US unemployment rate with a Gooble job search index explains how Google search statistics can improve forecasts of unemployment. The authors create a typical forecasting model based on past unemployment levels and data from the Survey of Professional Forecasters, a quarterly survey of experts carried out by the Philadelphia Fed. The authors then add a variable which captures the frequency of Google searches for "jobs." Including the Google search data reduces the model error by 30 to 40 percent.
It seems to me there is something really interesting in this idea. In economics, there are many behaviors we try to track: hiring, unemployment, consumption, investment, etc. I'm sure that is true of many fields. The problem is that there is a long lag between households' actions and when we get the data. Online activity gives us an alternative, real-time measure that may help us improve forecasts. [Note: I am less excited about what Google does with personally identifiable information. The data referred to here is aggregate activity that isn't linked to any particular person.]
If you are interested in looking into trends for search terms, go to www.google.com/insights/search/#.
When you do your taxes, take a look toward the end of the 1040 instructions. Apparently the US government is collecting a little extra from Microsoft in exchange for promoting Excel's "fancy," tilted, 3-D pie chart. The tilt in this case appears to be laying the pie on an incline no greater than 15 degrees. Take a look:
I've never seen such a beautiful shot of the side of a pie chart before. While the pair of charts purportedly provide information about the distribution of income and outlays, the tilt is so distortionary that it is impossible to distinguish the 24% of the budget spent on National Defense from the 38% spent on Social Security, Medicare, and other retirement programs. That's a 50% difference obliterated by what Tufte terms "chart junk." Alternatively, there is no way you'd guess from looking that we spend almost the same on Social Programs as on National Defense.
While one could argue that little harm is done because no one really reads this page of the 1040 instructions, I'd still rather that my procrastination be rewarded with cleaner graphics.
Ultimately, Politifact conclude Wyden got those numbers right. In fact, they add some more measures of the pain:
- The tax code is 3.8 million words, up more than 170% since 2001.
- If you want a copy of the code all for yourself to consult as you do your taxes (and who wouldn't!), you'll need to buy 25 volumes and provide 9 feet of shelf space.
- No doubt a result of the complexity, 99% of filers resort to help from software or tax preparers.
If you put all of those hours into dollars (using the average compensation of US workers reported in the Statistical Abstract of the US), we devote more than $200 billion per year on taxes.
I hope this post gives you comfort as you work on your own taxes; you've got company!
The statistics of this problem suggest you are better off switching. The contestant owns a door with a 1/3 probability of containing the prize. The other two doors collectively hold the remaining 2/3 probability. Monte Hall's offer boils down to this: Would you like to hold the option on one, randomly chosen door or the other two? (Because he will reveal one of the remaining two to be a loser, the contestant gets the prize if is was behind either of the two non-chosen doors to begin with.)
Esther and Elin gave a nice demonstration about how the counter-intuitive nature of this result can be overcome by having students play the game repeatedly with playing cards. But what I am writing about today is a question they asked at the end: Can anyone give an example of the Monte Hall problem in real life. One of the session attendees threw out the academic job search. We typically bring in 3 candidates. We get a sense of who we like. Then one of the other two bows out due to exogenous reasons. Do we switch preferred candidates?
I'm in the middle of hiring and so have been thinking about this. My first thought has been that my process isn't really like the Monte Hall problem. I don't have a choice between one car and two goats. I have three goods of varying quality. And I am not randomly picking. I am assessing them and then sorting out an expected value. So, when one job candidate bows out, it is nothing like the choice: Two random doors or one?
However, suppose my objective function was simply that I had to get the best candidate. Perhaps I have a strong sense of regret and just can't stand to learn that I didn't pick the best colleague when I had the chance. My guess is that even though I do my best to assess candidates, many times I really can't rule out the possibility that any of the three would be the best of the bunch. So long as none of the candidates is so clearly dominant that s/he has a probability of more than 50% of being the best, I'm back in Monte's world. So, if we assume someone with this kind of objective, the Monte Hall problem does apply.
Curious what others think. Is your hiring practice similar to the Monte Hall problem? Either way, do you know of other "real" examples of the problem in everyday life?