The Rule of 70

The Rule of 70 provides a quick and dirty method of calculating how long it will take an asset, economy, etc. growing at a constant growth rate to double in size.

• If my savings grow at a 2% rate each year, it will take approximately 35 years for my savings to double.
• If a country's economy grows at 5% each year, it will take 14 years to double in size (in nominal terms).
• If a town's population is growing at 3.5% per year, it will take 20 years for the population to double
• If a tree grows 15% per year in height, it will take the tree about 5 years to double in height. 

People in finance use this rule all the time. For example, John Bogle of Vanguard in a recent interview with the WSJ:

Over the next decade, Mr. Bogle said stocks are likely to generate an average annual return, including dividends, of around 7%. "Your money will double in 10 years," he said.

70/7 = 10 years. Nice! If he is right, it's time to put my money in the stock market. But where does this rule of thumb come from? In many undergraduate finance classes, the rule is taken as given. Here is how it actually works! (click to enlarge)

This handy rule of thumb gives us a reasonable approximation of the length of time it would take something to double in size with a constant growth rate.

I put together an illustration of the rule of 70 concept in Excel. You can play around with the growth rate and see how the rule of 70 approximation compares to the actual time to double.

The Impact of Moneyball on the MLB

Yesterday, Skip Sauer, an economist from Clemson University, posted over at TSE about how the impact of Michael Lewis's Moneyball on Major League Baseball.

When Jahn Hakes and I embarked on our first academic paper on the subject, we thought there was a decent chance that we could refute the economic claims in Moneyball, in particular that players with high OBP were under-priced in the labor market.  Any card-carrying economist knows this is inconsistent with equilibrium in a well-functioning, competitive labor market, and were not baseball teams intensely competitive?  But instead, Jahn and I found that high OBP players did come cheap, relative to the contribution of their skill to winning baseball games.  Intriguingly however, we found that the “OBP discount” vanished in 2004, the year that Moneyball was published.  The likely reason:  other teams, like Michael Lewis, had looked into what was going on in Oakland, and hired people out of the A’s front office.  Now there were multiple bidders for high-OBP players in baseball’s labor market, thus driving up their price.

OBP refers to on-base-percentage. And more from his second paper inspired by Moneyball.

In the early, pre-expansion period of 1986-1993, the estimated percentage boost in salary from a one standard deviation increase in the ability to take walks was a measly 2.8%.  Post-Moneyball, the figure was 14.0%.  The financial returns to the overlooked skill increased by a factor of five. Is that not indicative of a fundamental change in the game?

Pretty impressive findings. I've been thinking about sports economics as a potential career for several years now. Perhaps this movie will generate some buzz and increase demand for people trained in economics, statistics, finance, and mathematics that want to work in professional sports for a career. Or even college sports for that matter. As someone who grew up in a great college town, I wonder about the extent to which big-time college football programs are actively implementing advanced statistical analysis to improve their teams.

The Best American Sports Writing 2011 - FREE!

One of the most popular posts on this blog to date has been the The Best American Sports Writing 2010 - Free that I posted earlier this year. I guess people like free stuff. In that post, I linked to as many articles of the 2010 edition of the book as possible, since most of them could be found somewhere on the internet.

Well, I have done the same thing for the latest edition, The Best American Sports Writing 2011, which is coming out on October 4th. There are a few articles that I have not been able to locate yet, so if you are able to find them, let me know and I'll link to them here. If you prefer reading in book format, you can pre-order the book right now for $10 on Amazon for a both the paperback and Kindle editions. Enjoy!

Risks, Danger Always in Play by John Powers from the Boston Globe (subscriber access only)
 

Breathless 4 by Chris Jones from ESPN The Magazine

The Surfing Savant by Paul Solotaroff from Rolling Stone

School of Fight: Learning to Brawl with the Hockey, Goons of Tomorrow by Jake Bogoch from Deadspin.com

The Franchise by Patrick Hruby from ESPN.com

Eight Seconds by Michael Farber from Sports Illustrated (unable to locate)
 

ABC News Investigation: USA Swimming Coaches Molested, Secretly Taped Dozens of Teen Swimmers by Megan Chuchmach and Avni Patel from ABCNews.com
 

Own Goal by Wells Tower from Harper’s Magazine

 

Culture of Silence Gives Free Rein to Male Athletes by Sally Jenkins from the Washington Post
 

High School Dissonance by Selena Roberts from Sports Illustrated
 

Gentling Cheatgrass by Sterry Butcher from Texas Monthly

Pride of a Nation by S. L. Price from Sports Illustrated

The Crash by Robert Sanchez from 5280

The Patch by John Mcphee from The New Yorker (subscriber access only)

 Fetch Daddy a Drink by P. J. O'Rourke from Garden and Gun

Trick Plays by Yoni Brenner from The New Yorker 

The Short History of an Ear by Mark Pearson from Sport Literate (unable to locate)
 

If You Think It, They Will Win by Bill Shaikin from the Los Angeles Times (unable to locate)

The Dirtiest Player by Jason Fagone from GQ

Old College Try by Tom Friend from ESPN.com

Dusty Baker a Symbol of Perseverance by Howard Bryant from ESPN.com

Icarus 2010 by Craig Vetter from Playboy (not even going there)
 

Danny Way and the Gift of Fear by Bret Anthony Johnston from Men’s Journal
 

The Tight Collar by David Dobbs from Wired.com

Life Goes On by Mark Kram Jr. from the Philadelphia Daily News

The Courage of Jill Costello by Chris Ballard from Sports Illustrated

Above and Beyond by Wright Thompson from ESPN.com

A Gift That Opens Him Up by Bill Plaschke from the Los Angeles Times
 

New Mike, Old Christine by Nancy Hass from GQ 

I haven't had a chance to read any of the articles yet, but I'll update this post with my personal favorites when I do.

What is an economist? Cartoon Edition

This is the second post in the series "What is an Economist?"

I am re-posting this cartoon from Greg Mankiw's blog because I enjoyed it so much. I also thought it fit well with this series.

Click picture to enlarge

From time to time this cartoon will pop into my head during class as we are discussing spurious assumptions that are made for economic theories and models. One of the wonderful things about economics is that models are usually built off of "reasonable" assumptions and proven laws of economics. Then we see where those assumptions lead us. Hopefully to some conclusions that we can cleverly test with real-world data. If those assumptions turn out to be unreasonable or flat-out wrong, we should go back and adjust our models.

What this cartoon points out, I think, is a major problem in many fields, but specifically in econ. Economists must be willing to go back and adjust assumptions and models to conform to real-world data and observations... If the catapult doesn't work, maybe a better strategy structure would be a bridge!

The FRED Excel Add-In - Getting Economic Data Has Never Been Easier

Paul Krugman posted briefly on his blog last month about a free excel tool called the FRED add-in (Federal Reserve Economic Data). This tool by the St. Louis Fed is a simple, yet essential for anyone who likes working with and analyzing economic data. Basically, this excel add-in streamlines the process of downloading/importing economic data into a spreadsheet. And it fits nicely into the current excel interface (see screenshot below).

I won't bore you with how to download and install it, but I would like to highlight some of the useful features.

• You have over 30,000 economic time series just a click away.
• You can easily update data once new information has been published.
• Data manipulations can be performed on any data set that you download. My favorites are percent change from the previous period and the natural log (I'm finding out in grad school that economists are quite fond of this transformation).
• Ability to change the frequency of aggregation (daily, weekly, bi-weekly, monthly, quarterly, and annual)
• A streamlined graphing process! Other than the actual importing process, I think the graphing feature is my favorite thing in the FRED add-in. I mean, mainly because I can shade US recessions on my graphs for the first time ever. It doesn't get much better than that!
•  You can also create a multiple series graph in a matter of seconds and create a secondary vertical axis while you are at it. 

Recession shading...

I hope you find this tool as useful as I have. As I play around with it more, I'll update this post with any other cool features that I stumble across. Here is the user's guide if you want to learn more about the FRED add-in.

What sort of economics tools, software, or websites do you use to look at economic data? Are there any other excel add-in's out there like this one? I would love to here from you in the comments section below or tweet me with your comment @zack0liver.

Moneyball on the Big Screen

As someone with a personal interest in sports economics, I am looking forward to the new Moneyball movie that is coming out later this month. It is based on the sports classic by Michael Lewis, one of my all-time favorite writers who I have blogged about previously here.

 

I hope that the movie touches some on the advanced sabermetrics that are used, but I'm assuming there it will just scratch the surface. It's Hollywood after all.

(HT Marion for sharing the trailer with me)

Does Maternal Race Impact Adult Outcomes?

Last week, I attended an interesting seminar about a new paper in the works by Peter Arcidiacono and Seth Sanders from Duke University titled Maternal Race and Black Outcomes. Peter Arcidiacono presented the research and did a great job handling a multitude of questions and challenges to the paper. I considered applying to Duke's MA Program, so I was excited to have a Duke professor come to present his work. Anyway, here is the abstract:

Differences between blacks and whites in test scores and labor market outcomes are stark. While much catchup occurred post-Civil rights, convergence has slowed. We examine how differences across education and labor market outcomes vary by maternal race and own race with identification coming from mixed-race families. While black students with white mothers come from families with similar demographics to black students with black mothers, their education and labor market outcomes are very different. There are no significant differences in test scores, grades, college graduation, and wages between black and white males with white mothers, yet large differences exist between these groups and black males with black mothers. These results are insensitive to alternative measures of own-race, using skin tone instead of own race, and including school fixed effects.

The paper is somewhat controversial depending on how the results are interpreted. One caveat is that these results are only statistically significant for boys, although girls' outcomes follow a similar pattern. Several major points stuck with me from the seminar.

1) Although black children with white mothers are demographically more similar to black children with black mothers, black children with white mothers have adolescent and adult outcomes that are more similar to outcomes of white children.

2) Skin tone of the child was insignificant in terms of impact on adult outcomes when maternal race of is accounted for.

3) These results held for a variety of outcomes including wages, college completion, test scores, etc.

As you can see, this paper could likely take a lot of heat simply due to the issue it is trying to tackle. The fact that the mother's racial background is statistically more important than than her child's is a novel idea in this field. Is it culture, social networks and access, the inter-generational impact of discrimination on families, etc. or a combination of many factors? What mechanism is at work here? Here is the authors' conclusion:

That fact that the results seem to be different depending upon whether race is coded as race of the mother or race of the child is suggestive that race of the mother may have an affect on outcomes distinct from its effect through the race of the child. This pattern is supported by the findings in this paper which points towards differential investment patterns across mothers of different races.