voluntaryXchange

An Overconfidence Quiz

Matt Hood gave this quiz to a seminar I attended.*

The directions are to state an interval for each question that you are 95% sure contains the right answer. No using reference materials.

1. How many countries are there in the U.N.?
2. How many votes did Obama get in 2008?
3. What year was the Battle of Waterloo?
4. How many protons are in a gold atom?
5. How many runs did the Giants score in the 2010 World Series?
6. What’s the lowest temperature ever recorded in Alaska?
7. What’s the population of Mississippi?
8. How many miles it to the moon (on average)?
9. What is the height of the Eiffel Tower?
10. When did King Tut die?

Matt’s goal with this quiz is to motivate the idea that people are overconfident of what they know, as a lead in to how behavioral finance differs from conventional finance.

I knew the goal of the test was to “trick” me. And, I know how confidence intervals work. And yet the correct answers was only in 3 of the intervals I answered with.

Touché, Matt.

* If you want the answers, e-mail me directly. That way I’m not blabbing Matt’s trade secrets.

Technorati Tags: behavioral,finance,overconfidence,quiz

Usefulness of Basic Math

In the kitchen this morning …

Mix # 1 for waffles required 3/2 cups of mix, 3/4 cup of water, 3 tablespoons of water, and 1 egg.

But, I have only 3/4 cups of the mix, so the egg is going to be a problem.

Mix # 2 from a second box required 2 cups of mix, 3/4 cup of water, and 1/3 cup of oil, but no eggs.

I don’t want to try and come up with half an egg, and it’s clear from the first recipe that it’s substituting an egg for some oil. But how much?

A quick trip to the internet shows that 1/4 cup of oil can be substituted for 1 egg.

So, I measure out a half batch of Mix # 1: 3/4 cup of mix, 3/8 cup of water, 3/2 tablespoons of oil, and 1 egg.

Knowing there’s 1/2 egg extra in there, I substitute the extra 1/2 egg for 1/8 cup of oil in the second recipe. I’m making a half-batch of that too, so I use: 1 cup of mix, 3/8 cup of water, and 1/6 cup of oil minus the 1/8 cup of oil I’m getting from the egg.

To simplify, you note that the denominators 6 and 8 are common factors of 24. Then 1/6 cup is the same as 4/24 cup, and 1/8 cup is the same as 3/24 cup. So what I needed was 4/24 minus 3/24 equals 1/24 cup of oil.

A cup has 8 ounces. There’s two tablespoons in an ounce, so that’s 16 tablespoons in a cup. There’s 3 teaspoons in a tablespoon, so that’s 48 teaspoons in a cup. And 1/24 of a cup is then 48/24, or exactly 2 teaspoons. That’s how much extra oil I needed to add.*

I added that oil, whisked both half-batches together, started pouring onto the new waffle iron I got for Christmas, and the kids were happy with the waffles.

Tim Worstall is probably going to comment back that he just would’ve gone out for breakfast, but he’s not as geeky as me.

* The beauty of the customary system of weights and measures is that it is based on multiples of 2’s and 3’s, making the sort of arithmetic I used much more straightforward for someone with a basic grasp of fractions than using a calculator.

Technorati Tags: waffles,basic,kitchen,math

Correlation vs. Causation

Here’s some cute graphics that appeared in Business Week. These might prove useful for that inevitable lecture on correlation and causation:

Technorati Tags: correlation,causation

A Tax On Math Skills

Pearls Before Swine:

I hope my favorite management professor, and lottery player, doesn't see this.

Technorati Tags: tax,math,skills,lottery

Obama Exploits Public Innumeracy

Tyler Stillman shared this video with me.

Innumeracy is like illiteracy, except with numbers. Many people are simply not good at understanding the scale of numbers that come up commonly in macroeconomics. And that probably effects policy choices …

Technorati Tags: innumeracy,obama,budget,cuts

Innumeracy in Forbes

Forbes tried to pull a fast-one, exploiting innumeracy to make a politically correct point.

In the article “Girls Rule” they presented a table, and I’ve extracted the meaty part below:

.	.	STOCK PERFORMANCE
Rank	Name / Company / Industry	Change During Tenure	Relative to Industry	Relative to Market
24	Anne Lauvergeon / Areva / electrical prods	394%	360	448
63	Marjorie Scardino / Pearson / publishing	65	170	119
36	Lynn Laverty Elsenhans / Sunoco / oil refining	-15	157	96
54	Carol Meyrowitz / TJX Cos / apparel retailing	60	152	184
57	Andrea Jung / Avon Products / personal care prods	102	150	240
89	Shikha Sharma / Axis Bank / banking	307	119	173
97	Angela Ahrendts / Burberry Group / apparel	94	116	217
52	Guler Sabanci / Sabanci Holding / financial services	141	113	71
92	Chanda Kochhar / ICICI Bank / banking	280	111	146
82	Laura Sen / BJ's Wholesale club / discount retailing	27	110	91
8	Gail Kelly / Westpac / banking	-13	103	115
71	Chua Sock Koong / Singapore Telecom / telecom	49	103	100
26	Patricia Woertz / Archer Daniels Midland / food	5	102	119
20	Ursula Burns / Xerox / electronic equipment	59	102	123
77	Nancy McKinstry / Wolters Kluwer / publishing	35	101	112
12	Angela Braly / Wellpoint / health care services	-30	99	89
32	Maria Ramos / Absa Group / banking	80	91	95
18	Ellen Kullman / Dupont / chemicals	1	90	114
2	Irene Rosenfeld / Kraft Foods / food processing	-4	90	108
6	Indra Nooyi / PepsiCo / soft drinks	5	89	117
75	Susan Ivey / Reynolds American / tobacco	-10	85	116
65	Annika Falkengren / SEB / banking	-27	80	50
85	Janet Robinson / New York Times Co. / publishing	-81	78	20
14	Cynthia Carroll / Anglo American / metals & mining	-9	77	117
38	Ana Patricia Botin / Banco Espanol de Credito / banking	-7	77	46
42	Carol Bartz / Yahoo! / Internet services	16	61	92
	Average		115	128

So what could possibly be wrong? The data support the position that women CEO’s deliver better investment performance to investors. Don’t they?

The problem is the use of an average. The number 115 in the last row, indicating that female CEO’s beat their industry’s average return by 15% is fine.

But, it isn’t the number one should use to answer this question.

The reason is that the way the data is measured is bounded going down, and unbounded going up: no female CEO can do worse than –100, but conceivably they could do as well as positive infinity.

When you average numbers like that, you get a value that is not in what most people would consider the center of the data. This is why you probably don’t live in the average house: Bill Gates’ house skews the average.

What’s worse, is that the table actually contains the appropriate data to analyze, and then doesn’t use it. You don’t get much better evidence of political correctness than that.

With data like this, you should look at the median. This is easy to spot from the dark gray column: there are 26 female CEO’s, so the median is between the 13th and 14th values: 102.

Well … you can still say that female CEO’s outperform their industries.

But good practice suggests that you have to give some sort of interval estimate to make that claim. It’s standard with data like this to use the interquartile range which runs from 87 to 117. Since that range includes 100, it would be conventional to conclude that there is no evidence that female CEO’s outperform male ones.

This isn’t what Forbes says. Instead we have:

… There's a ringingly clear answer: Women deliver the goods on a far more consistent basis.

It gets worse:

These results were not skewed by a couple of supercharged gains, as 16 of the women bosses outgained their respective markets.

Ooh ooh – 16 out of 26 beat their industry. That’s like saying your baseball team is good because they won 16 of their first 26 games. It’s pretty simple to plug that into a first semester statistics text (they do make reporters take stats, don’t they) to find that you’d really need to find more like 19 of them beating their industry average to draw that conclusion.

The pity in all this is that I’ve had enough female bosses, and worked with enough brilliant female business students, that I’m pretty sure this assertion may be true.

Technorati Tags: girls,rule,ceo,industry,return,innumeracy

Number Quotes for Trivial Comparisons

Putting numbers in context can be hard. Number quotes does it for you. You input a number, it gives you a bunch of “that’s as big as” comparisons from which to choose.

For example, there’s the Obamacare: they say it will cost $940,000,000,000 but it will reduce the deficit by $138,000,000,000. That’s like spending the GDP of South Korea to save the GSP of Oklahoma.

Ooh ooh.

Technorati Tags: number,quotes,comparisons

Sudden Acceleration Stem-and-Leaf

Megan McArdle’s spreadsheet on the known ages of drivers involved in sudden acceleration accidents with Toyotas is perfect for a stem-and-leaf diagram.

1|8

2|1

3|246

4|457

5|6678

6|00368

7|12255779

8|37

The great thing about these is that a journalist could actually put one of these together in the body of a piece with no special tools, and their readers would be able to get the big picture.

Of course … that assumes that the data actually shows the message they want to convey: that accidents are distributed randomly throughout the Toyota fleet. They aren’t.

Technorati Tags: toyota,sudden,acceleration,driver,age

Comparing Apples to Oranges: Driving vs. Flying Edition

Via, the magazine of AAA compares the costs of driving vs. flying from San Francisco to Los Angeles.

I’m sure no economists were harmed in the construction of this article. How can I be sure?

The article puts together information on 4 different costs of the trip — time, money, pollution, and risk — so that they can be compared across the 2 trips, without putting them in the same units so that one could compare the total costs of the two trips.

Here’s their data:

	Driving	Flying
Time	6 hours	3.5 hours
Cost	$103	$82
Greenhouse gas emissions	169 pounds of CO2	181 pounds of CO2
Chance of a fatal accident	1 in 300,000	1 in 8,000,000

The value of time is subjective, but the metric ought to be opportunity cost: how much would we have to pay you to be in a car for the trip when you’d rather be doing something else. I think this would range from $10-50 per hour for most people, and I think we’d get a bunch for $20/hour. It just isn’t that odious to sit in a car.

The value of the greenhouse gas emissions is even more subjective, since even our most objective sources can’t agree on ballpark numbers. One plausible assumption is how much the government might pay you not to incur those emissions. Here, the optimal carbon tax of Nordhaus comes in handy: $30/ton. A ton of carbon is what is carried around in 7330 pounds of carbon dioxide. That’s less than a dollar for either driving or flying. One wonders what would motivate the authors to even worry about that?*

The value of avoiding a fatal accident probably has the firmest numbers. Forensic economists can ballpark the value of a human life fairly well based on the risky choices we can’t be bothered to avoid. The typical result is in the mid 7 figures. Here, it makes sense to call it an even $8 million. Then we can say the cost of the risk of driving is about $27, while that of flying is $1.

Here’s the revamped table:

	Driving	Flying
Time	$120	$70
Cost	$103	$82
Greenhouse gas emissions	$1	$1
Chance of a fatal accident	$27	$1

Clearly, these are guesstimates, but we can probably safely conclude that the trip is 50% more expensive by car.

* Note that the much more pessimistic Stern Report used a value about $10 times as high, which again won’t matter much to the overall decision.

Technorati Tags: aaa,via,drive,fly,los angeles,san francisco,cheaper

Putting the Lie to Root Causes: Baltimore Blizzard Edition

For a couple of generations now people have been pushing the idea that the "root causes" of crime are social problems like poverty, income inequality, discrimination, and so on.

I'm of the opinion that this is all nonsense and always has been, but it's a difficult proposition to refute - we just don't get natural experiments that allow one to test this very often.

Katrina gave us one a few years ago: murder rates dropped by 100% for a period of 3 months after Katrina (yes, you read that percentage correctly).

The Baltimore example is that over the period of the recent blizzards – when most potential victims were stationary, and not accessible to the police, the crime rate dropped.

For example, murders – of which there were 18 in the first 37 days of the year – dropped to 0 in 9 days.

Statistically, that’s close to impossible – akin to flipping 9 heads in a row (try it: you’ll get bored before you do it). That is, unless there is some interfering factor.

In this case, it was that potential murderers were not intersecting with potential victims over those 9 days.

This sort of natural experiment should make it fairly clear that crime is about interactions between criminals and other people, rather than root causes that might leave those criminals with … low self-esteem.

It also should make it clear that policing isn’t that much of crime preventive. I hate to point it out, and the police did too. They’d probably be the first to point out that they couldn’t patrol during the blizzards like they do on most days. Perhaps policing is better viewed as reactionary.

Technorati Tags: crime,baltimore,blizzard,root,causes