Thursday, April 30, 2009

Eyeball Economics

Those of us who wear contact lenses always find ourselves doing a fun math problem that requires multiplying by two. For you who have perfect vision and you who choose spectacles, this is an exercise in commonplace approximation and ordinary economics. For my fellow contact wearers, consider this math problem to be our secret handshake!

Suppose you have two eyes and you need one contact in each eye to see properly. Contacts cost money -- $25 per box. Contacts also wear out every couple of weeks (or in my case four months). There are six contacts in each box. With a different prescription in each eye, a person needs two boxes to function as a normal human being.

As with most semi-durable, somewhat costly goods, several questions come to mind:
  1. How long does a box last?
  2. How many boxes do I use in a year?
  3. How much do contacts cost per year?
To figure this out, we can use some staightforward eyeball math. Each contact lasts two weeks. With a different prescription (and separate box) for each eye, each box lasts 12 weeks. That's 52/12 or 4.33 boxes per year... per eye.

Unfortunately, they don't sell boxes in 0.33 units. They're sold in whole numbers. To cover our yearly eye demands, we need five whole boxes. Per eye, that's $125 annually. For both eyes, that's $250 per year. Yowza! Wearing glasses looks really smart now.

But, that's the calculation if you change your contacts every two weeks. If you stretch the limits of your contact lenses as I do, you can get away with cheaper eyewear. For example, I only switch lenses every four months. Annually, that's three contacts per eye, six contacts per head, and I only have one head. Because I have the same prescription in each eye, I can get away with one box per year. So, my contacts cost $25 per year. What a bargain!

I need to insert a disclaimer. Stretching the capabilities of my contact lenses is not following doctor's orders. I am no doctor of optometry, but I am still sure it is bad medical advice to tell people to wear their contacts longer than prescribed. Don't take the fact that this is a bargain as an endorsement of wholesale neglect of doctor's advice. They probably know what they are talking about, and I bet I have worse eyes for the strain. If I abuse my eyes too much, there is a chance that I will die blind.

That doesn't change the fact that rational people make the calculation to not follow doctor's orders. Given my own incentives, I suspect other contact-wearing individuals make the same calculation and a similar decision. This year alone, I saved $225 over the alternative. That's no small potatoes. If I place a low likelihood on dying blind (or less severely, having eye problems when old), saving $225 every year until I start having those problems may be the right calculation.

That's what our incentives tell us, but our incentives are not aligned with the doctor's advice. This leads me to have a couple of questions for the readers:
  1. Given our incentive to not follow their advice, do you think eye doctors give stronger (or weaker) advice regarding the care of our eyes?
  2. Aside from threatening blindness, can you think of any strategies eye doctors can use to make us account for the costs of not following their advice?
  3. Vision insurance may make these costs a moot point for incentives, but only for a select group of people. How many people have vision insurance anyway? And, why might they sign up?

Eye doctors face a difficult problem in communicating the right information with the right incentives to ordinary people. I wonder if some other system would make everyone better off.

Wednesday, April 29, 2009

Downlifting and Pandora

In the 2000s, music piracy (now called downlifting) was the number one issue facing the music industry. It was so pervasive that ordinary people became criminals en masse. We all knew that downlifting was stealing, but many of us felt that the music industry was already stealing from us at the rate of $20 per CD (that's compact disc, not certificate of deposit).

From an economic perspective, we should have seen this coming. Two factors made a showdown between music executives and Internet pirates inevitable:
  1. Existing forms of music were basically files stored on awkwardly shaped discs. As memory cards became smaller and bandwidth became faster, it made less sense for people to carry around CDs. Companies came out with iPods and other portable music players (the Walkman, anyone?) -- understandably, consumers ate these up. This was precisely where the market was going.
  2. These new forms of digital storage were much less secure from theft. In electronic file format, music became easy to copy and easy to distribute. Quite literally, the only remaining obstacle to owning our favorite song was our sense of morality. Those with fewer scruples from downlifting had more songs in their collections.

These new innovations made music non-excludable from those who don't pay. The word non-excludable sounds like a good thing, but it is terrible for the good's sellers, and therefore, for the good's buyers. Why's that? If nothing was done about the emerging non-excludability of music, no one would ever want to pay for music. If no one wants to pay for music, why would anyone make music?

Internet radio gives an interesting model for dealing with non-paying customers in the music industry. Internet radio's solution? Don't charge a listener when you can charge an advertiser. Radio and television stations figured this out long ago. In these industries, the secret to success is to expand your audience and charge advertisers for air time.

Loads of Internet radio stations are out there, but my favorite is Pandora. Pandora began in 2000 with the "Music Genome Project," an attempt to systematically match aspects of songs and genres of music to one another. This mapping of the terrain of similar songs allows Pandora to be a general use music station that adpats to what the listener likes to hear.

Your Pandora experience starts with telling Pandora what artist or song you would like to hear. With this information, Pandora plays a range of songs with similar tonality, rhythm, and musicality. I am not familiar with all of the aspects of songs, but Pandora definitely has it down. 99.9 percent of the time, I am very happy with the songs that Pandora plays. For the other 0.1 percent of songs, just click "I don't like it" and Pandora won't play that song ever again.

Two words of caution:

  1. Pandora is not an outlet to play specific songs you want to hear. Pandora will start a radio station that plays that song and more, but you cannot rig Pandora to just keep repeating the same song.
  2. Pandora relies on your feedback to improve the mix of music it feeds to your personalized station. If you don't provide feedback, Pandora will eventually stop playing music. The price you pay for personalized music is just sporadic, periodic feedback. And, the result is a better listening experience.

On the other hand, I would never learn the names of the music artists if it were not for Pandora. Also, Pandora has exposed me to new music that I really enjoy: I have become a fan of Jim Brickman because of Pandora, and that would not have happened otherwise. So, I say give Pandora a try. At the very least, it will be music to your ears!

Tuesday, April 28, 2009

Do you have a Macy*s card? Part Two

A couple of days ago, I discussed the reason given by department stores to actively sell their own store credit cards: people who use store credit cards spend more on average than people who do not. I outlined in part one why I think this comparison is like comparing apples to tomatoes. In a nutshell, here's the argument of my previous post:
  1. We observe that department stores expend loads of effort to sell credit cards.
  2. We hear department stores say something like "people who use our card spend more money than people who don't. Therefore, our card must cause more sales."
  3. We have fun pointing out that more sales could be explained by lower prices or by adverse selection.
  4. Implicitly, we brand all department stores who sell their own credit card as incompetent and unable to analyze data.
Steps one through three seem reasonable to me, but the spirit of step four bothers me. I usually think that companies know more about their business than I do. In that vein, step four seems to be missing something. Therefore, I left you, the reader, with a question, "Could there be some other profit motive for issuing store credit cards?"

Some of you brought up the point that having a Macy*s logo in your wallet might actually serve as advertising. To the extent that advertising in someone's wallet is effective, this may lead to more sales. This suggestion is worth some consideration. My understanding of the evidence on advertising is that well-placed ads seem to have very real effects on a company's bottom line.

If we accept that department store credit cards are merely in-wallet advertising, this begs the question: why do department stores spend so many resources (special managers, extra pay for selling credit cards, etc.) on in-wallet advertising when it seems more cost effective to reach many people at the same time by sponsoring a performance on Dancing with the Stars?

One explanation is that in-wallet advertising is effective (though I have not seen compelling evidence). Another explanation is that the store has no idea what it is doing. Yet, another explanation is that the department store is scamming its customers, and collecting huge interest payments on the store credit card purchases. This last explanation really makes me sad. That's not because I don't believe it is part of the reason, but because it is a dangerous world if the scamming motivation is the truth.

That said, if we doubt that in-wallet advertising is effective, if we think that companies are smart, and if we want an explanation that does not make department stores appear sinister, we're still searching for an explanation.

Here's what I had in mind: the department store uses credit cards to divide its customers into two groups.
  1. Group 1 is credit card prone. These people are responsive to the lure of coupon offers and special discounts that come with the store credit card. Members of this group not only buy more merchandise at discounted prices, but they buy so much more merchandise that their expenditures go up. This is what economists call elastic demand.
  2. Group 2 is not credit card prone. These people refused to hold a credit card even though the card comes with special discounts. This fact tells the department store that Group 2 consumers will pay a premium to avoid using the store card.

After distinguishing the two groups of consumers: charge Group 2 more, and give Group 1 discounts. The special discounts to Group 1 lead to more volume, which means more revenue because Group 1 people respond to sales by buying a lot. At the same time, the higher prices for Group 2 lead to greater profit margins for those items. If department stores can successfully navigate this dual-price strategy, peddling credit cards can increase profit.

This strategy of market segmentation to offer better prices to a subset of consumers is known as price discrimination and we see it all the time. For example, students and seniors get discounts at the movies and locals get discounts at Chicago museums. According to price discrimination theory, these groups get discounts because they're the groups who are most responsive to price changes.

Is price discrimination a reason why department stores sell credit cards? Maybe. When it comes down to it, I think department stores sell their own cards for many reasons. For all I know, their motivation could be equal parts advertising, scam, and market segmentation. But, who knows? Maybe they really don't know what they're doing after all!

Monday, April 27, 2009

A Hair-Brained Proposal

I dread going to a hair salon to cut my hair. Mainly, this is because my haircut is so simple: high and tight, no fuss. Yet, the stylist always seems to mess it up, either leaving too much hair on my head or trying to get fancy.

Aside from my usual substandard trimming, most of the time the stylist has a line (I've waited over an hour before), which I do not appreciate. If I am waiting in line for food or entertainment, I can justify it. But, a bad haircut? No thanks. On top of that, I have to pay $10 to $15 per trip to the cutters. My hair grows at an astonishing rate, so I need to cut my hair every four to six weeks. That's six to twelve times per year, $10 to $15 per trip, for the rest of my hair's life.

So, a couple of years ago, my wife and I converted the cutting of my hair into what Gary Becker calls household production: we do it ourselves using inputs you can find at any Walmart. My haircut is simple, so this works well for us.

Here's what we did and do:
  1. We bought a full-fledged clipper set from Walmart. It only cost $20, and it came with barber-style clippers, guards for different lengths, lubricating oil for the blades, and even a cape. How fun! After two months, it paid for itself and my friends and colleagues were none the wiser.
  2. Every four to six weeks, we set up in the bathroom with one of the dining room chairs. I put the cape on (until it ripped, now we use a towel), and my wife trims my hair. Simple as that!

If you want a haircut like mine (be careful, my hair is short), just apply a one-guard to the back and sides and a three-guard to the top, blending it together with a two-guard. You don't need to go to cosmetology school to know that!

Most people like fancier stylings than I do. If this is you, there's a household production solution for your styling needs as well. Here's a video that outlines how to cut a man's hair if the stylings are a bit longer than I prefer. Even if you love your hairstylist, the video is worth a watch. It is surprisingly professional and comprehensive.

So, there you have it. Now you guys out there can save money, look great, and avoid lines. With all that extra time and money, you should take your significant other out on a date!

Sunday, April 26, 2009

Do you have a Macy*s card?

If you ever shop at Macy*s, you have heard the all-too-familiar question, "Do you have a Macy*s card?" A similar question awaits you at Herberger's (Carson-Pirie-Scott), Dilliards, and JC Penney. Virtually all department stores market their own credit cards.

But, why does the sales associate ask this question? Quite simply, most department stores pay sales associates for each account they initiate. At first, this seems strange: most people go to a department store for clothing, not high-interest credit. Strangeness aside, the fact that department stores pay employees to sell credit cards suggests it is profitable to do so... provided that department stores know what they are doing.

From my inside source on department stores, I learned that a primary reason department stores sell store credit cards is that "Customers who have store credit cards buy more than customers who do not." This motivation to sell store credit cards saddens me because it is such bad logic.

This is horrible logic because correlation does not imply causation. The department store wants to know whether selling a credit card to a customer causes that customer to buy more. Knowing that cardholders spend more than non-cardholders tells nothing about causation for two obvious reasons:
  1. Customers who agree to holding a store credit card are different than customers who refuse to sign up. Those who obtain cards know they'll be more likely than average to use the card. They're the big spenders, and big spenders stand to benefit more from the credit card offer. For you econ nerds, this effect is adverse selection.
  2. The second effect is even more obvious. Having a store card entitles the customer to lower prices, extra discounts, and special store coupons. As introductory economics students know, people consume more when the price is low. If people are especially responsive to prices, the effect of buying more outweighs the discounted price in the revenue calculation. Expenditures go up, but only because of the special discounts: it had nothing to do with the card.

Given these reasons to expect customers with cards to spend more, it seems unlikely to me that people spend more money because their card has a Macy*s logo on it. But, don't tell that to managers at department stores. The number of "loyalty accounts" (as they are called) is an important metric for employee performance. At performance reviews, credit card peddling is almost as important as actual sales of clothing! These stores even have special managers whose sole purpose is to get associates to initiate more "loyalty accounts."

If the cards do not actually cause more customer spending, all of these efforts are a pure waste of time, energy, and company resources. Without spending so much time on credit cards, sales associates could focus on selling merchandise and providing good customer service. Such efforts would have a more direct (and perhaps, more effective) link to the company's bottom line.

This explanation really troubles me because the practice of selling store credit cards is a pervasive practice in the retail clothing industry. If selling credit cards is just pure waste of profits, wouldn't we expect someone to figure that out and make millions? To the readers, do you see other profit-seeking reasons to peddle credit cards? I have some ideas, which I will share in Tuesday's post, but I want to see what the readers think before I reveal my hand.

Saturday, April 25, 2009

Great Rates: For a Reason?

The other day, I saw an advertisement for "Great CD Rates." Immediately, I was skeptical. Great CD Rates in this economy? Our bank is offering 1.50 percent APY, and I certainly don't think that is "great." Could there really be much difference between my bank and the one down the street?

Fighting my skepticism, I followed the link to investigate what was so great. I was led to a page that advertised the highest CD rates in all the land. For a two-year CD, there were seven banks who were offering 2.75 percent APY or more. I could not believe my eyes!

If you're not good with percentages, this is a huge difference. Over a two-year span, starting an account with $10,000, the difference between 1.50 and 2.75 is around 250 dollars. Is it really possible that one bank thinks my money is worth $250 more than another bank? The $250 premium these banks were offering was almost the entire interest payment ($300) offered by my bank.

My search through those pages on CD rates reminded me of a famous joke about economists:

An economist and his wife are walking down the street. His wife stops him and points at a $20 bill laying on the ground. "Do you see that $20 bill?" she says. The economist laughs and says "That can't be there! If it were, someone would have already picked it up."
This joke captures the typical economist's firm belief that there won't be free money laying around in an economy. Economists call this the no arbitrage condition. The joke sounds absurd, but when you study something like an economy (where nothing is as it seems), sometimes an analyst cannot trust his eyes.

When I was staring at the screen with these interest rates, I felt like I was staring at 12.5 twenty dollar bills. It was very much like a Geiko commerical! I was tempted to transfer my whole bank account balance to one of these banks. But, I could not believe it. I had to be convinced that these banks were legitimate.

First, I checked to see if they were FDIC insured. All but one (State Bank of India) were FDIC insured. Does that settle it? For the remaining six banks, I still couldn't believe it. There had to be a good reason why these banks were offering such high rates. And, silly economist me -- I had to investigate further.

Two of the remaining six banks had been in the news: GMAC Bank and Discover Bank. They had been bailed out! GMAC has received $6 billion, whereas Discover has received $1.2 billion. Is this a sign of good management? You may say that the government gets some say in their operations now. I repeat. Is this a sign of good management? I crossed these two off the list.

One of the remaining four banks is called Intervest National Bank. I looked it up. Judge for yourself, but I would not put my money there. Maybe they're saving on costs, but their signal is no good.

The remaining three banks are all online banks that are subsidiaries of some other, more recognizable bank.

First, there is UFBDirect.com, which is a subsidiary of Waterfield Bank. I had never heard of Waterfield Bank, so I searched further. I found that they recently changed their name from American Partners Bank to shed themselves of the reputation that came with an "unusual history."

Next, there's UmbrellaBank.com, which is affiliated with New South Federal Savings Bank, the sixth largest bank in Alabama. A Google search for "What's wrong with 'New South Federal Savings Bank'" did not uncover any skeletons.

Lastly, there's NewDominionDirect.com. I could not trace their bricks-and-mortar affiliation, nor could I establish that there were any skeletons in their closet.

When you find a basket of seven apples where the first five have worms, you have to wonder about what's wrong with the other two. The fact that the best looking apples after my investigation are named UmbrellaBank.com and NewDominionDirect.com also does not reassure me.

Maybe there is a reason for these "Great Rates" after all.

Friday, April 24, 2009

Teachers, Why Write a Hard Exam?

Two years from now at my ten-year high school reunion, I'll be explaining to my former high school classmates that I am still in school. At the college level, I have taken over 200 semester credits. I have also had a chance to teach my own classes. My lifetime dedication to school and my focus on economic principles give me unique ideas on education.

Personally, I find these ideas useful both as a student and as a teacher. That's why I am posting about this. From my perspective, the process of teaching and learning is an economic problem. By this, I mean that teaching and learning are both guided by scarcity and optimization.

In my experience, this has been true whether I was receiving exceptionally poor instruction or exceptionally good instruction. I will save my thoughts on what makes good teaching good for another post. This post examines the question of when giving a difficult exam is good idea.

This is a normative (value-based) question, so depending on what you think is a good outcome from teaching, you may disagree with me. This also means that for a cohesive argument, I need to define what I mean by "good" versus "bad." In my view, a good teacher's objective is for students to learn as much as possible about the subject. I think this is a reasonable objective for a teacher (or an education system in general), so this is my criterion. Therefore, if a practice leads to more learning, I call it a good idea. If not, I call it a bad idea.

So, what of giving exams? Why do we give exams if our objective is to maximize student learning? After all, time spent administering an exam is time that cannot be spent learning new material. So, what's the point?

Is giving exams a bad idea? I don't think so. I think the point of giving an exam is that we really, really, really want our students to understand the material covered in class. If the subject is worth teaching, the median student probably did not sufficiently understand what was taught on the first go-around. Periodically, we need a status check. But, in an economic sense, it is more than that!

If the median student does not meet expectations prior to exam time, that does not imply bad teaching. In fact, most subjects worth teaching usually lead the median student into confusion before he eventually gets it. I think this happens because points of misunderstanding are annoying to clear up. Most people dread having to study something that they failed at understanding in the first place. This leads us to neglect important concepts and miss the big picture. As time goes on, the median student accumulates misunderstanding, and this leads to general confusion.

This is where exams come in. Viewed from an economic perspective, students in the previous paragraph do not face a high enough price for small points of misunderstanding. Most people need a credible threat that if they do not understand something important, they will be punished for that lack of comprehension. What's more threatening than a challenging exam? And, what more credible than doing it over and over again (year after year, final after midterm)?

This gives us a reason to challenge our students. Students who are held to the fire tend to learn more than otherwise. This is one reason why employers place a premium on hard degree programs. All else equal, we expect more value added.

That's all well and good, but can an exam be hard in the wrong way? I think so. Moreover, I think that well-intentioned instructors often write pointlessly hard exams.

To be sure, students need to be pushed hard to understand tough material, but exams should give students an incentive to review all that was covered to that point in class. To that end, it is counterproductive to write an exam that is intentionally vague or takes students to "new and interesting places." This is because such exams cannot be studied for, so students rationally do not study as much as they should. As a result, less learning takes place.

Being intentionally vague on an exam makes the exam difficult, but in the wrong way. Such exams are also painful for everyone involved: students feel dumb, and the grader has to make some tough choices. To me, it sounds like this practice uses more resources to get less learning. That's clearly a bad idea.

Tough exams have their place and I generally think they are a good idea. But, teachers should be careful about how they ask tough questions. Tough for its own sake is usually a bad idea, but tough for the sake of learning leads to better outcomes. How do I decide on whether to include a difficult question on an exam? I ask whether showing the question to next year's students will get them to study harder. If yes, that's a hard question that I can agree to asking.

Thursday, April 23, 2009

Poll: Where is the better place for a carriage ride?

Having moved to Chicago from Montana, a place where horses are numerous, I initially found it strange that carriage rides are offered in downtown Chicago. Now that we have lived in Chicago for seven months, the sight of horses next to taxicabs and skyscrapers has grown on me. But, it makes me wonder where I would rather have a carriage ride.

On one hand, there's the novelty of a carriage ride in the crisp, open air of Big Sky Country. On the other hand, a carriage ride in downtown Chicago could be just as breathtaking (especially at night with the skyline in the background).

What do you think? I have started a poll in the sidebar. Vote early. Vote often. Polls close at 2:30 pm CST on Friday, April 30th (that's 1:30 for you folks in Montana).

Google: a study in economics

Google became popular by helping us find what we want on the Internet. Google search results are always helpful. Gmail is easy to use. Google sites and blogs are convenient to set up and share. I am merely a casual user, yet I feel lucky that Google has come into existence. The rich set of Google tools available are clearly the product of a bunch of smart people working really hard.

On its face, this is mysterious. The rise of Google to produce so many nice things for Internet users is a boon to the common person. Every day, Google employees are working hard to create tools they think I would like. They are very good at doing this: I love using anything Google. But, I know no Google employees and I doubt that Google cares about me as a person, so this begs the question: Why would smart people work so hard to make me happy?

In the Wealth of Nations, Adam Smith had something to say about this:

Every individual...generally, indeed, neither intends to promote the public interest, nor knows how much he is promoting it....by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention.
So, there we have it. Google is guided by an invisible hand. Google wants me to be happy because making me happy makes Google money. That's a good reason to make me happy, but I have never written Google a check -- nor has anyone I know. Wherein lies the cash cow?

I was recently exposed to one of Google's money-making enterprises when I looked into placing ads on this blog. I had been exposed to Google ads before, but I never really appreciated what Google was doing because I was busy enjoying Google's other services.

Like everything else that Google does, Google is incredibly good at placing targeted ads in unobtrusive places. If you do a Google search for "Houseplant," eight advertisements regarding where you can buy houseplants appear next to your search results. There's even a sponsored link to a professional agency that provides advice regarding how to care for houseplants.

What's smart about this? By conducting the search, you told Google that you want to know something about houseplants. Google provided you with good information (see search results), but Google also provided those who profit from selling houseplants access to your eyes. That's a service worth paying for, and companies do pay Google for it. There's Google's cash cow.

Back to my ads on this blog. I never told Google what ads to place, but the ads are mysteriously on point. I blogged about our houseplant, "Bob." Google placed houseplant ads. I blogged about unions and academic research. Google linked my readers to something called "Labor Unions Research." Someone at Google wrote a very innovative computer program.

Now, that's targeted advertising and its success is a testament to Google's vision. For now, just enjoy the many services Google provides and give thanks to "the invisible hand" for bringing Google to the market.

Wednesday, April 22, 2009

Why Take Causation Seriously?

Introductory statistics students are taught that "correlation does not imply causation." If you are unfamiliar with this mantra. Here's an example:
A researcher analyzes data on the relationship between test scores (SAT, ACT, etc.) and performance in college. He finds that higher scores on the SAT predicted higher GPA in college. Does this mean that the fact that a student scored well on the SAT causes better grades in college?
Obviously, no! In this example, there's likely a third factor (say, intelligence) that is positively related with SAT and GPA, which drives our observed correlation. That's the "correlation does not imply causation" mantra. If we see a relationship between two events in the world (say Y=a+bX), there are three classes of explanations.
  1. X causes Y: "Lipitor lowers cholesterol"
  2. Y causes X: "bad health causes more doctor visits"
  3. Z causes X and Z causes Y: "smarter hard-working people score better on the SAT and have higher college GPA"

Notice that in this view of the world, correlation does not imply causation, but there is some true model of causation out there! Our statistical model just does not inform which model of causation is right.

Having lived among statisticians while earning a master's degree in statistics, I encountered a strange philosophy regarding the treatment of the causal question. I am not sure how pervasive it is among all statisticians, but this philosophy is predominant among the statisticians I know. Basically, it is a two-step approach.

  1. First, divide the types of studies into experimental and observational. The statistician does this because in an experiment, the researcher can control (2) and (3), so we can conclude (1) X causes Y. In an observational study, the researcher cannot do so.
  2. Second, observational studies are still interesting, so study them. But, be very careful with interpreting estimates. We cannot rule out (2) or (3), so do not under any circumstances rule these options out in an interpretation.

The conclusions offered in the second step are valid, but when it comes to practicing applied statistics (for example, estimating factors correlated with costs of wildfires or estimating factors correlated with the likelihood of Indian casino investment), we want to know more than just correlation. We want to draw lessons from our analysis. If not, what's the point?

The two-step strategy leads to a statement like "an additional house within one mile of a fire perimeter is correlated with $13,000 in additional fire suppression cost." But, if we take the second step of the statistician's solution seriously, we cannot offer any policy implications without reasonably ruling out (2) or (3).

Can we safely conclude that "more money devoted to fire suppression leads to more houses near a fire perimeter" is an unreasonable interpretation? Can we safely conclude that "fire suppression cost and number of houses are correlated with an omitted explanation" is an unreasonable explanation?

If the answer is no to either of these questions, any discussion after the standard interpretation is nonsense. But, applied statistics in many observational studies is all about creating estimates that warrant interesting policy discussion. If it is not safe to conclude that X causes Y, my view is that there are two appropriate responses:

  • Drop the research question. Your audience always wants to know what's causing what. If you report a correlation without ruling out alternative interpretations, people will either (a) not care because you did not answer their question, or (b) misinterpret you and think that you told them X causes Y when you could not offer that strong of a conclusion.
  • Investigate Causation. Every observational study should investigate the extent to which important omitted factors can be driving observed correlations. This statement applies to everyone who even thinks about applied research.

The set of tools available to investigate causation is available (Google IV or 2SLS if you're technically inclined), but it requires careful thought. Basically, investigating causation boils down to different ways to reasonably rule out explanations for an observed correlation aside from "X causes Y." But, isn't that what your audience wants anyway?

Tuesday, April 21, 2009

Discounting and the Scientific Consensus

Climate change is real. The consequences are going to be costly. Clearly, something must be done. That's usually where the cost benefit analysis stops in the public debate over climate change. The implicit suggestion is that it is worth a substantial chunk of our creative energies and a large fraction of our national wealth to solve the problem of climate change.

For the science of climate change, Nobel Peace Prizes have been awarded. For the votes of climate change, campaign promises have been made. Heck, even actors on the television show, 24, have a series of public service announcements that vaguely warn of the dangers of climate change. All of this is taking place based on a scientific consensus that climate change is real, and that 50 to 100 years from now, there will be costly consequences.

In the face of this overwhelming consensus, it is useful to ask how costly climate change will be. There are studies pushing in this direction, but given that the most substantial costs of climate change are projected to occur 50 years or so from now, even the most precisely estimated costs deserve our scrutiny. Important questions do not go away (even with perfect foresight and no uncertainty). In particular, this post addresses the question:

How much is it worth to avert a billion dollar catastrophe that we know will happen 50 years from now?
No one has a perfect answer about how to weight these future costs against current demands on our resources, but there are clearly some wrong approaches. In particular, we should not treat a billion dollars in the year 2059 the same as a billion dollars in 2009. Nevertheless, I fear that our scientific consensus exaggerates the costs of climate change by making this mistake.

To see why a billion dollars is not worth a billion dollars whenever it is owed, think of putting some amount of money in a 50-year certificate of deposit that will pay a billion dollars at maturity. It is clear you would not have to set aside one billion dollars today. In fact, a bank would be happy to give you a three percent interest rate if they knew they had access to your money for 50 years. They would do this because they know there are better uses for your money (i.e., investments with a better return than three percent).

To see what effect this has on cost estimates, it helps to take a concrete example where we have perfect foresight and no uncertainty about future costs. Suppose we also know the following facts with certainty:
  • In 2059, there will certainly be an environmental catastrophe that costs one billion dollars (in today's dollars) to clean up after the fact.
  • A savings account gets three percent real return per year for every year between now and 2059.
If we set aside $228 million dollars today [$1 billion / (1.03^50)] , the account will mature in 2059 with one billion dollars -- enough to cover the expense of the catastrophe. This means that $228 million is the real cost of a billion dollar expense 50 years into the future.

$228 million may sound like a lot of money, but it is nearly five times less than the original number. Merely neglecting the fact that our current resources have alternative uses, therefore, leads to an overstatement of costs by a factor of five. What can we cost forecasts for the year 2100? In that case, a billion dollars is only worth $67 million [$1 billion / (1.03^91)]. Forgetting to discount in this setting overstates the costs by a factor of nearly 15!

To be fair, economists have yet to agree on the exact interest rate for these calculations. Some economists advocate using the historical return to capital investment (~8 percent) as the discount rate. Others are less conservative, using rates closer to two or three percent.

One thing is for sure -- zero percent is the wrong rate to use. Using no interest rate can vastly overstate future costs (even in a world where the right interest rate is small). If we look far enough into the future, our scientific consensus could be off by a factor of 10, and with the numbers they're throwing around, that's no small change.

Monday, April 20, 2009

Growing a House Plant -- A Metaphor

Around early November, my wife and I made a long-term commitment: we bought a house plant, which we named "Bob." The timing of our purchase had nothing to do with the fact that a historic election took place around the same time. But, the house plant under our guidance, just like our economy under the guidance of a new administration, has had a turbulent couple of months.

Here is a picture of young Bob when we first brought him home.

Bob was young and fragile. Indeed, it would have been easy to kill our new house plant with bad management. What's more, we had no real experience taking care of a plant. Neither one of us had any clue about how frequently to water, where in the room to place Bob, or even whether Bob needed to be placed in a larger pot. We did our own research, tried an assortment of strategies, and we consulted our advisers (family). Some of our advisers thought we needed to transplant Bob into a new pot, or he wouldn't survive the month.

We searched for a pot at our favorite stores (Walmart, Costco, Jewel-Osco, etc.), but we were unable to find anything suitable. In the meantime, we watered Bob sporadically (whenever he looked droopy), but we did little to care for our house plant.

Two months came and went under our naive management. Bob survived our first month, but he began looking sickly. Moreover, we were not sure how to cure an ailing house plant. We tried watering more frequently and placing Bob nearer to the sunshine. These strategies were merely transitory. What Bob needed was a long term fix. He needed a larger pot.

Then, we made a big mistake. In all of our planning for a week-long trip to Montana to visit family, we forgot to watch out for Bob. We left Bob alone for an entire week without anyone to water him. What's even worse? We had not watered Bob for a few days leading up to our trip. When we realized what we had done, we thought that would be the end of Bob. In retrospect, we are ashamed we treated Bob so poorly, but we do have other priorities!

When we arrived home from our trip, Bob looked like this:


We were horrified that Bob was in such bad shape because of our negligence. From that point onward, we pledged to be better stewards of our plant. The next day, we finally looked hard enough to find a suitable pot. We also bought some good potting soil and some Miracle-Gro fertilizer. Bob was going to need all the help he could get.

Cautiously and vigilantly, we nurtured Bob back to health. Now, our plant has a bunch of new growth. He's perky and healthy. To be sure, Bob is a vibrant addition to our apartment!

Here's how Bob looks now:

Through our ordeal, we learned some powerful lessons about growing a house plant:

  1. House plants need a proper foundation. This includes good soil and a pot that is large enough for the roots to take hold.

  2. House plants need the right amount of water. Too little water can cause the plant to wilt. Too much water can also cause wilting. We found that watering Bob once every couple of days is the right amount of care.

  3. House plants need to be given the right amount of space. When we left for a week, that was too much space. But, when we were initially hovering over our new plant, we just about smothered the life out of Bob.

As I said at the beginning of this post, Bob has had a turbulent first few months in our house. Now, his outlook is good and we are seeing signs that Bob will be a beautiful part of our apartment for some time to come. Here's hoping that our economy experiences a similar change of course.

Sunday, April 19, 2009

Unions and Universities -- A New Deal?

Just this week, the faculty at my alma mater (Montana State University) voted to unionize. The measure passed by a small margin (only 52 percent in favor). Not surprisingly, only 39 percent of tenured faculty voted to unionize, whereas 66 percent of adjunct and non-tenured faculty voted in favor of unionization. I wonder who expects to gain from this measure...

Unionizing the faculty at a state school raises a bunch of questions. In fact, a short article by the Chronicle of Higher Education had numerous interesting user comments. My favorite is #8:


What exactly are they getting for their union dues besides another hierarchy to deal with? Is there any power in a strike with a state school?

I like this comment because I'm skeptical that professors at MSU (even adjuncts and non-tenured faculty) have much to gain from unionizing. As a former adjunct professor at MSU, I can see little marginal benefit from unionizing. When I worked at MSU, I could not complain about the pay for two reasons: (1) I loved the work, and (2) the pay was actually pretty good. Honestly, having a university job in a town like Bozeman is living the good life. Pushing for better treatment seems horribly out of place at Montana State.

However you feel about unions, you can still wonder what they do to the broader economy. As a first-year doctoral student in economics, I tend to think that unions sap productivity by compressing wages: less productive workers get more money under unions, while the best people get to finance that with union dues. Wherein lies the incentive to be a good worker?

Taking that logic a couple of steps further: mo' unions, no mo' productivity, less stuff being produced, less income for everyone (on average). That's what the theory tells us anyway. But, what do the data say?

A fairly recent study by Cole and Ohanian (Journal of Political Economy, 2004) looks to the uncharacteristic persistence of the Great Depression as a setting to study the significance of unions (and cartels) on macroeconomic performance. Most reasonable macroeconomic models predict the Great Depression to end by 1936. But, the Depression lasted until the onset of World War II in 1941-2. Cole and Ohanian cite the New Deal's cartel and union-friendly policy as a significant reason why the United States did not see rapid recovery to trend.

As Cole and Ohanian document, the United States only saw recovery to trend by 1941 after the FDR administration reversed course on unionization and cartelization policy. By incorporating the negative productivity effects of unionization and cartelization into their macroeconomic framework, they were able to explain 60 percent of the lack of recovery. That's a heck of an omission by previous research which neglected the role of unions and cartels.

As a kid who grew up in a pro-union mining town, this punchline rocked my world. What's even better? The research is careful, well-documented, and so widely respected that it is taught in first year graduate macroeconomics at University of Chicago. It is encouraging that research can be so relevant to actual policy. But, it is too bad to see past mistakes made again.

Saturday, April 18, 2009

30-20-10 Pricing

Department store pricing has always bothered me.

The other day, I faced a dilemma when assessing whether it was worth buying a green shirt. The shirt was $50 dollars, but 30 percent off for that day's sale, an additional 20 percent off for using a particular credit card, and 10 percent off because the item is green.

I had no trouble figuring out the final price -- I'm pretty good at math. In fact, I often enjoy the challenge of figuring out department store prices. It just bothers me that retail stores try to hide the price from customers. Ultimately, people will find out what the shirt really costs (the money leaves their possession at some point), so why put them through three flaming hoops of grade school math?

Honestly, I don't know of any good reason to torture the mathematically-challenged and that's what bothers me. But, in this post, I want to show why 30 percent off + 20 percent off + 10 percent off does not equal 60 percent off.

Let's take my shirt example. Most grade schools teach that 30 percent off of $50 is like multiplying by 0.7. Similarly, taking an additional 20 percent off is like multiplying the result by 0.8. Take another 10 percent off by multiplying again by 0.9. Most people do this in three steps:

  1. 30% off of $50 = (1-0.3)*50= 0.7*50 ($35)
  2. 20% more off = 0.8*35 ($28)
  3. 10% more off = 0.9*28 ($25.20)
Now, that's a lot of mental exercise if you don't know how to use your cell phone calculator. But, notice one sleezy thing about this pricing. The final price ($25.20) is only 49.6 percent off of the original price ($50). It is not 60 percent off as the store would want you to believe.

Why is this? As we saw above, the right calculation is at each step to multiply by the percentage paid, not add the percentage off. Therefore, no matter what the original price is, the percentage paid equals (0.7*0.8*0.9)*100=50.4 percent. That's 49.6 percent off!

This is not addition like the word "additional" suggests, so there's no reason to believe that adding percentages off will get the right answer. That's how a store can take 75 percent off and then an additional 40 percent off AND still take some of your money.

Surprisingly, the percentage off does not depend on the order in which the discounts are taken. To see this, rewrite the final price of my green shirt as 0.9*[0.8*(0.7*50)]. This is mathematically equivalent to taking 30 percent, then 20 percent, then 10 percent off of that. But, we could have just as well taken 20, then 30, then 10 and we would have gotten the same result because 0.9*0.8*0.7=0.8*0.9*0.7 (multiplication commutes).

So, the next time you are in a department store, remember your grade school math, and you'll easily know what you pay at the register.

Friday, April 17, 2009

The Pilot

Why write a blog?

I study economics. As a result, I often get questions from friends who want my take on a particular issue. Economics is a fascinating field and a useful perspective. To the extent that my ideas are thoughtful and thought-provoking, I want others to read them.

I watch (too much) television. I wonder if there is anyone out there who can relate. I am especially interested in Lost. I will post a thought or theory I have about one of my shows.

I am new to the city. My beautiful wife (Shanna) and I moved to Chicago from Montana last August. It has been an adjustment, so we often have stories to tell.

For whatever other reason, I've been drawn to the blog-o-sphere. This may be my journal to myself, my journal to my friends, or my journal to the world. I hope you enjoy what I have to say.