Faith, an empirical question? Yes and no.

Recently I read two very interesting posts that I want to comment on. The first is by Joe Carter here, and the second is a response to it by JT here. The issue at hand is point #10 of Carter's post. My reading of the point is that Carter thinks if a belief is true, he uses the example of same-sex marriage, then there will be strong and convincing logical and or empirical evidence to support it. Specifically, he wants the Christian Right to support positions in public policy debates with empirical evidence and without resorting to 'because the Bible says so.' Carter writes "Fortunately, God provides us general revelation--conscience, rationality, empirical observation--which is often more effective in expressing his foundational principles in a way that all people can accept and understand."

Disclaimer: I am not sure that I fully understand what JT is driving at in his response and hope he will leave a clarifying comment. It seems to me that JT's biggest concern is that trying to come up with arguments to justify beliefs is an ass backwards approach to life. If you have a belief it is because of evidence. If you are trying to work the other way around you desperately need a philosophy course.

Now here is where I think the tricky part comes in. I hold a great many beliefs about the best way to live my live because of the testimony in the Bible. I believe what the authors' of the Bible say about Jesus is true. I believe it because I have met people in my life who I believe to be reliable witnesses who had credible sources before them. I also believe because the Bible makes many claims about the human condition that I believe are the best explanation of the world I see every day. I hold many beliefs not because of direct empirical evidence about them, but because of indirect evidence about the source that makes them. This I think is God's plan. He lets us see a piece of the puzzle, provides us witlessness and gives signs, but he wants us to take a lot on faith. Faith is what saves us. Faith is what makes us justified. If in the public policy arena someone can convince someone else to agree to vote for a specific policy because of empirical evidence and not faith, what reward do we have. Even worse, if Joe Carter could keep two men from marrying because of threat of violence from the state how has he advanced the Kingdom of God?

I agree with JT whole heartedly that there is some objective truth out there. Jesus was raised from the dead or he wasn't. If he was then we should all heed his words. If in the public policy arena a group such as the Christian Right wants to advocate a particular policy because they believe it to be a good idea--it comes from the teaching of the Gospels-- (environmental stewardship perhaps?) that is fine. I think that the evidence they should cite about of the truth of this belief the exact reasons they believe it, IE a belief in the claims about Jesus as Christ. It is a fools errand to try and develop empirical evidence to justify every position that a Christian could advocate. In summary I will quote Mr. Bastiat, "statistics won't get you into heaven."

linguistic modality and estimating probabilities

It is well documented in the economics literature that individuals often mis-estimate the likelihood of low probability events. The likelihood of a place crashing comes to mind. I wonder how much of this phenomenon has to do with the vocabulary available in the English language. In linguistics, modality deals with how people express thoughts about the likelihood of future events. For instance words like doubtful, probably, hope, impossible are all examples. I think one problem is that these words do not provide a good framework for describing low probability events. If I told you that something is extremely unlikely what does that mean to you in terms of probability? 1 in 10,000? 1 in 100,000?

So here is the experiment I would be interested in seeing. Different languages have different levels of modality to them. That is they have varying ability to express the likeliness or improbability of certain events. I think it would be interesting to see if these linguistic differences impact the ability of individuals to estimate the likelihood of low probability events. The reason that I find this interesting is because the structure of our native language has an important, but subtle, influence in how we approach and think about problems.

So how could someone credibly pull off such a study? I think one way to do it would be to look at the existing literature and see what kind of experiments for estimating probability have been done in the past. I bet some of these could be done through a web application. Then you send out some sort of survey to people across the globe asking them to participate and enter them in a random drawing. Perhaps pay them some flat rate plus a chance to win a bigger prize. One of the first problems that I see is that a referee would argue that what you are really doing is picking up national characteristics more than linguistic characteristics. If you were to use major languages, one could survey English, French, Japanese and German speakers both in their native countries as well as in other parts of the world. For instance English is spoken extensively in the US, England and Australia. French is spoken in Morocco and several other countries in Africa. I am not sure how you get Moroccan French speakers to take a web survey, but in principle it's possible.

A simpler experiment would be to go to major research universities and just seek out international students from these countries already in the US and survey them. These are not the average kind of speakers, but it would be a lot simpler.

Game theory solution concepts and applied economics

I have written a number of posts recently about algorithmic game theory. While there are some very interesting ideas in this area, many of them have little bearing on applied economics. So today I wanted to talk about how the concepts in algorithmic game theory could be applicable.

Making better predictions

One of the things that makes the Nash equilibrium an appealing idea is that, for finite games, there is guaranteed to be at least one. In practice, however, Nash equilibrium are not always very good at predicting the results of economic experiments. One case where they fail rather markedly is in 2X2 games where one player has a single strategy large payoff. In a 2X2 game, Nash equilibrium predicts that the probabilities that a player will assign to a particular payoff are independent of their payoffs. What they should do is make their opponent indifferent between their strategies. In reality, changing one player's own payoffs can have a profound affect on the empirical results.

So what are we to make of this? Goeree and Holt take a stab at this problem by introducing the notion of a logit equilibrium. They have another great paper here about when Nash shines and falls short. That is an equilibrium concept in which players do consider their own payoffs. It is, in a sense, a kind of learning mechanism. I like the idea, but I wonder how it would compare to other learning mechanism type explanations.

I think what algorithmic game theory focuses on is processes by which equilibrium will come about. This is in sharp contrast to modern mathematical economics (Nash included) which relies on fixed point theorems to say that equilibrium do exist, but not how to get there. Many of the algorithmic game theory processes rely on some version of regret minimization. Regret minimization is one of the many alternatives to expected utility theory. Thus, it has some grounding in economic theory. It can be shown that computer agents following certain kinds of learning rules can converge to certain correlated equilibrium. I would be interested to see if these predictions do a better job of predicting than Nash equilibrium predictions. Given the many kinds of regret minimization (internal regret, external regret and swap regret) this could be quite a study.

I think the problem with these kinds of learning techniques is that they aren't a very believable approximation for how people think. They are unabashedly machine learning techniques. Perhaps, if they prove to be better predictors, then they can serve as a first step for understanding the human thought process on making game theoretic decisions.

On the future of e-books

I read the following post on MR the other day. It was an excerpt of an Ezra Klein piece on the kindle. His comment was that e-books have the potential to be a very cool new type of medium and Amazon has the potential to develop it. Looking at history, Klein noted that the first television programs were just radio shows with moving pictures and that e-books now are just glorified pdf files. So I got thinking about what cool things e-books might be able to do someday that would set them apart.

1. I think it would be great to include video content in reference of non-fiction books. Currently we have graphs in math books and the like, but how much better would it be to be able to include a short video about how to solve different kinds of math problems?
2. Including more sound and graphics content in books. Often murder mysteries center around a few key clues or pieces of evidence. I bet an enterprising author could think of someone way to incorporate a distinctive sound or set of images into a novel that would enhance the reading experience
3. Flash objects. What if, in a book like the Da Vinci Code, flash objects with puzzles or other things could be included mid-book. What if they were made especially devious and you couldn't advance to the next page until you had completed the puzzle? This could also be useful in educational books as practice tests.

I think one of the big limitations to e-books at the moment is that the highly innovative screen that Amazon has developed isn't well suited to any of these ideas. The screen is essentially a static object, very similar to paper. Your computer screen on the other hand is updating 60ish times per second. This causes more eye strain than reading on paper or Amazon's new "electronic paper". The downside to this screen is that it takes longer to redraw images than would be feasible for video. But perhaps the next generation Kindle will solve these sorts of problems.

Inflation and speculation

At some point, I would like to take a careful look at how inflation makes it way through the economy. When the Federal Reserve creates new money, there are certain channels that it flows into first. How these first recipients spend this money might have important information for how inflation, new money, works its way through the economy. I realize that rational expectations macroeconomics models can be created that show that if people have a good prior information about what inflation will be that it shouldn't matter much one way or the other, but I don't place a whole lot of faith in these type of models. To be fair though, I am not much of a macro person.


Here is my worry and my theory. I worry that one of the first stops of new money from the Federal Reserve are large investment banks that have accounts with the Federal Reserve Branches. How these investment banks choose to invest could greatly affect the order in which sectors experience inflation (price increases).

This by itself isn't much of a worry. What concerns me more is how this interacts with theories of bubbles and speculation. Lets say there is an unexpectedly large amount of new money injected into economy one month. Well that particular month investment banks are focused in on Real Estate Investment Trusts or perhaps agricultural commodities. This could cause the prices in these particular sectors and commodities to increase faster than other investments. This is not necessarily because of market fundamental, its about inflation showing up in these sectors before it reaches other sectors. But this unexpected increase in prices might attract so called "moment investors" and then we have the making of a bubble.

Agricultural prices have had a huge increase in the last few months. Some of it has been an increase in ethanol demand, oil prices and weak currency but I think there is some amount of speculation and demand for commodities as a hedge against inflation. Could inflation moving through the economy at an uneven pace account for some of it too?


This is more of a worry than a theory. I am curious though, how could one go about testing such a hypothesis? It seems like a tough nut to crack. One could look at the correlation between the rate of inflation in certain months and the change in prices being most heavily invested in by investment banks. Market capitalization of various funds at investment banks might be one approximation of where investment banks are putting most of their money. There is probably no way to learn gain information about hedge funds. Then there is also the problem that inflation could start a bubble, but that wouldn't explain how large it gets before popping. Any thoughts on how to test this hypothesis?

America's founding father's were rogues and scoundrels

I recently read an article by Walter Williams in the Washington Times. America's founding fathers are hardly what the average person would call role models by today's standards. They incited the Boston Tea party, which I am sure would be called a terrorist act today. John Paul Jones, the founding father of the US Navy, was little better than a pirate. He happened to be a successful pirate fighting on our side. There are many colorful stories about our founding fathers one of which is pointed out in Williams article and which I was unaware.

John Hancock was a smuggler. He felt that the taxes on molasses were unreasonable and he smuggled millions of gallons of the stuff to avoid the taxes. Williams compares him to a modern day cigarette runner. The smuggler is the hero of Williams' story.

Asking someone who their heroes are will tell you a lot about them. There aren't a lot of people that I think are compelling enough to warrant the title of hero in my world view. I think that Frank Knight was spot on about a lot of things but he was mostly a teacher in life. I am not sure how I feel about being a teacher as my profession or calling. Part of me deeply admires the entrepreneurs in the high tech field. Many are both business savvy and contribute a great deal of technical innovation to the world. Free market environmentalists are also a very cool group. Thoughts?

A truely thorny problem, Algorithmic Game Theory Part 2

I often hear people talking about auction theory and have met some very mathy people who work in this area. I have wondered at times how much you could really do in this area. There are only so many practical ways to hold an auction right? It seems that for certain kinds of auctions, called combinatorial auctions, the problem of even identifying which bids the auctioneer should choose to maximize their revenue is deeply hard.

For example lets think about the spectrum auctions that the Federal Communication Commissions holds from time to time. In these auctions different sections of the radio spectrum are licensed for use in different parts of the country. In the last auction more than 1000 different licenses were for sale. It is very likely that companies have preferences and valuations not only over individual licenses, but over sets of licenses. For instance, a company looking to expand their operations in the Midwest may place a high value on holding licenses for Chicago, Madison and Minneapolis, but is not interested in expanding into only two or one of them. Perhaps there are fixes costs that must be offset.

While it is possible to have preferences over every conceivable set of bundles most companies probably don't analyze it that in-depth. Just to represent one company having complete preferences over 1000 licenses would require ten raised to the 300th power valuations. While theoretically this is a sticky point, I think reality will be easier to work with.

Skipping ahead, if a number of different firms each submit bids for different sets of licenses how does the auctioneer choose the set of bids that maximizes revenue? This turns out to be equivalent to the well known knapsack problem in computer science. For the economists, this is essentially a binary programming (as opposed to linear programming) problem with the constraint that you can't sell the same license twice. The problem is NP-Hard and in general short of checking every conceivable combination of bids there is no way to know for sure whether you have the global maximum. That is you need to check 2^(#of bids) combinations before you can say anything with certainty. If you think it is conceivable that there would be a 1000 different bids for 1000 licenses then the problem is just as bad as the one we skipped over in the previous paragraph.

Working around these sorts of problems definitely got more interesting to me. There are also the important problem of structuring the auction so that there is no collusion between companies and that companies have an incentive to reveal something close to their true valuation.

I know that Mr. Bastiat will not think much of this post. Its a lot of math and it doesn't really go anywhere. It is much more of a consulting type problem than a market problem. Thus I digress to some more big picture question.

First, should the FCC try to maximize the revenue from the auction? Clearly the FCC has a monopoly on the radio spectrum. As economists should we support them in their attempt to exert market power? Is there another market mechanism that might have equally good welfare properties as these very difficult combinatorial auctions but without making the FCC a ton of money? What if the number of licenses were dramatically cut and the FCC auctioned off pieces of the bandwidth for the entire country instead of by regions? Regional firms could form a coalition to buy a the spectrum and divide it among themselves. It might not put them at too great a disadvantage. Perhaps replicating treasury auctions? This is problematic because it might be that a firm needs a certain bandwidth or none at all. Other thoughts about what the important big picture questions are ?

economics as keeping score

It seems that often economists serve as society's score keepers. What is the cost benefit ratio of this program, what the the affect of this job program, etc. There is a lot of money out there for this kind of work. It is a specialized skill that requires a great deal of mathematical knowledge. Sadly, it has almost nothing to do with how markets work. At least this kind of work cross-subsidizes the more interesting stuff. What fraction of economic work do you think focuses on cost-benefit analysis and program evaluation?

Value capture

This is the second part to an earlier post. As a recap, localities have considered using tax-incremental financing to fund projects. What this means is that after they complete a public works project they expect property values near the project to increase and that they plan to pay for this project by using the increase in property tax revenues that result from the project.

A different but related concept is Value capture. Lets suppose that a state is thinking about expanding a highway or building an on ramp. A set of properties near this project are about to experience an increase in property values (and thus wealth) not through their own action but because of public investment. There are some that feel that this encourages a great deal of pork barrel legislation and road expansions that don't really benefit society as a whole (I am trying to minimize my cynicism here). An idea to combat this tendency is with value capture. Value capture works by picking a reference year before the project has affected property values, this may need to be before it is announced. Then they create a higher marginal tax rate for values on that property above the value in the reference year. In essence the state is trying to capture back some of the wealth that they transferred to land owners near the project.

There are some serious problems with the most simplistic versions of this idea. For instance, if property values rise for the city as a whole (unrelated to the public works project) then land owners near public works projects would be taxed more than would seem 'fair' at first glance. A better system would be to have some sort of regression where the incremental impact of the public works project on property value is calculated and just taxing that value at a higher rate. The value capture districts, like TIF districts, expire at some point. To the extent that it might reduce pork barreling I would think about supporting it. Then again, if a group of individuals is powerful enough to get a multi-million dollar road built near them they can probably find a way to kill a value capture proposal. Its food for thought.