## Archive for the ‘Economics’ Category

### Wiener on robots

May 21, 2013

An essay by Norbert Wiener written in 1949 intended for the New York Times was recently uncovered.  He pretty much had it right 64 years ago. Below is the rather serious last section. Earlier in the piece, we find out that programming was  called “taping” at that time.

New York Times:

The Genie and the Bottle

These new machines have a great capacity for upsetting the present basis of industry, and of reducing the economic value of the routine factory employee to a point at which he is not worth hiring at any price. If we combine our machine-potentials of a factory with the valuation of human beings on which our present factory system is based, we are in for an industrial revolution of unmitigated cruelty.

We must be willing to deal in facts rather than in fashionable ideologies if we wish to get through this period unharmed. Not even the brightest picture of an age in which man is the master, and in which we all have an excess of mechanical services will make up for the pains of transition, if we are not both humane and intelligent.

Finally the machines will do what we ask them to do and not what we ought to ask them to do. In the discussion of the relation between man and powerful agencies controlled by man, the gnomic wisdom of the folk tales has a value far beyond the books of our sociologists.

There is general agreement among the sages of the peoples of the past ages, that if we are granted power commensurate with our will, we are more likely to use it wrongly than to use it rightly, more likely to use it stupidly than to use it intelligently. [W. W. Jacobs’s] terrible story of the “Monkey’s Paw” is a modern example of this — the father wishes for money and gets it as a compensation for the death of his son in a factory accident, then wishes for the return of his son. The son comes back as a ghost, and the father wishes him gone. This is the outcome of his three wishes.

Moreover, if we move in the direction of making machines which learn and whose behavior is modified by experience, we must face the fact that every degree of independence we give the machine is a degree of possible defiance of our wishes. The genie in the bottle will not willingly go back in the bottle, nor have we any reason to expect them to be well disposed to us.

In short, it is only a humanity which is capable of awe, which will also be capable of controlling the new potentials which we are opening for ourselves. We can be humble and live a good life with the aid of the machines, or we can be arrogant and die.

### Discounting the obvious

April 24, 2013

The main events in the history of science have involved new ideas overthrowing conventional wisdom. The notion that the earth was the center of the universe was upended by Copernicus. Species were thought to be permanent and fixed until Darwin. Physics was thought to be completely understood at the end of the nineteenth century and then came relativity theory and quantum mechanics to mess everything up. Godel overthrew the notion that mathematics was infallible. This story has been repeated so many times that people now seem to instinctively look for the counterintuitive answer to every problem. There are countless books on thinking outside of the box.  However, I think that the supplanting of “linear” thinking with “nonlinear” thinking is not always a good idea and sometimes it can have dire consequences.

A salient example is the current idea that fiscal austerity will lead to greater economic growth. GDP is defined as the sum of  consumption, investment, government spending and exports minus imports. If consumption or investment were to decline in an economic contraction, as in the Great Recession, then the simple linear idea would be that GDP and growth can be bolstered by increased government spending. This was the standard government response immediately after the financial crisis of 2008. However, starting in about 2010 when the recovery wasn’t deemed fast enough instead of considering the simple idea that the stimulus wasn’t big enough, the idea that policy makers, especially in Europe, adopted was that government spending was crowding out private spending so that a decrease in government spending would lead to a net increase in GDP and growth. This is very nonlinear thinking because it requires a decrease in GDP to induce an increase in GDP. Thus far this idea is not working and austerity has led to lower GDP growth in all countries that have tried it.  This idea was reinforced by a famous, now infamous, paper by Reinhart and Rogoff, which claimed that when government debt reaches 90% of GDP, growth is severely curtailed. This result has been taken as undisputed truth by governments and the press even though there were many economists who questioned it.  However, it turns out that the paper has major errors (including an Excel coding error). See here for a summary.  This is case where the nonlinear idea (as well as conflating correlation with causation) is probably wrong and has inflicted immense hardship on a large number of people.

### Failure at all scales

March 12, 2013

The premise of most political systems since the enlightenment is that the individual is a rational actor. The classical liberal (now called libertarian) tradition believes that social and economic ills are due to excessive government regulation and intervention. If the individuals are left to participate unfettered in a free market then these problems will disappear.  Conversely, the traditional Marxist/Leninist left posits that the capitalistic system is inherently unfair and can only be cured by replacing it with a centrally planned economy. However, the lesson of the twentieth century is that there is irrationality, incompetence, and corruption at all levels, from individuals to societies. We thus need regulations, laws and a government that take into account of the fact that we are fallible at all scales, including the regulations, laws and the government.

Markets are not perfect and often fail but they are clearly superior to central planning for the distribution of most resources (particularly consumer goods). However, they need to be monitored and regulated. When markets fail, government should intervene. Even the staunchest libertarian would support laws that prevent the elimination of your competitors by violence. Organized crime and drug cartels are an example of how businesses would run in the absence of laws. However, regulations and laws should have built-in sunset clauses that force them to be reviewed after a finite length of time. In some cases, a freer market makes sense. I believe that the government is bad in picking winners so if we want to promote alternative energy, we shouldn’t be helping nascent green industries but rather tax fossil fuel use and let the market decide what is best. Making cars more fuel-efficient may not lead to less energy use but just encourage people to drive more. If we want to save energy, we should make energy more expensive. We should also make regulations as universal and simple as possible to minimize  regulatory capture. I think means testing for social services like medicare is a bad idea because it will just encourage people to find clever ways to circumvent it. The same probably goes for need-based welfare. We should just give everyone a minimum income and let everyone keep any income above it. This would then provide a safety net but not a disincentive to work. Some people will choose to live on this minimum income but as I argued here, I think they should be allowed to. If we want to address wealth inequality then we should probably tax wealth directly rather than income. We want to encourage people to make as much money as possible but then spend it to keep the wealth circulating. By the same reasoning, I don’t like a consumption tax. Our economy is based on consumer spending so we don’t want to discourage that (unless it is for other reasons than economic).

People do not suddenly become selfless and rational when the political system changes but systems can mitigate the effects of their irrational and selfish tendencies. As the work of Kahneman, Tversky, Ariely, and others have shown, rational and scientific thinking does not come naturally to people. Having the market decide what is the most effective medical treatment is not a good idea. A perfect example is in a recent Econtalk podcast with libertarian leaning economist John Cochrane on healthcare. Cochrane suggested that instead of seeing a doctor first, he should just be allowed to buy antibiotics for his children whenever they had an earache. The most laughable part was his idea that we have rules against self-administering of drugs to protect uneducated people. Actually, the rules are to protect highly educated people like him who think that expertise in one area transfers to another. The last thing we want is for even more antibiotic use and more antibiotic resistant bacterial strains. I definitely do not want to live in a society where I have to wait for the market to penalize companies that provide unsafe food or build unsafe buildings. It doesn’t help me if my house collapses in an earthquake because the builder used inferior materials. Sure they may go out of business but I’m already dead.

There is no single perfect system or set of rules that one should always follow. We should design laws, regulations, and governments that are adaptable and adjust according to need. The US Constitution has been amended 27 times. The last time was in 1992, which just changed the rules on salaries for elected officials. The 26th amendment in 1971 made 18 the universal threshold age for voting. We are thus due for another amendment and I think the 2nd amendment, which guarantees the right to bear arms, is a place to start. We could make it more explicit what types of arms are protected and what types can be regulated by local laws. If we want to reduce gun violence then gun regulation makes sense. People will do things they later regret. If one is in the heat of an argument and there is a gun available then it could be used inadvertently. It takes a lot of training and skill to use a gun effectively. Accidents will happen. In the case of guns, failure often leads to death. I would prefer to live in a society where guns are scarce rather than one where everyone carries a weapon like the old wild west.

### The monopoly of finance

March 2, 2013

Given the recent post by Noah Smith on the profitability of finance, I thought I would put up a link to a previous post of mine that asked the same question.

### Minimum wage and the efficient market

February 19, 2013

The current debate about the effect of raising the minimum wage on employment poses an interesting question about how efficient the labour market is. According to the classical view of economics (and the Freshwater school) raising the minimum wage should decrease the number of people working because it will induce employers to shed workers to minimize costs. However, multiple studies of the effects of minimum wages seem to show that small changes do not decrease employment and sometimes even increases it (e.g. see here). If people were completely rational, equally competent and the market were efficient then raising wages should decrease employment. If it turns out that this does not happen then one or more of these assumptions is false. My take is that they are all suspect.

According to basic economics theory, the wages employers offer is set by the marginal cost of adding an additional worker. This means that they will select a wage such that the productivity gains for the last worker they hire is balanced by the cost of that worker. However, this assumes that there is a readily available pool of workers willing to take that wage and that the productivity of a worker is independent of the wage offered. Neither of these assumptions may be true. The argument of the Freshwater school is that during times of high unemployment there should be lots of people willing to take jobs at any wage. However,  there is likely to be a distribution for the lowest acceptable wage. In fact, Keynesian theory is predicated on the fact that wages and prices are ‘sticky’ so in an economic downturn, neither fall fast enough for the market to clear. A person is probably unwilling to take a lower paying job because it may affect her prospects of securing a higher paying one in the future when the economy rebounds. Hence, employers attempt to set a wage at some point on the lower tail of the acceptable wage distribution so that the cost of waiting to find someone willing to take that wage plus the cost of hiring is balanced by the expected increase in sales. Increasing the minimum wage could then actually increase employment by forcing employers to hire at a wage point where the wait time is much shorter. The savings from the shortened wait time and possibly lower turnover balances the cost of the higher wage.

Employment may also increase if productivity scales with the lowest acceptable wage.  By forcing employers to pay a higher wage, they may actually hire much more productive workers that increases sales enough to hire another worker. In fact, the employers may not even realize that increasing the offered wage would actually increase sales because they never sampled that part of the distribution. They could be stuck in a local minimum where they offer low wages to low productivity workers when they could have offered slightly higher wages to much higher productivity workers. In that scenario, the minimum wage would actually benefit the employers more than the employees.

Both of these situations are plausible indications of a market failure in the labour market. The market may be locally efficient in that the wages are optimal for small changes but not globally efficient in that there could be another more efficient fixed point somewhere far away on the wage curve. Government intervention could actually push the market to a more efficient point and this is not even accounting for the fact that the increased wages would be spent, which could cause a Keynesian multiplier boost to the economy. This is not to suggest that the government knows any better than the employers but just that unintended consequences can go both ways.

### Saving large animals

January 11, 2013

One  story in the news lately is the dramatic increase in the poaching of African elephants (e.g. New York Times). Elephant numbers have plunged dramatically in the past few years and their outlook is not good. This is basically true of most large animals like whales, pandas, rhinos, bluefin tuna, whooping cranes, manatees, sturgeon, etc. However, one large animal has done extremely well while the others have languished. In the US it had a population of zero 500 years ago and now it’s probably around 100 million.That animal as you have probably guessed is the cow. While wild animals are being hunted to extinction or dying due to habitat loss and climate change, domestic animals are thriving. We have no shortage of cows, pigs, horses, dogs, and cats.

Given that current conservation efforts are struggling to save the animals we love, we may need to try a new strategy. A complete ban on ivory has not stopped the ivory trade just as a ban on illicit drugs has not stopped drug use. Prohibition does not seem to be a sure way to curb demand. It may just be that starting some type of elephant farming may be the only way to save the elephants. It could raise revenue to help protect wild elephants and could drop the price in ivory sufficiently to make poaching less profitable. It could also backfire and increase the demand for ivory.

Another counter intuitive strategy may be to sanction limited hunting of some animals. The introduction of wolves into Yellowstone park has been a resounding ecological success but it has also angered some people like ranchers and deer hunters. The backlash against the wolf has already begun. One ironic way to save wolves could be to legalize the hunting of them. This would give hunters an incentive to save and conserve wolves. Given that the set of hunters and ranchers often have a significant intersection, this could dampen the backlash. There is a big difference in attitudes towards conservation when people hunt to live versus hunting for sport. When it’s a job, we tend to hunt to extinction like  buffalo, cod, elephants, and bluefin tuna. However, when it’s for sport, people want to ensure the species thrives. While I realize that this is controversial and many people have a great disdain for hunting, I would suggest that hunting is no less humane and perhaps more than factory abattoirs.

January 4, 2013

The US National Debt is currently slightly above the US GDP, which has the pundit class up in arms about how we will be imposing a huge cost on our children and grandchildren or we are at risk of interest rates sky rocketing and be like Greece. Another worry is that the US will end up printing lots of money to service the debt and we will head into hyperinflation like Zimbabwe or Weimar Germany. However, much of this hand wringing is misplaced. None of these outcomes are necessarily true when applied to a nation that issues its own currency. The Japanese debt is well over twice GDP and they still have low interest rates and are even slightly deflationary.

The first misconception is that the US government just prints money when it wants to. Actually, the Federal Reserve creates money by buying US Treasury bonds or other debt and issues money in return. Currently, it is buying a lot of mortgage-backed securities in an attempt to increase the money supply and boost the economy. However, you will notice that inflation isn’t particularly high and that is because even though there is more pubic money there is much less private money. Companies aren’t investing because they see no demand in a depressed economy. If and when the US economy starts to grow again then this extra money is a threat for inflation. The Federal Reserve could then sell the bonds it owns and then simply destroy the money to reduce the money supply. However, remember that true inflation is a situation where prices and wages both increase. In such a case, the big losers are the creditors. If you have a big mortgage, nothing is better than inflation. A situation where prices increase but your wages don’t is not inflation. That is your standard of living going down.

The second misconception is that foreigners like China and Japan  hold all of our debt. In actuality, the US public and government entities hold about two thirds of our debt and foreigners hold the other third or about five trillion. So, we really are mostly in debt to ourselves. Our situation is not like a Dickens’ novel where the child has to go to debtor’s prison because of the father’s debts. Rather it is more like a family where some of the children will owe money to the other children. A US default on the US part of the debt would just result in a massive redistribution of money within the US. So, if you don’t own a lot of US treasury bonds, you really shouldn’t worry about a default. Of course, a default could cause other economic problems but that is a side effect.

The third misconception is that the US is in massive debt because government spending has increased drastically. Actually, the major reason that the debt and deficit is so high is that the economy is depressed. This reduces tax revenue and increases automatic outlays like unemployment insurance and food stamps. Additionally, the Bush tax cuts and the two unfunded wars of the past decade have cost about four trillion dollars. The fiscal cliff that we just partially averted was not a debt crisis. It would have been a massive hit to the GDP through a tax increase and spending reduction. It was about reducing the debt too fast and inducing another recession. What we need now above all is to increase economic growth. We have a massive unemployment problem, not a debt crisis. Right now, interest rates are extremely low. We should be borrowing as much money as we can to invest in our infrastructure and promote growth.

A corollary to too much government spending is that we need entitlement reform. The truth is that we need healthcare reform. Social security is actually in fairly decent shape. Yes, the retiring baby boomer population will be a large burden but that can be solved with some minor tweaks. The real problem is that Medicare and Medicaid costs are increasing much faster than GDP growth. Although, I have argued before that spending 80% of our GDP on healthcare may not be so unreasonable (see here). Also, discretionary spending like scientific research, national parks, infrastructure projects and so forth are a minuscule part of the federal budget. We could double it and it would just be rounding noise.

The fourth misconception is that people will suddenly stop buying US bonds and interest rates will increase leading to a Greek-like situation. This can never happen because the US controls its own currency. The Federal Reserve can always buy enough bonds to keep interest rates low. What will happen is that the US dollar will go down in value compared to other currencies but this will only help exports. Greece is stuck with the Euro and most of its debt is owned by foreign banks. The forced austerity has also caused their economy to shrink, which makes servicing the debt even more difficult. If Greece had its own currency, it could simply devalue it or inflate to get out of its debt. The solution for Greece is to either default, to have the European central bank buy its debt (effective default), or for the European central bank to induce inflation.

### Economic growth and reversible computing

November 12, 2012

In my previous post on the debt, a commenter made the important point that there are limits to economic growth. USCD physicist Tom Murphy has some thoughtful posts on the topic (see here and here). If energy use scales with economic activity then there will be a limit to economic growth because at some point we will use so much energy that the earth will boil to use Murphy’s metaphor. Even if we become energy efficient, if the rate of increase in efficiency is slower than the rate of economic growth, then we will still end up boiling. While I agree that this is true given the current state of economic activity and for the near future, I do wish to point out that it is possible to have indefinite economic growth and not use any more energy. As pointed out by Rick Bookstaber (e.g. see here), we are limited in how much we can consume because we are finite creatures. Thus, as we become richer, much of our excess wealth goes not towards increase consumption but the quality of that consumption. For example, the energy expenditure of an expensive meal prepared by a celebrity chef is not more than that from the local diner. A college education today is much more expensive than it was forty years ago without a concomitant increase in energy use. In some sense, much of modern real economic growth is effective inflation. Mobile phones have not gotten cheaper over the past decade because manufacturers keep adding more features to justify the price. We basically pay more for augmented versions of the same thing. So while energy use will increase for the foreseeable future, especially as the developed world catches up, it may not increase as fast as current trends.

However, the main reason why economic growth could possibly continue without energy growth is that our lives are becoming more virtual. One could conceivably imagine a future world in which we spend almost all of our day in an online virtual environment. In such a case, beyond a certain baseline of fulfilling basic physical needs of nutrition and shelter, all economic activity could be digital. Currently computers are quite inefficient. All the large internet firms like Google, Amazon, and Facebook require huge energy intensive server farms. However, there is nothing in principle to suggest that computers need to use energy at all. In fact, all computation can be done reversibly. This means that it is possible to build a computer that creates no entropy and uses no energy. If we lived completely or partially in a virtual world housed on a reversible computer then economic activity could increase indefinitely without using more energy. However, there could still be limits to this growth because computing power could be limited by other things such as storage capacity and relativistic effects. At some point the computer may need to be so large that information cannot be moved fast enough to keep up or the density of bits could be so high that it creates a black hole.

### Debt is relative

November 9, 2012

One of the memes that is dominating American political discourse is that the US national debt is too high. The debt is currently around 16 trillion dollars which exceeds the current GDP of 15 trillion. This may seem large but keep in mind that the debt-to-GDP ratio in Japan is over two. The federal government will bring in about 2.6 trillion in revenues this year but spend about 3.7 trillion dollars, giving us an annual deficit of a trillion dollars. However, our borrowing costs are also very low. The yield on a 10 year Treasury bond is under 2% and the 30 year yield is under 3%. The general fear of having large debt is that it may cause interests rates to rise because people fear a default. This then leads to higher borrowing costs until you get to a point where you can never repay the debt. This is where Greece is now and where Spain, Portugal, Ireland, and Italy may be heading.

However, an important fact that should be kept in mind when thinking about debt is that the absolute amount is irrelevant. This is because economics, like biology, is about flux and growth.  As long as the nominal GDP growth rate (real GDP growth plus inflation) exceeds the borrowing rate, then the debt ratio will shrink in the future.  In fact the power of exponential growth shows that you can always be in deficit and the debt to GDP ratio can shrink.  We can see this in a simple calculation.  Let $D$ be the debt, $I$ be the annual deficit, and $y$ the borrowing rate.  The debt then grows as$\dot{D}=I+y D$, which has the solution $D(t)=(I+D(0))e^{yt}/y-I/y$.  Now suppose that the nominal GDP $G$ grows with rate $r$ so $G(t) = G(0)e^{rt}$.  So in the short term deficits do matter but as long as $r > y$, the debt-to-GDP ratio will always shrink in the long run.  In fact, this is what happened after World War II.  The debt was never officially retired.  It just faded away into insignificance because of growth and inflation.  Given the low interest rates, there is an arbitrage opportunity to borrow as much as possible and invest the money in infrastructure to promote future growth.

### Time constants in the economy

October 17, 2012

I was struck recently by a figure that economist Paul Krugman posted on his blog of the recovery time from recessions.

The interesting point to me was that there seems to be some consistency in the rate of recovery from different types of recessions. In other words, there are fixed time constants in the economy. A recession is defined as a period with negative GDP growth rate, i.e. it is a time when the economy shrinks.  Generally, the US has been growing a few percentage points a year in real terms for the past several decades. This is interrupted by occasional recessions such as a severe one in 1980-81 and the most recent Great Recession of 2008-2009.

However, not all recessions are created equal and economists have made a distinction between those caused by disinflation and financial crises.  An example scenario for a disflationary recession is that the economy is initially overheated so while there may be lots of growth there is also lots of inflation. The causes of inflation are complicated but they are sometimes linked to the interest rate. When rates are low, it is cheap to borrow, so people can acquire more money to spend and too much money chasing too few goods leads to inflation. A recession can then be induced by interest rates increasing, either through direct action by the Federal Reserve Bank or some exogenous factor, which makes it more expensive to borrow money and also incentivizes saving. This reduces the money supply.  This is what happened in the 1980-81 recession.  Inflation was extremely high in the 1970′s so Fed chairman Paul Volker dramatically increased interest rates. This induced a recession and also curbed inflation.  How the Fed controls interest rates is extremely interesting and something I may post about in the future. A recession can also be caused by no apparent external event if people simply decide to decrease spending all at once. A beautiful example is given by the famous story of a babysitting coop (see here). In a disinflationary recession, the economy can start growing if you can get people to start spending again. This can be done by lowering the interest rate or through a fiscal stimulus plan where the government starts to spend more. The time constant for recovery will be about the time it takes for people who lost jobs to find new ones and this is usually less than two years.

Recessions due to financial crises are generally preceded by a financial bubble where some asset, such as real estate, increases dramatically in price and then people, companies and banks take on more and more debt to try to make money by speculating on this asset. This is what happened in the run up to the Great Recession and the Japanese financial crisis in the 1990′s. When the bubble finally bursts, people are left with lots of debt and little money  to spend, thereby inducing a recession. In the case of real estate, the debt is in the form of mortgages, which are usually long term. The time constant will be the average duration of the mortgage or the time it takes to refinance. In both cases, this will take longer than two years. Thus, the recession will persist until people can pay off or unload their debts and both are difficult when the economy is depressed. It also shows why monetary policy may have little effect. Lowering interest rates can’t directly help the people trapped in long-term mortgages. However, if the interest rates can be kept low enough and long enough to induce some inflation then house prices increase while effective debt decreases so people can sell their homes or refinance and get more money to spend. This is basically what current Fed chairman Ben Bernanke is trying to do.  Another option would be for the federal government to take advantage of low interest rates and start buying property. They could have started a buy-and-lease program where underwater homeowners could sell their homes to the government and then rent it back from them. This would keep people in their homes, bolster the economy and also ensure that people who made bad decisions during the bubble do not profit from their mistakes. When house prices rise again, the government would pocket the profits.

### More on health care costs

October 1, 2012

I posted previously that the rising cost of health care may not be a bad thing if it ends up providing jobs for the bulk of the population.  The Economist magazine blog Free Exchange had an interesting piece on how health care can become both more expensive and more affordable simultaneously. The argument comes from William Baumol of Baumol’s cost disease, (of which I posted on previously here). In simple terms, Baumol’s argument is that as society gets more productive and richer the salaries of everyone goes up including those in professions, like art and health care, where productivity does not increase. Now, given that the bulk of costs of most sectors are salaries, productivity increases generally imply decreases in the number of people in that economic sector. At current rates of growth, health care expenditures will be 60% of US GDP by 2105. However, as long as the economy as a whole grows faster than the rate of increase in health care costs then we will still have plenty leftover to buy more of everything else. If we make the simple assumption that contribution to GDP is proportional to population then an increase in health care’s share of GDP simply means that the share of the population working in health care is also increasing. Basically, at current rates of growth, we will all become health care workers. I don’t think there is anything intrinsically wrong with this.  How a nation’s wealth is distributed among its population is more important than how it is distributed among sectors.

### A new strategy for the iterated prisoner’s dilemma game

September 4, 2012

The game theory world was stunned recently when Bill Press and Freeman Dyson found a new strategy to the iterated prisoner’s dilemma (IPD) game. They show how you can extort an opponent such that the only way they can maximize their payoff is to give you an even higher payoff. The paper, published in PNAS (link here) with a commentary (link here), is so clever and brilliant that I thought it would be worthwhile to write a pedagogical summary for those that are unfamiliar with some of the methods and concepts they use. This paper shows how knowing a little bit of linear algebra can go a really long way to exploring deep ideas.

In the classic prisoner’s dilemma, two prisoner’s are interrogated separately. They have two choices. If they both stay silent (cooperate) they get each get a year in prison. If one confesses (defects) while the other stays silent then the defector is released while the cooperator gets 5 years.  If both defect then they both get 3 years in prison. Hence, even though the highest utility for both of them is to both cooperate, the only logical thing to do is to defect. You can watch this played out on the British television show Golden Balls (see example here). Usually the payout is expressed as a reward so if they both cooperate they both get 3 points, if one defects and the other cooperates then the defector gets 5 points and the cooperator gets zero,  and if they both defect they both get 1  point each. Thus, the combined reward is higher if they both cooperate but since they can’t trust their opponent it is only logical to defect and get at least 1 point.

The prisoner’s dilema changes if you play the game repeatedly because you can now adjust to your opponent and it is not immediately obvious what the best strategy is. Robert Axelrod brought the IPD to public attention when he organized a tournament three decades ago. The results are published in his 1984 book The Evolution of Cooperation.  I first learned about the results in Douglas Hofstader’s Metamagical Themas column in Scientific American in the early 1980s. Axelrod invited a number of game theorists to submit strategies to play IPD and the winner submitted by Anatol Rappaport was called tit-for-tat, where you always cooperate first and then do whatever your opponent does.  Since this was a cooperative strategy with retribution, people have been using this example of how cooperation could evolve ever since those results. Press and Dyson now show that you can win by being nasty. Details of the calculations are below the fold.

### The flipside of medicare efficiency

August 26, 2012

The selection of Paul Ryan as the Republican vice presidential candidate for the upcoming US federal election has brought health care reform back into the spotlight.  While the debate has been highly acrimonious, the one point that everyone seems to agree on is that the rate of increase in health care and in particular medicare spending is unsustainable.  Health care is currently one sixth of the economy and it will take up an increasing share if the growth is not reduced.  I think that a really expensive health care system may actually be a good thing.  What people tend to forget is that there are two sides of a cost.   When we pay for healthcare, that money goes to someone.  Making something more efficient, means producing the same amount of stuff with fewer people.

The official unemployment rate is currently about 8% but the actual fraction number of people who don’t work or wish they had more work is much higher.  Efficiency eliminates jobs.  People like Tom Friedman of the New York Times thinks (e.g. see here) that this will just free us up to do “creative” jobs.  However, what if you are a person that doesn’t want or is unable to do a “creative” job?  My guess is that as we become more efficient, more and more people will be left with nothing to do.  The solution is either to have a massive welfare system or we become less efficient.

However, not all inefficiencies are equal. We wouldn’t want monopolies where all the money flows to a small number of individuals.  What we need is a highly stochastic form of inefficiency that involves lots of people. Healthcare may be just what we need. It’s something that is highly decentralized and affects everyone.  It can’t be easily outsourced. I’ve argued before that having 80% of the economy be devoted to healthcare doesn’t seem that outlandish.  After all, how many flat screen TVs do you need?

### Log normal

May 25, 2012

A comment to my previous post correctly points out that the income distribution is approximately log-normal. What this means is that while income itself is not normally distributed, the logarithm of income is.  The log-normal distribution has a pretty fat tail for high incomes. A variable will be log-normal if it is the product of a lot of random variables, since the log of a product is a sum. It has been argued for many years that achievement should be log-normal because it involves the product of many independent events. This is why a good programmer can be hundreds of times better than a mediocre one.  I even gave a version of this argument here. Hence, small differences in innate ability can lead to potentially large differences in outcome. However, despite the fact that income may deviate from log-normality in some cases and in particular between sectors of the economy (e.g. finance vs. philosophy), there is still a question of whether the compensation scheme needs to follow log-normal even if productivity does. After all, if small differences in innate ability are magnified to such a large extent, one could argue that income should be pegged to the log of productivity.

### Nonlinearity in your wallet

May 25, 2012

Many human traits like height, IQ, and 50 metre dash times are very close to being normally distributed. The normal distribution (more technically the normal probability density function) or Gaussian function

$f(x) = \frac{1}{\sqrt{2\pi}\sigma}e^{-(x-\mu)^2/2\sigma^2}$

is the famous bell shaped curve that the histogram of class grades fall on. The shape of the Gaussian is specified by two parameters the mean $\mu$, which coincides with the peak of the bell, and the standard deviation $\sigma$, which is a measure of how wide the Gaussian is. Let’s take height as an example. There is a 68% chance that any person will be within one standard deviation of the mean and a little more than 95% that you will be within two standard deviations. The tallest one percent are about 2.3 standard deviations from the mean.

The fact that lots of things are normally distributed  is not an accident but a consequence of the central limit theorem (CLT), which may be the most important mathematical law in your life. The theorem says that the probability distribution of a sum of a large number of random things will be normal (i.e. a Gaussian). In the example of height, it suggests that there are perhaps hundreds or thousands of genetic and environmental factors that determine your height, each contributing a little amount. When you add them together you get your height and the distribution is normal.

Now, the one major thing in your life that bucks the normal trend is income and especially wealth distribution. Incomes are extremely non-normal. They have what are called fat tails, meaning that the income of the top earners are much higher than would be expected by a normal distribution. A general rule of thumb called the Pareto Principle is that 20% of the population controls 80% of the wealth. It may even be more skewed these days.

There are many theories as to why income and wealth is distributed the way it is and I won’t go into any of these. What I want to point out is that whatever it is that governs income and wealth, it is definitely nonlinear. The key ingredient in the CLT is that the factors add linearly. If there were some nonlinear combination of the variables then the result need not be normal. It has been argued that some amount of inequality is unavoidable given that we are born with unequal innate traits but the translation of those differences into  income inequality is a social choice to some degree. If we rewarded the contributors to income more linearly, then incomes would be distributed more normally (there would be some inherent skew because incomes must be positive). In some sense, the fact that some sectors of the economy seem to have much higher incomes than other sectors implies a market failure.

### Marginal economics

May 11, 2012

The recent financial crisis and  great recession has spurred an ongoing economics blog war.  The blog Noahpinion keeps a running summary. The battle is largely between the Keynesian view of macroeconomics, spearheaded by Paul Krugman, versus the Chicago school, represented by the likes of  John Cochrane. In very simple terms, the Keynesian explanation of recessions are that they are due to decreases in aggregate demand. By that, it simply means that economic activity shrinks due to some shock like the bursting of the real estate bubble or an inexplicable decrease in consumer confidence (Keynes called them animal spirits). Keynesian’s think in terms of reduced phenomenological models with names like the IS/LM (Investment-savings/Liquidity preference-Money supply) model or the AD/AS (aggregate demand/ aggregate supply) model. These models apply supply and demand ideas of microeconomics to the entire economy. Although the models are simple, they can give very specific prescriptions for what to do about certain economic situations. The AD/AS model is analogous to demand/supply curves of microeconomics for single products. It consists of an AD curve and an AS curve on a graph of global price level versus global output (i.e. GDP).   The AD curve slopes down to the right since the higher the price the lower the demand for goods and services while the AS curve slopes up to the right since the higher the aggregate price the higher the aggregate supply.

Unlike in microeconomics, the reasons for why these curves do what they do is not completely self-evident and takes some reasoning to justify.  The problem in a recession is that the entire demand curve shifts to the left so the equilibrium GDP also shifts to a lower level. Keynesians argue that in order to get out of a recession, we need to move the demand curve back to the right and the simplest way to do that is to increase demand through government spending. This was the rationale for the 2009 stimulus although many of the Keynesians like Paul Krugman and Christina Romer (who was in the Obama administration) cautioned beforehand that the amount was too small to get us completely out of the recession. Hence, the fact that we are still in recession is not evidence that the stimulus failed.

### Financial crisis on Frontline

April 25, 2012

If you have any interest at all in economics, finance, or the financial crisis, then I highly recommend PBS Frontline’s series on Money, Power and Wall Street, which can be accessed here.  I watched episode two last night on how the 2008 bank bailouts were engineered in 2008.   Then New York Fed president Tim Geithner favored bailouts, following the game plan established by Robert Rubin, Larry Summers and Alan Greenspan during the 1990′s.  While then Treasury Secretary Hank Paulson was initially hesitant because of the moral hazard.  However, he did approve of the bailout of Bear Stearns in March, 2008 where the US Federal Reserve basically gave JP Morgan 30 billion dollars to buy it. Paulson had a total change of heart after he let Lehman Brothers fail in September, 2008.  The credit market seized and he started to panic when even non-financial institutions started to complain that they would have trouble operating because their access to loans had dried up.  This led to the Troubled Asset Relief Program (TARP) where Paulson forced all the major banks to take money without any conditions.  I thought that we should have let the banks fail in 2008.  The US Fed could then temporarily nationalize the failed banks and start anew.  They could even retain most of the lower level staff so institutional knowledge would not be completely lost.   Instead of bolstering insolvent banks, we could have lent to small businesses and homeowners directly.

### Financial Fraud and incentives

April 12, 2012

I highly recommend this EconTalk podcast on financial fraud with William Black.  It gives a great summary of how financial fraud is perpetrated.  It also clearly highlights the difference in opinions on the cause of the recent financial crisis.    What most people seem to agree on is that the financial crisis was caused by a system wide Ponzi scheme.  Lots of mortgages were issued (some were liar loans where the recipients clearly were not qualified, while some were just risky); these loans were then packaged into mortgage-backed securities (e.g. CDOs) by investment banks who them sold them to other banks and institutional investors like hedge funds and pension funds.  As long as housing prices increased, everyone made money.  Homeowners didn’t care if they couldn’t pay back the loan because they could always sell the house.  The mortgage lenders didn’t care if the loans go bad because they didn’t hold the loans and made money off of the fees. Like a classic Ponzi scheme, when the bubble burst everyone lost money, except for those who got out early.

The motivation for the mortgage lenders seem quite straightforward.  They were making money on fees and the more mortgages the more fees.  When they ran out of legitimate people to lend to, they just lent to riskier and riskier people.  The homeowners were simply caught in the bubble mania at the time.  I remember people telling me I was an idiot for not buying and that house prices never go down. The question at dispute is what were the incentives for the investment banks and institutional investors to go along with this scheme. Why were they fueling the bubble? Libertarians like Russ Roberts, the host of EconTalk, believes that they didn’t care if the bubble burst because they knew they would be bailed out by the government.  To him, the moral hazard due to government intervention was the culprit.   The pro-regulators, like Black, believe that this was a regulatory failure in that the incentives were to commit and reward fraud.  The institutional investors simply didn’t do the due diligence that they should have because the money was rolling in.  He cites the example of Enron, where incredible profits were booked through accounting fraud, which not only didn’t raise alarm to investors, but only attracted more money leading to  more incentives to perpetuate the fraud.  He also says that thousands of people were prosecuted for fraud in the eighties after the Savings and Loans crisis but no one has been prosecuted this time around. He believes that unless we criminalize financial fraud, this will only continue.  The third view, shared by people like Steve Hsu and Felix Salmon, was that the crisis was mostly due to incompetence (Steve calls this bounded cognition).  The investment banks had too much confidence or didn’t fully understand the risks in their financial instruments. They thought they could beat the system. The fourth possibility is that people knew it was a Ponzi scheme but either felt trapped and couldn’t act or thought they could get out in time. It was a pure market failure in that the rational course of action led to a less efficient outcome for everyone.

### Income, wealth, and being rich

March 8, 2012

An article in Bloomberg recently told of how some Wall Street bankers were struggling to make ends meet because of the drop in bonuses. There was the obvious backlash and schadenfreude.  Although I agree that if you’re making upwards of 350 thousand per year you shouldn’t get much sympathy, most people are still confused about the difference between wealth and income.  Your are rich if you have lots of wealth.  Having a high income will help you attain wealth but if you spend more than your income then you will be struggling.  To be truly rich, you should be able to sustain your current lifestyle on just your wealth (e.g. savings and investments) and not require any additional income.  The easiest way to become “rich” is to reduce your expenses.

This can be made concrete with the simple model of wealth change:

$\frac{dW}{dt}= I +r W - E$

where W is wealth, I is annual income, r is the annual return on investments, and E is annual expenditure.  In the absence of income (I = 0), you can maintain your lifestyle and wealth, if $rW\ge E$.   You are rich if the annual return on your wealth exceeds your annual expenditures.  If you’re annual expenditure is 100 thousand dollars, and your annual rate of return is 5%, then you’ll need 2 million dollars to be rich.  However, this is a conservative estimate because you’ll still have $2 million when you die. Suppose, you just want to maintain your lifestyle while you’re alive and have nothing left when you die. Then, we need to solve the differential equation, yielding $W(t) = \frac{(E-I)}{r}(1-e^{rt}) + W(0)e^{rt}$ or $W(0)=W(t)e^{-rt}+\frac{E-I}{r}(1-e^{-rt})$ for the current wealth you need if you want to have $W(t)$ dollars in t years. If we suppose no income and zero wealth at time t, then we get $W(0) = E(1-e^{-rt})/r$, for the necessary current wealth, which gives the intuitive result that you need t times your annual expenditure if the growth rate is very slow. The above formula also works if we include the rate of inflation (and taxes) if we let r be the real annual rate of return that includes inflation and taxes. So putting in some numbers, if we suppose that you want to have zero wealth in 50 years time and you have a real rate of return of 3%, then you’ll need about 26 times your annual expenditure to be rich. If you get 5% real return then you’ll need 18 times the expenditure and if you can get the historical 7% from the stock market then you’ll only need 14 times the expenditure. If you can get your expenditure down to$50K per year then you’ll only need $700,000 to be self-sufficient. However, if you wanted to be really rich such that you could live basically anywhere, travel wherever you want, own a summer home, send your kids to private school, then let’s say you’ll need to spend about a million dollars a year. If you can get 7% real returns, then you’ll need$14 million dollars to be rich.

Mar 8: Corrected some errors