Efficient Markets if P=NP

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Philip Maymin of the Polytechnic Institute of NYU wrote an intriguing paper (with this accompanying video) on the efficiency of markets in which he claims that efficient markets (as defined by the efficient market hypothesis) would mean P=NP; the famous open problem in computer science that is thought to be untrue. I find the idea fascinating due to the bridge the paper tries to develop between two distinct fields. It is always interesting to consider how seemingly different ideas and disciplines are all interlinked.

In the paper, the professor of finance and risk engineering comes to the conclusion that if markets are efficient, then P has to equal NP and vice-versa since all relevant information (what is relevant depends on whether markets are considered weak efficient, semi-strong, or strong) is incorporated into the present price. This would mean that the value of P in polynomial time equals NP- the search equals the verification. It is an interesting idea and one that applies to the efficient market hypothesis, but not necessarily to market efficiency in reality.

As I have written about before, I do not believe markets are completely efficient nor can they be. I also do not completely believe in the efficient market hypothesis, especially not the strong or semi-strong forms. Such simple definitions of market efficiency do not account for cognitive biases and individual future predictions. Maybin’s research is interesting nonetheless and still certainly relevant due to the prevalence of the efficient market hypothesis in finance and economics.

The Failure of Success

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In the aftermath of the housing bubble it is apparent that one thing many seem to be afraid of, even ashamed of, and perhaps in denial of is failure. The world was in shock as it saw the failure of the banks, the failure of government in ensuring stability, and even the failure of the general public in not seeing it coming. It was a miserable moment. Some in power took it upon themselves to rid the world of this failure. The fear of further failure within themselves and others (partly induced by political rhetoric) led to the support of certain “solutions” that would supposedly stave off failure. Ironically, these “answers” were also very risky with high chances of failure, to the point where they [arguably] had the potential to make things worse than would have otherwise been the case.

Regardless, it is safe to say that as a world we are pretty damn scared of failing. Of course no one likes to fail or tries to fail on purpose, but is this fear of failure really prudent? After all, it is through the failure in trial and error that we learn so many things in the world from how to walk as babies to in many cases figuring out complex systems and machines. Economically, some of the most successful systems have also been those with the highest failure rates. Allowing mistakes to happen and letting people learn from them has been extremely beneficial- many capitalist models serve as great examples. Even the United States today in its quasi-capitalist state, has a business failure rate of over 10% per year- 1 out of 10 businesses in the country fails every year (according to economist Tim Harford whose research involves studying failure). And yet, despite the failure, the United States, as other relatively capitalist states in times past, has been more successful by many measures, including arguably the kingpin of utility, than states with greater central control and drastically lower failure rates.

The Internet is another fantastic and perhaps more lucid example of the undeniable success that can arise out of a stream of failures. The low barriers to entry and tremendous potential of the web results in millions of websites being made every year, most of which do fail and die. And yet despite that, the Internet continues to thrive and grow at amazing rates. New websites arise all the time (quite literally) and despite the competition many still prevail.

Should failure be completely eliminated, or even significantly minimized, the chances of success in these scenarios, whether they are personal, national, or otherwise, would most likely be much lower. Historically, such has been the case. Taking it to the extreme of reducing failure rates to 0 by taking no action whatsoever in any endeavor further strengthens this point because while there is no failure, there is also no success. At times, failure must be allowed in order to achieve success. It is not so much the opposite of success as it is the brother of success.

The Buy American Myth

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Economic patriotism in the United States and elsewhere has created movements in which citizens attempt to support local markets and employment by favoring locally produced goods over those produced in foreign markets. “Buy American” is a great example of such a movement that exists today, in which proponents argue that buying goods made by American companies will benefit the United States, even if the goods come at higher prices and lower quality than competing foreign goods. This idea has been especially prevalent in some industries, namely the automobile industry in which Ford and GM have pushed strong “Buy American” campaigns to sell more cars to well-intentioned patriots.

The notion of local or regional pride may be a noble one (depending on one’s values) and consumers should be able to freely pursue what they deem best, but the idea that buying locally is always the best thing for local people and markets is a logically flawed one. It ignores the reality of comparative advantages and the benefits that free trade can bring to nations and municipalities. The intuitive appeal of such movements has also led to special interest groups taking advantage, once more notably in the automobile industry.

The reality is that different organizations and nations are better at making certain goods than others, both domestically and on the international scale. This naturally makes it beneficial to specialize production based on production advantages and then to trade based on demand. It is an idea that is supported by both empirical evidence and strong correlationary evidence. The “Buy American” movement neglects these trade advantages and pushes consumers to buy locally regardless of the production efficiency in those goods or the benefits they might bring consumers. In doing so it attempts to bring about a socially created protectionist market. Much of the growth and wealth accumulation of the United States has historically been due to free trade policies, whereas others such as 20th century India and China suffered greatly from restrictions on such trade.

Of course the difference between those situations and movements such as “Buy American” are that the latter is voluntary and as such there is a much lower participation rate and the harm done is less. But, there is potential harm there nonetheless, and most likely many of the non-special interest proponents of such a movement might no longer see the benefit in partaking upon an analysis of the data.

When it comes to automobiles, there has been something even more devious at play than special interest support of such a movement (which is driven almost purely by self-interest and not national or consumer interest). Despite the claims by American automakers of being made in the United States, a substantial portion of the parts are often made abroad and only assembled domestically. The specific foreign parts content varies by make and model. Ironically, many of the “foreign” car makers have assembly plants within the United States and purchase some of their parts domestically as well- Toyota and Honda included. In fact, in Cars.com’s annual American-Made Index, the top two American vehicles were made by Toyota and Honda respectively as were five of the top ten.

The consequences of “Buy American” exemplify that even markets can fall prey to bad ideas, but through information exchange, things can improve. And when all is said and done, voluntary protectionism still does less damage than government protectionism, even though neither is really desireable.

Free Immigration and Entitlements

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The United States benefited tremendously from the influx of immigrants driven by free immigration policies in the 19th and early 20th centuries. New immigrants contributed to the economy, helping it grow while improving their own lives and creating new opportunities for themselves and others. Free immigration has historically had such effects, helping both the immigrants and the country in which it is implemented. This phenomenon would undoubtedly hold true even in today’s America if it were not for the current entitlement system.

It is one of the many [perhaps unintended] costs that come with unconditionally guaranteeing citizens costly benefits. Such entitlements incentivize people to immigrate to the United States, but not to necessarily work and contribute. While new immigrants might still contribute to the economy, the net effect can potentially be negative if the cost of entitlements surpasses the benefits of the added productivity. Certain entitlements might also incentivize some immigrants to move here not to work, but to only receive benefits. It is the infamous free rider problem in economics.

There is of course a middle ground where an entitlement system could work with free immigration and produce a net positive effect, but the benefits and costs are often hard to measure. Implementing such a system with these uncertainties would be nothing short of playing with fire, especially if the entitlement system is of the magnitude and structure of that in today’s America. The notable exception to this in today’s state is in some skilled labor markets where the addition of new workers would almost certainly create a net positive effect per individual added. These are the labor markets where there is great demand for such labor or high salaries, which leads to production and collected taxes that would irrefutably surpass entitlement costs for those new immigrants.

Despite restricted immigration and the millions of dollars being spent on its enforcement, the United States has over the years become home to a sizeable population of illegal immigrants from all corners of the world. This illegal immigrant population has been beneficial to the United States as many of the positive effects of a free immigration policy are present and the negative costs in entitlements are not. These people came here in search of a better life and many of them have found one, even living in the shadows of a nation that does not officially accept them. This brings up a policy possibility for free immigration on the condition of not being admitted into the entitlement system.

Illegal immigrants come to this country on their own will in search of a better life and they often find it, once more by being productive and helping the nation as well. If this benefit were extended to them without the cost of entitlements per person, then legal immigration for this labor would help both the nation involved and the immigrants. It might however go against any morally driven argument for entitlements, but is a worse alternative for the immigrant in their country of origin really a better moral position?

The Minimum Wage Myth

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The minimum wage is one of the most overvalued and misunderstood policies in practice today. The policy creates a legal price floor for labor in an attempt to ensure every working man earns a decent hourly wage. While the goal might seem noble, the reality is that the price floor effectively destroys parts of the labor market, increasing unemployment and unintentionally removing natural costs to discrimination in hiring.

Perhaps the primary shortcoming of the policy is that it ignores that there is a natural market for workers below most current minimum wage levels. Consider the situation in which a business expects a particular worker to add five dollars of productivity per hour doing a particular job. The manager might look to hire the worker at four dollars per hour, but certainly not at six. If the minimum wage is at six dollars per hour, the business will not legally hire that person because it makes no economic sense to do so. This costs the person a job and the business the added productivity it might have received. These losses are not in the interest of the worker, business, market or government. And all of these costs come despite the fact that the worker might have been happy with the four dollar compensation.

Now, consider the situation in which a business has to choose between two workers of equal expected productivity and only a difference in an unimportant characteristic such as race, gender, or age. Under a minimum wage system, a prejudiced manager might hire the worker with the characteristic he prefers simply because his intolerance comes at no extra cost. There is very little the disadvantaged worker can do to get the position over his competitor. However, if there is no price floor, the unfortunate worker might be able to reduce his asking wage, thus incentivizing the manager to hire him. In fact, even by simply offering a lower wage, this worker adds a cost to intolerance for the manager who is then forced to pay an extra sum should he go with his bias. This is not only to the benefit of the worker, but also society if one of our goals should be to promote tolerance.

The idea that a worker is being taken advantage of simply because of low monetary compensation is a greatly misguided one. That worker not only voluntarily accepts any job and any wage amount, but he might have other benefits from the job. His lower wage might be offset by the experience he receives, which he knows will, in time lead to greater and more profitable opportunities. He might also have taken a low-paying job which comes with considerably less work than a higher paying one because he prefers such a job or is incapable of the other.

These possibilities are very real and backed by several empirical studies on the matter. In practice, the market, as always has responded to the law in various manners to its benefit. The market demand and supply for below minimum wage labor can be seen in voluntary labor black market, in the internship market where many people work for low wages or even voluntarily for the experience, and in outsourcing scenarios where companies send jobs to markets where there is a lower or no legal price floor, but plenty of workers happy to take those jobs. The unintended consequences of the minimum wage have led a law of good intention to be costly, undesirable, and harmful to those who are at the greatest disadvantages.