Sunday, May 4, 2008

Markets with Asymmetric Information

I had a terrible hangover this morning and could not sleep. As usual I was surfing the Internet and came across an introduction to asymmetric information (well, introduction to Akerlof, Spence, and Stiglitz work) on the Nobel Prize website.

The paper is titled "Markets with Asymmetric Information"

It provides a neat explanation of stuff related to asymmetric information and briefly describes the contributions made by Akerlof, Spence, and Stiglitz on this front. Highly recommended for those who believe/realize that free market is actually an imperfect market!

Hangover is bad thing. :)(:


Akerlof's work:

Akerlof's idea may be illustrated by a simple example. Assume that a good is sold in indivisible units and is available in two qualities, low and high, in fixed shares λ and 1 − λ. Each buyer is potentially interested in purchasing one unit, but cannot observe the difference between the two qualities at the time of the purchase. All buyers have the same valuation of the two qualities: one unit of low quality is worth wL dollars to the buyer, while one high-quality unit is worth wH > wL dollars. Each seller knows the quality of the units he sells, and values low-quality units at vL < wL dollars and high-quality units at vH < wH dollars.

If there were separate markets for low and high quality, every price between vL and wL would induce beneficial transactions for both parties in the market for low quality, as would every price between vH and wH in the market for high quality. This would amount to a socially efficient outcome: all gains from trade would be realized. But if the markets are not regulated and buyers cannot observe product quality, unscrupulous sellers of low-quality products would choose to trade on the market for high quality. In practice, the markets would merge into a single market with one and the same price for all units. Suppose that this occurs and that the sellers’ valuation of high quality exceeds the consumers’ average valuation. Algebraically, this case is represented by the inequality vH > ¯ w, where ¯w = λwL + (1 − λ)wH. If trade took place under such circumstances, the buyers’ (rational) expectation of quality would be precisely ¯ w. In other words, the market price could not exceed ¯ w (assuming that consumers are risk averse or risk neutral). Sellers with high-quality goods would thus exit from the market, leaving only an adverse selection of low-quality goods, the lemons.


Spence's work:

Spence's analysis of how signaling may provide a way out of this situation can be illustrated by slightly extending Akerlof's simple example above. Assume first that job applicants (the sellers) can acquire education before entering the labor market. The productivity of low-productivity workers, wL, is below that of high- productivity workers, wH and the population shares of the two groups are λ and 1−λ, respectively. Although employers (the buyers”) cannot directly observe the workers productivity, they can observe the workers’ educational level. Education is measured on a continuous scale, and the necessary cost — in terms of effort, expenses or time to reach each level is lower for high-productivity individuals. To focus on the signaling aspect, Spence assumes that education does not affect a worker's productivity, and that education has no consumption value for the individual. Other things being equal, the job applicant thus chooses as little education as possible. Despite this, under some conditions, high-productivity workers will acquire education.

Assume next that employers expect all job applicants with at least a certain educational level sH > 0 to have high productivity, but all others to have low productivity. Can these expectations be self-fulfilling in equilibrium? Under perfect competition and constant returns to scale, all applicants with educational level sH or higher are
offered a wage equal to their expected productivity, wH, whereas those with a lower educational level are offered the wage wL. Such wage setting is illustrated by the step-wise schedule in Figure 1. Given this wage schedule, each job applicant will choose either the lowest possible education sL = 0 obtaining the low wage wL, or the higher educational level sH and the higher wage wH. An education between these levels does not yield a wage higher than wL, but costs more; similarly, an education above sH does not yield a wage higher than wH, but costs more.


Stiglitz's work:

Initially, all individuals have the same income y. A high-risk individual incurs a loss of income d < y with probability pH and a low-risk individual suffers the same loss of income with the lower probability pL, with 0 < pL < pH < 1. In analogy with Akerlof's buyer and Spence's employer, who do not know the sellers’ quality or the job applicants’ productivity, the insurance companies cannot observe the individual policyholders risk. From the perspective of an insurance company, policyholders with a high probability pH of injury are of “low quality”, while policyholders with a low probability pL are of “high quality. In analogy with the previous examples, there is perfect competition in the insurance market.9 Insurance companies are risk neutral (cf. the earlier implicit assumption of constant returns to scale), i.e., they maximize their expected proÞt. An insurance contract (a, b) specifies a premium a and an amount of compensation b in the case of income loss d. (The deductible is thus the difference d−b.)

In a pooling equilibrium, all individuals buy the same insurance, while in a separating equilibrium they purchase different contracts. Rothschild and Stiglitz show that their model has no pooling equilibrium. The reason is that in such an equilibrium an insurance company could profitably cream-skim the market by instead offering a contract that is better for low-risk individuals but worse for high-risk individuals. Whereas in Akerlof's model the price became too low for high-quality sellers, here the equilibrium premium would be too high for low-risk individuals. The only possible equilibrium is a unique separating equilibrium, where two distinct insurance contracts are sold in the market. One contract (aH, bH) is purchased by all high-risk individuals, the other (aL, bL) by all low-risk individuals. The first contract provides full coverage at a relatively high premium: aH > aL and bH = d, while the second combines the lower premium with only partial coverage: bL < d. Consequently, each customer chooses between one contract without any deductible, and another contract with a lower premium and a deductible. In equilibrium, the deductible barely scares away the high-risk individuals, who are tempted by the lower premium but choose the higher premium in order to avoid the deductible. This unique possible separating equilibrium corresponds to the socially most efficient signaling equilibrium...Rothschild and Stiglitz also identify conditions under which no (pure strategy) equilibrium exists.

Paul Collier on food prices

Paul Collier responds to Martin Wolf's column on food crisis. As always, Collier provides an excellent, to the point commentary:

The sharp increase in the world price of staple foods is an inconvenience for consumers in the rich world, but for consumers in the poorest countries, especially in Africa, it is a catastrophe. Despite the predominance of peasant agriculture, most African countries are net food importers and food accounts for over half of the budget of low-income households. This is the result of decades of agricultural stagnation combined with growing populations. Although many of the net purchasers are rural, evidently the problem is at its most intense in the urban slums. These slums are political powder kegs and so rising food prices have already triggered riots. Indeed, they sow the seeds of an ugly and destructive populist politics.

Why have food prices rocketed? Paradoxically, this squeeze on the poorest has come about as a result of the success of globalization in reducing world poverty. As China develops, helped by its massive exports to our markets, millions of Chinese households have started to eat better. Better means not just more food but more meat, the new luxury. But to produce a kilo of meat takes six kilos of grain. Livestock reared for meat to be consumed in Asia are now eating the grain that would previously have been eaten by the African poor. So what is the remedy?

...The remedy to high food prices is to increase food supply, something that is entirely feasible. The most realistic way to raise global supply is to replicate the Brazilian model of large, technologically sophisticated agro-companies supplying for the world market. To give one remarkable example, the time between harvesting one crop and planting the next, in effect the downtime for land, has been reduced an astounding thirty minutes. There are still many areas of the world that have good land which could be used far more productively if it was properly managed by large companies. For example, almost 90% of Mozambique’s land, an enormous area, is idle.

...In Africa, which cannot afford them, development agencies have oriented their entire efforts on agricultural development to peasant style production. As a result, Africa has less large-scale commercial agriculture than it had fifty years ago. Unfortunately, peasant farming is generally not well-suited to innovation and investment: the result has been that African agriculture has fallen further and further behind the advancing productivity frontier of the globalized commercial model. Indeed, during the present phase of high prices the FAO is worried that African peasants are likely to reduce their production because they cannot finance the increased cost of fertilizer inputs. While there are partial solutions to this problem through subsidies and credit schemes, large scale commercial agriculture simply does not face this problem: if output prices rise by more than input prices, production will be expanded because credit lines are well-established.

...Around a third of American grain production has rapidly been diverted into energy production. This switch demonstrates both the superb responsiveness of the market to price signals, and the shameful power of subsidy-hunting lobby groups.

...The ban on both the production and import of genetically modified crops has obviously retarded productivity growth in European agriculture: again, the best that can be said of it is that we are rich enough to afford such folly. But Europe is a major agricultural producer, so the cumulative consequence of this reduction in the growth of productivity has most surely rebounded onto world food markets. Further, and most cruelly, as an unintended side-effect the ban has terrified African governments into themselves banning genetic modification in case by growing modified crops they would permanently be shut out of selling to European markets. Africa definitely cannot afford this self-denial.

Keeping the private sector at an arm's length

There is an interview in the New Business Age with a businessman whose company is a major dealer in food trade in Nepal. He argues that unless the government initiates some action in the agricultural sector, the private sector is hesitant to invest in it. For a poor country like Nepal where about 73% of the population directly depend on agriculture, the government has to back this sector in a structured way through an industrial policy, which should help increase productivity and encourage production of few varieties that would help tap niche market abroad. Meanwhile, the IP should also help free surplus labor from this sector to the industrial sector, the ultimate decider of long term economic growth in an economy in the long run.

...It is difficult for the private sector to hold even one square kilometres of land for farming in the country. Only the government can remove this hurdle. If the government comes with proper planning, private sector can do a lot. If the government initiates action towards this direction, the private sector can support the process.

...Cardamom and ginger have been the major export items of Nepal for years. But the government has not facilitated these exports properly. For instance, we are growing and exporting big cardamoms while there is a growing demand for small cardamom which is more expensive. We should, therefore, begin to grow small cardamom as well. But we are not able to do that. Likewise, farmers here are growing Sona Mansuli rice. With the proper management and guidance from the government they can easily grow Basmati rice which can fetch more than double the price of Sona Mansuli. But the government has not thought about this for various reasons including the political instability. However, we are hopeful that the political impasse would be over soon and the government would take proper action to uplift this sector.

...Take an example of Yarsha Gumba. If its harvesting is properly managed by the government then the farmers can highly benefit from it and the government also would collect higher revenue. Proper management from the government is needed also to save the lives of the Yarsha Gumba collectors. Every year many people die while collecting Yarsha Gumba. If the fruit farming is managed properly then it would be of permanent nature. It would not be a temporary farming like that of rice or wheat.

...In India, the government pays special attention to the farmers’ problems. It provides appropriate financial support to the farmers and sends technologists to the fields to demonstrate the use of modern technology for improvement in the quality as well as quantity. We don’t have that system. In Nepal, there are lots of opportunities. We can produce world class apple juice and other fruit products, but sadly we are failing to do that.

...In Nepal, some 200 thousand tons of mustard oil is produced annually. We can increase it up to one million tons if the government provides the required support.

The role of the government is far from being realized and the private sector is simply not able to take risks. First the government has to do growth diagnostic to identify the most binding constraints for progress in the agricultural sector. Then, the government need to do intervention diagnostic to identify the best course of intervention that would be consistent with the available resources and would not temper individual and market incentives.