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.