Stiglitz's research on risk mainly focuses on a series of papers published by him and M.Rothschild in the early 1970s.
In the paper "Incremental Risk: Definition" (1970) co-authored with Rothschild, Stiglitz summarized the traditional definition of risk for the first time and put forward a new definition method. They think that people usually use four definitions to explain that one random variable (Y) is more risky than another random variable (X) (assuming their mean values are the same), namely: (1) Random variable Y equals random variable X plus interference term Z (noise with zero mean value); ⑵ Every risk averse person prefers X, that is, for a concave utility function, EU (x) ≥ EU (y); ⑶ Compared with the random variable X, the probability density function of the random variable Y has greater weight at its tail; (4) The variance of random variable Y is greater than X. By testing the partial order of random variables, they point out that the first three definitions are equivalent, while the fourth definition is different. In order to grasp the meaning of risk more accurately, they also gave a formal definition of "higher risk", that is, if the density function of one random variable is the density function of another random variable plus a "MeanPreservingSpreads", then this random variable has higher risk. Where "the difference with constant average value" is a piecewise function with zero average value. This definition of Stiglitz and Rothschild has become the analytical basis of most risk literature.
In the paper "Risk Increase: Economic Impact" written by Stiglitz and Rothschild (197 1), the economic impact of risk increase and its specific application are further discussed, and the impact of uncertainty on savings rate of return, portfolio selection, manufacturer's production problems and manufacturer's multi-period planning problems are deeply analyzed and investigated respectively. The main conclusions are as follows: (1) mean square error analysis generally leads to ⑴ the output of manufacturers under uncertain conditions is always lower than that under certain conditions, and the best response of manufacturers to the increase of risks is to reduce production rather than reduce prices (this is one of the cornerstones of new Keynesian economics).
These papers published in the early 1970s established Stiglitz's academic position and partly established his research direction and style. It has been vividly pointed out that Stiglitz's academic career is the process in which his basic views on risk and incomplete information spread to the whole field of economics.
The second is the theory of principal-agent and moral hazard, information screening and imperfect competition.
Stiglitz's research on risk and uncertainty directly led to his research on principal-agent and moral hazard, information screening and imperfect competition. These studies are not only the theoretical application of the aforementioned analytical tools and basic ideas, but also his foothold in analyzing various specific economic problems.
1. Principal-agent and moral hazard. Stiglitz used incomplete information and asymmetric information to study principal-agent and moral hazard. The main achievements are embodied in his papers "Basic Analysis of Moral Hazard" (1998) and "Moral Hazard and Non-market System" (199 1) co-authored with Arnot.
Stiglitz and others believe that the existence of incomplete information and asymmetric information will cause principal-agent and moral hazard problems. Because the interests and motives of the agent and the principal may be inconsistent and there is information asymmetry, the agent's behavior may not be in line with the interests of the principal. They point out that even if this happens (the agent's action is not the best for the principal), the principal may still prefer the result of the agent's participation to the situation where the agent does not participate. For example, in a criminal trial, a murder suspect may prefer the result of hiring an agent (lawyer) (convicted of manslaughter) to the result of not having an agent (sentenced to death). Of course, the result that is most in line with the interests of the client (acquittal) may be obtained through other acts of the agent (such as bribing the judge, perjury, etc.). ). Because the client can't completely infer the real behavior of the agent from the observable information, and can't accurately understand the ability of the agent and the extent to which the agent acts in accordance with the interests of the client. Therefore, Stiglitz and others describe the characteristics of the principal-agent relationship as: the risk of the principal due to the existence of some asymmetric information.
The effort function is introduced into the analysis model, which makes the contract signed by both parties have an indirect impact on the preference set and opportunity set of both parties, making the market activities more complicated. According to this, Arnot and Stiglitz (1988) pointed out: "Even if the basic functions such as expected utility function and the relationship between effort and accident probability are quite good, the indifference curve and feasible set are not necessarily convex; The price consumption line and income consumption line may be discontinuous; The degree of effort is generally not a monotonous function or a continuous function of parameters such as insurance policies or commodity prices. " Obviously, discontinuity will weaken people's confidence in the market mechanism. In addition, they believe that non-market factors will further aggravate the moral hazard problem. Therefore, Arnot and Stiglitz (199 1) came to the conclusion that "when there is obvious market failure, non-market factors at least partially have strong motivation to overcome market defects".
Neo-Keynesianism
2. Information screening model. Akerlof's "second-hand car market model" and Spencer's-"labor market model" respectively analyze the mechanism of adverse selection and the role of signal transmission; Stiglitz put forward information screening model and insurance market model, which greatly expanded the study of adverse selection and signal theory in economics.
In his paper "Information Screening Theory, Education and Income Distribution" (1975), Stiglitz studied the internal mechanism of information screening with "education level" as the market signal. In the article "The Causes and Consequences of Quality Dependent on Price" (1987), this paper investigates the situation that price level is a market signal and has the function of information discrimination, especially gives a more general analysis of the problem of information discrimination. Stiglitz believes that the price level not only has the function usually described by traditional economic theory, but also has the function of serving as a market signal-transmitting information and influencing the behavior of market participants. In the case of asymmetric information, price changes have two effects: the movement along the demand curve under the condition of constant information and the movement of the demand curve itself caused by information changes. For example, in the insurance market, the insured who is willing to pay a higher price is often more likely to have an accident; Insurance companies can distinguish between policyholders according to the price they are willing to pay, so that different types of policyholders can choose different insurance contracts.
Stiglitz's model has four outstanding characteristics: (1) Many conclusions depend on the assumption of increasing returns to scale; ⑵ All models have certain information asymmetry; (3) When there is information screening, the supply and demand in a certain market price may be unequal; (4) Even for the same commodity, there will be multiple market prices, that is, the market price is a distribution, not a single value. In the information screening model, incomplete information and asymmetric information may make the market fail and make the market equilibrium deviate from the optimal level. Their application in the labor market, credit market and insurance market provides a micro-foundation for the new Keynesian questioning attitude towards laissez-faire.
3. Incomplete competition. The analysis of imperfect competition is another important academic contribution of Stiglitz. In a series of related papers, he modeled manufacturers as production units facing risks (output depends on random variables), market structure (the number of manufacturers in the industry) and game theory (entry strategy and exit strategy, etc.). ).
Stiglitz pointed out in the paper Monopoly Competition and Optimal Product Diversity (1977) co-authored with dixit that external effects, economies of scale and fair distribution are the main reasons for imperfect market structure. Therefore, they put forward the monopoly competition model of scale economy and compared the relationship between market equilibrium and social optimization under different assumptions. At first, they skillfully transformed the problem of economies of scale into the relationship between product types and product quantities. They believe that under the condition of economies of scale, by reducing the types of products and increasing the output of each product, the cost of enterprises can be reduced and social and economic resources can be saved; At the same time, the reduction of product types will reduce the types of products consumed by consumers, resulting in the loss of social welfare (consumers prefer the diversity of consumption). Therefore, they turn the problem of scale economy into the problem of product variety and product quantity, and its social welfare nature depends on the form of consumer utility function (because utility function reflects consumers' preference for product variety).
In order to reflect the function of product variety in consumer utility function and the influence of product substitution on consumer utility and social welfare, dixit and Stiglitz constructed the famous "dixit-Stiglitz utility function" (later expanded to D-S production function, which has been widely used in modern endogenous growth theory, especially in the economic growth model of increasing variety or improving quality), and applied it to fixed substitution elasticity, variable substitution elasticity and non-substitution elasticity respectively. Their research shows that: under the condition of fixed substitution elasticity, the market equilibrium and constrained optimization of monopoly competitive market are completely consistent, that is, they have the same number of enterprises, the same number of products and output; Unconstrained optimization has more enterprises and more kinds of products than market equilibrium and constrained optimization, but none of them has reached the lowest point of the average cost curve. Therefore, social optimization is not a case of expanding output and exhausting all economies of scale. In addition, under the condition of fixed substitution elasticity, they derived the familiar Chamberlain dd curve and DD curve for the first time.
Three. Insurance market, financial market and labor market
Applying the above research results to the analysis of specific markets such as insurance, finance and labor is another important contribution of Stiglitz to economic theory. In Stiglitz's research, these markets have the following remarkable characteristics: (1) The output of each market is random, and at least one market trader faces the risk problem; ⑵ The market faces information asymmetry; (3) Every market is full of principal-agent problems and moral hazard problems; Therefore, these markets are generally unclear, and their output often deviates from the optimal level.