Introduction

This book deals with applications of statistics to the social sciences, including economics and other areas usually styled as ‘social’, such as sociology, social policy and planning. Examples are drawn mainly from those disciplines, but some applications extend to the natural sciences. The discussion does not stretch to the higher reaches of epistemology, semantics and general philosophy; rather it looks more practically at the purpose of indicators and, from there, to their nature and construction.

Sections 1.2 to 1.4 that follow discuss the statistical derivation of indicators, their structure and typology, and their use in scientific analysis. Then Chapter 2 ‘Indicator techniques’ outlines some of the major statistical techniques and characteristics used for indicators. This material is based on the general statistical textbook literature, to which reference should be made for further detail. In Chapters 3 to 5 particular indicator applications in various fields of economics and social analysis are discussed. There are brief descriptions of some of the major subject matter, and references to sources in the bibliography, but the main emphasis is on identification of the processes involved and on appropriate socioeconomic measurement. Finally, Chapter 6 presents a summary of the main features of indicator analysis.

The bibliography covers some classic texts but concentrates otherwise on a selection of fairly recent titles, which themselves list further references, chosen from the very large literature in the various branches of the social sciences.

INTRODUCTION

Despite a spurt of progress on the theory of incomplete security markets over the past decade or so, there is relatively little yet in the way of testable implications or practical prescriptions. This essay presents a synopsis of some of the available models and points toward some of the important issues still standing in the way of the theory's fruition. This is not a general survey of the topic.

An incomplete security market is widely taken to be one in which certain contracts are not available for trade, a definition that is perhaps too rigid. The point is that active trading is observed only in contracts with satisfactory enforcement mechanisms, sufficiently low transactions costs, and enough incentive for exchange, relative to general market opportunities. Most economists would surely agree that markets will and do open in response to the emergence of these conditions. On the other hand, there is no well-understood reason to believe that the resulting constellation of traded contracts is therefore “appropriate” in some constrained sense of efficiency, or that “markets are as complete as they ought to be.” There is also strong empirical evidence that security prices are not even approximately consistent with complete markets, at least under standard preference assumptions.

Most currently active security markets seem to have arisen in response to entrepreneurial incentives to provide markets for insurance, the need for corporations to raise capital in a convenient form, and historical accidents. The process of security market innovation, interesting in itself, also affects the pricing of securities and the allocation of contingent consumption. It is only beginning to be modeled. As yet, most of the theoretical attention of financial economists has been on complete markets models, for which wehave a reasonably clear and elegant theory without much empirical basis, or to models with an exogenously fixed set of contracts. The theory's real success story has been the application of arbitrage-free restrictions to obtain relative prices for securities that are theoretically redundant, without saying much about the allocation of consumption or the pricing of the “primitive” set of underlying securities.

READER'S GUIDE

Part one of the chapter is written in an easy style, to try to demystify the subject (it is based on the lecture given at the World Congress). The Biblical story of the Judgement of Solomon is used as a running example for presenting different notions of implementation. Inevitably, perhaps, this part of the chapter contains a number of statements that are rather loose. This is compensated for by the more formal part two, which amplifies certain results and topics - though here, too, some degree of detail has been sacrificed for the sake of readability.

The chapter deals with situations in which agents are presumed to have complete information about each other's preferences. Thomas Palfrey's chapter in this volume, “Implementation in Bayesian Equilibrium: The Multiple Equilibrium Problem in Mechanism Design,” is a companion to this, and looks at environments with incomplete information.

Even though the complete-information environment is a restrictive case, the literature on it is vast and still growing. I have therefore had to be quite selective. The chapter should be seen as an overview of recent research, not as a comprehensive survey; I regret that I have not been able to do justice to the work of a number of authors.

INTRODUCTION

Collusion and the social sciences

The phenomenon of collusion, and the concomitant concepts of “group,” “power,” “bureaucracy,” and “politics” figure prominently in political science and sociology. Political scientists have always been concerned by the possibility that politicians and bureaucrats might identify with interest groups rather than serve the public interest. Montesquieu's plea for building a system of checks and balances among branches of government to limit the perversion of public policy, and the writings of the American federalists, in particular Madison, have deeply influenced the design of many constitutions. Later, Marx suggested that the State uses its coercive power to benefit large trusts. This vision of the capture of political life by interest groups was considerably enriched in the twentieth century by political scientists (Bentley, Truman) and especially by the political economists of the Chicago school (Stigler, Peltzman, Becker) and the Virginia school (Buchanan, Tollison, Tullock).

Concurrently, sociologists (Crozier, Dalton) and organization theorists (Cyert and March) have emphasized that behavior is often best predicted by the analysis of group as well as individual incentives. It would be naive to build incentives for individual members of an organization without considering their effect on collective behavior. In other words, incentive structures must account for the possibility that members collude to manipulate their functioning.

INTRODUCTION

Non-cooperative game theory studies the question of what constitutes rational behavior in situations of strategic interaction in which players cannot communicate nor sign binding agreements. The traditional answer to this question centers around the notion of Nash equilibrium. Such an equilibrium is a vector of strategies, one for each player in the game, with the property that no single player can increase his payoff by changing to a different strategy as long as the opponents do not change their strategies. The Nash equilibrium concept is motivated by the idea that a theory of rational decision-making should not be a self-destroying prophecy that creates an incentive to deviate for those who believe in it. To quote from Luce and Raiffa (1957, p. 173):

In other words, for a (commonly known) norm of behavior to be self-enforcing it is necessary that the norm (agreement) constitutes a Nash equilibrium.

The increased use of non-cooperative game theory in economics in the last decades has led to an increased awareness of the fact that not every Nash equilibrium can be considered as a self-enforcing norm of behavior. Very roughly, the Nash concept is unsatisfactory since it may prescribe irrational behavior in contingencies that arise when somebody has deviated from the norm. In applications, one typically finds many equilibria and intuitive, context depending arguments have been used to exclude the “unreasonable” ones. At the same time game theorists have tried to formalize and unify the intuitions conveyed by applications and examples by means of general refined equilibrium notions.

ANTEDILUVIA

Writing on the foundations of game theory is a Herculean task. I don't know which of the labors of Hercules provides the most apt metaphor. It is tempting to cite the Augean stables, which housed three thousand oxen but had not been cleaned for thirty years, but this would imply too harsh a judgment. The nine-headed Hydra, which grew two heads for each that was struck off, would do very well for a piece on refinements of Nash equilibrium, but this task has fallen to Eric van Damme (1990). I shall therefore settle for the wrestling match with the giant Antaeus, although I fear his feet are so firmly entrenched that it would truly take a Hercules to move them.

In brief, I believe the foundations of game theory to be a mess. Much of what we say in defending what we do does not hang together properly. Even when something coherent is on offer, it is hard to find two game theorists who are able to agree on whether it is right. This does not mean that the models game theorists have developed are worthless. As Aumann (1985) put it, while lecturing in Finland:

I am not sure that I share Aumann's confidence in the laws of economic activity, but I agree that “we must be doing something right,” and that it would be folly to abandon the insights that game theory has brought to economics on the grounds that foundational issues remain unresolved. After all, people formulated correct and useful theorems in mathematics long before proper logical foundations for the subject were developed. Why should the same not be true of game theory?

INTRODUCTION

In the last decade a number of new theories have been proposed to explain individual behavior under risk where, following Knight (1921), risk is defined as randomness with a known probability distribution. Some of these theories are formally atemporal and generalize the classical expected utility model of choice. Their development was inspired primarily by the growing body of laboratory evidence regarding static or one-shot choices, that has cast doubt upon the descriptive validity of the expected utility model. Other theories are explicitly intertemporal and generalize the time-additive expected utility model which is standard in capital theory. The noted laboratory evidence also provides some motivation for this work since it is clearly desirable that a theory of intertemporal utility, when restricted to static gambles, be consistent with the evidence.

The capacity to explain behavior in the laboratory is one criterion that might be applied to a theory of choice under risk. At least as important, however, is that the theory be useful as an engine of inquiry into standard market-based economic questions. The expected utility model has proven extremely successful in this respect. By application of now standard techniques, modelers have been able to derive a rich set of predictions in a variety of contexts. Moreover, a substantial body of non-experimental evidence has been shown to conform well to the expected utility hypothesis. The ultimate influence of the new theories on the profession at large will probably depend on whether they can match the elegance and power of expected utility as a tool of analysis and whether they can significantly improve the explanation of non-experimental evidence. In order to cast light upon these questions, I will survey some of the new theories of choice and their applications to a number of standard problems in macroeconomics, finance, and game theory.

INTRODUCTION

In economic, political, and personal life, the terms under which individuals or institutions interact are rarely determined fully by explicit, enforceable contracts. Within the bounds of the law, there is enormous scope for variation in the way in which commercial rivalries, international relations, and social affairs are conducted. Often, the same parties interact repeatedly. As a consequence, there is a large role for implicit, self-enforcing contracts to play: agents have an incentive to conform to an implicit agreement today because they believe that this will influence the nature of subsequent interactions. Repeated games provide perhaps the simplest model in which self-enforcing arrangements can be studied formally. It is this aspect of repeated game theory that I attempt to survey here. The chapter focuses on the structural and conceptual issues that have arisen in recent years in the study of repeated discounted games of complete information.

This choice of subject matter embraces a large literature, but excludes some important topics in repeated games. There is a substantial and challenging body of work on repeated games of incomplete information, much of which is surveyed by Mertens (1987). Following Kreps and Wilson (1982) and Milgrom and Roberts (1982), many papers have explored the effects of reputation formation in finitely repeated games with (initially) small amounts of incomplete information. These are covered by Fudenberg (1992) in chapter 3 of this volume. The latter survey also touches on the growing literature that investigates how play evolves as success is rewarded by survival.

The first part of the chapter chronicles the progress that has been made in the past decade in understanding supergame equilibria from a technical point of view. Many problems that had been considered intractable yielded to systematic analysis. Whereas earlier work on discounted repeated games had to content itself with studying artificially restricted behavior, a number of papers revealed that it was possible to drop those restrictions and still obtain strong results. Theorists began to explore more complicated and satisfying models, suggested by features of various economic situations. Players may observe different parts of the history of play, and some of their information may be stochastic, for example. They could meet different partners or rivals over time, or have different time horizons.

One of the oldest and most important questions in corporate finance is what determines how firms finance their investments and operations. This question has been referred to as the “capital structure” problem. The modern theory of capital structure began with the celebrated paper of Modigliani and Miller (1958). Here Modigliani and Miller (MM) pointed the direction that such theories must take by showing under what conditions capital structure is irrelevant. Since then, many economists have followed the path mapped by MM. Now, some thirty years later it seems appropriate to take stock of where this research stands and where it is going. Our goal in this survey is to synthesize the recent literature, summarize its results, relate these to the known empirical evidence, and suggest promising avenues for future research.

Capital structure theories have traditionally been concerned with what determines the relative amounts issued by firms of various given securities, mainly debt and equity. A much deeper question, however, is what determines the specific form of the contract (security) under which investors supply funds to the firm. Investors provide such funds with the expectation of sharing in the returns generated by the firms' investments. Therefore, financial contract design must resolve the problem of allocating the cash flows generated to investors. For example, debt contracts generally promise a fixed payment not contingent on firm performance. If the firm fails to make this payment, returns to debtholders are negotiated under the bankruptcy law of the relevant jurisdiction. Equity contracts specify that the holders share the residual returns after debtholders are paid, subject to limited liability. Returns to be allocated by financial contracts depend, however, on decisions made within the firm such as choice of project, assignment of personnel, day-to-day operating decisions, etc. As a result, returns depend on who is in control of these activities.

INTRODUCTION

Economic time series usually display deviations from their trends that, although irregular, have recurrent patterns. The explanation of such patterns of fluctuations is a subject that has received considerable attention from the economics profession.

Fluctuations may be generated by economic shocks that are due either to variations of private sector behavior originating in tastes or technological changes or to stochastic shifts in government policy. Under such an hypothesis, the variables subject to shocks will be modeled as exogeneous uncertain parameters. Typically, in exogenous shock models of economic fluctuations, the equilibrium is well defined, often unique - at least locally unique, in the terminology we will adopt later determinate - and stable: in the absence of recurrent exogenous shocks, the economy would tend to a steady state, but because of shocks a (possibly stationary) pattern of fluctuations will be observed.

Such a general structure of explanation is so familiar that some typologies of business cycle theories only refer to it, and classify models according, on the one hand, to the dominant type of “impulse” and, on the other hand, to the nature of “propagation mechanisms” that are posited. Textbook models, either "Keynesian" or “monetarist,” describe exogenously generated fluctuations. Also, the recent theory of “real business cycles” is the last avatar of a popular exogenous shock theory.

INTRODUCTION

Implementation theory links together social choice theory and game theory. At a less abstract level, its application provides an approach to welfare economics based on individual incentives. The underlying motivation for implementation theory is most easily seen from the point of view of a relatively uninformed planner who wishes to optimize a social welfare function that depends on environmental parameters about which relevant information is scattered around in the economy. Thus, the planner wishes to both collect as much of this relevent information as possible, and, with this information, make a social decision (e.g., an allocation of resources). This is the classic problem identified by Hurwicz (1972). In the twenty years since, we find numerous research agendas falling into the general category of implementation problems: the study of planning procedures, contracts, optimal regulation and taxation, agency relationships, agendas and commitee decision-making, comparative electoral systems, non-cooperative foundations of general equilibrium theory, and even much of the recent theoretical work in accounting and the economics of law.

The dilemma such a planner faces is that the individuals from whom the information must be collected will not necessarily want to share their information, or worse, they may wish to misrepresent their information. Moreover, exactly how they choose to conceal and misrepresent their information (what we will call their deception decision) depends upon three things. First and foremost, it depends on expectations of how the planner intends to put to use the information that is being collected. Second, it depends upon their expectations about the deception decisions of the other agents. Third, it depends on their information, so it is convenient to think of a deception decision as a plan of what to reveal as a function of information.

INTRODUCTION

Consider a small underdeveloped country. A new government is empowered and is looking for advice on how to speed the process of development. How might this government affect the quantity and types of foreign investment attracted through the explicit choice of its policies? Should they encourage this investment? Discourage it? Could and should this be done through explicit tax and spending policies? How would a policy of erecting tariff barriers to keep out imports of consumption goods affect their process of development? Should they undertake such a policy?

Does a government's “social security” policy adversely affect the incentives for private saving and the formation of capital? Should policies be adjusted because of this?

Is there “too much” trading in financial assets? Are the prices that these assets trade at too volatile? Should governments adopt explicit policies (such as transaction taxes) designed to reduce either the quantity of trading or the movements of prices in these markets?

Consider a one-dimensional beach along which bathers are uniformly distributed (more generally, a continuum of potential varieties and consumers with varying tastes). A local entrepreneur is considering opening a snack bar. Where along the beach should he locate? What if there are several entrepreneurs all competing for the same clientele, where will they locate? How would an omniscient social planner choose the locations and number of snack bars and how would this compare with the non-cooperative solution arrived at by the entrepreneurs? Should the government enter the picture and regulate entry and/or location of new snack bars? What should antitrust policy look like in this environment? Should something akin to patents be granted in this case? If so, for how long should they last?

There is little I can possibly add to the thorough account of the current state of equilibrium theory with infinitely many commodities that has been given in the chapter of L. Jones. But since the duty of the commentator is to offer comments I will oblige by touching on two points. The first concerns a contrast between the analytical treatment of exchange and of production economies, the second refers to the difficulties to extend the theory to environments where the first fundamental theorem fails and, in particular, to incomplete markets economies.

But before plunging into my specific comments perhaps I will be allowed a word on the purposes of the theory. The following observation is evident enough but it nonetheless bears repeating. While from a purely formal point of view an equilibrium model with infinitely many commodities includes, and therefore generalizes, the standard model with finitely many commodities, the justification of the theory is not generality but, on the contrary, concreteness. If all we wanted to know is, say, that an equilibrium exists we would do as well with the finite number of commodities model. After all the number of commodities can be arbitrarily large and since large can be very large indeed there can be no loss of substance in doing so.

INTRODUCTION

The general conception of this line of inquiry is to broaden the canonical Walrasian or competitive equilibrium paradigm - a la Arrow-Debreu - to encompass (with regard to the economy's financial sector) richer institutional structure and various market failures. I believe that this is a very important undertaking for (somewhat) generalist-type theorists like myself: the Walrasian tradition is simply much too fundamental to be left to (purely) mathematical-type theorists with their excessive concern about existence in ever more abstract settings, or to (impurely?) macro- or finance-type theorists with their excessive reliance on non-robust or overly parametric examples. Be that as it may, the range of specific developments thus far has been quite modest, concentrating on inside (i.e., private) financial transactions within incomplete financial markets (using Arrow's famous reformulation of complete contingent goods markets as the benchmark), while maintaining the simplifications of perfect information, price-taking behavior, etc.

As one might have predicted, this research has focused on the three classical issues in general equilibrium theory: existence, optimality, and uniqueness or, better, determinacy. I will not have much to say about either existence or optimality - the first because I view it as primarily a technical issue (and, unsurprisingly, one which has received an inordinate amount of attention), the second because I cannot claim to be an expert on its intricacies. Fortunately, an excellent discussion of recent results on both problems can be found in John Geanakoplos' introduction to the special issue of the JME devoted to “Incomplete Markets” (Geanakoplos, 1990).