The next class of models stresses interactions between agents that reflect various forms of trading externalities. Here the linkages between agents do not arise directly in preferences or the production process but rather in the way agents come together to trade. Thus, these models rest firmly on the view that the Walrasian auctioneer does not function to bring together traders. Instead, trade frictions arise from the process of search and recruitment.

The complementarity in these models stems from the “thick market.” This is essentially a restriction on the relationship between trading costs and the level of economic activity. In particular, the economies we explore have the property that if there are many agents in the market searching for trading partners, then the returns to participating in the market are higher as a result of reduced costs of search. Thus thick market effects are just the opposite of congestion effects: the thicker the market the lower are trading costs.

AN EXAMPLE

The flavor of these models can be seen through a simple example of a participation complementarity. Denote by Z(p) the return to an individual from participating in an activity if a proportion, p, of others are participating. Assume that Z'(·) > 0 so that thicker markets are more desirable. The economics underlying this assumption will be the focus of the discussion to follow. Suppose that agent i's opportunity cost of participating is ki and that these costs are distributed across the population with a cumulative distribution function given by H(k), for k ε [0, 1].

The goal of the previous chapter was to provide an introduction to coordination games and some evidence on coordination failures. In the end, we find that coordination failures can arise in fairly simple experimental settings. While these experiments are certainly suggestive that coordination problems may arise, they leave open an important question: what are the underlying economic interactions that lead to coordination games?

The answer offered in this chapter takes the form of two abstract frameworks for analysis. The first, drawing upon Cooper and John [1988], stresses the interaction between agents in strategic settings where strategies are simply scalars in a closed interval. This formulation leads to a relatively straightforward equilibrium analysis, including conditions for multiple equilibria and some welfare results. The main point is that coordination games, such as those illustrated in the previous chapter, rest upon an interaction between agents termed strategic complementarity. As suggested already, this interaction implies that increased effort by other agents leads the remaining agent to follow suit. Besides becoming the basis for multiple equilibria, the strategic complementarity gives rise to multiplier effects.

The second part of the chapter looks at more general interactions. While almost all current macroeconomic applications of coordination games can be cast in the Cooper–John framework, the more general structure, investigated most recently by Milgrom and Roberts [1990] and Vives [1990], is quite powerful and worthy of study.

COOPER–JOHN MODEL

Cooper and John [1988] consider a game which highlights the key theme in this literature: the concept of strategic complementarity.

In this final section of the book we are interested in studying the problem of policy determination between a government and a set of private agents. The inefficiencies created by the presence of external effects as well as the prospects of multiple equilibria studied in the previous chapter set the stage for a consideration of government intervention to resolve these problems. Thus this topic is a natural conclusion to our study of macroeconomic complementarities.

The starting point of the chapter is an illustration of the coordinating power of the government. If coordination problems reflect the inability of agents to select the Pareto-optimal (optimistic) Nash equilibrium, then the government may be able to take actions to achieve the desired outcome. As we shall see, the government's actions can eliminate some undesirable equilibria by turning the strategies that support them into dominated strategies. These policies can be thought of as “confidence building measures” that work by eliminating the pessimistic beliefs that support the Pareto-inferior (pessimistic) Nash equilibria.

One important theme here is that in the optimistic equilibrium, the government never takes an action. Instead, its commitment to an action is sufficient for stabilization through removal of the pessimistic equilibrium. Thus governments may appear to be doing “nothing” when, in fact, they are quite successful.

To illustrate, we study the Diamond and Dybvig [1983] model of bank runs and the role of the government in supporting the Pareto optimal equilibrium through the creation of deposit insurance.

We begin the study of economic environments underlying coordination games by considering the most direct form of interaction across agents: through a production function. As we shall see, this simple structure forms the basis for new insights into both aggregate economic fluctuations and growth. Further, this source of complementarity is most tractable in terms of quantitative analysis since it is most easily incorporated into the stochastic growth model.

Consequently, the discussion in this chapter contains both theory and quantitative evidence associated with the behavior of these economies. This focus reflects, in fact, recent developments in quantitative analysis which allow us to go beyond the stochastic growth model studied by Kydland and Prescott [1982] and King, Plosser and Rebelo [1988] to understand macroeconomic dynamics of economies with distortions.

INPUT GAMES AND TECHNOLOGICAL COMPLEMENTARITY

Assume that I agents provide effort into a joint production process. The per capita output of this process is f(e1, e2, …, eI) where ei is the effort level of agent i in the production process. We assume that e ∈ [0, 1] so that the strategy space is a complete lattice. Per capita output is also the consumption for each agent. Implicit here is an assumption about the nature of the compensation scheme: agents share equally in the output from their joint production.

Let U(Ci) be the utility from goods consumption and g(ei) be the disutility of effort for agent i. Hence

σ(ei, e) = U(f(e1, e2, …, eI)) – g(ei) (1)

Assume that U(-) is strictly increasing and concave and that g(-) is strictly increasing and strictly convex.

The goal of this book is to provide a synthesis of research on the topic of complementarities in macroeconomics. Its primary goal is to isolate the various sources of complementarity and then to explore their implications for the behavior of macroeconomies. The success of this approach is seen through the numerous theoretical and empirical applications of the basic structure inherent in model economies built upon the macroeconomic complementarities structure.

As this is principally a book about applications in macroeconomics, it has been necessary to leave aside a number of topics that relate to the implications of complementarities for other branches of economics, such as industrial organization. Still, the reader interested in applications outside macroeconomics ideally will find the more general discussion of models of complementarities as well as the presentation of experimental evidence of some value.

The first two chapters as well as the next section of this Preface focus on general issues arising in models of complementarities, thus providing a framework for the more applied analysis that will follow. In particular, the first two chapters discuss experimental evidence on coordination games and theories of selection and put forth a general model of macroeconomic complementarities.

The remaining chapters explore applications of the general structure by investigating particular channels of interactions across agents. This includes the study of economies in which (i) externalities are present in the technology of the individual agent, (ii) markets are imperfectly competitive, (iii) agents come together through a search process and (iv) information is imperfect. As we shall see, all of these deviations from the standard general equilibrium model of Arrow and Debreu can give rise to macroeconomic complementarities.

One feature of aggregate behavior is the synchronization of discrete decisions such as the purchase of durable capital by firms and durable goods by households. These expenditures are important to understand in that they are extremely volatile elements of aggregate spending. Put differently, these are the elements of total expenditure that display the most time series variance. Introducing these discrete choices into traditional general equilibrium models is somewhat difficult because of the nonconvexity associated with lumpy expenditures on consumer and firm durables. One means of dealing with these nonconvexities is to look for equilibria in which there is some “smoothing by aggregation.” The effect of doing so, however, is that these discrete choices are, by construction, no longer synchronized so that their macroeconomic importance is dramatically reduced. In fact, this approach works only if agents have an incentive to take actions at different points in time.

When, in contrast, agents have an incentive to synchronize their discrete choices, then smoothing by aggregation is no longer possible. In this case, synchronized discrete decisions can matter for the macroeconomy. They can create endogenous fluctuations of the aggregate economy and magnify underlying disturbances to that economy.

The focus of this chapter is on the basis for synchronization and, more generally, the issue of the timing of economic activity. The first part of the chapter looks at incentives for the synchronization of activity. The second part goes on to explore the issue of delay.

The goal of this book is to explore the macroeconomic implications of a particular class of model economies: those built around the presence of complementarities. These models stand in sharp contrast with more standard general equilibrium models, both in their structure and in their implications.

From the perspective of structure, interactions dominated by complementarities provide agents with an incentive to follow the behavior of others. The chapters have been structured to present a wide range of environments in which complementarities naturally emerge.

Informally, economic life is simply different in environments characterized by complementarities. In the usual general equilibrium model, there is a sense that tradeoffs, such as moving along a production possibility frontier, are of primary importance. Here the question is whether we should produce more of some goods at the expense of others. Imbedded in this class of models is a sense of conflict in the interest of the agents: more for one means less for another.

In contrast, models of complementarities are really about life “inside the production possibility frontier.” Here there is the distinct possibility for producing more of all goods if activities can be properly coordinated. So conflicting interests can become subordinate to the more general needs of coordination.

In a related way, models with complementarity provide novel insights into economic policy. First, the government can play a major role in supporting confidence in an economy. For many countries, this is seen through the wide range of public guarantee funds, such as those for deposits, pensions, etc.

In this chapter we study models of imperfect competition. These economies display complementarity from a very simple mechanism. If others in the economy are producing more output, then they will be spending more as well and this induces increased demand for the product of an individual producer. Generally, the response of the producer will be to increase output as well. The linkage across agents is thus the familiar income–expenditure relationship common to many “Keynesian” style models of price rigidities. However, these interactions do not require price rigidities as they derive simply from the assumed normality of goods. In fact, this type of linkage across agents is present in general equilibrium models without any distortions whatsoever. As we shall see, though, these interactions are much more powerful in imperfectly competitive economies. In particular, the income–expenditure linkages can create multipliers and, when combined with nonconvexities in technology, can lead to multiple, Pareto–ranked equilibria.

The exact specification of market structure is, of course, quite important in any study of imperfect competition. Here we study two economies. The first is a multisensor economy in which there are a small number of firms producing an identical product in each sector. This is an interesting model in that it combines strategic substitutability (across firms in a given sector) with a complementarity across sectors.

The second economy is one of monopolistic competition. We use this economy first to elaborate on the nature of welfare losses due to imperfect competition and second to study the effects of money in the presence of menu costs.

More than eight decades ago, Joseph Schumpeter (1918) published an outstanding essay on the fiscal state. He argued that the ability to tax lies at the very heart of political power and that the rise of the modern political state was shaped by fiscal evolution in medieval and postmedieval times. Although he was primarily interested in the influence of fiscal power on political power, he also raised a related set of questions about what forces shape fiscal structure itself. He clearly recognized that revenue systems consist of a number of related components chosen in the light of three types of influences: economic, political, and administrative. But he did not provide a framework of how these factors interact to shape evolving revenue systems, perhaps because he had not yet formed an economic theory of political action.

This chapter represents an exploration of a more inclusive welfare economics of taxation. Its nature, like that of any new enterprise, is of necessity somewhat tentative. The emphasis is on presenting an outline of ideas and illustrating them with relevant examples. Whereas some sections develop a formal analysis, others take a more intuitive approach. The organization of the material is based on the conclusions reached in the preceding chapter, where we sketched three steps required for a comprehensive welfare analysis in the presence of collective choice. (See Section 5.3.)

We begin here with the selection of the standard of reference against which to judge collective choice outcomes. This, together with a consideration of the conditions under which equilibrium policy outcomes will achieve the standard, constitutes the first step. Economists have devoted much effort to working out such an analysis for an economy with private markets, and it has been one of the important achievements of the discipline to show that an economic system with competitive markets will yield optimal (Pareto-efficient) outcomes under carefully defined conditions.

Is tax policy improperly limited, or even corrupted, by politics? What is a valid counterfactual for judging tax systems and choices on taxation made by public decision makers? What steps are needed to define the elements and characteristics of a desirable or “good” tax system?

So far we have not directly confronted issues of this nature. Although the concept of Pareto efficiency was introduced in Chapter 4 in connection with the discussion of the Representation Theorem, the previous chapters have focused primarily on the presentation and development of theories that explain the structure of tax systems observed in democratic nations without evaluating outcomes in relation to a particular standard.

Doing research in economics, as in other social sciences, differs from the writing of a good story or play. Successful work in both fields starts with an initial premise, but the economist, unlike the playwright, will rarely reach a final cathartic conclusion. To use Frank Knight's phrase, there is simply too much “unfinished business.” In fact, one may want to go farther than Knight and claim that good research, like life, consists of unfinished business.

WHAT HAS BEEN ACHIEVED

Like other large research undertakings, this book presents new insights and also leaves significant areas to be explored. In order to provide an overall perspective, it is useful to describe briefly what, in our view, has been achieved in the preceding chapters. The book presents a new approach to the study of taxation that integrates collective choice with economic analysis and views fiscal policies as equilibrium outcomes. The resulting framework allows us to treat a wide range of issues in a unified manner. Moreover, the analysis is based on a collective choice model that allows exploration of multidimensional issues in an equilibrium setting.

Institutions do not appear explicitly in the voting model that serves as the framework for the preceding chapters. Nonetheless, the institutions of democracy are essential to the meaning of the model. It makes sense to use voting analysis as a basis for the study of fiscal systems in situations where political competition for public office is a well-established tradition. Democratic institutions are therefore an essential aspect of any such investigation, even if they are not formally part of the mathematical formulation.

In this chapter we investigate the role that certain institutional arrangements in democratic states may play in the determination of tax structure. In particular, we consider the nature of intragovernmental or structural competition in the congressional system of the United States and the parliamentary system of Canada, and we investigate the importance of differences in such competition for the determination of tax structure in the two countries.

Structural competition is an aspect of political systems that differs from competitive behavior related to political parties. The essence of such competition is best captured by the expression “checks and balances.” Following Albert Breton (1996), we may say that it exists in any situation where there are competing centers of power within a governing structure.

Explaining observed differences in the use of taxation and in the structure of fiscal systems is an important task for political economy. Taxation lies at the heart of political power and is crucial to the operation of the public sector, thus providing a test case for judging the relevance of collective decision models. At the same time, empirical research is facilitated by the existence of excellent quantitative information on government revenues, including data of both a cross-sectional and a historical nature.

In the preceding chapter we showed how applied equilibrium modeling could be used to gain a better empirical understanding of fiscal history. This chapter sets the stage for statistical modeling. We derive a general set of estimating equations that are consistent with the framework we have developed, and we use it for a discussion of the issues that arise when making the transition from theory to statistical work. The specific nature of the research presented in the following two chapters is introduced, and previous empirical work on the political economy of tax structure is reviewed.