Knowledge that Transforms

In most natural sciences (physics, chemistry, biology) theories are validated by controlled experiment. However, in other natural sciences (astronomy, meteorology), and in most social sciences, including economics, the data are characteristically generated not by experiment but by measurement of uncontrolled systems. In economics, theories take the form of restrictions on the models assumed to generate the data, and statistical methods replace experimental controls in testing these restrictions. And here is the difficulty: in economics, particularly macroeconomics, the theory used to derive tests ordinarily does not generate a complete specification of which variables are to be held constant when statistical tests are performed on the relation between the dependent variable and the independent variables of primary interest. Accordingly, in such cases there will be a set of often very different candidate regression-based tests, each of which has equal status with the others since each is based on a different projection of the same underlying multivariate model. Except in the unlikely event that the explanatory variables are mutually orthogonal, the conditional regression coefficients, which generally form the basis for the test statistic, will depend on the conditioning set. We conclude from this that, if a theory which does not generate a complete specification of the regression test is nonetheless to have testable implications, these implications must be robust over the permissible alternative specifications. If the restrictions indicated by the theory are satisfied in some projections, but not in others that have an equal claim to represent implications of the theory, one cannot conclude that the theory has been confirmed. The fact that the observable implications of valid theories must obtain over a broad (but usually incompletely specified) set of regressions rather than for a single regression introduces a large and unavoidable element of imprecision into hypothesis testing in macroeconomics. Generally it appears to be appropriate to weaken the statistical criterion for rejecting theories. Consider, for example, the theory of money demand, which will engage our attention in this paper. The Tobin-Baumol square root formula implies that the elasticity of money demand with respect to the interest rate is exactly one-half. But which interest rate? Should wealth be held constant? Inflation? In view of such uncertainties it would be inappropriate to insist in a literal-minded fashion on rejecting the Tobin-Baumol model if in some regression the measured interest elasticity differed from one-half by more than two standard deviations, and only then. Obviously a more flexible approach is called for. The practice has been to conclude that the statistical evidence is consistent with the Tobin-Baumol model as long as the interest rate coefficient is negative. If it is negative and significant, or negative and insignificantly different from minus one-half, that would provide somewhat stronger confirmation. But a positive coefficient, particularly a significantly positive coefficient, would be viewed as raising questions about the validity of the theory. In macroeconomics generally, as in the money demand application, the typical response to specification uncertainty has been to regard a theory as supported if the signs of the estimated coefficients agree with those expected from theory, and as disconfirmed otherwise. There is no theoretical justification for this procedure, but it seems to be a reasonable course to follow. The point that economic theory ordinarily generates incompletely specified statistical *University of California, Santa Barbara. We have received helpful comments from Andrew Abel, Robert Clower, Michael Darby, Robert Engle, Stephen Goldfeld, David Laidler, Edward Leamer, Robert Lucas, Frederic Mishkin, and Edward Prescott. Thomas Hall provided able research assistance.

The theory of oligopoly price is very sensitive to behavioral assumptions. Even given identical assumptions about costs and demand, different models can predict every price between marginal cost and monopoly. This paper selects a single oligopoly model, and thus predicts a single oligopoly price. The selection criterion is consistency of conjectures; each firm's conjectures about the way other firms react to it will be correct. The two classical oligopoly theories, Bertrand and Cournot, make identical assumptions about costs and demand, but different assumptions about firm behavior. In Cournot equilibrium, each firm maximizes profit given the quantity of output other firms produce. In Bertrand equilibrium, each firm maximizes given the prices other firms charge. This difference in behavioral assumptions leads to a large divergence in predicted prices. Cournot predicts positive markups that decline as the number of firms increases, while Bertrand predicts marginal cost pricing even in duopoly. Clearly both models cannot be correct. Is their truth an empirical question, as recent work suggests?' This paper attempts to decide on theoretical grounds. No attempt to decide among Bertrand, Cournot, and their more modern competitors can be based on mathematical correctness. Economic criteria must guide the decision. Oligopoly models are examples of what game theorists call Nash equilibrium. In them, every firm maximizes profits given the of all other firms. The mathematics does not care whether actions are defined to be prices (Bertrand), quantities (Cournot), or any other variables. Yet these distinctions are crucial to the economics of the situation. The notion of Nash equilibrium already entails one economic condition-individual rationality. This paper will determine the correct definition of by imposing a further economic conditionconsistency of conjectures.2 The precise sense in which conjectures are to be consistent is this; the conjectural variation and the reaction function will be equated. The conjectural variation is the firm's conjecture about other firms' behavior. In Cournot, for example, each firm conjectures that all other firms' quantities are constant. The reaction function is the firm's actual behavior. It is the solution to the profit-maximizing problem, and tells what the firm will do as a function of all other firms' actions. Clearly, what the firm conjectures affects how it reacts. This paper will search for cases where conjectures and reactions are the samewhere each firm's conjectures about other firms' reactions are perfectly correct, locally.3 Every notion of Nash equilibrium has the feature that, in equilibrium, each firm's beliefs about the level of all other firms' are confirmed. For example, in Cournot duopoly, each firm's equilibrium quantity is that one which induces the other firm to produce its equilibrium quantity. The firms are right in their beliefs, in Fellner's famous remark, but right for the wrong reason. That is, it is not actually true, as conjectured by the firm, that the other firm's quantity is a constant. The other firm's quantity depends nontrivially on ours-the reaction function does not have zero slope, although the conjecture does. This paper will find Nash equilibrium notions in which firms are right for

New evidence shows that the commonly-held assumption that the 1973-74 oil price increase directly affected US and world inflation and subsequent recession is consistent with the empirical data. An extended Lucas-Varro real-income equation applied to the US, United Kingdom, Canada, France, Germany, Italy, Japan, and the Netherlands gives mixed results, partly because of price control and decontrol programs. Simulation experiments on the price-control variable using US data finds strong effects. Further studies can be made when consistent international data is available for the 1979-80 period. 18 references, 4 figures, 3 tables. (DCK)

Almost all of the serious economic work on savings decisions within the past decade has relied on some variant of the life cycle hypothesis in which savings arise out of individual choices of an optimum lifetime consumption path. This paper reexamines the incidence and welfare consequences of capital income taxes within a realistic life cycle model. The results suggest that the elimination of capital income taxation would have very substantial economic effects. For example, a complete shift to consumption taxation might raise steady-state output by as much as 18 percent, and consumption by 16 percent. The long-run welfare gain from such a shift would for plausible parameter values exceed $150 billion annually. Stated somewhat differently, shifting to consumption taxation would raise the lifetime utility of the representative consumer by the equivalent of about six years' income in the new steady state. These estimates dwarf estimates of the static welfare cost of taxation, and significantly exceed even extreme previous estimates of the dynamic loss. This study departs from earlier analyses of the effects of taxes on capital income in several respects. Probably the most important difference between this treatment and most preceding ones lies in the assumptions about the interest elasticity of saving. It is shown below that the common two-period formulation of saving decisions yields quite misleading results. A more realistic model of life cycle savings demonstrates that, for a wide variety of plausible parameter values, savings are very interest elastic. This implies that shifting away from capital income taxation would significantly increase capital formation, making possible long-run increases in consumption. Many studies of the welfare effects of capital income taxation have ignored the general equilibrium effects of increased capital formation. In an economy with life cycle savings, there is no presumption that the undistorted growth path corresponds to any sort of social optimum. As Peter Diamond has shown, life cycle savings can lead to a steady-state capital intensity either greater or less than the Golden Rule level. More generally, it is clear that there is no reason to believe that a life cycle economy will maximize any particular intertemporal social welfare function. A fundamental tenet of welfare evaluation is that preexisting distortions must be considered in evaluating the consequences of tax changes. The results presented in this paper take explicit account of the nonoptimal character of the no-tax steady state. This explains in large part why such a sizeable welfare effect of capital taxes is found. In an economy far from the Golden Rule level of capital intensity, there are substantial gains in steady-state consumption achievable through increased capital formation. Section I of the paper examines the aggregate savings function in a continuous-time life cycle framework. The second section clarifies the differences between wage and consumption taxes. An aggregate production function is added to complete the model in the third section. The effects of changes in capital taxes on both steady-state incidence and welfare are considered within a general equilibrium framework. The final section of the paper discusses some implications of the results and suggests areas which appear to warrant further study. *Assistant professor of economics, Massachusetts Institute of Technology, and research analyst, National Bureau of Economic Research. I am grateful to Alan Auerbach, Martin Feldstein, Laurence Kotlikoff, to the participants in the NBER Workshop on Business Taxation, and to the Harvard Public Finance Seminar for useful discussions. James Poterba and James Buchal performed the numerical calculations.

The standard analysis of firm-specific human capital argues that the cost of and the return to the investment will be shared by the worker and the employer. By sharing the investment, the parties reduce the likelihood of either party unilaterally terminating the employment relationship and imposing on the other party a loss in his return. This argument, originally advanced by Gary Becker (pp. 10-15), has become accepted almost as a theorem.' The sharing decision is particularly important in determining the shape of the wage profile and the behavior of labor turnover in the labor market. The exact decision process involved in determining the sharing arrangement, however, appears to have received little attention in the literature.2 In this paper, a formal statement of the sharing model is presented. The model allows a systematic analysis of the incentive to share the investment in firm-specific human capital. My analysis reveals that whether or not the investment is shared depends on the existence in the post-investment years of costs of evaluating and agreeing on the worker's productivities in the firm and elsewhere. This paper and two others (my 1979 article and my article with Ben Yu) demonstrate the usefulness of the sharing model. My 1979 article develops and tests the hypothesis that the ubiquitous bonus payments in Japan can be understood as payments for the returns to firm-specific human capital. The paper with Yu extends the analysis of firm-specific human capital by considering the incentives for introducing wage flexibility in employment contracts. Various dismissal and quitting rules are also compared in that paper. In this paper, I use the model in its simplest form to offer a formalization of Becker's hypothesis concerning the sharing of the gains and costs of specific training. In so doing, I demonstrate that the Becker hypothesis can be viewed as a direct application of the Coase Theorem. Implications of the model for the experience-earnings profile are also discussed. This paper also clears up some confusion in the literature about the validity of the sharing hypothesis (see fn. 1).

One of the perennial problems of business cyde theory has been the search for a convincing empirical description and theoretical explanation of the behaviour of wage rates during fluctuations in output and employment. Even the empirical question is hardly settled, although the most recent careful study (Geary and Kennan) confirms the prevailing view that real-wage movements are more or less independent of the business cycle. There are really two subquestions here. The first presumes that nominal wage stickiness is the main route by which nominal disturbances have real macroeconomic effects, and asks why nominal wages should be sticky. The second focuses on real wages, and asks why fluctuations in the demand for labour should so often lead to large changes in employment and small, unsystematic, changes in the real wage.