Knowledge that Transforms

This paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients. The Kuhn-Tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the Wald test are examined. It is shown, in particular, that these relationships are the same as in the equality constrained case. It is emphasized, however, that their common asymptotic distribution is a mixture of chi-square distributions under the null hypothesis.

THIS PAPER REPRESENTS an attempt to make Aaron and McGuire's [1] approach to incidence operational.2 The tax paid by any individual is interpreted by Aaron and McGuire as the sum of two components. The first is a Lindahl tax equal to the individual's marginal rate of substitution between the public good and income times the amount of the public good provided. The second component is a negative or positive transfer equal to the Lindahl tax minus the tax the individual has actually paid. This second component is used to measure the incidence or redistributional impact of a particular budget program. Empirically, Aaron and McGuire found that the computation of Lindahl taxes is highly sensitive to the choice of individual utility functions. Under certain assumptions that sensitivity is reflected in the value of a coefficient related to the marginal rate of substitution between the public good and income. Maital [16], later on, used three separate identical estimates of this coefficient to reduce the ambiguity in the computation of Lindahl taxes. This paper offers an alternative computational approach to Aaron and McGuire's. The key information on Lindahl tax prices or marginal rates of substitution is obtained from individual demand curves for public goods which are estimated using the median voter model (see [5]). An advantage of this approach over Aaron and McGuire's is that it does not assume separability of the public good and income in taxpayers' preferences. The present approach also permits the study of the incidence of a budget policy on groups defined by socio-demographic characteristics other than income. On the other hand, and because of empirical reasons which will become apparent below, the present approach is useful for the study of incidence at the local level only. Section 1 of the paper restates the measure for the simultaneous incidence of taxes and one public good, henceforth called fiscal incidence, in the context of a formalized political process. This section also discusses some of the theoretical difficulties involved in extending the case with one public good to the multi

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Treble correct when he states that the integral representing consumer surplus is increasing in D(, where Do stands for market radius for the firm. But he incorrect in his speculation that the CV solution under L6schian competition according/v yields an increasingly smaller consumer surplus in the aggregate. Note that the decreasing surplus with decreasing Do created by each one of the individual firms which are increasing in number under free entrv. The aggregate consumer surplus therefore not necessarily greater under spatial monopoly than it under conditions of spatial competition. In fact, it can readily be shown to be increased, not decreased, with an increasing entry under the CV model. To prove our contention consider the average consumer surplus a la W. Holahan [3] which given below by evaluating Treble's integral S in [4, p. 1328] and in turn dividing both sides of the resulting equation by Do:

[We propose a new criterion for equilibria of extensive games, in the spirit of Selten's perfectness criteria. This criterion requires that players' strategies be sequentially rational: Every decision must be part of an optimal strategy for the remainder of the game. This entails specification of players' beliefs concerning how the game has evolved for each information set, including informaiton sets off the equilibrium path. The properties of sequential equilibria are developed; in particular, we study the topological structure of the set of sequential equilibria. The connections with Selten's trembling-hand perfect equilibria are given.]

A fundamental assumption in much of game theory and economics is that all the relevant information for determining the rational play of a game is contained in its structural description. Recent experimental studies of bargaining have demonstrated effects due to information not included in the classical models of games of complete information. The goal of the experiment reported here is to separate these effects into components that can be attributed to the possession of specific information by specific bargainers, and to assess the extent to which the observed behavior can be characterized as equilibrium behavior. The results of the experiment permit us to identify such component effects, in equilibrium, including effects that depend on whether certain information is common knowledge or not. The paper closes with some speculation on the causes of these effects.

The equilibrium growth model is modified and used to explain the cyclical variances of a set of economic time series, the covariances between real output and the other series, and the autocovariance of output. The model is fitted to quarterly data for the post-war U.S. economy. Crucial features of the model are the assumption that more than one time period is required for the construction of new productive capital, and the non-time-separable utility function that admits greater intertemporal substitution of leisure. The fit is surprisingly good in light of the model's simplicity and the small number of free parameters. THAT WINE IS NOT MADE in a day has long been recognized by economists (e.g., Bdhm-Bawerk [6]). But, neither are ships nor factories built in a day. A thesis of this essay is that the assumption of multiple-period construction is crucial for explaining aggregate fluctuations. A general equilibrium model is developed and fitted to U.S. quarterly data for the post-war period. The co-movements of the fluctuations for the fitted model are quantitatively consistent with the corresponding co-movements for U.S. data. In addition, the serial correlations of cyclical output for the model match well with those observed. Our approach integrates growth and business cycle theory. Like standard growth theory, a representative infinitely-lived household is assumed. As fluctuations in employment are central to the business cycle, the stand-in consumer values not only consumption but also leisure. One very important modification to the standard growth model is that multiple periods are required to build new capital goods and only finished capital goods are part of the productive capital stock. Each stage of production requires a period and utilizes resources. Halffinished ships and factories are not part of the productive capital stock. Section 2 contains a short critique of the commonly used investment technologies, and presents evidence that single-period production, even with adjustment costs, is inadequate. The preference-technology-information structure of the model is presented in Section 3. A crucial feature of preferences is the non-time-separable utility function that admits greater intertemporal substitution of leisure. The exogenous stochastic components in the model are shocks to technology and imperfect indicators of productivity. The two technology shocks differ in their persistence.

[A new class of tests for heteroscedasticity in linear models based on the regression quantile statistics of Koenker and Bassett [17] is introduced. In contrast to classical methods based on least-squares residuals, the new tests are robust to departures from Gaussian hypotheses on the underlying error process of the model.]