Otto A. Davis

Bio: Otto A. Davis is an academic researcher from Carnegie Mellon University. The author has contributed to research in topics: Majority rule & Externality. The author has an hindex of 16, co-authored 27 publications receiving 2573 citations. Previous affiliations of Otto A. Davis include Carnegie Institution for Science.

An Expository Development of a Mathematical Model of the Electoral Process

Abstract: The fundamental process of politics is the aggregation of citizens' preferences into a collective—a social—choice. We develop, interpret, and explain non-technically in this expository essay the definitions, assumptions, and theorems of a mathematical model of one aggregative mechanism—the electoral process. This mechanism is conceptualized here as a multidimensional model of spatial competition in which competition consists of candidates affecting turnout and the electorate's perception of each candidate's positions, and in which the social choice is a policy package which the victorious candidate advocates.This approach, inaugurated by Downs's An Economic Theory of Democracy, and falling under the general rubric “spatial models of party competition,” has been scrutinized, criticized, and reformulated. To clarify the accomplishments of this formulation we identify and discuss in section 2 the general democratic problem of ascertaining a social preference. We review critically in section 3 the definitions and assumptions of our model. We consider in sections 4 and 5 the logic of a competitive electoral equilibrium. We assume in section 4 that the electorate's preferences can be summarized and represented by a single function; the analysis in section 5 pertains to competition between two organizational structures or two opposed ideologies (i.e., when two functions are required to summarize and represent the electorate's preference). Finally, we suggest in section 6 a conceptualization of electoral processes which facilitates extending and empirically testing our model.

A Theory of the Budgetary Process

Abstract: There are striking regularities in the budgetary process. The evidence from over half of the non-defense agencies indicates that the behavior of the budgetary process of the United States government results in aggregate decisions similar to those produced by a set of simple decision rules that are linear and temporally stable. For the agencies considered, certain equations are specified and compared with data composed of agency requests (through the Bureau of the Budget) and Congressional appropriations from 1947 through 1963. The comparison indicates that these equations summarize accurately aggregate outcomes of the budgetary process for each agency.In the first section of the paper we present an analytic summary of the federal budgetary process, and we explain why basic features of the process lead us to believe that it can be represented by simple models which are stable over periods of time, linear, and stochastic. In the second section we propose and discuss the alternative specifications for the agency-Budget Bureau and Congressional decision equations. The empirical results are presented in section three. In section four we provide evidence on deviant cases, discuss predictions, and future work to explore some of the problems indicated by this kind of analysis. An appendix contains informal definitions and a discussion of the statistical terminology used in the paper.

Social preference orderings and majority rule

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An Elementary Political and Economic Theory of the Expenditures of Local Governments

Abstract: It seems clear that problems in the field of public finance contain both political and economic elements. Yet, political scientists do not seem to have devoted a major part of their research efforts to the area, and economists traditionally have overlooked the political aspects of the problems.' This paper proposes a particular "political" theory of the expenditures of local governments with the aid of some of the traditional tools of economic analysis, and examines some data referring to the governments of the counties of Pennsylvania in light of the proposed theory. It should be admitted at the outset, however, that the model developed herein is overly simple and, perhaps, naive. Yet, the authors believe that it has explanatory power, despite the fact that it requires the usual economic assumption of full knowledge, and that it represents a step in a desirable direction. Although the conceptual possibility of subjecting the model to a "direct test" is clearly evident, available data do not permit such a test and a sympathetic interpretation of the empirical results requires the admission of additional and rather strict assumptions. Hence, the empirical results do not constitute a convincing test of the major implication but merely serve to indicate that this theory, even when augmented with additional assumptions, seems to add explanatory potential to the standard models.

Externalities, Welfare, and the Theory of Games

Abstract: T HAS traditionally been argued that, if firms create external economies and diseconomies, the proper role of a welfare-maximizing government is to constrain the behavior of firms by arranging rates of taxes and subsidies in order to equate private with social benefit. We attempt to establish both the conditions under which this classical policy prescription might work and is needed, and those under which it cannot be expected to work. First, we argue that motivation exists for firms themselves to try to eliminate externalities in production through merger. Second, we attempt to show that technological externalities can be divided neatly into two cases, which we label "separable" and "non-separable," respectively. Third, if merger has not eliminated the externalities, we argue that the classical scheme of per unit taxes and subsidies can be clearly successful in equating private with social benefit only in the separable cases. Fourth, if the externality is non-separable, we argue that it is not clear that the classical prescription can work even at the conceptual level, since problems of uncertainty and the non-existence of equilibrium arise. Finally, we note that this latter possibility poses some difficult problems for policy-makers, and we attempt to outline and explore briefly alternative policy approaches. The analytic approach which we shall employ involves the consideration of two firms in a competitive industry. The traditional or classical approach, on the other hand, often involves an analysis of externality between competitive industries. We choose to depart from this traditional approach for several reasons. First, the firm is an entity which fits more easily into the framework of our analysis. Second, and more fundamental, it is individual decision units-firmswhich react to externalities so that it seems more "natural" to conduct the analysis at that level.2 Furthermore, concentration upon the industry (as opposed to the firm) requires a certain amount of aggregation which tends to mask some of the more important and interesting points at issue. This aggregation is especially misleading with respect to public policy regulation, where the problem is made to appear much more simple than it actually is. Finally, utilization of the firm as the basic analytic unit gives a level of generality 1 This paper was written as part of the project "The Planning and Control of Industrial Operations" under a grant from the Office of Naval Research and the Bureau of Ships at the Graduate School of Industrial Administration, Carnegie Institute of Technology. The authors would like to express their appreciation to Professors W. W. Cooper and J. F. Muth, both of Carnegie Institute of Technology, Dr. R. R. Nelson, Council of Economic Advisers, and Professor James M. Buchanan, University of Virginia, for their very helpful comments and criticisms. 2 Interestingly enough, J. de V. Graaff also considers that externalities are a phenomenon which relates to the firm rather than the industry, and, furthermore, he seems to think this point quite important (see his Theoretical Welfare Economics [Cambridge: Cambridge University Press, 1957], p. 19).

Techniques for Testing the Constancy of Regression Relationships Over Time

Abstract: Methods for studying the stability over time of regression relationships are considered. Recursive residuals, defined to be uncorrelated with zero means and constant variance, are introduced and tests based on the cusum and cusum of squares of recursive residuals are developed. Further techniques based on moving regressions, in which the regression model is fitted from a segment of data which is moved along the series, and on regression models whose coefficients are polynomials in time are studied. The Quandt log-likelihood ratio statistic is considered. Emphasis is placed on the use of graphical methods. The techniques proposed have been embodied in a comprehensive computer program, TIMVAR. Use of the techniques is illustrated by applying them to three sets of data.

The Economics of Schooling: Production and Efficiency in Public Schools.

Abstract: N RECENT YEARS, public and professional interest in schools has been heightened by a spate of reports, many of them critical of current school policy.' These policy documents have added to persistent and long-standing concerns about the cost, effectiveness, and fairness of the current school structure, and have made schooling once again a serious public issue. As in the past, however, any renewed interest in education is likely to be short-lived, doomed to dissipate as frustration over the inability of policy to improve school practice sets in. This frustration about school policy relates directly to knowledge about the educational production process and in turn to underlying research on schools. Although the educational process has been extensively researched, clear policy prescriptions flowing from this research have been difficult to derive.2 There exists, however, a consistency to the research findings that does have an immediate application to school policy: Schools differ dramatically in "quality,"

Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement:

Abstract: This study explored whether and how teachers’ mathematical knowledge for teaching contributes to gains in students’ mathematics achievement. The authors used a linear mixed-model methodology in which first and third graders’ mathematical achievement gains over a year were nested within teachers, who in turn were nested within schools. They found that teachers’ mathematical knowledge was significantly related to student achievement gains in both first and third grades after controlling for key student- and teacher-level covariates. This result, while consonant with findings from the educational production function literature, was obtained via a measure focusing on the specialized mathematical knowledge and skills used in teaching mathematics. This finding provides support for policy initiatives designed to improve students’ mathematics achievement by improving teachers’ mathematical knowledge.

The power to tax : analytical foundations of a fiscal constitution

Abstract: Commenting on his collaboration with Geoffrey Brennan on "The Power to Tax", James M. Buchanan says that the book is "demonstrable proof of the value of genuine research collaboration across national-cultural boundaries." Buchanan goes on to say that "The Power to Tax" is informed by a single idea - the implications of a revenue-maximizing government." Originally published in 1980, "The Power to Tax" was a much-needed answer to the tax revolts sweeping across the United States. It was a much-needed answer as well in the academic circles of tax theory, where orthodox public finance models were clearly inadequate to the needs at hand. The public-choice approach to taxation which Buchanan had earlier elaborated stood in direct opposition to public-finance orthodoxy.What Buchanan and Brennan constructed in "The Power to Tax" was a middle ground between the two. As Brennan writes in the foreword, "The underlying motivating question was simple: Why not borrow the motivational assumptions standard in public-choice theory and put them together with assumptions about policy-maker discretion taken from public-finance orthodoxy?" The result was a controversial book - and a much misunderstood one as well. Looking back twenty years later, Brennan feels confirmed in the rightness of the theories he and Buchanan espoused, particularly in their unity with the public-choice tradition: "The insistence on motivational symmetry is a characteristic feature of the public choice approach, and it is in this dimension that "The Power to Tax" and the orthodox public-finance approach diverge."