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Essays on Economic Semantics
Three-Stage Least-Squares and Full Maximum Likelihood Estimates
Games, Gods, and Gambling
Spectral Analysis of Seasonal Adjustment Procedures
This paper discusses one of the uses to which two powerful techniques of modem time series analysis may be put in economics: namely, the study of the precise effects of seasonal adjustment procedures on the characteristics of the series to which they are applied. Since most economic data appearing at intervals of less than a year are to a greater or lesser extent manufactured from more basic time series, the problem of assessing the effects of the manufacturing processes upon the essential characteristics of the raw material to which they are applied is not unimportant. Perhaps the most common type of adjustment applied to raw economic time series is that designed to eliminate so-called seasonal fluctuations. The precise nature of seasonality is not easy to define, but an attempt is made in Section 2.1 below. The techniques employed to study the effects of seasonal adjustment procedures are those of spectral and cross-spectral analysis. In somewhat oversimplified terms the basic idea behind these types of analysis is that a stochastic time series may be decomposed into an infinite number of sine and cosine waves with infinitesimal random amplitudes. Spectral analysis deals with a single time series in terms of its frequency content; cross-spectral analysis deals with the relation between two time series in terms of their respective frequency contents. The two techniques are discussed in both theoretical and practical terms. Spectral analyses have been made for about seventy-five time series of United States employment, unemployment, labor force, and various categories thereof. Cross-spectral analyses have been made of the relations between these series and the corresponding series as seasonally adjusted by the procedures used by the Bureau of Labor Statistics. Two major conclusions regarding the effects of the BLS seasonal adjustment procedures emerge from these analyses. First, these procedures remove far more from the series to which they are applied than can properly be considered as seasonal. Second, if the relation between two seasonally adjusted series in time is compared with the corresponding relation between the original series in time, it is found that there is a distortion due to the process of seasonal adjustment itself. Both defects impair the usefulness of the seasonally adjusted series as indicators of economic conditions, but, of the two, temporal distortion is the more serious defect. Examples of some of these
Contributions to Probability and Statistics. Essays in Honor of Harold Hotelling
On the Economics of Road Congestion
This paper presents a model in which (1) the market demand for urban automobile travel is a function of a time-price as well as a money-price and (2) the market supply is represented by a flow function that is derived from assumed relationships between traffic density and average speed. Two qualitatively different types of traffic congestion are identified. Marginal cost pricing in terms of both time and money taxes is proposed as an efficient and feasible means of controlling both types of traffic congestion. Using the results of existing empirical studies, tax schedules for three types of urban roads are computed. THERE APPEARS to be unanimous agreement that traffic congestion is prevalent in contemporary urban areas and that certain social costs are incurred as a consequence. The more important questions: how to measure these social costs and how to reduce or eliminate them, remain under debate. Arguing from the premise that the essential physical nature of traffic congestion must be clarified before measurement and remedial action are possible, this paper attempts to (1) define traffic congestion in a precise fashion, (2) develop a model consistent with both traditional price theory and this formal notion of congestion, and (3) bring available empirical evidence to bear on the implications of the model. The analysis rests on the proposition that both time costs and dollar operating costs of automobile trips are relevant to the individual decision process. Formally, it is assumed that individuals face time-price parameters as well as dollar-price parameters and that market demand functions for automobile trips can be expressed in terms of these parameters.