Knowledge that Transforms

For more than three decades, economic columnist Joseph A. Livingston has canvassed a panel of economists twice a year, eliciting their six-month and twelve-month forecasts for more than a dozen key variables. This study analyzes whether experts' predictions are unbiased, and whether complete use was made of all relevant, known information (unbiasedness and completeness being necessary conditions for fully rational expectations). Little bias was found in either half-year or full-year predictions, but extensive underutilization of information-particularly data on monetary growth-occurred. To prophecy is extremely difficult-especially with respect to future. Chinese proverb Do ECONOMISTS' EXPECTATIONS regarding key price and nonprice variables utilize all known, relevant information, in an unbiased, efficient manner? This is a worthy subject for research, for several reasons. Properties of experts' predictions likely form an upper bound for those of laymen. Further, as John Muth [14] has noted, the character of dynamic processes is typically very sensitive to way expectations are influenced by actual course of (p. 316); hence, we need to know precisely how events do affect expectations. Finally, common practice of replacing a variable's (generally unobserved) expectation with a proxy based on its past values will be unbiased (and will not cause bias in other

[The purpose of this paper is to provide a method for characterizing efficient allocation processes and efficient allocations for a large class of environments in which asymmetric information is an important factor. This method is based on a rigorous application of statistical decision theory and makes explicit both the information available to agents ex ante and the way in which information is transmitted during any multistage allocation process.]

This paper presents a precise characterization of the bias of least squares in two limited dependent variable models, the Tobit model and the truncated regression model. For the cases considered, the method of moments can be used to correct the bias of OLS. For more general cases, the results provide approximations which appear to be relatively robust. 13, and o, . In this paper we present a precise characterization of that bias for the particular case in which xt, as well as -,, is normally distributed. We also show that the bias of the OLS slope estimator can be corrected by dividing each estimate by the sample proportion of nonlimit observations. Other structural parameters can be consistently estimated in a similar fashion. We present some evidence on the effect of nonnormality with respect to the predictions obtained in the normal model. The case in which the sample contains only nonlimit observation (the truncated regression model) is considered elsewhere (Olsen (7)). We analyze the relationship between his results and ours, and derive some predictions of the normal model with respect to the seriousness of truncation bias.

[This paper investigates the distribution of the least squares estimator of the coefficient α in the model @c"t = @a@c"t -"1 + @?"t where the @?"t where the @?"t are independently distributed N (O, @s extasciicircum2). The exact finite sample and limiting distributions are calculated when α ≥ 1 and finite sample distributions when α extless 1. These distributions are used to compute the power functions of tests of the random walk hypothesis α = 1 as well as the hypotheses.]

modities (such as various consumer goods and labor), M fixed factors (such as land, natural resources and various types of fixed capital), and a government which taxes commodities and fixed factors in order to finance various govern- ment expenditures. It is well known2 that if the government can raise its required revenue by taxing the fixed factors alone, then the resulting allocation of resources is Pareto optimal-no single household's utility or real income can be increased without decreasing the utility of some other household. Suppose we are at an initial equilibrium where government revenue is being raised by taxing the fixed factors alone. Then the resulting equilibrium can be rationalized by maximizing a certain weighted sum of utility functions subject to various feasibility constraints. Now think of the government replacing the taxes on fixed factors with distortionary commodity taxes. In Section 3, we calculate the second order directional derivative of the above weighted sum of utility functions with respect to any feasible direction of tax change, evaluated at the initial equilibrium which is Pareto optimal. Of course, the first order directional derivatives of the weighted sum of utility functions with respect to feasible directions of tax change are zero evaluated at this initial equilibrium. We obtain a measure of economic due to tax distortions which is virtually identical to that of Boiteux (3, p. 113) and which bears a resemblance to the dead loss of Hotelling (22, p. 254), the consumer's surplus measures of Hicks (19; 20, pp. 330-3), and the deadweight loss measure of Harberger (16, p. 61; 17, p. 788). In Section 4, we calculate a measure of welfare based on Debreu's (4, 5) coefficient of resource utilization (which is a modification of a measure of due to Allais (1, 2)) and we show that under certain conditions, the Hotelling,

Conditions which imply the existence of strict rational expectations equilibria for most static pure exchange economies where prices convey information about the state of the world are analyzed. Information is aggregated and transmitted by prices because agents have different initial information and maximize the conditional expectation of state-dependent utility functions. Major results state that if, with probability one, agents' characteristics do not vary too much as the state of the world varies, then, generically, there exist equilibrium price functions which reveal all initial information. More precisely, if the support of the image measure is contained in a compact C1 manifold (satisfying some technical conditions) which is of sufficiently low dimension relative to the number of commodities, then existence of completely revealing equilibria is generic. Any economy satisfying these assumptions can be approximated by a sequence of economies which also obey these assumptions and have completely revealing equilibrium price functions. Slight perturbations do not destroy the existence property.

[A study is made of a competitive trading process in which a specific price-maker calls prices periodically under the obligation of supporting these prices by trading for his own account to satisfy excess demand. Specifically, the paper considers price formation in an organized securities exchange using the specialist system to facilitate trading. Following procedures developed in an earlier study, characteristics of the price-maker's optimal behavior are derived. These characteristics are used to obtain properties of stationary distributions of market prices and to compare the operation of the specialist system with an alternative market clearing system.]

Econometric analysis of time series data is frequently preceded by regression on time to remove a trent component in the date. The resulting residuals are then treated as a stationary series to which procedures requiring stationarity, such as spectral analysis, can be applied. The objective is often to investigate the dynamics of transitory movements in the systems, for example, in econometric models of the business cycle. When the data does consist of a deterministic function of time plus a stationary error then regression residuals will clearly be unbiased estimates of the stationary component. However, if the data is generated by (possibly repeated) summation of a satisfactory and inevitable process then the series cannot be expressed as a deterministic function of time plus a stationary deviation, even though a least squares trend line and the associated residuals can always be calculated for any given finite sample. In a recent paper, Chan, Hayya, and Ord (1977) hereafter CHO) were able to show that a residuals from linear regression of a realization of a random walk (the summation of a purely random series) on time have autocovariances which for given lag are a function of time and thereafter that the residuals are not stationary. Further, CHO established that the expected sample autocovariance function (the expected autocovariances for given lag averaged over the time interval of the sample) is a function of sample size as well as lag and therefore an artifact of the detrending procedure. This function is characterized by CHO in their figure 1 as being effectively linear in lag (although the exact function is a fifth degree polynomial) with the rate of decay from unity at the origin depending inversely on sample size.

Abstract An important purpose in pooling time-series and cross-section data is to control for individual-specific unobservable effects which may be correlated with other explanatory variables, e.g. latent ability in measuring returns to schooling in earnings equations or managerial ability in measuring returns to scale in firm cost functions. Using instrumental variables and the time-invariant characteristics of the latent variable, we derive: 1. (1) a test for the presence of this effect and for the over-identifying restriction we use; 2. (2) necessary and sufficient conditions for identification of all the parameters in the model; and 3. (3) the asymptotically efficient instrumental variables estimator and conditions under which it differs from the within-groups estimator. We calculate efficient estimates of a wage equation from the Michigan income dynamics data which indicate substantial differences from within-groups and Balestra-Nerlove estimates — particularly a significantly higher estimate of the returns to schooling.