[In this paper, I attempt to peek into the "black box" of the firm and explore some very simple models of expectation formation and planning using data on a group of French and German manufacturing firms who report over time on both expectations and their subsequent realizations. Important differences are obtained between the results for French firms and for German firms. For both groups, however, firms' expectations or plans are found to be much more concentrated in the no change category than are the realizations they forecast. Consistent biases in the other categories are found for the German, but not the French firms; for the former the conditional distributions of realizations, given prior expectations or plans, are stable over time, while they are unstable for the latter. Of the simple models dealing with the formation of price and demand expectations, the error-learning model (a form of adaptive expectations) gives the best and most parsimonious explanation of the data. Estimation of a joint error-learning model for price anticipations and production plans suggests that the two processes are nearly independent of one another for both groups. A conditional probability model relating production plans to expectations of future demand, inventory level, or order backlog appraisals and recent changes in demand, explains the data about as well as a mechanical error-learning model, but offers scope for improvement and more economic content. Deviations between prior expectations of demand and realizations in the current period are found to affect the deviations between price expectations and production plans from their respective realizations, except for French firms' price expectations. These and related variables and relationships are further explored in a recursive conditional log-linear probability model which is discussed in a sequel to the paper.]

[This note develops a slightly different formulation of one of the basic results presented in a recent paper by Wallace and Hussain [5] on error components models for disturbances in relationships designed to explain cross-sectional observations over time. In their discussion, Wallace and Hussain derive the inverse of the variance-covariance matrix of the disturbances by trial and error. Unfortunately, their formulation does lead to a "natural" interpretation of the generalized least squares estimates, or of the relationships of these estimates to other estimates in the same way diagonalization of the variance-covariance matrix by means of an appropriate orthogonal transformation does. The characteristic roots of the variance-covariance matrix for the disturbances in a three component model which has been studied by Wallace and Hussain are derived here. It is shown how knowledge of these roots and the characteristic vectors associated with them leads to a form of the inverse matrix which may be more readily interpreted, as well as a number of other useful results, including an interpretation of the poor small sample properties of estimates which incorporate dummy variables for each individual.]

[Availability of data on a large number of individuals, but on each individual only over a very short period of time, has become increasingly common in a number of different fields in economics. Very often we would like to use such data to study behavioral relationships that are dynamic in character, i.e., that contain a distributed lag or other form of autogressive relationship. Since only a few observations are available over time, but a great many observations are available for different individuals at a point in time, it is exceptionally important to make the most efficient use of the data across individuals to estimate that part of the behavioral relationship containing variables that differ substantially from one individual to another, in order that the lesser amount of information over time can be used to best advantage in the estimation of the dynamic part of the relationship studied. As it turns out, the problem is far from simple: obvious devices such as the pooling of all observations and estimation by ordinary least squares, or the introduction of dummy variables for individuals, produce estimates having serious small sample bias. In earlier papers, the author and others have formulated a simple variance components model for the disturbance term in a relationship to be estimated from cross section data over time. This paper presents a series of Monte Carlo studies designed to explore the small sample properties of various types of estimates within this context. Not only is the bias of the obvious methods of estimation mentioned above confirmed, but certain serious deficiencies of the maximum likelihood approach which had been suspected earlier are also confirmed. A two-round estimation procedure is proposed which appears to work well for a wide variety of parameter values.]

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

SUMMARY IN TWO RECENT articles Messrs. Stone and Rowe have proposed an interesting dynamic model of demand.' They have applied this model to a variety of commodities, both durable and perishable. It is not the purpose of this note to criticize the underlying conceptual framework of the Stone-Rowe approach, but merely to point out that in the actual application of their model to durable goods, Stone and Rowe make assumptions which are unduly restrictive. Much of the difficulty lies with the assumption of relations linear in logarithms. When semilogarithmic or strictly linear relations are allowed, it becomes possible to estimate the appropriate depreciation rate rather than to assume its value as is done by Stone and Rowe.

IN RECENT years the Durbin-Watson statistic has been used uncritically to test for serial correlation the of relationships containing lagged endogenous which are estimated by single or simultaneous equations methods. When lagged endogenous are included an equation estimated by ordinary least squares, however, the Durbin-Watson statistic is asymptotically biased towards 2 (the value which it should have if no serial correlation is fact present). is doubtful, therefore, that the statistic should be used either to test for serial correlation the or to provide any indication of the extent of such correlation when the estimated equation contains lagged values of any endogenous variable. The widespread use of the Durbin-Watson statistic inappropriate situations may stem from misinterpretation of a remark one of Durbin's later papers. the original papers setting forth their test, Durbin and Watson stated: It should be emphasized that the tests described this paper apply only to regression models which the independent can be regarded as 'fixed variables'. They do not, therefore, apply to autoregressive schemes and similar models which the lagged values of the dependent variable occur as independent variables [2, p. 159]. a subsequent paper, however, showing that the statistic could be used with some slight modification systems of simultaneous equations, Durbin wrote: In some formulations certain of the x's coincide with lagged values of the y's. The theory becomes much more complicated such cases, and we shall not consider them except to point out that the results obtained later the paper, which are exact for the model specified above, may be expected to hold approximately for models containing lagged dependent variables [1, p. 370]. This later paper discussed the distribution of the Durbin-Watson statistic under the null hypothesis of no serial correlation and did not cover the test's power against alternatives. While the original Durbin and Watson papers showed that the test has high power against Markov alternatives, the asymptotic result, derived from a result obtained by Malinvaud and presented below, indicates that this conclusion does not hold when lagged endogenous are included. a paper which expressions for the asymptotic bias of least squares estimates of regression coefficients various models containing lagged dependent and serially correlated were derived, Griliches commented that in most cases the addition of the lagged dependent variable to the regression will reduce the serial correlation of the residuals and hence increase the Durbin-Watson statistic [3, p. 70]. The asymptotic results were extended to cover the bias the estimated 235