As maintained by J. M. Clark the amplitude of the investment cycle is larger and that of the consumption cycle smaller than that of the income cycle, provided only the consumption constant is larger than zero. On the other hand, it is true that acceleration is neither a necessary nor a sufficient condition for magnification: not a necessary condition since (4) is independent of the investment function; not a sufficient condition since, for co = o, magnification is absent regardless of the investment function and even if Baumol's equation (3) were valid and his conditions for magnification were satisfied.

expand investment as one in which underlying investment opportunities are impaired. If underlying investment opportunities are defined in relation to the natural rate of growth, this situation would have to be described as one in which the incentive to exploit investment opportunities is reduced. This seems quite as reasonable a use of words, at least if this type of situation is regarded as the exception rather than the rule.

THE purpose of this paper is to analyze the formal structure of the matrix as an accounting tool (I to 7), to review actual inputoutput matrices under the aspect of their formal structure (8), and finally to construct an income-product matrix (g to I 2 ). i. A matrix, as used in macro-accounting, is a form of presentation of accounting material. It is distinguished from other forms of presentation mainly by four technical features: economy in figures, consolidation of interaccount flows, absence of narrations, and specific grouping of the accounting material. The economy in figures is obtained by making one figure serve two purposes simultaneously. According to the direction in which it is read, either vertically or horizontally, a figure is either a debit entry or a credit entry. This feature has the advantage that the number of figures required to communicate a given volume of information is in a matrix roughly one-half of that required in any other form of accounting statement. On the other hand, difficulties arise if the volume of information becomes large. The usual device of making statements manageable in size, which is to relegate part of the information to subsidiary schedules, is not available in the case of a matrix, because, in consequence of the double purpose served by each figure, figures cannot be taken out of the context within the matrix. A matrix grows therefore in direct proportion to the volume of information and, after a certain point, becomes an unwieldy instrument. The second feature is the necessity of consolidating inter-account flows. Transactions affecting any two accounts have to be contracted into two figures, because the framework of a matrix has only two places available for the record of flows affecting two accounts. One is the place of intersection of the row representing the credit entries to the first account with the column representing the debit entries to the second account; in this place, the flows from the first to the second account are recorded. The other place is the intersection of the row of the second account with the column of the first account, which is the place for the flows from the second to the first account. The matrix thus allows an expression of the direction in which transactions flow between any two accounts. But no more. If the transactions between two accounts are for instance composed of a number of heterogeneous flows and that occurs quite regularly in macro-accounting the social accountant faces an inconvenient choice. One alternative is to consolidate different transactions among the same transactors. This entails a loss of information or even of meaning, though the macro-accountant may help himself to some extent by cumbersome devices such as double rows 1 or footnotes. The other alternative is to split one transactor into as many accounts as different intertransactor-relations are to be recorded. This entails a loss of institutional or other transactor unity. In any case, the number of meaningful flows between two transactors which can be shown in a matrix is technically limited by the number of available accounts. The third feature of a matrix is the absence of what accountants call narration, that is a short explanation of the meaning of an entry. An economy in text is thus added to the economy in figures, making the matrix a still more concise form of presentation. Without the guidance of narrations, the reader of a matrix can derive the meaning of an entry solely from the captions of the row and column at whose intersection the figure stands. In this way, captions in a matrix are charged with two functions. They have to describe not only the account as a point of reference, but also the kind of transactions entered in the account. To call a personal account by the name of the transactor, or the impersonal account by the subject-matter assembled in it, is not sufficient. A way must also be found to describe the transactions entered in the account; otherwise

This paper tests how a major cap-and-trade program, known as the NOx budget trading program (NBP), affected labor markets in the manufacturing sector. The cap-and-trade program dramatically decreased levels of NOx emissions and added substantial costs to regulated firms. Using a triple-differences approach, I examine how labor markets adjusted in manufacturing industries that were exposed to the program. I find that overall employment in the manufacturing sector dropped by 1.3%, with energy-intensive industries losing up to 4.8%. Employment declines are shown to have occurred primarily through decreased hiring rates rather than increased separation rates, thus mitigating the impact on incumbent workers. Young workers experienced the largest employment declines, and earnings of newly hired workers fell after the regulation began.

This paper analyzes how the implicit difference in time horizons between refugees and economic immigrants affects subsequent human capital investments and wage assimilation. The analysis uses the 1980 and 1990 Integrated Public Use Samples of the Census to study labor market outcomes of immigrants who arrived in the United States from 1975 to 1980. I find that in 1980 refugee immigrants in this cohort earned 6% less and worked 14% fewer hours than economic immigrants. Both had approximately the same level of English skills. The two immigrant groups had made substantial gains by 1990; however, refugees had made greater gains. In fact, the labor market outcomes of refugee immigrants surpassed those of economic immigrants. In 1990, refugees from the 1975-1980 arrival cohort earned 20% more, worked 4% more hours, and improved their English skills by 11% relative to economic immigrants. The higher rates of human capital accumulation for refugee immigrants contribute to these findings.

A “grid” bootstrap method is proposed for confidence-interval construction, which has improved performance over conventional bootstrap methods when the sampling distribution depends upon the parameter of interest. The basic idea is to calculate the bootstrap distribution over a grid of values of the parameter of interest and form the confidence interval by the no-rejection principle. Our primary motivation is given by autoregressive models, where it is known that conventional bootstrap methods fail to provide correct first-order asymptotic coverage when an autoregressive root is close to unity. In contrast, the grid bootstrap is first-order correct globally in the parameter space. Simulation results verify these insights, suggesting that the grid bootstrap provides an important improvement over conventional methods. Gauss code that calculates the grid bootstrap intervals-and replicates the empirical work reported in this paper'is available from the author's Web page at www.ssc.wisc.edu˜bhansen

Willard F. Mueller and Frederick E. Geithman (1991) test the competing free-rider (efficiency) and market-power explanations of certain vertical restraints once used by the Sealy mattress company and declared illegal after 1980. They estimate that eliminating the restraints increased sales and argue that this supports only the market-power explanation. However, Mueller and Geithman overlook the rise in Sealy's profits that occurred after 1980, a fact which renders their test inconclusive.

It sometimes happens that the unobservable state vector of a linear dynamic model expressed in the state space is subject to known restrictions. Incorporation of this information into the Kalman filter procedure will increase the efficiency of estimation. It is shown that a simple augmentation of the measurement equation constrains the estimated state vector to obey the restrictions. The method applies whether the restrictions are time-invariant, time-varying, linear, or nonlinear.

The labor and entrepreneurial components of reported physician net income are separated in an analysis of input and output market performance. A wage equation, corrected for selectivity bias, is estimated for employee physicians and the results indicate that the performance of the labor market for primary care physicians is consistent with competitive theory. The parameters are used to predict opportunity wage rates for self-employed physicians. Differences between net income per hour and the predictions indicate that 16 percent of net income from practice is attributable to entrepreneurship. Evidence of negative selectivity into employee status is also found.