Knowledge that Transforms

PpTO date, the bulk of portfolio theory has evolved on the basis of a single-period model. Those writers who have considered sequential portfolio models, for example Tobin [24] and Mossin [19], have invariably assumed investment yields in the various periods to be stochastically independent. The purpose of this paper is to generalize the capital growth model, apparently originated by Latane [17] and Breiman [6], [7], to the case in which investment returns in one period are not statistically independent of returns in previous periods.' The assumptions employed in the present model are given in section II. Essentially, a distinction between risk due to broad market forces and risk due to individual asset factors, similar to that made by Sharpe [23] and King [16], is made. Furthermore, the no-easymoney condition is assumed to hold and the investor is required to remain solvent with probability 1. The formal model is developed in section III and section IV gives some preliminary results, including conditions for long-run growth and ultimate ruin. In section V, an optimal investment strategy is obtained on the basis of a slightly generalized and weakened version of the innocuous criterion that more is preferred to less in the very long run. The properties of the optimal strategy are discussed in section VI; it is noted that the optimal policy is myopic, that it maximizes the long-run growth rate, and that the optimal mix of assets is independent of wealth. Some concluding comments are given in section VII.

A LTERNATIVE strategies for economic development have frequently invoked the doctrines of balanced and unbalanced growth.' Policy recommendations in favor of balanced or unbalanced growth are based on a priori notions about the relationship between (lack of) balance and the process of development. For balanced-unbalanced growth to become an empirical hypothesis, rather than a doctrine, it has to be formulated in a way that it is given the chance to be proven wrong. An operational formulation involves three steps: balance (or imbalance) is defined in an unambiguous way that renders itself to quantification; an observable relationship between balance and economic development is postulated; this observable relationship is further specified by establishing causality and by determining the flow of causation. The hypothesized observable relationship between balance and economic development is sufficiently clear in the literature. The proponents of the balanced growth theory specify positive association between balance on the one hand and overall growth rate in national income (per capita). The relationship is reversed for the unbalanced growth theorists. The discussion on causality between balance and development is less unequivocal. In general, the flow of causation is supposed to run from balance (or imbalance) to development.2 Two examples will suffice for illustrative purposes. Nurkse [8] [31 advocates balanced growth on the grounds that it increases the reinvestible surplus, it provides inducements to invest, it creates external economies in complementary industries and as a result it leads to higher economic development. On the opposite side of the field Hirschman [4] perceives the causal link between imbalance and development in terms of external economies of vertical type and in terms of decision-making which is induced by disequilibria.3 The operational definition of the concept of balance or imbalance is probably the weakest part in the formulation of the theory. In a recent article Swamy [9] formulated the criterion of balance in terms of the dispersion of sectoral growth rates and he tested the hypothesis by correlating the resulting index with the overall rate of growth for an international cross section and time periods between 1948-1960. In this article we basically employ the same operational framework, data sources and time periods with Swamy. The significant divergence in results is due to the more suitable index of imbalance and the more refined data set that we use. In section I we discuss the different variants of balanced-unbalanced growth and we introduce the appropriate for each measure of dispersion. After a brief description of the data in section II, section III presents the evidence on the relationship between growth rates and indices of imbalance. In section IV the indices of imbalance are related to the level of development, as determined by a country's national income per capita. Finally, we draw the conclusions from our analysis and we compare our results with parallel investigations.

Bharat R. Hazari, J. Krishnamurty, Employment Implications of India's Industrialization: Analysis in an Input Output Framework, The Review of Economics and Statistics, Vol. 52, No. 2 (May, 1970), pp. 181-186

T O measure a nation's wealth, an industry's productive potential or the consumption of a durable stock, we must be able to add machines with different characteristics and different vintages to form an aggregate. Ideally, such a measure would change with machinery deterioration and obsolescence but not with pure price level changes which leave the use of the machinery the same. The aggregation task would be easier if we had information about the nature of depreciation. For example, if depreciation is a constant rate, and that rate remains the same over time, then the aggregate is a simple weighted average of the component machines, the weights being derived from the known depreciation rate. This model is not uncommon, yet its assumptions are clearly restrictive. It would be very useful if there were sufficient empirical evidence pertaining to the nature of depreciation patterns to either confirm or reject such a simple model. It is the intent of this paper to provide some of that evidence. One natural approach to studying decay of capital is to study the in-use cost of machines as they age. Depreciation values could be estimated from changes in rental prices throughout a machine's life. In the absence of welldeveloped rental markets, however, resale values would yield approximations of the remaining value of machinery after a period of use. This paper constructs actual depreciation figures for automobiles from purchase prices, and studies assumptions and hypotheses about the relationship between new and used machinery. In particular, three assumptions are common. First, it is often assumed that depreciation patterns remain fixed over time. For this assumption to be valid, any technological change must be either nonexistent or smooth. There can be no sudden, dramatic innovations, since these would change the nature of depreciation schemes. Similarly, it is often assumed that machinery of the same type depreciates in the same fashion. This assumption will also be studied. The third and most common assumption is that equipment depreciates at a constant rate.' This is a very useful assumption, since it greatly simplifies the relationship between new and used pieces of equipment. These assumptions will be tested for automobiles using figures for nineteen different makes from 1950 to 1969.

T HIS paper is concerned with the effect of schooling and learning on the level of workers' earnings. Individual data obtained from the 1/1000 sample of the 1960 United States Census for the North Central region 1 and information on scholastic achievement obtained from Equality of Educational Opportunity,2 popularly known as the Coleman Report, are used to measure the effect of educational achievement and various other personal characteristics on the earnings of those with twelve or fewer years of schooling. The first section discusses the data and the specification of earnings functions. In the next section it is shown that, for whites, a significant relationship exists between an individual's scholastic achievement and his earnings and that achievement explains more of the variance in earnings than does the number of years in school. The third section presents findings that the effect of education on earnings is less for blacks than for whites and that the black's lower average achievement does not account for the difference in the mean earnings of blacks and whites. The fourth section describes a recursive model of income determination.

R ECENT empirical studies in international trade, by Junz and Rhomberg [10], Kreinin [14] and in a major contribution, by Houthakker and Magee [6], have stressed the importance of different price and income elasticities of demand for exports and imports among countries as determinants of trade patterns. However, questions as to why such differences in elasticities arise remain open. An important component of the problem is whether the price and income elasticities of demand for individual exporters' products vary systematically across customer markets. This paper attempts partially to address the latter issue by examining the elasticities of United States exports of manufactured goods. The major finding is that a relationship exists between the competitiveness of United States manufactured goods exports in various foreign countries and the nature of the customer market. The result has implications, outlined below, for projections of future United States trade balances.

There are two primary questions confronting program planners of educational facilities: 1) At what is the minimum cost per pupil achieved, i.e., what is the of school? 5 2) Ascertaining if economies of exist and the magnitude of such economics, i.e., at what rate does expenditure per pupil decrease as increases? Table 1 provides the results of expenditures per pupil regressed on selected independent variables. Use of the regression equation to find the net relationship between cost and is as follows for the different school sizes: 1) Change in cost from 200 to 500 pupils .0503 (500) + .00001121 (500)2 .0503 (200) + .00001121 (200)2 $12.74. 2) Change in cost from 500 to 1000 students is -$16.74. 3) Change in cost from 1,000 to 1,500 students is -$11.14 per pupil. 4) Change in cost from 1,500 to 2,000 students is $5.53. 5) Change in cost from 2,000 to 2,244 is -$.66 per pupil. In other words, the total net effect of increasing school from 200 to 2,244 students would result in a savings of approximately $47 per pupil. Riew, on the other hand, found the total savings would amount to well over $200 per pupil from a school with 200 to 1,675 students. A possible explanation for such a large discrepancy in the rate of decrease in per pupil expenditures is that Riew excluded transportation costs from his expenditure variable. The results of this analysis regarding the net relationship between current expenditures per pupil and of school provides guidelines regarding the added costs incurred if the optimum size school was not provided. Note that most of the economies had been realized as student numbers approached 1500. 5 DY/DX8 =-.0503 + 2 (.00001121) X8. Setting DY/DX8 equal to zero and solving for X8 yields 2,244 students. TABLE 1. REGRESSION RESULTS OF CURRENT PER PUPIL EXPENDITURES REGRESSED ON SELECTED INDEPENDENT VARIABLES MISSOURI SCHOOL SYSTEMS, 1966

Maurice Wilkinson, European Migration to the United States: An Econometric Analysis of Aggregate Labor Supply and Demand, The Review of Economics and Statistics, Vol. 52, No. 3 (Aug., 1970), pp. 272-279

SOME OF THE FACTORS WHICH INFLUENCE THE COMMUTER'S CHOICE OF MODE ARE EXPLORED BY PROVIDING QUANTITATIVE ESTIMATES OF THE DEGREE OF TRANSIT IMPROVEMENT WHICH WILL BE NECESSARY TO ATTRACT COMMUTERS. THERE IS DEVELOPED AND ESTIMATED A BEHAVIORALLY-ORIENTED MODEL OR MODAL CHOICE. THE TWO MAIN RESULTS WERE: ESTIMATE OF THE VALUE OF TRAVEL TIME TO COMMUTERS (WHICH WAS ESTIMATED AS 42 PER CENT OF THE COMMUTER'S WAGE RATE); AND ESTIMATE OF THE TIME AND COST ELASTICITIES OF CHOICE BETWEEN MODES (WHICH TURNED OUT TO BE RELATIVELY SMALL). UNLESS COMFORT TURNS OUT TO BE A MUCH MORE IMPORTANT FACTOR THAN EITHER TIME OR COST, THE POSSIBILITY FOR ANY SUBSTANTIAL DIVERSION OF AUTO USERS ONTO THE PROPOSED RAPID TRANSIT SYSTEMS DOES NOT APPEAR TO BE VERY GOOD. /AUTHOR/

W ITH the pathbreaking article by Arrow, Al Chenery, Minhas and Solow [1] introducing the constant elasticity of substitution (CES) production function, interest in production theory has multiplied. No longer is the Cobb-Douglas function the workhorse for neoclassical theory; rather, the role of the production function has been examined anew in the theory of the firm, in growth theory, and in the theory of international trade. This re-examination has taken the form (1) of theoretical analysis of the role of the elasticity of substitution, (2) of empirical estimation of the elasticity, and (3) of the introduction of new forms for the production relation, e.g., Zellner and Revankar [14] and Revankar [8]. Unfortunately, knowledge about the appropriate micro-economic or macro-economic production function seems further away now than before 1961, the year of the ACMS article [1]. Nerlove [7, p. 58] reports that even slight variations in the period or concepts tend to produce drastically different estimates of the elasticity [of substitution] and he presents a summary of empirical studies of the CES production function to support his conclusion. In this paper it is first shown that Nerlove's conclusion on the definition of time periods is an inappropriate interpretation of previous estimates (however, part of the difficulty was outside Nerlove's control); that in fact changes in period do not produce significantly different estimates of the elasticity. To demonstrate this contention, estimates of the elasticity from the factor demand equation for labor for two consecutive years are obtained. However, evidence of serial correlation leads to a correction of the labor and wage rate variables for quality variation in the workers over states. Since this correction does not remove the serial correlation, the estimation is then undertaken using the efficient estimation technique of Zellner [12] and the results suggest that use of different time periods does not produce different estimates of the elasticity. Second, the estimates of the elasticity are constrained to be equal for the two years and the efficient estimation techniques are again used with the labor quality correction included. A test on the null hypothesis that the elasticity of substitution equals one for each industry indicates that the elasticity does not in general depart significantly from one. This conclusion from estimates of the labor demand equation supports a similar conclusion of Griliches [3, p. 292] based upon least squares regressions for two-digit manufacturing industries. However, he uses a smaller sample (only 1958 data) than here, and his estimates are biased toward one because labor quality variation was not included in his two-digit industry estimates (he only considers labor quality variation in his estimates for manufacturing as a whole). Third, direct estimates of the CES production function are obtained for each industry using Kmenta's approximation [5]. Again, using efficient estimation and correcting for labor quality differences across states, the elasticity of substitution is not in general significantly different from one. It is incidentally shown that returns to scale can be accepted as being equal to unity for most industries.