Knowledge that Transforms

In a recent issue of this journal, Professor Norman Kaplan discusses the retardation in the rate of growth of output in the Soviet Union during the last decade. Assuming a Cobb-Douglas production function he concludes that is established independently of the capital share that the rate of increase of factor productivity for industry declines between 1951-1958 and 1958-1963. In his model this conclusion holds not only for industry, but for every other sector as well and for the economy as a whole. In using the Cobb-Douglas function, Kaplan implicitly assumes that the elasticity of substitution between the factors of production is unity. There is some evidence, however, that the elasticity of substitution is less than unity in many Western countries and a recent study by Weitzman [8] suggests a similar result for the Soviet Union. It is the purpose of this paper to examine the sensitivity of Kaplan's results to variations in the elasticity of substitution. In the model I propose, bounds will be derived on the elasticity of substitution consistent with either of two extreme assumptions concerning the cause of the retardation in output growth. These assumptions are that the decline is entirely due to a decline in technological progress or that the decline is entirely due to a decline in the rate of growth of combined factor inputs. It is not my purpose to get very involved in the question of data reliability or consistency. Rather, I take as a point of departure the data recently compiled in Kaplan [4] which I believe are relatively reliable. His results for output are presented in table 1. For national and nonagricultural product and for each sector except services, the average annual rate of growth in 1958-1963 evidently is less than in 1950-1958 or 1953-1958. Comparing the periods 1953-1958 and 1958-1963, we find the average annual rate of output increase declined 30 per cent i-n industry, 25 per cent in transport and communications, and 46 per cent in construction. This retardation assumes more significance when it is noted that these are the very sectors the Soviets have counted on to lead their economic development.

Joe S. Bain, Changes in Concentration in Manufacturing Industries in the United States, 1954-1966: Trends and Relationships to the Levels of 1954 Concentration, The Review of Economics and Statistics, Vol. 52, No. 4 (Nov., 1970), pp. 411-416

,3, of course, is the estimate of _qTY in the logarithmic form of (2). This technique characteristically yields high estimates of qTy. For example, Soltow [7] and Groves and Kahn [3] both estimated that for Wisconsin during the 1933-1951 period of constant (quite progressive) state tax rates, rjTY was at least 1.75. Harris [4] estimated elasticities of about 1.22.4 for different states by applying constant state tax rates to distributions of federal adjusted gross income by states, and derived an overall income-elasticity of 1.8 for aggregate state income tax revenues. In an earlier study [6], I used dummy-variable techniques to estimate elasticities of 1.4-2.2 for a selected group of states. These estimates of state income-tax elasticities have not gone unnoticed by public officials. When Maryland adopted a new income-tax law in 1967, the State's Board of Revenue Estimates issued a set of revenue forecasts that showed an annual growth rate of approximately 15 per cent, compared to a growth rate of about 10 per cent in aggregate personal income. The implicit elasticity estimate of 1.5 was well within the range of estimates made for Maryland and other states with similar tax laws. Experience with the tax in calendar years 19671969, however, has shown the actual incomeelasticity of revenues to be much closer to 1.0, although actual collections appear to be very sensitive to the rate of price inflation and variations in collections procedures. These observations underlie the model presented below.

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.