Knowledge that Transforms

An article by Michael D. Intriligator entitled Embodied Technical Change and Productivity in the United States 1929-1958 appeared in the February 1965 issue of this REVIEW. To judge the importance of embodied and disembodied technical progress, Intriligator computed 40 correlations of gross national product, excluding GNP originating in government and housing, with capital and labor input. All 40 regressions resulted from combining four alternative measures of labor input, three of them mine, with five alternative capital series based on different assumptions about embodiment, and two methods of handling trend. To match Intriligator's GNP measure, labor input must exclude all general government employees. The data Intriligator actually used, however, include all government employment: civilian, military, and work relief. The period covered, 19291958, spanned the Great Depression, World War II, and the Korean War, periods in which the share of government employment was fluctuating violently, as well as a postwar period in which most of the employment increase was devoted to government. Intriligator's results consequently seem to have no apparent meaning. An interesting feature of the article is that all 40 regressions Intriligator computed have high correlation coefficients despite his use of irrelevant data; only one is below 0.95 and most are above 0.98. This may give further reason for skepticism about the utility of inferring causation -in this case, degree of embodiment-from minor differences in the goodness of fit of time series.

In recent years, several case studies have been conducted on the operations of individual foreign subsidiaries of United States firms.1 While these are useful, they do not provide a means of comparing the operating characteristics of direct foreign investments as they may relate to the level of development of the countries in which they reside. There also have been some excellent comparative studies.2 These have concentrated upon comparisons of United States controlled enterprises abroad with those controlled either by other expatriate groups or by nationals. Perhaps the only intercountry comparison of the operating characteristics of United States direct foreign investments was that by Anthony Y. C. Koo.3 Koo's analysis utilized data from an Office of Business Economics survey of United States investments in Latin America. Thus it was confined to a group of countries which were all relatively less-developed (as of 1955). Because that survey did not provide country data on an industry sector basis, Koo was unable to examine for country differences within industry sectors. The purpose of this article is to partially close this gap. Our objective is to explore the question: Are the performance characteristics of direct foreign investments within industry sectors significantly influenced by the level of development of the country or region which harbor those investments? To examine this question comprehensively, it would be useful to have time series data on a large cross section of countries and several industry sectors. Data should be designed to reflect the economic contribution of investments in various sectors. We could then evaluate the extent to which there may be inherent difficulties faced by lessdeveloped countries difficulties which restrain them from fully realizing the potential contributions of direct foreign investment. To evaluate and compare the economic contribution of various sectors to the host country, it would be useful to know the effects of investments upon:

Aggregate measures of output per man or output per man-hour, such as those regularly published in the Economic Report of the President, are frequently used as indicators of changes in aggregate productivity. These measures reflect both changes in output per man (or man-hour) in individual sectors of the economy and sectoral shifts in the composition of output. While this dual nature has been long recognized, it has not received sufficient attention.' The causative forces for productivity growth in a particular sector are entirely different from those accounting for shifts among sectors.2 Table 1 presents a measure of composition effects which allows for the separate analysis of sectoral productivity change and sectoral shifts. The measure which is used here has been discussed at length elsewhere.3 Briefly the procedure used derives from the following propositions: (1) Aggregate measures of output per man are derived by dividing aggregate output by an aggregate input measure, be it the total number of men or man-hours. (2) The output per man measure thus derived is an implicitly weighted average of output per man in all sectors of the economy, number of men being used as weights.4 As a result the aggregate input measure is equally weighted while the aggregate productivity measure is differentially weighted. (3) Because there is no justification for differentially weighting productivity that would not apply to the input measure, it is less arbitrary to isolate the weighting factor as a third component of output, which might be termed the effect of composition.5 Consistency is thus afforded in the treatment of aggregate input and productivity measures, and greater emphasis is placed on sectoral shifts as a source of growth in output.

T HE effective tax rate on individual returns (to be denoted etr) remained approximately constant at 23.4 per cent from 1955 to 1962, while taxable income increased more than 50 per cent. Since the individual income tax structure is progressive, this seems at first glance to be a strange result. Explanations which exist in the literature allude to the possibility that shifting between types of returns has occurred, that the pattern of deductions and exemptions has changed over time, and that the tax rate of new taxpayers has been less than the existing average. The objectives of this paper are to evaluate these arguments and to analyse in detail the nature of the etr constancy. The first problem in analysing the etr is to decide whether or not the constancy is in fact a surprising result. That is, although almost everyone would be willing to predict a larger etr as a result of a taxable income increase of 50 per cent, most would be hard pressed to predict the magnitude of the increase. Yet the constancy can hardly be considered a curiosum if the etr is, in general, very insensitive to taxable income growth. In fact it should be realized that under certain general conditions an increase in the taxable income of every taxpayer will result in a decrease in the etr. Assume first that only incomes in the lowest tax bracket increase, and that no income increases sufficiently to move it to a higher tax bracket. Then the overall etr will decrease since the lowest bracket rate is weighted relatively more heavily. But clearly a reduction in the etr may result without such extreme assumptions. What is required is that taxable income in low brackets grows sufficiently rapidly (relative to taxable income in high brackets) to enable the effect of increased densities of returns with marginal tax rates less than the average, to offset the effect of higher rates on certain incomes. Since marginal rates in the two lowest brackets are less than 23.4 per cent, rapid taxable income growth at these income levels will tend to prevent the etr from rising, and may in fact even cause it to decline.1 Further, the etr may be reduced even without an increase in the density of returns with marginal rates less than the average. Suppose, for example, that a joint return taxable at $5,000 in 1955 increases to $9,000 by 1962, thus decreasing the density of returns with marginal rates below the aggregate etr, and increasing the density of those with marginal rates above. But the growth from $5,000 to $9,000 consists of an increase in income of $3,000 taxable at 22 per cent and $1,000 taxable at 26 per cent which is equivalent to adding $4,000 at 23 per cent, and hence the aggregate etr of 23.4 per cent will be reduced. Similarly, the average and not the marginal rate on a new return is the relevant factor in determining whether or not the aggregate etr will decline when the return becomes taxable. For example a new return with a marginal tax rate of 26 per cent will also involve income taxable at 20 and 22 per cent, and provided the weighted average of the rates is less than the aggregate etr, the latter will fall. The extent to which taxable income growth diverges from proportionality (across individuals) is therefore of great interest. There are three major reasons for expecting taxable income growth to be nonproportional. First, proportional growth of adjusted gross income (to be denoted AGI) is probably a more realistic assumption than proportional growth of taxable income.2 Second, the annual distribution of new taxpayers probably differs from the distribution of existing taxpayers. Third, the growth in deductions and exemptions differs for various income levels. As discussed below all

Bierwag and Grove [ 1 ] have recently presented an interesting model of the term structure of interest rates which is analytically more appealing than the Meiselman model [5]. In particular, they are able to dispense with the assumption of identical singlevalued expectations and show that individual wealth holders seeking to maximize utility will determine an equilibrium forward rate which is a weighted average of the individual predicted rates. The original Meiselman model is incorporated into this model as a special case. Tests of these new models give good results for the United States using the Durand data [3] but for Britain, using the Grant data [4], the results are generally very poor. This note shows that an alternative set of annual British data, covering yields on government securities for 1933 to 1963, gives results which compare favorably with those for the United States and it is not necessary to conclude, as do Bierwag and Grove, that the expectations mechanism is different in the United Kingdom. The improved results also illustrate the point, elaborated in [2], that the method of yield estimation is the critical factor in tests employing forward interest rates derived from an estimated yield structure. The theoretical model of the term structure developed by Bierwag and Grove shows how a given investment fund is allocated among short and long term bonds given the investor's utility function and the first two moments of his probability distribution of expected interest rates.' The market equilibrium forward rate is then shown to be a weighted average of individual predicted rates. In order to make the model operational, empirical specifications for the formation of interest rate expectations are required. These specifications are of two types: a traditional adaptive expectations function and a Meiselman type adaptive function.2 The relevant equations are specified for each type before the empirical results of the British test are reported.3

can take all the Sj and try to minimize the variance of vj via factor analysis. We could then find S and also see which Sj was most closely correlated with S. Unfortunately this technique requires that the Sj does not have common measurement error. Since none of the Sj are completely independent of all others (some common source of data is used), common error can creep in. In principle, if one data sourcebut not another -gave answers unacceptable in terms of the a priori considerations dictated by economics, we could eliminate the series. In the present instance, the only possibility would be the significance of NTW1 in the Sggc equations but not in the SOBi}B forms. The differences in cyclical behavior between series are disturbing. But none of the responses violate all saving theories especially since the more recent theoretical innovations, such as permanent income and the ratchet effect define saving to include purchases net of depreciation. Finally the relative quality of the data could be judged by a detailed examination of the primary data sources and subsequent manipulations. This cannot be done now since the last time the SEC and the OBE published detailed descriptions of their sources and manipulations was more than a decade ago and those descriptions in [3, 5] are out of date. Besides, the number of primary data sources used is quite large and diverse. Only a group of individuals familiar with the separate parts could hope to do a competent study. The conclusion, thus, is quite pessimistic. For the saving function, one of the most basic elements of macro-economics, the dynamic and cyclical characterization depends upon our choice of measurement of a given concept and we do not know which measurement is correct.