Knowledge that Transforms

This paper attempts to shed new light on the extent to which college education brings financial returns. It recognizes the existence of a number of variables that are likely to affect the financial returns that education produces for a given person -particularly the student's ability and motivation, and the quality of his schooling. It attempts to isolate returns to education from returns to these other related variables.

goodness of fit when compared to the results of tests based on the Grant data. The coefficients show no irregularities and the second coefficient in A* has the correct sign although it is not significantly different from zero. The derived a, in Model B are inconsistent with the constraints (0 a. < 1) for which the Meiselman model was developed. Since ai = 0.920 and a2 = -0.402, the weights, Wj, explode to infinity which is of course impossible to rationalize. This highlights the necessity of imposing constraints on the parameters of the estimating equation. The linear restriction 2-r. + 7r2= 0 was rejected at the 1 per cent level but given the inco-nsistency of the estimates of ai it would be incorrect to consider this as evidence in favor of the two poles of opinion model. Comparing the two models, the Meiselman version gives a better fit in the case of model A and A*, but the model based on the traditional expectations function is distinctly better than the Meiselman version in the case of two poles of opinion. This superiority would undoubtedly be enhanced because constrained estimation of the Meiselman version of Model B would increase the difference in R2. To conclude, an alternative set of British data has been shown to be consistent with the models developed by Bierwag and Grove and there is no need to infer that the expectations mechanism in the United Kingdom differs from that in the United States. It must be emphasized, nonetheless, that the improved results for the British test have been obtained by resorting to data taken from a smoothed yield curve. Theoretical reasons must be advanced to justify the smoothing process if support for hypotheses can only be established by using smoothed data. The dangers of spurious correlations must not be discounted.

tempted to go a little further and suggest that the degree of concentration as such does not contribute materially to the explanation of high profitability. Perhaps this is not surprising because although a highly concentrated industry may be associated with high profitability a large number of situations are possible depending, amongst other things, on whether the industry is expanding or contracting, and on the degree of internal, intra industry, and potential competition. Secondly, the analysis shows clearly the importance of very high barriers to entry arising for instance, from control over raw materials, patent protection and economies of scale. In these cases the means exist whereby firms can maintain high profitability over a long run of years. A concern for barriers to entry should certainly be central to the implementation of a monopoly policy. Thirdly, the highly significant relationship between growth and profitability is a well established one,3 and any monopoly policy which is based on realised profitability should at least distinguish between fast and slow growing industries or (ideally) firms, and attempt to assess the extent to which high profitability is 'justified' by a high rate of growth. STATISTICAL APPENDIX

T HE results presented in this paper are (1) A time series of personal savings is well explained by the dynamic savings function st = ast 1 + 8z A Yt + ut. This model was previously formulated (but tested only for the United States and Canada) by Professors Houthakker and Taylor [1]. (2) The steadystate or long-run savings function implicit in the above dynamic formulation, s/y = a2 + 12 (Ay/y) fits remarkably well to international cross-section data. (3) The coefficients of the long-run savings function, as obtained by application of least squares on the function, is statistically equal to the coefficient obtained indirectly from the dynamic savings function. This implies that both dynamic and steady-state savings behavior are adequately described by st = ast+ /3Ayt + ut. (4) A few pitfalls in estimation of economic relationships when employing cross-section time series data are revealed. It will be shown that the long-run savings function implied in the Houthakker-Taylor function supplemented by some additional conditions, is precisely the long-run savings function of Modigliani [2]. Therefore, the present attempt must be regarded as a synthesis of the two theories. We shall have the benefit of more observations per country than the above mentioned authors in deriving our empirical results. II The Dynamic Savings Function Let St, yt, and at denote (personal) savings, (personal disposable) income, and non-depreciating assets at time t, in per capita terms. The Houthakker-Taylor model in terms of these variables is: St = a +at+yyt (1) dat/dt = st (2) Thus, savings is a linear function of assets and income, and the rate of change of assets at any moment of time is the savings at that moment. The long-run implication of this model has not been explored and this we shall do below. To derive the long-run effects of equations (1) and (2), we need to know something about the growth of income. Let us assume 1 that: (3) y= p, where p is a positive constant. This equation thus implies that the rate of growth (of

where ut is a random disturbance with zero mean. Koyck pointed out that subtracting Xyt-i from (1) produced the equation yt = A'+xyt_i+ bxt+ut' (2) where A' = A(1 -X) and ut' = ut -Xut1. Thus instead of being forced to deal with the model in its distributed lag form (1), which involves the seemingly intractable task of estimating a relation with an infinite number of explanatory variables from a finite amount of data, we can estimate the parameters of the autoregressive form of the model given in equation (2). However, this apparent simplification is purchased only at a cost, for consistent estimation of relation (2) requires that we face several estimation problems associated with equations in which lagged dependent variables appear as explanatory variables. While ordinary least squares estimates of the parameters of (2) are consistent provided that the disturbances ut' are serially independent and follow a distribution which satisfies the assumptions of the central limit theorem, even in this case a small sample bias exists. If the disturbances are serially dependent, an asymptotic bias exists.' Moreover, the transformation from (1) to (2) has changed both the variance and the serial correlations of the disturbances. Hence, if the disturbances in (1) are serially independent, those in (2) are necessarily autocorrelated, which means that applying least squares to equation (2) yields inconsistent estimates of the parameters. In addition to ordinary least squares (OLS), several techniques for estimating such distributed lag relations are available. Generally these techniques have been recommended on the basis of their desirable asymptotic properties. However, for economists, who are forced to work in a world where data are scarce, asymptotic properties are frequently of little relevance. What is more often required is knowledge of the properties of the estimators in small samples. Unfortunately, it has proved difficult to investigate these properties analytically. In the absence of such results, sampling or Monte Carlo experiments provide an alternative, if less elegant, source of information. Accordingly, this paper presents the results of a Monte Carlo study of several lag estimators under conditions in which the disturbances ut' of relation (2) are serially correlated. In addition to ordinary least squares, the following five methods were studied. 1) Two Stage Regression (TSLS): This is an application of Leviatan's instrumental variable approach. Leviatan [12] has suggested that xti1 be used as an instrument for yt-i in estimating relation (2). In order to increase the efficiency of the technique, we employed a linear combination of lagged x's as the instrument. The linear combination was determined by first estimating the equation

T HE recent development of spectral analysis as a tool for analyzing economic time series has provided a particularly neat method for independently testing the existence of Kuznets cycles. Researchers who have applied this technique, however, have produced mixed results. Adelman shows that such cycles do not exist in the United States data ' while Hatanaka and Howrey, in a criticism of Adelman's work, leave readers with, at best, an agnostic view.2 But both these studies have been poorly conceived with respect both to spectral analysis and to the particular version of the longswing hypothesis tested. The intention of this paper is to attempt to resolve the long-swing controversy, insofar as the Canadian data are concerned, by the application of spectral analysis to a large number of historical time series. For the purpose of comparison with results obtained in the United States this will initially mean applying what might be called the Adelman-Hatanaka-Howrey test. Finally, however, this test will be reformulated and reworked in a manner which is more compatible with spectral analysis and which makes more sense with respect to the long-swing hypothesis. Section II briefly describes and lists some important properties of spectral analysis while section III presents some of the practical considerations involved in applying this technique to the long-swing controversy. Section IV summarizes the results of the spectral estimates. Conclusions are in section V. IL

T HE volume under review is the result of the collective effort of twenty-five economists. It consists of a set of chapters each representing a building block for a large scale model of the United States economy, and an attempt at the end of the volume to put all these blocks together into one coherent and potentially useful structure. To review a volume which ranges so widely over almost all aspects of economics, the reviewer himself would have to be a committee. To review the final model adequately, one would need computer and programing resources which are beyond anything currently available to individuals. I shall, therefore, concentrate on reviewing the volume rather than the final model produced by the Brookings-SSRC group. This may be also desirable, since a final version of the model which the authors would stand by and take responsibility for may not yet exist.' One of the original ideas which led to this volume was that by parceling out different sectors and aspects of the economy to different one could integrate all of the best available theoretical and empirical knowledge into the model and thereby improve it greatly. To a great degree, therefore, the final quality of the model rests on the success with which the individual sectors were specified and estimated. Ideally, the job of a specialist would consist of first surveying the theoretical literature in a field (at the level of an AER or EJ review article), then surveying the associated quantitative-econometric knowledge and evidence, running a race between all the plausible econometric models which have not been eliminated on a priori grounds earlier, and submitting the winner to the final model. Taken seriously, this is a task of very great magnitude. By using the model builders implicitly assumed that much of this has already been accomplished by the specialists in the process of becoming specialists. This may have been a somewhat too optimistic assessment both of the processes of education in economics and the state of research in most of its subfields. Nevertheless, it must be assumed that each of the pieces would try to represent as well as possible the current state of quantitative economic knowledge about the various sectors of the economy. To be useful in constructing an econometric model of the whole economy, one would hope that each of the proffered relationships would be based as much as possible on existing (correct! ) economic theory (which derives the implications of purposive behavior of consumers, producers, and other economic actors from the interaction of their tastes and the constraints facing them) and will reflect those structural and institutional aspects of the economy which remain relatively stable from period to period and not the accidental confluence of different time series. It is in this light that I will examine below the sixteen individual chapters which constitute the bulk of the book.2

ECONOMISTS have recently begun to devote an increasing amount of attention to the relationships among interest rates on various instruments. Rates on instruments which differ with respect to maturity alone, all other features supposedly being held constant, have in particular received a great deal of attention since the publication of Meiselman's [7] work in 1962. While the term structure has certainly received the most concern, import-ant contributions have been made to the broader problem of studying relationships among rates on bonds which differ with respect to features other than maturity.' An especially important aspect of this broader area of research lies in examining the relationships between rates on government and corporate bonds. Knowledge of the characteristics of these relationships is important for an understanding of the paths through which monetary policy affects yields on corporate bonds, and hence, perhaps, expenditures on investment. This paper presents the results of an examination of the relationships among several interest rates on government and corporate bonds for the period January 1951 through December 1960. Monthly data are used, and series for the rates on three-month treasury bills, one, two, three, four, five, ten, and twentyyear government bonds, commercial paper, and Moody's Aaa's and Baa's are studied.2 This list represents an array of instruments ranging over a broad maturity spectrum and featuring various levels of quality. Tools of spectral and cross-spectral analysis are used to study the behavior of the series and the relationships among the series at various important components of oscillation.3 In addition to calculating the standard statistics associated with the spectrum and cross-spectrum, the relatively new tool of complex demodulation is employed to study the seasonal behavior of selected rates.4

The article shows that innovations are induced, since they become more profitable with the expansion of output. The amount of resources devoted to innovating activity, however, is in general not the optimal one because of the pressure of two opposing forces. On the one hand, competition between potential innovators tends to make this amount too large, on the other, the inability of innovators to capture all the benefits tends to make the amount too small. When all benefits are captured by the innovator either there is no economic growth due to innovations or else innovators are the sole beneficiaries from that growth. When benefits are diffused the innovation will always lead to economic growth, but only by sheer coincidence will it lead to maximum growth, which may be missed because the innovation is introduced either too early or too late. The rate of growth is always positive if the innovation is introduced too late. It may fall to zero with too-early introduction or even become negative if innovational activity is subsidized.