Knowledge that Transforms

the value of exports. The analysis is based on cross-sectional value and quantity series, and it is conceivable that the quantity data, from which our unit value series are constructed, contain a fair margin of errors. The reliability of unit values with respect to the aggregation problem is examined, and measurement errors in the quantity series may have biased our estimates of elasticities towards minus one. Since it is often the case that the estimation of price elasticities in international trade has to rely on unit value series, we maintain that bias due to inaccurate quantity data should be taken seriously.

EMPIRICAL studies of the investment decision have been restrained by the lack of data to the examination of investment expenditures anticipated or realized. A consequence of this empirical bias may be the diversion of attention away from the complete decision-making process and to the misleading impression that the investment decision is primarily and essentially one of timing and financing investment outlays. (See, however [2, 5, 6, 12-14].) The underlying hypothesis of this paper is that there are two investment decisions: The first, reflecting long-run plans and expectations, is whether or not to invest at all; the second, chronologically, is when to make and how to finance the actual expenditures. The latter is likely to be a function of the actual market conditions faced or the short-term expectations of those market conditions. While the need to include plans and expectations into the analysis may be fairly obvious, the necessary algebra remains elusive. However, objective data can capture most of what we need to know about expectations, leaving the algebra to be uncovered by empirical research. All that is needed are data that can be deemed to embody expectations without necessarily specifying their origin. Accordingly, a rather general model will be developed using capital appropriations data and initial conditions, which will illustrate the method proposed. In this paper, only the first decision, the formal commitment to invest, will be examined further. Given the capital appropriation, the question is what constitutes the set of relevant initial conditions and how much of the capital appropriations can be accounted for by reference to it. If the hypothesis of two investment decisions is correct, then there is a subset of initial conditions influencing this first investment decision and another subset which does not. This is essentially an empirical question. To examine the relationship between capital appropriations and initial conditions, cross-section data are used. They are generally regarded as reflecting long-run tendencies, and since the first decision is more or less a stock one, variables which vary over time and thus more appropriate for the flow decision prices, interest rates are eliminated. Two years have been selected for study 1956 and 1961-which are the best years available in the basic data. These years exhibit roughly the same movements in the business cycle and are far enough apart so that structural changes are permitted. The initial approach to the data and the immediate task for the present is to determine: (a) What the relationship is between capital appropriations and various selected variables for selected industries in each of the two years; (b) Whether the structure of expectations the same variables dominating was the same for each industry in 1956 as in 1961; (c) Whether there are significant differences among industries in the variables which are important. The data used were supplied by the National Industrial Conference Board (NICB) which since 1953 has conducted a quarterly survey of capital appropriations for the top corporations in the United States. These are large corporations and account for a sizeable proportion of investment expenditures. For a more detailed description of the data see Cohen [13]. Out of seventeen industrial groups of NICB, seven were selected for study: Primary Iron and Steel, Primary Nonferrous Metals, Machinery (except electrical), Fabricated Metals, Food and Beverages, Textiles Mill Products, and Paper and Allied Products. These industries were selected for their possible differing structure of expectations and because they rep* The author is an Assistant Professor of Economics at the University of Vermont. Parts of this paper are based on his Ph.D. dissertation, Expectations and The Investment Function (Rutgers The State University, Jan. 1966). He is indebted to Rutgers The State University for grants received, and to The Bureau of Economic Research at Rutgers University for additional financial support. The author is also indebted to K. K. Kurihara and M. Dutta for many helpful suggestions.

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