Knowledge that Transforms

CONSIDERABLE attention has recently I ~~been given to the theory of foreign exchange operations and its implications for government policy. Central to this is the analysis of forward exchange speculation.' Although the essence of speculative behavior is the balancing of uncertainty and expected gain, the analysis of uncertainty in the current theory of forward exchange speculation has generally been less rigorous than other parts of that theory. The purpose of this paper is to present a more explicit theory of the role of uncertainty in forward exchange speculation in the framework of von Neumann-Morgenstern expected utility maximization and to explore its implications for speculator behavior and government policy. Section I is a brief review of the contemporary analysis of foreign exchange speculation. Section II presents the expected utility maximization theory and derives a mean-variance framework for analyzing speculator behavior. The effects of changes in the mean and variance of anticipated gain is discussed in section III, with speculation assumed to occur only in terms of one currency. The theory is extended to multiple currency speculation in section IV. Some policy implications are discussed in section V. Finally, section VI provides a brief summary.

n a pioneering paper in 1958 Phillips [6] advanced the proposition that in the United Kingdom there is a statistically significant relationship between the level and the rate of change of unemployment (U and A U) and the rate of change of money wage rates (AW) which has been remarkably stable during the hundred years since 1862.1 Phillips, Lipsey [5] and others have advanced theoretical grounds on which it has been concluded that unemployment is the causal variable in the observed relationship. There is reason to believe that this proposition is widely accepted today and there is evidence to suspect that it has reinforced arguments in favour of controlling the price level through the level of unemployment. The Phillips hypothesis has been the subject of considerable discussion. Kaldor [3] in 1959 accepted the empirical evidence which supports it but disputed the postulated chain of causation. His argument may be taken to mean that the observed relationship between AW and U is consistent with the hypothesis of no causal connection between the two variables since, within certain limits, both could be concomitants of variations in the level of activity. Dicks-Mireaux and Dow [1] in 1959, Hines [2] in 1964, and others have drawn attention to factors such as the rate of change of the price level (AP) and the rate of change of the percentage of the labour force unionised (AT) which may affect AW independently of U and AU. Knowles and Winsten [4] in 1959, doubted whether the results of Phillips had any implication for public policy. They observed that, on his own data, the critical range of unemployment, between 0 and 3 'A per cent of the labour force, is compatible with any range of inflation between 2 per cent and 28 per cent per annum, while a stable wage level is compatible with between 2 per cent and 22 per cent of the labour force being unemployed. In this paper, we propose to re-examine the hypothesis and the statistical evidence concerning the relationship between the level of unemployment and the rate of change of money wage rates. Specifically, it will be shown that although there was a strong relationship between unemployment and changes in money wage rates in the 19th century, in subsequent years, the association has been very much weaker. Moreover, in the post 19th century years, the level of unemployment does not make a significant contribution to the explanation of the variance in money wage rates in models which include such variables as changes in the cost of living and the level and the rate of change of unionisation. Further, when the coefficients of the unemployment variables are used to predict subsequent values of AW conditional on U and AU, rather poor predictions are obtained. It will be suggested that there are good reasons why these results should have been obtained. In the years since the 19th century, new institutions and relationships have come to dominate the wage bargain. Since unemployment is now a relatively unimportant determinant of wage rate changes, its role in the control of wage inflation must in consequence be severely reduced.

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.

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.