Knowledge that Transforms

a, B, y, and X are stable over the tight and the loose money subsamples is rejected at the 5 %, 10% and 20% significance levels for equations (6), (5), and (4), respectively. (2) The coefficients of m for loose money years is always negative and smaller by about 0.16 to 0.23 than the corresponding coefficient for tight money years. The latter is positive when current I is not included in the equation and becomes negative, even if it is not significantly different from zero, only in equation (5) where current I is added. It is therefore clear that m has a positive influence on output only when tight money prevails. Even in this case, however, its influence is mainly due to its correlation with investment.

over this business would depend upon the size of the advantage and the rate with which the advantage becomes recognized. The apparent parabolic growth path displayed by Eurodollar deposits so far is consistent with theories of the early stages of a new product. The path of Eurodollar expansion can be formulated as a cumulative response to a gradually recognized cost advantage. Such factors as the stringencies of Regulation Q ceilings on interest rates and the exchange controls can be viewed as sources of the residual variation from the growth path.

IN the literature of economic theory it is well known that in a steady state monetary economy, a rational consumer's excess demand for commodities is homogeneous of degree zero in prices, and Phelps in an earlier paper (1962), and Hakansson more recently (1970), have extended this theoretical result to a time-sequenced analysis, and have by way of a dynamic programming solution shown that the consumer's optimal strategy is reflected by a function that is linear and linearly homogeneous in real and real wealth.' When considered in a macro-economic context, this theoretical proposition is subject to empirical tests for a number of reasons. Intuitively, the world in which the consumer makes his spending decisions may not conform in every detail to the one that is delineated in the theoretical model. On the conceptual level, some more fundamental issues are involved. The notion of an optimal consumption strategy expounded by Phelps and Hakansson has its micro foundation in utility maximization. The important question is whether the consumption-savings choice should be posed as a utility maximization problem where wealth is not desired per se but only as a source of a permanent flow of income, or as one where wealth is treated as a part of the choice problem. The different approaches would lead to different strategies. This point has been demonstrated, although in a somewhat different context, by Levhari and Patinkin (1968).2 In addition, as Pesek and Saving (1967, chapter 10) have pointed out, the question whether human and non-human capitals are homogeneous or whether they are subject to the same capitalization rate also has important bearings on the result of the intertemporal utility maximization problem. For many empirical purposes, the use of a linear consumption function has several implications that are either highly restrictive or inconsistent with actual experience. For instance, a linear function implies that the wealth effect on the aggregate consumption is a constant over GNP cycles, independent of the general condition of the economy or the current incomewealth ratio. It also implies that and wealth (strictly speaking, non-property and the capitalized value of non-human wealth) are infinitely substitutable in terms of their influence on the consumption decision, an implication partially due to the assumption that human and non-human capitals are homogeneous. Thus, there seem to be sufficient reasons for looking into the linearity property more closely. This paper is intended for this purpose. In the sequel, the appropriate form of the per capita consumption function will be determined on the basis of actual data. In addition, two closely related questions, the liquid asset effect and the possible influence of public debt and outside money on consumption, will also be looked into. Received for publication December 4, 1973. Revision accepted for publication May 8, 1974. * I am indebted to Ronald G. Ehrenberg for his helpful comments on an earlier version of this paper, and to Alvin K. Klevorick for providing part of the data used in the estimation. I am also grateful to the referee for his comments which improved the paper considerably. Any remaining errors are, of course, solely my responsibility. 1 In both papers, optimal consumption is actually shown to be proportional to the amount of capital (debt) on hand, which is equivalent to the notion of consumer net worth, and to the present value of the stream of future nonproperty income, which may be compared to the notion of expected income under the Ando-Brumberg-Modigliani life-cycle hypothesis. See in particular equations (6.3) and (6.5) in Phelps (1962), and equation (23) in Hakansson (1970). The reader is also referred to p. 737 of Phelps' paper, and pp. 601-602 of Hakansson's paper, op. cit., for their comments on the analytical properties of the optimal consumption strategy. 2 Although their theory deals primarily with money, the essence of the argument is retained when the role which assumes in their model is extended to wealth. See, for instance, equation (70) in the Levhari-Patinkin paper (1968, p. 748).

SINCE the formulation of the Fisher-Clark hypothesis of structural change, which associates changes in the distribution of employment between industries with changes in levels of real income per head, economists have been interested in the reasons behind changes in industry structure.' interest has received a fillip in recent years with an apparent acceleration in the rate of growth of employment in the service sector compared with that in the manufacturing sector.2 Recent empirical studies by, for example, Fuchs (1965) and Dowie (1970) have sought to explain the relatively faster rate of growth of employment in service industries than in manufacturing (or goods) industries in terms of the supply and demand characteristics of the products of the two sectors. In both studies it was found that the ratio of product of the two sectors remained fairly constant but that there was an appreciably faster rate of growth in productivity in manufacturing than in the service industries. It is concluded that difference in the supply characteristics of the two sectors is the main cause of the structural change. Both writers also suggest that constancy of product shares implies similar income elasticities of demand for the product of the two sectors. These conclusions, however, must be subject to two qualifications. First, the approach adopted does not allow for possible interaction between demand and supply.3 Demand and supply effects are assumed to be independent. But, as shown below, supply effects, as a result of differences in rates of productivity change, are likely to affect the relative rates of growth of product of the two sectors. Hence, constancy of product shares does not necessarily imply that demand factors are neutral. Interactive effects occur because different rates of productivity change, affect relative prices, which in turn lead to price substitution between the products of the two sectors.4 importance of these effects depends therefore on the differences in the rates of productivity change and the price elasticities of demand for the products of the sectors. following illustration shows how the effect operates.5 Let m equal the continuously compounded percentage rate of change in service sector employment over time minus the percentage rate of change in goods sector employment. Then as an approximation where r is the percentage rate m -r(nn,) + (rr,)(-1), of increase in real income, ns is the income elasticity of demand for services, nt0 is the income elasticity of demand for goods, rs is the percentage rate of increase in total factor proReceived for publication January 23, 1973. Revision accepted for publication January 30, 1974. * All the computer simulations required for this study were carried out by Margaret Wood. Helpful comments on an earlier draft were made by Dr. C. I. Higgins, Dr. R. G. Gregory, Mr. J. S. Marsden. Some of the data needed for this study are not available in official Australian statistics and were specially estimated. Notes on estimates are available from the author. complete set of equations used in the model, together with the usual tests of significance, are also available from the author. 1 In the first (1940) edition of The Conditions of Economic Progress Clark observed that studying economic progress in relation to the economic structure of different countries, we find a very firmly established generalization that a higher average level of real income per head is always associated with a high proportion of the working population engaged in tertiary industries . (pp. 6-7). Clark was not, of course, the first economist to discuss changes in industry structure; see, for example, Marshall (1938), pp. 276-277, and Clark himself drew attention to Petty's writings on this topic, in the 17th century (Clark (1957), pp. 176-177). But Clark's analysis is, however, more comprehensive than that of earlier writers. 2 For example, in Australia (Dowie (1970), p. 222) and in the United States (Fuchs (1957), pp. 6-8). Comparison of rates of increase in employment by sector for other countries is given in O.E.C.D. (1970). 3 This does not imply that Fuchs and Dowie are unaware of the importance of the interaction, but the results assume that they are insignificant. 4 cf. Baumol (1967) for a discussion of the relationship between changes in productivity, prices and demand. 5 This formulation was suggested by a referee.

I have entirely avoided in this comment the important question of whether the empirical difficulties, especially correlation between pollution and unmeasured neighborhood characteristics, are so overwhelming as to render the entire method useless. I hope that with the air cleared of theoretical misconceptions, future work can proceed to solving these practical problems. For example, recent improvements in pollution measurements and in county assessors' data on individual homes might be combined to permit regressions within a more uniform area. The degree of attention devoted to this kind of detail is what will really determine whether the method stands or falls, once it is recognized that its theoretical underpinnings are sound.

N the study of optimal economic policy using a linear econometric model and a quadratic welfare function the parameters of the model are often assumed to be known for certain. Under this assumption the solution in the form of an optimal feedback equation can be obtained easily. Although one recognizes that in a realistic situation the parameters of an econometric model are never known for certain, he might still apply the above solution, using a set of estimates of the parameters as if they were the true values, if he believes that it is a good approximation to optimal policy. Such a procedure is well known to be a certainty equivalence solution. In a recent paper (Chow, 1973b), I have presented a method of obtaining the optimal feedback equations and the associated welfare costs by allowing for uncertainty in the parameters as expressed in the posterior density function computed from data available at the time of the current decision but not for possible future revision of this posterior density in the derivation of the current policy. Because future learning about the model is not explicitly taken into account in the design of the current policy, the above method is not truly optimal. However if the sample period is long as compared with the planning period, this method will probably be close to being optimal. The purposes of this paper are to present an approximate solution to optimal when learning is taken into account and to contrast this solution with the first two solutions. In the literature, the term control is used for a problem having the dual purpose of improving the system performance and of learning more about the system for the sake of future control. Numerous approximate solutions to this problem have been suggested.' The solution of this paper appears to be the simplest in conception, and yet it incorporates all theoretical elements in the calculations. It contains a logical structure which brings out clearly the effect of learning on the optimization process and enables the effect to be measured numerically. It provides useful contrasts to the certainty equivalence solution and the solution for unknown parameters without learning, being a natural generalization of these two solutions. We will set up the problem and describe the method of solution in section II. This method will be compared in section III with the two other methods just mentioned, both in conceptual terms and in terms of computations. Two simpler, modified versions of the method will also be briefly described. They are simpler to compute but they still take learning partially into account. Some numerical results using a simple one-equation model will be presented in section IV to bring out the effects of learning on the optimal solution. This paper is confined mainly to presenting the method and providing some illustrative calculations. A comprehensive study of the effect of learning on optimal policies using the method of this paper remains to be undertaken. From the viewpoint of economics in general, other than the study of quantitative economic policy using econometric models, the content of this paper may also be relevant. Maximization is in the heart of economics. Most of economic theory assumes maximization to take place in Received for publication December 26, 1973. Revision accented for publication July 8, 1974. * I am much indebted to Andrew Abel for extremely able research assistance, to Edison Tse, Ray C. Fair and several members of the Econometric Research Program seminar at Princeton for valuable suggestions and discussions, to a referee for comments on an early draft, and to the National Science Foundation for financial support through Grant GS32003X. 1 The references in the literature are too numerous to cite. In the economics literature, Prescott (1972) deals with the problem of learning using a very simple model but provides no new method of solution; its results were computed by complete enumeration. MacRae (1972) and Tse (1974) provide interesting approximations to the optimal solution and are highly recommended to the reader.