COWLES FOUNDATION For Research in Economics at Yale University Studies in The Cowles Foundation for Research in Economics at Yale Uni­ 'l:et·sity, established as an activity of the Department of Economics Econometric Method in 1955, has as its purpose the conduct and encouragement of research in economics, finance, commet·ce, industry, and tech­ nology, including problems of the organization of these activities. The Cowles Foundation seeks to foster the development of logical, mathematical, and statistical methods of analysis for application Edited by in economics and t·elated social sciences. The professional research Wm. C. Hood and staff are, as a rule, faculty membe1·s with appointments and teach­ Tjalling C. Koopmans ing responsibilities in the Department of Economics and other departments. The Cowles Foundation continues the work of the Cowles Com­ ( ~~~3) mission for Research in Economics founded in 1932 by Alfred Cowles at Colorado Springs, Colorado. The Commission moved to Chicago in 1939 and was ajjUiated with the University of Chicago until 1955. In 1955 the professional 1·esea1·ch staff of the Com­ mission accepted appointments at Yale and, along with other members of the Yale Department of Economics, formed the ?'e­ seat·ch staff of the newly established Cowles Foundation. A list of Cowles Foundation Monogmphs appears at the end of this volume. r:. -, ··-. ,,or~~"'~"'"'~... (, .. ~ff'JO.co t:•; r;c,,•,-,. \)J s"" '"~·.;.-t.a:/~·~~::~· ~:: t .,. ·: ··- .. -· I;'~:~ ~r Ia y ... ". ' . - r, E ·~ :·· ;· • ·.·. · [: i! ,,H ....... r-.1 .... ~.. ... C. ..: New Haven and London, Yale University Press CHAPTER I ECONOMIC MEASUREMENTS FOR POLICY AND PREDICTION BY .JACOB MARSCHAK Page 1. Useful Knowledge ..................................................... 1 2. Structure....................... ................. 3 3. Maintained Structure and Change of Structure ... 4 4. Controlled and Uncontrolled Changes ........................ 8 5. Some Definitions Extended ..... 8 6. The Technician and the Policy-Maker .. 10 7. Random Shocks and Errors ........ 12 8. The Need for Structural Estimation ............. 15 9. The Time Path of Economic Variables; Dynamic Structures.......... 17 10. "Steering Wheel" and Automatisms..................................... 24 11. Mathematics and Prediction. 25 12. Conclusion............................................................. 26 1. USEFUL KNOWLEDGE \..Knowledge is useful if it helps to make the best decisions. To illustrate useful knowledge we shall take an example from the century-old elementary economics of the firm and of taxation. Such examples are admittedly crude (or, if the reader prefers, neat) compared with the complex actual world since their very purpose is to isolate the essentials of a problem by "idealizing reality." Later sections (beginning with Section 5) will deal with ways of eliminating at least some of the legitimate realistic objections. What kinds of knowledge are useful (A) to guide a monopolistic firm in its choice of the most profitable output level and (B) to guide the government in its choice of the rate of excise tax on the firm's product? Let q represent quantity produced and sold per unit of time; p, price including tax; e, tax per unit of product; 'Y, total cost of producing and selling q units. To fix ideas, suppose that the demand for the product of the firm is known to be (approximately) a linear function of the price and that all costs are known to consist of fixed charges. (This is almost the case with hydroelectric plants.) Write for the demand curve (1) p =a- {3q ({3 > 0). The firm's profit (net revenue) per unit of time is (2) r = (p - e)q - 'Y, SEC. 2] MEASUREMENTS FOR POLICY AND PREDICTION 3 2 JACOB MARSCHAK [CHAP. 1 interested in high output, it will choose the smaller of the two real roots, or, using (1), say 01 < 02 • If T* exceeds a certain level To , the roots will be not real 2 (3) r = (a - 0 - {Jq)q - 'Y = -{Jq + (a - O)q - 'Y· (i.e., a tax revenue T* > To is unattainable). We thus conclude that if the government knows a and {3 it can choose the best value of 0 for any CASE A: If the firm knows a, {3, and 0, it can use equation (3) to com­ desired and attainable level T* of tax revenue. pute the difference between the profits that would be attained at any two alternative output levels. To choose the most profitable output of We can sum up as follows: all, it therefore suffices to know a, {3, and 0. It happens in our example, CAsE A: Desired: maximum r. Decision variable: q. Useful knowledge: as in most discussions of classical economies, that the functions inn>lved the form of relations (1) and (2) and the values of the parameters a, are differentiable/ so that the best output level, say q = q, ean be found {3, 0. by putting dr I dq = 0. Hence CASE B1. Desired: maximum T. Decision variable: 0. Useful knowledge: the fact that profits are maximized, the form of (1) and (2), and the (4) q = (a - 0)/2{3. value of a. CASE B2 • Desired: maximum q for given T = T*. Decision variable: CASE B: Assume that the government knows that the firm maximizes 0. Useful knowledge: same as in Case B 2 , plus the knowledge of {3. its profit. What other knowledge is useful to the government? This de­ pends on its aims: 2. STRUCTURE CASE B1 : Suppose, first, that the government, which collects from the In all of our examples so far, useful knowledge pertains to certain firm the ta.x revenue T, economic relations. In Case A the firm has to know something about relations (1) and (2). Relation (1), the demand equation, describes the (5) T = Oq, behavior of buyers. The form and the coefficients (a, {3) of this relation wants to maximize this revenue by the proper choice of the excise-tax depend on social and psychological facts, such as the frequency distri­ rate 8. Then, by equations (4) and (5), bution of consumers by tastes, family size, income, etc. Relation (2), the profit equation, registers the institutional fact that the tax rate is (6) T = O(a - 0)/"2 :i. fixed at 0, and the fact (reflecting the technology of the firm as well as the price and durability of its plant and the interests and rents stipulated Therefore, if the government knows a, it can compute the ratio between in its contracts) that the total cost consists of given fixed charges, 'Y· the tax revenues resulting from fixing any two alternative excise rates. With respect to the decision problem of Case A, relations (1) and (2) This ratio is independent of {3. Hence, to make the best decision (i.e., are called structural relations and are said to constitute the structure; to choose the value of 0 that will bring in the highest tax revenue) it they involve constants (a, {3, 0, 'Y) called structural parameters. In Case is sufficient for the government to know a. In fact, the best value of B the assumed structure includes, in addition to (1) and (2), the as­ 8 is b = a./2. sumption of profit maximization, which results in relation (4); and defi­ nition (5) may also be counted as part of the structure. If (1) or (2) or CASE ~: Suppose, on the other hand, that the government wants to both had included a definite pattern of change-say, a linear trend­ goad the monopolist into maximum production, provided that a fixed this would also be a part of the structure. tax revenue T = T* can be collected. The best tax rate is found by solv­ In each of the problems studied the form of the structural relations ing the (quadratic) equation (6) for 0 with T* substituted for 1'. The and the values of some (not necessarily all) of their parameters prove to equation will have two real roots, say 8 and 8 (which, in a limiting case, 1 2 constitute useful knowledge. However, we shall presently see that under may coincide), provided that T* is not too large. Since, by equation (4), certain conditions other kinds of knowledge, possibly more easily at­ q is larger the smaller 8 is, and since the government was assumed to be tained, are sufficient to make the choice of the best decision possible. 1 But see Section 5. 4 JACOB MARSCHAK (CHAP. I SEC. 3] MEASUREMENTS FOR POLICY AND PREDICTION 5 3. MAINTAINED STRUCTURE AND CHANGE OF STRUCTURE predicting r) is a quadratic equation, that the knowledge of structure is not necessary if the We shall show (7) r = Xl + M + "' structure is not expected to have changed by the time the decision takes its effect.2 Again consider Case A. Assume that the form of the struc­ say, whose coefficients are related to the coefficients of the structural equations as follows: tural relations (1) and (2) and the values of coefficients a, {3, 'Yare known to have been unchanged in the past and to continue unchanged in the (8) X = -{3, IJ. =a- 0, "= -"(. future, and make three alternative assumptions about the tax rate 0: If the structural relations (I) and (2) are assumed to retain in the fu­ ture the same (linear) form and the same values of parameters as in the CASE A': 0 has not changed in the past and is not expected to change. observed past, the firm can predict r for a given q by fitting a quadratic equation (7) to past observations on output and profit. It can thus CAsE A": 0 has not changed in the past but is expected to change in determine empirically the parameters X, IJ., " of the reduced form with­ a known way. out having to pay any attention to the manner [described by equations (8)] in which these parameters are related to the demand and cost con­ CASE A"': 0 has changed in the past.