Knowledge that Transforms

THE St. Petersburg paradox constitutes a fascinating chapter in the history of ideas. What other subject can link together Edward Gibbon and the father-inlaw of Thomas Mann? Or can, in the conceit of Maynard Keynes, link together the Bernoullis and Darwin?' Substantively, the Petersburg paradox served as a dramatic paradigm, alerting people to the fact that their utility of gain exceeded their utility of equivalent money lost. As a byproduct, the discussion generated an interest of its own: the idiocies it evoked from various writers are scarcely less fascinating than the lasting insights. Yet when I came recently to review the matter, I found to my surprise that no one seems to have provided anything like a complete survey of the subject. The standard sources provide us with tantalizing glimpses: the useful 1954 English translation of the classic Latin work of Daniel Bernoulli [4, 1738]; the references and discussion in histories of probability, such as those of Isaac Todhunter [39, 1865] and Leonid Maistrov [17, 1966]; the selective but perspicacious accounts in the work of Keynes [15, 1921] and George Stigler [37, 1950]; the new lease on life given to the subject by Karl Menger [19, 1934] with the discussion there of SuperPetersburg paradoxes creatable when the utility function is unbounded; the recent observation by Kenneth Arrow [2, 1971] that not all stochastic processes can be ordered by the expected value of their utility outcomes when such Mengerian super-paradoxes are allowed to exist. The number of post-Mengerian writers is large, including L. S. Shapley [36, 1972], D. L. Brito [6, 1975], Samuelson [28, 1960], Robert J. Aumann [3, 1975], and many others. Given my own limited linguistic abilities and leisure time, I have not been able to provide anything like a definitive survey, one that checks back on and quotes copiously from the original sources. After all, the list of writers connected with the St. Petersburg paradox reads like a veritable who's who in probability and the social sciences. Here is but a sample: Nicholas Bernoulli (1687-1759), Montmort (1678-1719), Gabriel Cramer (1704IThe continuity and oneness of modern European thought may be illustrated, if such things amuse the reader, by the reflection that Condorcet derived from Bernoulli, that Godwin was inspired by Condorcet, that Malthus was stimulated by Godwin's folly into stating his famous doctrine, and that from the reading of Malthus on Population Darwin received his earliest impulse [15, Keynes, 1921, p. 83, n. 1].

COMMENCING in 1920, major domestic spark plug manufacturers have sold their original equipment (OE) plugs to the larger automotive vehicle assemblers at a price well below marginal manufacturing cost.' Prior to 1953, when F.T.C. complaints prohibited discriminatory pricing on replacement plugs, the manufacturers gave assemblers lower than wholesale prices on those plugs as well. This discount pricing practice was adhered to whether the sales were interfirm, as, for example, from Autolite to American Motors, or intrafirm, e.g., from General Motor's AC Spark Plug to its car divisions. It has been argued that the below-cost discount price to automobile assemblers is explainable by the existence of an OE-tie, that factory installation of a manufacturer's proprietary brand plug generates profitable replacement sales. Thus, to the extent that spark plugs are replaced with the factory brand, the plug manufacturer realizes a return on his investment in below-cost OE sales. The actual motive force behind the OE-tie is psychologically obscure. It is conceivable that the reason why the OE plug is preferred is that it takes very little effort to know which model to replace, i.e., it is a matter of convenience. But since each of the major plugs is readily available from wholesale distributors and since each manufacturer has a suitable alternative, it is difficult to argue that an appropriate non-OE plug cannot be obtained. Futhermore, it makes little sense to argue, as some have, that the mechanic is wary of customer complaints in case an incorrect plug is installed. Few tune-up customers specify the brand of plug which they wish installed, tending to rely upon the mechanic's superior know-how. Why then do mechanics not use nonOE lesser known or private brands? It could be argued that the service station mechanic, the person who usually chooses the brand, should rationally be indifferent to OE-status and should choose an available cheaper plug, unless he too has been convinced of the importance of OE-status, believing that the replacement plug is the same as that which came with the car when it was new. Recent information indicates that factory authorized dealers sell only about 10% of all replacement plugs, but they are encouraged to use plugs wholesaled to them by their supplying assemblers-the brand supplied being that used by the assembler. Interestingly though, mechanics at these outlets -as well as at automotive service centers operated by firms such as Goodyear, Firestone and Sears, which have or have had their own private branded plugs-also seem to prefer the factory installed OE plug that came with the car. Whatever the reason then, original equipment status appears to be significant in explaining replacement plug sales. Our major contention with regard to brand rivalry within this industry is that having original equipment status should be viewed as an investment, in many ways analogous to expenditures on advertising. Each vehicle maker's spark plug supplier is, by definition, the source of plugs identical in all respects, including brand, to those selected as original equipment by the vehicle manufacturer's engineers. Through its advertising and promotional campaigns, each plug manufacturer stresses that the original equipment plug approved (i.e., purchased) by the vehicle manufacturer is the correct plug to be used for replacement purposes. Once established as Received for publication May 25, 1976. Revision accepted for publication August 30, 1976. *This paper is adapted from my doctoral dissertation (1975). I am deeply indebted to Charles Berry and Stephen Goldfeld of Princeton, Michael Visscher and Dennis Epple of Carnegie-Mellon University, and Jack Ochs of the University of Pittsburgh for their valuable suggestions and criticisms. I Until 1973, an identical price of 5.88a per OE plug was charged by each of the major manufacturers. Since the industry is not subject to substantial scale economies, marginal cost is reasonably approximated by average cost. At no time since World War II has the average cost of manufacture been estimated at less than 1 5a per plug. Information and data used in this article were obtained from the transcripts and exhibits of two District Court trials: U.S. v. Ford Motor Co. et al. (1968 and 1970). I express my gratitude to the Antitrust Division of the U.S. Department of Justice for having granted access to these documents.

The current magnitudes of foreign investment (both on a cumulated-stock and annual-flow basis) call into question the treatment of the foreign investment sector in the U.S. national income accounts. While not a very significant problem, say, 20 years ago, the dimensions of U.S. investment abroad, both in absolute terms and in relation to the U.S. economy now call for further statistical recognition than given in the national income accounts, where foreign-investment income-earning activities are only partly included and those flows which are included are netted out and shown in insufficient detail.

Draper, N. R., and H. Smith, Applied Regression Analysis (New York: John Wiley and Sons, 1966). Geary, R. C., Relative Efficiency of Count of Sign Changes for Assessing Residual Autoregression in Least Squares Regression, Biometrika 57 (April 1970), 123-127. , Two Exercises in Simple Regression, Economic and Social Review 3 (July 1972), 551-559. Granger, C. W. J., and P. Newbold, Spurious Regressions in Econometrics, Journal of Econometrics 2 (July 1974), 111-120. Johnson, James A., and Ernest H. Oksanen, SocioEconomic Determinants of the Consumption of Alcoholic Beverages, Applied Economics 6 (Dec. 1974), 293-301. Kendall, Maurice G., and Alan Stuart, Advanced Theory of Statistics, vol. 2, second edition (London: Charles Griffin & Company Limited, 1967). Koopmans, Tjalling C., The Bias in Single-Equation Methods of Estimating Behavior Equations Relating to a Small Sector of the Economy, Cowles Commission Discussion Paper, Statistics, no. 336 (dittoed) (Chicago, 1949). Maddala, G. S., The Use of Variance Components Models in Pooling Cross Section and Time Series Data, Econometrica 39 (Mar. 1971), 341-358. Nerlove, Marc, Further Evidence on the Estimation of Dynamic Economic Relations from a Time Series of Cross Sections, Econometrica 39 (Mar. 1971a), 359-382. A Note on Error Components Models, Econometrica 39 (Mar. 1971 b), 383-396.

The presence or absence of seasonal influences on interest rates is an important issue both for policy (Gibson, 1970) and for estimation of monetary relationships (Lombra and Kaufman, 1975). Thus conflict between recent research findings of Barth and Bennett (1975) (hereafter B-B) in this REVIEW and previous work is unsettling.' B-B examined two sets of data: (a) monthly observations on several interest rate series over period 1947-1970, and (b) daily observations on 90-day Treasury bill rate from May 1961 to December 1965. Using monthly dummy variables they concluded that seasonal effects do not appear to be present in interest rates examined. However, daily observations do yield significant seasonal effects for short term Treasury rate. B-B resolve this conflict by suggesting that the process of averaging daily data into monthly arithmetic means reduces variation in interest rate enough that one cannot detect (1975, p. 82). In what follows we reformulate their model in a framework consistent with problems noted by Bagshaw and Phaup (1977) and Bolch and Huang (1977).2 Our results using monthly data from April 1951 to March 1973 indicate statistically significant seasonal influences. Moreover, we demonstrate that averaging a data series will not eliminate seasonal pattern underlying B-B model. Thus B-B explanation of conflict of their results with daily and monthly data is not appropriate.3 The method selected for estimating seasonal components of an economic time series will depend on definition selected for seasonality.4 B-B's findings are relevant to only one such definition and implicitly assume one can model seasonal influences on interest rates independently from modeling of process of change in rates themselves.5 Accordingly discrepancy with past evidence supporting seasonality may be result of these factors. To illustrate this point we have selected an amended model consistent with Barth and Bennett's own suggestions (1975, p. 80, fn. 2) and following Nelson's (1970) analysis of term structure of interest rates. Equation (1) defines our model: