Knowledge that Transforms

T HE most frequently used estimating technique for applied economic research has been ordinary least squares (OLS). There are two theoretical justifications for its use. First, the Gauss-Markov theorem suggests that OLS estimators will outperform all other techniques in the class of linear unbiased estimators.1 Secondly, under the assumption that the error terms are normally distributed, OLS estimators can be derived as the maximum likelihood estimates. Frequently when OLS is introduced in elementary texts, the method of minimizing the sum of absolute deviations (MAD) is presented for comparison purposes, but rarely is it given serious consideration for applied uses.) Certainly one reason for such behavior stems from previous evaluations of OLS versus MAD estimators. Asher and Wallace (1963) found that the use of MAD meant one should be prepared to give up considerable efficiency 3 More recently Glahe and Hunt (1970), suggested several estimators derived under the general minimization criterion. In contrast to the Asher-Wallace study, the Glahe-Hunt model was a two-equation linear simultaneous system. Their results show that neither form of absolute deviation estimator outperformed either OLS or two-stage least squares.4 The purpose of this paper is to suggest that in at least one aspect these comparisons have given OLS a differential advantage. That is, both of these studies employed errors for their hypothesized models which were drawn from normal distributions. Consequently the OLS estimators are both maximum likelihood and best linear unbiased estimators (BLUE) under such circumstances. Since recently published works by Zeckhauser and Thompson (1970), Fama (1965) and others have called into question the assumption of normally distributed error terms, attention has begun to shift to other alternatives.5 Blattberg and Sargent (1971) have examined three techniques including both OLS and MAD when the errors are drawn from a stable Paretian distribution. Their findings indicate that the MAD estimator . performs sufficiently well that it deserves further study and elaboration. G Accordingly we have chosen to explore the relative merits of OLS and MAD for a single equation model whose errors are drawn from a double exponential parent distribution. This distribution was chosen because both estimators will exhibit theoretically desirable properties. OLS remains the BLUE estimator, while MAD is the maximum likelihood estimator. Furthermore, this distribution is one member of the power distribution suggested by Zeckhauser and Thompson as an alternative to the normal. This paper is divided into, three sections. The first describes the design of the experiments. Section II presents the empirical results and the last summarizes the primary findings of the paper.

where X1 represents a series of T observations (t = 1, . .. , T). This ratio is not appropriate for testing the independence of residuals from least squares regression; its purpose is to test for autocorrelation among observed variables. The Durbin-Watson development (1950, 1951) of the von Neumann ratio was concerned with testing residuals from regression for serial correlation. They test the null hypothesis H,, that there is no serial correlation between the residuals (Ut) against the alternative hypothesis H1 that the Ut are positively correlated. The Durbin-Watson test statistic is

M ANY cross-section studies exist in the literature attempting to explain variations in per capita state and local expenditures on such services as highways, municipal services, health, and education. Differences in per capita expenditures across states are explained in terms of such factors as differences in population densities, urban-rural distributions, average income levels, age distributions, and numbers of school-age children.' In most of these studies, however, the underlying theory has not been carefully spelled out and, in particular, it is never made clear whether the demographic variables are thought to enter on the demand side or on the supply side of the market for state and local services. In the first part of this paper we look at the theory underlying such regression studies of the determinants of state and local expenditures. We attempt to distinguish between the demand side of the market for such services and the supply (cost) side. In the second part of the paper we obtain empirical estimates of price and income elasticities of demand for state and local services for three broad classifications of services. Finally we discuss a number of interesting applications of our results.

T HE geographic extent of the market has long been recognized as an important element of industry structure. For lack of systematic and direct measures, however, previous studies have relied either on rough classifications of geographical market size (local, regional or national) (Comanor and Wilson, 1967, p. 433; Kaysen and Turner, 1959, appendixes, pp. 283-285; Stigler, 1963, pp. 265-269 and 56-57) or on output dispersion indexes such as the number of states needed to account for 75 per cent of total shipments (Collins and Preston, 1968, 1969; Fuchs, 1962). This paper develops an alternative index of market size based on the Census of Transportation. Some attempts are made to evaluate various measures of market extent by comparisons with indexes of output dispersion and with an element of transport cost. It ends with a brief summary of the geographic market sizes of United States manufacturing industries.

T HE purpose of this paper is to estimate a labor supply or participation rate function for period 1948 through 1968, for various age-sex groups that comprise secondary labor force.' There are three major findings of paper. First, participation behavior is primarily explained by real wages. There are, however, two hypotheses, relative and permanent wage models that may underlie wage variables. The relative wage variable is adapted from recent research in demography and is found to predominate over more traditional permanent wage effect for a number of female age groups. (As will be seen, in labor force equations, permanent and relative wage theories predict opposite signs for a wage variable so that a test of two hypotheses is possible.) Secondly, supply of labor responds positively to a variable that reflects rate of inflation. The inclusion of this variable follows a formulation proposed by Friedman (1968). He conjectures that a form of money illusion in supply function of labor is foundation of an empirically observable, short-run Phillips curve. Thirdly, labor supply is found to respond to changes in excess demand conditions in labor market only during period of chronic, high 1958-1966 and even during that period, effect observed is considerably smaller than that noted in earlier studies. The model is compared with more traditional labor force equation that contains rate and a time trend. Both equations are fitted for period 1948-1968 and are then used to forecast most recent data for quarters 1969.1 through 1970.3. The equation presented in this paper dominates alternative model in terms of adjusted R 2's and Durbin-Watson statistics (in estimated period) and it uniformly forecasts better. Finally, implications of labor force equation are explored. It is suggested that recently adopted concepts such as unemployment, the labor force, and potential need redefinition in light of findings presented here. There are, at present, two basic approaches to study of labor force participation. The first is generally associated with Tella (1965) and Dernburg and Strand (1966) (and will hereafter be referred to as unemployment model). They found that labor force participation rate varied inversely with rate. This finding was identified with worker effect. The model may be estimated in form (LIP)i = a( + a, U + a9T'a1 < 0 (1) where (LFP)i is labor force participation rate of subgroup i, and U is aggregate rate. The time trend, T, may be interpreted as representing gradual, sociological change of preferences which is sending women from home into labor force and older workers from labor force into home. This equation has gained wide acceptance in literature, and its results have had an important impact on public policy discussions. Thus finding that discouraged workers leave labor force when (measured) is high is used to adjust rate and level of output to take account of hidden unemployed. The adjusted series has become an independent variable in empirical wage equations since work of Simler and Tella (1968). The adjusted output series and resulting measure of GNP gap are used in planning fiscal and monetary policy. Clearly to extent, however, that equation (1) does not describe labor force behavior and overstates Received for publication May 17, 1971. Revision accepted for publication July 23, 1971. * The author thanks Richard A. Easterlin, Benjamin M. Friedman, Robert J. Gordon, Lawrence R. Klein, Thomas Sargent and Susan M. Wachter for helpful suggestions. ' The secondary labor force is defined here to include males 16-19 and 65+ and females 16 through 65+. The dependent variable is a form of participation rate and hours worked are not included. 2See, for example, Tella (1965), Dernburg and Strand (1966) and Bowen and Finegan (1969). Models of Barth (1968) and Vroman (1970) also found a low elasticity for labor force in terms of participation rate.

Center of Indiana University, to whom I would like to express my appreciation.' For instance, in an introduction to a presenitation of French concentration ratios, Jacques Loup ("La concentration dans l'industrie francaise," E~tztdes et con joncture, XXIV (Feb. 1969) expressly notes that the United States concentration ratios are lover but does not bother to carry out any actual empirical comparisons Nwhich vould, in point of fact, show the reverse conclusion (see table 2 ).2This point was emphasized to me in cori-espondence by Peter Pashigian; for a detailed analysis of certain other critical aspects of the relationships between market size and monopoly, see his "The Effect of Market Size on Concentration,"

Finally, for completeness we should note that later work (Harvard Discussion Paper No. 234, 1971) has shown that when investors' risk-aversions are functionally related to their ending wealth, the investor's personal equilibrium depends upon a combination of his risk-aversion and its first derivative, but the market price of risk aggregates the investor's more complex marginal rates of substitution of return and risk in exactly the same way as it aggregates investors risk-aversions per se in simple situations. iMoreover, all the statements made above on the basis of aggregations of risk-aversions are shown to be valid in the more complex analysis.

W HILE many aspects of conglomerate firms have been studied, empirical tests of their performance remain limited. Most of the studies to date test aspects of mergers generally.' Professor Eamon Kelly (1967) compared a sample of 21 firms which grew 20 per cent or more by acquisitions during the period from 1946 to various terminal dates through 1963, with firms of similar size and products but with growth mainly internal (Kelly, 1967). He found no significant difference in profitability between the two groups. Gort and Hogarty (1970) also examined a number of general aspects of mergers. Their statistical analysis indicated that the stockholders of acquired firms gained on the average, while the owners of acquiring firms lost on the average. They found that mergers have an approximately neutral effect on Ithe aggregate worth of firms that participated in them (Hogarty, 1970). Reid's studies (1968) included data evaluating a sample of conglomerate firms for the decade ending in 1961. He utilized three measures which he characterized as reflecting the interests of managers, and three reflecting the interests of stockholders. Reid concluded that more actively merging firms and firms that diversified to a greater extent in their merging activity scored higher on the criteria related to managers' interests and lower on criteria related to stockholders' interests. Lorie and Halpern (1970) studied the performance of 117 mergers taken from the Federal Trade Commission listing for 1954-1967 of all mergers in manufacturing and mining in which the acquired firm had assets greater than 10 million dollars. In the Lorie and Halpern study, the focus was particularly on the possibility of deception of investors. The mergers which they studied, therefore, were ones in which the shareholders of the acquired company received relatively complex instruments such as convertibles or warrants.2 The investment return to, stockholders of the acquired firms was analyzed on various bases measured in the period six months prior to the merger to two years after the merger. In general, the investment return performance to stockholders of the acquired firms was superior to the market performance of broad market indexes for comparable periods of time. For example, the mean rates of return for the 12and 14-month periods subsequent to the mergers were 9.34 per cent and 9.52 per cent, respectively, while corresponding rates for the market index were 7.73 per cent and 7.38 per cent. Hogarty (1970) analyzed the success of 43 mergers by the criteria of post-merger investment performance (capital gains plus dividend returns) adjusted by an Investment Performance Index (IPI) for the industry of the acquiring company. Using measurements including reinvestment of dividends, he classified 14 failures (F), 24 ambiguous (A), and 5 successes (S). For an IPI of 10 per cent, a failure was defined as a return of 9 per cent or less, a success was a return of 11 per cent or more, and the ambiguous category represented returns between 9 and 11 per cent. Not assuming reinvestment of dividends, the distribution was 3 S, 19 A and 21 F. Hogarty found these Received for publication April 5, 1971. Revision accepted for publication June 21, 1972. * This study was supported by the Research Program in Competition and Business Policy, UCLA. We appreciate the helpful suggestions of the reviewer. ' The 1171-page special edition of the Spring 1970 St. John's Law Review on conglomerate mergers contains no article with empirical data on the comparative performance of conglomerate firms. Two empirical articles in the volume deal with other aspects of performance. The S. E. Boyle paper analyzes the premerger growth and profitability characteristics of acquired companies. The paper by T. F. Hogarty reviews earlier historical studies of the success of mergers generallv. 2 Since this kind of funny money (Lorie and Halpern's term) was alleged to be characteristic of conglomerate mergers, their sample of firms is presumed to be of conglomerates. However, no formal criteria for selection were emnlnved .