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Comment: Portfolio Theory and Industry Cost-of-Capital Estimates
Published online by Cambridge University Press: 19 October 2009
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Litzenberger's and Rao'ps (L-R) econometric estimate of the cost of capital is in some ways ingenious as well as interesting. The methodology of the estimating procedure is that of the two-stage least squares (2SLS) instrumental variable (IV) approach which was previously used by Miller and Modigliani in their 1966 study. The product differentiation of the L-R study emanates primarily, though not exclusively, from the fact that the valuation equation is derived from capital market line theory. This feature results in the indirect econometric estimates being “useful” for deriving insights into cost of capital variations cum interfirm differences in operating risk. Ergo, Litzenberger's and Rao's empiricism is in no way dependent upon the homogenous risk class concept of Miller and Modigliani.
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- Copyright © School of Business Administration, University of Washington 1972
References
1 Miller, M. H. and Modigliani, F., “Some Estimates of the Cost of Capital to the Electric Utility Industry, 1954–1957,” American Economic Review (June 1966), pp. 333–391.Google Scholar
2 Another important “ingredient” of Litzenberger's and Rao's investigation is that the surrogate of the growth rate reflects investors' expectations in the market rather than being a magnitude derived from the rate of expansion of assets.
For a study which showed that “the estimates of the volume of expected investment opportunities based on the retrospective model were generally superior to those based on a prospective model,” see Wenglowski, Gary M., “Estimates of the Cost of Capital and the Markets Valuation of the Average Electric Utility Firm: 1954–1964” (Ph.D. diss., University of Pennsylvania, 1967) p. 283.Google Scholar
3 The second requirement that the instrumental variables are uncorrelated with the error terms cannot be rigorously established empirically and is probably never completely satisfied.
4 For a discussion of the statistical analysis of the residuals see Anscombe, F. J., “Examination of Residuals,” Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, ed., Neyman, J., Volume I, pp. 1–36, (Berkeley, California: University of California Press, 1961)Google Scholar, and Anscombe, F. J. and Tukey, J. W., “The Examination and Analysis of Residuals,” Technometrias (1963), pp. 141–160.Google Scholar
5 The estimation of returns by Blume, Fama, Mandelbrot, and Roll indicates that the distribution is a member of the stable Paretian family. This implies that least squares even if admissible is certainly not the best approach for estimation. Blume, Marshall E., “The Assessment of Portfolio Performance: An Application of Portfolio Theory” (Ph.D. diss,, Graduate School of Business, University of Chicago)Google Scholar; Fama, Eugene F., “The Behavior of Stock Market Prices,” Journal of Business (January 1965), pp. 34–105Google Scholar; Mandelbrot, Benoit, “The Variation of Certain Speculative Prices,” Journal of Business (October 1963), pp. 394–419Google Scholar; and Roll, Richard, “The Efficient Market Model Applied to U.S. Treasury Bill Rates” (Ph.D. diss., Graduate School of Business, University of Chicago, 1968).Google Scholar
6 Marshall Blume and Irwin Friend, “A New Look at the Capital Asset Pricing Model” (unpublished paper, Symposium on Methodology in Finance-Investments, Rutgers University—Graduate School of Business, May 13–14, 1971).
7 This argument concludes by indicating that the issue is still unresolved. It is recognized that the various objections to the use of the D-W may not be internally consistent though what is important is whether they singularly or collectively cast doubt on the linearity conclusion of Litzenberger and Rao.
8 Suggestions that might alleviate this problem include formation of the first stage regressions on a small number of instruments selected on the basis of a principle components or factor analysis of the dependent variable. See, for example, Kloeck, T. and Mennes, L. B. M., “Simultaneous Equations Based on Principal Components of Predetermined Variables,” Econmetrica (January 1960), pp. 45–61.Google Scholar
9 Given the simultaneity of jointly determined variables via a larger system of equations, Haavelmo and others have demonstrated that OLS gives parameter estimates which are asymptotically biased while Theil, Theil and Zellner, and Basman have shown that 2SLS estimates are consistently asymptotically unbiased. See Haavelmo, T., “Methods of Measuring the Marginal Propensity to Consume,” in Studies in Econometric Methods, ed., Hood, W. C. and Koopmans, T. C., (New York: John Wiley and Sons, Inc., 1953), pp. 75–91Google Scholar; Theil, Henry, Economic Forecast and Policy, 2nd ed. (Amsterdam: North Holland Press, 1961)Google Scholar, Appendices 6B and 6C; Theil, Henry and Zellner, Arnold, “Three-Stage Least Square: Simultaneous Estimation of Simultaneous Equations,” Econometrica (January 1962), pp. 54–78Google Scholar, and Basman, R. L., “A Generalized Classical Method of Linear Estimation of Coefficients in a Structural Equation,” Econometrica (January 1957), pp. 77–83.Google Scholar
However, it should be noted that Klein is prepared to argue the general proposition that 2SLS estimates are more sensitive than OLS estimates to the presence of multicollinearity. See Klein, L. R. and Kakamura, Mitsugu, “Singularity in the Equation Systems of Econometrics: Some Aspects of the Problem of Multicollinearity,” International Economic Review (September 1962), p. 284.Google Scholar
10 It is important to realize that empirical studies of the cost of capital are “not intended to be directly useful for decision making at the level of the individual firm. [Their] main purpose still is to help economists and finance specialists understand how the world works.” Miller, Merton, “Discussion,” in Financial Research and Management Decisions, ed., Robichek, Alexander A. (New York: John Wiley and Sons, Inc.), p. 33.Google Scholar This point about the state of the art apparently is often neglected in an appraisal of empirical studies. See, for example, Brigham's argument concerning the lack of dynamic properties of the timing of stock issues, “Discussion,” Journal of Finance (May 1971), p. 41.
11 For an interesting exchange concerning the methodology of determining the validity of the M-M framework and the role of the underlying theoretical assumptions vis-à-vis economic positivism see Weston, J. Fred, “On Miller- Modigliani and Lintner,”Determinants of Investment Behavior, A Conference of the Universities—National Bureau Committee for Economic Research, ed., Ferber, Robert (New York: National Bureau of Economic Research, 1967), pp. 255–256Google Scholar; and Miller, Merton A. and Modigliani, Franco, “Reply to Friend and Weston,”Determinants of Investment Behavior, A Conference of the Universities— National Bureau Committee for Economic Research, ed., Ferber, Robert (New York: National Bureau of Economic Research, 1967), p. 266.Google Scholar
12 Dhrymes, Phoebus J., Econometrics: Statistical Foundations and Applications (New York: Harper and Row Publishers, 1970), p. 296.Google Scholar
13 Malinvaud, E., Statistical Methods of Econometrics (Chicago, Ill.: Rand McNally & Co., 1966), p. 350.Google Scholar