^{page 480 note 1} See Neuburger, H. and Stokes, H. H., “German Banks and German Growth, 1883–1913: An Empirical View,” this Journal, 34 (Sept. 1974), 710–31Google Scholar; Neuburger, H. and Stokes, H. H., “German Banking and Japanese Banking: A Comparative Analysis,” this Journal, 35 (March 1975), 238–52Google Scholar; Neuburger, H. and Stokes, H. H., “German Banks and German Growth: Reply to Fremdling and Tilly,” this Journal, 36 (June 1976), 425–27Google Scholar; Fremdling, R. and Tilly, R., “German Banks, German Growth and Econometric History,” this Journal, 36 (June 1976), 416–24Google Scholar; and Sylla, R., “Financial Intermediaries in Economic History: Quantitative Research on the Seminal Hypotheses of Lance Davis and Alexander Gerschenkron,” in Gallman, R., ed., Recent Developments in Business and Economic History: Essays in Memory of Herman E. Krooss (Greenwich, Conn., 1977)Google Scholar.

^{page 480 note 2} See n. 26 (pp. 721–22) of our 1974 paper. The values of ρ used in equations 7 through 9 are 6320, 6043, and 5274.

^{page 480 note 3} A discussion of the B34S regression program is contained in H. H. Stokes, “The B34S Data Analysis Program: A Short Write-Up,” Report FY 77–1, College of Business Administration Working Paper Series, Univ. of Ill. at Chicago Circle, p. 88ff. B34S is a further development of the B34T program written by H. Thornber. For a discussion of the B34T program, see H. Thornber, “Manual for (B34T, 8 March 1966) a Stepwise Regression Program,” Report No. 6603, Center for Mathematical Studies in Business and Economics, Univ. of Chicago, March 1966. Information concerning the Faddeeva algorithm is contained in Faddeeva, V. N., Computational Methods of Linear Algebra (New York, 1959)Google Scholar.

^{page 481 note 4} Komlos does not indicate whether he used double precision values of the correlation matrix for his test or whether he merely used the values given by his program. The latter approach suffers from extreme rounding problems and is not a suitable test for multicollinearity, since as the correlation matrix is rounded, it will approach collinearity.

^{page 481 note 5} In a classic paper on production functions, Solow discusses the problem of measuring capital (see Solow, R., “Technical Change and the Aggregate Production Function,” Review of Economics and Statistics, 39 [Aug. 1957], 312–20)CrossRefGoogle Scholar. If raw capital stock data are used, these data will measure capital in place rather than capital in use. While Solow notes that adjustment of capital stock data by one minus the employment rate is not ideal if other measures of utilization are available, he comments that such a procedure “probably gets closer to the truth than making no correction at all” (p. 314). More recent work, such as that of Christensen and Jorgenson, has adjusted for utilization “based on the consumption of electricity relative to installed electric motors” (L. Christensen and D. Jorgenson, “U.S. Real Product and Real Factor Input, 1929–1967,” Review of Income and Welath, ser. 16 [March 1970], 19–50). Such an adjustment procedure is not appropriate for the period of our study. Further discussion of the problem is contained in Nadiri, M., “Some Approaches to the Theory and Measurement of Total Factor Productivity: A Survey,” Journal of Economic Literature, 8 (Dec. 1970), 1137–78Google Scholar.

^{page 482 note 6} Eistert, E., Die Beeinflussung des Wirtschaftswachstums in Deutschland von 1883 bis 1913 durch das Bankensystem (Berlin, 1970), p. 91Google Scholar.

^{page 483 note 7} The inappropriateness of Komlos' choice is illustrated by the highly implausible suggestion of decreasing returns to scale in his third equation (indicated by a sum of labor and capital coefficients smaller than one). Because significant coefficients for labor and capital have not been obtained in this equation, it cannot be used to test the effect of CA/MB. Moreover, the reported Durbin-Watson test statistic indicates that serial correlation of the residuals cannot be ruled out at the 5 percent level.

^{page 483 note 1} If it were, then would the development of ridge regression not have been superfluous?

^{page 483 note 2} Their suggestion that multicollinearity is not substantiated by my finding that the “sum of mean square errors is one hundred times greater than that needed for a perfectly orthogonal system” is clearly a mistake.

^{page 483 note 3} Hoerl, Arthur E. and Kennard, Robert W., “Ridge Regression: Application to Nonorthogonal Problems,” Technometrics, 12 (Feb. 1970), 70Google Scholar.

^{page 483 note 4} To be sure, one does not have perfect multicollinearity, and the absence of a zero eigenvalue means that a four-dimensional space is defined, but two of the eigenvalues are so small (.007 and .019) that most of the variation can be accounted for in only two dimensions. See ibid.

^{page 483 note 5} Multicollinearity increases the absolute values of the coefficients. The fact that Neuburger and Stokes found the sum of the coefficient of capital and labor to exceed one may be a confirmation of multicollinearity, rather than of economies of scale which is their interpretation. Multicollinearity also makes the estimated parameters sensitive to sample coverage. If their model is left intact but the data divided into two parts, neither regression passes the usual tests.

Between 1883 and 1898 neither capital nor is significant. Between 1898 and 1913 none of the variables is significantly different from zero at the 95% significance level.

^{page 484 note 6} Thornber introduced the Faddeeva algorithm into the B34T program in order to estimate “the numerical error in the regression coefficients resulting from rounding error in inverting the cross product matrix.” Hodson Thornber, “Manual for (B34T, 8 March 1966) a Stepwise Regression Program,” Report No. 6603, Center for Mathematical Studies in Business and Economics, Univ. of Chicago, March 1966, p. 31. Faddeeva wrote that the “Inversion of a matrix … offers no certainty as regards the accuracy of the results obtained, owing to the inevitable rounding errors. …” To check the accuracy of the computation she suggests subtracting the product of the matrix and its inverse from the unit matrix, which will “indicate the degree of inaccuracy in the results obtained.” Faddeeva, V. N., Computational Methods of Linear Algebra, trans, from the Russian by Benster, Curtis D. (New York, 1959), p. 99Google Scholar.

^{page 484 note 7} Johnston, Jack, Econometric Methods (2nd ed.; New York, 1972), p. 163Google Scholar.

^{page 484 note 8} Thornber, “Manual for B34T,” p. 31.

^{page 484 note 9} Solow, Robert M., “Technical Change and the Aggregate Production Function,” The Review of Economics and Statistics, 39 (Aug. 1957), 314CrossRefGoogle Scholar.

^{page 485 note 10} Sylla, Richard, “Financial Intermediaries in Economic History: Quantitative Research on the Seminal Hypotheses of Lance Davis and Alexander Gerschenkron,” in Gallman, Robert, ed., Recent Developments in Business and Economic History: Essays in Memory of Herman E. Krooss (Greenwich, Conn., 1977), p. 79Google Scholar.

^{page 485 note 11} Neuburger, Hugh and Stokes, Houston H., “German Banks and German Growth, 1883–1913: An Empirical View,” this Journal, 34 (Sept. 1974), 711Google Scholar.

^{page 485 note 12} Sylla, “Financial Intermediaries,” p. 79.

^{page 485 note 13} Neuburger and Stokes, “German Banks and German Growth,” p. 723.

^{page 486 note 14} Third order generalized least squares was used. No heteroscedasticity was indicated. Capital was adjusted for utilization by the Neuburger/Stokes index.

^{page 486 note 15} That is, the regression was performed with non-agricultural output and included the incorrect capital utilization index. The denominator of this shift parameter does not include credit extended through securities, a very small share of total credit, for which no year-end figures were found.