¹ In particular, see Goldsmith, Raymond W., Financial Structure and Development (New Haven, 1969)Google Scholar.

² See Gerschenkron, Alexander, Economic Backwardness in Historical Perspective (Cambridge, 1962)Google Scholar.

³ For example, see the following works written or edited by Cameron, Rondo: “The Credit Mobilier and the Economic Development of Europe,” Journal of Political Economy, LXI (December 1953), 461–488CrossRefGoogle Scholar; France and the Economic Development of Europe, 1800–1914 (Princeton, 1961)Google Scholar; Banking in the Early Stages of Industrialization (New York, 1967)Google Scholar; and, Banking and Economic Development (New York, 1972)Google Scholar.

⁴ Many economic historians would argue that the latter hypothesis is correct. For example, Ralph Nelson suggested that the first merger wave of 1894–1905 required the existence of well-developed capital markets, while Ralph Andreano suggested that the opposite hypothesis (i.e., that large-scale capital markets developed in response to the merger wave with its security issues) is just as possible and plausible. See Ralph Nelson, Merger Movements in American Industry (Princeton, 1959), ch. iii; and, Andreano, Ralph, “Four Recent Studies in American Economic History/Some Conceptual Implications,” in New Views on American Economic Development, Andreano, Ralph, editor (Cambridge, Mass., 1965), pp. 15–19Google Scholar.

⁵ In particular, see Davis, Lance E., “The Investment Market, 1870–1914: The Evolution of a National Market,” Journal of Economic History, XXV (September 1965), 355–399CrossRefGoogle Scholar; Sylla, Richard E., “Federal Policy, Banking Market Structure, and Capital Mobilization in the United States, 1863–1913,” Journal of Economic History, XXIX (December 1969), 657–686CrossRefGoogle Scholar. Davis, Lance has used a very similar examination of the same period in “Savings Sources and Utilization,” in Davis, L. E., Easterlin, R. A., Parker, W. N. et al. , American Economic Growth (New York, 1972) 311–339Google Scholar; and, “Capital Mobility and American Growth,” Essay 22 in Fogel, R. W. and Engerman, S. W., editors, The Reinterpretation of American Economic History (New York, 1971), pp. 285–300Google Scholar. Sylla, Richard has rather similar analysis in “American Banking and Growth in the Nineteenth Century: A Partial View of the Terrain,” Explorations in Economic History, IX (Winter 1971 /72), 197–227CrossRefGoogle Scholar; and, “The United States 1863–1913,” ch. viii in Banking and Economic Development, Cameron, Rondo, editor (New York, 1972), pp. 232–262Google Scholar. There are several other important studies of the American capital markets during the 1865–1914 period. Hugh Rockoff has studied the subject in “Risk, the Cost of Information, and the Evolution of the American Capital Market,” (October 1973), unpublished manuscript. Richard Keehn has concentrated upon a single state in “Federal Bank Policy, Bank Market Structure, and Bank Performance: Wisconsin, 1863–1914,” Business History Review, XLVIII (Spring 1974), 1–27Google Scholar; and, “Bank Ownership and Control Patterns: Wisconsin 1860–1900,” a paper presented at the 1974 Western Economic Association Meetings, June 9–11, 1974.

⁶ Davis' assertion of interest rate convergence was unsatisfactory for three basic reasons. First, his interest rate estimates—the net and gross rates of return—were unsatisfactory. The rates of return are net earnings and gross earnings divided by the assets generating those earnings. The national bank's gross earnings were generated by the private market earning assets (stocks, non-U.S. bonds, securities, and, mainly, loans and discounts), the U.S. bonds held almost solely to secure national bank notes and public deposits, and the banker's balances held as part of the bank's reserves (i.e., reserve deposits). Davis included U.S. bonds in his earning asset base (biasing the calculated gross rate down from the actual average interest rate on private market earning assets) but did not include reserve deposits even though not attempting to separate out earnings of reserve deposits (banker's balances) from gross earnings. Differences in gross rates of return can arise simply because various banks held different relative proportions of their earning assets in the lower rate U.S. bonds and reserve deposit balances. Secondly, Davis said the gross rates of return were good approximations of average rates of interest that national banks earned (Davis, “The Investment Market,” p. 357). The gross rates of return, however, could only be calculated from 1888–1914. The net rates of return could be calculated from 1870–1914. Net earnings are equal to gross earnings minus losses and U.S. bond premiums charged off against gross earnings and operating expenses and taxes charged off against gross earnings. Davis said, “… since operating expenses tended to be relatively constant between regions and years and since losses are a short-run phenomenon, the net rates of return are a fairly good proxy for long-term movements in the average interest rates earned” (Davis, “The Investment Market,” p. 357). This is not so. Taxes, which were relatively large, were based on capital and note circulation—not on earning assets or gross earnings. The timing and amount of U.S. bond premiums charged off was an arbitrary decision since premiums could be carried as an asset prior to being charged off against gross earnings. For some regions relative losses rise very sharply and stay quite high for periods of up to five to six years both in the 1870's and 1890's; see Table A-8. The best illustration of the lack of consistent relationships between the gross and net rates of return is found by examining the sample correlation coefficients between the net and gross series for each country and of average short-term interest rates of various areas during the 1870–1888 period. Thirdly, Davis evaluated rate convergence by visual inspection of graphs of threeyear moving averages of the average rates for the regions. This nonrigorous and rather impressionistic approach is not a satisfactory method of evaluating rate convergence. A more accurate method is to use a measure of the relative dispersion of the rates; in particular, the coefficient of variation. It seems rather odd that Davis did not use the coefficient of variation to measure the convergence of the short-term rates he constructed, since later in his study when he evaluated the convergence of long-term mortgage rates (for the same regions) he used the coefficient of variation to measure convergence; Davis, “The Investment Market,” p. 374. In addition, Davis' analysis uses regional average rates even though the rates were apparently derived on a state and city level. The variation of the rates within regions was considerable, and the dispersion of the regional average rates can be changed by redefining the regions. A more appropriate analysis (more accurately reflecting the variation of rates in the United States) is to analyze rate convergence and/or divergence using state or city rates.

⁷ See Smiley, William Gene, The Evolution and Structure of the National Banking System, 1870–1913, unpublished Ph.D. thesis (Iowa City: University of Iowa, 1973)Google Scholar. The rates and other ratios used in this study as well as a detailed discussion of the method of derivation can be found in Smiley, William Gene, “Short-Term Interest Rates of National Banks for States and Reserve Cities, 1888–1913,”Working Paper 74–12, Bureau of Business and Economic Research, College of Business Administration, The University of Iowa, Iowa City, Iowa (June 1974)Google Scholar.

⁸ This brief description of the derivation method makes the procedure appear less complex than it is. Par values of U.S. bonds and the coupon interest rates on par values were used rather than market rates of return and market values. The national banks carried U.S. bonds at par value on their balance sheets and charged off the premiums (cost above par value) at purchase or carried the premiums as a separate asset and arbitrarily charged them off from time to time. For a discussion of the balance sheet items in the Comptroller's reports, see, Alcorn, Edgar G., The Duties and Liabilities of Bank Directors, third edition (Indianapolis: U.S. Bank Note Co., 1915), pp. 138–153Google Scholar. For separating out the dollar earnings of the U.S. bonds from total gross earnings, the use of par values and coupon interest rates on U.S. bonds is appropriate and accurate.

⁹ The loan interest rates are from the 1902 Report of the Comptroller of the Currency (Washington: U.S.G.P.O., 1902), pp. 252–278Google Scholar. The interest rates that the Comptroller reported were estimated by each bank. The Comptroller then averaged these for each class of banks for each state and each reserve city. The average interest rates in Appendix Table A-1 were calculated as weighted sums of those rates—the weights were relative shares of average loans and discounts for each state or city. The accuracy of the Comptroller's reported rates therefore depends upon how accurately each bank estimated its average rate of interest on loans and upon how the Comptroller constructed his average for each capital stock class of banks for each state or city. The sample coefficient of correlation, r, for both the state and city sets of rates is 0.8839. The sample correlation coefficient for the set of state rates only is 0.8988; and, the sample correlation coefficient for the set of city rates only is 0.6186.

All three sample correlation coefficients are significantly different from zero at the 0.5 percent level of significance.

¹⁰ The commercial paper rates are calculated from data given in Greef, Albert O., The Commercial Paper House in the United States (Cambridge, 1938), pp. 80–82Google Scholar. Both rates covered approximately the same twelve-month period. The sample coefficient of correlation, r, for the two series is 0.634, and is significantly different from zero at the 0.5 percent level of significance. Several aspects of the rates explain the lack of a closer relationship. First, the R_p rates cover a broader set of earning assets; particularly broker's loans. Secondly, the yearly R_p rate is conceptually a weighted average or rates prevailing during the year, while the commercial paper rate could only be calculated as an arithmetic average of the monthly rates during the year.

¹¹ The states in each non-reserve city national bank region are:

I: Maine, Vermont, New Hampshire, Massachusetts, Connecticut, and Rhode Island.

II: New York, New Jersey, Pennsylvania, Delaware, Maryland, and the District of Columbia.

III-A: Virginia, West Virginia, North Carolina, Kentucky, and Tennessee.

III-B: South Carolina, Georgia, Florida, Alabama, Mississippi, Louisiana, Texas, Arkansas, and Oklahoma.

IV: Ohio, Indiana, Illinois, Michigan, Wisconsin, Minnesota, Iowa, and Missouri.

V: North Dakota, South Dakota, Nebraska, Kansas, Montana, Wyoming, Colorado, and New Mexico.

VI: Washington, Oregon, California, Idaho, Utah, Nevada, and Arizona.

The cities in each reserve city national bank region are:

I: Boston.

II: New York City, Albany, Brooklyn, Philadelphia, Pittsburgh, Baltimore, and Washington, D.C.

III-A: Louisville.

III-B: New Orleans, Savannah, Dallas, Fort Worth, Galveston, Houston, San Antonio, Waco, Muskogee, and Oklahoma City.

IV: Cincinnati, Cleveland, Chicago, Detroit, Milwaukee, Des Moines, St. Paul, Minneapolis, St. Louis, Kansas City (MO), St. Joseph, Columbus, Indianapolis, Cedar Rapids, Dubuque, and Sioux City.

V: Lincoln, Omaha, South Omaha, Kansas City (KA), Topeka, Wichita, Denver, and Pueblo.

VI: San Francisco, Seattle, Spokane, Tacoma, Portland, Los Angeles, and Salt Lake City.

These regions are a modification of the Comptroller's regional definitions. They were defined on the basis of fairly similar national Danking characteristics among the states in the region. Jay R. Mandle has suggested a somewhat similar division of the South into two regions. See, Mandle, Jay R., “The Plantation States as a Sub-Region of the Post-Bellum South,” Journal of Economic History, XXXIV (September 1974), 732–738CrossRefGoogle Scholar.

¹² Three points should be noted. First, the sharp rise in the 1900 rates in Appendix Tables A-3 and A-4 and the rise in the rates centered on 1900 in Figures A-2 and A-3 should be viewed with considerable skepticism. The 1900 rates may not accurately reflect relative rate differences. The rate derivation was appropriate for all years except 1900. The Gold Standard Act authorized the exchange of older higher rate bonds (securing note issues) for a new issue of 2 percent to secure notes. Direct money compensation was paid to reflect the premiums on the older, higher rate bonds. There is no way to separate out these extranormal bond earnings from the 1900 gross earnings, thus, the method overstates the 1900 earnings from private market assets. Secondly, the rise in the rates for the reserve city banks in Region III-B (the lower South states) near the end of the period was due to the appearance of new reserve cities with relatively higher rates. From 1903 through 1910, five Texas cities and two Oklahoma cities became reserve cities. The rates of the oldest reserve cities (New Orleans and Savannah) did not show this marked rise. Finally, Davis observed similar graphs in asserting that rates were converging. Obviously, judgments on rate convergence (or divergence) can vary substantially when using this method. It is not clear Davis was justified in his conclusions. Using the coefficient of variation (which Davis used at another point in his 1965 article) on the weighted country bank gross rates there is, essentially, a fairly constant level of relative dispersion (with a peak at 1905) throughout the period. For the reserve city bank weighted regional gross rates that Davis derived, the coefficient of variation shows rate divergence from 1888 through the late 1890's and early 1900's and convergence (generally) from then through to 1914. The levels of relative dispersion at the end of the period are consistently lower than at the beginning of the period (1888–1914) for reserve city banks. The movement of the coefficient of variation calculated for the regional rates in Appendix Tables A-3 and A-4 is roughly similar to the coefficient of variation for Davis regional rates—except for a rise (i.e., rate divergence) in the measure through the late 1890's and early 1900's for the country bank rates in Appendix Table A-3, and convergence thereafter. This evaluation is inappropriate, however, since it omits consideration of any rate variation within any region.

¹³ The “equal weights” version uses an arithmetic mean average rate, and the squared deviation of each state or reserve city rate is given an equal weight of (1/n-1) where n is the number of states or reserve cities. The “A_p weights” version uses weights which are relative shares of total private earning assets for all nonreserve city banks or reserve city banks. The mean rate is then a weighted average using the relative share weights, and each squared deviation is then weighted by that state or reserve city's share of total A_p. The A_p weights form of the coefficient of variation is rather easily decomposable into the interregional variance, the weighted sum of the intraregional variances, and an interaction term; see Chapter 3 of Smiley, The Evolution and Structure. The use of the coefficient of variation as a measure of the relative dispersion of interest rates and thus (over time) the convergence and/or divergence of interest rates is not new. Lance Davis used the coefficient of variation to measure rate convergence in the long-term capital market—but not the short-term capital market; Davis, “The Investment Market,” p. 374. Kenneth Lewis and Kozo Yamamura also used the coefficient of variation to measure interest rate convergence in Japan; Kenneth A. Lewis and Kozo Yamamura, “Industrialization and Interregional Interest Rate Structure, The Japanese Case: 1889–1925,” Explorations in Economic History, VIII (Summer 1971), 473–499. The absolute dispersion of the rates (rather than the relative dispersion) should be used to measure rate convergence and capital reallocation between areas if the transactions costs (excluding differentials in risk premiums) were an absolute or constant value. But, if transactions costs were a relative value tending to move with the general movement in prices and interest rates, then the relative dispersion measure is appropriate, since no matter what the general movement of interest rates, changing relative rate differentials would indicate a spatial reallocation of capital. Little direct evidence exists on the level or character of transactions costs. Some meager evidence on open market commercial paper brokerage fees (an important means of interregional capital transfers) does exist. Roy Foulke and Albert Greef both indicated that brokerage fees were generally stated as a percentage rate. In the late 1870's these rates probably averaged about 0.50 percent By the mid-1880's, brokerage houses in the larger cities were accepting paper on fees of 0.25 percent; Foulke, Roy A., The Commercial Paper Market (New York, 1931), p. 254Google Scholar; and, Greef, Albert O., The Commercial Paper House in the United States (Cambridge, 1938), pp. 106–108Google Scholar. “… After about 1896, when commercial paper rates began to fall below the levels that had prevailed in the earlier years of the period, the spread between dealers' buying and selling rates, and therefore the gains which could be realized from the differences between these rates, declined also” (Greef, p. 109). These comments suggest that transactions costs would have been relative wedges between regional interest rates, thus suggesting that the relative dispersion measure is appropriate for evaluating rate convergence.

¹⁴ The sharp decrease in dispersion in 1900 should be viewed with considerable skepticism, since it is due almost certainly to the inability to derive accurate rates for 1900; see footnote 12.

¹⁵ As far as I know there is no statistical test for the homogeneity of coefficients of variation, though there are tests for the homogeneity of variances and means. In Appendix Table A-5 one can see that since the mean rates fall, then the absolute dispersions (the standard deviations) fall more than the relative dispersions. I tested the hypothesis that the variances for 1888 through 1893 and 1908 through 1913 were not equal against the null hypothesis that the variances were equal. At a 5 percent level of significance the null hypothesis was accepted. I used the M test for the homogeneity of variances as given in Crow, Edwin L., Davis, Frances A., and Maxfield, Margaret W., Statistics Manual (New York, 1960), pp. 78–81 and 240Google Scholar. Their source was Thompson, Catherine M. and Merrington, Marine, “Tables for Testing the Homogeneity of a Set of Estimated Variances,” Biometrika, XXXIII (1943–1946), 296–304.Google Scholar

¹⁶ From 1888 through 1913, the Comptroller's data only gave the value of losses plus premiums charged off against gross earnings. Using the 1885, 1886, and 1887 data, losses were clearly the majority of losses plus premiums. Loans and discounts are used as the base rather than private earning assets since it seems probable that the losses the banks suffered were on loans and discounts rather than stocks, securities, and non-U.S. bonds.

¹⁷ The main use that Davis made of his net rate of return estimates was as proxies for interest rates during 1870–1887 so as to evaluate interest rate convergence during that period. It has already been suggested that these are unsatisfactory for that purpose; however, in a footnote on p. 358 of his 1965 article, Davis also implies that the net rates of return represent a “riskless” return, and differences in net rates of return must be explained by uncertainty (in particular), transactions costs, or market imperfections (There is an element of ambiguity in Davis' discussion since he apparently differentiates between uncertainy and risk, without describing how they are different or to be distinguished from each other.). A potential investor in projects or securities (i.e., loans and discounts) in another area would be interested in the net return. After deducting the costs of making the transactions and the (expected) losses, the investor will invest in the other region if the (expected) net returns are greater than the (expected) net returns in his own area. The net rates of return for national bank regions, however, do not represent the “riskless” return on loans and discounts (i.e., the potential investments for an individual private lender). They are the net earnings from all of the banks' earning assets, which include relatively important amounts of U.S. bonds and reserve deposits, and not just from the assets the potential investor would be interested in. Additionally, the net earnings are gross earnings minus losses plus premiums and minus operating expenses plus taxes. The potential individual private investor would not consider premiums as a “loss.” Also, the banks' operating expenses were largely interest payments on deposits and other borrowed funds. The interest payments on borrowed funds certainly were not the transactions costs relevant to the investment decision of an individual residing in another region. The net rates of return, in fact, do not have any convenient nor obvious interpretation, such as “riskless returns.” The proper and highly relevant use for net earnings is in calculating the rates of return to the net worth (capital plus surplus plus undivided profits) of the banks. This certainly was the relevant data necessary in deciding where to invest in (or start up) national banks.

¹⁸ For a discussion of risk averse behavior of bankers in Boston, Philadelphia, and New York during the 1850's see, Hinderliter, Roger H. and Rockoff, Hugh, “The Management of Reserves by Antebellum Banks in Eastern Financial Centers,” Explorations in Economic History, XI (Fall 1973), 37–53Google Scholar.

¹⁹ There is little doubt that the majority of all reserve deposits were in New York City's national banks. For the rest of the national banks in the United States (excluding St. Louis and Chicago) a study for 1889, 1890, and 1891 showed that 61.31 percent of all drafts drawn upon all banks in the U.S. were drawn upon New York City banks. These drafts were a common means of moving funds (including reserve balances) between banks and areas; see Sprague, O. M. W., History of Crises Under the National Banking System, National Monetary Commission (Washington: U.S.G.P.O., 1910), pp. 126–127Google Scholar.

²⁰ These percentages are not reserve ratios, though their movement follows the movement of reserve ratios.

²¹ For example from 1891 through 1898, the average number of national banks decreased 2.99 percent in the deep South, 27.35 percent in the Plains states, and 24.53 percent in the Pacific Coast states. The number of banks increased between 1891 and 1898 in the New England, Middle Atlantic, Upper South, and East North Central states.

²² This, of course, is not the only possible explanation for the observed country bank behavior. One alternative is Richard Sylla's hypothesis that the power of monopolies among local (country) banks prior to the passage of the Gold Standard Act in 1900 was reduced by sharply increasing competition in the years that followed (causing relative reductions in bankers' balances). This alternative, however, does not seem very plausible. The build up of reserve deposits was very rapid during the 1897–1900 years for all country bank regions (more so for the agriculturally oriented ones) and it seems difficult to believe that the monopolistic powers of country banks were sharply increasing in those few years. It should also be noted that Sylla was highly selective in the empirical evidence used to justify his hypothesis. In his Tables 6, 7, and 8, Sylla presents data on bankers' balances at five-year intervals from 1870 through 1890 (i.e., 1870, 1875, 1880, 1885, and 1890) but only at ten-year intervals for the following two decades (i.e., 1890, 1900, and 1910); Sylla, “Federal Policy, Banking Market, Structure,” pp. 682–683.

A more plausible alternative would be something like the following. The year 1897 was the trough of a severe depression and 1900 was approximately the year that full-employment (of labor and presumably capital) was regained. As a result, during the restoration of full-employment, output and incomes could increase sharply simply by putting idle manpower and idle physical plant and equipment into use. Thus, during the 1897–1900 years the demand for financial capital (loans) to create additional physical capital was low due to the availability of idle capacity. Consequently, reserves increased due to the lack of loan demand rather than due to risk averse behavior.

I fail to find this alternative as acceptable as the risk aversion hypothesis for several reasons. First, the largest part of the loans and discounts made by national banks were the “self-liquidating” type of loans (i.e., “real bills” doctrine) and not of a longer-term nature needed to construct physical capital. Secondly, for nearly all country banks there was also a shift away from loans and discounts toward the relatively safer stocks, non-U.S. bonds, and securities. Third, the relative increase in reserve deposits was much greater in regions III-B, V, and VI than in regions I, II, III-A, and IV. It would also seem to be much more than coincidence that regions III-B, V, and VI had sharply higher relative losses in the 1893–1897 years and also in the 1897–1900 years. The risk aversion hypothesis offers a highly consistent and plausible explanation for the behavior of the country banks in this period.

²³ The twenty-two reserve cities are: Boston, New York City, Albany, Brooklyn, Philadelphia, Pittsburgh, Baltimore, Washington, D.C., New Orleans, Louisville, Cincinnati, Cleveland, Chicago, Detroit, Milwaukee, Minneapolis, St. Paul, St. Louis, Kansas City (Missouri), St. Joseph, Omaha, and San Francisco. These were the major reserve cities. Their share of total reserve city A_p was 90 percent or more through 1909 and never less than 88 percent. The thirty-seven reserve cities include the twenty-two given above plus Savannah, Des Moines, Lincoln, Dallas, Houston, Columbus, Indianapolis, Cedar Rapids, Dubuque, Kansas City (Kansas), Wichita, Denver, Portland, Los Angeles, and Salt Lake City.

²⁴ The 1905 peak was caused by sharp declines in the gross rates of return—particularly for the largest cities. The year 1905 for these rates actually covers approximately the calendar period of September 1904 through August 1905. O. W. M. Sprague said there was a “decline in trade” in 1904. “Loans were made at such abnormally low rates in New York that outside banks and the trust companies of the city found it to their advantage to increase their balances with the banks, upon which they received a return of 2 percent” (Sprague, History of Crises, footnote a, p. 222). As a result, there was an exceptionally sharp and large increase in deposits in New York City banks and rates there fell very sharply. The rates in several other large eastern and midwestern cities also dropped sharply—though usually not as much as in New York City.

²⁵ As mentioned there is no test for the equality of coefficients of variation. Using the test for the equality of variances mentioned in footnote 14, the equality of the “equal weights” variances for the sets of twenty-two and thirty-seven reserve cities was examined. For the twenty-two reserve cities the variances for 1891 through 1895 and 1908 through 1913 were used. At the 5 percent level of significance, the null hypothesis was rejected and the alternative hypothesis that the variances were not homogeneous (were unequal) was accepted. For the thirty-seven cities the variances of the years 1904 through 1913 were used. Again, at the 5 percent level of significance, the null hypothesis of equality of variances was rejected.

²⁶ Davis quotes Greef on dates when commercial paper brokers began business in several cities. Examination of the dates and cities cited in the Greef and Foulke books indicates several things. First, the appearance of brokerage houses in cities outside of the East, North Central, and Northeast regions seems to have been concentrated in the 1906–1910 period. Secondly, the cities cited were almost all larger cities which were, or shortly became, reserve cities. This suggests that the effects during this period were mainly on reserve city banks; see Roy A. Foulke, The Commercial Paper Market, pp. 250–253; and, Albert O. Greef, The Commercial Paper House, pp. 38–45.

²⁷ Foulke, The Commercial Paper Market, p. 249.

²⁸ Greef, The Commercial Paper House, p. 57.

²⁹ Myers, Margaret G., The New York Money Market, Vol. I (New York, 1931), 321Google Scholar. Myers is citing the testimony of Mr. Andrew Frame of Waukesha, Wisconsin, before the House Sub-Committee on Banking and Currency Reform, 1913, p. 425; 62nd Congress, 3rd Session.

³⁰ Foulke, The Commercial Paper Market, p. 249.

³¹ Greef, The Commercial Paper House, p. 60. In the statement Greef cites Naumburg, W. W., “Commercial Paper,” Annual Financial Review section, New York Times, January 7, 1912, p. 25Google Scholar.

³² Although I have made some specific criticisms of Davis' work, I wish to acknowledge my debt to his seminal work. My rates and their derivation methods were extensions and refinements of Davis' rates and methods.