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Notes on the Social Saving Controversy

Published online by Cambridge University Press:  11 May 2010

Robert William Fogel
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Abstract

This paper explores a number of the unresolved issues posed by the debate on the social saving of railroads. The final section includes a brief summary of the main findings of the new economic history of transportation.

Type
Papers Presented at the Thirty-Eighth Annual Meeting of the Economic History Association
Information
The Journal of Economic History , Volume 39 , Issue 1 , March 1979 , pp. 1 - 54
Copyright
Copyright © The Economic History Association 1979

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References

1 The discussion was held at the first annual Cliometrics Conference, Purdue University, December, 1960.

2 In this JOURNAL, 22 (06 1962), 163–97Google Scholar.

3 Much of the social saving literature is cited in the bibliography to O'Brien, Patrick, The New Economic History of Railways (London, 1977)Google Scholar. To this listing one should add: Coatsworth, John, “Growth Against Development: The Economic Impact of Railroads in Porfirian Mexico,” mimeo 1976, which is a translation and revision of Crecimento contra desarrollo: El impacto economico de losferrocaniles en el porfiriato. 2 vols., Sepsetentas No. 271–72 (Mexico City, 1976)Google Scholar. Williamson, Jeffrey G., Late Nineteenth-Century American Development: A General Equilibrium History (Cambridge, 1974), cially ch. 9.Google Scholar; Williamson, Jeffrey G., “The Railroads and Midwestern Development, 1870-1890: A General Equilibrium History,” in Klingaman, David C. and Vedder, Richard K., Essays in Nineteenth Century Economic Histor. (Athens, Ohio, 1975), ch. 11Google Scholar; Tunzelmann, G. N. von, Steam Power and British Industrialization to 1860 (Oxford, 1978), chs. 3, 6, and 11Google Scholar; Vamplew, Wray, “Nihilistic Impressions of British Railway History,” in McCloskey, Donald N., ed., Essays on a Mature Economy: Britain after 1840 (Princeton, 1971), ch. 10Google Scholar; Vries, Jan de, “Barges and Capitalism: Passenger Transportation in the Dutch Economy, 1632-1839,” A. A. G. Bijdragen. 21 (1978), ch. 8Google Scholar; McCloskey, Donald N., “New Model History,” Times Literary Supplement. 12 12, 1975Google Scholar; Temin, Peter, Causal Factors in American Economic Growth in the Nineteenth Century (London, 1975), ch. 5CrossRefGoogle Scholar; Lee, C. H., The Quan titative Approach to Economic History (London, 1977), ch. 4Google Scholar; and Elster, Jon, Logic and Society: tradictions and Possible Worlds (Chichester, 1978), ch. 6Google Scholar. This supplement to O'Brien's list is far from exhaustive. In addition to other relevant works that are cited below, there are numerous interesting reviews and brief commentaries, especially in essays analyzing the methodology of the New Economic History. Some of these are listed in McClelland, Peter D., Causal Explanation and Model Build ing in History, Economics, and the New Economic History (Ithaca, 1975)Google Scholar. Social saving calculations did not originate with present-day economists and economic historians. Such calculations were carried out by legislators and men of affairs who were involved in the decision processes on government aid for internal improvements during the nineteenth century, not only in America, but also in Europe. Fishlow, Albert cites two early social saving estimates in American Railroads and the Transformation of the Antebellum Economy (Cambridge, 1965)Google Scholar. Richard H. Tilly called my attention to an essay by Ernst Engel (the Prussian statistician identified with “Engel's Law”) which presents a calculation of the social saving attributable to German railroads during 1840-80. Engel, Ernst, “Das Zeitalter des Dampfes in technisch-statistischer Beleuchtung”, Zeitschrift des Königlichen Preussischen Statistischen Bureaus, (Berlin, 1880)Google Scholar. Hodne, Richard in his An Economic tory of Norway 1815-1970 (Tapir, 1975), p. 221Google Scholar, cites a study of the social saving of railroads in Norway by Svanøe, E. O. J. that appeared in Statsøkonomisk Tidsskrif. in 1887Google Scholar.

4 The model which follows differs from that presented in Fogel, Robert W. and Enger-man, Stanley L., eds., The Reinterpretation of American Economic History (New York, 1971), p. 101Google Scholar, by allowing part of the output of the transportation sector to be purchased for use in the production of other output.

5 The Williamson model is discussed in the third section of this paper. Lewis, in a dissertation under way at the University of Chicago, is investigating the effect of railroads on the location of economic activity and other consequences stemming from the impact of railroads on relative prices.

6 Fishlow, Albert, American Railroads. p. 93Google Scholar.

7 Fogel, Robert W., Railroads and American Economic Growth: Essays in Econometric History (Baltimore, 1964), ch. 3Google Scholar.

8 Cf. Fogel, , Railroads. pp. 92–107Google Scholar. David has pointed out that the reduction in the? estimate of the social saving due to the extension by 5,000 miles of the canal system implies a social rate of return on the investment in excess of 50 percent per annum. David, Paul A., “Transportation Innovations and Economic Growth: Professor Fogel On and Off the Rails,” Economic History Review. 2nd Ser., 22 (12 1969), 506–25CrossRefGoogle Scholar, rpt. as ch. 6 of Paul A. David, Technical Choice, Innovation, and Economic Growth (Cambridge, 1975), pp. 291-314.

9 Lebergott, Stanley, “United States Transportation Advance and Externalities,” this JOURNAL 26 (12 1966), 443, 445Google Scholar. Lebergott puts the ton-miles of freight carried per dollar of cost at.413; the reciprocal yields a rate of 0.24 cents per ton-mile. Over the period from 1852 to 1857, the freight carried by the Philadelphia and Reading averaged 25,226 tons per mile of road per annum. Poor, Henry V., History of the Railroads and Canals of the United States of America (New York, 1860),.pp. 484–85Google Scholar. Fishlow, , American Railroads. p. 337Google Scholar, put the average railroad freight rate in 1859 at 2.58 cents per ton-mile.

10 I have located the price and output points for 1859, 1900, and 1970 on the same curve. This, of course, stretches the argument very much in Lebergott's direction since it implies that all of the decrease in railroad rates was due to a movement along a fixed long-run supply curve, allowing naught to downward shifts in the supply curve. However, Fishlow has shown that at least 50 percent of the increase in total factor productivity between 1830 and 1910 can be attributed to various technological improvements in rails, cars, locomotives, and other equipment. Cf. Fishlow, Albert, “Productivity and Technological Change in the Railroad Sector,” in Conference on Research in Income and Wealth, Output Employment and Productivity in the United States After 1800. Vol. 30 of Studies in Income and Wealth (New York, 1966), pp. 583–646Google Scholar.

11 Coal accounted for about three quarters of the total freight hauled by the Philadelphia and Reading Railroad during 1852-57. Poor, , History. p. 485Google Scholar.

12 Boyd, J. Hayden and Walton, Gary M., “The Social Saving from Nineteenth-Century Rail Passenger Services,” Explorations in Economic History. 9 (Spring 1972), 247-48, 253–54Google Scholar.

13 Fogel, , Railroads. pp. 219–34Google Scholar; Fogel, Robert W., “Railroads as an Analogy to the Space Effort,” Economic Journal. 76 (03 1966), 16–43CrossRefGoogle Scholar.

14 Nerlove, Marc, “Railroads and American Economic Growth,” this JOURNAL, 26 (03 1966), 111–15Google Scholar; Fishlow, , American Railroads. pp. 52–54Google Scholar.

15 If the social rate of interest was a function of the level of investment in railroads, equation (16) would become

where h(K) is the function for the social rate of interest.

16 Quite similar points were made by David, , “Transportation Innovations,” p. 521Google Scholar, and by Hawke, G. R., Railways and Economic Growth in England and Wales 1840-1870 (Oxford, 1970), pp. 10–12Google Scholar.

17 McClelland, Peter, “Railroads, American Growth and the New Economic History,” this JOURNAL, 28 (03 1968), 106Google Scholar; Scheiber, Harry N., “On the New Economic History-and Its Limitations,” Agricultural History. 41 (10 1967), 387Google Scholar.

18 Only the third digit is changed. The interregional social saving would have risen from 0.61 to 0.64 percent of GN P and the overall social saving on agricultural products would have been raised from 1.78 to 1.81 percent of GNP. “Less-than-carload” rates are irrelevant since virtually all inter-regional shipments went at “carload” rates.

19 The railroad rate from St. Louis to New Orleans was 0.572 cents per ton-mile. This is based on a railroad rate of 20 cents per hundred pounds and a rail distance of 699 miles. See U.S. Inland Waterways Commission, Preliminary Report of the Inland Waterways Commission. U. S. Senate, Doc. 325, 60th Cong., 1st Sess. (1908), pp. 344–45 (hereinafter referred to as Preliminary Report.Google Scholar; U.S. Pay Department (War Department), Official Table of Distance. (Washington, D.C., 1906), p. 427Google Scholar.

20 McClelland, , “Railroads,” pp. 111–13Google Scholar; David, , “Transportation Innovation,” p. 513Google Scholar; Fogel, , Railroads. pp. 46-47, 87–88Google Scholar.

21 Lebergott, , “United States Transportation,” p. 440Google Scholar.

22 In 1889 state and private canals had net earnings equal to 1.3 percent of the cost of construction (at book value). U.S. Bureau of the Census, Eleventh Census of the United States: 1890, Report on Transportation Business in the United States. Vol. 14, Part II, pp. 475, 480 (hereinafter referred to as Census of Transportation 1890).

Discounting the stream of annual expenditures on construction and operation, as well as the annual net earnings of the New York canals at 6 percent, it appears that over 90 percent of the capital cost had been paid by 1882. The computation is based on data in New York State, Annual Financial Report of the Auditor of the Canal Department: 1884. “Statement of Receipts and Payments in Each Year on Account of All the State Canals.” Revenues were obtained by adding “Tolls” and “Rent on Surplus Water.” The annual sum of capital and operating costs was estimated by adding the following annual payments: “Canal Commissioners and Superintendent of Public Works,” “Repairs of Canals,” “Expenses of Collectors and Inspectors,” “Weighmasters,” and 70 percent of “Miscellaneous Expenses.” It was estimated that approximately 30 percent of “Miscellaneous Expenses” was unrelated to the operation of the canals. This procedure of obtaining the combined capital and operating expenditures was adopted because direct information on annual capital expenditures was not available before 1875, but the cumulated sum of capital expenditures for the period 1817-74 is available, as are the annual construction costs for 1875-92 (see New York State, Annual Report of the State Engineer and Surveyor: 1893. pp. 47–57). Of course if “Miscellaneous Expenditures” had been dis-aggregated, the desired annual combined cost series would have been directly available. It was possible to test the assumption that 70 percent of “Miscellaneous Expenditures” was canal costs. If the annual operating costs in the Annual Financial Repor. (p. 63) are subtracted from the total costs computed from “Statement of Receipts,” one obtains a series of estimated annual construction costs. The cumulated sum of this estimated series for the period 1817-74 comes to within 1.06 percent of matching the cumulated sum of actual construction costs for the same period reported in the Annual Report of the State Engineer. For the period 1875-82, when both annual construction and operating costs are directly available, the indirect procedure yields annual totals that are within 4.0 percent of the actual annual totals of operating and construction costs.

23 Cumulated federal expenditures on rivers and harbors during 1822-90 were $180.4 million. Ton-miles of transportation in 1889 were 1.4 billion by canal and 48.3 billion by all other domestic contiguous waterways. See Appendix, Section A, for a discussion of the method of computing ton-miles of water transportation and the average water haul. Barger, Harold, The Transportation Industries 1889-1946 (New York, 1951), pp. 254–55Google Scholar; Census of Transportation 1890. Part II, pp. xi-xiii, and passi.; U.S. Bureau of the Census, Historical Statistics of the United States, Colonial Times to 1970. (Washington, D.C., 1975), p. 765 (hereinafter referred to as Historical Statistics.Google Scholar; New York State, Committee on Canals, Report of the Committee on the New York Canals, 1899-1900. pp. 181–84 (hereinafter referred to as New York Canals.Google Scholar; George G. Tunnell, “Statistics of Lake Commerce,” U.S. House of Representatives, Doc. No. 277, 55th Cong. 2d Sess., passim. 24 By “long-run” I mean that capital is fully variable, so that the size of canal locks, prisms, and vessels on all the relevant waterways (actual or potential) could be increased as warranted by the increased traffic.

25 This evidence is discussed below.

26 Desai, Meghnad, “Some Issues in Econometric History,” Economic History Review. 2nd Ser., 21 (1968), 1–16CrossRefGoogle Scholar; Wellington, Donald, “The Case of the Superfluous Railroads,” Economic and Business Bulletin. 22 (Fall 1969), 33–38Google Scholar; White, Colin M., “The Concept of the Social Saving in Theory and Practice,” Economic History Review. 2nd Ser., 24 (1976), 82–100CrossRefGoogle Scholar.

27 Much of the discussion has failed to distinguish between the equity and efficiency effects of monopoly pricing. As will be shown below, to the extent that canals used monopoly power to set rates above marginal costs, the increased revenue was mainly an income transfer.

28 In this connection it should be noted that my estimate of the effect of an extension of the canal system on the social saving (cf. Fogel, , Railroads. pp. 94–98Google Scholar) is also robust with respect to a plausible range of error in the estimate of construction costs. Assuming that the combined annual interest and depreciation rates were 0.07, the annual rental cost of the canal extensions would be $11.3 million. Consequently, if construction costs were twice that indicated by the regression, my estimate of the agricultural social saving would rise from 1.8 to 1.9 percent of GNP.

The same point holds with respect to the argument that some of the rivers designated as navigable by the Army Engineers were too shallow to handle the volume of traffic that would have been diverted to these waterways in the absence of railroads. Such a contingency could have been handled by canalizing these rivers or building parallel canals along the necessary portions of the rivers in question. If we suppose that the increased traffic would have required parallel canals along 5,000 miles of such rivers (this is considerably greater than the mileage of the navigable rivers thus far contested), the additional construction costs would once again raise the social saving by just one tenth of 1 percent of GNP. Cf. Fite, Gilbert, review in Agricultural History. 40 (04 1966), 147–49Google Scholar; Shaw, John A., “Railroads, Irrigation, and Economic Growth: The San Joaquin Valley of California,” Explorations in Economic History. 24 (Winter 1973), 211–27CrossRefGoogle Scholar.

29 New York State, Annual Financial Report of the Comptroller, Relating to Canals: 188. Assembly, Vol. 1, No. 4, p. 17Google Scholar, commented on the devastating effects of the business cycle recession that began in 1882 on canal operators. Their difficulties, the report said, were due to their failure to combine and act monobolistically:

On the 1st of January, 1883, there were 4,749 boats of all classes registered as navigating the State canals…. If the canals with their equipments were owned by a corporation, or even if the equipments only were under one management, they would represent a single harmonious system competing with the railways in the transportation of freight. As they are now operated and managed, the equipments are furnished by almost as many individual owners as there are boats, and representing as many conflicting interests. These owners are without organization….

30 Hawke, , Railways. pp. 80–86Google Scholar.

31 Census of Transportation 1890. Part II, pp. 469-79; cf. Preliminary Repor. (1908), pp. 188–209.

32 As pointed out in footnote 22, state and private canals reported combined net earnings in 1889 that amounted to just 1.3 percent of their cost of construction. Census of Transportation 1890. Part II, pp.* 475, 480. See the section, The Representativeness of the Water Rate. for a discussion of my upward adjustment in water rates to compensate for the subsidy of the capital employed in water transportation.

33 Ransom, Roger L., “Government Investment in Canals: A Study of the Ohio Canal, 1825-1860,” unpublished Ph.D. dissertation, University of Washington, 1963, pp. 135-36Google Scholar. The tolls represent the. receipts of the canal but not the entire benefit of the canal. When external benefits were added to the canal receipts, Ransom obtained a social rate of return for the 1840s that exceeds the market rate of return.

34 Cited in Haupt, Lewis M., “Canals and their Economic Relation to Transportation,” Papers of the American Economic Association. Series I, Vol. 5, No. 3 (1890), p. 67Google Scholar.

35 Kirkaldy, Adam W. and Evans, Alfred Dudley, The History and Economics of Transport (London, 1915), p. 221Google Scholar; Franzius, Otto, Waterway Engineering (Cambridge, 1936), pp. 433–35Google Scholar; U.S. Senate, Select Committee on Transportation Routes to the Seaboard. Report No. 307, 43d Cong., 1st Sess., Vol. 1, p. 247Google Scholar. Cf. also Jeans, J. Stephen, Waterways and Water Transport (London, 1890), ch. 27Google Scholar; Johnson, Edwin F., The Navigation of the Lakes and Navigable Communications Therefrom to the Seaboard, and to the Mississippi River (Hartford, 1966)Google Scholar; Meyer, John R., Peck, Merton J., Stenason, John, Zwick, Charles, The Economics of Competition in the Transportation Industrie. (Cambridge, Mass., 1959), pp. 111–13Google Scholar; Palmer, J. E., British Canals: Problems and Possibilities (London, 1910), ch. 3Google Scholar. See also the sources cited in Judson, William Pierson, History of the Various Projects, Reports, Discussions, and Estimates for Reaching the Great Lakes from Tide-Water, 1768-1901. Oswego Historical Society, Pub. No. 2. (Oswego, N.Y., 1901)Google Scholar. The Index to the Reports of the Chief of Engineers, U.S. Army, 1866-1912. U.S. House of Representatives, Doc. No. 740, 63d Cong., 2d Sess., 2 vols., lists many reports investigating the relationship between waterway costs and vessel size, prism size, distance, and so forth.

36 David, , “Transportation Innovation,” p. 511Google Scholar.

37 See the sources cited in footnote 35.

38 Desai, , “Some Issues,” p. 10Google Scholar; Tunzelmann, von, Steam Power. pp. 39–41Google Scholar.

39 New York Canals. p. 171; U.S. Bureau of Statistics (Treasury Dept.), “The Grain Trade of the United States,” Monthly Summary of Commerce and Finance. No. 7, Series 1899-1900 (01 1900), p. 1972Google Scholar; Preliminary Report. pp. 193–209; Cranmer, H. Jerome, “Canal Investment, 1815-1860,” in Conference on Research in Income and Wealth, Trends in the American Economy in the Nineteenth Century. Vol. 24 of Studies in Income and Wealth (Princeton, 1960), p. 564Google Scholar; Census of Transportation 1890. Part II, pp. 474-77; Tunnell, , “Statistics,” pp. 3, 4, 26Google Scholar.

40 Barger, , The Transportation Industries. p. 184Google Scholar, and the Appendix,. Section A, below.

41 New York Canals. pp. 181–83.

42 Cranmer, , “Canal Investment,” pp. 547–64Google Scholar. Figures in parentheses are standard errors.

43 The data for this regression are from Census of Transportation 1890. Part II, pp. 475-83, 484.

44 Assuming that the depreciation and interest rates summed to 0.07, the annual rental value on the construction costs (book value) of state and private canals in operation in 1889 is $10.5 million. The operating expenses of the same canals in 1889 were $2.1 million. Census of Transportation 1890. II, pp. 475, 480.

45 McClelland, , “Railroads,” pp. 115–20Google Scholar.

46 The data for this regression are from New York State, Annual Financial Report of the Comptroller Relating to Canals: 1884. p. 63; New York Canals. pp. 156-57, 181. Co was deflated by the Warren-Pearson price index. i

47 Since operating costs were less than 20 percent of the annual long-run cost of the New York canals, one cannot rule out a prior. the negative coefficient on Xd. On the other hand, it is possible that the mix of commodities transported was changing over time in such a way that an appropriate measure of this mix would be positively correlated with distance and negatively correlated with costs (or vice versa), when total tonnage shipped is held constant. Then the negative coefficient of Xd would be due to the omission of a mix variable. Tests of such an hypothesis were unsuccessful because of difficulties in constructing an appropriate index of commodity mix from published data, although all the regressions attempted yielded a negative coefficient on the Civil War dummy. An alternative approach is to regress total costs on the logarithm of ton-miles and'a Civil War dummy; this is equivalent to imposing the constraint that the coefficients on tons and on distance are the same.

The results of this regression were as follows:

A likelihood ratio test rejects the restriction at the 5 percent level but not the 2.5 percent level. Note that the Civil War dummy is still negative and is now statistically significant. The various regressions suggest the need for further research into canal cost functions, and especially into the effect of the shifting commodity mix on total costs. Pursuit of this line of analysis, however, requires the retrieval of unpublished data.

48 The same basic point was made by Fishlow who noted that “McClelland's … own data show that a doubling of canal traffic between 1859 and 1863 left canal freight rates virtually unchanged! Over the interim, they had temporarily risen owing to adjustment problems, to be sure, but tjiat is totally irrelevant to the long-run question under consideration.” See Fishlow, Albert, “Internal Transportation,” in Davis, Lanceet al., American Economic Growth: An Economist's History of the States (New York, 1972), p. 516Google Scholar. It might be added that it is unlikely that the supply of canal boats had reached long-term equilibrium by 1863.

49 Lebergott, , “United States Transportation,” p. 439Google Scholar. Cf. David, , “Transportation Innovation,” p. 513Google Scholar; McClelland, , “Railroads,” p. 114Google Scholar; McClelland, Peter D., “Social Rates of Return on American Railroads in the Nineteenth Century,” Economic History Review. 2d Ser., 22 (08 1972), 477–78Google Scholar; White, , “The Concept,” p. 85Google Scholar; White, Colin M., “Railroads and Rigor,” Journal of European Economic History. 4 (Spring 1975), 194Google Scholar. The preceding writers held that I failed to recognize that railroads and waterways provided a homogeneous product. Desai (“Some Issues,” p. 10), on the other hand, held that I assumed perfect substitutability. He contended that it was the heterogeneity of railroad and waterway services that undermined my analysis.

50 The average haul of railroads in 1899, was 247 miles (Historical Statistics. p. 733). The method of estimating the average distance of a water haul in 1889 is given in the Appendix, Section A.

51 Hawke, , Railways. pp. 20–21Google Scholar.

32 Coatsworth, “Growth Against Development,” chs. 3 and 4.

53 See his “Review of The New Economic History of Railways,” Journal of Business Histor. (forthcoming).

54 New York Canals. pp. 190, 208. Cf. footnote 55.

55 Data for these regressions were derived as follows: R w for 1868-95, from Tunnell, , “Statistics of Lake Commerce,” p. 29Google Scholar; R w for 1896-98, from New York Canals. p. 190, col. 4; all values were deflated by the Warren-Pearson price index. M, from Historical Statistics. p. 512 (converted to tons). Rr, from New York Canals. p. 190, col. 1 minus col. 5. The years 1868 through 1878 were years in which a premium existed on greenbacks, but the values of Rr in Tunnell were given in gold. To obtain a consistent currency series, the rates for these years were multiplied by an implicit deflator (A/B, where A is the currency values of lake freight rates from Tunnell, p. 29; and B is the undeflated lake freight rate from New York Canals. p. 109, col. 4). The entire series was then deflated by the Warren-Pearson price index. Qg is from U.S. Bureau of Statistics, “The Grain Trade,” pp. 1964–65 (converted to tons)Google Scholar. N is calculated from the number of days between the opening of the lake at Buffalo and the closing of the Welland Canal. For the years in which the closing date of the Welland Canal was missing, the average difference between the closing dates of the Welland Canal and of the port of Buffalo (over the entire period) was added to the closing date at Buffalo (see the Annual Report of the Buffalo Merchants' Exchange, Including Statistics of the Trade and Commerce at Buffalo: 1884. pp. 37-8; 1891, pp. 95-6; 1899, pp. 88-9; see also Buffalo Chamber of Commerce, Statistics of the Trade and Commerce of Buffalo, 1875. p. 66). B. since average sizes of grain-carrying vessels were not available, the index was calculated from a weighted average of the average sizes of sailing vessels (Br) and steam vessels (Bs). Br was obtained from New York Canals. p. 198, col. 2 + col. 1; Bs from col. 4+ col. 3. The respective weights were the estimated proportions of grain-carrying vessels which were sailing and steam vessels. The estimated number of sailing vessels carrying grain was 0.5 x Kr/Br, where Kr is the total tonnage of sailing vessels (from New York Canals. p. 198, col. 2). The estimated number of steam vessels carrying grain was (Ks/144117)027428 x (48049/Bs), where Ks is the total tonnage of steam vessels (from New York Canals. p. 198, col. 4); 144117 is the value of Ks in year 1868, the first observation; 48049 is one third of the steam tonnage in 1868; and 0.27428 is the elasticity of Qg with respect to Ks, obtained from a previous regression. The weight in each case was therefore the number of sailing vessels carrying grain and the number of steam vessels carrying grain, each divided by the sum of the two. Kb: since the capital stock of grain-carrying vessels in tons was not available, the index was calculated from a weighted average of Kr and Ks (denned above). The respective weights were 0.7904 and 0.2096. These were obtained by dividing the elasticities of Qg with respect to Kr and to KSvby the sum of the two elasticities.

56 The coefficient on R, was quite robust to various alternative data series and specifications of the demand and supply functions, varying between a low of 0.95 and a high of 1.12.

It should be noted that I have treated Rr as an exogenous variable. During the period covered by the regression, railroad rates on wheat were set by a cartel. The cartel did not allow rates to vary from day to day, as dictated by supply and demand. To the extent that the cartel took market conditions into account in setting rates, it did so with a lag. Moreover, the rates set were frequently the outcome of a political process that subordinated profit maximization to external pressures as well as to the internal compromises needed to maintain the cartel. When the cartel was successful, the rates it set tended to persist for relatively long periods of time, unlike the water rates, which fluctuated from day to day. When the cartel broke down and rate wars ensued, prices also deviated from the levels dictated by supply and demand, but were determined by the exigencies of the struggle between the cartel and the “cheaters.” Thus a coefficient of variation (computed as the standard error around a time trend, divided by the mid-period trend value of rail charges on wheat between Chicago and Buffalo) was less than 40 percent of that of the corresponding coefficient of variation of water rates. Cf. Gilchrist, D. T., “Albert Fink and the Pooling System,” Business History Review. 24 (Spring 1960), 24–29CrossRefGoogle Scholar; Edward C. Kirkland, Industry Comes of Age: Business, Labor, and Public Policy 1860-1897. Vol. 6 of The Economic History of the United States. David, Henry, et al. eds. (New York, 1961), 85–93Google Scholar; MacAvoy, Paul W., The Economic Effects of Regulation: The Trunk-Line Railroad Cartels and the Interstate Commerce Commission Before 190. (Cambridge, Mass., 1965), chs. 3-5Google Scholar; Chandler, Alfred D. Jr, The Visible Hand: The Managerial Revolution in American Busines. (Cambridge, Mass., 1977), pp. 137–43.Google Scholar The sources of the data for the computation are cited in footnote 55, under variables Rw, Rr, Qg.

57 The word aggregate was emphasized because some of the arguments made for an infinite cross elasticity really apply to individual shippers. Even if each individual shipper had a n infinite cross elasticity of demand, the cross elasticity of the aggregate demand curve could still be in the neighborhood of 1 because of differences among individuals in the slopes of the linear portions of their isoquants as well as in the range over which linearity prevailed.

58 Fogel, , Railroads. pp. 71, 107–09Google Scholar; Historical Statistics. p. 733; Hawke, Railways. pp. 62, 86, 180.

59 Hawke, , Railways. pp. 61, 86Google Scholar. Cf. the discussion of Figure 1.

60 O'Brien, , The New Economic History. pp. 40–45Google Scholar; Lebergott, , “United States Transportation,” pp. 439–40. Cf. McClelland, “Social Rates,” passimGoogle Scholar.

61 Historical Statistics. p. 737.

62 Ulmer, Melville J., Capital in Transportation, Communications and Public Utilities: Its Formation and Financing (Princeton, 1960), p. 256Google Scholar.

63 Fishlow, , “Productivity,” p. 606Google Scholar. The 1890 value for real net capital stock was obtained by interpolating between Fishlow's 1889 and 1899 figures. The interpolated figure was then converted into dollars of 1890 with the Warren-Pearson price index in U.S. Bureau of the Census, Historical Statistics of the United States, 1789-1945. (Washington, D.C., 1949), p. 231Google Scholar.

64 Kuznets, Simon, National Product Since 1869 (New York, 1946), p. 201Google Scholar.

65 Historical Statistics. p. 1003; Homer, Sidney, A History of Interest Rate. (New Brunswick, N.J., 1963), p. 320Google Scholar.

66 Historical Statistics. p. 737.

67 Fogel, , Railroads. pp. 42, 72, 86–87Google Scholar; cf. note 50 on pp. 84–85.

68 This calculation gives the order of magnitude of a possible divergence between rates and marginal costs on a fixed quantity of railroad transportation. One could also compute the effect on the estimated social saving of allowing the quantity transported to respond to the lower rate. If we assume that the elasticity of demand was 1, and that the marginal cost of transportation was approximately constant over the range of increase in transportation service, then the combined effect of a reduction in rates and in quantities carried would be to raise the agricultural social saving from 1.78 to 1.93 percent of GNP.

69 McClelland, , “Railroads,” pp. 108–109Google Scholar.

70 Fogel, , Railroads. p. 56Google Scholar.

71 The total factor productivity index was constructed from the price dual, in the rate-of-change form. The rate of change in wagon rates implied by McClelland's conjecture is obtained by solving 20.5 = 20e*47. A divisia index of the rates of change in input prices between 1859 or 1860 and 1906 was constructed using wages of farm labor from Historical Statistics. p. 163, and prices of horses and mules from Towne, Marvin W. and Rasmussen, Wayne D., “Farm Gross Product and Gross Investment in the Nineteenth Century,” in Conference on Research in Income and Wealth, Trends, p. 286Google Scholar. It was assumed that the price of wagons moved with the wholesale price index (Historical Statistics,. pp. 200, 201). The weights applied were: labor, 0.44; teams, 0.40; wagons, 0.16. Cf. Fogel, , Railroads,. p. 72Google Scholar. If the 1906 wagon rates are projected backward to 1859 on the basis of the index of input prices, we obtain an 1859 wagon rate of 13.4 cents. Even this figure may be too high since the USDA rates were based on the assumption of zero backhauls and because very few fanners hired commerical service but used their own wagons, teams, and labor. Highway engineers argued that the cost of wagon transportation to farmers was less than half the commercial rate. An investigation of rates paid to farmers for hauling in central Illinois c. 1906 revealed rates in the neighborhood of 10 cents per ton-mile. The last figure projected back to 1859 by the index of input prices yields a figure of 6.5 cents. Cf. Fogel, , Railroads. pp. 107–09Google Scholar.

72 The procedure followed was described in footnote 71. Taylor's figure implies that wagon rates rose at an annual rate of 0.7 percent.

73 Rothenberg, Winifred, “The Marketing Perimeters of Massachusetts Farmers, 1750-1855,” mimeo, Brandeis University., 1978Google Scholar.

74 In the long run a rise in the price of transportation would lead to a shift away from transportation-intensive goods as well as to a change in the locus of economic activity. As pointed out below, the Williamson model implies that with increases in the price of transportation of the magnitude indicated by Fishlow's social saving, all transportation of agricultural goods from the Midwest to the' East could have halted and the United States could have become a net importer of foodstuffs.

75 The data required for these computations come from Fishlow, , American Railroads. p. 51, and from McClelland's one-third increase in the wagon rateGoogle Scholar.

76 This work includes, in addition to studies previously cited in connection with the social saving controversy, Fenoaltea, Stefano, “Railroads and Industrial Growth, 1861-1913,” Explorations in Economic History. 9 (Summer 1972), 325–51CrossRefGoogle Scholar; Vamplew, Wray, “The Railways and the Iron Industry: A study of Their Relationship in Scotland,” in Reed, M. C., ed., Railways in the Victorian Economy (Newton Abbot, 1969), pp. 33–75Google Scholar; Fremdling, Rainer, “Railroads and German Economic Growth: A Leading Sector'Analysis with a Comparison to the United States and Great Britain,” this JOURNAL, 37 (09 1977), 583–604Google Scholar; and Chandler, The Visible Hand.

77 Quotations of David, in this section are from his “Transportation Innovation,” pp. 515–19Google Scholar. His diagram, which is reproduced as Part A of Figure 5, makes the “total indirect social benefit” from economies of scale equal to about 97 percent of the f.o.b. value of the end-period output of the transportation-using industry. My estimate of the agricultural social saving equals 6.9 percent of the gross farm product of agriculture in 1890. Cf. footnote 79 and Part A of Figure 5.

In a paper published three years after Railroads and American Economic Growth. I noted that the best case for demand-induced economies of scale attributable to railroads was in the Bessemer steel industry. In the absence of the railroad's demand for this type of metal, it is possible that only open-hearth steel would have been available. During the late nineteenth century, open-hearth firms were small scale and produced a more expensive product than Bessemer firms, which were large scale. Taking into account the difference in the cost of production in the two types of firms, the estimated maximum gain in income not already covered by the social saving due to economics of scale in Bessemer production was just $7.0 million or 0.06 percent of GNP in 1890. See Fogel, , “Railroads as an Analogy,” pp. 27–30Google Scholar.

78 The scale coefficient is 1.0645. See Fogel, Robert W. and Engerman, Stanley L., Time on the Cross: The Economics of American Negro Slavery, (Boston, 1974), Vol. 2, p. 143Google Scholar. Cf. Wright, Gavin, The Political Economy of the Cotton South (New York, 1978)Google Scholar, who argues against a scale effect in slave agriculture.

79 My estimate of the agricultural social saving of railroads in 1890 is $214 million: Towne and Rasmussen put farm gross product in the same year at $3,107 million. Consequently, if $214 million of resources had been shifted from agriculture to transportation, the scale of agriculture would have been reduced to 93.1 percent of its actual 1890 level. Fogel, , Railroads. pp. 47, 110, 220Google Scholar; Towne, and Rasmussen, , “Farm Gross Product,” pp. 255–312Google Scholar.

80 Cf. Fogel, Robert W. and Engerman, Stanley L., “Explaining the Relative Efficiency of Slave Agriculture in the Antebellum South,” American Economic Review. 67 (06 1977), 275–96Google Scholar; Ralph A. Loomis and Glen T. Bartin, Productivity of Agriculture: United States 1870-1958. U.S. Dept. of Agriculture, Technical Bull. No. 1238 (Washington, D.C., 1961), pp. 24–25Google Scholar.

81 See the Appendix, Section B, for a discussion of the procedure used in inferring the scale coefficient implicit in David's f.o.b. cost curve. Griliches's estimation of production functions in U.S. manufacturing on data for 1954, 1957, and 1958 yielded scale coefficients that varied between 1.043 and 1.127. According to Denison, “most economists believe that in the United States the number can hardly be higher than, say, 20 percent [that is, a scale coefficient of 1.2] at the outside.” Griliches, Zvi, “Production Functions in Manufacturing: Some Preliminary Results,” in Conference on Research in Income and Wealth, The Theory and Empirical Analysis of Production. Vol. 31 of Studies in Income and Wealth (New York, 1967), pp. 304–8Google Scholar; Dension, Edward F., Why Growth Rates Diffe. (Washington, D.C., 1967), p. 227Google Scholar.

82 These elasticities were estimated by geometric procedures from David's diagram.

83 David, Paul A., “Learning by Doing and Tariff Protection: A Reconsideration of the Case of the Ante-Bellum United States Cotton Textile Industry,” this JOURNAL 30 (09 1970), 521–601Google Scholar; Zevin, Robert Brooke, “The Growth of Cotton Textile Production After 1815,” in Fogel, and Engerman, , The Reinterpretation. pp. 122–47Google Scholar; Fogel, Robert W. and Engerman, Stanley, “A Model for the Explanation of Industrial Expansion During the Nineteenth Century: With an Application to the American Iron Industry,” Journal of Political Economy, 1. (06/06 1969), 306–28CrossRefGoogle Scholar; Wright, Gavin, “Cotton Com petition and the Post-Bellum Recovery of the American South,” this JOURNAL, 34 (09 1974), 610–35Google Scholar.

84 Fogel, , Railroads. p. 21Google Scholar.

85 See Williamson, Late Nineteenth-Century American Development. ch. 9.

86 Several of the points which follow were also raised in McCloskey, “New Model History.”

87 U.S. Bureau of Statistics, Monthly Survey. pp. 1964–67Google Scholar; Tunnell, , “Statistics,” pp. 30–59Google Scholar.

88 This result obtains when, following Williamson, the social saving is computed in 1870 prices. If 1890 prices are used, the dynamic effects are nearly wiped out. The sensitivity of the dynamic effects to the prices employed serves to re-emphasize the seriousness of the index number problem alluded to above.

89 Some aspects of this problem are addressed by Lewis, Frank (“Explaining the Shift of Labor from Agriculture to Industry in the United States: 1869 to 1899,” unpublished Ph.D. dissertation, University of Rochester, 1976)Google Scholar, who stressed the unrealism of models in which the United States can import agricultural goods at the same price at which it exports them. Lewis uses a simpler framework than Williamson's, allowing him to have separate international buying and selling prices for wheat (the difference being the trans-Atlantic shipping costs). For intermediate prices, demand is the inelastic domestic demand rather than the elastic international demand. Including this international transportation wedge reverses many conclusions about the effects of changes in agricultural productivity. In Williamson's model, declining domestic transportation costs act in many respects like increases in agricultural productivity. Thus, allowing a Lewis-like refinement in the Williamson model could well increase the transportation social saving.

90 As Fishlow, (“Productivity,” pp. 642–44)Google Scholar has pointed out, the social saving can be interpreted as a measure of total factor productivity. Cf. Fogel, and Engerman, , The Reinterpretation. p. 102Google Scholar.

91 The specialized pre-eminence of waterways during the last half of the nineteenth century has been neglected by economic historians because of a preoccupation with canals, which were, in many cases, superseded by railroads, and which only provided a small share of total waterway transportation. Cf. the Appendix, Section A.

92 North, Douglass C., “Sources of Productivity Change in Ocean Shipping,” Journal of Political Economy. 76 (09/10 1968), 965CrossRefGoogle Scholar. Harley, Charles K., “The Shift from Sailing Ships to Steamships, 1850-1890: A Study in Technological Change and Its Diffusion,” in McCloskey, Donald N., ed., Essays on a Mature Economy (London, 1971), p. 228Google Scholar. The rate of growth in total factor productivity for freight transported by sailing ships can be computed from Harley's essay. The rate of productivity growth for freight carried by steamships, however, requires information on the growth of productivity in the building of steamships, which was not reported. I am grateful to Professor Harley for supplying the needed information.

93 Haites, Erik F., Mak, James, and Walton, Gary M., Western River Transportation: The Era of Early Internal Development, 1810-1860 (Baltimore, 1975), pp. 183–84Google Scholar. Interestingly enough, Haites, Mak, and Walton found that the total factor productivity of flatboats increased at an annual rate of 3.8 to 4.4 percent between 1815 and 1860 (ibid., p. 76). Fishlow, (“Productivity,” p. 626) indicates that railroad total factor productivity rose at an annual rate of 2.3 percent between 1870 and 1900Google Scholar.

94 Fishlow, , “Productivity,” p. 626Google Scholar.