Total factor productivity growth on Britain’s railways, 1852–1912: A reappraisal of the evidence

Explorations in Economic History Explorations in Economic History 44 (2007) 608–634 www.elsevier.com/locate/eeh

Total factor productivity growth on Britain’s railways, 1852–1912: A reappraisal of the evidence q Nicholas Crafts a

a,*

, Terence C. Mills b, Abay Mulatu

c

Department of Economics, University of Warwick, Coventry CV4 7AL, UK Department of Economics, Loughborough University, Loughborough, UK c School of Social Sciences, University of Manchester, Manchester, UK

b

Received 24 January 2005 Available online 26 February 2007

Abstract This paper revisits the issue of the productivity performance of Britain’s railways with an improved dataset and modern cliometrics. We find a slowdown in TFP growth between 1850 and 1870, after which it stabilized at about 1.1%. An analysis of company-level productivity performance reveals large discrepancies in TFP growth and substantial cost inefficiency. The evidence suggests that there was managerial failure in companies with agency problems in a context of collusion and high entry barriers. A wider implication is that the neoclassical exoneration of late-Victorian British management may be less convincing for the services sector than for manufacturing.  2007 Elsevier Inc. All rights reserved. Keywords: Total factor productivity; Railways

q

Financial support from the Economic and Social Research Council under Grant R000239536 is gratefully acknowledged. We wish to thank Brian Mitchell for generously making available to us his data and Peter Cain for helpful advice. We have benefited from comments by Tony Arnold, Dudley Baines, Steve Broadberry, Terry Gourvish, Peter Howlett, and three anonymous referees. The usual disclaimer applies. * Corresponding author. Fax: +44 2476 523202. E-mail address: [email protected] (N. Crafts). 0014-4983/$ - see front matter  2007 Elsevier Inc. All rights reserved. doi:10.1016/j.eeh.2007.01.002

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1. Introduction Before the new economic history came along, it was commonplace to allege that late nineteenth century Britain experienced ‘entrepreneurial failure’ and a climacteric in productivity growth (Landes, 1969; Saul, 1968). Now these claims are much more muted or nuanced as it has been recognised that the quantitative evidence offers relatively little support for them (Crafts, 2004a). Indeed, as the excellent summary in Nicholas (2004) makes clear, the neoclassical view, backed up by substantial cliometric research, is that the economy was growing as fast as exogenous constraints allowed with no serious evidence of failure to maximize profits and competition eliminating entrepreneurial failures. Moreover, the suggestion originally made by Phelps-Brown and Handfield-Jones (1952) that there was a climacteric in industrial productivity growth resulting from the exhaustion of steam as a General Purpose Technology has been rejected (Crafts and Mills, 2004). However, railways have not received the exoneration that has been given to most other sectors of the economy and the quality of their management and their productivity performance are still seen as, at best, deficient and, at worst, dismal. The best-known textbook account concludes that ‘‘there was waste and inefficiency in the railway system of Great Britain between 1870 and 1914’’ (Cain, 1988, p. 120). The most recent assessment of railway management based on financial performance is that of Arnold and McCartney (2005). They conclude that returns to investors were consistently disappointing and that any increase in the net return on capital after 1900 was slight as mean returns on capital employed for the industry as a whole were below 4% throughout the period 1892–1912. Arnold and McCartney argue that management incurred unnecessary costs and paid relatively little attention to creating shareholder value. The most recent review of productivity performance stresses that British railways were greatly inferior to their American counterparts and attributes this largely to managerial failure facilitated by weak shareholders and barriers to entry: ‘‘total factor productivity growth. . .declined continuously after 1870 becoming negative in the Edwardian period’’, and ‘‘organization and customs that had been appropriate to one epoch of railway technology persisted when opportunities and challenges changed. Inertia was encouraged by an absence of competition. . .’’ (Foreman-Peck and Millward, 1994, pp. 88, 90). It is important to recognize that the exoneration of the late Victorian and Edwardian British economy from the allegation of entrepreneurial failure announced by new economic historians is problematic in the case of railways. The general argument stressed by McCloskey and Sandberg (1971) was that competition punished firms that failed to perform well. It is striking that the one well-established case of entrepreneurial failure in the manufacturing sector, the non-adoption of the Solvay process in alkali production, occurred in a cartelized industry largely sheltered from foreign competition (Magee, 2004). Railways differed from the typical sector represented in the neoclassical exoneration. In particular, agency problems arising from the separation of ownership and control were relatively severe and competition, a potential antidote to such problems, was relatively weak compared with manufacturing. In these aspects, railways are precursors of a more general problem that was central to British relative economic decline after World War II (Broadberry and Crafts, 2003). In recent discussions of British relative economic decline, the pivotal role of the service sector, in which the initial British productivity lead was later reversed by Germany and the United States, has been highlighted. Broadberry (2006) stresses that Britain did

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particularly badly in services which became ‘industrialized’, i.e., they switched to high-volume, low-margin business with hierarchical management, thereby obtaining substantial productivity gains. Railways were the first sector to make this transition. Table 1 reports new estimates of relative labor productivity on American and British railways.1 These show that there was already a substantial productivity gap in 1870 which then widened markedly over time. It is apparent that this derives from freight rather than passenger business and there is no doubt that the much larger ton-miles per worker in the US reflects much longer average hauls and constraints imposed by the original design of the British railway system. Even so, such a massive gap is a worrying diagnostic of British productivity performance. It is timely, therefore, to re-examine productivity performance in Britain’s railways during the Victorian and Edwardian periods. In this paper, we first construct a new aggregate TFP index for Britain’s railways, drawing heavily on unpublished estimates of the net capital stock and expenditures on wages in 30 major railway companies made by Brian Mitchell and based on revised estimates for the transport of freight. We use this index to conduct an econometric analysis of trends in each of capital, labor and total factor productivity. We also examine TFP growth in individual railway companies for the period 1893–1912 and attempt to measure this on a basis as consistent as possible with our national estimates. We then investigate explicitly how close to an efficient cost frontier individual companies were through these years and whether inefficiency and lagging TFP growth were persistent. By reviewing this micro evidence insights can be obtained relating to the extent of failure in the performance of the sector as a whole. In particular, we address the following specific questions: (1) What was the chronology of TFP growth on Britain’s railways before World War I? (2) How much did productivity growth and efficiency levels vary across major railway companies in the late Victorian and Edwardian periods? (3) Were costs too high in Britain’s railways at this time? (4) Are railways an important exception to the neoclassical exoneration of British management and growth performance? As a by-product of this investigation it will also be possible to clarify the part railways played in the alleged climacteric, i.e., to quantify their impact on the growth of GDP per worker. 2. A new total factor productivity index Aggregate railway total factor productivity (TFP) growth was first estimated by Hawke (1970). His estimates were later refined and extended from 1890 to 1910 by Foreman-Peck (1991). Nevertheless, these estimates have weaknesses and can be improved, in particular, to provide a continuous annual series for TFP which can be used for econometric analysis. This section describes and presents our new TFP index and its components for the British railway system prior to World War I. We then go on to compare the results with those of 1 These estimates differ from those in Broadberry (2006, Table 3.2). This is mainly because employment for British railways has been revised upwards. We are grateful to Steve Broadberry for his help in preparing the new estimates which change the detail but not the overall thrust of his argument.

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Table 1 Labor productivity on British and US railways

1870 1890 1910

US Index (GB = 100)

000 US passenger-miles /worker

000 UK passenger-miles /worker

000 USTon-Miles /worker

000 UKTon-Miles /worker

165 293 330

17.8 16.1 19.1

17.4 20.3 33.2

50.9 106.7 150.1

25.7 20.8 22.2

Note: Following Broadberry (2006) output is measured in terms of a weighted average of passenger-miles and ton-miles with weights based on revenue shares in Britain. Sources: US data from Fishlow (1966). GB data for passenger miles derived from revenue in Mitchell (1988) and fares in Cain (1988) and for ton-miles using tons carried from Mitchell (1988) and estimates of average haul from Table 2, below. GB employment is based on Hawke (1970) and Munby and Watson (1978), see the text, p. 613.

Hawke and Foreman-Peck and to examine the implications for the contribution made by railways in particular and steam in general to growth in GDP per worker. Estimates of railway output growth present serious difficulties.2 Ideally, in common with Dodgson (1993), we would like to create an index based on revenue-weighted estimates of passenger-miles and freight ton-miles, with the latter distinguishing between minerals, which generated very low receipts, and merchandise. Following Dodgson (1993), we use passenger train miles taken from the Railway Returns. This source also gives data on revenue for each of these types of output, and thus permits calculation of the required revenue shares, and for tons of minerals and merchandise carried.3 As Dodgson points out, distinguishing between minerals and general merchandise matters because the latter was a declining proportion of traffic, and failure to separate out these two types of freight appears to be a serious weakness in earlier estimates. For freight, the problem comes in calculating ton-miles, which requires an estimate of the average length of haul, and it is here that the major differences with previous studies lie. We have based our estimates of haul length for 1871–1912 on estimates for receipts per ton-mile for different types of freight given by Paish (1902). He found that the most common estimate for these in the companies that he studied was 0.7d for minerals and 2.0d for merchandise in 1900, and he reported that these rates were also typical of the whole period 1880–1900 for the largest company, the London and North Western Railway.4 Using these rates per ton-mile, together with receipts and tons carried for different classes of traffic from the Railway Returns, produces estimates of ton-miles and thus haul length. Basing the estimates back to 1871 on these 0.7d/2.0d receipts goes beyond the period covered

2

In common with all the other studies cited in this paper, in measuring output growth we do not address the issue of the quality of service provided by the railways. Clearly, this improved over time, especially for passengers with regard to comfort and speed, and was a dimension on which railway companies might compete. 3 For the years 1852–1855 we estimated tons carried from revenue on the basis of a regression estimated for the next 10 years. Similarly, we interpolated for missing and apparently deficient data on tons carried in 1868, 1869 and 1870 using the revenue data. The revenue shares for the middle year (1882) are 0.43 for passengers, 0.25 for minerals and 0.32 for merchandise. 4 Paish emphasized the strong contrast between British and North American railways which saw rapid reduction in both costs and charges in this period. Thus, on the Pennsylvania Railroad receipts per ton-mile in 1900 were 0.27d in 1900 compared with 0.459d in 1880 and costs were 0.181d in 1900 compared with 0.27d in 1880 whereas, for the London & North Western receipts were 1.189d per ton-mile in 1900 compared with 1.19d in 1880 while costs had risen from 0.554d in 1880 to 0.686d in 1900 (Paish, 1902, p. 36).

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by Paish, but does not seem unreasonable since it produces an average receipt of 1.14d per ton-mile, just slightly below the estimate in Hawke (1970) of 1.21d in 1865. Similarly, assuming that the same 0.7d/2.0d receipts were still representative of the years through to 1912 is stretching the use of Paish’s data but after 1894 railways were prevented from raising charges by regulation and were under increasing pressure from rising costs, which made reducing charges difficult, and it seems likely that any bias is small.5 In order to check the reasonableness of using the assumption that freight receipts per ton-mile were constant over the period 1871–1912, we investigated the evidence on freight charges for minerals and for merchandise by distance presented in the Report of the Royal Commission on Railways (1867), the Report of the Select Committee on Railways (1882) and in the Bureau of Railway Economics, Comparison of Railway Freight Rates (1915). These data allow regressions of the form Gross Charge/Ton-Mile = f(Year 1, Year 2, Distance*Year 1, Distance*Year 2), which allow tests of the restrictions that the period-specific intercepts and period-specific slope coefficients are the same in each year where the null hypothesis is that the restriction is not valid. For minerals, there are data for 1881 and 1915 while for merchandise there are data for 1867, 1881, 1882, 1906, and 1915. In each case all of the null hypotheses were rejected. The estimated equations did not reject the null that at the average distance in the sample the charges were 0.7d and 2.0d per tonmile for minerals, and for merchandise, respectively. Prior to 1871, the only estimates of haul length that we have are those of Hawke (1970), who obtained a reasonably solid estimate for minerals of 31.5 miles in 1865 using evidence from the Royal Commission on Coal, and complemented it with a speculative estimate for other traffic. Hawke also used an estimate of 22.5 miles for all traffic in 1847, which originally appeared in Lardner (1855) and which came from unpublished estimates made by the Railway Commissioners and was consistent with a plausible average receipts figure of 1.67d per ton-mile. Similar to Hawke, we have assumed a steady trend increase between 1847 and 1871. Our estimates for haul length are shown in Table 2, where the estimates used by Hawke (1970) and by Foreman-Peck (1991), who adopted estimates based on Cain (1988), are also reported, together with the implied average receipts per ton-mile for all freight. The following points should be noted. First, the rising haul lengths after 1871 suggested by Hawke (1970) on the basis of interpolating non-comparable figures for 1865 and 1920 are clearly implausible, because they would imply big falls in average receipts per ton-mile which were not observed, as Cain (1980) pointed out. Second, our estimates are devised to be consistent with the evidence on receipts per ton-mile, as were those of Cain (1988) for the post-1870 period, but we explicitly distinguish between minerals and merchandise, which matters given the changing composition of traffic and the much higher charges for the latter category. Third, the decline in average receipts from 1.28d in 1871 to 1.00d in 1911 embodied in Cain (1988) is too big to be consistent with the evidence presented above that charges for the two categories of freight were unchanging from 1867– 1915. Fourth, our estimates for minerals haul in 1865 and average haul for 1900 are very 5 Cain (1980) suggests that rates fell after 1900 based on the detailed statistics for the North Eastern Railway Company presented in Irving (1976). If these reductions were typical of other companies, which is unlikely because cost savings in freight train operation were much greater at this time on the NER, then by 1911 receipts per ton-mile for minerals would have fallen by 1.7% and for merchandise by 5.1%. Incorporating an adjustment for this would only add about 2% to the increase in total output between 1900 and 1912.

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Table 2 Estimates of average haul length (miles) and receipts/ton-mile (d) Period

1847 1852 1865 1871 1880 1890 1900 1911

Caina

Hawke Haul

Receipts

22.5

1.65

33.0b 33.5 37.4 40.5

1.21 1.14 0.98 0.82

Haul

30 30 30 27 28

Present study Receipts

Minerals haul

Merchandise haul

Average haul

Receipts

1.28 1.22 1.11 1.12 1.00

26.2 31.3 33.6 30.3 27.8 25.5 24.8

21.2 25.3 27.2 34.0 31.8 29.2 33.6

24.3 29.0 31.1 31.4 28.9 26.5 26.6

1.58 1.27 1.14 1.11 1.10 1.09 1.05

Notes: aForeman-Peck (1991) accepted Cain’s estimates for average haul length. b Hawke’s estimates imply a haul length for minerals of 31.5 miles in 1865. Sources: Derived from Hawke (1970), Cain (1988) and see text for present study.

similar to those in Hawke (1970) and Paish (1902), respectively.6 Fifth, our estimates show a marked decline in mineral hauls after the mid-1870s, which is consistent with the growing competition from coastal shipping on long hauls and is epitomized by a declining share of railways in London’s coal traffic (Armstrong, 1987). Sixth, the implied receipt of 1.58d per ton-mile for 1852 in our estimates fits well with the 1.67d estimate of Lardner (1855) for 1847. Thus, our procedures seem to be consistent with more of the available corroborative evidence than the earlier methods. Three inputs are aggregated to form Total Factor Input (TFI), namely capital (with a weight of 0.63), labor (0.34) and coal (0.03). The weights are based on cost shares at midperiod (1882) taken from Mitchell’s worksheets.7 Estimates of the net capital stock in each year are obtained directly from Mitchell and they are consistent with the estimates for gross capital formation published in Mitchell (1964), together with his assumed lifetimes for each type of capital asset.8 These estimates were accepted as very reliable by Feinstein (1988), who noted that they are consistent with the capital stock estimates in the Railway Returns for 1920. The capital stock series is actually quite similar to that of Hawke (1970) for 1852–1890, which was based on unpublished work by Kenwood. However, our estimates show lower growth of capital inputs in every decade from 1870 to 1910 than those in Foreman-Peck (1991), even though his estimates were based on the gross capital formation series in Mitchell (1964). This discrepancy appears to result from his surprising use of a different price deflator. For our index of labor inputs, we follow Hawke (1970, p. 262) to obtain estimates for 1852–1860, 1873 and 1884, and also have estimates for 1898, 1901, 1904, 1907 and 1910 from Munby and Watson (1978). We have interpolated between these years using the annual estimates of expenditure on wages and salaries in Mitchell’s worksheets. Hawke

6

The data in Paish (1902) imply an average haul length of 26.4 miles according to Cain (1980, p. 12). Foreman-Peck and Hawke use weights of 0.73, 0.23 and 0.04. The difference in weighting makes no material difference. Mitchell’s worksheets were compiled from the accounts of 30 major railway companies and formed the basis of his estimates of capital formation which appeared in Mitchell (1964). 8 Thirty years for rolling stock and 100 years for permanent way and works. 7

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(1970) interpolated the known data points on the assumption of a constant relationship between employment and railway revenues, which seems a clearly inferior approach, while Foreman-Peck (1991) adopted Hawke’s estimates and extended them with observations only at 10-yearly intervals also using data from Munby and Watson (1978). Differences between the three sets of estimates in the long run trends of employment growth are, however, not very great. For coal, we have linearly interpolated between the years where coal consumption is known and reported in Mitchell (1988).9 We report the annual series that are obtained as the first three columns of Table 3, while TFI is in column 4. We believe that the annual series for capital and labor inputs are superior to those used previously and they are actually the first on an annual basis for 1890–1912. In Table 4 we present our index of TFP and the series of labor and capital productivity. Table 5 displays endpoint calculations for each decade of rates of growth of output, TFI and TFP and also of labor productivity, in order to get an initial sense of the timing of any deceleration in productivity growth and to highlight the differences between our estimates and those of earlier writers. Our estimates do suggest a decrease in TFP growth from the 1850s through each decade to the 1880s, with a modest recovery after 1900. Over the whole period from 1852 to 1912 labor productivity increases by less than 3%. During this period labor productivity growth is somewhat erratic and is actually strongest after 1900. Compared with Hawke, our estimates show lower productivity growth with the exception of the 1860s. This is primarily because our estimates of output growth are lower and, in turn, this reflects our rejection of Hawke’s inference of rising average haul length after 1870. Compared with Foreman-Peck, we have lower TFP and labor productivity growth except in the 1890s. Both in the 1880s and 1900s our estimates of output growth are lower and this primarily results from splitting freight into separate minerals and merchandise components. In each of the decades from 1870 to 1910, TFP growth was slower on British than on American railways. For the 1870s the estimate of 1.1% per year compares with 2.1% for the US (Fishlow, 1966); for the 1880s, 1890s, and 1900s, the comparisons are 0.7 versus 2.3%, 0.7 versus 2.7%, and 1.0 versus 1.4%, respectively. A reasonable inference is that American railways were more technologically progressive but it must be remembered that the scope for advance may have differed. Our new estimates of capital stock and TFP growth for the railway sector can be used to revise the growth-accounting estimate of the contribution made by railways to growth of labor productivity in the British economy presented in Crafts (2004b), which used the work of Hawke (1970) and Foreman-Peck (1991). Table 6 sets out railways’ contribution in each of three twenty-year periods. It is notable that the TFP growth contribution of the railways fell by 0.08 percentage points after 1870 compared with before, which amounts to about a quarter of the decline in TFP growth in the economy as a whole (Feinstein et al., 1982). Thus Phelps-Brown and Handfield-Jones (1952) were right to identify railways as a sector whose contribution to productivity growth diminished after 1870. However, the overall Phelps-Brown and Handfield-Jones thesis of a steam-driven climacteric remains unpersuasive. There was only a very small reduction in steam’s total contribution (including stationary steam engines, steamships, and railways) to labor

9

These years are 1855, 1869, 1887, 1903 and 1913. This is obviously a crude procedure but the weight on coal is so small that any bias must be trivial.

Table 3 Inputs and outputs in British railways, 1852–1912 (1912 = 100) (1) Capital

(2) Labor

(3) Coal

(4) Total input

(5) Passenger train miles

(6) Mineral ton miles

(7) Merchandise ton miles

1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883

35.6 36.8 38.3 39.6 40.5 41.4 42.3 43.4 44.5 46.3 48.2 50.6 53.4 56.8 59.5 61.0 61.7 62.3 62.8 63.8 64.8 66.1 67.8 69.7 71.4 72.9 74.2 75.1 75.9 77.2 78.3 79.7

11.0 13.1 14.7 15.9 16.6 17.5 17.8 18.9 18.3 20.8 21.2 21.2 23.3 25.4 28.2 29.6 30.3 31.3 32.7 35.7 40.1 44.6 46.9 49.9 52.5 53.3 53.5 52.3 53.8 55.4 57.5 59.0

10.8 12.8 15.7 17.7 19.7 21.7 22.6 23.6 23.6 22.6 21.7 21.7 21.7 21.7 19.7 18.7 15.7 21.9 23.7 25.5 27.3 29.1 30.9 32.8 34.6 36.4 38.2 40.0 41.8 43.7 45.5 47.3

26.5 28.0 29.6 30.9 31.7 32.7 33.4 34.5 35.0 36.9 38.2 39.7 42.2 45.0 47.7 49.0 49.7 50.5 51.4 53.1 55.3 57.7 59.6 61.8 63.9 65.1 66.1 66.3 67.4 68.7 70.2 71.7

13.5 14.0 14.6 14.9 15.5 16.8 17.7 18.7 19.8 20.1 21.4 22.7 24.9 26.6 27.4 28.1 29.6 30.5 32.7 33.9 35.3 36.0 37.0 38.6 40.4 41.7 43.3 44.1 47.0 48.2 50.6 53.0

8.1 9.9 11.2 11.4 11.5 13.1 13.7 15.1 17.8 19.0 19.2 20.9 23.4 24.5 26.5 28.5 28.8 30.7 32.4 34.5 38.7 43.4 42.9 46.2 46.6 47.3 45.8 46.9 50.4 52.2 53.6 55.8

9.1 10.8 12.0 12.2 13.5 14.1 14.8 15.7 17.5 18.3 18.3 20.0 21.8 23.2 26.6 30.1 35.1 29.9 41.1 46.0 49.8 53.8 54.9 55.5 56.4 56.8 56.4 55.7 59.5 60.4 62.4 63.6

(8) Total output

615

10.7 11.9 12.9 13.2 13.8 15.1 15.8 16.8 18.6 19.3 19.9 21.4 23.5 25.0 26.9 28.8 31.1 30.4 35.3 37.9 40.8 43.6 44.2 45.9 47.1 48.0 48.1 48.5 51.9 53.1 55.1 57.1 (continued on next page)

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Year

616

Table 3 (continued) (1) Capital

(2) Labor

(3) Coal

(4) Total input

(5) Passenger train miles

(6) Mineral ton miles

(7) Merchandise ton miles

(8) Total output

1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912

81.5 82.7 83.4 83.9 84.4 85.0 85.7 86.9 88.0 88.8 89.6 90.5 91.4 92.6 94.2 95.7 97.0 98.3 99.3 100.4 101.4 102.2 102.8 103.0 102.6 102.0 101.3 100.6 100.0

59.8 59.7 59.9 61.2 61.7 63.9 67.5 70.6 72.3 72.7 75.0 76.4 79.6 83.4 86.8 90.3 92.6 93.5 94.7 94.7 94.5 94.6 97.1 100.9 99.0 98.1 98.9 99.9 100.0

49.1 50.9 52.7 54.6 56.4 58.2 60.0 61.8 63.6 65.5 67.3 69.1 70.9 72.7 74.5 76.3 78.2 80.0 81.8 83.6 85.4 87.2 89.1 90.9 92.7 94.5 96.3 98.1 100.0

73.1 73.9 74.5 75.3 75.8 77.0 78.7 80.6 81.9 82.6 84.0 85.0 86.8 88.8 91.1 93.3 94.9 96.1 97.2 97.9 98.6 99.2 100.5 102.0 101.1 100.5 100.3 100.3 100.0

55.1 55.9 57.1 58.3 59.5 61.9 64.0 66.0 67.6 68.0 69.2 70.9 74.5 77.7 80.6 83.4 85.0 86.2 87.9 89.5 92.7 94.3 98.0 101.2 102.0 102.0 103.2 104.9 100.0

53.3 52.4 51.6 53.8 55.5 58.6 60.3 62.1 61.3 56.4 62.2 62.3 65.0 67.7 69.5 74.9 78.5 76.3 80.6 86.9 88.0 90.1 94.7 101.0 96.7 97.4 100.1 102.0 100.0

62.5 54.9 59.9 61.0 63.7 68.0 69.8 71.2 71.0 69.4 71.1 73.1 77.7 80.2 82.8 86.7 87.6 89.0 89.2 84.6 84.6 86.0 88.0 90.6 87.2 88.3 91.8 95.9 100.0

57.0 54.7 56.6 58.0 59.9 63.0 64.9 66.7 67.1 65.6 68.1 69.5 73.1 76.0 78.5 82.4 84.2 84.6 86.5 87.3 89.0 90.6 94.0 97.8 96.0 96.5 98.8 101.3 100.0

Source: See text.

N. Crafts et al. / Explorations in Economic History 44 (2007) 608–634

Year

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617

Table 4 TFP on British railways, 1852–1912 (1912 = 100) Year

Labor productivity

Capital productivity

1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902

97.7 91.4 88.0 82.8 83.4 86.0 88.8 89.1 101.5 92.6 93.8 101.0 101.0 98.4 95.5 97.5 102.8 97.1 108.2 106.3 101.7 97.7 94.2 92.1 89.7 89.9 90.0 92.7 96.3 95.9 95.9 96.8 95.4 91.6 94.6 94.9 97.1 98.6 96.2 94.4 92.8 90.2 90.7 91.0 91.9 91.2 90.5 91.1 91.0 90.5 91.3

30.1 32.5 33.7 33.3 34.2 36.4 37.3 38.8 41.7 41.6 41.2 42.2 44.1 44.1 45.3 47.3 50.4 48.8 56.2 59.5 62.9 65.9 65.1 65.9 65.9 65.8 64.9 64.6 68.3 68.8 70.4 71.7 70.0 66.2 67.9 69.1 70.9 74.2 75.8 76.7 76.3 73.8 76.0 76.8 80.0 82.1 83.4 86.1 86.8 86.1 87.1

TFP 40.5 42.6 43.6 42.7 43.6 46.1 47.3 48.9 53.1 52.1 51.9 53.8 55.7 55.5 56.5 58.8 62.7 60.1 68.8 71.5 73.8 75.6 74.1 74.2 73.7 73.6 72.9 73.2 76.9 77.2 78.5 79.7 78.0 74.0 76.0 77.1 78.9 81.9 82.5 82.7 81.9 79.3 81.1 81.7 84.3 85.6 86.2 88.3 88.7 88.0 89.0 (continued on next page)

618

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Table 4 (continued) Year

Labor productivity

Capital productivity

TFP

1903 1904 1905 1906 1907 1908 1909 1910 1911 1912

92.2 94.1 95.8 96.8 96.9 96.9 98.4 99.9 101.4 100.0

86.9 87.7 88.7 91.4 94.9 93.5 94.6 97.6 100.7 100.0

89.1 90.2 91.4 93.5 95.9 94.9 96.0 98.5 101.0 100.0

Source: See text.

Table 5 Estimates of Output (Y), Total Factor Input (TFI), Total Factor Productivity (TFP), and Labor Productivity (Y/L) Growth Rates (% per year) Period

Hawke a

1850–60 1860–70 1870–80 1880–90 1890–1900 1900–10

Foreman-Peck

Y

TFI

TFP

Y/L

9.4 6.0 5.5 3.5

4.2 4.0 2.6 1.6

5.2 2.0 2.9 1.9

1.1 0.6 1.1 1.2

Y

3.8 2.9 2.5 2.3

TFI

2.6 1.7 2.1 0.9

Present Study TFP

1.2 1.2 0.4 1.4

Y/L

Y

TFI

TFP

Y/L

0.7 0.6 0.9 1.8

7.2 6.6 3.9 2.3 2.6 1.6

3.5 3.9 2.8 1.6 1.9 0.6

3.7 2.7 1.1 0.7 0.7 1.0

0.6 0.6 1.2 0.0 0.6 1.0

Sources: Derived from Foreman-Peck (1991), Hawke (1970), and Tables 2 and 3. a The period in the present study starts from 1852 rather than 1850.

Table 6 Contributions to British labor productivity growth from railways, 1850–1910 (% per year) 1850–70

1870–90

1890–1910

1870–1910

Rates of Growth Railway Capital per Worker TFP in railways

5.9 3.2

0.6 0.9

0.2 0.9

0.2 0.9

Contributions Capital deepening TFP Total

0.12 0.13 0.25

0.01 0.05 0.06

0.00 0.05 0.05

0.01 0.05 0.06

Memoranda items Railway profits share Railway output share

2.1 4.0

2.4 5.8

2.4 6.0

2.7 6.0

Sources: Derived using the growth accounting formula D(Y/L)/(Y/L) = sRKD(RK/L)/(RK/L) + sKOD(KO/L)/ (KO/L) + hTFPGRR + uTFPGRNR, where Y and L are output and labor, RK is railway capital stock, KO is other capital stock, sRK and sKO are the factor income shares of these kinds of capital, and TFPGR is the rate of growth of total factor productivity divided into Domar-weighted railways and non-railways components. Railways capital stock growth and TFP growth are based on Tables 2 and 3 and railway profits and output shares based, respectively, on net and gross receipts derived from Foreman-Peck (1991, p. 76), Hawke (1970, p. 406) and Mitchell (1988, pp. 545–6).

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productivity growth after 1870 of 0.10 percentage points per year, according to the growth accounting study by Crafts (2004b). The revised estimates for productivity growth in railways do not change this estimate, although they imply that the total steam contribution reported in Table 8 of that paper, including both capital-deepening and TFP growth, should be revised down from 0.41 to 0.40% per year between 1850 and 1870 and from 0.31 to 0.30% per year from 1870 to 1910. True, the reduction in the total contribution of railways to labor productivity growth before and after 1870 is nearly 0.2 percentage points per year but the other components (stationary steam engines and steamships) contributed more after 1870 than before. 3. Modeling trend growth rates In this section, we model the time series for output, capital and labor productivity and TFP with the aim of estimating their trend rates of growth. The general framework that we employ is to suppose that an observed time series Zt can be decomposed as Zt ¼ St þ N t with the objective being to use the data on Zt to estimate the unobserved component series St and Nt, which may be taken to represent ‘signal plus noise’. Models for the components may be defined within the setup of the basic structural model (BSM), which has been used in previous studies of output growth by Crafts et al. (1989), Crafts and Mills (1994), and Mills and Crafts (1996) . This assumes that the signal is the sum of trend and cycle components, i.e., St = Tt + Ct. The trend, Tt, follows a random walk with a stochastic slope, which also follows a random walk: T t ¼ T t1 þ bt1 þ v1t bt ¼ bt1 þ v2t Generally, the cyclical component, Ct, is formulated as a stochastic combination of sine and cosine waves, but for the data being analysed here, it was found that a simpler first order autoregression is appropriate: C t ¼ qC t1 þ wt where 0 < q < 1. The cycle thus has a characteristic decay time scale of 1/lnq, which may be interpreted as the expected length of time a shock to Ct takes to dissipate. The level and slope innovations, v1t and v2t, the cycle innovation, wt, and the noise component Nt = ut are assumed to be mutually uncorrelated white noises. If both level and slope innovation variances, r21 and r22 , are zero, then bt = bt1 = b and Tt will be the deterministic linear trend T t ¼ l þ bt where l = T0 is the ‘initial condition’. If b = 0 as well, then Tt is constant. If just r22 ¼ 0, the slope is fixed and the trend reduces to a random walk with drift: T t ¼ T t1 þ b þ v1t If, however, just r21 ¼ 0, then the trend becomes D2 T t ¼ v2;t1

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which is an integrated random walk and is often referred to as the ‘smooth trend’ model, since fitted models of this type often produce a signal that is relatively smooth. The BSM can be fitted and the components estimated using the software provided by the STAMP package: see Koopman et al. (2000) for technical details and Mills (2003) for a convenient review. Logarithms of each of the four series were taken to help induce homogeneity of variance and to linearize trend behavior where it exists. 3.1. Output Fig. 1 plots log output (denoted Zt below) for the period 1852–1912. A BSM fitted to Zt resulted in the estimates ^2 ¼ 0:0052 ^1 ¼ 0:0262 r r

^w ¼ r ^u ¼ 0 r

thus showing that there are no cyclical or noise components, so that Tt and Zt are identical. A plot of the slope, bt, which may be interpreted as a trend growth component, is shown in Fig. 2. This declines throughout the sample, from around 6.5% in the 1850s to 1.3% by 1912, with a fairly stable period of 2.5% between the early 1880s and the late 1890s. This, of course, leads to the flattening trend shown in Fig. 1. It appears that railways are another example of the ‘inverted-U’ or ‘hump’ shape for trend growth, similar to other steam-intensive sectors such as coal, cotton and iron (Crafts and Mills, 2004, p. 164).10 3.2. Capital productivity Fig. 3 shows the logarithms of capital productivity. The best fitting BSM has ^1 ¼ 0:0300, r ^2 ¼ 0:0025 and rw = ru = 0 and thus is of the same form as output, so that r there are no cyclical or noise components and Tt and Zt are identical. A plot of the esti^t is shown in Fig. 4, where it is seen that trend growth fell from 3% per mated slope b annum at the start of the 1850s to 1.5% by the beginning of the 1880s, after which it stabilized at this value until the end of the sample. 3.3. Labor productivity Fig. 5 shows the logarithms of productivity with the estimated ‘level’ superimposed. This is a consequence of the best fitting BSM, which has r1 = r2 = ru = b = 0 and ^w ¼ 0:0343, and implies the model r Z t ¼4:549 þ C t ð0:019Þ C t ¼0:762C t1 þ wt ð0:086Þ ^ ¼ 4:55, around which are deviations following a first order autoThus the trend level is l regression with parameter 0.76. The characteristic decay time scale of these deviations is 3.6 years, which is clearly seen in the figure. The implied stationarity of this series is also 10

We only observe the right hand side of the inverted U in our output index, but if that is spliced to Hawke’s output series for 1840 to 1852 then this result is more apparent.

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4.5

4.0

3.5

3.0

2.5 1855

1860

1865

1870

1875

1880

1885

1890

1895

1900

1905

1910

Fig. 1. Logarithm of output; 1852–1912.

.07

.06

.05

.04

.03

.02

.01 1855 1860 1865 1870 1875 1880 1885 1890 1895 1900 1905 1910 Fig. 2. Growth component, bt, of output: 1852 –1912.

an outcome of conventional modelling, which would typically begin with testing for the presence of a unit root. A battery of such tests tend to reject such a null hypothesis and, if we assume a null of stationarity around a constant level, then tests cannot reject this null. It is therefore quite legitimate to assume that Zt is stationary around a fixed level, which is equivalent to the model fitted above. 3.4. TFP ^1 ¼ 0:0261, r ^2 ¼ 0:0021 Fig. 6 shows the logarithms of TFP. The best fitting BSM has r ^u ¼ 0:0078, so that, unlike output and capital productivity, there is a noise and r

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4.6 4.4 4.2 4.0 3.8 3.6 3.4 1855

1860

1865

1870

1875

1880

1885

1890

1895

1900

1905

1910

Fig. 3. Logarithm of capital productivity.

.032

.028

.024

.020

.016

.012 1855 1860 1865 1870 1875 1880 1885 1890 1895 1900 1905 1910 Fig. 4. Growth component, bt, of capital productivity: 1852–1912.

component. However, this noise component is very small, and hence Zt and Tt are very ^t is shown in Fig. 7, where it is seen that close to each other. A plot of the estimated slope b trend growth fell from 2.3% per annum in the 1850s to 1.1% by the beginning of the 1880s, after which it stabilised at this value until the end of the sample. In summary, trend output growth declines throughout the period from 6.5 to 1.3% per annum, except for the 1880s and 1890s, where it remained fairly constant at around 2.5%. Trend labor productivity was constant throughout the period, so that trend growth is absent. Capital productivity and TFP trend growth both fell consistently until the early

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4.70

4.65

4.60

4.55

4.50

4.45

4.40 1855 1860 1865 1870 1875 1880 1885 1890 1895 1900 1905 1910 Fig. 5. Logarithm of labor productivity with the level l ^ ¼ 4:55 superimposed.

4.6

4.4

4.2

4.0

3.8

3.6 1855

1860

1865

1870

1875

1880

1885

1890

1895

1900

1905

1910

Fig. 6. Logarithm of TFP: 1852–1912.

1880s, after which both stabilized for the rest of the period at 1.5% and 1.1% per annum, respectively. The implications of these results are as follows. First, continuing growth in capital productivity throughout the period suggests that Irving (1978) was right to argue that claims that railway managers indulged in a spree of wasteful investment projects are mistaken. Second, there is a recovery in labor productivity after 1900, which the econometric evidence might suggest could be seen as an ‘error correction’. This is consistent with the improvement in operating practices at that time noted by both Cain (1988) and Irving

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.024

.020

.016

.012

.008 1855

1860

1865

1870

1875

1880

1885

1890

1895

1900

1905

1910

Fig. 7. Growth component, bt, of TFP: 1852 –1912.

(1978). Third, trend growth in TFP is better than a reader of Foreman-Peck and Millward (1994) would suppose, since it stabilizes in the early 1880s at 1.1% per year. On the other hand, these authors are right to say that there is no increase in TFP growth in the Edwardian period and it turns out that the apparent improvement shown by the endpoints calculation in Table 5 is misleading. There is no support in this analysis for a suggestion that tighter regulation led to faster TFP growth after 1890. 4. TFP growth in 14 railway companies It is also possible to compare the performance of major railway companies with a view to evaluating the productivity record through highlighting possible failure. This approach was adopted by Dodgson (1993), who constructed TFP growth estimates for each of 14 major railway companies for 1903–12 and found a big discrepancy between the ‘best practice’ North Eastern Railway and a tail of poor performers, which he saw as symptomatic of serious managerial failure. In this section we refine Dodgson’s results and extend them to cover the whole period, 1893–1912, for which data are available. The major source of the data available to analyze TFP growth at the company level is the Railway Returns, published, annually, by the Board of Trade. With respect to output, the Returns provide data for each company on passenger train miles, merchandise tons, mineral tons, and revenue from each of the three types of output, which are used for the calculation of the required shares to derive total output. We converted each category of freight tons to ton miles in the same manner as we did for the aggregate analysis, i.e., by using Paish’s (1902) rate per ton mile figures of 0.7d and 2d for minerals and merchandise freight, respectively. As noted in Section 2, receipts per ton-mile were falling after 1900, so this will bias output and TFP growth down slightly.11 11

The alternative is to follow Dodgson (1993) and assume constant haul lengths. Adopting this alternative does not make any material difference with regard to any of the main points developed in this section.

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Various sources are used to construct the growth rates of TFI. Following Dodgson (1993) we proxy capital input by total route miles which are provided in the Railway Returns. The same source provides data on annual expenditures on wages and coal, which we use to estimate, respectively, employment and fuel use by deflating using a price index. We used the Board of Trade wage index, based on average weekly earnings for 20 British railway companies, which goes back to 1898 and is given in Munby and Watson (1978, p. 58). We extended this back to 1893–1912 by interpolating from reported railway wages for 1891 from the Earnings and Hours Enquiry using wage data for bricklayers. With respect to coal prices, the cost per ton of coal consumed in locomotive power is considered. Such information is available from the public record office (PRO RAIL 414 595) for 14 of the 15 companies under consideration. Following Dodgson (1993), estimates for the Taff Vale railway company and some missing data for the South Eastern railway company are obtained on the basis of a regression of cost per ton of locomotive coal for the companies with available information on fuel cost per train-mile. The results reported in Table 7 show an average TFP growth between 1893 and 1912 of 0.7% per year, with 1900–1912 slightly lower at 0.6%, which is slightly above the average of 0.4% that Dodgson (1993) found for the latter period. Average TFP growth is lower

Table 7 Estimates of Company-Level Output (Y) Total Factor Input (TFI) and Total Factor Productivity (TFP) (% per year) Company

1893–1912

1893–1900

1900–1912

Y

TFI

TFP

Y

TFI

TFP

Y

TFI

TFP

Great Eastern Great Northern Great Western Lancashire and Yorkshire London, Brighton, and South Coast London and North Western London and South Western M+S+L (after 1897, Great Central) Midland North Eastern South Eastern (+ Chatham after 1899) Taff Vale Caledonian North British

2.2 1.8 2.7 1.8 1.9 2.1 2.2 4.5 1.9 2.3 5.2 2.1 2.0 2.4

1.1 1.4 2.0 1.4 1.4 1.4 1.3 4.1 1.5 1.2 4.6 0.9 1.3 1.6

1.1 0.4 0.8 0.4 0.5 0.7 0.8 0.4 0.4 1.1 0.6 1.2 0.7 0.8

4.2 4.4 3.3 2.4 3.3 2.6 3.4 6.5 4.5 3.9 12.4 3.5 3.5 3.4

2.6 4.0 2.2 1.8 2.6 2.4 2.5 6.6 3.8 2.5 11.4 1.5 2.4 2.1

1.7 0.5 1.1 0.6 0.7 0.2 0.8 0.1 0.7 1.4 1.0 2.1 1.1 1.2

1.1 0.3 2.4 1.4 1.1 1.8 1.5 3.3 0.4 1.3 1.0 1.3 1.1 1.9

0.5 0.2 1.9 1.2 0.7 1.0 0.6 2.7 0.3 0.4 0.5 0.5 0.3 1.2

0.6 0.1 0.5 0.2 0.3 0.8 0.8 0.6 0.1 0.9 0.4 0.8 0.8 0.7

Average

2.4

1.7

0.7

3.9

3.0

0.9

1.5

0.9

0.6

Notes: Output consists of passenger train miles, mineral ton miles and merchandise ton miles weighted by the revenue shares in 1882 for Britain’s railways as a whole. These weights are 0.43, 0.25 and 0.32, respectively. We have also experimented with the average revenue shares derived from the sample of the 14 companies alone. The results obtained are similar. TFI consists of capital, labor and coal weighted by the average cost shares in 1882 for Britain’s railways as a whole. These weights are 0.63, 0.34 and 0.03, respectively. We have also experimented with four inputs including iron and steel and the average cost shares derived from the sample of the 14 companies alone. The results obtained are similar. The average figures in the last row are weighted by average total route miles. Source: See text.

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than in our national estimates (Table 5) and this comes from faster growth of TFI after 1900. Clearly, the national estimates are to be preferred since they derive from estimates of the capital stock rather than route miles and are anchored by estimates of employment rather than relying entirely on deflating the wage bill by an imperfect measure of wage rates. The value of Table 7 is in the information that it conveys about the dispersion of productivity performance. The estimates in Table 7 indicate a wide range of TFP growth across these 14 companies—over the whole period 1893–1912 there is a gap of 0.8 percentage points per year between the best and the worst performer. This gap did not narrow after 1900 and in the years 1900–1912 three companies had TFP growth of less than or equal to 0.2% per year. Only two companies achieved an increase in TFP growth in 1900 to 1912 compared with 1893–1900, whereas TFP growth fell in 11 cases. Most companies whose TFP growth prior to 1900 was below average remained below average after 1900.12 These results support the view of Dodgson (1993) that TFP growth in the railway industry as a whole could have been faster in the years before World War I. We see a sustained discrepancy over a twenty-year period between companies like the Great Northern and Midland Railways at one extreme and the North Eastern Railway at the other. There is no evidence of catch-up by initially poor performers. 5. Cost inefficiency in 14 railway companies The hypothesis of under-performance on Britain’s railways can be further investigated by examining cost inefficiency, i.e., the ratio of observed to minimum feasible costs. This will allow quantification of the claim made by Cain (1988) that the railway system exhibited waste and inefficiency together with a diagnosis as to whether such problems were being addressed by management. A standard stochastic cost frontier model for the ith firm in time t can be expressed as TCit ¼ a þ bX it þ vit þ uit where TCit is total cost, Xit is a vector of outputs or input prices, a is the intercept term, b is a vector of response parameters, vit is an idiosyncratic random error component; and uit P 0 is the non-negative cost inefficiency component, assumed to be orthogonal to vit. The stochastic frontier literature contains a variety of specifications for the ‘‘composed error’’ vit + uit.13 In a panel data context, a widely used form of the so-called Random Effects stochastic frontier model is that of Battese and Coelli (1992). In this model, the idiosyncratic component vit is assumed to be N ð0; r2v Þ, while the cost inefficiency component is defined as uit = Œ uiŒe(g(tT)), where ui is N ðl; r2u Þ, g is a parameter to be estimated and T is the end year of the time series. This setup contains several Random Effects stochastic frontier models as special cases. For example, setting g = 0 results in the time-invariant model of Battese et al. (1989), while the further restriction l = 0 gives the model of Pitt and Lee (1981).

12 If our growth accounting formula is used to calculate TFP levels, there is a wide spread across companies and the rank correlation between TFP level in 1900 and TFP growth post 1900 is 0.01. 13 See Kumbhakar and Lovell (2000) for an extensive survey.

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Greene (2005) identifies three major drawbacks with the Random Effects model. The first is the implicit assumption of the absence of correlation between the random effects and the included explanatory variables, and the second is that the inefficiency remains the same in each period. Although the Battesse and Coelli models seem to allow time variation of inefficiency, the random component remains time invariant and inefficiency is constrained to vary systematically according to a monotonic function of time (defined by the sign of the parameter g). This is a particularly troubling restriction in panels involving long time series like the one here. The third drawback is that the inefficiency component captures both the inefficiency and any time invariant firm specific unobserved heterogeneity (Greene, 2005, p. 285). The model used here is what Greene (2005) calls the ‘‘true fixed effects’’ model, which is formulated as TCit = ai + bXit + vit + uit. This formulation allows us to distinguish between unobserved firm-specific heterogeneity and inefficiency which is time variant. This feature of the model is appealing given the fact that the railway industry is characterised by a high degree of operational heterogeneity (Farsi et al., 2005). The particular form that heterogeneity takes is to allow it to enter the mean of the inefficiency distribution as follows TCit ¼ bX it þ vit þ uit ;

ui  N ðlit ; r2u Þ;

lit  N ðai ; d0 zit Þ

where zit contains Xit and any other covariates. As Greene (2005, p. 273) argues, this formulation is more natural than, for example, allowing heterogeneity to appear in the cost function, because inefficiency may be time persistent and so leaving it in the cost function will only partially solve the problem.14 To estimate the cost frontier model we adopt the Cobb-Douglas functional form.15 The model that we employ is a two outputs, one output quality, and three inputs model with dummy variables for time periods to capture technical progress and year-specific shocks, and normalized by one of the input prices to impose the theoretical requirement of linear homogeneity in input prices: lnðTCit =F it Þ ¼ a0 þ bP ln PTMit þ bF ln FTMit þ bD ln DENit þ

1912 X

st d t þ cK lnðK it =F it Þ þ cL lnðLit =F it Þ þ vit þ uit

t¼1894

where TC is total cost, calculated as the sum of working expenditures and capital costs, PTM is passenger train miles, FTM is freight ton miles; DEN is density, d is a vector consisting of 19 year dummies from 1894 to 1912 (year 1893 being the omitted category), K is the price of capital, L is the price of labor and F is the price of coal.16 These are fairly standard output and input variables considered 14

The variant where the heterogeneity appears in the cost function itself would be: ui  N ðli ; r2u Þ, li = d0 zi. We have also experimented with the more flexible translog function. However, the estimated coefficients were unsatisfactory in terms of signs, magnitudes and statistical significance and, since on a likelihood ratio test we could not reject the more restrictive Cobb-Douglas specification, we discarded the translog function. Similar problems have been encountered by other researchers, e.g., Farsi et al. (2005) and Greene (2005) who also reverted to a Cobb-Douglas specification. 16 Note that we are estimating a long-run cost function where no fixed factors are included in the set of explanatory variables. It should also be noted that output is considered to be exogenous, i.e., firms are not allowed to choose output levels and entrepreneurial choice involves only optimal inputs. 15

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in the literature (see, e.g., Caves et al., 1981; Dodgson, 1993). The most popular measures of railway output are passenger miles and freight ton-miles (so called ‘revenue measures’), but for passenger services such a measure is not available, so we resorted to passenger train miles.17 Our measure of density is defined as total train miles divided by total route miles. It is, of course, possible that the results from estimating the model will partly reflect differences in the nature of the business and operating environment across companies. However, any such problems will matter only if these factors vary significantly over time because our model accommodates unobserved firm-specific effects. Data on various measures of cost, output and traffic density for a panel of 14 railway companies during 1893–1912 were obtained from the Railway Returns, published annually by the Board of Trade. Specifically, the Returns provide data on total working expenditures, capital costs (calculated as the sum of all payments on capital), passenger/train miles and length of lines. To obtain freight ton miles we assumed that the average haul length figures for 1920 in Railway Returns (1921) also applied to our period, 1893–1912.18 Data on input prices, i.e., wages and coal prices, were constructed as in Section 4. With respect to the cost of capital, we followed the approach used by Farsi et al. (2005), where capital costs are calculated as residual costs after deducting expenditure on labor and coal from total costs. The residual costs are then divided by the length of route miles (which we take to be a proxy for capital stock) to obtain the price of capital. All monetary figures were converted to 1900 price levels using the Board of Trade Wholesale Price Index (Mitchell, 1988). Estimation results of the stochastic frontier Cobb-Douglas cost function are presented in Table 8. We note that all the estimated coefficients have the expected signs and are statistically significant, except for that of labor, which is negative (although insignificant), an anomaly that is hard to explain. The estimated coefficients on the output variables can be interpreted as average elasticities. Thus, a 1% increase in passenger train miles and freight ton-miles would lead to a rise in total cost of about 0.57 and 0.23%, respectively, fairly similar to the results obtained by Dodgson (1993) of 0.63 and 0.39% for passenger and freight train miles, respectively. On the basis of the standard measures of scale and density economies (see, e.g., Caves et al., 1981), our estimate of economies of scale,1/[(o lnTC/olnPTM) + (olnC/olnFTM)] is about 1.26, suggesting some increasing returns to scale. The estimate for economies of density, 1/(olnTC/ olnDEN), is similar at -1.25, thus implying increasing returns to density. These results for economies of scale and density are different from those of Dodgson (1993), who found constant returns to scale and a statistically insignificant and negligible figure for decreasing returns to density.19 Table 9 reports the cost inefficiency scores obtained from our estimation. The entry for Great Eastern in 1893 means that costs were 7.5% greater than minimum feasible costs; the 17

Train miles have been used in other similar studies, e.g., Filippini and Maggi (1993) and Ivaldi and McCullough (2001). 18 This was the first time these data were published. The discussion in Cain (1980) suggests that this assumption will not be in serious error, while it is important to capture heterogeneity across companies in haul length in examining cost inefficiency. 19 This probably reflects our use of ton-miles for freight output compared with Dodgson’s use of train miles.

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Table 8 Regression Results of the cost frontier model, 1893–1912 Coefficient

Estimate

t-ratio

bP bF bD cK cL s1894 s1895 s1896 s1897 s1898 s1899 s1900 s1901 s1902 s1903 s1904 s1905 s1906 s1907 s1908 s1909 s1910 s1911 s1912 ai Observations Log-Likelihood pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi function r ¼ r2u þ r2v k ¼ r2u =r2v

0.567 0.226 0.801 0.651 0.061 0.104 0.128 0.142 0.171 0.185 0.203 0.201 0.168 0.147 0.140 0.164 0.173 0.178 0.168 0.149 0.142 0.115 0.093 0.037 Not shown 280 233.293 0.237 1.462

6.619 5.438 3.181 2.405 1.167 1.645 1.965 2.080 2.401 2.590 2.823 2.779 2.551 2.250 2.097 2.433 2.603 r2.649 2.586 2.411 2.271 1.870 1.526 0.568

7.399 3.975

Note: PTM, passenger train miles; FTM, freight ton miles; DEN, density; K, capital; L, labour.

rest of the table is read in similar fashion. The picture that Table 9 presents is one where cost inefficiency is both substantial and persistent.20 The overall average cost inefficiency score is 13.1% and the general tendency is for cost inefficiency to increase somewhat towards the end of the period.21 This does not suggest that railway managers were successfully addressing the problems identified by critics such as Cain (1988). Indeed, a clear implication of these calculations is that managerial inefficiency hurt profitability quite appreciably, as Arnold and McCartney (2005) suggested. The adverse impact on

20

The cost inefficiency estimates are much higher if the specification does not allow separate stochastic terms for inefficiency and firm-specific heterogeneity as other investigators have found, e.g., Farsi et al. (2005). By adopting a specification with firm-specific heterogeneity we have made the test for finding inefficiency much more stringent. In our experiment with the widely used form of a class of the so called Random Effects stochastic frontier models of Battese and Coelli’s (1992) mean inefficiency is shown to have risen from about 36% in 1893 to about 59% in 1912. 21 The average inefficiency score of 13.1% exceeds that of 7.8% obtained by Farsi et al. (2005) based on the same methodology in their study of Swiss railways in the period 1985–1997.

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profits was about 20%.22 These results give further reason to think that TFP growth in the British railway industry in the late Victorian and Edwardian periods could have been stronger.23 6. Discussion We have established that trend TFP growth on Britain’s railways fell steadily between the early 1850s and the early 1880s. The decrease was substantial and the railways can be seen as a sector whose productivity performance was conducive to a climacteric. Such a productivity slowdown could simply represent maturity rather than failure, however. Moreover, it should be noted that throughout the second half of the nineteenth century railway TFP growth by far exceeded that in the aggregate economy. Even when trend railway TFP growth bottomed out at about 1.1% per year after 1880, this was more than double aggregate TFP growth of a little under 0.5% per year (Feinstein et al., 1982). So pessimism about productivity performance on the railways should be kept in perspective. Nevertheless, it seems clear that TFP growth on British railways could have been faster in the late Victorian and Edwardian period. TFP growth varied markedly across companies, some of which were persistent laggards, while cost inefficiency was substantial throughout the period. By 1910, labor productivity on American railways was 3.3 times the British level, a gap which was twice that of 1870. Given differences in operating conditions, it is not possible to establish the extent to which this was unavoidable but the micro evidence presented above suggests that it probably reflects a significant British failure. Both Cain (1988) and Irving (1978) argued that there were improvements in railway management after 1900, especially in terms of freight operating efficiency, which enabled better cost control and placated angry shareholders by stemming a decline in profits. The immediate stimulus was regulation. Effective price control was introduced by the Railway and Canal Traffic Act of 1894 which, following a test case in 1899, was interpreted by the courts as a freeze on freight charges. Given rising costs, this was a threat to profits and galvanized railway management.24 However, the ‘Cain-Irving defense’ of railway managers actually highlights that they operated in an uncompetitive environment in which agency problems were deeply embedded and shareholder value was neglected. Only when taken out of the comfort zone by the threat of profits falling below a threshold level that would create shareholder unrest did management adopt cost-reducing innovations. This is behavior that is characteristic of managers who were satisficers rather than profit-maximizers. 22 A conservative calculation can be made by applying the cost inefficiency score to working expenditure. For example, in 1906, when the cost inefficiency score equalled the sample average of 13.1%, operating at minimum feasible costs would have raised profits for these companies by £8.15 million from £37.73 to £45.88 million and the return on capital employed from 3.63 to 4.42% based on the dataset used by Arnold and McCartney (2005) which was generously provided to us by the authors. 23 However, it should be recognized that changes in cost inefficiency and TFP growth were only weakly correlated in this period: DCI = 17.98(5.00) + 11.63(2.23)TFP Growth, R2 = 0.23 (t-statistics in parentheses). This is not surprising given that TFP growth includes gains from economies of scale and of density while cost inefficiency normalizes for the heterogeneity across companies in their access to these economies. 24 Our evidence on the chronology and dispersion of TFP growth and the persistence of cost inefficiency suggests that this regulatory stimulus did not have a dramatic impact.

Table 9 Estimated cost inefficiencies: Britain’s railway companies 1893–1912 Caledonian North Mean British

0.075 0.089 0.091 0.102 0.113 0.103 0.111 0.090 0.115 0.159 0.156 0.168 0.170 0.164 0.154 0.129 0.167 0.176 0.234 0.230

0.091 0.105 0.110 0.119 0.123 0.115 0.120 0.092 0.109 0.154 0.146 0.134 0.134 0.131 0.128 0.120 0.159 0.162 0.208 0.239

0.138 0.156 0.152 0.149 0.141 0.122 0.125 0.110 0.097 0.131 0.135 0.125 0.123 0.115 0.106 0.103 0.113 0.124 0.170 0.209

0.093 0.105 0.122 0.130 0.115 0.107 0.109 0.091 0.100 0.136 0.129 0.125 0.147 0.146 0.137 0.124 0.159 0.166 0.226 0.267

0.105 0.107 0.125 0.123 0.119 0.105 0.122 0.116 0.139 0.157 0.145 0.142 0.142 0.130 0.120 0.113 0.132 0.134 0.165 0.178

0.118 0.144 0.150 0.150 0.140 0.125 0.122 0.111 0.113 0.151 0.144 0.122 0.115 0.113 0.109 0.091 0.115 0.129 0.177 0.211

0.140 0.132 0.145 0.142 0.148 0.113 0.125 0.100 0.091 0.121 0.124 0.116 0.119 0.209 0.114 0.092 0.128 0.145 0.193 0.178

0.102 0.147 0.155 0.166 0.165 0.174 0.119 0.087 0.091 0.125 0.109 0.097 0.105 0.113 0.128 0.112 0.139 0.147 0.201 0.258

0.089 0.119 0.126 0.134 0.130 0.120 0.117 0.100 0.124 0.150 0.131 0.120 0.128 0.123 0.124 0.105 0.138 0.150 0.205 0.245

0.115 0.114 0.123 0.132 0.131 0.118 0.123 0.102 0.114 0.142 0.138 0.131 0.127 0.126 0.124 0.100 0.135 0.139 0.196 0.221

0.089 0.096 0.109 0.107 0.102 0.090 0.117 0.109 0.138 0.155 0.146 0.136 0.141 0.141 0.139 0.141 0.156 0.165 0.209 0.230

0.215 0.232 0.230 0.206 0.173 0.097 0.165 0.147 0.167 0.169 0.142 0.122 0.094 0.089 0.088 0.077 0.082 0.091 0.121 0.152

0.111 0.112 0.129 0.116 0.098 0.092 0.110 0.103 0.155 0.141 0.154 0.129 0.131 0.121 0.111 0.122 0.149 0.168 0.214 0.238

0.101 0.115 0.125 0.123 0.117 0.126 0.124 0.115 0.139 0.147 0.152 0.143 0.134 0.110 0.103 0.103 0.130 0.141 0.182 0.220

0.113 0.127 0.135 0.136 0.130 0.115 0.122 0.105 0.121 0.146 0.139 0.129 0.129 0.131 0.120 0.109 0.136 0.145 0.193 0.220

Mean 0.135

0.129

0.128

0.130

0.128

0.128

0.131

0.131

0.128

0.128

0.131

0.142 0.130

0.128

0.131

1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912

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London and London M+S+L Midland North South Taff Great Great Great Lanca- London, Eastern Eastern Vale Eastern Northern Western shire Brighton, North & South (after and and Western Western 1897, (and York- South Coast Great Chatham Central) after 1899) shire

Year

631

632

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The railway sector operated behind massive barriers to entry and collusive behavior was rampant (Cain, 1972). Indeed, in the early twentieth century railway companies operated agreements which amounted almost to de facto amalgamation (for example, Great Central, Great Eastern, Great Northern or Lancashire & Yorkshire, London & North Western, Midland) while devoting significant management effort to lobbying government to allow mergers (Irving, 1978). Persistent discrepancies in productivity performance across railway companies with no evidence of catch-up by the laggards are indicative of the weakness of competition (Oulton, 1998). Railway management had ample opportunity to pursue their own objectives while neglecting cost reductions and productivity improvement in a context where shareholders were weak (Arnold and McCartney, 2005) and takeover threats were non-existent (Hannah, 1974). 7. Conclusions We posed four explicit questions at the outset. Our answers are as follows. First, on the basis of our new TFP index for British railways and a time-series analysis of its properties, we conclude that labor productivity was stationary over the long run while trend TFP growth fell steadily from a little under 2.5% per year in the 1850s to about 1.1% per year in the early 1880s, at which rate it continued without any further decline till World War I. Second, TFP growth varied considerably across major railway companies in the period 1893–1912, with a gap of 0.8 percentage points between the best and worst performers. There is no evidence of catch-up by the laggards. Third, actual costs were well above minimum feasible costs on Britain’s railways. In the years 1893–1912 cost inefficiency averaged about 13% and the situation was not improving as the period drew to a close. Fourth, railways appear to have missed opportunities to raise TFP growth and can be accused of managerial failure. The railway sector appears to be a non-trivial exception to the neoclassical exoneration of late-Victorian Britain, given that it accounted for 20.4% and 14.6% of the economy’s capital stock in 1870 and in 1913, respectively (Feinstein, 1988). The substantial labor productivity gap between British and American railways could have been reduced by better management. Managerial failure on Britain’s railways has wider significance. It underlines the importance of competition in sustaining performance in sectors where entrepreneurial failure was not a problem. It also points to the need for a greater emphasis on research into service sector productivity both because of the key role that this played in British relative economic decline (Broadberry, 2006) and because it has received relatively little attention from cliometricians investigating allegations of British entrepreneurial failure. References Armstrong, J., 1987. The role of coastal shipping in UK transport: an estimate of comparative traffic movements in 1910. Journal of Transport History 8, 164–178. Arnold, A.J., McCartney, S., 2005. Rates of return, concentration levels and strategic change in the British railway industry, 1830–1912. Journal of Transport History 26, 41–60. Battese, G.E., Coelli, T.J., Colby, T.C., 1989. Estimation of frontier production functions and the efficiencies of Indian farms using panel data from ICRISAT’s village level studies. Journal of Quantitative Economics 5, 327–348.

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