COST ANALYSIS FOR THE WORLD BANK:
THE CASE OF ARGENTINE RAILWAYS

When in the year 1960 the Argentine Republic applied to the World Bank for credit to reconstruct and develop her transportation systems, a Transport Planning Group consisting of foreign and local consultants was set to work on devising a comprehensive sectoral plan for the country. One of the cornerstones of that plan was the estimation of the costs of transport by various modes. The method by which railway costs were arrived at was explained at length in their report, together with a numerical summary of the results, which are transcribed in the table below.

ESTIMATED COSTS OF GOODS TRANSPORT BY RAIL, ARGENTINA, 1960 --- in pesos per ton-km.
BROAD GAUGE STANDARD GAUGE NARROW GAUGE
Gross Ton Density Operating Expenditure Interest & amorti- zation of additional capital Total Gross Ton Density Operating Expenditure Interest & amorti- zation of additional capital Total Gross Ton Density Operating Expenditure Interest & amorti- zation of additional capital Total
UNDER CURRENT OPERATING CONDITIONS
121,680 3.991 - - 244,915 1.349 - - 57,655 6.540 - -
206,880 2.262 - - 331,600 1.261 - - 209,560 1.780 - -
421,200 1.633 - - 367,380 1.197 - - 285,480 1.452 - -
695,760 1.192 - - 474,708 1.096 - - 399,360 1.202 - -
970,320 1.033 - - 712,049 1.020 - - 542,100 1.191 - -
1,244,880 0.931 - - 1,021,560 0.778 - - 920,088 0.923 - -
1,794,000 0.840 - - 1,282,630 0.759 - - 1,413,100 0.770 - -
2,343,120 0.788 - - 1,521,000 0.737 - - 1,846,635 0.719 - -
4,612,120 0.724 - - - - - - - - - -
AFTER RECOMMENDED INVESTMENTS WITH 5 PER CENT. INTEREST ON THE ADDITIONS
134,160 2.627 1.357 3.984 241,280 0.966 0.867 1.833 71,760 3.656 2.237 5.893
294,320 1.436 0.768 2.204 445,945 0.684 0.629 1.313 234,000 1.271 0.877 2.158
469,248 0.983 0.568 1.551 570,825 0.643 0.573 1.216 327,600 0.954 0.729 1.683
722,800 0.714 0.464 1.178 663,935 0.587 0.560 1.147 378,295 0.846 0.629 1.475
1,078,520 0.576 0.459 1.035 848,630 0.531 0.592 1.123 647,500 0.689 0.491 1.180
1,528,800 0.491 0.347 0.838 1,226,435 0.430 0.479 0.909 790,900 0.603 0.497 1.100
2,212,080 0.416 0.490 0.906 1,486,850 0.414 0.461 0.875 1,240,090 0.515 0.427 0.942
2,895,360 0.385 0.430 0.815 2,131,667 0.366 0.580 0.946 1,536,500 0.480 0.534 1.014
5,709,600 0.339 0.320 0.659 - - - - - - - -
Source: Argentine Republic, Ministry of Public Works and Services, A Long Range Transportation Plan for Argentina, Buenos Aires: 1962, Appendix III, pages 22-25.

Since the costs per ton-kilometre of freight before and after recommended improvements are not shown for comparable traffic densities per kilometre of line, a direct comparison of these costs is not possible without interpolation. An interpolation can be made by fitting the figures given in the above tables to exponential functions by the method of least squares. The results---showing the logarithm of the cost C as a function of the logarithm of the traffic density X--- are as follows:(1)

BROAD GAUGE STANDARD GAUGE NARROW GAUGE
CURRENT SITUATION, excluding capital costs
ln(C) = 6.5956 -0.4672 ln(X) ln(C) = 4.7402 -0.3558 ln(X) ln(C) = 8.0931 -0.5972 ln(X)
(0.1620) (0.0491) R² = 0.9283 (0.0439) (0.0245) R² = 0.9723 (0.2198) (0.0738) R² = 0.9161
AFTER INVESTMENT, including the interest and amortization of additional capital
ln(C) = 6.597 -0.4629 ln(X) ln(C) = 4.5294 -0.3243 ln(X) ln(C) = 8.0219 -0.5800 ln(X)
(0.1729) (0.0517) R² = 0.9197 (0.0846) (0.0456) R² = 0.8941 (0.1800) (0.0685) R² = 0.9228

The equations fitted to the estimates were applied to construct a table of goods transport costs at comparable levels of traffic density. In the following table, the operating expenses without interest and amortization of sunk capital are shown in the table with the "Old" heading, and the costs after recommended improvements, both operating and total including the cost of additional capital, are expressed as percentages of the "Old."

Gross Ton Density BROAD GAUGE STANDARD GAUGE NARROW GAUGE
OLD NEW OLD NEW OLD NEW
Operating Total Operating Total Operating Total
pesos in % of the old pesos in % of the old pesos in % of the old
100,000 3.377 74.5 105.2 1.905 72.8 116.4 3.378 70.5 113.5
200,000 2.443 69.8 105.5 1.488 68.3 118.9 2.233 68.1 114.9
300,000 2.021 67.2 105.7 1.288 65.7 120.4 1.753 66.8 115.7
400,000 1.767 65.4 105.8 1.163 64.0 121.5 1.476 65.9 116.3
600,000 1.462 63.0 106.0 1.007 61.6 123.1 1.159 64.6 117.1
800,000 1.278 61.3 106.1 0.909 60.0 124.2 0.976 63.7 117.7
1,000,000 1.152 60.0 106.2 0.840 58.8 125.1 0.854 63.0 118.1
1,200,000 1.058 59.0 106.3 0.787 57.8 125.8 0.766 62.4 118.5
1,400,000 0.984 58.2 106.4 0.745 56.9 126.4 0.699 62.0 118.8
1,600,000 0.925 57.4 106.4 0.710 56.2 127.0 0.645 61.6 119.1
1,800,000 0.875 56.8 106.5 0.681 55.6 127.4 0.601 61.2 119.3
2,000,000 0.833 56.2 106.5 0.656 55.1 127.9 0.565 60.9 119.6

The Transport Planning Group's report did not explain why, for any traffic density, transport by narrow or standard gauge should be cheaper than by broad gauge. Neither did they notice that their calculated economies of density are more pronounced on the narrower gauge lines.

Five observations can be made on the above results.

First, the recommended improvements by investment of additional capital, while reducing the operating costs, increase the total cost. The increase would be tolerable if it meant also an improved quality of service. However, no service quality change was mentioned in the consultant's report of their calculations nor can it be implied in the consultant's use of average costs supplied by the Argentine railway administration that were based on existing operating experience.

Second, the difference between operating costs before and after investment of additional capital reflects a substitution of labour for capital made in the effort to continue railway service with the existing, sunk and depreciated capital. That substitution was not entirely wrong at a time when real wages were stagnant or falling and both capital and foreign exchange were in short supply.

Third, the substitution of labour for capital was economical for so long as the investment of new capital could be postponed, so long as the sunk capital remained serviceable at a cost below the total including improvements recommended by the World Bank consultants.

A fourth observation is in regard to the credibility of the estimates in the first table. Those estimates show very large "economies of traffic density" that must be attributed to an improper application of some system-wide averages that were treated as constant costs independent of traffic density. The resulting economies of density are suspect because they do not correspond to the actual experience of railways. No comparison of expenditures by separate railway companies with widely different traffic densities will show cost differences as large as those estimated by the Transport Planning Group. The absence of large economies of density was observed already in 1907 by the statistician of the US Interstate Commerce Commission and later by Milton Friedman.(2)

The true costs for any traffic density are to be taken as something close to the average of the values computed for the whole range of traffic densities. That means that the operating costs of low-density railway lines have been over-estimated and therefore all branch-line abandonment recommendations based on such cost estimates were made in error.

The final observation is about the total operating costs implied by the above cost estimates. Given the gross ton densities and the average costs per ton-km. given in the very first table, one finds, by taking the product of the two quantities, that---at some low traffic volumes--- the estimated total cost is less for a larger quantity of traffic than for a smaller one:
CALCULATED TOTAL COSTS
before improvement by investment
Broad gaugeNarrow gauge
Gross
Ton
Density
PesosGross
Ton
Density
Pesos
121,680485,62557,655377,064
206,880467,963209,560373,017

This last result cannot be defended and seriously calls into question the quality of the consultants' work.

Sylvester Damus.
First draft, August, 1970
Final draft, October 2002.


1. The numbers in parentheses are standard errors of the estimated coefficients.

2. Cf. M. O. Lorenz, Constant and Variable Costs and the Distance Tariff, Quarterly Journal of Economics, 21 (1907), 283-98; and Milton Friedman, Comment on Caleb Smith's Survey of the Empirical Evidence on Economies of Scale, in Business Concentration and Price Policy, Princeton University Press, for the National Bureau of Economic Research, 1955, pages 230-38.

The following table suggests observations like those made by M. O. Lorenz:

The expenses and revenues (columns 6 and 7) and traffic density (column 5) of any railway company reflect peculiar circumstances without demonstrating economies of density or any correlation between expenses or revenues and traffic density.

Among the narrow gauge lines, the Santa Fe, Cia. General and Cordoba Central show little variation in average expenses and yet there was large variation in traffic density.

The three privately-owned railways that operated standard gauge lines, the North Eastern, Entre Rios and Buenos Aires Central, showed an unexpected relationship between their operating expenses and traffic density, the expenses being higher where the traffic density was also higher.

In the broad gauge, the Central Argentine, which had maximum traffic density, also had average expenses in excess of those of the Pacific, Western and Southern lines. The expenses of the Rosario to Puerto Belgrano were almost equal to those of the Pacific, although its traffic density was very much lower.

These observations suggest that the operating expenses calculated by the authors of the so-called "Larkin Plan" are not credible. The economies of density shown in their cost tables have resulted from defective cost accounting.

In the cases of the Rafaela Steam Tramway and the Patagonian Lines, the enormity of their average expenses is due to the fact that they operated as semi-independent enterprises instead of being simple branch lines. Considering the Steam Tramway's experience over four years one finds maximum average expenses in the year of maximum traffic density.

Finally, a regression of operating expenses on gross ton-miles (R² = 0.9732) is far more significant than a regression of average cost per gross ton-mile on gross-ton-miles per km. of line or traffic density (R² = 0.3155) when using all 20 observations, including those on government railways. Using only the observations on 14 private railways the R²s are 0.9819 and 0.3828, respectively. In any case, traffic density is less significant than total traffic. Gross ton-miles can explain 98 percent of total operating expenditure; gross ton-miles per mile explain only 38 percent of total operating expenditure per mile of line. The constants in the regression equations of total expenses on total gross-tonnage amount to from 4 (N=14) to 6 (N=20) per cent of the total operating expenditure at the mid-points of the regressions. This means that fixed expenses are rather light and cannot be adduced in reference to large economies of density.

GROSS TONNAGE, OPERATING EXPENSES AND REVENUES.
YEAR 1928

(1) (2) (3) (4) (5) (6) (7)
Railway Gros Ton-km. Kms. of
Lines
Expenses Revenues Gross Ton-km. Expenses Revenues
per km. per Gross Ton-km.

$ gold $ gold cents gold cents gold
Source:
M.O.P., Estadística de los ferrocarriles en explotación, tomo xxxvii, año 1928, Bs. As., 1931. Table 13 Table 5 Table 28 Table 28 (5)=(1)/(2) (6)=100*(3)/(1) (7)=100*(4)/(1)
Col. 28 Col. 7 Col. 17 Col. 16
NARROW GAUGE
Central Norte 5,093,683,563 5,294 25,870,148 23,671,062 962,162 0.5079 0.4647
Embarcación a Formosa 42,757,044 298 247,181 328,633 143,480 0.5781 0.7686
Provincia de Santa Fe 1,597,051,422 2,006 6,888,691 10,496,818 796,137 0.4313 0.6573
Compañía General en la Pcia. de Bs. As. 1,467,205,937 1,268 5,985,285 8,263,094 1,157,102 0.4079 0.5632
Cordoba Central 3,232,320,608 1,960 13,396,478 18,083,924 1,649,143 0.4145 0.5595
Trasandino 40,238,542 179 990,756 1,126,456 224,796 2.4622 2.7994
Rafaela Steam Tramway 4,286,881 84 85,345 75,660 51,034 1.9908 1.7649

SUB-TOTAL 11,477,543,997 11,089 53,463,884 62,045,647 1,035,039 0.4658 0.5406
STANDARD GAUGE
del Este 69,639,259 330 497,267 667,344 211,028 0.7141 0.9583
North Eastern 717,223,978 1,209 2,873,594 4,143,701 593,237 0.4007 0.5777
Entre Ríos 1,055,215,406 1,090 4,911,483 8,155,585 968,088 0.4654 0.7729
Buenos Aires Central 411,270,611 379 2,226,217 3,919,094 1,085,147 0.5413 0.9529

SUB-TOTAL 2,253,349,254 3,008 10,508,561 16,885,724 749,119 0.4664 0.7494
BROAD GAUGE
San Antonio al Nahuel Huapi 132,312,021 743 652,116 851,239 178,078 0.4929 0.6434
Comodoro Rivadavia 18,320,407 198 279,074 396,781 92,527 1.5233 2.1658
Puerto Deseado 16,558,055 286 174,830 196,133 57,895 1.0559 1.1845
Southern 11,221,377,685 6,375 39,918,581 57,250,514 1,760,216 0.3557 0.5102
Bahía Blanca & Northwestern 1,011,312,502 1,229 4,378,824 7,210,606 822,874 0.4330 0.7130
Western 4,884,519,524 3,098 17,580,502 26,576,953 1,576,669 0.3599 0.5441
Central Argentine 12,827,197,328 5,346 50,388,053 71,096,764 2,399,401 0.3928 0.5543
Pacific 9,902,767,896 4,447 29,612,877 44,064,010 2,226,842 0.2990 0.4450
Rosario a Puerto Belgrano 577,307,043 826 1,743,577 3,045,210 698,919 0.3020 0.5275

SUB-TOTAL 40,591,672,461 22,548 144,728,434 210,688,210 1,800,234 0.3565 0.5190

TOTAL 54,322,565,712 36,645 208,700,879 289,619,581 1,482,400 0.3842 0.5331
GOVERNMENT-OWNED (in italics) 5,373,270,349 7,149 27,720,616 26,111,192 751,611 0.5159 0.4859
PRIVATELY-OWNED 48,949,295,363 29,496 180,980,263 263,508,389 1,659,523 0.3697 0.5383

RAFAELA STEAM TRAMWAY
Year 1926 3,368,210 84 57,110 46,092 40,098 1.6956 1.3684
Year 1927 4,080,024 84 62,657 84,212 48,572 1.5357 2.0640
Year 1928 4,286,881 84 85,345 75,660 51,034 1.9908 1.7649
Year 1929 3,672,765 84 65,915 66,181 43,723 1.7947 1.8019