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|
|AFTER RECOMMENDED INVESTMENTS WITH 5 PER CENT. INTEREST ON THE ADDITIONS|
|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|
|pesos||in % of the old||pesos||in % of the old||pesos||in % of the old|
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 gauge||Narrow gauge|
This last result cannot be defended and seriously calls into question the quality of the consultants' work.
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.
|Railway||Gros Ton-km.||Kms. of
|per km.||per Gross Ton-km.|
|$ gold||$ gold||cents gold||cents gold|
|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|
|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|
|Rafaela Steam Tramway||4,286,881||84||85,345||75,660||51,034||1.9908||1.7649|
|Buenos Aires Central||411,270,611||379||2,226,217||3,919,094||1,085,147||0.5413||0.9529|
|San Antonio al Nahuel Huapi||132,312,021||743||652,116||851,239||178,078||0.4929||0.6434|
|Bahía Blanca & Northwestern||1,011,312,502||1,229||4,378,824||7,210,606||822,874||0.4330||0.7130|
|Rosario a Puerto Belgrano||577,307,043||826||1,743,577||3,045,210||698,919||0.3020||0.5275|
|GOVERNMENT-OWNED (in italics)||5,373,270,349||7,149||27,720,616||26,111,192||751,611||0.5159||0.4859|
|RAFAELA STEAM TRAMWAY|