Growth accounting is a methodology that breaks down increases in an economy's productive potential into different components. The first is the contribution to greater output made by additional production inputs (machinery, labour etc.). This "more from more" growth is known as "extensive' growth." The second is the contribution made when an economy becomes able, perhaps through better technology or organisational innovations, to produce more output from fewer inputs. This "More from less" or "intensive" growth results from what economists term total factor productivity (TFP) growth.
A new technology such as railways contributes to growth both by allowing the economy to invest in new (capital) inputs and by raising TFP. TFP growth could occur both through improvements over time in railway technology itself, so reducing the real cost to users and, in addition, through the emergence of TFP improvements in other sectors caused by the coming of the railways ("spillover effects"). The overall contribution of the innovation to growth is calculated by summing its intensive and extensive growth effects, weighting each by their importance relative to the economy as a whole.
We can estimate the extensive and intensive growth effects of railways using the data in Charles Feinstein and Gary Hawke's works. Over the period 1840-1870 the capital stock of the railway grew at about 8.2 per cent per year and received on average about 1.6 per cent of national income. The extensive contribution can be calculated by multiplying these two figures together, (8.2 percent x 0.016), giving an estimate of 0.13 percent per year. During the same period TFP growth in railways averaged about 3 per cent per year and railways accounted for about 3.2 per cent of total output. Their intensive contribution was therefore 0.10 percent per year (3.0 percent x 0.032). It is difficult to pin down TFP spillovers but the detailed discussion in Hawke suggests that they were probably very small. As a result, our best estimate of the total effect of the railways is that the extensive and intensive growth effects sum to 0.23 percent per year.
Stephen Oliner and Dan Sichel carried out a similar exercise to estimate the contribution of the ICT revolution to economic growth in the United States in the late twentieth century. They found that the ICT capital stock grew very rapidly and that TFP growth in ICT production was also very rapid. Against that the sector had quite a small share in income and output; even in the late 1990s it accounted for only about 6 per cent of capital income and 2 per cent of output. They found that, between 1974 and 1995, ICT contributed 0.55 percent per year through the extensive contribution and 0.19 percent per year through intensive growth, a total of 0.74 percent per year. As with railways, TFP spillovers have proved elusive and there is no firm evidence that they have been important. In the late 1990s the size of both the extensive and intensive growth effects roughly doubled, to 1.12 percent and 0.45 percent respectively, given a total effect of 1.57 percent. We can see that, in absolute terms, the effect of the computing in its early years was substantially greater than that of the early years of the railways. This is also true of ICT's relative contribution; whereas railways accounted for about a tenth of total growth, ICT accounted for over a fifth even prior to the late 1990s acceleration.
The social savings methodology set out in Box 1 provides an estimate which should equal the intensive growth contribution of railways, while disregarding the extensive growth contribution. The intensive growth contribution is equivalent to the rate at which transport prices to consumers can (and if conditions are competitive, will) be reduced as a result of input savings. Deducting Hawke's 1970 estimate of social savings from national income in 1870 reduce the estimated growth rate for 1840 to 1870 from 2.64 to 2.55 per year, that is, by 0.09 percent per year. This is very close to our earlier estimate that the intensive growth from railways was equivalent to 0.1 percent per year, giving us considerable confidence in these figures.
Why does the social saving methodology ignore the extensive contribution arising from the additional capital input? The rationale of those who use the social savings methodology is that this capital merely displaced other investments that could also have earned the going rate of return. As such the return to railway capital would have accrued to the economy in any case, although it would have done so through alternative investments had the railways not been invented. This means that the "unique" contribution of railways was to be found only in the cost reduction benefits of intensive growth. The counter argument from those favouring the growth accounting methodology is that railway technology must be embodied in a new and special form of capital equipment. As such it is more intuitive to include extensive growth in the effects of railways on the economy.
There are arguments for and against both positions. The growth accounting method is the more common, although economic historians have generally preferred to use the social savings methodology. In the case of railways and ICT the choice of method is not crucial. As we have noted, the growth accounting method gives the contribution of ICT prior to 1990 as 0.74 percent, while the figure for railways was 0.23 percent. When we restrict ourselves to the social savings/intensive growth measure, we find that the two figures are then 0.19 percent and 0.10 percent. Although the ratio is different, both measures show that the effect of computing was unambiguously greater than that of railways in the early stages of their development.
