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Pithead Prices. Coal is anything but a homogenous good, varying widely—both among and within mines—in such qualities as thermal content, length and type of burn, and ‘sootiness.’ So pithead prices were estimated from a variety of printed and archival sources on Newcastle prices and true pithead prices for individual mines from 1730 to 1869 (detailed in the appendix). They were combined in a regression of the form
where pit is the quoted price from source i in year t, LOCi is an indicator variable for each of the sources we have on prices of types of coal (such as Wallsend), and DUMt is an indicator variable for the year. Then the prices obtained were linked to the pithead prices of coal from the northeast reported by Church (1986) for the years 1882 on using export prices as the linking series. The resulting estimated prices, controlling for differences in coal quality, are those shown in the last column of table 1. To extend these back to the 1710s, when we have no actual northeast prices, the ratio of pithead to London prices was assumed to be the same as in the 1740s.
Wages. There is no series available for coal miners’ wages in the northeast in the years 1740 to 1869.
Instead we have 38 scattered estimates and measures of hewers wages per shift reported by authors such as Ashton and Sykes, Flinn and Church. These estimates are shown in figure 6. Hewers wages should be a good index of mining wages in general since the wages of some other workers, especially putters (those employed in transporting the coal from the face to the pit bottom or head), were set explicitly in terms of hewers’ wages and also there are indications of strong correlation between hewers’ wages and the whole of those employed in mining, including some lower-level management type positions such as overman (Church, 1986; Griffin, 1977). When we compare these scattered quotes of wages over time to farm wages in the north of England we find that, while there are short run deviations, over the long run of 1740 to 1869 they increase by exactly the same amount. Thus when we regress the ratio of hewers’ wages to farm wages (WH/WA) on a constant plus a time term, T, measuring as years since 1740, we find that the time trend term is both statistically and quantitatively effectively 0. Thus,
with the standard error on the coefficient estimate for T being 0.00141. Figure 6 shows also hewers wages as predicted from equation (3), shown as the bold line. As can be seen, for the long run, hewers’ wages can be reasonably well approximated by farm wages. Since the major recruitment for labor for the coalfields was farm workers this result is not surprising. Notice also that the hewer in the northeast earned more than double the agricultural wage, as compensation for the danger and unpleasantness of underground working.
Hewers in the northeast also received free housing and coal allowances which are not incorporated in these wage estimates. The housing is included under the capital costs of the mine.
The coal allowance is subsumed under the coal consumed at the pithead for pumping and other purposes when estimating TFP. Table 7 shows the resulting decadal estimate of northeast daily coal wages. Also shown are the average daily wages of building craftsmen and their helpers in the northeast. In the productivity estimates we assume that such workers maintaining pit structures and equipment were 10% of total costs.
We assume half of the 18% spent for craftsmen and supplies was for labor. The wage used here is that of northern building craftsmen from Clark (2004).
Coal Rents. The rental payment per ton of coal in table 1 is calculated from leases of coal land. Since mine operators had to undertake large fixed investments in mines coal leases were generally for 21 years or more. The form of the lease in the north east was generally that the lessee paid a fixed rent for all coal extracted up to a certain minimum quantity, and then a payment per unit of output— known as the tentale rent—for all output above the allowance. Often the tentale rent was the same as the fixed payment divided by the allowance. Thus it is possible to estimate from these leases the average coal rents paid per ton of output. A sample of over 203 leases from the 1710s to the 1860s was collected (see Appendix I). From this sample, estimates were made of the general course of lease payments in each decade. In estimating these we again used a regression of the form
where rentit is the quoted tentale rent from source i in year t, LOCi is an indicator variable for the location or the colliery, and DUMt is an indicator variable for the year.
These rental payments we assume to reflect the value of coal land in free competition.
Throughout this period, however, colliery owners in the north east attempted, through the ‘limitation of the vend’, for example, to restrict output and bolster prices. If limitation of output was present earlier in the history of the industry, but not later, it would bias upwards the estimated movement of productivity over these years (see Harrison, 1994). Various studies of competition and monopoly in the industry in these years, however, have generally concluded that the attempt to limit output was generally unsuccessful, due to a poorly designed system of positive and negative incentives (Sweezy, 1938), indifferent enforcement (Hausman, 1984a, 1984b), and an inability to erect substantial barriers to entry (Cromar, 1977; Hausman, 1984a, 1984b).
Fodder. Fodder costs were assumed to be half those of oats and half those of hay. These prices are available from Clark (2004) for England as a whole and are shown in table 7.
Supplies. These we assume to be 9% of costs. There is no clear breakdown of these in the accounts of the industry. We know timber, iron, ropes, candles, and oil all were components. Table 7 shows the estimated prices for timber, iron and candles, which we assign weights of 5%, 2% and 2% respectively in total costs.
Capital Costs. Capital costs in the productivity calculation will be
where r is the rate of return on mining capital, d the depreciation rate of capital, and pk the cost per unit of the capital goods employed in mining.
To estimate the cost of mining capital, pk we used five price series: estimated northeast hewers wages (50%), estimated northern builders wages (20%), the price of bricks (10%), the price of iron (10%), and the price of timber (10%). The weights were those suggested by Roy Church for circa 1850 (Church (1986), p. 175). The major capital goods in mining were the shaft, the pithead structures and buildings, and railways and wagons. Table 8 shows estimated brick prices for England as a whole. The other prices necessary to construct capital costs are all shown in table 7.
Table 8 shows the resulting index of the price of mining capital in the northeast per unit. For comparison Church’s index of capital costs for the 1830s to 1860s is also shown. These two series both move little for this interval and are quite consistent.
For the years before the 1850s there are no direct measures on the long-term return on capital in mining, or on the cost of the capital involved. The records needed to calculate an industry-wide average rate of return are no longer extant. Even in the fragmentary records that have survived, accounting practices, especially for the earlier parts of the period, seem to be a jumbled confusion of entries. There is little delineation between charges for, say, circulating and fixed capital, depreciation, and returns and little concern for consistent and fundamental accounting principles (Flinn, 1984).
Given this we estimated the return on capital in mining as the average rate of return on bonds and mortgages in the same interval. Most coal mine owners were landowners or merchants in addition (Buxton,1978; Flinn, 1984; Griffin, 1974). Thus the return on investing in mines cannot have strayed too far in the long run from investments in other assets such as mortgages. We took as our rate of return proxy the rate of return on bonds and mortgages in England from Clark (1998).
These returns are shown in table 8. They were not much lower than the return reportedly earned in coal mining in the 1850s and 1860s when we get accounts good enough to estimate returns. Table 9, for example, shows some estimates of the net return on mining capital in the UK in the 1850s and 1860s. As can be seen these returns exceed those on bonds and mortgages in the same period by less than 1%. So while we do not have direct measures of the return on capital in mining, it did not exceed the mortgage rate by much. We calculate the rental cost of capital in mining thus as
premium, and pk is the price of capital goods. The allowance for depreciation is in line with estimates in the nineteenth century by Church of the gross return on mining capital compared to the net return. Gross returns, which incorporate capital consumption and depreciation as part of the return, were about double estimated net returns. Table 8 also shows the resulting estimated rental cost of capital in mining by decade.
Total Factor Productivity. Table 10 shows as an index the extraction cost of coal at the pithead in the northeast by decade (price minus coal rents). Also show is an index of the input costs of mining coal, under the lower bound assumption that all seams were equivalent, and under the upper bound assumption that a set of costs were directly proportional to depth. The associated Total Factor Productivities are then just the index of costs divided by the index of extraction costs. These are shown as the fourth and sixth columns of the table. These productivity indices are shown in figure 8.
Even though mining wages rose much faster than the extraction costs, overall input costs rose only very slightly more than extraction costs because so many other elements of cost increased much more slowly – coal rents, iron, timber, bricks, and candles in particular. Thus between the 1730s and the 1860s measured productivity rose by only about 6% overall on the measure that assumes the seams were unchanged over time. When we overcorrect for higher costs through deeper seams, the measured productivity gain was still modest, at about 25%. This still implies a productivity growth rate of less than 0.2% per year over the Industrial Revolution period, slower than for the economy as a whole.
Given that these two productivity estimates are upper and lower bound estimates of productivity growth, the best estimate is an average of the two. These estimates are all subject to error. From the standard errors of the individual components we estimate that the productivity estimates for any decade relative to the 1860s have a standard error of 10%. But since we observe many decades for the overall trend we have much less error than this. From the four decades 1710to 1830-1869 for example, our best estimate is of a growth rate of 0.14% per year, with a standard error of about 0.04% on either side. This estimate is quite consistent with the estimate made above of the benefits from the addition of steam power to mines by the 1860s of a productivity gain of 10-20 percent. This implies that we can say with 95% confidence that productivity in coal mining grew at less than 0.22% per year from the early eighteenth century to the mid nineteenth century.
Coal and the Industrial Revolution This productivity result above is entirely consistent with the cliometric interpretation of the coal industry. Output expansion was driven by factors external to the industry – increased urban demands for coal, increased demand from iron production, and reduced taxation and transport costs. In contrast to the estimated 0.14% productivity growth rate of coal mining, productivity in cotton textile production increased by 3.1% per year (Clark (2001b)). TFP in iron and steel manufacturing is estimated to have increased in the same years by about 0.9% per year (McCloskey (1981), p. 114). Further productivity growth in coal mining is much below the 0.55% per year productivity growth for the economy as a whole found by Crafts and Harley (1996). Coal mining really was a bit actor in the productivity advances of the Industrial Revolution drama. The aggregate productivity growth rate in an economy is the sum of productivity growth rates in each sector, weighted by the share of output in that sector in GDP. Thus
where gA is the overall productivity growth rate, θi is the share of each industry in GDP, and gAi is the productivity growth rate of each industry. If we calculate sectoral productivity growth rates on a value-added basis, then the weights θi will be value-added in each sector relative to GDP. If we calculate productivity growth rates treating intermediate inputs as factors of production in each industry, then the weights will be the ratio of gross output of each industry to GDP, and these weights will add to more than 1. Over the years 1760-1869 the average share of GDP produced in coal mining was only 1.6%. Thus the contribution of coal mining productivity growth to overall TFP growth in the Industrial Revolution era was 0.003% per year. Had there been no productivity growth in coal mining output in the economy in the 1860s would only have been 0.2% less than actually observed. In contrast cotton textiles alone contributed about 0.20% per year to productivity growth. Had the entire textile revolution never occurred output per capita would have been at least 23% lower in the 1860s.
Transport Improvements and Coal Consumption The major reason for the huge increase in consumption of coal per capita in England in the Industrial Revolution period seems to have been a combination of increased demands for coal from greater populations and higher incomes, increased demands following on improvements in iron smelting technology, reduced taxation of coal used for domestic purposes in cities like London, and declining real transport costs.