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Soft Coal, Hard ChoicesThe Economic Welfare of Bituminous Coal Miners, 1890-1930$

Price V. Fishback

Print publication date: 1992

Print ISBN-13: 9780195067255

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780195067255.001.0001

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(p.266) Appendix G Piece Rate Regressions for West Virginia Counties

(p.266) Appendix G Piece Rate Regressions for West Virginia Counties

Soft Coal, Hard Choices
Oxford University Press

Chapter 5 and Chapter 10 contain regressions that examine the relationships between piece rates, how tough it was to mine coal, and the location of blacks and immigrant workers. The regressions treat piece rate wages as a function of the price of coal at the mine, the effect of mine conditions on the workers’ productivity, the percentage of workers who were black, the percentage of workers who were southern European immigrants, and a random error term, which includes unmeasured factors not mentioned above.

The West Virginia Department of Mines reported information by county on each of the variables listed above. The basic equation is estimated for pick mining rates and for loading rates. The measure of the pick mining piece rates used is the average run-of-mine rate per long ton, in other words, the rate for 2240 pounds of coal before it was run over the screens.1 The West Virginia mining reports do not specify how the county averages were obtained. Since the statewide average reported is a simple average of the county information, the county averages are also probably simple averages of the wages at the mines. Pick mining became less important as the cutting machine technology spread and the job of loader, also known as machine miner, became the primary occupation in the coal industry. The Department of Mines also reported the piece rates paid to these workers, defined as run-of-mine rates per long ton of coal paid to machine miners.2 Regressions are estimated with both pick rates and machine mining rates as the dependent variable.

In general, the selling price of coal should be positively related to the piece rate paid in the county. It should reflect the demand conditions for the final product, which in turn help determine the demand for labor in coal mining. The measure used is the average selling price of a long ton of coal for each county as reported by the West Virginia Department of Mines. As with the wage rates, this average is probably an unweighted arithmetic average of the prices at the mines in the county.

To measure the effect of mine conditions on the productivity of miners, a measure of output per man day was developed. For pick miners, the pick-mined tonnage of coal per pick miner per day is used; for the loader, or machine miner, the measure is the amount of machine-mined coal per machine miner (loaders plus machine cutters) per day. These figures are rough estimates obtained by dividing the coal tonnage, pick-mined or machine-mined, by the number of pick miners or machine miners, respectively. These tonnage-per-man measures are then divided by the average days worked by the mines in the counties.3 The analytical framework implies that piece rates rise when the conditions in the mine worsen. The only problem with this measure is that it may capture differences in the productivity of the miners (p.267) themselves as well as differences in the natural conditions of the mines in the county. At this level of aggregation the average productivity of the miners probably did not differ much between counties. If it did, the better miners probably were concentrated in the counties offering better employment packages. With zero information costs, it is uncertain how this would bias the coefficient, because the better employment package might be in counties with high wages and worse conditions or in counties with low wages and better conditions. In this case, the variance in the coefficient would increase, but the coefficient would not be biased. With positive information costs, the wages would not have adjusted fully to differences in mine conditions; they would not rise as much for worse conditions nor would they fall as much for better conditions; therefore, employment packages would be better in counties with better conditions and lower wages, and the better miners would be concentrated in these counties. In this case the estimate of the coefficient for the mine conditions proxy would be less negative than the true coefficient.

An additional variable is added to the machine mining rate equation to adjust for differences in the machine miner’s tasks in the various mines. In some mines the machine miner drilled holes, blasted the coal, loaded it and did his own timbering of the roof and bailing of water. In these mines the only difference between the loader and the pick miner was that the pick miner made the cut at the base of the wall. In other mines the loader might specialize in only loading coal, as other workers, such as shotfirers and timbermen, performed the other tasks. The loader’s piece rate would be lower in these mines. The Department of Mines did not report the number of timbermen, shotfirers, and other workers in each occupation; it lumped them into a group labelled inside laborers. If the loader specialized, the number of inside laborers per loader in the mines should have increased. This figure is included in the regression and should be negatively related to the machine mining piece rate.4

The estimate used for the percent black for both the pick mining rate and the machine mining rate is the percentage of workers of known nationality inside the mine who were black. For southern Europeans a similar estimate is used; the division of immigrants into southern European and northern Europeans followed that used in Appendix E. The percent of inside workers is a reasonable proxy for the concentration of blacks and immigrants in these jobs, because both loader and pick mining jobs were open to all ethnic groups.5

Linear regressions for several years are estimated using weighted least squares. The number of workers in each county varied dramatically, creating problems with heteroskedasticity. (See the notes of Chapter 6 for further discussion of heteroskedasticity). The variance of the error terms is probably inversely correlated with the number of workers in the county. The pick mining regression is weighted by the square root of the number of pick miners. Several years are selected to test the robustness of the results under a variety of market conditions, including 1907, 1910, 1914, 1915, 1918, and 1923. Piece rates in 1907–10 were close to the average rates for the early 1900s. The average pick rate in the state reached a minor peak in 1907, was slightly lower in 1910, and reached another minor peak in 1914. The wage dipped to a minor trough in 1915. The years 1918 and 1923 were chosen to represent the run-up in wages during World War I and the period afterward, when the wage had leveled off at the high peak. A future consideration is to check the wages in later periods, when coal demand has declined and black employment had become more concentrated in southern West Virginia again.

The coefficients reported in Tables G-1 and G-2 for the output per man-hour variable are the bases for the elasticities reported in Table 5–1. As discussed in Chapter 5, nearly all the coefficients are negative as expected, and roughly half of them were statistically significant. In most cases the coal price had the expected effect on piece rates. The coefficient was usually positive, although statistically significant in only five of the twelve regressions.


Table G-1. West Virginia Pick Mining Piece Rate Regressions, 1907–23 (Dependent Variable = Pick-Mining Piece Rate, per 2240 lb. ton)





















Coal Price













Pick Mining Output per Pick







  Miner per Day







Percent Black













Percent Southern European













Number of Observations







Source: West Virginia Department of Mines, Report, 1907, 1910, 1914, 1915, 1918, 1923. See also notes to Appendix. G.

Notes: The weight is the square root of the number of pick miners. Student,’ t-statistics are in parentheses.

Coal counties with missing values which were center out of regression: 1907, Gilmer, Lewis. 1910, Lewis, Clay, Lincoln, Logan, Brooke, Hancock, Marshall, Ohio. 1914, Gilmer, Putnam, Wayne, Lincoln. 1915, Gilmer, Greenbrier, Lincoln, Mason, Putnam, Wayne, Lewis, Logan, Boone, Upshur. 1918, Wetzel, Webster. 1923, Summers.

* Statistically significant at the 90 percent level in a two-tailed t-test.

Blacks were apparently concentrated in counties with low pick rates, but not in counties with low machine rates. The sign of the coefficient of the black variable is negative in all six of the pick mining rate regressions. In four of the years the coefficient was negative and significant. The lack of significance in the other two equations may be a statistical artifact, but it is interesting to note the years in which the coefficient is not significant in these regressions. Black employment in the southern counties, except McDowell County, declined during 1915, just prior to the surge in coal demand. It increased rapidly during World War I as piece rates and coal prices increased to their peak in 1918. These changes would appear to be consistent with expanding opportunities for blacks during World War I. According to the regressions, by 1923 they were once again concentrated in low wage regions, despite geographical expansion of employment within West Virginia. A heartening fact for blacks was that they were not concentrated in counties where machine mining rates were low. Although the coefficients of the black variable are negative in five of the six machine mining rate regressions, only the one for 1918 is significant at the 90 percent level. If this result is not a statistical artifact, the black,’ relative wage status was continually improving as the new machine cutting technology spread within the fields. Blacks were not cut off from entering these machine mines. The correlation between the percent black and the ratio of pick miners to machine miners in southern West Virginia mines is only about 0.28 for 1910 and 0.25 for 1913.6 Southern Europeans do not appear to have been located in low piece rate counties in West Virginia. The coefficents of the southern European variable are negative in five of the six regressions, but in only two is the coefficent significantly negative. In the machine mining rate regressions, the coefficents are positive in four of the regressions, and one of them is significant at the 90 percent level.


Table G-2. West Virginia Loader Piece Rate Regressions, 1907–23 (Dependent Variable = Loader Piece Rate, per 2240 lb. ton)





















Coal Price













Machine Mining Output per







  Loader and Machine Cutter per Day







Percent Black













Percent Southern European













Laborers per Loader













Number of Observations







Source: West Virginia Department of Mines, Report, 1907, 1910, 1914, 1915, 1918, 1923. See also notes to Appendix G.

Notes: The weight is the square root of the number of loaders. Student,’ t-statistics are in parentheses.

Coal counties with missing values which were center out of each regression: 1907, Hancock, Ohio, Gilmer, Lewis, Upshur, Mineral, Randolph, Braxton, Putnam, Greenbrier, Wayne. 1910, Brooke, Hancock, Braxton, Putnam, Greenbrier, Wayne, Logan, Clay, Lewis. 1914, Greenbrier, Lewis, Putnam, Wayne, Wyoming, Gilmer, Lincoln. 1915, Greenbrier, Lewis, Putnam, Wayne, Wyoming, Lincoln, Logan, Boone, Mason, Tucker, Upshur. 1918, Braxton, Greenbrier, Lewis, Putnam, Summers, Wayne, Webster, Wetzel. 1923, Lincoln, Summers, Webster.

* Statistically significant at the 90 percent level in a two-tailed t-test.


(1) . Several different rates were given for McDowell and Fayette Counties for three years: 1907, 1910, and 1914. I chose the rates that represented the largest percentage of types of coal produced in the area. For McDowell County, the Pocahontas No. 3 and No. 4 wage was used; for Fayette, the Kanawha River Series. After 1914 a single rate was reported for each county.

(2) . The pick mining rates and the average coal price appear in the table titled “Wages Paid and Selling Price of Coal and Coke?” and the loading rates in the table “Summary of Wages Paid Machine Miners, Runners, and Helpers,” in the West Virginia Department of Mines, Report, 1907, 1910, 1914, 1915, 1918, and 1923.

(3) . The total tonnage figures are from the table entitled “A Comparative Statement of the Pick and Machine Mined Coal, by Counties.” The number of pick miners, machine miners, and average days worked are from the table “Detail of Men Employed at the Mines and Ovens,” in the West Virginia Department of Mines, Report.

(4) . There is one problem with this measure. The number of inside laborers should also increase as the size of the mine expands. In the pure machine mine this should create few problems, but in a mine with a large group of pick miners, the number of inside laborers may (p.270) rise even when the loader does all the tasks. This variable will understate the task performed by the loader in these mines and therefore where pick mining is prevalent. Therefore, it will overstate the actual number of specialized workers performing tasks like shotfiring and timbering in the rooms.

(5) . The information on the number of workers of different ethnicities is from tables titled “Nationalities of Mine Employees,” in the West Virginia Department of Mines, Report, various years.

(6) . The correlation is from information on 353 mines in 1910 and 443 mines in 1913 in southern West Virginia counties. For each mine the West Virginia Department of Mines reported the ethnic breakdown and the number of pick miners and machine miners, but wage and price information was not reported by mine.