The last could be deemed endogenous, but a short-run profit function takes the number of machines as fixed. The remaining four instruments are a year indicator, the number of small mines (<10 men), the percent of miners illiterate, and the number of mining machines used. Another mine feature used is the thickness of the coal seam.

Drift, slope, and shaft describe the type of mine opening: horizontal, angled, and vertical. Mine geology seems an obvious source of exogenous instruments. Exact identification of the profit function requires eight instruments. In practice, the choice of instruments is a matter of judgment and available data. Ideally, the covariance between the instruments and the error term is zero, and the covariance between the instruments and the regressors is not zero. Alternately, an income elasticity of 1, often cited in the literature, yields an adjusted VSL of about $2,300, 000, still much below modern values.ġ3 Instrumental variables estimation is meant to correct potential OLS bias due to simultaneity, omitted variables, or measurement errors.

Substituting L* back into the profit equation yields the maximum profit function π*=π( P, w, K ¯, z, ρ) of equation (1).ġ1 The online consumer price index calculator at the BLS Web site is used.ġ2 Real GDP per capita has grown at about 2% per year since 1914, and Viscusi–Aldy estimate the income elasticity is 0.5 (36–42). Differentiating the profit equation with respect to w gives the profit-maximizing input demand (Hotelling’s lemma), L*= L( P, w, K ¯, z, ρ). The first-order conditions for L and ρ are ∂π/∂ L= P Thus, mine accidents affect production via Q and wages via w(ρ). ) is the output production function, L is labor, ρ is the accident rate, z environmental variables, and K ¯ is fixed capital.The hypothesis of homoscedastic residuals is not rejected the Breusch–Pagan chi-square test statistic is 9.7 versus a critical value of 14.07 (7 df, 0.95). Ohio coal production averaged 31 million tons in 1911–1912, rose to 36.2 million in 1913, and fell to 18 million in 1914 due to strikes it rose to 22.4 million in 1915 and 31.7 million in 1916.Ħ Accidental deaths were high in 1913 and lower in 19 because of reduced industry output (Ohio Statistics of Mines and Quarries 1916, 51).ħ 1916 accidents are omitted on the grounds they could not affect 1915 or 1916 wages.Ĩ A serious injury is defined as resulting in a loss of more than three weeks of work.ĩ This inference is independent of the assumed distribution of u. By 1914, the respective rates were 3.5 and 6.1 (Mines and Quarries of Ohio 1914, 49).ģ The US Coal Commission found only 25% of Ohio miners lived in company housing in 1922 versus almost 80% in West Virginia (1467).Ĥ Because there was little inflation between 19, all the data employed here are in nominal terms.ĥ Fishback’s (1992) data involves state-level observations covering 1912–1923 for 23 states, but omits 1915, 1916, and 1918. 1 The recommended solution was often German-style syndicates and cartels (Tryon 1921, 72) these are part of the intellectual roots of New Deal efforts to restrict the “evils” of competition.Ģ In 1895, average tons per day per miner were 3.4 tons in pick mines and 5.9 tons in machine mines.

Hedonic wage function