The Productivity Effects of Inanimate Power: Evidence from the Transition to Machine Labor

Tables Table 1: Block Links, Hand and Machine Labor Study Panel A: Hand Labor Block Link Number of Links Fraction Steam Fraction Water Fraction Mechanized 0.016 0.048 0.038 0.025 0.146 0.050 0.052 [0.051] 1:0 431 0.009 0.007 1:1 4,275 0.014 0.035 1:M, M > 1 897 0.029 0.009 N:M, N, M > 1 220 0.007 0.018 N:1, N> 1 385 0.008 0.139 Total 6,208 0.015 0.035 Total, 5,777 0.016 [0.014] 0.037 [0.037] Regression Sample Notes to Panel A: computed from digitized version of Hand and Machine Study, see text and (United States. Department of Labor. 1899). 1:0: hand labor operations that “disappeared” (have no counterpart) in the transition to machine labor. 1:1: a single hand labor operation is mapped to a single machine labor operation. 1:M, M> 1: a single hand labor operation is mapped to a block of M machine operations, M> 1. N:M: A block of N hand labor operations is mapped to a block of M machine labor operations, N and M > 1. N:1, N> 1: A block of N (>1) hand operations is mapped to a single machine labor operation. Regression sample excludes 1:0 observations by construction. Mechanized = 1 if operation used steam or water power or both. Fraction Steam, etc: is computed in two steps: (1) within each block, fraction of operations that use steam or water (2) overall fraction is equal weighted average across units. [ ] computed in two steps (1) time-weighted average across within the block (2) overall figure is equal weighted average across units Panel B: Machine Labor Block Links Number of Links Fraction Steam Fraction Water Fraction Mechanized 0.508 0.625 0.724 0.770 0.372 0.479 0.557 [0.555] 1:1 4,275 0.485 0.028 1:M, M> 1 897 0.621 0.037 N:M, N, M > 1 220 0.694 0.033 N:1, N> 1 385 0.738 0.034 0:1 4,240 0.363 0.012 Total 10,017 0.459 0.022 Total, 5,777 0.531 [0.529] 0.030 [0.030] Regression Sample Notes to Panel B: computed from digitized version of Hand and Machine Study, see text and (United States. Department of Labor. 1899). 1:0: hand labor operations that “disappeared” (have no counterpart) in the transition to machine labor. 1:1: a single hand labor operation is mapped to a single machine labor operation. 1:M: a single hand labor operation is mapped to a block of M machine operations. N:M: A block of N hand labor operations is mapped to a block of M machine labor operations, N and M both greater than 1. N:1: A block of N hand operations is mapped to a single machine labor operation. 0:1: new operations under machine labor. Regression sample excludes 0:1 observations by construction. Mechanized = 1 if operation used steam or water power or both. Fraction Steam, etc: is computed in two steps: (1) within each block, fraction of operations that use steam or water (2) overall fraction is equal weighted average across units. [ ] computed in two steps (1) time-weighted average across within the block (2) overall figure is equal weighted average across units Table 2: The Productivity Effects of Inanimate Power in the Transition from Hand to Machine Labor: OLS Estimates and Percent Explained Panel A: OLS Estimates, Productivity Effects of Inanimate Power Dependent Variable Ln (Time spent in hand labor block) ∆ Fraction Steam ∆ Fraction Water ∆ Ln (Time spent in block) ∆ Ln (Time spent in block) -1.04 (19.27) -0.35 (3.29) -0.38 (10.96) -0.76 (15.22) -0.22 (2.24) ∆ Ln (Time spent in block) ∆ Ln (Time spent in block) -0.38 (11.20) ∆ Fraction -0.99 -0.72 Mechanized (17.55) (14.93) Adjusted R2 0.500 0.597 0.500 0.594 Note: sample consists of 1:1, 1:M, N:1 and N:M block links for which there was complete information on the relevant variables (N = 5,747). See Table 1 for source information. ∆: difference between machine and hand labor. All regressions include product fixed effects and dummy variables for block type (the left out dummy is 1:1). Standard errors are clustered at the product level. Absolute values of t-statistics are shown in parentheses (Table 2 continued) Panel B: Percent Explained of ∆ Ln (Time) by ∆ Power Regression No Yes No Yes includes Ln (Time spent in hand labor block)? Mean Value of -1.90 1.90 -1.90 -1.90 Dependent Variable Mean Value of ∆ 0.52 0.52 Fraction Steam Mean Value of ∆ -0.007 -0.007 Fraction Water Mean Value ∆ 0.51 0.51 Fraction Mechanized Predicted Change -0.54 -0.39 -0.51 -0.37 in Mean Value of Dependent Variable Percent Explained 28.4% 20.7% 26.6% 19.5% (Predicted Change/Mean Value of Dependent Variable) x 100 percent Predicted change in mean value of dependent variable: computed by multiplying OLS coefficients of power use dummies (e.g. ∆ (Steam = 1) by mean value of change in power use (e.g. ∆ (Steam = 1). Example, column 1: -0.54 = (-1.04 x 0.52) + (- 0.35 x -0.007). Table 3: Instrumental Variable Regressions Dependent Variable ∆ Ln (Time spent in operation ∆ Ln (Time spent in operation block) block) Includes Ln (Time spent in hand operation block)? No First Stage Coefficient Mean Value of Instrument (Fraction MECHABLE) Yes 0.23 0.23 (11.27) (11.78) 0.62 0.62 -1.25 -1.18 (7.10) (8.06) 0.64 -0.60 2SLS: ∆ Fraction Mechanized Predicted Change in Dependent Variable Percent Explained 33.6% 31.7% Instrument variable (Fraction MECHABLE) is based on gerunds in the text description of the hand operation; see text. First stage coefficient: coefficient of instrument in a regression of ∆ (Mechanized = 1) with product and block link type fixed effects, column 2; or product and block type fixed effects and ln (Time spent in hand labor block), column 3. Standard errors clustered at unit level. Absolute t-statistics shown in parentheses. Percent Explained: predicted change in dependent variable using 2SLS coefficient and mean value of ∆ Percent Mechanized, divided by mean value of dependent variable; see Table 2, Panel B. Table 4: Robustness Checks Panel A: OLS Coefficients Robustness Check Include ln (time in hand block) on right hand side? Weighted, pooled sample 1:1 block links Sample Size (number of block links) OLS, ∆ Fraction Steam No OLS, ∆ Fraction Water No OLS, ∆ Fraction Steam Yes OLS, ∆ Fraction Water Yes 5,745 -0.99 (15.91) -1.12 (18.73) -0.75 (5.03) -1.07 (17.81) -0.36 (3.07) -0.35 (2.79) -0.41 (1.05) -0.35 (1.98) -0.74 (13.76) -0.84 (15.22) -0.64 (5.18) -0.79 (14.45) -0.22 (2.00) -0.27 (2.26) -0.18 (0.45) -0.24 (1.41 4,265 Non-1:1 block 1,482 links Pooled sample, 4,940 drop Watch/Clock units Weighted sample: observations are weighted by the number of underlying operations in the block link; for example, if the observation is a 1:M link, the weight is 1+ M. Watch/clock units are units 201-205. Panel B: IV Coefficients Robustness Check Include ln (time in hand block) Weighted, pooled sample 1:1 block links Non-1:1 block links Pooled sample, drop Watch/Clock unites 2SLS, ∆ Fraction Mechanized No Percent Explained -1.15 (4.72) -1.36 (8.26) -0.65 (1.01) -1.44 (10.18) 29.9% No 36.5% 17.0% 42.0% 2SLS, ∆ Fraction Mechanized Yes Percent Explained -1.11 (6.59) -1.17 (7.48) -0.95 (3.01) -1.26 (9.27) 28.7% Yes 31.4% 24.8% 36.8% Table 5: Census of Manufactures Estimates and Percent Explained Coefficient of Steam Dummy 0.242 (17.15)) Coefficient of Water Dummy 0.039 (2.13) Adjusted R-Square 0.248 ∆ Mean, 1850-1880 of: Ln (Real value added/worker) 0.244 Fraction Steam 0.373 Fraction Water -0.159 Predicted ∆ in ln (real value added/worker) 0.076 Percent Explained [ = (row 8/row 5) x 100 percent] 31.1% Rows 1, 2: coefficients from a regression analysis of ln (value added/worker) using the sample of establishments from the 1850-1880 censuses of manufacturing analyzed by Atack, Bateman, and Margo (2008). See text for discussion of regression specification. 1880 observations are reweighted to account for under-reporting in the original census; see Atack, Bateman, and Margo (2008). Nominal value added converted to real value added using the output price deflator in Atack, Bateman, and Margo (2008).