Popular observers often place the adoption of inanimate power, especially steam power, at the heart of the first Industrial Revolution. Noting the “sudden, sharp, and sustained jump in human progress” after 1780, Brynjolfsson and McAfee (Reference Brynjolfsson and McAfee2014, p. 6) in their influential book on the future of work assert that “steam started it all” by overcoming “the limitations of muscle power, human and animal.” They further declare that the Watt steam engine was the “most important” technological development of the era. They are hardly alone in treating the steam engine as the prime mover of industrialization (see, e.g., Rosenberg and Trajtenberg Reference Rosenberg and Trajtenberg2004), but economic historians are generally more cautious recognizing, for example, the earlier development of waterpower and the potential importance of scale economies and related organizational changes (Chandler Reference Chandler1977; Hilt Reference Hilt, William and Robert2015; Hunter Reference Hunter1979, Reference Hunter1985; Hunter and Bryant Reference Hunter and Bryant1991). The analysis in this paper provides quantitative support for our profession’s wariness of monocausal narratives of complex historical events such as industrialization while providing fresh evidence on the productivity impact of mechanization across a wide swath of manufacturing. In this paper, we will equate “mechanization” in nineteenth-century manufacturing with the use of steam or water-powered machinery.Footnote
^{1}

To conduct this investigation into the relative importance of mechanization, we analyze the remarkably detailed data in the U.S. Commissioner of Labor’s 13^{th} Annual Report (United States, Department of Labor 1899) on *Hand and Machine Labor* (hereafter HML study). This report was commissioned by the U.S. Congress in 1894 to “investigate and report upon the effect of the use of machinery upon … the relative productive power of hand and machine labor” (United States, Congress 1894). To this end, it recorded all individual tasks from start to finish associated with the production of over 620 highly specific manufactured goods using “machine methods” in the late nineteenth century, along with those involved in the production of the same good by the traditional “hand methods.” The observations were paired with the production method, and the HML staff generated a crosswalk for the operations listed for hand and machine labor. It is a subset of these (*n* = 4,405), which are analyzed in this paper. The extraordinarily complex structure of the HML study overwhelmed statisticians at the time, preventing the computation of even summary productivity figures, let alone any kind of systematic analysis. Nor did the Cliometrics Revolution solve the challenges posed by the HML data until recent advances in computing and econometrics have allowed the analyses that Carroll Davidson Wright (the Commissioner of Labor), his team of agents, and prior generations of scholars were unable to deliver.

We employ a “task-based,” or production operations approach to investigate the reductions in time devoted to specific production activities (Acemoglu and Restrepo Reference Acemoglu and Restrepo2018). This was the HML study’s measure of labor productivity. Our main regression analysis of the HML operations data uses ordinary least squares (OLS) with fixed effects for the specific individual goods (called “units” in the HML study).Footnote
^{2}
We find that (1) the more frequent use of inanimate power in factory production had significant positive effects on labor productivity but that (2) these effects accounted for just one-third of the average difference in production operation times between hand and machine labor. Further probing using an instrumental variables estimator suggests that this OLS effect of mechanization is likely biased upwards compared with the true causal impact. We then conduct a broader, if less exacting, study of the roles of other factors measured in the HML study, including the division of labor and the adoption of high-volume or “quantity” production. We find that these additional factors are of roughly similar importance in accounting for the average difference in productivity between hand and machine labor. Because the HML study focused on what it called the “most modern” of machine labor, the average difference in productivity in the sample may overstate the true difference in the economy. However, there is no reason to believe that the relative explanatory power of mechanization is misstated, and the superior quality of the HML data makes our findings more convincing than the usual growth accounting studies of aggregate time series or conventional production function estimation.

## THE HAND AND MACHINE LABOR STUDY

Published in two volumes totaling almost 1,600 pages, the HML study detailed the tasks (including what and how) involved in the production of what the study termed “units.” These units were specific quantities of precisely defined goods such as “50 dozen regular taper, triangular saw files, 4 inches long, tapering 23/64 inch” (United States, Department of Labor 1899, 1: 241–6 and 2: 1026–9). The report covered 672 units in various economic sectors, including transportation services, mining and quarrying, and agriculture. Ninety-three percent of the units—626 (units 28–653) of 672—were manufactures. Although the products in the study embrace almost the entire range of broadly defined manufactured goods (2-digit SIC codes 20–39), including those in the first industrial revolution as well as the second, in no sense can it be claimed that they are a representative sample of manufacturing at the time (see Online Appendix Table 1).

*Notes*: Block links are defined as follows—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; H:1, H > 1: A block of H (>1) hand operations is mapped to a single machine labor operation; H:M: A block of H hand labor operations is mapped to a block of M machine labor operations, H and M > 1. *Mechanized* = 1 if machine block used steam or waterpower or both; see text. NA: not applicable. Figures in brackets are geometric means of *∆ ln T* (e.g., 0.172 = exp (–1.761) for the regression sample in the final row).

*Sources*: Computed from digitized HML study (United States, Department of Labor 1899, 2). See Atack, Margo, and Rhode (2022).

For each unit, the HML staff collected production data from multiple establishments that were using “hand labor” or “machine labor.”Footnote
^{3}
To preserve the confidentiality of respondents, the HML staff anonymized the information in the published report. We never know the names of the establishments and, except in a few instances, do not know their location other than that 15 of the hand labor establishments were foreign.Footnote
^{4}
The HML staff was aware of the widely held belief that the machine methods yielded a lower quality product than the hand methods, and they expended great efforts to find units producing factory goods that were not of inferior quality to artisan products. Based on textual comments regarding quality in the report, the Bureau was remarkably successful in keeping with the goal of the study.Footnote
^{5}

In collecting data, the HML staff took the actual output of the establishment as a given. However, because the machine labor output almost always exceeded that of hand labor, the staff scaled all production times to match a standardized output level. This normalization varied across units but in a manner that would be “recognized and commonly used in the trade” (United States, Department of Labor 1899, 1: 15).Footnote
^{6}
Virtually all machine production data were contemporaneous with the report. For hand production, however, the HML staff found contemporaneous matching observations from the 1890s for only a quarter of the units. For the remainder, the staff assiduously sought out historical records, one of which was as early as 1813.Footnote
^{7}

The central goal of the HML study was to measure differences in production times for specific operations, and for each unit overall, between the “most modern machine method[s]” compared with the “old fashioned hand process … in vogue before the general use of automatic or power machines” (United States, Department of Labor 1899, 1: 11). The HML staff had no trouble finding machine establishments such that all units in the machine method used inanimate power at some point in production. Perhaps more surprisingly, the staff came fairly close to achieving its goal for hand production “before the general use of … power machines” because only a small fraction of hand operations involved the use of inanimate power, mostly by waterpower. We have excluded all units in which any operation in the “hand method” used inanimate power to approximate the Bureau’s ideal comparison. This reduces the sample size from the 626 manufacturing units in the published report to 551, which we call our base sample.

Our regression analysis uses a subset of “paired” production operations from this base sample where the HML staff was able to match operations between hand and machine labor and reported the time taken to complete each. This complex matching procedure, which involves the “HML crosswalk,” is discussed later. Figure 1 displays a histogram of the unit-level mean values of the dependent variable used in the regression analysis. This variable is *∆ ln T,* the log difference between hand and machine in the time to complete the matched production operations. The overall mean value across all units is shown by the dark line, –1.761. The associated geometric mean, 0.172 [= exp (–1.761)], implies that, on average, it took just 17.2 percent of the labor time to complete operations producing the same intermediate product using machine labor methods that it took using hand labor—an almost 6-fold productivity gain. We emphasize that these are the total labor times of all workers involved in the operation (or “block link” as discussed momentarily in the text); that is, the total labor input of that step in production. Because the HML study holds “output” fixed (literally), the geometric mean (or, equivalent, *∆ ln T*) is an exact index number of the inverse of labor productivity.Footnote
^{8}
The overwhelming majority of the differences are negative, indicating that machine labor almost always took less time than hand labor. The support of the distribution is very large, suggesting a degree of variation across units that are unlikely to be explained by any single factor.

By the early twentieth century, the vast majority of value-added in manufacturing was produced in mechanized establishments, whereas to a first approximation, almost none was at the start of the nineteenth century.Footnote
^{9}
To reach a mean (ln) gap in production operation times of the size (–1.761) shown in Figure 1, labor productivity in U.S. manufacturing would have to have grown steadily at about 1.8 percent per year over the entire nineteenth century. A back-of-the-envelope estimate of the actual growth rate is 1.5 per year, which suggests that the machine labor establishments surveyed by the HML staff were somewhat more productive than the average such establishment in the late nineteenth century, consistent with the study’s goal.Footnote
^{10}

The HML study provided a cornucopia of anecdotal examples of machine labor operations that were sped up through the use of powered machinery but also many examples of operations that were not mechanized. “The term ‘machine’,” Wright acknowledged, “as applied to a method of production, does not imply that every operation … is performed by machine. On the contrary, it is often found that … work [by] …. hand is necessary in certain operations … even under the most modern machine methods.” He also conceded that machine labor differed from hand labor in other ways, most notably in its embrace of a far more intricate division of labor in which “every workman has his particular work to perform, generally but a very small portion of that which goes to the completion of the article” (United States, Department of Labor 1899, 1: 11).Footnote
^{11}
Hence, in addition to quantifying the overall difference in productivity, Wright hoped to pin down the extent of mechanization of machine labor as well as the proportion of the difference in productivity that could be attributed to operations that were mechanized under machine labor.

Wright knew, however, that he and his staff lacked the mathematical tools to do any of these computations. “This report,” Wright lamented, “answers in a measure the many demands for information … but no aggregation can be made because it is impossible to carry out calculations through the innumerable ramifications of production under hand and machine methods … although such a summary would be of the greatest possible value in the study of the question” (Wright Reference Wright1900, p. 211).

### The HML Crosswalk, “Blocks,” and “Block-Links”

The tables in Volume One of the HML study summarize the data in terms of industry categories and product descriptions, the actual and standardized outputs, the reference year, the number of operations, the number of different workers employed in producing the good, total hours worked, total labor costs, and daily hours at the unit level. Volume Two then breaks down the hand and machine production data to the operation level, providing a brief description of operations in the order in which they were performed; a list of tools or machines used; the type of motive power; the number of workers assigned to that operation; some information on the worker characteristics; the time spent on the task; and the labor cost of each employee engaged in the operation along with any miscellaneous comments.Footnote
^{12}

These data lie at the heart of our analysis in this paper. Consider, for example, data on the production of 14-tooth steel garden rakes by machine labor (see Unit #30, United States, Department of Labor 1899, 2: 480) was originally gathered from a plant that produced a batch of 300 rakes through 16 distinct operations done by 6 adult males, but the data were normalized to the production of a dozen rakes by dividing the actual time spent on each operation by 25 (=300/12). The first, operation #1, was “cutting iron into sizes” using shears and waterpower by a 40-year-old who was paid $3.00 per day would have taken 2 minutes and 24 seconds to yield the pieces to make a dozen rakes. The last, operation #16, was “inspecting rakes and overseeing the establishment” done without any tools or assistance, again, by a 40-year-old male, paid $3.00 a day taking the operative a total of 24 minutes. The HML staff assigned consecutive numbers to each of these (1–16) machine labor operations in the “Operation Number” column.

The HML staff then followed the same protocol for recording the hand labor data, once again arranging the data in the order in which it was performed. This order was not necessarily the same as that in machine production. The information in the Operation Number column, however, now consisted of letters, numbers, or combinations thereof; each with a distinct interpretation, but a number always referred to the analogous operation in machine production. These assignments were made by the HML staff based on their detailed knowledge and observation and provided a crosswalk between the hand and machine operations within units.

This HML crosswalk is the key to our empirical analysis of the operations-level data. To understand how we use the crosswalk, it is helpful to employ the concepts of an operation “block” and an operation “block link.” An operation block is a collection of underlying operations of size H (for hand labor) or M (for machine labor), and H and M are non-negative integers. A block link is a mapping, designated H:M, between the hand (H) and machine (M) blocks. The HML crosswalk provides the information to link together the specific machine and hand operations required to perform what Wright termed the “equivalent” work to make the product. Some hand operations could not be matched by the HML staff to any machine operations because the operations were no longer performed under machine labor—1:0 block links. Analogously, some machine blocks could not be matched to any hand blocks because the machine operations were not performed under hand labor—0:1 block links. For all other block links, H and M can take any integer value equal to or greater than one.

Table 1 shows the distribution of the block links in the regression sample that we use, along with some key sample statistics. There are no 0:1 or 1:0 block links in the regression sample because the former represented hand operations that were no longer performed under machine labor, and the latter represented novel machine operations that were not performed under hand labor.Footnote
^{13}
The block links that are relevant for our regression analysis are those that overlapped between the two methods—1:1, 1:M, H:1, and H:M—as these are the operations that were matched by the HML crosswalk. By the HML’s construction, the intermediate output of these block-links was the same under both hand and machine labor and is therefore held fixed in the productivity comparison. We report the mean fractions using steam, water, or mechanized (that is, using steam and/or water) for each block link type under machine labor. These are “one-touch” or extensive margin estimates—that is, if any activity within the machine block used inanimate power, we code the block link as “mechanized.”Footnote
^{14}

All told, there are 4,405 block links in the regression sample. Table 1 shows the distribution by block link type and select sample statistics. Approximately 78 percent of these were singleton tasks under hand labor that the HML staff matched up to singleton tasks under machine labor (1:1 block links), slightly less than half (48.4 percent) of which were mechanized under machine labor. The remaining quarter of the regression sample block links was more complex, reflecting operations in which some task reorganization took place under machine labor compared with hand labor (1:M, H:1, or H:M block links). Three-quarters (*n* = 743) of the more complex block links (*n* = 993) were 1:M or H:M, in which one or more hand operations were mapped into M machine operations. Overall, these were the most mechanized (79.9 percent) block links.Footnote
^{15}

Although less common than 1:M or H:M block links, the H:1 links were also highly mechanized (74 percent). All told, about 55 percent of the block links in the regression sample were mechanized under machine labor. The final column of Table 1 shows the mean values of *∆ ln T* by block link type and overall (also shown in Figure 1). As previously discussed, *∆ ln T* is the log difference between hand and machine labor in the time to complete the operation represented by the block link, and it is the dependent variable in our regression analysis. The associated geometric means by block-link type are shown in brackets.Footnote
^{16}

Given that not much more than half of the machine labor block links were mechanized, if mechanization is to “account for” (see below) a large fraction of the mean (ln) productivity gap in the regression sample, then the direct impact of mechanization on productivity must necessarily be relatively large or the productivity differences for non-mechanized operations relatively small. The implications of this are addressed next through our empirical analysis of productivity differences at the operation level.

## PRODUCTIVITY DIFFERENCES AT THE OPERATION BLOCK LEVEL: THE ROLE OF MECHANIZATION

In this section, we perform regression analyses of *∆ ln T* using the sample of 4,405 block links that are matched between hand and machine labor through the HML crosswalk. We seek to measure the mean differential in the labor productivity gain between the mechanized (inanimately powered) and non-mechanized operations within the same production units. We present OLS estimates first followed by an instrumental variable analysis. The discussion in the text focuses on our base specification (Equation (1)).Footnote
^{17}

### OLS Estimation

The regression specification is given by Equation (1):

The index *j* refers to the unit and *a* to the block link. The *β*(*j*) are unit fixed effects. We include these because the manufactured goods represented by the units were very different (such as circular saw blades vs. shoes) and there is no reason to believe that machine labor would be equally good at improving productivity across all manufactures, controlling for the extent of mechanization. Equally important, the *β*(*j*)*’s* control for any unit-level differences between the hand and machine labor establishments that were the same for all block links within the unit, such as the total number of workers in machine vs. hand labor, the year(s) to which the data pertain, and so on. As the unit fixed effects soak up all unit-level differences, we cannot include any unit-level differences in Equation (1).Footnote
^{18}
Because of the complexities potentially introduced by multi-operation grouped tasks, which involve about a quarter of the blocks, our base specification also includes dummy variables for the block link types, *γ*(*a*).Footnote
^{19}
In Table 2, we report the value of the coefficient *λ* for the single mechanization variable, *Mechanized*, which is the “one-touch” measure of mechanization of a machine labor block introduced in the previous section. While *Mechanized* = 1 means that either steam or waterpower was used somewhere in the block, the overwhelming majority used steam. The reason for the single mechanization variable will become clear shortly. The OLS estimate of *λ* is identified through the variation in *Mechanized* across block links within units. The fundamental premise of the HML study was that mechanization sped up production times, implying that *λ* should be negative.

*Notes*: The decomposition (“Percent Explained of Mean Value of *∆ Ln T*”) is computed by multiplying the regression coefficient of *Mechanized* (–1.037) by the mean value of *Mechanized* (0.552) and dividing the product (–0.572) by the mean value of *∆ ln T* (–1.761) = (–1.037 x 0.552)/(–1.761) = 0.325, or 32.5 percent. The sample size for the regression is 4,405 block links. The regression also includes dummy variables for block link types and for units (see the text). Standard errors are clustered at the unit level. Sample means are from Table 1.

*Sources*: See Table 1; also Atack, Margo, and Rhode (2022).

Equation (1) provides the basis for a decomposition exercise *via* regression, familiar in modern economics (if not to Carroll Wright or his staff), which we perform in Table 2. The expected value of the dependent variable, E(*∆ ln T*), equals a baseline effect that depends on the coefficient of the unit dummy and that of the relevant block link type, plus a uniform effect (*λ*) for block links that were mechanized. Specifically, *λ* measures the average difference in (ln) labor productivity between mechanized and non-mechanized operations, controlling for the unit fixed effects and block link dummies. The average difference in productivity reflects gains in technological efficiency (total factor productivity) and in capital per worker (“more” capital was embodied in the steam engine and other machines than in hand tools), but the regression does not tell us how much of the increase is due to efficiency versus higher capital intensity.Footnote
^{20}

Table 2 shows the OLS estimate of *λ*, –1.037, which is precisely estimated (s.e. = 0.060). Taking the exponent of *λ*, subtracting from one, and multiplying by 100 percent computes the (approximate) additional percentage reduction in production time above baseline from mechanization—65 percent [= (1– (exp (–1.037))) x 100 percent]. This is a substantial and statistically significant gain in average labor productivity—clearly, mechanization mattered. The table also shows the percent of the mean productivity gap accounted for (“explained”) by mechanization, which is the estimate of *λ* multiplied by the mean value of *Mechanized*, divided by the mean value of *∆ ln T*. The percent explained is 32.5 percent [= ((–1.037 x 0.552)/–1.761) x 100 percent], or about one-third. By construction, the remaining gap (67.5 percent) is accounted for collectively by the coefficients of the unit level and block link dummies.Footnote
^{21}

### Instrumental Variables Estimation

Up to this point, we imagine that Carroll Wright would be both pleased and puzzled by our results. Pleased—because we have been able to compute the average difference in production times between hand and machine labor in the HML data, a calculation that he wanted to make but which eluded him and his staff. Moreover, this average difference is large, consistent with the study’s professed aim and what Wright expected. But also puzzled—because Wright surely would believe that mechanization should account for a larger portion of the mean productivity gap than it evidently did. As we noted, Wright acknowledged that many machine labor operations were performed by hand, but he thought that “in the main” these were “simple and unimportant” (United States, Department of Labor 1899, 1: 11). Clearly, this was not the case.

However, before pressing forward to investigate what else besides mechanization might have mattered, it is worth pausing to ask if the OLS estimate of *λ* is affected by endogeneity bias. The HML study was observational; the staff did not randomly assign steam power to machine labor operations—they would not have known what this meant. Someone, presumably an owner or manager, made the decision to mechanize (or not) the operations in the survey’s machine labor establishments.

One standard source of OLS bias, measurement error in the independent variable of interest, *Mechanized*, is almost certainly not present due to our use of the “one-touch” measure and the exceptionally careful data collection by the HML staff.Footnote
^{22}
Omitted variables are a second source of bias; however, we believe that the most likely omitted variables, those of worker characteristics, are unlikely to be a major problem in the study.Footnote
^{23}
However, a third source, reverse causality, cannot be readily dismissed.

In our view, the most likely source of reverse causality would create a negative correlation between *Mechanized* and the error term, *ε*. This would happen if the owner and/or manager of the machine labor establishment were more likely to mechanize an operation if the expected time savings were large and the expected time savings were positively correlated with *ε*.Footnote
^{24}
In this case, the OLS estimate of *λ* would be biased upwards in absolute value, thus overstating the casual impact of mechanization.

To address reverse causality, we need an instrumental variable (IV) for *Mechanized* at the block link level, a difficult problem. Our identification strategy makes use of certain information in the textual descriptions of production operations. These descriptions, which are very brief, appear in the “General Table – Production by Hand and Machine Methods” in the column titled “Work Done,” organized by unit number and production method in Volume Two of the HML study.

Specifically, we extracted all unique occurrences of gerunds appearing in the “Work Done” columns.Footnote
^{25}
In general, the first word in the description of work is almost always a gerund, which describes the principal action taking place in the operation, so we call this the “principal gerund.”Footnote
^{26}

To understand the conceptual basis for our gerund IV, it is useful to step back and view the problem through the lens of Acemoglu and Restrepo’s (2018) model of automation. In their model, production activities are arrayed on the unit interval in order of labor’s comparative advantage over capital (automation) in performing them. Initially, technology is primitive, and it is impossible to automate any production activities. Over time, however, scientific and engineering knowledge advances and it becomes technologically feasible to automate a subset of activities, starting from the left bracket of the unit interval to some point in it, T*. The activities that, in fact, are automated, [0, T], T < T*, depend on the relative cost of labor and capital. The Acemoglu–Restrepo model provides an important clue to making progress on our identification problem—if a historical indicator of T* can be constructed that varies exogenously across production operations, this becomes a candidate instrumental variable.

To implement this approach, a member of our research term with expertise in the history of technology was given just the list of gerunds and asked to sort them into two bins without consulting the HML study.Footnote
^{27}
Based solely on the expert’s knowledge of the history, activities described by the gerunds where the expert believed there was some technical feasibility of mechanization worldwide by the end of the nineteenth century were sorted into one bin (bin #1), while those for which there was very little or none were sorted into the other (bin #0). Once the sorting was completed, we used the results for the principal gerunds in the hand blocks in the regression sample to construct the IV.

Table 3 shows the distribution of the five most common principal gerunds for the hand blocks in the 1:1 and 1:M block links in the regression sample, grouped by bin #0 (little or no technical feasibility of mechanization) versus bin #1 (some technical feasibility). The five most common activities judged to have little or no feasibility of mechanization were “making,” “putting,” “overseeing,” “finishing,” and “marking.” For each, human judgment played a substantial role, and the requirements of the activity were idiosyncratic. Conversely, the five most common activities judged to have some feasibility of mechanization were “cutting,” “sewing,” “smoothing,” “stitching,” and “conveying.” These are all activities for which the activity was repetitive and for which special-purpose machinery was invented, often early in the nineteenth century.Footnote
^{28}

*Notes*: The table shows the distribution of the five most common principal gerunds classified into bin #1 (some feasibility of mechanization) versus bin #0 (little or no feasibility of mechanization) for the 1:1 and 1:M block links in the regression sample. Block-links with missing values for the principal gerund are coded into Bin #0.

*Sources*: See Table 1; also Atack, Margo, and Rhode (2022).

For the 1:1 and 1:M block links, there is a one-to-one mapping from the two bins to our IV, which is the “one-touch” analog to *Mechanized*, *MECHABLE* = 1 if principal gerund was sorted into bin #1, or 0 (if sorted into bin #0). For the H:1 and H:M block links, there is an intermediate step in the construction of the IV because when H > 1, there may be more than one principal gerund.Footnote
^{29}
*MECHABLE*, in other words, is our measure of T*, representing exogenous shifts in the likelihood of mechanization. Note that, because we have one instrument, we can only have one endogenous variable (*Mechanized*).

For the exclusion restriction to hold, it must the case that *MECHABLE* affects productivity solely by exogenously shifting the likelihood of use of inanimate power, as required by the Acemoglu and Restrepo framework. This would be violated, for example, if the expert used additional information about the unit to classify the gerund into bins but, as noted earlier, only the list of gerunds was used. The exclusion restriction might also be violated if *MECHABLE* affected unmeasured worker characteristics directly; however, as previously noted, we believe there is little evidence of omitted variables bias of this type.Footnote
^{30}

Table 4 shows the results for the IV estimation of Equation (1). The first stage coefficient of *MECHABLE*, 0.316 (s.e. = 0.020), is positive (as it should be) and the associated Kleibergen–Paap F-statistic (240.7) indicates that the instrument is very strong (p-value = 0.00001).Footnote
^{31}
The 2SLS estimate of *λ*, –0.749, is negative and significant (s.e. = 0.165) but about 28 percent smaller in magnitude than the OLS estimate, consistent with the presence of upward OLS bias due to reverse causality.Footnote
^{32}
If we repeat the decomposition exercise using the 2SLS estimate, the percent explained by mechanization is about 24 percent, compared with 33 percent for OLS.

*Notes*: The decomposition (“Percent Explained of Mean Value of ∆ *Ln T*”) is computed by multiplying the 2SLS regression coefficient of *Mechanized* (–0.749) by the mean value of *Mechanized* (0.552) and dividing the product (–0.413) by the mean value of ∆ *ln T* (–1.761) = (–0.413)/(–1.761) = 0.235, or 23.5 percent. The sample size is 4,405 block links. The first stage and 2SLS regressions also includes dummy variables for block link types and for units (see the text). The Kleibergen-Paap F-statistic refers to the instrumental variable *MECHABLE.* Standard errors are clustered at the unit level. Sample means of *∆ ln T* and *Mechanized* are from Table 1.

*Sources*: See the text and Table 1. Also Atack, Margo, and Rhode (2022).

Like all such instrumental variable estimates, ours is a local average treatment effect (LATE) which, theoretically, could be smaller in magnitude than the population average treatment effect (ATE). This does not seem likely to us, however, given the aims of the HML study, which sought to characterize the behavior of the “most advanced” machine labor establishments.

## PRODUCTIVITY DIFFERENCES: THE ROLE OF DIVISION OF LABOR, QUANTITY PRODUCTION, AND OTHER FACTORS

In answering the questions posed by Carroll Wright, our analysis of the HML data has uncovered a curious and unexpected puzzle. While mechanization clearly raised productivity at the production operation level, most of the superior productivity of machine labor on average cannot be explained directly by the greater mechanization of machine labor. But, if that is the case, what accounts for the unexplained portion, particularly that captured by the unit fixed effects?

The published study grouped the units in Volume One by broad product categories. However, the HML product descriptions were very detailed, often to the point where the separately reported units were producing goods that were literally the same (such as “Vicuna worsted single-breasted vests, notched collars, breast measure 37 inches, length 26 inches” by Units 214 and 215 (United States, Department of Labor 1899, 1: 38)) or very similar. Using these detailed descriptions of the goods produced, we found that we could map the HML units into 70+ four-digit SIC codes. These allow us to estimate Equation (2), which is a slightly more parsimonious version of our base specification, where the SIC codes substitute for the unit fixed effects:

The *η*(*s*) are coefficients of the 4-digit SIC fixed effects. Because Equation (2) does not include unit fixed effects, we can add differences between machine and hand labor in continuous or dummy variables, ∆ *X*(*j*), at the unit level—for example, measures of the division of labor or scale. However, because the unit variables of interest are not available for all units in the original regression sample, the sample size for Equation (2), about 3,900 block links, is smaller than the sample size in Table 1.Footnote
^{33}
Coefficients of the unit-level variables are identified by variation across units within the 4-digit SIC codes.

OLS estimates of *λ* and *δ* and the associated percent explained calculations are shown in Table 5. It is highly reassuring that the point estimate of *λ*, –1.072, is the same to the third decimal point as that obtained using the Equation (1) specification with the Table 5 sample, indicating that the combination of the 4-digit SIC dummies and particular unit-level variables shown in Table 3 does almost as well as capturing the salient variation in the data.Footnote
^{34}

*Notes*: Sample size is 3,876 block links because of missing data on some unit-level variables (see text). Mean value of ∆ *ln T* for this sample is –1.713. Regression includes 4-digit SIC code dummies and block link dummies (coefficients not reported). Coefficient of *Mechanized* = –1.072 (s.e. = 0.064) if Equation (1) specification is estimated instead. *Frac_oper* is the fraction of operations in the unit performed by the average worker. *Volume production* = 1 if actual quantity >1,500; 0 otherwise. All unit variables enter the regression as differences (∆) between the machine unit and hand unit values, except *Hand quality better* = 1 if HML staff judged the hand labor unit to be of better quality than the machine labor unit. Standard errors are clustered at the unit level.

*Source*: See Table 1; also Atack, Margo and Rhode (2022).

Three “returns to scale” variables are included in the regression—two measures of the division of labor, and a “quantity production” dummy.Footnote
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We know that Wright considered a high degree of division of labor to be an essential feature of machine labor methods. Indeed, as we previously pointed out, in describing machine production, Wright notes, “matters are so arranged that every workman has his particular work to perform, generally but a small portion of that which goes to the completion of the article to be produced” (United States, Department of Labor 1899, 1: 11). Since Adam Smith, economists have claimed that division of labor would raise labor productivity, as workers are allocated to production tasks based on their comparative advantage and by saving on any set-up costs from switching tools between tasks. However, the various nineteenth-century American censuses of manufacturing never attempted to measure the division of labor directly, and its presence (and potential impact on productivity) in census data can only be inferred from variation across establishments in the number of workers. To our knowledge, the HML study is the only data source for nineteenth-century U.S. manufacturing for which direct measures of the division of labor can be constructed.Footnote
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The first division of labor variable, *Frac_oper*, is the difference (∆) between machine and hand labor in the fraction of operations performed by the average worker. Holding constant the number of operations to be performed, if the average worker performs a greater share of total operations, there was less division of labor; conversely, if the share of operations performed by the average worker declines, the division of labor increases.Footnote
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Assuming that an increase in the division of labor raises productivity, therefore, the coefficient of this variable should be positive—if the average worker performs a larger share of total operations, it will take more labor time to do so. The second division of labor variable, *ln (# of operations)*, is the difference in the logarithm of the number of operations performed in manufacturing the unit by machine versus hand. Holding constant the fraction of tasks performed by the average worker, an increase in the number of tasks will imply a greater division of labor—hence, its coefficient should be negative.Footnote
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As can be seen in Table 5, the signs of both coefficients are as expected and are highly significant. The mean values of both variables are also as expected, indicating a greater degree of division of labor under machine production than under hand.

The third scale variable, *Volume production*, measures the difference between machine and hand labor in a dummy variable indicating whether the actual machine or hand quantity produced exceeded a critical cutoff level where substantial scale economies might have kicked in. While the ideal cutoff should be guided by historical examples and discussion, the relevant literature provides no operational guidance.Footnote
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The threshold we adopted was the quantity associated with the 75^{th} percentile of the machine labor distribution, 1,500. Volume production was more common under machine labor, as indicated by the positive mean value (0.139) of the dummy variable. If volume production did raise productivity, the coefficient of the dummy variable should be negative—which it is, –0.297, and highly significant (s.e. = 0.084).

The HML staff also collected data on average daily hours. Over the nineteenth century, there was a downward trend in average daily hours; on average, daily hours were shorter in the machine labor establishments, although the mean difference was slight. There is some evidence that shorter hours in nineteenth-century manufacturing were associated with increases in labor productivity (Atack and Bateman Reference Atack and Bateman1992; Atack, Bateman, and Margo Reference Atack, Bateman and Margo2003; Goldmark and Brandeis Reference Goldmark and Dembitz Brandeis1912). To test for this, we included the variable *ln (daily hours)*, the (ln) difference in daily hours of plant operation between machine and hand labor. This variable has a positive and significant coefficient, 1.49 (s.e. = 0.55), which is consistent with shorter daily hours being associated with higher labor productivity.

As previously mentioned, the HML staff attempted to assess the quality differences in goods produced by the machine and hand units in the surveyed establishments. For the most part, they concluded there was either no meaningful difference or a quality difference in favor of the machine labor version of the good. That said, if the hand product were of better quality, we would expect that the hand operations would take longer to perform, increasing the apparent productivity advantage of machine labor. To test this, we include a unit-level dummy, *Hand quality better*, in the regression; as can be seen, the coefficient is negative, –0.291, although it is imprecisely estimated (s.e = 0.205).

Lastly, the variable, *Year of observation*, is the difference in the observation year between machine and hand labor. This difference is almost always positive, and the mean is 27, indicating that, on average, the hand labor data were older than the machine labor data by 27 years. The coefficient of this variable is negative, –0.006, and significant (s.e. = 0.002), indicating that the older the hand labor data was relative to machine labor, the greater the productivity advantage of the latter, other factors held constant. This pattern makes sense because earlier hand labor establishments were likely closer to the “old-fashioned” methods that Wright had in mind for the study and, thus, less productive compared with the “most advanced” machine labor establishments in the 1890s.

Of course, we cannot and do not claim that the coefficients of these unit-level variables reflect causal impacts, and we have no way of instrumenting them individually. Still, the mere fact that we can include these measures at all in the regression goes far beyond what is possible with other nineteenth-century data. Further, each of the coefficients has its expected sign suggesting that it is still useful to compute their explanatory power (“percent explained”) at the sample mean values. These are shown in the last column of Table 5. Of the various unit-level variables, the three scale variables account for 18.7 percent of the mean productivity gap in concert, of which the two pertaining to the division of labor are the most important, accounting for 16.3 percent by themselves, equal to almost half of the explanatory power of mechanization alone. Machine establishments operated for fewer hours per day compared with hand, and this difference, too, contributed to the overall productivity advantage, albeit modest (2.6 percent). All told, the unit-level variables account for 31.3 percent of the mean value of *∆ ln T*, about nine-tenths (= 31.3/34.6) of that explained by mechanization in the Equation (2) specification (34.6 percent).Footnote
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## CONCLUDING REMARKS

Economic historians have long been interested in quantifying the sources of labor productivity growth during the historical Industrial Revolution. One common approach is growth accounting, attributing some portion of productivity growth to greater use of capital per worker, including that associated with inanimate power (see also Atack, Bateman, and Margo Reference Atack, Bateman and Margo2005). The results of such analyses (Crafts Reference Crafts2004a, Reference Crafts2004b; Crafts and Mills Reference Crafts and Mills2004) generally find a relatively modest role for inanimate power and, in that sense, are broadly consistent with our findings. But a growth accounting exercise, no matter how well-executed, can only reveal whether inanimate power mattered within the confines of the growth accounting framework. This requires assumptions about output elasticities or else time-series estimation of the same, with inherent limitations. In the American case, another approach is to use establishment-level data from the 1850–80 censuses of manufacturing (Atack and Bateman Reference Atack and Bateman1999) to estimate the extent of economies of scale in a production function framework (see, e.g., Margo Reference Margo, William and Robert2015), but the literature has yet to reach consensus on this because of serious econometric problems that may never be fully resolved.Footnote
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By contrast, the HML data are vastly more informative than any of the census data, allowing us to pinpoint exactly which operations were affected by the use of inanimate power and to develop and apply an identification strategy to explore endogeneity. Albeit with less rigor, we can also measure the effects of other key factors, including the division of labor, which is otherwise impossible for the period on any systematic basis.

Our OLS and 2SLS analyses of the HML operations data reveals that “mechanization” clearly did “take command”; it is likely that no other single factor was more important quantitatively in advancing productivity growth in the transition from hand to machine labor. At the same time, however, our results establish (solidly, in our view) that mechanization accounts for less than a majority of the large average productivity difference between machine and hand labor which, therefore, must be due to other factors. Our expanded analysis of the HML data in the final section of the paper is more speculative, but we believe it justifies a fresh effort to investigate the role of these other factors in raising labor productivity in nineteenth-century manufacturing.

In particular, the HML study suggests that division of labor, volume production, and improvements in the work environment within factories, such as shorter daily hours, are worthy of closer scrutiny. Of these, the role of division of labor may deserve the most attention. The HML study did not investigate why the division of labor increased in the transition from hand to machine labor, but there is little doubt that the transportation revolution was a critical factor (Atack, Haines, and Margo Reference Atack, Haines, Margo, Rhode, Rosenbloom and Weiman2011). The transportation revolution increased market access and in so doing, made a larger scale of operation more profitable—as the saying (from Adam Smith) goes, “the division of labor is limited by the extent of market.” As the division of labor increased, workers became more specialized in production, and the “average worker” was a convex combination of individuals performing different operations according to comparative advantage, more productive than a single artisan performing all tasks from start to finish. Compared with such artisans, the typical nineteenth-century factory operative had much less to learn on the job, lowering the costs of supplying labor to manufacturing. Although advances in technology and emerging complementarity with capital increased the skill demands on factory workers, this calculus remained the same until well into the twentieth century, when the forces of automation eventually caught up, making operatives highly vulnerable to displacement by machinery (Acemoglu and Restrepo Reference Acemoglu and Restrepo2018; Goldin and Katz Reference Goldin and Katz1998).