Monopsony power and factor-biased technology adoption Michael Rubens * February 10, 2020 Latest version here Abstract Monopsony power on input markets affects factor-biased technology adoption in two ways. First, it distorts relative input prices, which changes the benefits of directed technical change. Second, equilibrium input prices and quantities en- dogenously change when innovating. I show that monopsony power decreases the adoption of technologies that save on the input over which firms have monopsony power. Next, I test this result empirically using two inventions in the late 19th coal mining industry. Coal cutting machines augmented productivity of workers over which firms had monopsony power, while underground mining locomotives augmented inputs whose prices were exogenous. I find that mines at which mark- downs were 10% higher were 23% less likely to adopt cutting machines, but not less likely to adopt mining locomotives. Keywords: Monopsony power, Technology adoption, Innovation, Productivity JEL codes: L11, L13, O33, J42, N51 * KU Leuven and Research Foundation Flanders, [email protected]Preliminary, please do not circulate. I thank Jo Van Biesebroeck, Jan De Loecker, Frank Verboven, Chad Syver- son, Otto Toivanen, Penny Goldberg, Steve Berry, Suresh Naidu and participants at the KU Leuven and Yale IO prospectus workshops. This is the second chapter of my Ph.D. dissertation at KU Leuven. Financial support from BAEF, the Fulbright program and the Research Foundation Flanders (FWO) is gratefully acknowledged. Any errors are my own. 1
Transcript
Monopsony power and factor-biased technology adoption
Michael Rubens∗
February 10, 2020Latest version here
Abstract
Monopsony power on input markets affects factor-biased technology adoptionin two ways. First, it distorts relative input prices, which changes the benefitsof directed technical change. Second, equilibrium input prices and quantities en-dogenously change when innovating. I show that monopsony power decreases theadoption of technologies that save on the input over which firms have monopsonypower. Next, I test this result empirically using two inventions in the late 19thcoal mining industry. Coal cutting machines augmented productivity of workersover which firms had monopsony power, while underground mining locomotivesaugmented inputs whose prices were exogenous. I find that mines at which mark-downs were 10% higher were 23% less likely to adopt cutting machines, but notless likely to adopt mining locomotives.
∗KU Leuven and Research Foundation Flanders, [email protected], please do not circulate. I thank Jo Van Biesebroeck, Jan De Loecker, Frank Verboven, Chad Syver-son, Otto Toivanen, Penny Goldberg, Steve Berry, Suresh Naidu and participants at the KU Leuven and YaleIO prospectus workshops. This is the second chapter of my Ph.D. dissertation at KU Leuven. Financial supportfrom BAEF, the Fulbright program and the Research Foundation Flanders (FWO) is gratefully acknowledged.Any errors are my own.
The relationship between competition and innovation has widely been studied in economics ever sinceSchumpeter (1942). The main focus of this literature has always been on product market competition.An increasingly large literature finds, however, evidence for market power on input markets.1 Therelationship between such monopsony power and innovation is much less understood.
In this paper, I examine how monopsony power affects innovation incentives. I focus on the adop-tion of factor-biased technologies, that is, technologies that change the relative requirements for dif-ferent inputs in the production process. I start with a theoretical model in which I propose two mainchannels through which monopsony power affects technology adoption. First, it distorts relative inputprices, which alters the benefits from innovation. This corresponds to the ‘induced innovation’ theoryof Hicks (1932). Second, equilibrium input prices and quantities endogenously change when innovat-ing. Using a simple theoretical model, I find that the directionality of technical change and relativemonopsony power on different input markets jointly determine whether monopsony power increasesor decreases innovation. If a technology augments productivity of the input over which the firm hasmost monopsony power, then monopsony power decreases technology adoption.
Next, I empirically examine this relationship in a case study of two inventions in the late 19th cen-tury coal mining industry: coal cutting machines and mining locomotives. There are three reasonswhy this provides the ideal setting to study monopsony power and innovation. First, both coal cuttingmachines and mining locomotives were large factor-biased technology shocks, but they had an oppo-site technical directionality. While cutting machines augmented the productivity of skilled workers,locomotives augmented productivity of unskilled workers. Second, 19th century coal mining townsare a textbook example of oligopsonic labor markets. The structural estimates confirm that skilledminers were paid less than half their marginal revenue product. Third, coal is a nearly homogeneousproduct, and coal markets were not concentrated. Coal prices were hence most likely exogenous.This simplifies the identification of buying power. I rely on unique micro-data at the mine-level withinformation on both machine adoption and piece rate wages are available up to the invention of coalcutting machines for a period of 18 years.
Coal extraction consists of two main processes: (i) cutting coal, and (ii) hauling it to the surface.While cutting required significant skill, hauling did not. Both tasks were needed in fixed proportions:one cannot cut more coal and leave it under the ground. Cutting machines increased the productivityof the skilled ‘cutters’ but not of the unskilled ‘haulers’. Mining locomotives had the exact oppositeeffect: they made the hauling process more efficient. Mines did not have the same degree of monop-sony power on both labor markets: they were able to set wages of skilled miners, as these were betterpaid and had skills that were coal mining-specific. While these skilled workers could opt for a job
1See, among many others, Ashenfelter, Farber, and Ransom (2010); Naidu, Nyarko, and Wang (2016); Syverson andGoolsbee (2019); Rubens (2019).
2
outside coal mining, they would have lost their skill premium when doing so. Unskilled workerscould, in contrast, switch to any other industry without incurring a wage loss.
I use novel and unique plant-level production and cost data on the universe of Illinois coal minesbetween 1894 and 1902, in which detailed technology choices are observed. I infer markdowns overcutting wages using the first order cost minimization conditions, as in De Loecker and Warzynski(2012a). Due to the non-substitutability of cutters and haulers and perfectly competitive productmarkets, markdowns can be inferred directly from the input revenue shares. Secondly, I estimate scaleeconomies and factor-biased effects of each technology type, which confirms that both technologieshad a different direction of technical change. I bring these elements together to estimate the effectsof markdowns on the adoption of cutting machines and locomotives. I find that an increase in skilledwage markdowns of 10% was associated with a cutting machine usage rate that was 25% lower onaverage. Markdowns did, in contrast, not lead to lower locomotive adoption. This is consistentwith the theoretical model. Finally, I use the model to evaluate the effects of a counterfactual policymeasure: the institution of a state-wide minimum wage which was binding for 15% of all Illinoismines in 1900. Minimum wages were eventually introduced in Illinois, but only in the 1970s. I findthat minimum wages would have increased cutting machine usage by 2.8% per year during the sampleperiod, meaning that cutting machine adoption would have been two thirds higher in 1902 comparedto reality. Under this higher innovation rate, skilled labor-augmenting productivity would have grownby an additional 0.4% per year.
The main contribution of this paper is to examine the relationship between input market competi-tion and factor-biased technology adoption. There is a long-standing literature about the relationshipbetween product market competition and innovation (Schumpeter, 1942; Aghion, Bloom, Blundell,Griffith, & Howitt, 2005; Hashmi, 2013; Collard-Wexler & De Loecker, 2015; Hashmi & Van Biese-broeck, 2016; Igami & Uetake, 2017), but it focuses entirely on the relationship between productionmarket competition and innovation. Just and Chern (1980) allow for oligopsony power in their anal-ysis of tomato harvester adoption decisions.2 In their setting, however, the farmers who innovate facean oligopsonic buyer. The focus is hence still on the relationship between downstream competitionand innovation. This paper is crucially different, as it focuses on the innovation decision made by theoligopsonist, and hence on the relationship between upstream competition and innovation. Probablythe closest to this paper is Dechezlepretre, Hemous, Olsen, and Zanella (2019), which estimates the‘induced innovation’ effect of Hicks (1932); namely that higher wages increase the incentive to adopta labor-augmenting technology. They view input price variation across firms as exogenous, however.This leaves the crucial question of why input prices differ across firms in narrow geographical andindustry settings. This paper, in contrast, allows prices to be endogenous to the firm’s output andinnovation decisions.
There is a large literature about the causes and effects of monopsony power on input markets, both
2The same holds for Huang and Sexton (1996); Kohler and Rammer (2012)
3
in labor economics (Card & Krueger, 1994; Ashenfelter et al., 2010; Naidu et al., 2016), macroe-conomics (Berger, Herkenhoff, & Mongey, 2019; Morlacco, 2017; Brooks, Kaboski, Yao, & Qian,2019) and industrial organization (Rubens, 2019; Syverson & Goolsbee, 2019). I contribute to theseliteratures by showing that monopsony power does not just lead to static efficiency distortions, butcan also have adverse dynamic efficiency effects through lower innovation. This also contributes to alarge literature on barriers to technology adoption in developing countries, which is surveyed in Fosterand Rosenzweig (2010); Atkin, Chaudhry, Chaudry, Khandelwal, and Verhoogen (2017). Monopsonypower could be one reason why technology adoption is so puzzlingly low in many developing coun-tries today. Cutting machine adoption in 19th century Illinois happened very slowly as well: eventhough cutting machines increased productivity considerably, merely 12% of Illinois coal mines hadadopted them 20 years after their introduction.
Third, there is a literature about factor-biased technical change which spans various fields, such aslabor economics (Autor, Levy, & Murnane, 2003; Bloom, Genakos, Sadun, & Van Reenen, 2012),macroeconomics (Antras, 2004; Acemoglu, 2003) and industrial organization (Van Biesebroeck,2003; Doraszelski & Jaumandreu, 2017). Identification of factor-biased change usually hinges onexogenous input prices, such as in Doraszelski and Jaumandreu (2017) I allow, however, for factor-biased technologies in a setting with endogenous input prices. I also contribute to this literature byshowing that the directionality of technical change is crucial for how it interacts with monopsonypower.
The remainder of this paper is structured as follows. I start with a brief overview of the Illinois coalindustry and present key motivating facts in section 2. Next, I construct a model of coal extraction,monopsony power and innovation decisions in section 3. I use this model to estimate the relationshipbetween markdowns and technology adoption decisions in section 4. Finally, I quantify the effects ofminimum wages on technology adoption and labor-augmenting productivity growth in section 5.
2 Industry background
2.1 Coal mining in Illinois, 1884-1902
Extraction process
I study the extraction of bituminous coal in Illinois between 1884 and 1902. The extraction processconsisted of three consecutive stages. First, the underground coal layer had to be accessed eitherusing a vertical shaft or using a horizontal tunnel, wherever possible. As large parts of Illinois areflat, 60% of the mines were ‘shaft’ mines3. Second, upon reaching the underground seam, the coal
3Coal seams were sometimes accessible at the surface, but this holds for just 2% of the mines in the data.
4
itself was excavated, either by hand or using mechanized cutting machines. More than nine out often mines used a ‘rooms and pillars’ technique in which miners excavated everything except pillars,which were left to sustain the roof. This involved a significant amount of skill: when determining thethickness of the pillars, miners had to trade off lower output with the risk of collapse.4 These minerswill henceforth be called ‘skilled workers’. Third, coal had to be transported back to the surface andsorted from impurities. Both hauling and sorting were done by auxiliary laborers with lower wages,and did not require specific skills. These workers are henceforth called ‘unskilled workers’. Haulingwas done either using mules or underground mining locomotives. In 1884, there were 16,531 skilledand 4,543 unskilled workers. By 1902, this had increased to 33,060 skilled and 13,142 unskilledworkers. The proportion of unskilled workers hence grew almost by half, from 20 to 28%.
Coal markets
The number of mines in Illinois increased from 688 to 895 between 1884 and 1902, while the numberof firms increased from 655 to 824. As nearly all firms owned only one mine, I use the mine as levelof analysis throughout the paper and abstract from multi-mine firms. After being extracted and sorted,88% of coal production was transported by railroad and either sold in cities or used by railroad com-panies. As figure 1 shows, the Illinois railroad network was already very dense at the time, especiallycompared to the other US states, which is why coal markets were so integrated. Only 7% of outputwas sold locally without being transported by rail, while the remainder was re-used as an input in themines. The average mine-gate price of a ton of coal was $1.52 in 1884, with the bottom and top 5%percentiles being $0.87 and $2.00. Even though prices were exogenous, this did not mean they wereidentical across mines: geographical locations were a key driver of price differences, as there weretransport costs.
[Figure 1 here]
Labor markets
Skilled workers received a piece rate per ton of coal mined, while unskilled workers were paid a dailywage. Materials, such as picks and black powder, were purchased and paid for by the miners ratherthan by the firm. Both these payment schemes incentivized miners not to waste coal and materials.Skilled labor wages net of materials were on average 13% higher compared to unskilled workers,while they faced similar risks from working under the ground. The average piece rate of a skilledworker was 0.95 dollar per ton. The bottom 5% of mines paid wages under 40 dollar cents per ton,
4The other mines used so-called ‘longwall’ techniques in which miners temporarily constructed an artificial roof andallowed the room to collapse in a controlled way.
5
while the top 5% paid more than 1.25 dollar per ton. Unskilled workers received a daily wage, ratherthan a piece rate.
Mining areas were sparsely populated. In the average town in the dataset, the number of coalemployees constituted 34% of the town’s population. Considering that women and children under theage of 12 could not work in mines, this means that virtually the entire town was employed in coalmining. Four out of ten coal mines were in a village with three or less mines in total. The averageemployment share at the village level was 35 %. Many villages were very small and isolated: themedian village in the dataset had just 921 adult inhabitants.
Unionism in the Illinois coal mining industry started around the 1860, and the Knights of Laborwere a first attempt to form a union. These initiatives were largely unsuccesful in their attempts toraise wages (Boal, 2017). The first succesful labor union in Illinois was the United Mine Workersof America, founded in 1890. A major strike occurred in 1897-1898, and resulted both in wageraises and in a reduction of working hours to a maximum of eight per day. Due to their level ofviolence, these strikes became known as the ‘Illinois coal wars’. Various regulations existed to counterunionism, such as the usage of ‘yellow-dog contracts’ which stipulated non-membership of a unionas a condition for employment. These contracts were criminalized in Illinois in 1893, with fines of100 USD5 (Fishback, Holmes, & Allen, 2009). There was no minimum wage law and labor marketswere largely unregulated (Naidu & Yuchtman, 2017).
Aggregate productivity
Industry-wide output and employment are summarized in figure 2. Aggregate output per worker-day increased by almost a third between 1886 and 1898, from 2 ton per worker-day to 2.4 ton perworker-day. After 1898, the 8-hour workday was introduced, which means that the output per daywent down. Correcting for this change, labor productivity continued to rise to 2.5 ton per worker-dayin 1902. The average annual growth rate in output per worker-day was around 1.5% per year duringthe period observed.
[Figure 2 here]
Technological change
Up to the 1880s, coal cutting was entirely done by hand, using picks and shovels. The earliest proto-types of mechanical coal cutting machines were invented in Northern England by the late 1870s, andwere introduced in the U.S. in 1882 (Reid, 1876; Ackermann, 1902). The main mining machine used
5This was the equivalent of six average monthly miner wages
6
in the U.S.A. was the Harrison machine, of which the 1882 patent is pictured in figure 3.
[Figure 3 here]
Illinois was one of the first states in which cutting machines were used. In 1891, one out of two coalmining machines used in the U.S. were located in Illinois. By 1901, this share had decreased to onein ten, as other states started to adopt coal mining machines as well. The top graph in figure 4 showsthe evolution of cutting machine adoption in Illinois. In 1884, only 9 mines used cutting machines,but they produced a tenth of industry output. By 1902, the fraction of mines using cutting machineshad increased to 13%, which produced over 40% of industry output.
[Figure 4 here]
Cutting machines contributed to productivity growth. The bottom graph in figure 4 plots the evolu-tion of output per worker-day for machine and hand mines, with the corrected labor-days after 1898.Output per worker-day was around 50% higher across machine mines compared to hand mines before1896. Afterwards, hand mines started becoming more productive as well, but still were less productivethan machine mines. The spatial diffusion of machines is shown in figure 5. The blue dots representmining towns, each of which can contain multiple mines. Villages with red squares contain at leastone machine mine. Machine adoption happened rapidly around St. Louis, MO, where the Harrisoncutting machines were manufactured.
[Figure 5 here]
2.2 Data
I observe every of the up to 895 bituminous coal mines in Illinois between 1884 and 1902 with two-year intervals, resulting in 8307 observations. The data are obtained from the Biennal Report of theInspector of Mines of Illinois. I observe the mine’s owner, yearly coal extraction, employee counts forboth skilled and unskilled workers, days worked, intermediate inputs (black powder and dynamite) inquantities, dummies for the usage of various technologies (cutting machines, locomotives, ventilators,longwall machines) and technical characteristics such as mine depth, vein thickness and the mineentrance type (shaft, drift, slope, surface). For some years I observe additional variables such as minecapacities, the value of the total capital stock and a break-up of coal sales by destination. I supplementthis plant-level dataset with town- and county-level information from the population census and thecensuses of agriculture and manufacturing. I refer to appendix A for more details regarding the data
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and the construction of the capital stock variables.
2.3 Stylized facts
Fact 1 Machine mines used relatively less skilled workers compared to unskilled workers
As already explained, cutting machines increased skilled worker productivity, but not unskilledworker productivity: the rate at which unskilled workers could carry coal to the surface did not changewhen using a cutting machine. The 1888 report of the Illinois Coal Mine Inspector asserts that:
“Herein lies the chief value of the [cutting] machine to the mine owner. It relieveshim for the most part of skilled labor” (of Labor Statistics of Illinois, 1888)
Machine mines produced 67% more output per miner than hand mines, but only 36% more output perhelper. In the fully-specified empirical model, which takes into account endogeneity, I will flexiblyestimate the effects of cutting machines on both input requirements.
Fact 2 Skilled worker wages covaried with local market structure
Figure 6 compares skilled labor wages across towns depending on how many mines there were inthe town.6 Wages of underground miners were 10% lower in towns with just one mine, 7% lowerwith two , 2% lower with three - albeit only borderline significant -, and no longers different fromfour mines onward. More than one fourth of mines are in a town with either one or two mines. Thisevidence hence suggests that a considerable fraction of mines were able to set lower wages for miners.Note that wage differences cannot be due to productivity differences, as they are piece rates.
[Figure 6 here]
Fact 3 Miner and helper tasks were complementary
Cutting and hauling coal are complementary tasks conditional on the technology in use. It is notpossible to cut more coal while keeping hauling constant, or to haul more keeping cutting constant.In other words, mines could change the relative requirements for skilled and unskilled workers by,for instance, adopting mining locomotives or cutting machines, but conditional on this capital stockboth occupations were perfect complements. Being the most skilled workers, miners could of course
6Doing this exercise when using firms rather than mines gives nearly identical estimates
8
also haul coal and take over the unskilled labor tasks (the opposite was not possible), but would notmake sense as skilled workers were much more expensive. In the empirical section, I will formallyestimate the elasticity of substitution between skilled and unskilled workers, which confirms thatperfect complementarity between both cannot be rejected, conditional on technology usage.
3 A model of technology adoption with monopsony power
3.1 Production and costs
In this section, I specify a model of coal extraction with endogenous input prices. From this model, Iobtain a markdown expression and estimate returns to scale in both skilled and unskilled labor. Thetwo key features of the model are (i) input prices are endogenous, and (ii) different technologies canhave different factor-biased effects.
Production
Mines i extract Qit tons of coal per year t using skilled labor LSit, unskilled labor LUit , materials Mit
and capital Kit. I distinguish three types of capital: cutting machines KCUTit ∈ {0, 1}, locomotives
KLOCit ∈ {0, 1} and all other capital, such as elevators, KOTH
it ∈ R. Mines have an annual capacityconstraint Qmax
it . Let the production function be given by the Leontief function in equation (1).
Qit = min{ (LSit)
1
σS
F S(Kit);
(LUit)1
σU
FU(Kit),Mit
FMit
}s.t. Qit ≤ Qmax
it (1)
As explained in the industry background, skilled and unskilled workers are perfect complementsconditional on the capital stock. The input requirements for skilled and unskilled labor, F S and FU
depend on technology usage. Firms can change the relative requirement for skilled and unskilledlabor by acquiring cutting machines, mining locomotives, or other types of capital. Materials, such asblack powder, are complementary to both types of miners. I allow for scale economies in both typesof labor using the parameters σS and σU . If these parameters are above one (i.e. their inverse belowone), then there are decreasing returns to scale.
The capacity constraint is assumed to be non-binding, which is confirmed by the data: figure 7shows that capacity utilization was distributed unimodally around a utilization rate of around 30%,and the capacity constraint was binding for only 1% of all mines. This is important, as it will motivatethe assumptions made about marginal cost curvature.
[Figure 7 here]
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I assume a log-linear functional form for both F S(.) and FU(.). Denoting logs as lowercases, Irewrite the production function in logs as equations (2). Because locomotives and cuttingm machinesare measured as a dummy, they are included as KCUT and KLOC . The remainder part of the capitalstock is an integer value, and hence enters the equation in logs. The variables ωSit and ωUit are theunobserved part of variation in skilled and unskilled labor productivity. Mines with a higher ωS needless skilled laborers per ton of output, conditional on technology usage.qit = 1
σSlSit + βSCUTK
CUTit + βSLOCK
LOCit + βSOTHk
OTHit + ωSit
qit = 1σUlUit + βUCUTK
CUTit + βULOCK
LOCit + βUOTHk
OTHit + ωUit
(2)
The crucial coefficients are βSX and βUX , ∀X ∈ {CUT,LOC,OTH}. Their relative magnitude indi-cates the degree of factor bias of each technology:
βSXβUX
>
=
<
1⇔ technology X is
S-augmentingFactor-neutralU-augmenting
As already discussed in the stylized facts, cutting machines were skilled labor-augmenting technol-
ogy, βSCUT > βUCUT , while the opposite held for mining locomotives. I will confirm this intuition byestimating both equations in (2).
I assume both factor-augmenting productivity shocks ωsft and ωuft follow an AR(1) process with thesame functional form. The terms ξsft and ξuft are unexpected factor-augmenting productivity shocksfor skilled and unskilled labor respectively.ωSit = g(ωSit−1) + ξSit
ωUit = g(ωUit−1) + ξUit
Total costs
Skilled and unskilled laborers were paid differently: the first group received a piece rate, the secondgroup a daily wage. For now, I denote the resulting daily wages of skilled and unskilled labor as W S
it
andWUt , withW S
it > WUt . Materials and tools were not purchased by mine owners, but by the miners,
and are hence not a part of the firm’s cost function. Fixed assets of type X ∈ {CUT,LOC,OTH}have an associated fixed cost ΦX
it . Mines are assumed to be too small to set capital costs, which meansfixed costs are exogenous. The total cost of producing a coal quantity Qit for the mine owner is hence
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given by:
TC(Qit,Kit,WSit ,W
Ut ,Φit) = W S
itQσS
it FS(.) +WU
t QσU
it FU(.)︸ ︷︷ ︸
variable costs
+RtKit +∑X
ΦXitXit︸ ︷︷ ︸
fixed costs
Input supply
In line with the industry background, I allow for monopsony power on the market for miners, butassume wages of helpers to be exogenous from the mine’s point of view. Skilled labor wages dependon observed firm characteristics Zit, latent firm characteristics ζit and the quantity of skilled laborused:
W Sit = W S(LSit,Zit, ζit)
The inverse wage elasticity of skilled labor supply is denoted Ψ, and indicates the extent to whichfirms have monopsony power over skilled labor. The higher Φit is, the more inelastic labor supply is,and hence the more monopsony power a mine owner has.
Ψit ≡∂W S
it
∂LSit
LSitW Sit
If the labor supply curve can be non-linear, meaning that this elasticity is a function of how manyminers are employed at the firm.
Returns to scale
In order to simplify the model, I add two assumptions that are informed by the estimates of equation(2) in the empirical application. First, I impose constant returns to scale in both types of labor. Second,I assume that cutting machines only decrease the input requirement for miners, but do not affect therequirement for helpers: βSCUT < 0 , but βUCUT = 0.
Marginal costs
Marginal costs are given by equation (3). When increasing output by one unit, mines need to paythe unskilled worker wages, which are exogenous, and skilled worker wages, which endogenouslyincrease with skilled worker usage.
MCit = W SitF
Sit (1 + Ψit) +WU
t FUit (3)
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The absence of scale economies does not mean marginal costs are constant with output. Depend-ing on the curvature of the labor supply curve, marginal costs can both be decreasing, constant orincreasing with output. To see this, I take the first derivative of marginal costs to output:
∂MCit∂Qit
= F Sit
(∂2Wit
∂2Qit
Qit + 2∂Wit
∂Qit
)If the labor supply curve is linear or convex, then the marginal costs increase with output. Only ifthe skilled labor supply curve is sufficiently concave, marginal costs can be decreasing with size. Iassume this is not the case: if marginal costs would fall with output, all mines would operate at fullcapacity, which is not the case.
Decisions
Mine decisions take place in two stages. First, they choose machine adoption AX ∈ {0, 1}. Thishappens before the factor-specific productivity shocks ξS and ξU arrive, and I assume investmentdecisions in different machine types happen independently from each other. As the model is static, Iassume mine owners re-decide on whether to operate each machine type every year, so there is fulldepreciation.
Xit = AXit−1 for X ∈ {CUT,LOC,OTH}
In a second stage, the output level is chosen. This happens after the productivity shocks are ob-served. Due to the Leontief production function, mines do not choose miners and helpers separately,they just choose how much coal to extract. As capital has been set by this stage, input requirementsare fixed as well. The output level hence automatically implies how many miners and helpers areemployed.
I assume mine owners minimize costs, and hence choose the output level that equates marginalcosts to coal prices. As there are no cost dynamics, this is a static decision problem, and mine ownerssolve it every year independently from each other. If marginal costs would evolved dynamically withcumulative output, as in Aguirregabiria and Luengo (2017), this assumption would be violated. Ido not find evidence for cost dynamics, however: when I add mine depth as a control in the inputrequirement regressions (2), this yields a very small and insignificant coefficient. As Illinois coalmines were still abundant and far from depletion during the time period studied, cost dynamics arenot a first-order concern.
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Markdowns
Solving the firm’s first order cost minimization problem yields the expression for markdowns. Equat-ing prices to marginal costs gives:
Pit = W Sit
LSitQit
(1 + Ψit) +WUt
LUitQit
When denoting the revenue shares of skilled and unskilled labor as αS ≡ WSLS
PQand αU ≡ WULU
PQ,
this simplifies to equation (4), which is the markdown formula.
Ψit + 1 =1− αUitαSit
(4)
This markdown formula differs compared to the markup expression in De Loecker and Warzynski(2012b) in two aspects. First, due to the Leontief functional form and constant returns to scale, thereare no output elasticities to be estimated: these are one by definition. Second, both the skilled andunskilled revenue share enter the markdown expression, as both are part of marginal costs: one cannotincrease skilled labor and keep unskilled labor constant, or vice-versa. If revenue share of skilled laboris higher relatively to the unskilled revenue share, this indicates a lower degree of monopsony power,as skilled labor is more expensive.
In appendix B.1, I extend the markdown formula to allow for (dis-)economies of scale.
3.2 Cutting machine adoption
Machine benefits
I examine optimal machine adoption AX ∈ {0, 1}. Firms choose which machines to operate in thenext period in order to minimize total costs in the next period:
AXit = arg minEt[TC(Qit+1,Kit+1,W
Sit+1,W
Ut+1,Φit+1)
]s.t. KX
it+1 = AXit ,∀X
Under which conditions do machines increase profits? Taking the first derivative of profits withrespect to machine usage results in equation (5), which is derived in appendix B.2. Machines havetwo effects. First, they change the optimal scale at which the mine operates, because they decreasemarginal costs. This change in output has no effect on profits; firms keep choosing an output level atwhich the coal price is equal to the marginal cost. Second, machines lead to a different mix of skilledand unskilled workers per ton of coal. Finally, the fixed cost of operating machines of type X, ΦX ,
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has to be paid.
∂Π(.)
∂KXit
= W Sitβ
SXQit︸ ︷︷ ︸
skilled labor substitution
+ WUit β
UXQit︸ ︷︷ ︸
unskilled labor substitution
− ΦXit︸︷︷︸
fixed costs
(5)
Machines are profitable as long as the productivity-increasing effects are larger than the fixed costfrom adopting a machine. Machine adoption is hence more likely to be profitable if (i) wages arehigher (ii) productivity is increased by more (iii) mines are larger.
Machine adoption and monopsony power
Finally, I derive how the degree of monopsony power affects machine adoption. Deriving equation(5) with respect to markdowns gives equation (6).
∂
∂Ψit
(∂Π(.)
∂KXit
)=∂W S
∂ΨβSXQit +W SβSX
∂Q
∂Ψ(6)
The first term is negative: ∂WS
∂Ψ< 0. If mines have more monopsony power, they pay lower wages,
and hence incure less cost-savings from adopting the machines. The coefficient βSX is positive ifmachines decrease the number of skilled workers which are necessary. The second term is negativeas well: as marginal costs are increasing with the degree of monopsony power, which was shown inequation (3), higher markdowns imply a lower output level. At smaller mines, the cost saving frominstalling machines is lower, compared to fixed costs which do not depend on size.
I conclude that, under the assumptions made, monopsony power always leads to lower machineadoption in equilibrium if and only if the technology reduces the input requirement of the input overwhich the firm has monopsony power:
Theorem 1∂
∂Ψit
(∂Π(.)
∂KXit
)< 0⇔ βSX > 0
Allowing for both input and product market power
What if firms have market power on both input and product markets? I derive innovation benefitsin this case in appendix B.3. I find that the relationship between monopsony power and innovationincentives has the same sign as in the case with exogenous product prices. The effect is likely to beeven more outspoken. The reason for this is as follows: upon adopting a machine, firms increasetheir output level. If there is a difference between prices and marginal costs, this additional output issold at a profit. If monopsony power is larger, however, the output increase will be smaller, as firms
14
internalize increased wages when increasing output. The additional profit gain will hence be smallercompared to the case in which input prices are exogenous.
Caveat: single- vs. multi-agent adoption decisions
I model machine adoption as a single-agent decision problem, even though factor markets are oligop-sonic. It is clear that own machine adoption decisions will affect equilibrium miner wages of allother mines in the same local labor market, hence introducing strategic interaction. I follow Olleyand Pakes (1996) by still considering investment decisions as if they were single-agent, and leave themulti-agent extension for future work.
4 Estimation and results
I now bring the model developed in the previous section to the data. I start by estimating the produc-tion function in order to quantify the factor-biased effects of cutting machines, and to assess whetherthere were any scale economies. Second, I calculate markdowns. Third, I estimate how these mark-downs affected adoption of two technologies
4.1 Production
Estimation
There are two reasons to estimate the production functions, equation (1). First, it is necessary to quan-tify the effects of cutting machines and locomotives on miner- and helper-augmenting productivity.Second, it allows scale economies to be estimated both for miners and helpers. I follow the approachof Ackerberg, Caves, and Frazer (2015). The timing assumptions were already made in the theorysection: mine owners decide on cutting machine adoption and investment in other capital before theproductivity shock ξ hits. After this, they decide on how much output to produce. The output andlabor decisions for every labor type are the same decision due to the Leontief assumption. There aretwo sets of moment conditions, one for each type of labor τ :
E{ξτjt(β
τl ,β
τK)
(lτit−1
Kit
)}= 0 τ ∈ {S, U}
15
Results
The estimates are in table 1. Cutting machines augmented the productivity of skilled miners, but notof unskilled workers, and were hence a skill-biased technology. Locomotives did, on the contrary,increase unskilled worker productivity but not skilled worker productivity. The scale parameter isindicated by the coefficient on both types of labor. It is not signficantly different from one for skilledlabor and slightly below one for unskilled labor. There were hence constant returns to scale in skilledlabor and slightly decreasing returns to scale in unskilled labor.
[Table 1 here]
Unskilled and skilled worker-specific productivity are highly correlated conditionally on capitaland machine usage, this is shown in figure 8. The most productive mines hence usually have bothvery productive skilled and unskilled workers.
[Figure 8 here]
Elasticity of substitution
A crucial assumption for the model is the fact that miners and helpers cannot be substituted conditionalon the capital stock and mine characteristics. I test this assumption by estimating the elasticity ofsubstitution. As in Doraszelski and Jaumandreu (2017), I estimate equation (7). I include cuttingmachines, other capital and log output in the vector z.
luit − lsit = σ(wst − wuit) + zit + uit (7)
I estimate two versions of (7): one with mine fixed effects and one in which I instrument wagesfor how many other mines in the same town use cutting machines. The estimates in table 2 show thatthe estimated elasticity of substitution between miners and helpers is very small and not significantlydifferent from zero in both specifications. The Leontief production function is hence the right modelfor coal extraction.
[Table 2 here]
16
4.2 Markdowns
Results
There is no estimation involved to obtain markdowns because of the Leontief structure and becausethe constant returns to scale are assumed. I hence calculate markdowns using equation (4). The mark-down distribution is in figure 9. Very few mines have markdowns below one, as it should be, and veryfew are above 2, meaning that miners receive less than half their marginal product. Markdowns are onaverage 2.5, which means that miners were paid 40% of their marginal product. At the median firm,markdowns were lower, 1.3, implying a wage to marginal product ratio of 75%.
[Figure 9 here]
Drivers of monopsony power
At which mines were markdowns the highest? I regress the markdown estimates on a set of county andmine characteristics. The estimates are in appendix table A1. The first six regressors tell somethingabout outside options of skilled workers. If the number of firms in a county is higher, markdowns arelower. In counties with a higher percentage of immigrants, markdowns are higher: migrant workershad lower outside options due to, for instance, language barriers. Mines in counties at a larger distancefrom the main urban centers, Chicago and St. Louis, had higher monopsony power. Mines in counties,finally, without a railroad connection had higher markdowns as well, as workers could move lesseasily. The following three regressors are technical mine characteristics. Markdowns were smallerin larger mines and in mines in which skilled miners were more productive. For mines with moreproductive unskilled workers, the opposite holds, and markdowns over skilled labor were higher.Finally, in columns (2) and (3), I look how markdowns changed with the 1897-1898 strike. Column2 compares mines with and without a strike in 1898 in 1902, four years later. Mines in which minerswent on strike had lower markdowns, and the more strikers there were, the lower the markdown.
4.3 Adoption decision
Estimation
I estimate a static discrete choice model of cutting machine adoption. In line with the theoreticalmodel, innovation payoffs depend on expected markdowns, wages, firm size, productivity and latentfixed costs. As the evolution of both productivity shifters was assumed an AR(1) process, and as fixedcosts are assumed to evolve i.i.d. across mines and over time, firms condition their decisions on their
17
currently observed state variables. As adding a machine is assumed to take one time period, I regressthe usage of each technology in time t on mine characteristics at time t− 1.
Xit = AX(ψit−1, ωsit−1, ω
uit−1, qit−1, φit) (8)
I start by estimating equation (8) using a linear probability model, in which I control for countydummies. Secondly, I add mine fixed effects to control for time-invariant mine-level heterogeneity. Iestimate equation (8) both for cutting machines and locomotives.
Results
The adoption determinants for cutting machines are in the first two columns of table 3. Markdownsaffect cutting machine adoption negatively, and the size of the effects if very similar for the linearprobability and probit model. If markdowns would fall by 10%, cutting machine adoption wouldincrease by 0.57 percentage points, compared to an average adoption rate of 2.5%. This is a relativeincrease of 23%.
[Table 3 here.]
The adoption determinants for mining locomotives are in the last two columns of table 3. Whennot controlling for mine fixed effects, the correlation between markdowns and locomotive usage isclose to zero. Once mine fixed effects are added, I find that mines at which markdowns are higher aresomewhat more likely to use locomotives.
These estimates confirm the theoretical model’s main insight: higher markdowns over skilled work-ers lead to less adoption of the technology that saved on skilled workers (cutting machines), but didnot slow down adoptino of the technology that saved on unskilled workers (locomotives).
5 Back-of-the-envelope calculation
5.1 Overview
In this section, I consider the effects of the introduction of a state-wide minimum wage in Illinois in1900 on innovation and skilled labor productivity growth.
18
Policy description
I examine the effects of a state-wide minimum wage regulation in the coal mining industry in 1900.Illinois instituted minimum wages from 1971 onwards. I consider an industry-wide minimum wage of70% the median wage. This seems rather high, but it was actually binding for only 17% of the mines.I recompute markdowns under this counterfactual wage under the assumption that the marginal laborproduct remained constant. Next, I quantify the different machine adoption rate which is associatedwith this counterfactual markdown, using the estimates of equation (8). This equation tells us onlysomething about changes in machine usage, not about machine usage itself. As the first year in thedata, 1884, is also the time when mining machines were just invented, I set machine usage to be thesame for both counterfactual scenarios in 1884 and calculate machine usage using the counterfactualadoption rates from there to 1902 onwards.
Caveats
There are a number of caveats when doing this analysis. First of all, it is of a partial equilibrium nature.This is an important limitation: even if individual mines could not set coal prices, industry-widechanges in monopsony power would have had general equilibrium effects on, for instance, coal pricesas well. Second, as was already mentioned, strategic interaction in machine adoption is abstractedfrom. Third, a full counterfactual would need to impose more structure on input market competition inorder to know how equilibrium output and input quantities at each mine would change when minimumwages are impsoed. Nevertheless, the current reduced-form exercise is still useful to quantify the orderof magnitude of the dynamic effects of monopsony power on innovation and productivity growth.
5.2 Results
Machine usage
Average cutting machine usage per year under the two scenarios (reality, minimum wages) is in thetop graph of figure 10. In reality, the fraction of mines using a cutting machine increased from aroundzero in 1884 to 18% in 1902. With a minimum wage, this would have been 28% in 1902. Thelargest increase happens after 1892, because of increasing wage dispersion, meaning that the fractionof mines falling below the minimum wage increased as well.
[Figure 10 here].
19
Miner productivity
Cutting machines increased skilled miner productivity in important ways. I recompute skilled laborproductivity in each scenario. I plot the average skilled miner productivity both with and withouta minimum wage in the second graph of figure 10. In reality, average skilled labor productivityincreased from 7,3 Kton per skilled worker in 1884 to 11.6 Kton per skilled worker in 1902, anincrease of 2.6% per year. Under the minimum wage policy counterfactual, yearly output per skilledworker would have increased to 14.0 Kton, an increase of 21%. The average growth rate of skilledworker productivity would have increased by 1.1 percentage point per year, a relative increase of 42%.
6 Conclusion
In this paper, I investigate how monopsony power affects the adoption of factor-biased technologies.In theory, I find that monopsony power inhibits factor-biased technology adoption under plausibleconditions if productivity is augmented the most for the input over which firms have most monopsonypower. Applying this model to late 19th century Illinois coal mining shows that monopsony powerindeed decreased adoption of coal cutting machines, a skilled labor-augmenting technology. Thiswas not true for mining locomotives, another technology which was unskilled worker-augmenting.By decreasing cutting machine adoption, monopsony power led to lower skilled labor productivitygrowth in the coal industry. I find that a minimum wage which would have been binding for 17%of firms would have resulted in skilled labor productivity growth that was 42% higher compared toactual productivity growth.
20
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Observations 3,268 3,268 2,722 2,722R-squared 0.026 0.450 0.024 0.456Mine FE No Yes No Yes
Notes: All variables except dummies are in logs. Standard errors inparentheses
36
Appendices
A Data
A.1 Data sources
The main data source is the biennal reports of the Bureau of Labor Statistics of Illinois between 1884-1902. Every edition contains a list of all mines in each county, the name of the firm or individualoperating the mine, and information on mine characteristics, input usage, production and prices. Idigitized this data using a data entry firm, and checked the data for consistency by comparing thecounty totals mentioned elsewhere in the reports with the aggregates of the mine-level data.
I cleaned the data manually in order to ensure consistency of mine, firm, town and county namesover time. I always kept the original mine and firm names as reported in the data, next to the updatedfirm and mine identifiers which ensure consistency over time. Nevertheless, if a mine changed bothits name and changed ownership, it will be recorded as a false exit and re-entry. For this reason, thedata needs to be used with care when discussing entry and exit patterns. This is mainly an issue forsmaller mines, for larger mines I could track mines over time even when they changed owners.
A.2 Capital stock construction
I only observe the nominal value of the capital stock, in US dollars, in 1884. Besides this, I also havevery detailed information about nearly every type of capital. I therefore impute capital stock valuesfor all years by regressing the 1884 log capital stock on various capital stock indicators. I do notinclude cutting machines in this capital stock, as it is the main variable of interest. Therefore, I endup having two fixed assets in the model: a dummy for the usage of cutting machines and the value ofregular capital, which includes all fixed assets except cutting machines.
The regression to construct the capital stock is reported in table A2. I regress log capital in 1884 onmine depth, vein thickness, locomotive usage, whether the mine is a shaft or drift mine and on countydummies. These variables explain 80% of variation in the capital stock across mines in 1884.
[Table A2 here]
37
B Theory addendum
B.1 Allowing for (dis-)economies of scale
Markdown expression
If the scale parameters σU and σs are not equal to one, the markdown expression has to be adjusted.It becomes:
(1 + Ψft) =1− σUαUftσSαSft
If there are diseconomies of scale in skilled labor, this means that σs > 1. Markdowns are thensmaller than when measured by the CRS model. The reason for this is that the output elasticity ofskilled workers is smaller if there are diseconomies of scale. The gap between the wage and marginalrevenue product of skilled workers is then also smaller.
Returns from innovation
The effect of monopsony power on the returns to innovation with non-constant returns to scale aregiven by:
∂
∂Ψft
( ∂Πft
∂KXft
)=∂W S
ft
∂Ψft
βSXQσS + σS
∂Qft
∂Ψft
QσS−1ft βSX
The relationship between the sign of βSX and ∂∂Ψft
(∂Πft∂KX
ft
)remains valid.
B.2 Derivation of locomotive benefits
∂Π
∂X> 0⇔ ∂
∂X(PQ−W SF SQ−WUFUQ− ΦX) > 0
⇔ ∂Q
∂X(P −W SF S(1 + Ψ)−WUFU︸ ︷︷ ︸
=P−MC=0
) +W SβSXQ− Φ > 0
W SβSXQ > Φ
�
38
B.3 Allowing for markups and markdowns
Locomotive benefits
I now allow firms to have both markups and markdowns. Locomotive benefits are still given by:
∂Π
∂X=∂Q
∂X(P −W SF S(1 + Ψ)−WUFU︸ ︷︷ ︸
=P−MC
) +W SβSXQ− Φ
The difference between prices and marginal costs is now no longer zero. As firms have market poweron the product market, prices surpass marginal costs by a markup µ:
P −MC =(µ− 1
µ
)P
The benefits of machine adoption now depend both on their effect on output, as higher outputyields additional profits, and on the input substitution effect. As machines are productivity-increasing,marginal costs decrease upon adoption, and output increases. Moreover, markups are above one. Thefirst term is hence positive.
∂Π
∂X=∂Q
∂X
(µ− 1
µ
)P +W SβSXQ− Φ
Monopsony power and innovation
The effect of monopsony power on innovation is now given by:
∂
∂Ψ
( ∂Π
∂X
)=
∂
∂Ψ
( ∂Q∂X
)(µ− 1
µ
)P +
∂W S
∂ΨβSXQ+W SβSX
∂Q
∂Ψ
I already argued that the second and third term are negative if technology X augments the produc-tivity of factor S. What about the first term? The increase in output due to the technology is smallerif firms have higher monopsony power: the term ∂
∂Ψ
(∂Π∂X
)is negative. Hence, the overall effect of
monopsony power on innovation benefits remains negative.
39
Table A1: Markdown drivers
Dependent variable: Markdown
# firms -0.0494(0.0141)
% immigrants 0.0776(0.0176)
% Afro-Americans -0.0129(0.0129)
dist. from Chicago 0.0943(0.0385)
dist. from St. Louis 0.102(0.0377)
railroad connection -0.0566(0.0253)
output -0.366(0.0942)
skilled labor productivity -1.951(0.513)
unskilled labor productivity 2.404(0.616)
strike dummy -0.157(0.0654)
# strikers -0.136(0.0378)
# days on strike 0.00348(0.00107)
Observations 5,874 628R-squared 0.164 0.054
Notes: All variables except dummies and strike days are in logs.Standard errors in parentheses
40
Table A2: Capital stock
Dependent variable: Capital stock
Depth 0.688(0.0957)
Vein thickness 0.870(0.229)
Locomotive usage 2.193(0.162)
Shaft mine 0.756(0.148)
Observations 589R-squared 0.806
Notes: All variables except dummies are in logs.Standard errors in parentheses. Capital stock in1884 US dollars. Estimated on cross-section in1884 only.
