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Changes in the productive efficiency of U.S. flour mills in the late nineteenth century: an input-distance-function approach

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Abstract

The productive efficiency of the U.S. flour milling industry increased substantially between 1850 and 1880. Specifically, a typical flour mill in 1880 was able to produce the same value of output as a mill in 1850 with 25 percent fewer factor inputs. We use the concept of the cone technology, combined with an input-distance-function approach, to decompose this increase in productive efficiency into changes in technical efficiency, technological progress, and changes in scale efficiency, assuming unchanged allocative efficiency in combining inputs. We find that the average technical efficiency of flour mills was essentially constant throughout the period, implying that almost all the gains in productive efficiency were due to improvements in scale efficiency occasioned by more fully exploiting increasing returns. Furthermore, productive efficiency was positively related to mill size as larger mills were better able to take advantage of both economies of scale and technological progress. These results provide evidence in support of an important role for the increased scale of production in providing the preconditions for the emergence in the early twentieth century of an oligopolistic market structure in the U.S. flour milling industry.

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Data availability

The data for this paper are available from the corresponding author at warren@uga.edu.

Code availability

The code for this paper is available from the corresponding author at warren@uga.edu.

Notes

  1. These were factory farms that were sponsored by, or operated in cooperation with, railroad interests (Saloutos 1946, pp. 173–174).

  2. For a detailed discussion of the efficiency-structure hypothesis, see Molyneux and Forbes (1995).

  3. In smaller custom mills, there was no wheat cleaning or flour bolting. These two steps were completed separately at home.

  4. For a discussion of the nutritional value of wheat flour, see Chick (1958).

  5. It was well-known at the time that spring wheat flour produced 12 percent more bread than did a comparable amount of winter wheat flour.

  6. By the linear homogeneity of D(x, yA/τ) in x and letting γ = 1/τ, productive inefficiency can be expressed as DPE(x, y) = D(γ*x, γ*y), where γ* maximizes D(γx, γy); see Rasmussen (2010, p. 343).

  7. These criteria resulted in the exclusion of 22, 16, 30, and 31 observations in 1850, 1860, 1870, and 1880, respectively.

  8. The use of a time trend to model technological progress has been the norm since Tinbergen (1942), although other methods have been introduced. Baltagi and Griffin (1988) summarize the literature on this issue.

  9. Among other possible distributional assumptions about u are the half-normal, truncated-normal, and Student’s t-half-normal distributions. See, respectively, Aigner, et al. (1977), Stevenson (1980), and Wheat et al. (2019). However, any distributional assumption about u is ad hoc, as Sickles and Zelenyuk (2019, p. 366) point out. Alternatively, u could be treated as a parameter to be estimated, as in Atkinson and Cornwell (1994).

  10. For example, eighteen of the twenty mills in Minneapolis in 1876 were members of an organized oligopsony known as the Minneapolis Millers’ Association.

  11. See Färe, et al. (1988, p. 724, eq. 3.3). Atkinson and Primont (2002, p. 208) refer to ε as a measure of the returns to scale for the shadow distance function (RTSSD), and Rasmussen (2010, p. 344) terms ε the input-based elasticity of scale (EOS).

  12. We verified the (local) concavity of output with respect to the inputs by confirming the negative definiteness of the Hessian matrix of the input distance function, evaluated at the sample means.

  13. Unfortunately, data on individual mills from the 1890 Census of Manufactures were destroyed in 1921 in a fire at the Commerce Building in Washington, DC.

  14. Among smaller mills (those with five or fewer employees), the average technical efficiency of a water-powered mill was 0.880, while that of a steam-powered mill was 0.870.

  15. Notable in this regard were two mills in St. Louis, MO, one mill in Lee Co., IL, and one mill in Harrisburg, PA.

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Acknowledgements

We gratefully acknowledge the contributions of the late Fred Bateman to the early stages of this project. Jeremy Atack, Sergio Destefanis, four anonymous referees, and an associate editor provided very helpful comments on earlier versions of this paper. Responsibility for errors and omissions is ours alone.

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  1. Department of Economics and Finance, Mike Cottrell College of Business, University of North Georgia, 1201 Bishop Farms Pkwy., Watkinsville, GA, 30677, USA

    Yongseung Han

  2. Department of Economics, Terry College of Business, University of Georgia, 600 S. Lumpkin St., Athens, GA, 30602, USA

    Arthur Snow & Ronald S. Warren Jr

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  1. Yongseung Han
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Han, Y., Snow, A. & Warren, R.S. Changes in the productive efficiency of U.S. flour mills in the late nineteenth century: an input-distance-function approach. J Prod Anal 56, 115–132 (2021). https://doi.org/10.1007/s11123-021-00615-y

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