Estimation of Economies of Scale in Nineteenth Century United States Manufacturing

Jeremy Atack

• Publisher: Routledge
• Year: 2018
• Print ISBN:
  9781138567191
• eBook ISBN:
  9781351342094
• Topic: Business
• Subtopic: Business General
• Index: Business

On economies of scale during the nineteenth century, much is assumed, but little is known. This study, first published in 1985, seeks to close this gap in our knowledge by providing comprehensive empirical evidence on the status of economies of scale in mid-nineteenth century manufacturing industry. This evidence is in the form of production function estimates made using data from the manuscripts of the federal censuses of manufacturing for 1850, 1860 and 1870.

CHAPTER 1

ON THE HISTORICAL SIGNIFICANCE OF ECONOMIES OF SCALE

On economies of scale during the nineteenth century, much is written and assumed, but little is known. My study seeks to close this gap in our knowledge by providing comprehensive empirical evidence on the status of economies of scale in mid-nineteenth century manufacturing industry. This evidence is in the form of production function estimates made using data from the manuscripts of the federal censuses of manufacturing for 1850, 1860, and 1870. This chapter summarizes the assumptions and evidence on scale economies and addresses some of the specific issues to be resolved with the results presented herein. Chapter 2 outlines the methods of estimation used to derive these. This is followed by a discussion of the data sources and of the problems that are encountered when using census data, especially published census data. The third chapter is therefore likely to be of more general interest. The remainder of the work analyzes and discusses the results.

I. The Role of Constant Returns to Scale in Current Historiography

Probably the most widespread assumption on scale economies in the nineteenth century is of their absence, that is, of the presence of constant returns to scale. No evidence is usually offered in support of this. It is merely asserted that it was so. This assumption is most characteristic of theoretical works where it is a necessary condition for perfect competition or where it is needed for proportionality.

Thus, this assumption plays an essential role in the debate over the effects of abundant land (or of labor scarcity) on American manufacturing and technology.¹ It is the assumption of homogeneity of degree one in the ² production function that permits Temin to conclude that given the capital-labor ratio, the interest rate is determined and vice versa,³ but this assumption is essential to all studies of labor (and capital) scarcity.

Constant returns to scale also figure prominently in model building exercises such as that by Williamson.⁴ In such models, perfect competition is a necessary condition for resource transfer between sectors and occupations and also to determine factor shares. Indeed, it was to find an empirical basis for income distribution that the Cobb-Douglas production function was first used.⁵

Neither the work on labor scarcity nor that on general equilibrium offers evidence in support of the assumption of constant returns to scale, although, if pressed on the point, the authors would probably cite contemporary evidence on scale economies in the twentieth century. The Walters’ survey for example reports the results of fourteen time series which may be “interpreted as confirmation that the aggregate production function has constant returns to scale.”⁶ Further Walters reports the results of a small number of inter-firm estimates of the production function, concluding that “evidence of constant returns to scale is quite strong.”⁷

More recent time series studies notably those by Brown and Popkin ⁸ and by Bodkin and Klein⁹ have shown significant increasing returns to scale. Although Brown and Popkin caution their estimates of economies of scale have an upward bias, their study shows significant increasing returns to scale for the period 1890–1918, constant or marginally decreasing returns in the period 1918–1935, and constant returns to scale for the period 1935–1958.¹⁰ Bodkin and Klein also found evidence of increasing returns to scale for the period 1909–1949.¹¹

Since the publication of the Walters’ survey the focus of cross-sectional and interindustry studies has shifted and it now concentrates on data from the 1958 Census of Manufactures. However, the results are inconclusive, largely as a result of differing estimation procedures and the measurement of the relevant variables. Both Hildebrand and Liu¹² and Griliches¹³ conclude that “there appear to be indications of definite, even if not particularly large, economies of scale in U.S. Manufacturing.”¹⁴ On the other hand, Besen,¹⁵ Ferguson¹⁶ and Moroney¹⁷ conclude that “on balance the hypothesis of constant returns to scale cannot be rejected.”¹⁸

II. Economies
of Scale in Current Historiography

None of the studies noted above uses data for a period earlier than 1880. Hitherto no study of mid-nineteenth century production functions has been made, despite the “availability” of the relevant micro-economic data in the Censuses of Manufacturing from 1850 onwards.¹⁹

A number of studies of economies of scale in agriculture have been made. None is satisfactory. Gray²⁰ and Dickey and Wilson²¹ used the survivor technique (the theory of which is described in Chapter 2 below, with results for U.S. manufacturing given in Chapter 10) to identify those size categories of farms that survived market forces and succeeded in increasing their share of value-added or total farm output.²² Unfortunately, the survivor principle in isolation neither provides a measure of the importance of economies of scale nor even a test for the existence of economies of scale.²³ In particular, we cannot conclude on the basis of Dickey and Wilson’s preliminary results that the optimum plantation sizes of at least 24 slaves in the Old South, 49 slaves in the black soil belt counties and 212 slaves in the alluvial counties are determined by production relationships embodied in the returns to scale parameter.

Fogel and Engerman in Time on the Cross²⁴ demonstrate the existence of modest increasing returns to scale in southern agriculture using the Parker-Gallman sample. Their results suggest that a ten percent increase in all factors of production employed would on average raise output by approximately 10.6 percent.²⁵ Despite this, however, Fogel and Engerman go on to assume constant returns to scale when they address the issue of the relative efficiency of southern agriculture because constant returns are necessary for the product exhaustion implicit in their approach.²⁶

In manufacturing industries, Walsh has laid great stress upon the role played by economies of scale in the development of manufacturing in six Wisconsin counties.²⁷ Thus, for example, “Racine did not have the necessary local urban market nor the labor threshold to develop economies of scale and high productivity in a variety of industries.”²⁸ While in flour milling “by the late 1850’s Racine mills were becoming less able to compete with the economies of scale practiced by their larger Milwaukee counterparts.”²⁹ In Milwaukee “shoe manufacturers were also notable because they were clearly benefiting from economies of scale. In 1860 the three leading firms had a value-added per worker of $932, in contrast to $365 per worker for forty-eight small firms.”³⁰ No empirical basis for these claims is offered.

The work by Paul David on learning by doing in the New England textile mills provides such an empirical basis.³¹ Indeed, the precise form of the micro-data used by David is very similar to that used in this study except that David had sufficient observations to run the time series production function estimates, not possible with census data. On the basis of this work, he concluded that “no support for tariff arguments grounded on the existence of significant scale effects can be found…it is seen that the estimated sums of exponents fall in the range between 0.76 and 0.88, well short of the unitary value indicated by the null hypothesis.”³² Despite this result though, David concludes that it is “quite impossible to reject the null hypothesis that there were constant returns to firm scale in this branch of the ante-bellum textile industry.”³³

One of the most fundamental and important statements of scale economies in nineteenth century manufacturing industry, however, concerns the position of southern manufacturing before the Civil War vis à vis industry in the North. I have called this the Russel-Linden-Genovese hypothesis after its most serious proponents and it is this that is to be the central focus of this dissertation.

III. The
Russel-Linden-Genovese Hypothesis

Of the many reasons advanced for the relative underdevelopment of southern manufacturing, few have been more pervasive or had a more lasting impact than that first advanced by Robert R. Russel who argued that:

Population was comparatively sparce in the South, distances were great, and means of transportation poor. The poorer whites afforded little demand for manufactured goods. Neither did the slaves, but the masters, who exploited their labor, presumable compensated for them in this regard. So markets were too dispersed and inadequate to encourage large-scale manufacturing.³⁴

This same argument was later stressed by Fabian Linden who wrote:

“The scattered unconcentrated quality of Southern industry handicapped it badly in competition with the North. To each establishment it meant concretely a relative increase in the cost of production. As J. H. Taylor, the treasurer of Graniteville, pointed out, a superintendent who received a salary of $12000 to $15000 (sic) a year could manage a mill of 12000 spindles as efficiently as one of 3000. …Consequently, New England mills, which were by 1860 more than twice the size of Southern factories, could produce cheaply enough to compete effectively with the cotton states in the home market.”³⁵ (as published)

However, its most eloquent expression is in the work of Eugene Genovese³⁶.

In the Genovese hypothesis:

The South was caught in a contradiction similar to that facing many underdeveloped countries today. On the one hand, it provided a market for outside industry. On the other hand, that very market was too small to sustain industry on a scale large enough to compete with outsiders who could...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• List of Tables
• List of Figures
• Preface
• 1. On the Historical Significance of Economies of Scale
• 2. On the Estimation of Economies of Scale
• 3. The Data and Tests of the Samples
• 4. The Econometric Interpretation of the Production Function Estimates
• 5. Production Conditions for Intra-Regionally Traded Commodities
• 6. Production Conditions for Inter-Regionally Traded Commodities
• 7. The Aggregate Regional Production Function
• 8. The Sensitivity of Returns to Scale to Units and Methods of Measurement
• 9. Some Evidence on Decreasing Scale Elasticity
• 10. The Survivor Technique and Optimal Plant Size
• 11. Conclusion
• Bibliography
• Appendix