This paper is an outgrowth of my study in Professor Paul Uselding's seminar in American Economic History at Johns Hopkins. My hearty thanks are due to him, for had it not been for his helpful comments and encouragement this paper would never have materialized. I am also very grateful to Professors Stanley Engerman, Nathan Rosenberg, and an anonymous referee for their valuable comments and criticisms on the earlier versions of this paper.

¹ David, Paul A., “Learning by Doing and Tariff Protection: A Reconsideration of the Case of the Ante-Bellum United States Cotton Textile Industry,” Journal of Economic History, XXX (September 1970), 521–601.CrossRefGoogle Scholar

² For further econometric discussion of Professor David's paper see Jeffrey G. Williamson, “Embodiment, Disembodiment, Learning by Doing, and Returns to Scale in Nineteenth Century Cotton Textiles,” and David, Paul A., “The Use and Abuse of Prior Information in Econometric History,” Journal of Economic History, XXXII (September 1972), 691–705Google Scholar and 706–727. The thrust of my argument, however, is not affected by either of the two papers above.

³ Confronted by the almost equal statistical performance of the two alternative hypotheses of learning by doing, the cumulated output and the cumulated time hypotheses, Professor David bases his choice of the latter on the following two major considerations (David, “Learning By Doing,” pp. 573–585). (i) In consideration of relatively strong imperfections (oligopsony) in the labor market, the real wages paid are expected to be less than the marginal physical product; thus the wage share should be less than the estimated output elasticity coefficient for labor. However, Zevin's finding that the two are almost identical for his sample firm (i.e., Blackstone Company) (around 0.41) under the cumulated output hypothesis implies a rejection of the cumulated output hypothesis. On the contrary, the estimated value of the output elasticity coefficient for labor under the cumulated time hypothesis is consistent with this “exploitation” interpretation. Furthermore, the estimated labor elasticity coefficients for the two different sets of sample data under the cumulated time hypothesis are “very close” (à la Professor David) to each other (0.66 and 0.59), which is as it should be since constant returns, to scale are observed statistically and that Blackstone Company and other sample firms are similar in character, (ii) While the estimated magnitude of the learning coefficient under the cumulated time hypothesis is reasonable—doubling of experience gives about 20 percent increase in productivity—the estimated magnitude of that under the cumulated output hypothesis is far smaller than the figure above suggested by past studies.

The following comments seem pertinent to Professor David's argument. First, we must admit the fact that there is no unanimity in the literature with regard to the existence of monopsony elements. (For instance, Paul M. McGouldrick argues that there may have been rather strong competitiveness in the labor market: see his New England Textiles in the Nineteenth Century: Profits and Investment, Cambridge, Massachusetts: Harvard University Press, 1968, pp. 34–8.Google Scholar) Even if we assume the existence of the monopsony elements, however, his argument that the similarity of the estimated elasticity coefficients for labor between the two sample bodies is another piece of strong evidence for the cumulated time hypothesis should be seriously qualified. In fact, the very test which Professor David reports in footnote 73 (p. 573)—to the effect that the output elasticity coefficients for labor for the two samples are not identical statistically—indicates that the two sample bodies do not come from the same population. His interpretation of this “inconvenient” result (sic, p. 573), namely, the attribution of the cause of this difference to the shift in the sampling intervals of the two sets of data, is not correct, for both statistical models assume that each time series consists of stochastically independent sample points; otherwise, his argument concerning the similarity of the estimated elasticity coefficients itself loses its meaning. (For a criticism of this assumption see footnote 13 below.) Professor David's second argument ((ii) above) is no more cogent than the first. This is because the particular magnitudes of learning coefficients observed for a particular industry during a particular period have nothing to do with those observed in others.

In view of the points discussed above, Professor David's choice of the cumulated time hypothesis over the cumulated output hypothesis is not persuasive. On the other hand, the study of Professor Williamson (referred to above) also fails to provide cogent grounds for his choice of the cumulated output hypothesis. We are thus left with the two production models with the productivity growth largely explained by the two learning indexes whose correlation coefficient is 0.999 (David, “Learning By Doing,” p. 574, footnote 76).

⁴ The notion of second best used here concurs with Professor David's usage on page 528, which refers to the discussion of optimal intervention against domestic distortions. Cf. Bhagwati, Jagdish and Ramaswami, V. K., “Domestic Distortions, Tariffs, and the Theory of Optimal Subsidy,” Journal of Political Economy, LXXI (February 1963), 44–50CrossRefGoogle Scholar; Harry G. Johnson, “Optimal Trade Intervention in the Presence of Domestic Distortions,” in Baldwin, Robert, et al., Trade, Growth and Balance of Payments (Amsterdam: North Holland, 1965)Google Scholar. These authors have noted that in the presence of domestic distortions tariff policy may not be the optimal mode of intervention; but it may nonetheless help to rectify the distortion partially if not completely. In this very sense I use the word second best and I shall thus discuss the effectiveness of the tariff policy in this weak sense only.

⁵ As will be discussed further below, Professor David regards firms and not mills (plants) as unit learning entities. Thus the production function (1) is defined at the firm level basically, although in the empirical part he applies it to the aggregation of firms.

⁶ In the case where know-how is specific to, a firm, .no justifiable grounds for protection exist so long as (a) accumulation of specific knowledge is the only learning by doing effect, (b) firms can correctly foresee such effects, and (c) the capital market is perfect (David, “Learning By Doing,” pp. 529–30). For further theoretical discussion of this case, see Rosen, Sherwin, “Learning by Experience as Joint Production,” Quarterly Journal of Economics, LXXXVI (August 1972), 366–82CrossRefGoogle Scholar. For the historical relevance of “perfection” in the capital market, see David, “Learning By Doing,” p. 535.

⁷ Later (see the quotation from David, page 586 below) Professor David adds imitation as another means of transmission. There is the following rather subtle point to note: Discovery of new knowledge is made by technical-managerial cadre, but the information thus acquired is embodied in the production routines and institutional arrangements of firms and mills. This implies, first, that know-how once embodied in firms and mills will remain in place even if the technicians or managers who discovered or introduced it originally might leave the firms or mills in question; in other words, they cannot appropriate material ownership rights to this new information. Contrast this case with the case of ordinary workers in which skill leaves the firms with the departure of workers. Thus, insofar as transmission of information is concerned, technicians and managers function only as mediators (or more appropriately catalyzers) of the transmission process. This point, however, does not preclude the possibility that managers and technicians are remunerated for the knowledge they transmit and are also charged the cost of learning and training. In such cases no externalities are involved, and the logic of David (page 530, footnote 17) applies. The main source of externality, however, as we shall indicate below, lies in the production of new information. Another implication is that the information thus acquired is susceptible to imitation by others. The preceding interpretation makes his assumption of irreversibility of “learning” consistent with nis notion that know-how is carried around by technicians and managers among the firms. And indeed, if there is no permanent obstacle to the transmission of knowledge and also if there is no further discovery of new knowledge, then the level of know-how (N) of each firm which survives in the industry will after a certain time lag be equalized perfectly.

⁸ In this connection Professor David's terms “average practice” and “best practice” seemingly following the usage of Anne P. Gross, The Technological Structure of the Cotton Textile Industry,” pp. 360–420, especially pp. 402–420, in Leontief, Wassily, Studies in the Structure of the American Economy (New York: Oxford University Press, 1953)Google Scholar are by no means clearly defined concepts. Here we interpret the distinction between them to reflect differences in the amount and content of technical and managerial know-how, assuming that the forementioned technicians arid organizers' optimization procedures—the process to reach the efficient frontier—is achieved sufficiently rapidly so that what we are comparing are, in fact, the positions of two efficient frontiers.

⁹ I am grateful to Professor Stanley Engerman for questioning whether we should regard the pilot firm or the pilot plant as the relevant unit or learning. The consideration of this question led me to the point raised here.

¹⁰ “There is no gain in acquiring the same information twice,” p. 30 in Arrow, Kenneth J., “Classificatory Notes on the Production and Transmission of Technological Knowledge,” American Economic Review, Papers and Proceedings, LIX (May 1969), 29–33.Google Scholar

¹¹ For a closely related discussion, see Smith, Adam, The Wealth of Nations, Second edition (Oxford: Clarendon Press, 1880), Book I, pp. 10–11.Google Scholar

¹² Thus, so far as discovery of new information is concerned, the cumulated output measure of firms or mills seems to have much more relevance than the cumulated time measure. The passage of Zevin as quoted by Professor David (David, “Learning By Doing,” p. 543) also fails to provide a sufficiently cogent argument for the relevance of the cumulated time measure. Zevin's logic (in the last sentence of the quoted passage) applies mostly to the transmission process of already acquired information but not to the discovery of new information itself.

¹³ On page 562 Professor David writes:

“And if, as therefore seems most probable, efficiency gains largely reflected changes in best-practice methods that spread rapidly among this collection of mills, it is also reasonable to think that a substantial number of those improvements derived from the experience being acquired by these leading firms, rather than from ‘learning’ that was taking place elsewhere in a less progressive segment of the industry.”

He gives no substantial evidence for his assertion. Confirmation of his statement requires detailed historical studies concerning the relationship between innovative capacities of firms or plants and the measure of “leadingness” such as the size of a firm or that of a plant. For some evidence to the effect that innovations do not necessarily come from leading firms, see Gibb, George S., The Saco-Lowell Shops, Textile Machinery Building in New England 1813–1949 (Cambridge, Massachusetts: Harvard University Press, 1950), pp. 14CrossRefGoogle Scholar, acquired by these leading firms, rather than from 40, 76–77, and 192, especially pp. 76–7 where he concludes:

“Between 1825 and 1845, American textile machinery was immeasurably improved. Many inventions or adaptations of great value and universal application were made. The strange fact about these inventions is, however, that few of them originated in Lowell, in this period the greatest textile-manufacturing center in the country.”

and:

“The fact remains that in this period many new machines equal or superior to those developed earlier at Waltham were being built by machine shops outside Lowell—and even outside New England.”

Even if, contrary to Gibb's remark, it generally turns out that the probability distribution of discovery of new information per experience unit is favorably biased for the more advanced firms, this mere fact does not imply that the “average-practice” firms need not be protected unless the latter's probability distribution is close to nil. Moreover, the same fact by no means discredits the innovative efficiency of multiplant operations.

Somewhat related to the preceding argument is Professor David's proposition: “… the acquisition of further experience in the industry through multiplication of the number of similarly situated firms proved less effective in reducing costs than an equivalent rate of addition in the years of experience of a small cadre of pioneer, or ‘pilot enterprise.’” (David, “Learning By Doing,” pp. 585–6) His proposed evidence to the effect that the learning coefficient for a single Blackstone firm is larger than that for a six-firms aggregate, even though possible aggregation bias is taken into account (ibid., pp. 586–591), seems superficial and also logically unsatisfactory. (Here I shall grant, for the sake of argument, the relevance of the cumulated time hypothesis—note that in the case of the cumulated output hypothesis, there is little difference between the estimated learning coefficients for two sample bodies. See ibid., p. 565, Table 3). This is because the two sample bodies can hardly be regarded as isolated from each other, and, hence, the two “learning” processes cannot be regarded as independent of each other. In fact, it is conceivable that the Blackstone firm might have required the experience of the six firms as an essential step in acquiring new knowledge. In such a case comparison of two learning coefficients on the assumption that the two are based on independent experiments cannot be justified.

¹⁴ In general we may suppose that the production function is given by

where [K], [L], [M] represent various vintages of capital, labor and material, and where N and τ represent the level of know-how and the exogenous technical progress factor. We can then suppose learning by doing generates embodied technical changes in labor and material, say, Processes L and M, as well as in capital goods, Process K, as suggested in the text.

However, first, the changes in the quality of materials are conditioned largely by factors outside textile mills and therefore we may leave the Process M outside the scope of the present consideration. Second, before the arrival of immigrant workers the character of labor force (especially in Massachusetts mills) was temporary, and in a way, the industry was constantly engaged in the training of newcomers. For instance, Ware, Caroline F. in her The Early New England Cotton Manufactures (Boston and New York: Houghton Mifflin Co., 1931)Google Scholar acquired by these leading firms, rather than from, summarily states: “The result was a large body of unskilled labor continually drifting into mills, forming a stream of fresh, vigorous country workers rather than a permanent worker class.” (page 13) See also pp. 64–5 arid 224–6; Appleton, Nathan, Introduction of the Power Loom, and Origin of Lowell (Lowell, Massachusetts: 1858), p. 15;Google Scholar acquired by these leading firms, rather than from and Batchelder, Samuel, Introduction and Early Progress of the Cotton Manufactures in the United States (Boston: Little, Brown and Co., 1863), p; 89Google Scholar. acquired by these leading firms, rather than from Therefore, the skills, if any, acquired and embodied in laborers did not remain permanently within the industry. Furthermore, although the revolutionary change in the labor composition did establish a permanent work force (Ware, Cotton Manufactures, pp. 228–30), the generally unskilled nature of the operatives' work leads us to surmise that the Process L, if not totally irrelevant, was not very significant. These are the reasons why we concentrate our attention, on the Process K.

We also note at this point that the fact that the two forms of technical progress—embodied and disembodied—are impossible to distinguish empirically (because the total productivity index and the price index of investment goods which is supposed to reflect the quality of new capital goods are in dual relationship so that either one can be transformed into the other—Jorgenson's theorem—and, therefore, the two production functions (1) and (2) are empirically not distinguishable, is not relevant since we are here concerned only with the conceptualization of technical change. Cf. Jorgenson, Dale W., “The Embodiment Hypothesis,” Journal of Political Economy, LXXIV (February 1966), 1–17CrossRefGoogle Scholar

¹⁵ Professor David does not see this possibility of direct linkage between the two sectors in his discussion on pp. 532–4.

¹⁶ David, “Learning By Doing,” p. 534. There also was a development of independent textile machinery shops such as Saco-Lowell machinery works and these specialized shops gradually dominated the machinery field. See Gibb, The Saco-Lowell Shops, pp. 21–2.

¹⁷ In his discussion of the “price effects” and the “income effects” of tariffs on machinery production, Professor David seems to forget that the demand for machines should be regarded as a derived demand. Thus when the tariff raises the price of textile products, the direct effect is to raise the rental price of machines, resulting in expansion of machine production—contrary to Professor David's assertion. Note that this picture is not affected by the fact that the firms concerned built their machinery in their own machine shop.

¹⁸ The conditions raised here are a part—albeit an important part—of the necessary conditions for the justification of tariffs. Full justification further requires, on the one hand, that the real cost of discovery through learning is not significantly large (cf. Baldwin, Robert, “The Case Against Infant-Industry Tariff Protection,” Journal of Political Economy, LXXVII (May/June 1969), 295–305)CrossRefGoogle Scholar, and, on the other hand, that the textile industry during the period concerned deserves more protection than other industries—a broader question than the ones dealt with in this note. Our discussion so far assumes implicitly that there exists no significant distortion as caused by the similar learning by doing effect or other factors in any other part of the economy. On this point see David, p. 531 and the literature referred to in his footnote 99. I am again indebted to Professor Ehgerman for stressing this point.

¹⁹ For some suggestive remarks as to the condition (ii), see footnote 13 above. Somewhat related to the condition (i) is the study made by Schmookler about the relationship between the magnitude of production and that of invention in the railroad industry. See Schmookler, Jacob, Invention and Economic Growth (Cambridge, Massachusetts: Harvard University Press, 1967)Google Scholar, Chapters IV, V and VI. Schmookler provides an alternative or, more appropriately, a complementary explanation to ours, namely that inventions are conditioned by inventors' consideration of profitability as reflected in the size of the market or output, to the observed positive correlation between these two variables.

The condition (iii) may be regarded as having been satisfied. Among all categories of workers especially machine workers wandered among firms in order to accumulate experience and obtain the best remunerative opportunity. This tendency was strong enough that it is recorded, for instance, that Lowell mills attempted to make a reciprocal arrangement to issue a “discharge certificate,” conditioning members not to employ workers without certificate, which was issued to those employees who left the mills for reasons deemed “fair and adequate” by the former employers. It is also recorded, however, that this system apparently did not work well (Gibb, The Saco-Lowell Shops, p. 88). See also Ware, Cotton Manufactures, pp. 207–8, and David, “Learning By Doing,” pp. 537–8.

²⁰ Gibb, The Saco-Lowell Shops, p. 173 writes:

“Before 1830 the incidence of revolutionary inventions was particularly high. After this time progress was less spectacular and, with important exceptions such as the self-acting mule and the ring spinning frame, manifested itself in the form of innumerable improvements of existing machine types. The cumulative effect of these improvements over the next two decades, however, was probably as profound as that produced by the sweeping changes of Paul Moody's day…. These innovations and improvements were the work not of scientists but of practical mechanics, working by trial-and-error methods.”

See also Davis, L. E. and Stettler, H. L., “The New England Textile Industry, 1825–60: Trends and Fluctuations,” in Output, Employment and Productivity in the United States After 1800, Studies in Income and Wealth Series, Vol. 30, N.B.E.R., 1966, p. 230Google Scholar, whose passage is quoted by David on page 527.

²¹ For the process and implications of this change, see Thernstrom, Stephan, Poverty and Progress (Cambridge, Mass.: Harvard University Press, 1964)Google Scholar, Chapter 1, and Ware, Cotton Manufactures, pp. 109, 228–235.

²² Gibb notes “the recalcitrant attitude of certain groups of foreign skilled laborers” as an important stimulant to the introduction of automatic textile machinery (The Saco-Lowell Shops, p. 173). McGouldrick, on the other hand, suggests the following explanation to his finding that the period 1839–55 exhibited an increase in the capital/labor ratio: that is, in order to maintain work efficiency in the face of less qualified immigrant workers, various processes had to be broken down into simpler components that required more capital goods per man than before (McGouldrick, New England Textiles, p. 39).

²³ See Davis and Stettler, “The New England Textile Industry,” and the comment made by McGouldrick (Paul F. McGouldrick, “Comment” in Output, Employment and Productivity in the United States After 1800, p. 240).

²⁴ This possibility is in fact incorporated as an assumption into various economic growth models with embodied technical change. E.g., Kenneth J. Arrow, “The Economic Implications of Learning by Doing,” and Solow, Robert M., “Substitution and Fixed Proportions in the Theory of Capital,” Review of Economic Studies, XXIX (June 1962), 155–173Google Scholar, 207–218.

²⁵ Ware records the report of an experiment performed by a manufacturer of the time showing very high work efficiency of women machine operatives who are recruited from the country farms. Ware, Cotton Manufactures, p. 201. See also p. 232.