The author is indebted to Dennis Aigner, Ralph Andreano, Lau Christensen, Lance Davis, Donald Hester, Paul McGouldrick, Kenneth Smith and the students in Wisconsin's Seminar in American History for helpful comments.

¹ Davis, Lance E., “The New England Textile Mills and the Capital Markets: A Study of Industrial Borrowing, 1840–1860,” The Journal of, Economic History, XX (March 1960), 1–30CrossRefGoogle Scholar; “Stock Ownership in the Early New England Textile Industry,” Business History Review, XXXII (Summer 1958), 204–22.Google ScholarMcGouldrick, Paul F., New England Textiles in the Nineteenth Century: Profits and Investment (Cambridge: Harvard University Press, 1968).Google ScholarDavis, Lance E. and Stettler, H. Louis, “The New England Textile Industry, 1825–1860: Trends and Fluctuations,” in Output, Employment, and Productivity in the United States after 1800 (New York: National Bureau of Economic Research, 1966), 213–38.Google Scholar Robert B. Zevin, “The Use of a ‘Long Run’ Learning Function: With Application to a Massachusetts Cotton Textile Firm, 1823–1860” University of Chicago Workshop in Economie History (November 22, 1968), mimeo. Clayne Pope, “The Effect of the Ante-Bellum Tariff on Income Distribution,” Madison Cliometric Conference, Madison, Wisconsin (Spring 1970).

² Williamson, Jeffrey G., “Optimal Replacement of Capital Goods: The Early New England and British Textile Firm,” Journal of Political Economy, LXXIX (Nov./Dec. 1971), 1320–34CrossRefGoogle Scholar; D. L. Brito and Jeffrey G. Williamson, “Heterogeneous Labor Inputs and Nineteenth Century Anglo-American Managerial Behavior,” Social Systems Research Institute, EDIE 7104, The University of Wisconsin (April 1971).

³ David, Paul A., “Learning by Doing and Tariff Protection: A Reconsideration of the Case of the Ante-Bellum United States Cotton Textile Industry,” The Journal of Economic History, XXX (Sept. 1970), 521–601.CrossRefGoogle Scholar

⁴ The issues confronted in this paper deal with industry level sources-of-growth analysis and the associated problems of model specification. The economy-wide sources-of-growth analysis has even less to recommend it as currently practiced by economic historians and development economists. For a general equilibrium analysis of the sources-of-growth methodology applied to Meiji Japan see Kelley, Allen C. and Williamson, Jeffrey G.“Writing History Backwards: Meiji Japan Revisited,” The Journal of Economic History, XXXI (Dec. 1971), 729–76.CrossRefGoogle Scholar

⁵ Jorgenson, Dale W., “The Embodiment Hypothesis,” Journal of Political Economy, LXXIV (Feb. 1966), 1–17.CrossRefGoogle Scholar

⁶ David makes a similar assumption yet makes the estimation and interpretation unnecessarily complex by including intermediate inputs in the RHS throughout. Cotton costs were greater than 90 percent of the costs of all purchased materials and the Aldrich Report suggests stability in the cotton input coefficient between 1839 and 1884. Moreover, it was precisely because of this input output rigidity that short-run profit variability was so sensitive to the behavior of cotton prices. See McGouldrick, New England Textiles …, pp. 176 and 186.

⁷ Fellner, William, “Specific Interpretations of Learning-by-Doing,” Journal of Economic Theory, (Aug. 1969), 119–40.CrossRefGoogle Scholar

⁸ David, p. 585.

⁹ Davis and Stettler, p. 229.

¹⁰ What information we do have suggests considerable variation in δ(t) both in the short and long run. In the short run, replacement outlays tended to be heavily concentrated in periods of capacity expansion. (McGouldrick, New England Textiles…, p. 156). In the long run, enormous variability is observed at least in the Baker sample. The table following has R(t) = replacement expenditures and GI(t) = gross investment expenditures.

¹¹ David, Table 3, p. 565.

¹² The theoretical attacks are legion. Most recently, see Clemhout, S. and Wan, H. Y., “Learning-by-Doing and Infant Industry Protection,” Review of Economic Studies, XXXVII (Jan. 1970), 33–56.CrossRefGoogle Scholar

¹³ David, pp: 549 and 595, estimates ψ (1830–60) = −.0055, ψ (1833–39) = −.0042, and ψ (1855–59) = −.0067.

¹⁴ Lebergott, Stanley, Manpower in Economic Growth (New York: McGraw-Hill, 1964), Table 2–7, p. 70.Google Scholar

¹⁵ Let y' = In y(t), A' = In A, G'(t) = In G(t), and [Zθ(t)/L(t)]' = [InZθ(t)− In L (t)]. The embodiment model we fit is:

Estimation of all parameters with the exception of A′ are unbiased. In effect, Table 3 and 4 represent a search procedure implemented to find the maximum likelihood estimate of θ. Conditional on θ, the maximized likelihood function is (up to a constant)

where is the residual sum of squares computed from a regression of y'(t) on the other variables. Thus, minimizing will maximize Log L_max (θ). Since θ does not affect the dependent variable, minimizing σ²(θ) is equivalent to maximizing R²(θ). Confidence intervals can be constructed:

where Tables 3 and 4 exhibit how flat the log function is; e.g., varies little with relevant changes in θ. Thus, although we have made no attempt to do so, any reasonable confidence interval would encompass a very large range in θ s, including (presumably) θ <01 This interpretation was suggested by my colleague Dennis Aigner.

¹⁶ Estimates of effective rates of protection on consumer and capital goods 1824–1857 can be secured from the present author.