Earlier versions of this paper were presented at the Fourth Conference on the Application of Economic Theory and Quantitative Methods to Canadian Economic History, the Faculty Seminar at the University of British Columbia and the 1971 Cliometrics Conference. The analysis has been strengthened by comments of those present on these occasions.

¹ In the recent literature see, for example, Mansfield, Edwin, Industrial Research and Technological Innovation (New York: Norton, 1969)Google Scholar, particularly Part IV, and David Landes, “Technological Change and Development in Western Europe, 1750–1914,” in Postan, M. M. and Habakkuk, H. J. (eds.), Cambridge History of Europe, Volumè VI: The Industrial Revolution and After (Cambridge: University Press, 1965).Google Scholar

² A longer version of this paper including a more detailed discussion of the formal model is available as Discussion Paper No. 78, Department of Economics, University of British Columbia, May, 1972.Google Scholar

³ See data in Table 1. For a discussion of the shift from sail to steam see my article, “The Shift from Sailing Ships to Steamships, 1850–1890” in McCloskey, D. N., ed. Essays on a Mature Economy: Britain After 1840 (London: Methuen, 1971).Google Scholar

⁴ It should be apparent that, if the supply curve of British iron ships is perfectly elastic, certain econometric problems disappear. Price is determined exogenously to the supply curves of wooden shipbuilding and not simultaneously with demand conditions. Therefore, no problems of identification or simultaneous equation bias arise in the econometric estimation of the supply curves.

⁵ This calculation is the price dual of the more commonly employed Divisia index measure of productivity change that compares output quantify changes with weighted input quantity changes. See, for example, Jorgenson, Dale W.“The Embodiment Hypothesis,” Journal of Political Economy, LXXIV (Feb. 1966), p. 3. The data used in these calculations are presented in Appendix Table III.Google Scholar

⁶ The fitted regression equation was: Ln Index = −.05 +.009 Time, the F-ratio for the time coefficient was 93 and R² was.73.

⁷ These results have been calculated using continuous rates of change weighted by the appropriate share of the input in total costs (30-35 percent for iron and about 30 percent for wages). The price data are presented in Appendix Table III.

⁸ Under the well-known assumptions of homogeneity and neutrality of productivity change underlying use of Divisia indices to estimate productivity change it can be shown that between periods of long-run equilibruim

where the subscript q denotes output, x and y denote inputs, the notation denotes percentage changes on prices, the S denotes the ratio of expenditures on an input to value of sales and denotes the percentage shift of the production function. This expression has been used in this study under slightly different interpretations to estimate both the rate of productivity change and shifts of the supply curves. The estimate of productivity change () involves comparison of output price changes and input price changes actually observed in the industry between periods of longrun equilibrium. Estimates of the supply curve shift are estimates of the price change that would have occurred if quantity of output had remained unchanged. If quantity changed through time and input prices were influenced by the quantity demanded then the actual prices paid by the industry are inappropriate for this calculation. However, an appropriate solution suggests itself if the price of an input (say labor) to the industry is a function of the price of the input in the economy in general (an index of general wages) and the quantity demanded by the industry. Specifically, assume that:

where P_x is the price of x to the industry, X is the quantity used by the industry, and is the general price level of x (a = 1/elasticity of supply). It then follows that:

If industry output is constant, will equal zero if relative prices do not change and technology remains constant. For the analysis, therefore, the changes in levels of prices in the economy in general, rather than prices to the industry, have been used in calculating the shifts of the supply functions. Technological change was quite slow in wooden ship building (no more than ½ percent per year) and the elasticity of supply quite large. Both of these suggest the term was insignificant.

⁹ Data on ship prices and wages from the reports plus the prices of other inputs and the input shares reported in the Appendix have been used in estimating the rate of technological change. The following table summarizes the data from the reports. Unfortunately the data for the late 1850's in the Lynch Report refers to the indefinite period 1854/60 (see the circular letter sent by the Committee, Lynch Report, p. 185). The data used specifically refer to ships built in Maine.

Sources this table are: U.S. Congress, House, Report of the Select Committee on the Causes of the Reduction of American Tonnage, H. Rep. 28, 41st Cong., 2nd. Sess., 1870 (hereafter referred to as the Lynch Report), pp. 91, 130, 141–142, 195–197, 212–213; U.S. Bureau of the Census, “Report on die Shipbuilding Industry of the United States,” by Hall, Henry, Census Monographs, Tenth Census of the United States, Vol. VIII, 1882 (hereafter referred to as the Hall Report), pp. 96–105.Google Scholar

¹⁰ Alternative assumptions about changes in rates of return on capital yield a range of results between costs falling faster than ship prices and ship prices falling about 0.3 percent per year faster than weighted input prices.

¹¹ See Appendix Tables II-V for data on prices and cost shares use in these calculations.

¹² See Appendix Tables II-V for details of price movements.

¹³ Recall that the assumption of perfect elasticity in the supply of iron sailing ships implies that price is exogenous to the supply curves elsewhere. The regression results discussed below are presented in detail in Appendix A.

¹⁴ The regressions were estimated using a polynomial distributed lag (the actual formulation used is from Robinson, Sherman, Polynomial Approximation of Distributed Lag Structures, London School of Economics, Discussion Paper No. 1, June, 1970). The logarithmic specification of the supply curves and the explicit entry of the index of the levels of the supply curve as a divisor of price were necessary to achieve logical consistency between the estimated supply curves and the estimated supply curve shifts.Google Scholar

¹⁵ An essentially arbitrary but not unreasonable adjustment of allowing the American price to diverge from the British price in the late 1880's was attempted. The American price was allowed to increase at a rate of two percent per year relative to the British from 1886 to 1890. A regression using this price series had a slightly worse fit (R² =.67) and a somewhat greater estimated elasticity (3.86 rather than 3.48). The differences can hardly be deemed significant.

¹⁶ Hall Report, pp. 110–111, 116–118.

¹⁷ Ibid., p. 105.

¹⁸ McClelland, Peter, The New Brunswick Economy in the Nineteenth Century (unpublished Ph.D. dissertation, Harvard University, 1966), pp. 133–137, 156–157.Google Scholar

¹⁹ A regression of iron ship output on a second-degree polynomial distributed-lag of prices yielded no regression coefficients that were significantly different from zero to a five per cent level of significance. The F-ratio testing whether there is any significant relationship between output and all lagged prices considered was 3.11 with 2 and 23 degrees of freedom. This ratio is nowhere near being significantly different from zero. Results with higher degree polynomial lags were even worse. These results tend to support the hypothesis that iron sailing ship output was in fact, determined as the residual between total demand and the supply of wooden ships.

²⁰ Griliches, Zvi, “Hybrid Corn: An Exploration in the Economics of Technological Change,” Econometrica, XXV (October, 1957), pp. 501–522Google Scholar, and Mansfield, Edwin, The Economics of Technological Change (New York: W. W. Norton & Co., 1968)Google Scholar, Chapter IV, and Industrial Research and Technological Innovation: An Econometric Analysis (New York: W. W. Norton & Co., 1968)Google Scholar, Part IV. For a formal discussion of this type of function in a different context, see Lotka, Alfred J., Elements of Physical Biology (Baltimore: Williams and Wilkins Co., 1925)Google Scholar, Chapters VI and VII.

²¹ Griliches, “Hybrid Corn,” p. 503. Mansfield is never quite so explicit, but see Industrial Research, p. 137.

²² This, incidentally, is somewhat at variance with some of Mansfield's work. In his discussion of intrafirm diffusion of diesel locomotives, for example (Ibid., Chapter 9) he fits the logistic to the share of diesels in the total stock of locomotives and not to the share in new purchases. This appears to be inappropriate; it requires a more restrictive hypothesis yet provides a weaker test of the nypothesis. For the adjustment model to be appropriate for the stock of locomotives, diesels must not only have been better than steam as a new investment but must have been so superior as to justify the scrapping of the existing stock of steam locomotives (diesel has driven their quasi-rents below their scrap value). The test will be weaker because of a large over-hang from period to period. The stock could easily become more diesel in a year when no diesel were purchased, a large number of steam were purchased and an even larger number of old steam engines were scrapped. The fact that steam were purchased rather than diesel well along in the adjustment would be a very important fact with which to confront the hypothesis but looking at shares in the total stock would totally overlook this event. This example is by no means far-fetched; it happened several times in shipbuilding. Changes in the composition of a stock of capital goods are the result of two separate decisions: a decision about the composition of new additions and a decision regarding scrapping. In general, these decisions will be subject to different influences and should, if possible, be studied separately. The adjustment to technological change will clearly have its sharpest impact on the composition of addition to the stock.

²³ The logistic was fitted with a ceiling of 85 percent of the market using the fitting procedure used by Griliches, “Hybrid Com,” p. 504. The estimated share with the equilibrium model equals actual total iron ship equivalent output minus estimated wooden ship output divided by total actual output. British wooden ship output is estimated at zero after 1885.

For the period 1864–1890 the correlation between the logistic and the observed was 0.8 (R² =.65) and between the share of metal ships predicted by the supply curve based model and the observed, 0.83 (R² =.69). This test is almost certainly biased in favor of the logistic model since that estimate was made directly from the data on the observed share of metal ships.