¹ For a clear statement of this proposition see Gallraan, Robert E., “Commodity Output, 1839-1899,” in National Bureau of Economic Research, Trends in the American Economy in the Nineteenth Century, Studies in Income and Wealth, vol. 24 (Princeton, 1960), p. 27.Google Scholar

² The assumed value of 0.6 is less than most econometric estimates of the income elasticity of demand for food during the late nineteenth century [ Williamson, Jeffrey G., Late Nineteenth-Century American Development: A General Equilibrium History (New York, 1974), p. 268Google Scholar ]. This tends to results in favor of the per capita income argument.

³ Lipsey, Robert E., Price arid Quantity Trends in the Foreign Trade of the United States (Princeton, 1963), pp. 154, 157Google Scholar; , Gallman, “Commodity Output, 1839-1899,” p. 43Google Scholar.

⁴ Shannon, Fred, The Farmer's Last Frontier (New York, 1966), p. 145Google Scholar; Buck, Solon J., The Agrarian Crusade: A Chronicle of the Farmer in Politics (New Haven, 1920), p. 101Google Scholar. See also Kuznets, Simon, Modern Economic Growth (New Haven, 1966), p. 155Google Scholar; , Gallman, “Commodity Output, 1839-1899,” p. 27Google Scholar; Faulkner, Harold Underwood, American Economic History, eighth ed. (New York, 1960), p. 383Google Scholar; and Danhof, Clarence, “Agriculture,” in Williamson, Harold F., ed., Growth of the American Economy, second ed. (New York, 1951), pp. 133–53Google Scholar.

⁵ , Williamson, American Development, pp. 179–83.Google Scholar

⁶ For an excellent review of the safety-valve theory debate see Nardroff, Ellen von, “The American Frontier as Safety Valve,” Agricultural History, 36 (July 1962), 123–42Google Scholar.

⁷ Of course this is only one of the possible interpretations of the safety-valve theory. Another concerns not labor distribution but wage rates. In this version the frontier increases real wages in the eastern cities. Although this approach is consistent with my interpretation, it also is less restrictive. For example, even if labor were not attracted from the cities by the frontier, the additional land could still increase real wage rates by lowering the price of agricultural goods.

⁸ , Lewis, “Explaining the Shift of Labor,” p. 117.Google Scholar

⁹ Throughout, “manufacturing,” “industry,” and “non-agriculture” are used interchangeably.

¹⁰ See Jones, Ronald W., “A Three-Factor Model in Theory, Trade and History,” in Trade, Balance of Payments and Growth, Papers in International Economics in Honor of Kindleberger, Charles P., Bhagwati, Jagdish N. et ai, eds., (Amsterdam, 1971), pp. 3–21Google Scholar. Because this model captures some important features of the economy, it has been applied to other problems in nineteenth-century American economic history. For example, Passell, Peter and Schmundt, Maria, “Pre-Civil War Land Policy and the Growth of Manufacturing,” Explorations in Economic History, 9 (Fall 1971), 35–38CrossRefGoogle Scholar; Pope, Clayne, “The Impact of the Ante Bellum Tariff on Income Distribution,” Explorations in Economic History, 9 (Summer 1972), 375–422Google Scholar.

¹¹ Griliches, Zvi, “Research Expenditure, Education and the Agricultural Production Function,” American Economic Review, 54 (Dec. 1964), 961–74Google Scholar; and Kelley, Allan C., Williamson, Jeffrey G., and Cheetham, Russell, Dualistic Economic Development (Chicago, 1972), p. 228Google Scholar.

¹² The results are not sensitive to this assumption (see Lewis, “Explaining the Shift of Labor,” Appendix D).

¹³ Since the labor force and population are assumed given, it is not necessary to express the demand curve in per capita terms.

¹⁴ The term preceding the brackets,

is a scale term affecting the magnitude, but not the sign, of the result. The factor and labor force shares included in the expression varied during the period, and in making the calculation mean values are chosen; however, even selecting the end points would not significantly affect the results. The value of the scale term lies between 1.00 and 1.07. The one used is 1.04.

¹⁵ Note that

where n' = compensated price elasticity of demand for manufactured output, E' = income elasticity of demand for manufactured output.

¹⁶ Houthakker, H. S., “An International Comparison of Household Expenditure Patterns, Commemorating the Centenary of Engel's Law,” Econometrica, 25 (Oct. 1957), 541–42CrossRefGoogle Scholar; Lewis, Frank, “The Relative Movement of Labor from Agriculture in Manufacturing in the United States: 1869-1899; A General Equilibrium Approach,” University of Rochester (March 1971)Google Scholar, unpublished; Schultz, Theodore W., The Economic Organization of Agriculture (New York, 1953), pp. 186–91Google Scholar; Tintner, Gerhard, “Multiple Regression for Systems of Equations,” Econometrica, 14 (June 1946)CrossRefGoogle Scholar; Williamson, Jeffrey G., “Consumer Behavior in the Nineteenth Century: Carroll D. Wright's Massachusetts Workers in 1875,” Explorations in Entrepreneurial History, 4 (1967), 116Google Scholar.

¹⁷ In cases 2 and 3, differences in the elasticities of supply of land and capital also contribute to the movement of labor from agriculture.

¹⁸ For the values of these exports and imports see , Lipsey, Price and Quantity Trends, pp. 154, 157.Google Scholar

¹⁹ It follows, of course, that under the open-economy assumption the results support the indirect safety-valve theory.

²⁰ The only instance in which this result does not hold is under the open-economy assumption where the supply curves of both land and capital are assumed perfectly inelastic.

²¹ If fact, if the decline in agricultural productivity were large enough, the United States could have become a net importer of farm products. This possibility is explored below.

²² Kendrick's productivity estimates are used in the analysis. The production function on which they are based is different from the Cobb-Douglas function assumed in the second section. It is linear rather than log-linear, contains an explicit capital estimate, and assumes different factor shares. Nevertheless, the function used in my model generates results that correspond quite closely to those of Kendrick. For the periods 1869-99, 1879-99, and 1889-99, the estimates are 30.0, 12.6, and 7.8 percent, respectively.

²³ Implicit in the model is a balance-of-payments constraint that requires (ignoring changes in re serves): Exports = Imports + Net Capital Outflows. In making the transition from an open to a closed economy, I assume that when exports fall to zero, imports do as well. This implies that net capital flows would also be zero. In 1899 there were net capital outflows of $229 million [Historical Statistics of the United States, Bicentennial Edition, Part I (Washington, D.C. 1975), p. 564]Google Scholar; however, in the absence of agricultural productivity growth it is likely that these flows would have been reduced. In addition, since net capital flows were relatively small throughout the late nineteenth century, it is not unreasonable to assume that imports would have equalled zero once exports fell to zero.

²⁴ It should be emphasized that the 6 percent hypothetical decline in productivity in 1899 does not imply negative productivity growth between 1869 and 1899. It implies instead that had productivity increased by 26.8 percent [1.268 = 1.353.(1 —.0629)] between 1869 and 1899 rather than by 35.3 percent, which was the actual increase, exports of farm products would have been reduced to zero.

²⁵ For the derivation of equation (16), see Lewis, “Explaining the Shift of Labor,” Appendix F.

²⁶ The reason the effect was smaller can be illustrated by casting the analysis in terms of the equivalent counterfactual proposition: suppose that there were no increase in agricultural productivity and no increase in the level of supply of land between 1879 and 1899. Since the hypothetical decline in agricultural productivity is more than sufficient to drive the economy onto the inelastic portion of the demand curve, the hypothetical reduction in the supply of land increases the farm labor force, thus offsetting the negative effect on farm employment of reduced agricultural exports.

²⁷ Throughout this paper I have assumed that the United States would not have imported those agricultural goods that were exported in 1899. This condition was satisfied since it merely requires that agricultural prices increase by less than twice the per-unit transport cost between the United States and Europe. For example, the cost of shipping wheat from New York to Liverpool in 1899 was 7.6 cents per bushel [U.S. Bureau of the Census, Statistical Abstract of the United States: 1899 (Washington, D.C., 1900), pp. 391Google Scholar, 392. This is the difference between the Chicago-to-Liverpool and the Chicago-to-New York freight rate]. Since the price of wheat in the United States was 71.1 cents per bushel (Historical Statistics p. 208), the required increase was 21.4 percent. Had there been no increase in agricultural productivity and no increase in the supply of land between 1869 and 1899, the price of agricultural goods would have increased by only 19.2 percent (Case 1 with e = 0.6 and TJ = 0.2).

²⁸ An early version of the model included a non-tradable service sector. This added much complexity but little explanatory power to the model.

²⁹ Throughout this paper, output in agriculture and industry is defined as value added. This avoids the problem pointed out by Fogel that agricultural output was used as an intermediate input in the production of some manufactured goods [Fogel, Robert W., “The Specification Problem in Economic History,” this Journal, 27 (Sept. 1967), 283–308]Google Scholar. My procedure requires, however, the selection of appropriate price and income elasticities of demand for value added in agriculture. I have based these values (0.2 to 0.4 for the price elasticity and 0.6 to 0.8 for the income elasticity) on econometric estimates of the demand for food and the demand for agricultural output (see footnote 16). The range of elasticities that is used encompasses most of those derived in both types of studies. There are, however, a few estimates of the elasticity of demand for food that are higher, but this does not pose a serious problem because the demand for food includes the demand for the manufacturing value added embodied in food products.