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The Growth of Real Product in the United States Before 1840: New Evidence, Controlled Conjectures

Published online by Cambridge University Press:  03 February 2011

Paul A. David
Paul A. David
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Stanford University
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Scholarly opinion currently evinces disturbing symptoms of latent schizophrenia on the subject of economic growth in the ante-bellum United States. Virtually every student of the era now appears convinced that the long-term rate of growth of aggregate product per capita underwent a significant acceleration “somewhere during the period between 1815 and 1860,” as Douglass North recently phrased it. And, if many economic historians protest W. W. Rostow's labeling the years following 1843 as the period of the U.S. “take-off,” most do not seem to balk at accepting the guess hazarded by Raymond Goldsmith: “a fairly sharp break in the trend of real national product per head … occurred not very long before 1839,” quite probably during the 1830's. To the uninitiated, it might seem obvious that everybody also subscribes to an explicit set of assertions about the secular rate of growth of per capita product during the period from, say, the founding of the nation to the date of the putative acceleration; otherwise, how could all agree that a significant alteration in the trend had occurred?

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The Journal of Economic History , Volume 27 , Issue 2 , June 1967 , pp. 151 - 197
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Copyright © The Economic History Association 1967

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References

1 North, Douglass C., Growth and Welfare in the American Past, A New Economic History (Englewood Cliffs, N.J.: Prentice-Hall, 1966), p. 75.Google Scholar

2 Rostow, W. W., The Stages of Economic Growth (Cambridge, [Eng.]: The University Press, 1960).Google Scholar For criticism of Rostow's dating of the U.S. “take-off,” 1843-1860, and of the criteria on which that dating is based, North, cf., Growth and Welfare, pp. 85–89Google Scholar ; Fogel, Robert W., Railroads and American Economic Growth: Essays in Econometric History (Baltimore: The Johns Hopkins Press, 1964), pp. 111–29Google Scholar.

3 Goldsmith, Raymond W., Hearings Before the Joint Economic Committee, U.S. 86th Congress, First Session, Part 11–Historical and Comparative Rates of Production, Productivity and Prices (04. 7, 1959), pp. 277–78.Google Scholar

4 Parker, William N. and Wnartenby, Franklee, “The Growth of Output Before 1840,” in Trends in the American Economy in the Nineteenth Century, Studies in Income and Wealth, National Bureau of Economic Research, Vol. 24 (Princeton: Princeton University Press, 1960), p. 191.Google Scholar

5 Martin, Robert F., National Income in the United States, 1799-1938, National Industrial Conference Board Studies: No. 241 (New York: N.I.C.B. 1939), pp. 1–15.Google Scholar

6 Simon, Cf.Kuznets, S., “Long-Term Changes in the National Income of the United States of America Since 1870”: Appendix-“Current National Income Estimates for the Period Prior to 1870,” in Kuznets, Simon S., ed., Income and Wealth of the United States, Trends and Structures (Cambridge, [Eng.”: Bowes and Bowes, 1952), pp. 221–41.Google Scholar

7 Cf. Parker and Whartenby, “Growth of Output,” pp. 191-212.

8 Cf. Parker and Whartenby, “Growth of Output,” pp. 191-212.

9 Parker and Whartenby, “Growth of Output,” p. 211.

10 North, Douglass C., “Early National Income Estimates of the United States,” Economic Development and Cultural Change, IX (04. 1961), 387–96Google Scholar ; , cf. also North, Growth and Welfare, pp. 64–74Google Scholar.

11 Taylor, George R., “American Economic Growth Before 1840: An Exploratory Essay,” The Journal of Economic History, XXIV (12. 1964), 427–44.CrossRefGoogle Scholar

12 North, “Early National Income Estimates,” p. 387.

13 Taylor, “American Economic Growth,” p. 440.

14 The following statements are based on the estimates presented in Table 8, and the derived growth rates shown in Table 1.

15 , Cf., e.g., Moses Abramovitz, Statement in Hearings Before the Joint Economic Committee, U.S. 86th Congress, First Session, Part 2, Historical and Comparative Rates … (04. 7, 1959), pp. 411–66Google Scholar , and “The Nature and Significance of Kuznets Cycles,” Economic Development and Cultural Change, IX (04. 1961), 225–48Google Scholar.

16 Douglass, Cf.North, C., The Economic Growth of the United States, 1790-1860 (Englewood Cliffs, N.J.: Prentice-Hall, 1961), pp. 53, 190, 204.Google Scholar

17 Cf., e.g., Fishlow, Albert, American Railroads and the Transformation of the Ante-Bellum Economy (Cambridge: Harvard University Press, 1965), chs. iii, iv; Fogel, Railroads, ch. iv; North, Growth and Welfare, pp. 85-89.Google Scholar

18 Gallman, Robert E., “Gross National Product in the United States, 1834-1909,” Output, Employment, and Productivity in the United States After 1800, Studies in Income and Wealth, National Bureau of Economic Research, Vol. 30 (New York: Columbia University Press, 1966), pp. 3–76.Google Scholar

19 The term “conjectural estimates” is employed to preserve the distinction between figures which are in the nature of predictions, such as those developed here, and statistical estimates of aggregate production that are obtained directly by preparing estimates of the constant dollar values of the individul items in the flow of goods and services entering final demand, or of the constituent elements of gross product originating in the various sectors of the economy. As a practical matter, the principal difference between conjectural and direct historical estimates of aggregate output lies in the opportunities the latter afford for internal consistency checks.

20 Trends in the American Economy in the Nineteenth Century, Studies in Income and Wealth, National Bureau of Economic Research, Vol. 24 (Princeton: Princeton University Press, 1960Google Scholar ); and Output, Employment, and Productivity in the United States After 1800, Studies in Income and Wealth, National Bureau of Economic Research, Vol. 30 (New York: Columbia University Press, 1966Google Scholar ) are now standard items on the economic historian's shelf and are referred to hereafter simply as NBER Vol. 24 and NBER Vol. 30, respectively.

21 This should not, however, be taken to mean that the revised labor force estimates (Appendix Table I) are not crucial for the central argument developed here.

22 The simplest case is that of a two-sector, fixed technical coefficients model, with equal (zero or nonzero) rates of intrasectoral labor efficiency growth in both sectors. On the problems of measuring the effects of intersectoral shifts on average labor productivity, cf. , Kuznets, “Long-Term Changes,” pp. 123–26Google Scholar ; Gallman, Robert E., “Commodity Output, 1838-1899” (NBER Vol. 24), pp. 33–34;Google ScholarDenison, Edward F., “Improved Allocation of Labor as a Source of Higher European Growth Rates,” in Brennan, Michael J., ed., Patterns of Market Behavior: Essays in Honor of Philip Taft (Providence, R.I.: Brown University Press, 1965), pp. 65–88Google Scholar.

23 The selection of real gross domestic product (not GNP) as the measure of aggregate output is discussed below, as are the implications of some of the assumptions underlying the specification of the prediction equation.

Estimates of per capita real output (V/P), identical to those implied by the general specification given in the text, can be computed on the following more restrictive assumptions: (1) the ratio of agricultural output per worker TTA, to nonfarm output per worker, πN, remains constant through time; (2) since ( is a fixed parameter, the average intrasectoral labor productivity trend is identical to the trend of output per worker in either of the sectors, i.e., assumption.

Define real GDP per capita as (V/P) = v; the farm labor force as a proportion of the total labor force as sA; the ratio of the total labor force to the population as p. For any given date, we may then write the identity,

And, since it is assumed that , for all dates, the desired index may be computed from:

given observations of the variables ρ, πA, and sA.

24 Cf., e.g., Grunfeld, Yehuda and Griliches, Zvi, “Is Aggregation Necessarily Bad?,” Review of Economics and Statistics, XLII (02. 1960), 1–13.Google Scholar

25 Cf. Gallman, “Gross National Product,” (NBER Vol. 30), especially pp. 52, 54-55, 57, 62.

26 Cf. Kuznets, “Long-Term Changes,” pp. 224-26.

27 Stanley Lebergott, “Labor Force and Employment, 1800-1960” (NBER Vol. 30), pp. 117-204. Cf. Appendix Table I for the underlying labor force estimates.

28 The implications of relying on other estimates may be gauged from the alternative labor participation rate figures in Table 3, and the alternative farm labor share data in Table 4. A full account of the inconsistencies found in Lebergott's estimates, and a description of the revisions (leading to the sectoral totals presented here in Appendix Table I) has been set forth in a technical appendix to this paper. Pending publication elsewhere, this technical appendix–Research Memorandum 53-A, Stanford Research Center in Economic Growth (Dec. 1966), mimeographed, 33 pp. can be obtained from the author upon request.

29 Cf. Lebergott, “Labor Force and Employment” (NBER Vol. 30), pp. 139-46, and P. A. David, Stanford Research Center in Economic Growth Memo. 53-A, pp. 1-7, for discussion of the participation rates of slaves and free persons, which underiy the present labor force estimates.

30 Cf. U.S. Bureau of the Census, Historical Statistics of the United States, Colonial Times to 1957 (Washington, D.C.: U.S. Government Printing Office, 1960), hereinafter cited as U.S. Historical Statistics (1960), Series A 95-122, p. 11–12. The ratios of slaves to the total population in 1800, 1840, and 1860, were, respectively: 0.1694, 0.1450, and 0.1225.Google Scholar

31 Cf. ibid., p. 9, Series A 47, A 71-85. The proportion of the U.S. white population below age 10–i.e., the “dependent population” cited in the text–was 0.346 in 1800, 0.323 in 1840, and 0.284 in 1860. Yasuba, Cf. Yasukichi, Birth Rates of the White Population in the United States, 1800-1860, The Johns Hopkins University Studies in Historical and Political Science, Series LXXIX, II (Baltimore: The Johns Hopkins Press, 1961Google Scholar ), on fertility changes before 1860. On the rising importance of immigration as a source of U.S. population growth during the ante-bellum period, cf., J. Potter, "“he Growth of Population in America, 1700-1860,” in D. V. Glass and D. C. Eversley, eds., Population in History (Chicago: Aldine Press, 1965).

32 Note from Table 4 that according to Lebergott's estimates, as well as the figures presently used, the share of the labor force engaged in farming declined by slightly more than 20 percentage points between 1810 and 1840. Kuznets' data (given in Table 4), based on simple extrapolations for the years before 1820, indicated only a 3 percentage point shrinkage in the farm sector's share of the labor force during the same three decades.

33 Hutcheson, Cf. Harold, Tench Coxe: A Study in American Economic Development (Baltimore: The Johns Hopkins Press, 1938), p. 79Google Scholar ; Main, Jackson Turner, The Social Structure of Revolutionary America (Princeton: Princeton University Press, 1965), p. 67.CrossRefGoogle Scholar Main concludes: “One out of ten whites was an artisan, and [there was] a scattering of other men–shopkeepers, inn-keepers officials, some professional men and the like …” (Emphasis mine.) Following the same general procedure described in the technical appendix, I have made speculative estimates of the size of the U.S. labor force c. 1790. The total labor force is 1,263,000; of that, 408,000 are estimated to have been slaves, 387,500 of whom were engaged in agriculture. If one assumes that 90 per cent of the total labor force was engaged in agriculture, the implied proportion of the free labor force in farming works out at 0.876, a figure not inconsistent with Main's conclusion cited above. The over-all participation rate implied by my speculative estimate for 1790 is 0.321, which may be compared with the participation rate for 1800 in Table 3. (Details of these estimates for 1790 are available on request.)

34 Estimates of U.S. employment in ocean shipping, derived with reference to data on tonnage movements, show an increase from 45,000 workers in 1800 to 64,000 in 1810, followed by an absolute decline during the 1810-1820 interval. Thus, direct maritime employment expanded in relation to total nonfarm employment between 1800 and 1810, rising from 15 per cent to 17 per cent of the latter, and then shrank to a mere 8 per cent (half its former relative size) in 1820. Cf. Lebergott, “Labor Force and Employment” (NBER Vol. 30), pp. 166-67, for ocean shipping employment estimates; Appendix Table I for estimates of the nonfarm labor force.

35 Lebergott's estimates in “Labor Force and Employment” (NBER Vol. 30), Table 2, p. 119, show a comparatively insignificant decline between 1850 and 1880 in the proportion of the labor force engaged in agriculture. Thus, almost five-sixths of the 32 percentage point net structural shift away from farming during 1800-1880 was compressed within the brief span from 1820 to 1850.

36 Theoretically, as well as for prediction purposes, it is more satisfactory to work with GDP as the output measure, and not with GNP. GNP includes the net balance of interest and dividends on foreign assets, an item for which there is clearly no corresponding domestic input of labor. Our prediction equation assesses the effect of intersectoral shifts upon aggregate labor productivity by employing a fixed ratio of farm to nonfarm output per worker. Inasmuch as the numerator of that ratio must be estimated with reference to domestic (farm) production, the denominator should be measured on the same basis. Otherwise, the denominator would reflect the prevailing net asset position of U.S. nationals, a purely financial bookkeeping consideration from the point of view of production theory.

37 These correspond to the Variant II estimates of real GDP per capita, presented in Table 8. Some evidence is cited below regarding the relative rates of labor productivity growth in the farm sector and in nonfarm activities.

38 The Variant II conjectural real GDP indexes implied by Table 8 should not be confused with Gallman's Variant II measures of constant dollar output (GNP), which do include an allowance for value added in home manufacturing and in the form of improvements to farm land. The scope of all the conjectural output estimates discussed here (both Variants I and II ) is comparable to that of Gallman's Variant I estimates of GNP, save that the present estimates relate to GDP. Gallman's constant dollar GNP estimates inclusive of home manufacturing and farm land improvements show a slower rate of rise between 1834 and 1860 than his (Variant I) estimates, from which those forms of production are omitted. Cf. Gallman, “Gross National Product” (NBER Vol. 30), pp. 8-10.

39 Cf. Kuznets, “Long-Term Changes,” p. 224, Table 52. Martin's current dollar estimates of national income in 1839/40 indicated that the share of national income originating in agriculture was 33.6 per cent, whereas the present estimates (Table 5) reveal that gross farm product was 40.8 or 47.0 per cent of gross domestic product, depending upon the inclusiveness of the output definition. The 1840 labor force shares for the farm and nonfarm sectors used here also differ from those employed by Kuznets, as may be seen from Table 4.

40 Kuznets, “Long-Term Changes,” p. 225–26.

41 The present (minimum) estimate of the intersectoral shift effect is 15.7 per cent, which is more than twice as large as the percentage gain cited under this heading by Kuznets (ibid.); on the other hand, the estimated gain due to the rise in the labor participation rate is only one-third the size of Kuznets' estimate, as has already been pointed out in the text.

42 It is often supposed (cf, e.g., North, “Early National Income Estimates,” pp. 392-93) that Kuznets assumed a constant (0.5) ratio of agricultural labor productivity to nonfarm labor productivity and worked out the effects of the sectoral labor force redistribution between 1800 and 1840 on the assumption that labor productivity remained constant within sectors. Actually, the computations presented by Kuznets (“Long-Term Changes,” p. 224, n.l) are based on a quite different set of assumptions. Kuznets started by assuming that the ratio of farm labor productivity to average U.S. labor productivity remained constant (at 0.5) during the 1800-1840 period. He then made the further assumption that nonfarm labor productivity remained constant in relation to average U.S. labor productivity–and hence to farm labor productivity. But, if all three rates of increase in productivity are thus assumed equal, what does it mean to hold the intrasectoral levels of labor productivity constant? It is a simple matter to show that the form of the Kuznets computation yields an index of average U.S. labor productivity due to intersectoral shifts only under the condition that there was no change in average U.S. labor productivity between 1800 and 1840.

Using the notation set out in footnote 23, Kuznets' computational form yields a measured shift effect, X.

where t = 1840 and o = 1800, and it represents aggregate real output per worker. (Note Kuznets' assumption that (πA/π)t = (πA/π)o. It takes but a little algebra to show that one is correct to interpret × as a measure of the change in average output per worker, due to intersectoral shifts, only in the trivial case in which × = (πt/πo) = 1. However, had Kuznets simply stipulated an 0.5 ratio of agricultural labor productivity to aggregate labor productivity for the year 1800, without justifying the figure on the ground that that ratio remained constant between 1800 and 1840, his computational procedure would be correct.

43 Parker and Whartenby, “Growth of Output,” p. 211.

44 North, Cf., “Early National Income Estimates,” pp. 392-93; also, North, Growth and Welfare, p. 72.Google Scholar

45 Parker and Whartenby (Growth of Output,” p. 212) concluded their examination of the 1800-1840 period on the note that “answers to the more general questions about national income movement” would be impossible to secure “until the question of the movement of productivity in agriculture is directly tackled by the painful techniques of historical research.”

46 The 21.8 per cent decline cited in the text is derived from the computed value of , where, following the notation and relationship derived in footnote 23, we compute the farm labor productivity index required for vo = vt, under the assumption that , given the ratio , a known magnitude. The following general computational formula can be readily derived:

In making the calculation, observations for p and sA in 1800 and 1840 were drawn from Table 3, col. (2), and Table 4, col. (1), respectively. The Definition II estimate of S = 0.511 was used from Table 5, line 6.

The foregoing computation assumes that labor productivity in the nonfarm sector remained constant. If we suppose it increased by 31 per cent over the period 1800-1840–i.e., the rate of average intrasectoral productivity increase assumed in making the conjectural real GDP per capita estimates presented in Table 8–one can calculate the change in farm labor productivity required to hold per capita product constant (v0 = vt). The computational formula,

yields , or a productivity decline of 27.4 per cent.

47 Marvin W. Towne and Wayne D. Rasmussen, “Farm Gross Product and Gross Investment in the Nineteenth Century” (NBER Vol. 24), pp. 255-325. The Towne-Rasmussen farm labor productivity findings are cited by Taylor, “American Economic Growth,” p. 440, as one of the “chief considerations” leading to his conclusion that per capita real income was much the same in 1800 and 1840.

48 Towne and Rasmussen, “Farm Gross Product,” p. 257.

49 Ibid., Table 2, p. 269. Towne and Rasmussen muster qualitative evidence to account for this phenomenon, and Taylor (“American Economic Growth,” pp. 440-42) further elaborates their explanation for the putative failure of farm labor productivity to rise between 1800 and 1850. Clarence H. Danhof, however, takes issue with the Towne-Rasmussen view, in his perceptive “Comment” (NBER Vol. 24), pp. 312-15.

50 To argue about what constitutes a “large fall” or a “small fall” in agricultural labor productivity is really not very instructive, unless the implications of the changes are considered. Thus, even a 10 per cent decline in agricultural labor productivity would have involved a 30 per cent cut in per capita agricultural output over the 1800-1840 interval. Such implications can be quickly worked out by examining the changing relationship between total U.S. population and the farm labor force, presented in Table 6, line A.1.

51 A constant level of farm output per worker would, it has been seen, imply a significant fall in per capita agricultural output over the 1800-1840 interval. Yet, despite the marked relative decline in the share of real farm gross product originating within aggregate U.S. output during the second half of the nineteenth century, per capita real farm output in the U.S. rose by more than 20 per cent. Cf. Gallman, “Commodity Output” (NBER Vol. 24), p. 43, for constant (1879) dollar gross farm product estimates for the period 1850-1900.

52 Cf. Table 6, notes and sources to line C.1.

53 Cooper, Martin R., Barton, Glen R., and Brodell, Albert P., Progress of Farm Mechanization, U.S. Dept. of Agriculture Misc. Publication 630 (Washington, D.C.: U.S. Government Printing Office, 10 1947) Table 1, p. 3.Google Scholar

54 Cf. Parker and Whartenby, “Growth of Output,” p. 207.

55 Cf., e.g., ibid., p. 210; Taylor, “American Economic Growth,” p. 442.

56 This is the substance of the criticism Parker and Whartenby (“Growth of Output,” pp. 208-10) level against Kuznets' reference to the 1800-1840 trend in real wages of Vermont farm workers.

57 This may be seen from cols. (4) and (5) of Table 7A. The 1800-1818 decline in the real farm labor cost indexes [cols. (2) and (3)] is neither theoretically nor historically inconsistent with the stability indicated in average farm labor productivity over the 1800-1820 interval. First, if there were any improvement in labor efficiency, average product would rise relative to marginal labor productivity. Secondly, as the real wage cost index relates essentially to northern farming, rather than to U.S. agriculture as a whole, its decline during 1800-1818 is reconcilable with the indirect indications of diminishing marginal productivity in New England farming during the first two decades of the century (Cf., e.g., Taylor, “American Economic Growth,” pp. 441), as well as with an over-all stability of average labor product in U.S. agriculture during that period.

The comparatively rapid rise of the weighted regional real labor cost index [compare cols. (4) and (5) of Table 7A] during the 1840-1860 interval, might be equally explicable in terms of a relatively slower growth of labor productivity in southern agriculture during these decades. The 1840-1860 period, or course, saw a marked acceleration in the mechanization, and market-oriented specialization, of northern agricultural production. Towne and Rasmussen (“Farm Gross Product,” p. 260), however, have alleged: “the effects of this new technology were not to be felt until the period of the Civil War. No substantial rise in demand for grain products had occurred [during the 1840's and 1850's], and farmers generally felt no strong incentive to buy machines that would increase output. Besides, there was general resistance to the adoption of new ideas”. For evidence contradicting every one of these assertions, David, cf. P. A., “The Mechanization of Reaping in the Ante-Bellum Midwest,” in Rosovsky, H., ed., Industrialization in Two Systems: Essays in Honor of Alexander Gerschenkron, (New York: John Wiley and Sons, 1966), ch. iGoogle Scholar.

58 William N. Parker and Judith L. V. Klein, “Productivity Growth in Grain Production in the United States, 1840-60 and 1900-10” (NBER Vol. 30), pp. 523-80.

59 Ibid., Table 13, p. 545 for underlying data.

60 I am grateful to Professor William N. Parker for making available his unpublished regional estimates of unit labor requirements in U.S. cotton production c. 1839, from which the figure cited in the text has been derived.

61 Parker and Klein's data for the period 1839-1907/11 (“Productivity Growth,” and private communication) show convergence of regional unit labor requirements in corn production, as well as convergence between labor requirements in the Seaboard and Delta cotton regions. In the case of wheat, however, the long-term picture is one of divergence, and almost complete regional concentration of wheat production in the West. Needless to say, there is no reason to think that regional productivities in specific products necessarily tend to converge as a result of factor migration, so long as regional production functions remain different.

62 Cf. Notes and Sources to Table 7B for Professor Easterlin's regional farm labor productivity estimates.

63 Cf. Appendix Table II for estimates of the regional distribution of the U.S. total farm labor force at census dates from 1800 to 1840. Care has been taken in the estimation procedure to insure consistency between the labor force distributions and the Easterlin regional labor productivity figures for 1840.

64 Cf. Danhof, “Comment” (NBER Vol. 24), p. 313.

65 The ratio of nonfarm real labor costs to farm real labor costs was computed, for census years in the 1800-1840 period, from average nonfarm money wage estimates made by Stanley Lebergott (“age Trends, 1800-1900” [NBER Vol. 24], p. 493) and wholesale textile prices (C7.S. Historical Statistics [1960]), p. 115), and the farm real labor cost indexes presented in Table 7A, cols. (2), and (alternatively) (3).

66 Cf. Gallman, “Commodity Output” (NBER Vol. 24), pp. 33-34.

67 Real GDP, in “1840” constant dollars can be extrapolated back to 1800 from Table 8, Table 3, col. (2), and the Definition II estimate for 1840 in Table 5. Similarly, the Definition II figure for gross farm product can be extrapolated back to 1800 on the index in Table 6, line C.1.

68 Cf. Lance E. Davis and H. Louis Stettler, “The New England Textile Industry, 1825-1860: Trends and Fluctuations” (NBER Vol. 30), p. 221, Table 4.

69 From Table 8 we compute the growth rates during the second and third accelerations; the rate over the 1819/20-1834/35 interval averaged roughly 2.5 per cent per annum, while the rates for the intervals 1844/45-1854/55, and 1849/50-1859/60 work out at 2.05 and 2.18 per cent per annum, respectively. In order to get some idea of the order of magnitude of the per capita real product growth rate during the expansion following the depression of the 1780's, I have ventured a highly speculative real GDP per capita estimate for 1789/90. This conjecture rests on the following suppositions: (a) per capita gross farm product remained constant between 1790 and 1800; (b) the proportion of the labor force engaged in agriculture was 0.90 in 1790- a figure for which there is some corroborative evidence, discussed in footnote 33, above; (c) average intrasectoral productivity increased at the rate assumptions (a) and (b) imply for the growth of agricultural output per worker, i.e., by 9 per cent during the decade 1790-1800; (d) the labor force participation rate was approximately the same in 1790 and 1800, as the speculative 1790 labor force estimate discussed in footnote 33 suggests; (e) the ratio of farm to nonfarm labor productivity remained constant at 0.511–the level suggested by the Definition II estimate in Table 5. The resulting estimate places 1790 per capita real GDP at 85.8 per cent of the (Variant II) level conjectured for 1800, or at 55 per cent of the 1840 level. This suggests an annual average rate of increase of roughly 1.6 per cent during the 1790's. If the expansion of the economy followed a course similar to the volume of domestic export earnings, the rate of growth was retarded during the first half of the 1800's.

70 For discussion of instability in U.S. growth before 1860, cf., e.g., Abramovitz, JEC Hearings. Note, however, that the present estimates (Table 1) show much greater stability in the GDP growth rate than in the per capita product growth rate. The inference that surges of accelerated growth in the U.S. during the nineteenth century, or “long-swing expansions” as these have been called, were connected with waves of relatively rapid expansion of the urban-industrial sector, has been recently advanced by Richard A. Easterlin, Population and Labor Force during Long Swings in Economic Growth: The American Experience (National Bureau of Economic Research, October 1965, mimeo.) Fogel (Railroads, pp. 121-27) has drawn attention to some parallels between the episodes of rapid industrial expansion in the 1820's and the 1840's.

71 Cf. footnote 69 for the basis of the conjectural 1790-1860 average rate of growth, and Table 1, and the accompanying text, for the growth rates of real per capita product over the two “trend-intervals.”

72 North, Cf., Growth and Welfare, pp. 64–74Google Scholar , for the most recent statement of this argument. Actually, reference is made to the movements in total (export) credits, including the value of re-exports (ibid., p. 73, chart 15). Domestic credit items, exclusive of re-exports are, however, the more relevant variable from some points of view. The latter show the same pattern of rise and fall over the 1790-1815 period as total credits per capita, although the movements are rather less pronounced. Cf. Notes and Sources to Table 9, col. (1) for sources of balance of payments estimates.

73 Actually, an elision has been made here from current values to constant dollar values, following the same gloss in North's statement of the argument (ibid.), and Taylor's consideration of the trend in current values of merchandise exports (“American Economic Growth,” p. 442). This is an obvious defect in the way the evidence has been used, but it is only of subsidiary interest, compared with the problems discussed in the text.

74 On these general problems, cf. Geer Stuvel, “A System of National and Domestie Accounts,” Economica, n.s., XXII (Aug. 1955), 207-27, and “A New Approach to the Measurement of Terms-of-Trade Effects,” Review of Economics and Statistics, XXXVIII (Aug. 1956), 294-307.

75 We may define conventional real GDP, in year 0 prices, from the final demand side, as:

and (pm)0 are year 0 export and import prices, respectively.

A measure of real GDP, (RGDP)°, which treats foreign trade as a productive activity whose final output is imports, would value the net foreign balance at year 0 import prices. Thus,

in conjunction with equation (1), can be solved for the following expression:

which measures the proportional impact of the change in the terms of trade between year 0 and year t, as a percentage of conventional RGDP in year t (expressing the latter in year 0 prices). Note from the terms in the brackets on the right-hand side of equation (3) that all we need in order to measure the “terms-of-trade effect” is the proportional change in the commodity terms of trade, and the conventional real export ratio. Text references to “the real export ratio” refer to the latter, as defined by the second bracketed term in equation (3).

76 The pure terms of trade effect between any pair of years can be representedas the index:

where V and V are defined as in footnote 75, above. The index value 0.975 is obtained for t = 1810, o = 1800, using the terms of trade data in Table 9, col. (3), and assuming that the 1840 real export ratio applied at both dates. An index value of 0.975 implies a 2.5 percentage point adverse effect due to the alteration in the terms of trade alone. All estimates of pure terms of trade effects (expressed in percentage terms) are computed from similarly defined indexes.

77 Taylor (“American Economic Growth,” p. 442) cites, as one of the three principal considerations supporting his thesis that per capita real product was much the same in 1840 as in 1800, the fact that the average value of U.S. merchandise exports failed to rise as rapidly as the country's population in the interval between 1798-1806 and 1838-1842. Export prices, however, were declining. The average per capita volume of domestic merchandise exports, expressed in 1830 prices, was about 27 per cent higher during 1838-1842 than it had been during 1798–1806. The export volume figures are averages of annual volume estimates for the terminal period, computed from the sources given for Figure 1. The particular dates Taylor selected also make a substantial difference, since the volume of domestic exports was quite unstable in the years surrounding 1800. Thus the growth rate of per capita real domestic merchandise exports computed between averages for 1799–1800 and 1839–1840 is roughly 1.5 per cent per annum, whereas the rate of growth using Taylor's suggested terminal averages is only 0.6 per cent per annum.