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Family Limitation and the English Demographic Revolution: A Simulation Approach

Published online by Cambridge University Press:  11 May 2010

N. F. R. Crafts  and
N. J. Ireland
N. F. R. Crafts
Affiliation:
University of California, Berkeley and University of Warwick
N. J. Ireland
Affiliation:
University of Warwick
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Abstract

This seeks to examine the thesis of family limitation in pre-industrial England proposed by E. A. Wrigley on the basis of birth intervals evidence in his famous 1966 paper, “Family Limitation in Pre-industrial England.” A simulation model of a stochastic reproductive system is used to investigate the possible effects of a variety offerees acting on birth intervals. It is argued that although the Wrigley hypothesis remains plausible it is likely that he has exaggerated the role of birth control.

Type
Articles
Information
The Journal of Economic History , Volume 36 , Issue 3 , September 1976 , pp. 598 - 623
Copyright
Copyright © The Economic History Association 1976

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References

1 A useful summary and bibliography can be found in Flinn, M. W., British Population Growth, 1700–1850 (London, 1970)CrossRefGoogle Scholar.

2 See the useful reviews by Coale, A. J., “Factors Associated with the Development of Low Fertility: An Historic Summary,”Proceedings of the World Population Conference, 2(New York,1967), pp. 205–209Google Scholar, and Habakkuk, H. J., Population Growth and Economic Development since 1750 (Leicester, 1971)Google Scholar.

3 McKeown, T. S. and Brown, R. G., “Medical Evidence Related to English Population Changes in the Eighteenth Century,” Population Studies, 9 (1955), pp. 119–141CrossRefGoogle Scholar, reprinted in Drake, M. (ed.), Population in Industrialisation (London, 1969), p. 55Google Scholar. Subsequent page references are also to the reprint.

4 Ibid., p. 68.

5 Ibid., p. 52.

6 Ibid., p. 72.

7 Habakkuk, Population Growth, p. 8.

8 Chambers, J. D., Population, Economy and Society in Pre-Industrial England (Oxford, 1972), pp. 15–16Google Scholar.

9 Wrigley, E. A., Population and History (London, 1969), p. 112Google Scholar.

10 Carlsson, G., “The Decline of Fertility: Innovation or Adjustment Process,” Population Studies, 20 (1966), 150CrossRefGoogle ScholarPubMed.

11 Ibid.

12 Ibid.

13 See, for example, Demeny, P., “Early Fertility Decline in Austria-Hungary: A Lesson in Demographic Transition,” Daedalus, 97 (1968), 502–522Google ScholarPubMed.

14 Wrigley, Population, p. 113.

15 McKeown, T. S., Brown, R. G., and Record, R. G., “An Interpretation of the Modern Rise of Population in Europe,” Population Studies, 26 (1972), 355–356CrossRefGoogle Scholar.

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17 Habakkuk, Population Growth, pp. 38–39.

18 Wrigley, E. A., “Mortality in Pre-industrial England: the Example of Colyton, Devon, over Three Centuries,” Daedalus, 97 (1968), 546Google ScholarPubMed.

19 Wrigley, E. A., “Family Limitation in Pre-industrial England,” Economic History Review, 2nd ser., 19 (1966), 83CrossRefGoogle ScholarPubMed.

20 Ibid., p. 87.

21 Ibid., p. 106.

22 Ibid., p. 107.

23 Ibid., p. 100.

24 Ibid., p. 104.

25 As opposed to such ritual taboos as no intercourse during lactation.

26 This is not explicitly stated by Wrigley but appears to be a clear implication of the discussion on p. 87 of his Population.

27 Wrigley, “Family Limitation,” p. 105.

28 This was in essence the procedure adopted by McKeown and Brown; for a brief review of the problems associated with aggregate demographic statistics for eighteenth-century England and Wales see Crafts, N. F. R., “Local Population Studies in the Context of Aggregate Estimates for the Eighteenth Century,” Local Population Studies, 13 (1974), 19–29Google Scholar.

29 Jones, R. E., “Population and Agrarian Change in an Eighteenth Century Shropshire Parish,” Local Population Studies, 1 (1968), 6–32Google Scholar, and Loschky, D. J. and Krier, D. F., “Income and Family Size in Three Eighteenth Century Lancashire Parishes: A Reconstitution Study,” Journal of Economic History, 29 (1969), 429–448CrossRefGoogle ScholarPubMed. Both these studies seem to us to offer much weaker evidence of family limitation and we have therefore concentrated our attention in this paper on Wrigley's work, although many of our subsequent remarks would seem to apply to Jones' work also. Jones' paper appears to be plagued by small samples problems, and in the light of our subsequent remarks on the forces affecting birth intervals Loschky and Krier's method of inferring birth control seems to us highly suspect.

30 Flinn, British Population, p. 36.

31 Habakkuk, Population Growth, p. 14.

32 Chambers, J. D., “Some Aspects of E. A. Wrigley's ‘Population and History’,” Local Population Studies, 2 (1969), 21Google Scholar.

33 Chambers, Population, p. 75.

34 Hollingsworth, T. H., Historical Demography (London, 1969), p. 195Google Scholar.

35 Lee, R., “Population in Pre-industrial England: An Econometric Analysis,” Quarterly Journal of Economics, 87 (1973), 605CrossRefGoogle Scholar.

36 N. F. R. Crafts and N. J. Ireland, “A Simulation of the Impact of Changes in Age at Marriage before and during the Advent of Industrialisation in England,” Population Studies (forthcoming).

37 Wrigley, “Family Limitation,” pp. 93–97.

38 Henry, L., Anciennes families genevoises (Paris, 1956), pp. 93–110Google Scholar.

39 Crafts, N. F. R. and Ireland, N. J., “The Role of Simulation Techniques in the Theory and Observation of Family Formation,” Population Studies, 29 (1975), 90–91CrossRefGoogle ScholarPubMed. The problems arise in particular from the heterogeneity of unions with regard to the monthly chance of conception. Such “perverseness” is the major type of “truncation effect” impinging on closed birth intervals; see Sheps, M. C., Mencken, J. A., Ridley, J. C., and Lingner, J. W., “Truncation Effect in Closed and Open Birth Interval Data,” Journal of the American Statistical Association, 65 (1970), 678–693CrossRefGoogle ScholarPubMed.

40 Crafts and Ireland, “Simulation Techniques,” pp. 80–83.

41 This was termed the S1 control in that earlier paper; ibid., p. 82.

42 See the discussion and references in I. Holmberg, Fecundity, Fertility and Family Planning (2 vols.; Gothenburg, 1970 and 1972).

43 Wrigley, “Mortality,” passim and “Family Limitation,” pp. 86–88.

44 Crafts and Ireland, “Simulation Techniques,” p. 86.

45 Ibid., pp. 83–88.

46 James, W. H., “The Fecundability of U.S. Women,” Population Studies, 27 (1973), 493–500CrossRefGoogle ScholarPubMed.

47 Wrigley, “Family Limitation,” pp. 102–103.

48 It is thus consistent with at least some empirical evidence; see Ridley, J. C., Sheps, M. C., Iingner, J. W., and Mencken, J. A., “On the Apparent Sub-Fecundity of Non-Family Planners,” Social Biology, 16 (1969), 24–28CrossRefGoogle Scholar.

49 As possible starting points see the examples in our earlier paper which illustrate the capability of this kind of simulation to deal with more complicated models unamenable to analytical tools; Crafts and Ireland, “Simulation Techniques,” pp. 82 and 91–94.

50 As can be seen from Table 6, a rise in effectiveness from 0.8 to 0.9 can lead to falls in the last birth interval. This result is discussed in Crafts and Ireland, “Simulation Techniques,” p. 90.

51 It should be cautioned that our simulations indicated that this statistic could be rather capricious with small sample sizes.

52 Michael, R. T., “Education and the Derived Demand for Children,” journal of Political Economy, 81 (1973), S142CrossRefGoogle Scholar.

53 See, for example, the numbers in Berelson, B., “KAP Studies on Fertility,” in Berelson, B., ed., Family Planning and Population Programs (Chicago, 1966), pp. 655–668Google Scholar. The average for urban regions in the more developed areas of the third world is 3.8; there is no reason, however, to suppose that “ideal” is necessarily equivalent to “target” family size.

54 See, for example, the discussion and emphasis in North, D. C. and Thomas, R. P., The Rise of the Western World (Cambridge, 1973), p. 21CrossRefGoogle Scholar.

55 “Adjustment” in terms of a reduction in target might imply a greater return from more careful use of a given technique, thus increasing effectiveness. In any case, in the limit, an arbitrarily high target and zero effectiveness would produce the same outcome.

56 See above, p. 6.

57 Crafts and Ireland, “Simulation Techniques,” pp. 88–89.

58 The notion of the “truncation effect” is that birth intervals are affected by the finiteness of the reproduction period; this will tend to impart a downward bias on the observed last interval as some of the less fecund will become sterile before they can record their long last intervals. Changing the average fecundity of the sample will affect the magnitude of this bias.

59 Wrigley, “Family Limitation,” p. 93.

60 See the discussion in Holmberg, Fecundity, Vol. I, pp. 16–30.

61 See Bourgeois-Pichat, J., “Les facteurs de la fécondité non-dirigee,” Population, 20 (1965), 383–424CrossRefGoogle Scholar.

62 Wolfers, D., “Determinants of Birth Intervals and their Means,” Population Studies, 22 (1968), 407–409CrossRefGoogle ScholarPubMed.

63 Potter, R. G. and Sakoda, J. M., “Family Planning and Fecundity,” Population Studies, 20 (1967), 317CrossRefGoogle ScholarPubMed.

64 Retel-Laurentin, A., “Influence de certaines maladies sur la fécondité: Un exemple africain,” Population, 27 (1972), 841–860Google Scholar.

65 Lachenbruch, P., “Frequency and Timing of Intercourse: Its Relation to the Probability of Conception,” Population Studies, 21 (1967), 23–31CrossRefGoogle ScholarPubMed.

66 Hollingsworth, Historical Demography, p. 194.

67 See Holmberg, Fecundity, Vol. I, pp. 44–52.

68 Crafts and Ireland, “Age at Marriage.”