¹ The decline in fertility rates during the nineteenth century is well documented. Early studies by Seaman, Ezra C., Essays on the Progress of Nations (New York, 1853);Google ScholarTucker, George, Progress of the United States in Population and Wealth in Fifty Years (New York, 1855);Google ScholarBillings, John S., “The Diminishing Birth Rate in the United States,” Forum, 15 (06 1893), 470–75,Google Scholar and Willcox, Walter F., “The Change in the Proportion of Children in the United States and in the Birth Rate in France During the Nineteenth Century,” Publications of the American Statistical Association, 12(03 1911), 491–95,CrossRefGoogle Scholar have been reinforced by more recent work by Thompson, Warren S. and Whelpton, P. K., Population Trends in the United States (New York, 1933);Google ScholarGrabill, Wilson H., Kiser, Clyde V., and Whelpton, P. K., The Fertility of American Women (New York, 1958);Google ScholarYasuba, Yasukichi, Birth Rates of the White Population in the United States, 1800–1860 (Baltimore, 1961);Google ScholarCoale, Ansley J. and Zelnik, Melvin, New Estimates of Fertility and Population in the United States (Princeton, 1963);CrossRefGoogle Scholar and Forster, Colin and Tucker, G. S. L., Economic Opportunity and White American Fertility Ratios: 1800–1860 (New Haven, 1972).Google Scholar

² In an extensive study of Massachusetts (a state with an early system of recording both births and deaths), Vinovskis, Maris A., “A Multivariate Regression Analysis of Fertility Differentials Among Massachusetts Townships and Regions in 1860,” in Historical Studies of Changing Fertilty, Tilly, Charles, ed., (Princeton, 1978), has shown that the birth rate had declined during the period from 1790 to 1860 while the death rate remained stable.Google ScholarYasuba, Birth Rates;Google ScholarMeeker, Edward, “The improving Health of the United States, 1850–1915,” Explorations in Economic History, 9 (Summer 1972), 353–73;CrossRefGoogle ScholarPubMed and Haines, Michael R., “The Use of Model Life Tables to Estimate Mortality for the United States in the Late Nineteenth Century,” Demography, 16 (05 1979), 289–312, agreed that it is unlikely that a sustained decline in mortality rates had occurred in the United States before about 1880.CrossRefGoogle ScholarPubMed

³ Walle, Etienne van de, “Alone in Europe: The French Fertility Decline Until 1850,” in Historical Studies, Tilly, ed., in a study of France;Google ScholarKnodel, John E., The Decline of Fertility in Germany (Princeton, 1974), in a study of Germany;Google Scholar and Demeny, Paul, “Early Fertility Decline in Austria-Hungary: A Lesson in Demographic Transition,” Daedalus, 97 (Spring 1968), 502–22,Google ScholarPubMed in a study of Austria-Hungary, have shown instances where a concurrent decline in fertility and mortality had apparently occurred and have raised the possibility of a fertility decline preceding a mortality decline. Matthiessen, Paul C. and McCann, James C., “The Role of Mortality in the European Fertility Transition: Aggregate-Level Relations,” in The Effects of Infant and Child Mortality on Fertility, Preston, Samuel H., ed., (New York, 1978), provide evidence that the typical European experience had been characterized by a fertility decline following the decline in mortality.Google Scholar

⁴ Easterlin, Richard A., “The Economics and Sociology of Fertility: A Synthesis,” in Historical Studies, Tilly, ed., and “An Economic Framework for Fertility Analysis,” Studies in Family Planning, 6 (March 1975), 54–63.Google Scholar

⁵ Easterlin, “An Economic Framework,” proposes several scenarios for fertility determination, one of which is represented in Figure 1.Google Scholar

⁶ Although both Yasuba, Birth Rates, and Meeker, “The Improving Health,” discuss the possibility that mortality actually rose during the decades around the middle of the nineteenth century, this increase (which could have caused Cⁿ to decline) was thought to have been small and short-lived.Google Scholar

⁷ See la Sorte, Michael A., “Nineteenth Century Family Planning Practices,” The Journal of Psychohistory, 4 (Fall 1976), 163–83.Google ScholarPubMed

⁸ See Potter, J., “The Growth of Population in America, 1700–1860,” in Population in History, Glass, D. V. and Eversley, D. E. C., eds. (London, 1965).Google Scholar

⁹ Grabil, Kiser, and Whelpton, Fertility, have shown that the decline in rural fertility accounted for 56 percent of the decline in U.S. fertility during the period 1810–1940. Yasuba, Birth Rates, and Forster and Tucker, Economic Opportunity, agree that it is unlikely that urbanization played a dominant role in explaining the decline in fertility during the first half of the nineteenth century. In fact, Forster and Tucker attribute 78 percent of the fertility decline during the period 1810–1840 and 74 percent of the fertility decline during the period 1840–1860 to the decline in rural birth rates.Google Scholar

¹⁰ The only way in which urbanization-industrialization could have been responsible for the rural fertility decline would have been if the lower urban birth rates had somehow been diffused into the countryside, and, as Forster and Tucker, Economic Opportunity, pointed out, this is highly unlikely, particularly since there is no evidence showing that urban fertility decreased before rural fertility.Google Scholar

¹¹ While time-series data are scarce, cross-sectional data do exist. In a study of rural households in sixteen northern states in 1860, Easterlin, Richard A., Alter, George, and Condran, Gretchen A., “Farms and Farm Families in Old and New Areas: The Northern United States in 1860,” in Family and Population in Nineteenth-Century America, Hareven, Tamara K. and Vinovskis, Maris A., eds., (Princeton, 1978),Google Scholar find that these variables cannot explain the variation in fertility rates. They also look at a variety of other factors including the effect of immigration. Here, they conclude that immigration was more likely to have raised than to have lowered fertility, thus discrediting another possible explanation for the decline in U.S. fertility.

¹² As early as 1855, Tucker, Progress of the United States, discusses the inverse relationship between fertility and a variant of the land availability variable, population density.Google ScholarYasuba, Birth Rates, after a detailed analysis of the decline in rural fertility during the period 1800–1860, concludes that the availability of land was a major determinant of this decline. Forster and Tucker, Economic Opportunity, use a more sophisticated methodology and confirm Yasuba's findings.Google Scholar On a more disaggregated level, Leet, Don R., “Interrelations of Population Density, Urbanization, Literacy, and Fertility,” Explorations in Economic History, 14 (10 1977), 388–401;CrossRefGoogle ScholarPubMedEasterlin, Alter, and Condran, “Farms and Farm Families”; and, for Canada, Mclnnis, R. M., “Birth Rates and Land Availability in North America in the Nineteenth Century, With Special Reference to Ontario,” mimeographed (Queen's University, 1972)Google Scholar and “Childbearing and Land Availability: Some Evidence From Individual Household Data,” in Population Patterns in the Past, Lee, Ronald Demos, ed., (New York, 1977),Google Scholar also find that land availability had been a critical factor in accounting for variations in fertility. Nevertheless, there have been several studies challenging the significance of land availability in explaining the decline in U.S. fertility. For example, for a critical discussion of Forster and Tucker, see Vinovskis, Mans A., “Socioeconomic Determinants of Interstate Fertility Differentials in the United States in 1850 and 1860,” Journal of Interdisciplinary History, 3 (Winter 1976), pp. 375–98. Unfortunately, the lack of panel data on education and other variables that Vinovskis used as alternatives to land availability prevented their inclusion in the empirical analysis that follows.CrossRefGoogle Scholar

¹³ Easterlin, Alter, and Condran, “Farms and Farm Families,” find no evidence that the degree of settlement affected the child's contribution to family income or the opportunity cost of a wife's time.Google Scholar

¹⁴ Leet, “Interrelations,” examines the relationship between the availability of land and farm prices in Ohio during the middle part of the nineteenth century and finds that they were inversely correlated.Google Scholar

¹⁵ In addition, Yasuba, Birth Rates, finds that changes in marital customs (an increase in the age at first marriage and a decrease in the proportion married) played a significant role in reducing fertility during the first half of the nineteenth century. This may reflect the delay or cancellation of marriages due to poor income prospects associated with the decline in the availability of land. While, for some, rural-urban migration was an alternative to remaining on the farm, low levels of urbanization made this an unlikely possibility during most of the period in question.Google Scholar

¹⁶ These factors are discussed in Danhof, Clarence H., Change in Agriculture: The Northern United States, 1820–1870 (Cambridge, 1969);Google ScholarMcNall, Neil Adams, An Agricultural History of the Genesee Valley 1790–1860 (Philadelphia, 1952);CrossRefGoogle ScholarEasterlin, Richard A., “Farm Production and Income in Old and New Areas at Mid-Century,” in Essays in Nineteenth Century Economic History: The Old Northwest, Vedder, Richard K. and Klingaman, David C., eds. (Athens, Ohio, 1975);Google Scholar and Leet, “Interrelations.”Google ScholarEasterlin, Richard A., “Population Change and Farm Settlement in the Northern United States,” this JOURNAL, 36 (03 1976), 45–75, has conjectured that the reason for the persistence of unequal returns between older and newer areas stemmed from the nonpecuniary advantages to those residing in the more densely settled (older) areas.Google Scholar

¹⁷ Easterlin, “Population Change.”Google Scholar

¹⁸ In a rural area, this means providing either farmland itself or the funds needed to purchase farmland that supplied the same or better earning prospects as the farmland that the parents had inherited or had otherwise come into possession of when they had first set up their own farms. There have been many references to the desire of parents in rural areas to provide farms for their children. Greven, Philip J. JrFour Generations: Population, Land and Family in Colonial Andover, Massachusetts (Ithaca, 1970),Google Scholar in a study of Andover, Massachusetts during the seventeenth and eighteenth centuries found that it was common practice for parents to provide their children with land or the funds to purchase land on which to start their own farms. Bogue, Allan G., From Prairie to Corn Belt (Chicago, 1963), in a study of farming in Illinois and Iowa during the nineteenth century;Google Scholar and Danhof, Change in Agriculture, writing about the Northern United States during the middle of the nineteenth century, found similar evidence.Google Scholar Finally, Spillman, W. J., “The Agricultural Ladder,” American Economic Review, Supplement, 9 (03 1919), 170–79,Google Scholar writing about the early 1900s, found that a minimum of 64 percent of farm owners had acquired farms with the aid of their families. It is safe to assume that this percentage had been even higher during an earlier period. Based on testimony of this type, Easterlin, “Population Change,” concluded that family assistance with respect to the purchase of farms by children appeared to have been a common practice within the United States during the nineteenth century.

¹⁹ It may have been true that cheap farmland was once available in less developed areas, but these areas were generally far from the site of the parents' farm and the desire to keep the family together would have prevented the purchase of this farmland.Google Scholar

²⁰ See, for example, Berkner, Lutz K. and Mendels, Franklin F., “Inheritance Systems, Family Structure and Demographic Patterns in Western Europe, 1700–1900,” in Historical Studies, Tilley, ed., and Lutz K. Berkner, “Peasant Household Organization and Demographic Change in Lower Saxony (1689–1766),” in Population Patterns, Lee, ed.Google Scholar

²¹ This system tends to lead to a number of demographic effects including high levels of out- migration, a late mean age at first marriage, a relatively low proportion married, and the continuation of an extended family household organization. This is true when the bulk of the value of the parents' estate consists of farmland and, therefore, there are few additional assets that could be distributed among the other children.Google Scholar

²² The demographic manifestations of this system are the opposite of impartibiity, little outmigration, early marriages, and a breakdown in extended families.Google Scholar

²³ Unless family farms were large enough to subdivide into smaller farms, each with a minimum size (or income generating potential) at least as large as the parents' farm, impartibility would be prevalent.Google Scholar

²⁴ Play, Frederic Le, L' Organizarion de la Famille (Paris, 1871).Google Scholar

²⁵ Berkner and Mendels, “Inheritance Systems.”Google Scholar

²⁶ As discussed above, the decline in rural fertility was more rapid than the decline in urban fertility and was responsible in large part for the total fertility decline. Moreover, the area under consideration was largely rural with the percentage of the population residing in rural areas 91.1 percent in 1810, 85.9 percent in 1840, and 71.3 percent in 1870.Google Scholar

²⁷ For example, Tucker, Progress of the United States, uses a population density measure as a proxy for land availability. Rapid urbanization during the latter part of the nineteenth century contributed to the rise in population density, however, and therefore weakened the link between density and the availability of land.Google Scholar

²⁸ Yasuba, Birth Rates.Google Scholar

²⁹ Forster and Tucker, Economic Opportunity.Google Scholar

³⁰ The earliest maximum was reached in 1830 (Rhode Island) and the latest was reached in 1930 (North Dakota, South Dakota, and Nebraska). The median date was between 1890 and 1900.Google Scholar

³¹ The value for this variable started at.037 in 1760, reached.110 in 1800,.264 in 1830, and.594 in 1860.Google Scholar

³² Forster and Tucker, Economic Opportunity.Google Scholar

³³ There is no way to calculate the birth ratio by state before 1800 because the 1800 census contained the first age enumeration data.Google Scholar

³⁴ Fuller, W. A. and Battese, G. E., “Estimation of Linear Models with Crossed-Error Structure,” Journal of Econometrics, 2 (05 1974), 67–78, present a technical discussion of this method.CrossRefGoogle ScholarPindyck, Robert S. and Rubinfeld, Daniel L., Economic Models and Economic Forecasts (New York, 1976), pp. 202–11 have a more general discussion of pooling cross-sectional and time-series data.Google Scholar

³⁵ A complete set of data for each state was needed. Therefore, data for the first thirteen states listed in Table 3 for the dates 1800, 1810, 1820, 1830, and 1840 were used.Google Scholar

³⁶ The total density measure at each date is the same for all states and, therefore, it may have the properties of a time trend. If, for example, there were a change in tastes over time in favor of market goods, this variable would capture the shift in preferences away from children. Similarly, if the population were aging (leading to a decline in natural fertility) or immigration were increasing (and immigrants had lower fertility than native Americans), then the total density measure would take account of these factors. Yet, the age of the population, immigration, and other factors that potentially could have altered the level of fertility actually had little effect during the nineteenth century, and the substitution of a time trend for the total density measure produced inferior results. It is thus reasonable to assume that changes in the total density measure represent changes in the ability to acquire farmland, which affect the demand for children.Google Scholar

³⁷ While there are problems with the calculation and interpretation of a value of R² that arise when using this regression procedure (due to the ambiguity associated with the determination of the total sum of squares), an ordinary least.squares technique produces an R² of.87, indicating that a substantial part of the variation has been explained.Google Scholar

³⁸ Of the 65 cases that comprised the sample set, 97 percent had residuals less than or equal to 15 percent of the actual values while 88 percent had residuals less than or equal to 10 percent of the actual values.Google Scholar

³⁹ Easterlin, Alter, and Condran, “Farms and Farm Families,” showed that the ratio of males aged 15 and over to females aged 15 and over was 25 percent higher in their least settled farm area compared with their most developed area in 1860.Google Scholar

⁴⁰ It would be possible to estimate the proportion of reproductive females equation using only observations starting in 1800 and lasting until the middle part of the nineteenth century when the extent of urbanization was very small. But an arbitrary cut-off date would have to be selected and, in light of the fact that, even in 1870, over 70 percent of the total population lived in rural areas, the entire data set was used in the estimation of the equation. These data are presented in Yasuba, Birth Rates, pp. 62–63, for the period 1800–1860, and the information for 1870 was calculated from Table XXVI, vol. II, U.S. Census, 1870.Google Scholar

⁴¹ As for the birth ratio equation, an indication of the explanatory power of the internal and total density variables can be provided by examining the R² resulting from an ordinary least-squares regression procedure, which, in this case, was equal to.73.Google Scholar

⁴² Of the 104 cases, all had residuals less than or equal to 15 percent of the actual values while 96 percent had residuals 10 percent or less of the actual values.Google Scholar

⁴³ This is consistent with a land availability model since land tended to be more easily available in the south.Google Scholar

⁴⁴ Yasuba, Birth Rates.Google Scholar

⁴⁵ This assumes that the adjustment factors that apply to the northern area also apply for the entire group of states and, therefore, they cancel out.Google Scholar

⁴⁶ Since the proportion of reproductive females is assumed to have been the same in rural and urban areas (or, more realistically, that the rural proportion of reproductive females does not vary greatly from the total proportion of reproductive females since the percent of the population living in urban areas is quite small in most cases), the relationship between the rural birth ratio and the total birth ratio will be the sole factor used in the calculation of this adjustment factor.Google Scholar

⁴⁷ Grabill, Kiser, and Whelpton, Fertility, provide information on a variant of the birth ratio: the number of children under 5 years of age per 1000 white women aged 20 to 44. They divided their data into regions and into separate rural and urban components. Since almost all of the 23 states are either in the New England, Middle Atlantic, East North Central, or West North Central group (Delaware and Maryland are the two exceptions), a weighted average of the child-women ratios for these regions can be calculated that roughly corresponds to the birth ratio for the northern area. This value can then be compared with the child-women ratio for the entire United States. Similarly, the child-women ratio for the rural areas of the regions containing most of the northern states can be compared with the total ratio for these regions. Finally, after assuming that the percentage difference between the number of white women aged 20 to 44 in the entire United States and the number contained within the smaller group of states was equal to the difference in the proportion of reproductive females calculated above, the same two decades can be analyzed. For the decade 1790–1800, the crude birth rate for all areas of all of the states was only 0.2 percent higher than the crude birth rate for rural areas of the northern states and, for the decade 1830–1840, it was 1.2 percent lower.Google Scholar

⁴⁸ A number of fertility estimates have been made for the pre-1800 period. Grabill, Kiser, and Whelpton, Fertility, summarize the findings of both contemporary and modern researchers and place the crude birth rate during the Colonial and Early Federal periods within the 50–57 range.Google Scholar These values compare favorably with the early estimates of the fertility model. For the decade 1760–1770, about the time when birth rates apparently began their sustained decline, the birth rate estimate was 58.6. By the turn of the century, the estimated birth rate had fallen to about 53 as compared with a birth rate of about 51 given by Lotka, “The Size of American Families,” and a birth rate of 52–53 given by Blodget, Economica.Google Scholar

⁴⁹ While there are little reliable data concerning crude birth rate estimates for specific states, some information of this type does exist. Gutman, Robert, “The Birth Statistics of Massachusetts During the Nineteenth Century,” Population Studies, 10 (07 1956), 69–94,CrossRefGoogle Scholar estimates the crude birth rate for the state of Massachusetts during the mid-nineteenth century: 35.1 for 1844–1846, 33.2 for 1849–1851, 33.2 for 1859–1861 and 28.4 for 1869–1871. These estimates apply to the white population in all areas of the state and, therefore, they must be adjusted to be comparable to the predictions of the fertility model. In 1840, the crude birth rate for rural Massachusetts was 8.5 percent greater than the crude birth rate for the entire state (using, again, the ratio of the rural birth ratio to the total birth ratio). Thus, the adjusted values of Gutman's estimates equal: 38.1 for 1844–1846, 36.0 for 1849–1851 and for 1859–1861, and 30.8 for 1869–1871. The fertility model predicted a value of 37.0 for the decade lasting from 1840–1850, thereby lying within the range of the adjusted estimates. The prediction for the decade 1850–1860, 32.8, was slightly low when compared with Gutman's estimates, as was the prediction for the decade 1860–1870, 29.4. These differences are relatively small, however.

⁵⁰ Turner, Frederick Jackson, “The Significance of the Frontier in American History.” A paper read at the meeting of the American Historical Association in Chicago, 07 12, 1893.Google Scholar Reprinted in Turner, , The Frontier in American History (New York, 1947), pp. 21–22.Google Scholar

⁵¹ Coale, Ansley J. and Demeny, Paul, Regional Model Life Tables and Stable Populations (Princeton, 1966).Google Scholar

⁵² Coale and Zelnik, New Estimates, estimated that the enumeration error for native white males aged 0 to 9 in the 1880 census (the earliest census analyzed) was about 6.3 percent (the simple average of 9.1 percent for males aged 0 to 4 and 3.5 percent for males aged 5 to 9) while, for native white females, it was about 6.2 percent (the simple average of 9.1 percent for females aged 0 to 4 and 3.2 percent for females aged 5 to 9). Comparable figures for the 1890 census were 5.3 percent for males and 5.1 percent for females.Google Scholar

⁵³ Grabill, Kiser, and Whelpton, Fertility, estimated an error of 6.2 percent for the native white population under 5 in the 1880 census. This estimate is low compared with Coale and Zelnik (about 9 percent for the native while population under age 5) and, since the enumeration error for children aged 5 to 9 is expected to be smaller than that of children aged 0 to 4, the total error for children aged 0 to 9 would probably be about 4 or 5 percent. In an examination of earlier censuses, they estimated enumeration errors for native white children aged 0 to 4 of 11.6 percent, 8.0 percent and 9.8 percent in 1870, 1860 and 1850. Given the relationship between underenumeration of children aged 0 to 4 and those aged 5 to 9 (as found by Coale and Zelnik for the 1880 census), these estimates correspond roughly with enumeration errors for children aged 0 to 9 in the 5 percent–8 percent range.Google Scholar

⁵⁴ Coale and Zelnik, New Estimates.Google Scholar