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National Research Council (US) Committee on Population; Montgomery MR, Cohen B, editors. From Death to Birth : Mortality Decline and Reproductive Change. Washington (DC): National Academies Press (US); 1998.

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From Death to Birth : Mortality Decline and Reproductive Change.

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7The Relationshp Between Infant and Child Mortality and Fertility: Some Historical and Contemporary Evidence for the United States

Michael R. Haines


The demographic transition from high to low levels of fertility and mortality is a defining characteristic of the development process. Historically, the precise timing of both the fertility and mortality transitions has varied considerably. Furthermore, there are important questions as to how fertility and mortality interact during this process. The writings of Thomas R. Malthus (1830) are an early example of this inquiry. One area of particular interest has been the relationship of birth rates to infant and early childhood mortality, which has occasioned a number of studies on developing nations since World War II (e.g., Hobcraft et al., 1985; Potter, 1988; Lloyd and Ivanov, 1988). There has also been some inquiry into the historical experience of European nations that have passed through the demographic transition (for a survey, see Galloway et al., in this volume), notably in the context of the European Fertility Project (e.g., van de Walle, 1986) and other projects using micro-data sources (e.g., Knodel, 1988:Chap. 14). Finally, there has been some work on more recent history of developing nations (Pampel and Pillai, 1986).

Much of the recent interest has centered on the following questions: Might exogenously caused declines in infant and child death rates induce partially or wholly offsetting declines in birth rates? Or will mortality-reducing programs, valuable in and of themselves, simply exacerbate already high rates of population growth? These questions form the focus in this volume.

There is, however, the complicating issue of reverse causality (or endogeneity). Lower (or higher) mortality might induce lower (or higher) fertility, but it is well established that higher birth rates lead to higher infant and child mortality. This higher mortality is related to the effect on infants and children of earlier weaning and reduced care from mothers. When the evidence is simply bivariate in nature (as the zero-order correlations used to an extent in this chapter), the causal paths cannot be disentangled. But treating them separately is possible, and this is investigated here as well.


The number of studies dealing with the interaction between fertility and infant (or child) mortality for the United States is surprisingly small. This contrasts with historical research for Europe and for contemporary developing nations. (See essays by Cohen and Montgomery and by Galloway et al., in this volume.)

Among the few historical studies is a recent work using the Utah Population Database of genealogies collected by the Mormon Church (Bean et al., 1992; Lynch et al., 1985). Bean et al. (1992) looked at the reasons why high fertility rates may have resulted in high infant mortality rates for the western United States in the nineteenth and early twentieth centuries. They propose three possibilities (not mutually exclusive): the contagion and competition hypothesis, the biological insufficiency hypothesis, and the maternal depletion hypothesis. The first (contagion and competition) argues that more siblings disadvantage a recent birth by way of increased risk of infectious disease and increased competition for family resources. The second (biological insufficiency) links higher fertility to higher-risk young mothers and hence higher infant mortality. This is both a physiological and socioeconomic argument, since young mothers may not have acquired as many childrearing skills. The third (maternal depletion) asserts that higher fertility is related to more births among older women (age 35 and over) who also have increased risk of infant death for both physiological and social reasons. The results of the study show that, over time, birth intervals lengthened and (by the late nineteenth century) ceased to have a major effect on infant mortality. There was also some evidence for the biological insufficiency and maternal depletion views as fewer births occurred to older women and as age at marriage rose. Bean et al. (1992:344, Figure 1) also found that the infant mortality rate had a curvilinear relation to mother's age (highest at the youngest and oldest ages), an inverse relationship to birth interval length (lowest at longest intervals), an increasing relationship to birth order after the first two children, and a strongly positive relation to parity. This covered the mid-nineteenth to the early twentieth centuries.

A substantial group of studies was conducted earlier in this century by the Children's Bureau using matched birth and infant death records over the period 1911-1915 for eight cities (Johnstown, Pennsylvania; Manchester, New Hampshire; Saginaw, Michigan; Brockton, Massachusetts; New Bedford, Massachusetts; Waterbury, Connecticut; Akron, Ohio; and Baltimore, Maryland). These were summarized in a monograph by Woodbury (1926) (see Table 7-1). These studies reported information on 22,967 births and 2,555 linked infant deaths for which data on the families were obtained by interviews. Several relationships were uncovered that echo the findings from the genealogical data. Infant mortality increased with birth order with the exception of a decline between the first and second births. Infant mortality was also strongly inversely related to birth interval. The characteristic curvilinear pattern of infant mortality and mother's age is also seen in these data—higher rates at the youngest and oldest ages. Father's income (both total and per family member) had a strong inverse association with infant mortality. These fascinating studies include some data on breastfeeding, one piece of evidence pertinent to the influence of infant mortality on fertility. Panel C of Table 7-1 presents information on breastfeeding by race and nativity. Higher levels of artificial feeding were associated with higher infant mortality. Greater incidence of breastfeeding partly offset the negative effects of lower income among several of the foreign-born groups (Italian, Jewish, Polish) and among blacks. Here we have some direct evidence that breastfeeding is associated with lower infant mortality risk, although the data are only suggestive. No tabulations were presented, however, on differences in birth intervals for breastfeeding versus artificial feeding, so it is not possible to see the joint association with fertility.

TABLE 7-1. Mortality Analysis, Eight American Cities, 1911-1915.


Mortality Analysis, Eight American Cities, 1911-1915.

A more recent set of matched birth and death records (from the National Infant Mortality Survey of 1964-1966) have been analyzed by MacMahon and his colleagues (MacMahon, 1974; MacMahon et al., 1973). As of the 1960s, some of the effects that were seen earlier still persist. The infant mortality rate did increase with birth order, albeit not until parity six and above. Mother's age still had the same curvilinear relation to probability of infant death. Also, a previous infant or fetal death substantially increased the risk of subsequent infant death. This may have been because of shorter birth intervals, but more likely it reflected higher-risk mothers. This is a recurring finding in studies of developing nations (e.g., Hobcraft et al., 1985).

In general, however, work on this topic for the United States has been sparse. There have been numerous studies of fertility and of infant mortality separately, but few have attempted to link the two. Furthermore, previous studies have stressed the path from fertility to mortality rather than that from infant and child mortality to fertility.


The study of the transition from high to low levels of fertility and mortality in the United States is bedeviled by lacunae in the data. The United States was early in the activity of taking national censuses (decennially from 1790), and the census did provide useful published age and sex distributions from 1800 onward. This allowed the study of fertility by way of the use of child/woman ratios (Yasuba, 1962; Forster and Tucker, 1972; Okun, 1958; Schapiro, 1986). As can be seen in Table 7-2, these results point to a consistent decline in fertility from at least 1800, as measured by child/woman ratios or by crude birth rates or total fertility rates derived from them.

TABLE 7-2. Fertility and Mortality in the United States, 1800-1990.


Fertility and Mortality in the United States, 1800-1990.

Unfortunately, collection of vital statistics was left to individual states and municipalities, which resulted in tardy and uneven coverage. Massachusetts was the first to begin this activity at the state level in 1842 and achieved relatively good coverage by about 1855 (Abbott, 1897:714-715). But the official Death Registration Area was not formed until 1900 with ten states and the District of Columbia, comprising about a quarter of the nation's population. The official Birth Registration Area was not defined until 1915. Both were not comprehensive until 1933 with the admission of Texas. Hence, what we know about mortality before the 1930s, and infant mortality in particular, is limited to smaller geographic areas or to estimates. Some of these data are also presented in Table 7-2.

The United States was one of those cases of prior sustained fertility decline in which fertility and infant mortality exhibited little or no relationship. From Table 7-2 it is apparent that fertility had been falling since at least 1800. Mortality, in contrast, did not exhibit a sustained decline until about the 1870s. Table 7-2 does not show an unambiguous decline in expectation of life at birth of the infant mortality rate until 1880, although that date could have been an outlier with a decline occurring earlier. This does not appear to have been the case, however. Other mortality data, based on genealogies, and information on human stature, point to deteriorating mortality in the several decades before the American Civil War (Pope, 1992; Fogel, 1986), illustrated in Figure 7-1. The shorter life expectancy is consistent with anthropometric data showing declining heights of West Point cadets in the decades before the Civil War (Komlos, 1987). Thus, the United States constitutes a case in which, during the nineteenth century, fertility was being controlled, mostly by adjustments in marital fertility (Sanderson, 1979), whereas mortality came under control only very late. Under the circumstances, it is not surprising that there was little relation between fertility and infant mortality over time. It has been posited that only where there has been a prior decline in infant and childhood mortality would there likely be any replacement or insurance effect on fertility. If the relationship were from fertility to infant mortality and if infant mortality were mostly subject to exogenous environmental influences (e.g., summer gastrointestinal infections and winter respiratory infections), then the reduced birth ratios would have had only a damped effect on infant and child mortality.

FIGURE 7-1. A comparison between the trends in the mean final height of native-born white males and the trend in life expectancy at age 10 (e10) (height by birth cohort; e10 by period).


A comparison between the trends in the mean final height of native-born white males and the trend in life expectancy at age 10 (e10) (height by birth cohort; e10 by period). SOURCE: Fogel (1986).

The official data for the United States (from 1909) are presented in Figure 7-2. There it is apparent that the infant mortality rate was declining from 1915 onward, while fertility as measured by the general fertility ratio (births per 1,000 women aged 15-49) continued its decline until the baby boom.1 The baby boom may have retarded the decline in the infant mortality rate, which essentially plateaued in the 1940s and 1950s, but it certainly did not raise it. In sum, there appears to be little relationship between the birth rate and the infant mortality rate in aggregate time series data for the United States from the early twentieth century.

FIGURE 7-2. Fertility ratio and infant mortality rate, United States, 1909-1990.


Fertility ratio and infant mortality rate, United States, 1909-1990.

To go back to the nineteenth century requires narrowing the geographic focus. Massachusetts is the best choice, because it had the longest continuum of data of reasonable quality. Some of these data are presented in Figure 7-3 for the state as a whole for the period 1842 to 1960. Massachusetts was certainly not typical of the United States during that period. It was more urban and industrial and had a higher percentage of foreign-born population. For example, in 1900 Massachusetts was 86 percent urban as compared with 40 percent for the United States as a whole. About 30 percent of the Massachusetts population was foreign born at that date in contrast to 13 percent for the nation. On the other hand, Massachusetts was a forerunner in its process of urbanization and structural change. In any event, Figure 7-3 indicates that fertility (as measured by the general fertility rate) had leveled off by the 1870s whereas the infant mortality rate did not commence its decline until the 1890s. One interpretation is that further fertility declines awaited declines in infant mortality, but the birth rate then remained quite steady from the 1890s until the early 1920s, at which point fertility recommenced its decline until World War II. In the meantime, the infant mortality rate continued to be reduced steadily from the 1890s through the baby boom until 1960. Although this could be interpreted as a lack of a relationship between birth rates and death rates, it can also be seen as a lagged response of parents to the changing mortality environment. Parents could well have been waiting to see if the mortality decline was permanent. Meanwhile they practiced hoarding (the insurance motive).

FIGURE 7-3. Fertility ratio and infant mortality rate, Massachusetts, 1850-1960.


Fertility ratio and infant mortality rate, Massachusetts, 1850-1960.

Cross-sectional relationships across space are also revealing. For example, the simple zero-order correlations between the infant mortality rate and the general fertility rate for the counties and towns (or cities for 1905 and 1915) of Massachusetts are given in Table 7-3, along with the state levels of the general fertility rate and the infant mortality rate for the counties and towns (or cities) of Massachusetts. The correlations by county exclude the small (and unusual) islands of Martha's Vineyard and Nantucket. The correlations are always positive (in the expected direction), but are weak and rather unstable until the late nineteenth century. They then become quite strongly positive (e.g., 0.878 for counties in 1915), and only weaken again in the 1920s and 1930s (0.137 for counties in 1940). The town-level correlations are presented both unweighted and weighted by population size. Unfortunately, town-level data on infant deaths cease to be available after 1890. Shortly thereafter, reporting by cities was done, so those are the units given for 1905 and 1915. Again, the picture is rather unclear until the early twentieth century. The correlations all have the expected positive sign, but the results are unstable. Sometimes the weighted and sometimes the unweighted results are significant. By the early twentieth century, both county and city data exhibit larger, positive, significant correlations.2 These results are also consistent with the view that there is a connection between birth rates and mortality during periods of transition—especially mortality transition —although the response of birth rates may be delayed.

TABLE 7-3. Infant Mortality Rates, General Fertility Ratios, and Their Correlation, Counties, Towns, and Cities of Massachusetts, 1855-1941.


Infant Mortality Rates, General Fertility Ratios, and Their Correlation, Counties, Towns, and Cities of Massachusetts, 1855-1941.

Similarly, the simple correlations between the infant mortality rate and the general fertility rate for the states of the Birth Registration Area of the United States in the twentieth century are −0.3315 (1915), −0.1287 (1920), 0.6200 (1930), and 0.6750 (1940), the latter two data points being significant at the 1 percent level. Thus, once again, only later in the process did a significant positive relationship appear. Thus, only as both fertility and infant mortality became quite thoroughly under control did any perceptible positive association appear. This was apparently not the case during the earlier period of the fertility transition in the nineteenth century.


The availability of public use micro-data samples of the U.S. censuses of 1900 and 1910 (Graham, 1980; Strong et al., 1989) also affords an opportunity for further exploration of the fertility-childhood mortality relationship. The usefulness of these censuses lies in the inclusion of questions on children ever born, children surviving, and the duration of current marriage for adult women. These questions were not tabulated at the time, and only some results from 1910 were used in connection with the 1940 census. Analysis of childhood mortality using various indirect methods has now been conducted with both of these micro samples (e.g., Preston et al., 1981, 1994; Preston and Haines, 1991). As part of that work, an index of childhood mortality has been developed (Trussell and Preston, 1982; Preston and Haines, 1991:Chap. 3 and Appendix C; Preston et al., 1994:75-79). The index is based on the ratio of actual to expected child deaths for individual women or groups of women. Actual child deaths are calculated as the difference between stated children ever born and children surviving. Expected child deaths are calculated by multiplying children ever born for each eligible woman by the expected child mortality based on a national average or each marriage duration group (0-4, 5-9, 10-14, …, 30-34). It is a way of comparing actual child mortality to that expected by the national average. The use of marriage duration categories in calculating the index is a means of standardizing for the length of exposure to risk of mortality for the children. The overall totals (see Table 7-4) are close to the national average. That is, the ratio is close to unity (0.9894 for 1900 and 0.9800 for 1910). It is calculated only for once married, or currently married women for whom children ever born, children surviving, and marriage duration were known. The intuitive interpretation is that ratios above 1 showed greater than average mortality and vice versa.

TABLE 7-4. Fertility and the Child Mortality Index, United States, 1900 and 1910.


Fertility and the Child Mortality Index, United States, 1900 and 1910.

Some tabulations of the child mortality index by marriage duration, woman's age, and parity are given in Table 7-4. The results are presented for the total and for white and black populations. It is important to note that mortality was declining rapidly over this period. Hence, some of the increases in the index by marriage duration, age, and parity reflect the time trend. That is, the children of women who were older, married longer, and at higher parity had been exposed, on average, to earlier, higher mortality regimes. That being said, the relationship of childhood mortality to parity was increasing and the curvilinear pattern with age observed elsewhere is repeated.

Table 7-5 attempts to look at this in a multivariate framework to examine the robustness of the results. These regressions examine only the issue of the influence of fertility on childhood mortality. The child mortality index for individual women is on the left-hand side and woman's age, age squared, parity, and years married are on the right-hand side. The regressions are weighted by children ever born to bring the analysis closer to the unit of the child (rather than the woman) and to correct partially for heteroskedasticity. The problem with doing this is that the time trend is still present. Also, it is clear that the coefficients will be biased since parity (on the right-hand side) is endogenous. Nonetheless, introducing these variables, as well as a dummy variable for race, did reveal that the curvilinear pattern of child mortality with age persisted and had the correct orientation (convex from below). Child mortality did increase with parity and black child mortality significantly exceeded that of the white population (by about 24 percent in 1900 and 34 percent in 1910 when controlling for age, parity, and marriage duration). The relationship of marriage duration now becomes negative, however, which is puzzling.

TABLE 7-5. Mortality Analysis, United States, 1900 and 1910.


Mortality Analysis, United States, 1900 and 1910.

Finally, at each census date there was a positive zero-order correlation between the child mortality index and fertility (as measured by average parity): 0.1784 in 1900 and 0.1292 in 1910 for the same group of women in Table 7-4. Looking at aggregation data by state, the correlation between the child mortality index and average parity was weak in 1900 (-0.0132 unweighted and 0.1010 when weighted by population size). In 1910 the same exercise revealed a stronger positive correlation between the child mortality index and average parity (0.1669 unweighted and 0.3136 weighted) and between the index and estimated gross reproduction rates taken from the 1940 U.S. census (0.2627 unweighted and 0.3126 weighted) (Bureau of the Census, 1944). Again, there is evidence for the positive association, which appears to be strengthening over time.


The public use micro samples of 1900 and 1910 also afford the possibility of examining the interesting and pertinent opposite causal path: the replacement and hoarding effects. How extensively do couples replace an actual infant or child death with a new birth? Do families, even those who have not experienced a child death, have births in excess of the number that would be desired in the absence of child loss (hoarding)? It has already been mentioned that it is of interest whether reductions in infant and child mortality in developing nations, undertaken in conjunction with general public health programs or with specialized maternal and child health initiatives, might help reduce fertility and the population growth consequences of the mortality reduction (Lloyd and Ivanov, 1988:157-158). Typically the observed replacement effects have been small, in the range 0.1 to 0.4 for proportions adjusted for demographic and other covariates (Lloyd and Ivanov, 1988:Table 6).3

A method of estimating the pure replacement effect from basic data on children ever born and children surviving (or children dead) for individual women has been constructed by Olsen (Olsen, 1980; Trussell and Olsen, 1983; see also Mauskopf and Wallace, 1984).4 The idea is that simply regressing the number of births on the number of child deaths (i.e., CEBi = α0 + α1*Di where CEBi is births to woman i and Di is child deaths to woman i, will yield a biased and inconsistent estimate of replacement (α1)). As an alternative, an instrumental variable (IV) technique can be used. In stage one, children dead is regressed on the proportion dead (i.e., Di = β0 + β1*Pi, where Pi is the proportion dead to woman i). At stage two, the predicted value of child deaths from stage one is used in a regression with births (i.e., Image p2000a41cg243001.jpg where Image p2000a41cg243002.jpg is predicted child deaths). The coefficient γ1 is a good predictor of the replacement effect (net of hoarding) if the number of births (CEB) and the proportion of children dead (P) are uncorrelated. If this condition is not met, further corrections are necessary.

The basic correction uses the observed child mortality rate and the mean and variance of the birth distribution (which can be calculated from the data) to estimate a “true” replacement coefficient (γ1′). The final correction (IV[adj]) was done taking Olsen's assumption that births and the proportion dead have a joint bivariate lognormal distribution (Olsen, 1980; Trussell and Olsen, 1983). The corrected IV coefficient has been arbitrarily chosen in preference to the corrected ordinary least-squares estimate.5

Estimates of the replacement effect are presented in Table 7-6 for the simple ordinary least-squares (OLS) regression of births on child deaths, the two-stage instrumental variable approach (IV), and for the instrumental variable method corrected for the correlation between births and the proportion death (IV[adj]).6 The bias in the instrumental variable estimate of replacement (that is, (IV-IV[adj]) in Table 7-6) is a measure of the correlation between fertility and child mortality and hence the extent to which high infant and child death rates could induce higher birth rates, that is, hoarding. The assumption is that couples are aware of the ambient child mortality rates. The results are given for women of all ages. Analysis (not shown) was also done for women of age groups 25-29 through 45-49. In addition, the population has been divided by race, nativity (native versus foreign-born white), and residence (rural versus urban white) to account for observed, known heterogeneity in underlying mortality risks (Preston and Haines, 1991).

TABLE 7-6. Estimates of the Replacement Effect, United States, 1900 and 1910.


Estimates of the Replacement Effect, United States, 1900 and 1910.

In general, the results show that the direct replacement effects (IV[adj]) were quite modest in the United States around the turn of the century. Only about 10-30 percent of infant and child deaths were replaced. The replacement coefficients were shorter for younger women (not shown) who presumably had shorter birth intervals in the earlier stages of family building and hence had less latitude to make adjustments. The difference between the unadjusted IV estimate and the adjusted IV estimate is an approximate measure of hoarding (that is, gross replacement minus direct replacement) (Olsen, 1980:440-441). It was in the range of 0.3-0.5 of a child, generally between 0.4 and 0.5 of a child per woman. This results in a gross replacement effect (direct replacement plus hoarding) in the neighborhood of 60-80 percent. Finally, there did not appear to have been any clear differences in direct replacement of hoarding by race, nativity, or rural and urban residence across the census decade. If anything, the tendency toward direct replacement was smaller among older women in 1910 than in 1900, while the propensity to hoard changed little (not shown).

Overall, it must be concluded that direct replacement was relatively modest in the United States around 1900 and that there was still a substantial amount of hoarding. This was taking place during a period of both declining fertility and falling child mortality (see Table 7-2). Because both fertility and mortality were falling for a variety of reasons, there was little effect on natural increase from the declining death rate among children.7 Also, results on replacement are not out of line with contemporary estimates for developing countries (Lloyd and Ivanov, 1988).

Some additional macro-level evidence is present in Table 7-7 in the form of regressions of fertility on lagged and current infant mortality, along with other variables. The upper panel uses the states of the United States in 1910. The dependent variable is the estimated adjusted gross reproduction rate for 1910, taken from the U.S. census of 1940 (Bureau of the Census, 1944). In the first regression, the gross reproduction rate for each state in 1910 is regressed on the child mortality index for that state in 1900, along with the proportions nonwhite, foreign born, and living in urban areas of 25,000 and over. Dummy variables for regions were also included. In this case, birth rates should be responding to previous levels of infant and child mortality; this was found. The sign was in the expected positive direction, but the coefficient was not statistically significant. The second equation substitutes the child mortality index in 1910 for that in 1900. Again, the sign is positive, although the coefficient can be expected to be biased because of simultaneous equations error (i.e., both the gross reproduction rate and child mortality are endogenous). This is corrected in the third equation, which is a two-stage least-squares estimation of the second equation. The instrument chosen is the body mass index (kilograms of body weight per meters of height squared) of World War I recruits for each state. This index is taken as an indicator of health conditions in the 30 years prior to 1917-1918 (Davenport and Love, 1921). The coefficient on the child mortality index in 1910 was increased but still remained statistically insignificant. The other independent variables show that urban residence and living in the Northeast were associated with lower fertility and that higher proportions of nonwhite and foreign born as well as residence in the South were related to higher birth rates.

TABLE 7-7. Regressions on Fertility, United States, 1910, and Massachusetts, 1860, 1885, 1915.


Regressions on Fertility, United States, 1910, and Massachusetts, 1860, 1885, 1915.

The final set of regressions repeats this exercise for the towns of Massachusetts in 1860 and 1885 and for the 54 largest cities in 1915. (Infant mortality statistics ceased to be reported by town in 1890 and were published only for larger cities thereafter.) At all three dates, the general fertility ratio (births per 1,000 women aged 15-49) was regressed on the lagged infant mortality rate, urbanization, and the proportion of nonwhite and foreign born. (Proportion of foreign born was not available by town in 1860.) The city population size was used instead of the urban dummy variable used for 1860 and 1885 (equal to 1 if the town was greater than 5,000 persons in 1860 and greater than 10,000 persons in 1885). In all cases, a 3-year average of vital statistics around the census dates was used. The second equation at each date substituted the current for the lagged infant mortality rate. Finally, the last equation at each date reestimated the second equation with two-stage least-squares. The instrument selected was persons per dwelling, deemed to be an index of crowding and possible source of poor conditions for children.

For 1860, the coefficients on the infant mortality rate (lagged or current) were positive. They were significant in the lagged and two-stage least-squares specifications. The coefficient of infant mortality was again positive and significant in the lagged specification for 1885, but it became negative in the contemporaneous equation. It was not significant in the simultaneous specification equation. Finally, the lagged specification also exhibited a positive and significant effect of infant death rates on birth rates in 1915, although both the contemporaneous specifications yielded insignificant though positive effects.

Overall, these macro-level results support the idea that infant mortality did affect birth rates in the expected direction. For the Massachusetts results, the ordinary least-squares regressions with lagged infant mortality revealed the effect, and it was strongest in 1915.


This chapter began with an effort to explore the relationship of infant (and early childhood) mortality to fertility in the United States over time. The pattern both in time series and from cross-sectional data indicates, however, that the United States is one of those complicated cases also observed by van de Walle (1986) for Europe. Much of the current interest in this issue has focused on recent experience of developing countries where infant and child mortality was high and for which, in many cases, there was a decline in mortality at young ages before, or concurrent with, the fertility transition. This was not the case for the United States. Fertility was in decline from the late 1700s or early 1800s. The overall sustained mortality transition of the modern era did not begin until about the 1870s. For the best documented case—Massachusetts—infant mortality did not begin a sustained decline until the 1890s, at a point when fertility had plateaued after a period of reduction.

Although the time series patterns did not tend to indicate that fertility and mortality were related in the nineteenth century, there is evidence that birth rates responded to changes in death rates by the late nineteenth and early twentieth centuries. Furthermore, the relationship strengthened over the early part of the twentieth century as the decline in infant mortality proceeded rapidly. There is also a suggestion of a lagged response of fertility to mortality change, indicating hoarding (or insurance) behavior. This is confirmed by some cross-sectional evidence for Massachusetts from the 1850s to the 1940s and for the country as a whole from the early twentieth century. Two historical studies (Bean et al., 1992; Woodbury, 1926) found evidence for a relationship for the American West in the nineteenth and early twentieth centuries and for eight American cities, 1911-1915. But the focus was largely on the link from fertility to infant mortality and not the reverse causal path. The lack of an apparent historical association between fertility and mortality may have led to the paucity of studies, since basic data had not suggested much to study.

Some new estimates of both direct replacement and hoarding from the 1900 and 1910 public use micro samples of the United States census also indicate that the link from infant and child mortality to fertility was present, but was relatively modest and in line with what has been observed in a number of developing countries in recent decades. Only about 10-30 percent of all child deaths were directly replaced by births, although hoarding seems to have been more considerable. Gross replacement was thus in the range of 60-80 percent. Reductions in infant and child mortality, such as were occurring in the twentieth century, would thus have had a direct offset in reduced birth rates by about 25 percent. But there would have likely been another indirect offset of up to 50 percent if hoarding declined over time when parents gained greater assurance of child survival.

The relationship between fertility and mortality strengthened during the early part of the twentieth century. The evidence for the United States from the 1850s to the 1940s supports the view that modest direct reductions in fertility can be expected from reductions in infant and childhood mortality, but that more might be expected as hoarding behavior diminishes. The United States is now at quite low levels of fertility and mortality compared both with the past and with contemporary developing countries, and it is not clear that the analysis of these effects for the contemporary United States would yield much of interest in this debate.


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It should be noted that the Birth Registration Area was changing in composition from 1915 to 1933 as it was being augmented. The pattern for the original Birth Registration Area of 1915 was virtually the same, however (Linder and Grove, 1947:Table 27).


It does not make a difference if only the larger cities are used in 1855 and 1885.


In a survey of the literature to the mid-1970s, Preston (1975) found that the proportion of child deaths replaced by a subsequent live birth was about 0.25 in high-fertility populations (Bangladesh, Senegal, Morocco) where many women were not using contraception and were also breastfeeding. It was even lower in populations in the early states of the fertility transition (Mexico, Peru, Colombia). This rose again for countries with more advanced demographic transitions (e.g., Costa Rica, Taiwan) and was still higher for developed countries (e.g., 0.33 in France in 1962).


For a discussion and critique of these models and methods, see the chapter by Wolpin in this volume.


Where there is observable heterogeneity in the underlying mortality risk (e.g., by geographic area, rural or urban residence, racial or ethnic group), the estimates can be made separately for those groups, areas, etc. Where the underlying mortality risk varies across individuals and groups but is unobserved (e.g., by income), the Olsen correction may not be entirely sufficient. (See Wolpin in this volume for a discussion of this.) Trussell and Olsen (1983) conducted some simulations of this and found the effects to be small.


Randall Olsen has kindly provided the author with a copy of his FORTRAN program to perform the estimations.


Natural increase remained relatively constant at 12.8 per 1,000 from the 1890s to the decade of the 1900s (see Haines, in press, Table 1).

Copyright 1998 by the National Academy of Sciences. All rights reserved. Printed in the United States of America.
Bookshelf ID: NBK233807


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