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6 Infant Mortality and the Fertility Transition: Macro Evidence from Europe and New Findings from Prussia Patrick R. Galloway, Ronald D. Lee, and Eugene A. Hamme! INTRODUCTION Most attempts to understand secular fertility decline include some allusion to the European experience. It is generally thought that little or no relationship existed between fertility decline and infant mortality decline in Europe, or that the findings from relevant studies are inconsistent. We believe that these com- mon perceptions are mistaken. When more attention is given to the varying methods of analyses, a more consistent picture emerges. We argue that it is particularly important to keep in mind whether studies are bivariate or multivari- ate; whether studies estimate cross-sectional relations between levels of fertility and of infant mortality, or instead focus on the relation of changes in these variables; and whether studies take into account the possibility that causality flows in both directions from fertility to mortality as well as from mortality to fertility. We estimate both the impact of infant mortality on fertility and the impact of fertility on infant mortality, using aggregate data from Prussia from 1875 to 1910 and fixed effects models with instrumental variables. This is followed by an extensive review of previous research on fertility and infant mortality within the historical European context.1 By comparing our findings for Prussia with earlier research looking at both level and change effects, we find considerable evidence 1Our review of earlier research is restricted to those studies using aggregate data. There is a body of literature on fertility and infant mortality that uses micro-level data, see for example Knodel (1988). However, it is beyond the scope of this chapter to survey such studies. 182

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PATRICK R. GALLOWAY, RONALD D. LEE, AND EUGENE A. HAMMEL 183 for a positive association between the fertility level and the infant mortality level, as well as a positive association between fertility change and infant mortality change. The Long Term It is clear that in the very long run, in closed populations, fertility and mortal- ity are linked because of the finiteness of the resource base, which implies that the average rate of natural increase n must not exceed zero more than slightly. This is an abstract argument. The historical reality has been that rapid natural increase sustained over long periods (say an average rate of natural increase greater than 0.02 over a period of more than two centuries) has not been observed except in frontier regions2 such as North America. Much more typically, large populations appear to have had rates of natural increase of less than 1 percent per year until the Industrial Revolution, and usually with a strong positive statistical association between fertility and mortality in the cross section. Such a long-term positive association of fertility and mortality, and a limit to average rates of natural increase, can be explained in at least two ways. First, positive growth rates mean increasing population size and density, which under preindustrial conditions typically meant declining living standards. These in turn caused mor- tality to rise, or fertility to fall, and therefore growth rates to return toward zero. This is the Malthusian theory of population equilibration through negative feed- back (Lee, 1987~. Of course, emigration was another possible outcome, and technological progress or international trade might intervene between population growth and declining living standards. Second, it is sometimes argued that the sociocultural institutions governing fertility evolved in the context of some aver- age mortality regime so as roughly to balance fertility and mortality on average, leaving rates of natural increase close to zero. In this version there is no feedback from population size to the vital rates; rather, growth rates themselves tend to have average levels not far above zero. Again, migration, technological progress, and international trade might play a role (Smith, 1977; Yule, 1906~. The constraint on average growth rates, and hence on fertility and mortality, implied by these theories and the positive association of fertility and mortality observed in the historical record, may also help to explain the long-run shape of the demographic transition (Lee and Bulatao, 1983, for example). Demeny (1968:502) gave a classic description of the transition: "In traditional societies, fertility and mortality are high. In modern societies, fertility and mortality are low. In between, there is demographic transition." In fact, in those national 2By frontier regions we mean from the point of view of agricultural populations, that is, not from the point of view of hunter and gatherer populations who may have occupied the area at relatively low density before the arrival of agriculturists.

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184 MACRO EVIDENCE FROM EUROPE AND NEW FINDINGS FROM PRUSSIA populations that have "completed" the transition, fertility has dropped so low that growth rates may turn very substantially negative. Nonetheless, it is difficult to escape the conclusion that, in some vague and unspecified way, and despite all the accompanying structural changes in the economies and societies, the very long-term decline in fertility is ultimately due to a very long-term decline in mortality, or the two are interlinked. In fact, some theories link both declines to the same set of parental decisions concerning investment in children. These very long-run relations, both theoretical and empirical, are based on some sort of slow-acting feedback operating through the macro-economic or macro-societal level. The posited mechanisms might be expected to operate over the course of a century or more, but not over the course of decades. For this reason, they are of little relevance for questions about the policy-relevant time frame of adjustment over the medium range of, say, 5-30 years. The Short Term Although the long-run historical relation of fertility and mortality is doubt- less positive, it is equally true that the empirical relationship over short-run fluctuations has been consistently negative in historical populations. This has been established by a large number of studies of time series of births and deaths, once the long-term trends in the data have been statistically removed. It is easy to think of reasons to expect either a positive or a negative association of the two vital rates. For a positive relationship, note that high mortality will break many marriages, particularly those of older couples, and that the subsequent remar- riages of widows and widowers might result in higher fertility than if the mar- riages had been unbroken. Furthermore, higher mortality would free land hold- ings and create other economic opportunities permitting new marriages that would have high fertility. In existing unions, high infant and child mortality would interrupt breastfeeding, eliminating its contraceptive effects, and therefore lead to earlier conceptions and a temporary increase in fertility. Reconstitution studies have often demonstrated this lactation interruption effect. On the behavioral side, if we are not dealing with a natural fertility regime, we might expect couples who have experienced the loss of a child to attempt to replace it with another birth sooner than they normally would have, or by having one more birth than origi- nally intended. However, many historical demographers dispute that this actu- ally occurs to any appreciable degree, except in special subpopulations (Knodel, 1978~. For a negative relationship, note that many factors that tended to raise mor- tality would also tend to reduce fertility. For example, low real incomes appar- ently had this effect, as did unusually hot summer months or unusually cold winter months (see Lee, 1981; Galloway, 1986, 1988, 1994~. The variation of such factors in the short term would have led to a negative bivariate association of fertility and mortality, but if observable, they can be netted out in multivariate

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PATRICK R. GALLOWAY, RONALD D. LEE, AND EUGENE A. HAMMEL 185 studies. Perhaps more important were unobservable influences, of which ill health dominated. Fluctuations in morbidity both raised mortality and reduced fertility, leading to a strong negative association of short-term fluctuations in fertility and mortality, even after controlling for observed fluctuations in real incomes or grain prices and temperature. The estimated, strongly negative asso- ciation of short-run variations in fertility and mortality is not very informative about structural or causal influences of mortality on fertility or the reverse. The many short-run studies of the relation of fertility to mortality in historical popula- tions will therefore not answer the question before us. The Medium Term For policy makers, the most relevant time frame for fertility and infant mor- tality interactions is probably the medium term, say 5-30 years. Assuming a couple has some notion of a desired number of surviving offspring, infant and child mortality should be positively associated with the number of births. A couple can assume that some unknown number of offspring will die, and then stop when they think they have enough children (often called hoarding behavior). Or the couple can wait to see if the last child born survives past a certain age. If the child dies, the couple can then engage in replacement reproductive behavior. Both strategies are types of "inventory control" (Preston, 1978:10) leading to some desired number of surviving offspring. Within either strategy, the number of births should decline as infant mortality declines. There are also ways in which declining mortality might alter the desired number of surviving children. It reduces the costs of achieving a given target number, and therefore might raise the target by increasing discretionary income. Alternatively, declining mortality might raise the rate of return on investments in children, which could lead to a substitution of quality for quantity, and a reduced target. Here, however, we concentrate on the fixed target scenario. Once infant mortality begins to decline, it might take some time for couples to perceive the effect of infant mortality on child survivorship, which would ultimately lead to changes in fertility. It is also possible, however, that the effect could be almost immediate, as couples hear about and read about mortality de- cline.3 lit would be difficult to test for very short lags because censuses (from which we derive most of our independent variables) are nearly always at least 5 years apart, and because it is very likely that the level of infant mortality rates at year t will be highly correlated with the level of infant mortality rates at years t- 2, t- 3, or t - 4. using Prussian data and the model shown in Appendix Table 6A- 2, we added the variable infant mortality lagged 5 years and found that, in the fixed effects model which estimates changes, the regression estimate on infant mortality with no lag was 0.267 whereas the regression estimate on infant mortality lagged 5 years was -0.062, suggesting that the lagged variable was relatively unimportant.

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186 MACRO EVIDENCE FROM EUROPE AND NEW FINDINGS FROM PRUSSIA Elevated infant mortality tends to shorten the birth interval because the death of an infant curtails lactation amenorrhea along with its contraceptive effects. An increase in infant mortality will cause an increase in fertility, ceteris paribus, although few children may ultimately survive, of course. This short-term phe- nomenon can persist over time, becoming an important factor over both the medium and the long term. Fertility variations, whether deliberate or accidental, can also affect infant and child mortality as demonstrated by a host of contemporary studies. There is good reason then to expect that exogenous increases in infant and child mortality caused increases in marital fertility and that exogenous increases in fertility caused increases in infant and child mortality. (However, this micro-level reasoning about motives and relations does not translate exactly to the macro level because of expected nonlinearities in the relationships.) Infant and Child Mortality Matthiessen and McCann (1978) provide a useful overview of the findings of historical studies of macro-level data, with an emphasis on the early results of the European Fertility Project. They are particularly critical of the use of infant mortality as the explanatory mortality index, because they find that in practice other more appropriate measures, such as mortality of children age 0- 15, began to decline earlier than did infant mortality, so that the European Fertility Project's studies of timing, for example, are of little value. When they reexamine the timing of the fertility transition in relation to i5qo, they find that mortality decline almost always preceded fertility decline. We believe that it is very difficult to estimate the onset of secular i5qo decline. In general, we suggest that there is often no clear point at which one can categorically state that mortality or fertility has begun to decline, a suggestion with which Matthiessen and McCann (1978:52) clearly agree. Concerning the onset of infant mortality decline, van de Walle is appropriately cautious, noting that "in most instances we are left ignorant of past trends: the data do not allow us to go back in time and the existence of an earlier decline cannot be ascertained" (1986:213~. It might be useful to address the issue of infant (under age 1) versus child (age 1-9) mortality in multivariate analyses of secular fertility decline. When a husband or wife thinks about procreation in terms of offspring survivorship, he or she considers both infant and child mortality (Matthiesson and McCaan,1978:52~. Although infant mortality rates can generally be found in most historical registra- tion material, the more detailed measures of child mortality are often unavailable. However, in a high infant mortality regime, the bulk of infant and child deaths will be infant deaths, and infant mortality should be very highly correlated with infant and child mortality combined. Using 1890-1891 male mortality data for the 36 provinces (Regierungsbezirke) of Prussia, we find that the correlation r between ~qO and 5qo is 0.96, between ~qO and iOqo is 0.96, and between ~qO and

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PATRICK R. GALLOWAY, RONALD D. LEE, AND EUGENE A. HAMMEL 87 15q0 is 0.95 (Konigliches Statistisches Bureau, 1904:135-147~. The range of 1q0 in the provinces is 109-273. A similar analysis of the 15 largest cities in Prussia from the same source reveals respective r's of 0.98,0.97, and 0.91 with a range of GO of 170 to 326. Plots of each of the six graphs reveal essentially a straight line with no outliers. It seems likely that the infant mortality rate is an adequate proxy for infant and child mortality when using aggregate data in high infant mortality populations. Although it is difficult to say much about the timing or onset of secular infant and child mortality decline, we can examine their relative speed. It is clear from Figure 6-1 that GO and GO generally declined at about the same rate over the decades from the 1870s to around 1925. The quality of German infant and child mortality data before 1875 is questionable. Such consistency lends further sup- port to the notion that infant mortality is an adequate proxy for infant and child mortality, at least in Germany. ANALYSIS OF PRUSSIAN DATA From a theoretical perspective it seems likely that higher infant mortality should ultimately be associated with higher fertility, and vice versa. We attempt to evaluate both the effect of infant mortality on fertility and the effect of fertility on infant mortality using fixed-effects models and instrumental variables estima- tion applied to data from 407 Prussian Kreise (administrative districts) and 54 cities in Prussia from 1875 to 1910.4 The following equation system describes the structural relationships between fertility and mortality: Fi G = ale + maxi G + ~3Zi,G + ~4Mi,l + ~5,i + FIG + i,l' Mi G = 0lY1 + 02Xi G + 03Zi,G + 04Fi,l + P5,i + FIG + ~i,G. Here F and M refer to appropriate measures of fertility and infant (and/or child) mortality in the subpopulation of region i at time t. Y is a matrix of unchanging characteristics of the regions that influence fertility or mortality (indicated by superscripts). X is a matrix of changing influences on both fertility and mortality in the regions. Z refers to changing variables in the regions that influence just fertility or just mortality, respectively. OC5 i and ,135 i are disturbances or fixed effects in the two equations that do not change over time, but are specific to the regions. 6~ and 0~ are disturbances to the two equations that are the same across all regions, but that vary over time. Finally, Ei ~ and Aid are disturbances to the 4See Galloway et al. (1994, 1995) for details regarding these two data sets.

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88 MACRO EVIDENCE FROM EUROPE AND NEW FINDINGS FROM PRUSSIA 1~0 and 15qO of males in C;errnany 0~400 0.35a 0~3~ onto 0.200 0.150 0.100 at o 5t of 1 o 5 ~ i, - 1871-18~0 1881-18GO 1891-19~ 1901-1910 191~1911 1924-1026 Percent change in 1~0 and 1 5qO of males in Germany o : .~ o1~D _~ FIGURE 6-1 Level and change of male infant and child mortality rates in Germany, 1871-1926. SOURCE: Statistischen Reichsamt (1930:168~.

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PATRICK R. GALLOWAY, RONALD D. LEE, AND EUGENE A. HAMMEL 189 equations that are specific to time period and to region. Because our data repre- sent non-overlapping 5-year averages, the short-term relations will be largely masked, so long-term and medium-term relations will dominate the estimates. We use this pair of equations to attempt to approximate a far more compli- cated dynamic pair of equations that would explicitly include the long-run adjust- ment processes that bring fertility and mortality to similar levels. In the given equations, the fixed-effect terms are used to represent the outcome of these long- term adjustment processes. The coefficients ~4 and p4, which represent the influence of mortality on fertility and fertility on mortality, therefore abstract from these long-run adjustment processes and represent only the medium-term influences of one on the other. For example, they would not reflect the possible development of social institutions to motivate high fertility in the face of high mortality. When we estimate this model, which includes fixed effects, therefore, the estimated coefficients should reflect only the medium-term adjustment pro- cesses that we believe to be particularly informative for policy considerations. We often refer to such fixed-effect estimates as change estimates, because they are shaped entirely by the relation of changes over time within each Kreis, and not at all by differences in fertility and mortality between Kreise. By contrast, estimates of these equations based on a single cross section, as are common in the literature, mainly reflect the outcome of the long-term adjust- ment processes and of correlations of right-hand variables with persistent fea- tures of the different geographic units, such as agrarian system, local culture, political orientation, or breastfeeding practices, yielding coefficient estimates that are inconsistent or irrelevant for policy. When suitable instruments are available, two-stage least squares can be used to avoid the biases arising from correlations of right-hand variables with persistent influences; however, suitable instruments can rarely be found in this context. Furthermore, instruments will not solve the problem that long-term adjustment processes probably dominate cross-sectional estimates. We expect that over the long run, the levels of fertility and mortality will be positively correlated. These long-run correlations would show up in correlations of the fixed effect disturbances OC 5 i and ~5 i. These correlations would bias any estimate of the structural coefficients relating fertility and mortality directly. Furthermore, the system described by these equations is simultaneous, with both fertility and mortality endogenous. Attempts to estimate the equations by ordi- nary least squares would yield biased estimates. Now suppose we difference all the variables, representing the differenced values by lower case letters. We will actually be using fixed-effects estimators, but looking at the effects of differenced variables is a simple way to examine the consequences of using the fixed-effect model. Differenced disturbance terms are represented by the same Greek characters, but without the tildes. In this case, the region-specific disturbances that do not change over time disappear, as do all other variables that do not change over time. We then have

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190 MACRO EVIDENCE FROM EUROPE AND NEW FINDINGS FROM PRUSSIA fi,' = Loci,' + phi,' + fermi,' + 6' + Pi I, ml,' = 02xi,' + 03Zi,' + 04fi,' + 0t + ~i,{. The problem of correlated fixed effects has been removed, but the simultaneity remains. However, we can use the variables z to identify instrumental or two- stage least-squares estimates of the coefficients. These should, in principle, be unbiased except that there is an additional problem: We do not observe all the relevant x variables. For example, breastfeeding behavior, which affects both fertility and infant mortality, is unobserved.5 But extended breastfeeding re- duces both fertility and infant mortality, and failure to control for its influence will lead to a noncausal positive association of fertility and mortality. Put differ- ently, unobserved and therefore omitted variables in the x matrix will induce a correlation of the error terms in the two equations and lo. To be concrete, the omission of breastfeeding variables from the estimated model will lead to a positive correlation in the disturbances, resulting in an upward bias in the esti- mated structural coefficients on fertility and mortality; the omission of health and illness variables may have the opposite effect. This could be a serious problem for which we have no remedy. Therefore, this potential source of bias must be kept in mind when interpreting the results. Two-Stage Least-Squares Estimation Our estimation model reflects the general theoretical perspective outlined above in the use of fixed effects and controls for the endogeneity of infant mortality. However, we have taken a rather eclectic approach to inclusion of socioeconomic influences on fertility and have not imposed any mathematical structure on the relations to be estimated beyond the usual assumption that our linear model approximates some true but unknown nonlinear specification. One of the findings from our review of earlier research on fertility decline in Europe is that many studies that purport to say something about fertility decline (change) only examine fertility level. Preston (1978:1) states "a central problem in modern population studies . . . is . . . the degree to which changes in mortality can be expected to induce changes in fertility." This clearly poses the question in terms of changes and not of levels. We believe that this is indeed the appropriate question, and that it is not an issue that can be resolved by studying the relation- ship between levels of fertility and mortality. sin Prussia, longitudinal data on breastfeeding are available only for Berlin. sreastfeeding in Berlin decreased significantly from 1885 to 1910 (Kintner, 1985:169-170) while both marital fertil- ity and infant mortality were declining substantially. It is not known whether other areas in Prussia experienced similar trends.

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PATRICK R. GALLOWAY, RONALD D. LEE, AND EUGENE A. HAMMEL 191 In our analyses of pooled cross-sectional time series we first examine the "between" estimators, regressions on the means over time of each Kreise or city, that give US level effects. We also generate "within" or "fixed-effects" estima- tors, regressions that allow each Kreis or city to have its own intercept. This effectively measures how changes in our independent variables affect changes in our dependent variable and is the more appropriate approach for explaining fertil- ity change.6 We have dealt at length with the theoretical expectations and empirical find- ings of fertility decline in 407 Prussian Kreise (Galloway et al., 1994) and 54 cities (Galloway et al., 1995) using quinquennial data from 1875 to 19107 and pooled cross-sectional time series ordinary least-squares methods.8 A detailed analysis of infant mortality decline in the Kreise and cities of Prussia is in progress (Galloway et al., 1996~.9 We expect fertility to influence infant mortality and simultaneously we expect infant mortality to influence fertility. Instrumental variables estimation, two-stage least squares in this case, appears to be an appro- priate method for estimating these effects. All the variables in all the models are defined in Appendix Table 6-A1. Our fertility model is shown in Appendix Table 6-A2 followed by a summary of regression results in Appendix Tables 6 6Brass and Barrett (1978:212) also favor pooled cross-sectional time series studies done of areas within a country. 7Prussia became a state within Germany in 1871, but continued to maintain its own statistical bureau that published detailed demographic and economic data until the early 1930s. In 1910 the population of Prussia was just over 40 million, about 70 percent of Germany. If Prussia had been a country, it would have been the largest country in Europe excluding Russia. It covered most of modern-day Germany north of the Main River and most of the western half and northern quarter of modern-day Poland. Registration data are available annually and census data quinquennially from 1875 to 1910 for Kreise and major cities. Kreise are administrative units similar to U.S. census tracts though much larger (average population 60,000) and, like census tracts, tended to split over time. There were about 400 Kreise in Prussia in 1875 and about 600 by 1910, with the total area of Prussia being virtually constant. To maintain spatial consistency over time, we combined many of the split Kreise. This resulted in 407 Kreise, each with a constant area, from 1875 to 1910. Only seven of the 407 Kreise were 100 percent urban. To examine fertility decline within a strictly urban setting, we created another data set consisting of 54 cities, whose area we allowed to change over time, realizing that any area incorporated into a city was itself likely to be highly urban. 8We use general marital fertility rate (GMFR) as our measure of marital fertility in this and in all our previous analyses of Prussian Kreise. GMFR is defined as the number of legitimate births per 1,000 married women aged 15-49. A 5-year average centered on the census year is used. More , O detailed marital age structure data are not available. Coale and Treadway (1986:153) note that there would have been little difference in their findings if GMFR had been used instead of Ig. In fact we find that in 54 Prussian cities from 1875 to 1910 where data are available to calculate both Ig and the GMFR that Ig and GMFR are highly correlated (r = 0.97) and that the two measures are virtually interchangeable. 9The average infant mortality rate in Prussia in 1900 was 179, somewhat above that found in most less developed countries today. In 1992 Mozambique had an estimated infant mortality rate of 162, the highest of any county in the world (World Bank, 1994:214).

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192 MACRO EVIDENCE FROM EUROPE AND NEW FINDINGS FROM PRUSSIA AS and 6-A4. The infant mortality model can be found in Appendix Table 6-A5 with regression results summarized in Appendix Tables 6-A6 and 6-A7. We focus on the relationship between fertility and infant mortality. The findings for the other right-hand side variables have been discussed elsewhere (Galloway et al., 1994, 1995, 1996). Estimation of the Fertility Equation High fertility and the shorter birth intervals it involves might well cause higher infant and child mortality. To avoid the possible bias associated with ordinary least-squares estimation, we need instruments for infant mortality that are correlated with infant mortality but not correlated with the component of its variance that might be influenced by fertility. We believe that male mortality at older ages provides a nearly ideal instrument in this case. Fertility should affect only the mortality of children. We do not know the upper limit of the range of ages that might be affected by high fertility, so we avoided using the mortality even of teenagers. The mortality of women depends in part on maternal mortal- ity, which would depend on fertility, so we avoided using female mortality. For these reasons, we decided to use the mortality of adult males. Because of the cost of data entry, we limited ourselves to male mortality in the 30-34 age group. This choice was based in part on an examination of a correlation matrix for mortality at different ages for both Prussian Regierungsbezirke and historical Swedish data, which showed that death rates at age 30-34 were relatively highly correlated with infant mortality. Other age groups had correlations that were nearly as high, so the exact choice makes little difference, and ideally we would have used mortality over a broader range. The idea is that male mortality at age 30-34 is a useful index of the general level of mortality in the population, reflecting all local factors that influence mortality, such as standard of living, nutrition, general sanitary conditions, eco- logical and epidemiological conditions, and the quality of health care. At the same time, it does not reflect the particular influence of either breastfeeding conditions or of fertility and therefore should not correlate with marital fertility. Unfortunately, age-specific death rates are available only for Regierungs- bezirke (very large areas, similar to provinces) of which there were 36 in Prussia. Given 407 Kreise in Prussia, there were on average about 11 Kreise per Regierungsbezirk. We applied Regierungsbezirk male mortality at age 30-34 for each of the eight quinquennial periods from 1875 to 1910 to the Kreise or city within the Regierungsbezirk. This instrument captures only broad regional varia- tions in mortality, but not local differences, reducing its usefulness. Appendix Table 6-A3 presents the ordinary least-squares and two-stage least- squares findings for Kreise, for both levels and changes. Looking at levels, we find that when we use ordinary least squares the estimated coefficient on infant mortality is negative and marginally significantly different from zero, but, using

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216 MACRO EVIDENCE FROM EUROPE AND NEW FINDINGS FROM PRUSSIA TABLE 6-A1 Definitions of Variables Used in the Analysis Variable Definition Catholic Slav Church Education Health FLFPR GMFR General marital fertility rate (legitimate births per 1,000 married females 15-49). Catholics per 100 total population. Slavic speakers per 100 total population. Employees in religious occupations per 100 population over age 20. Teaching employees per 100 population aged 6-13. Health employees per 100 total population. Female labor force participation rate (employed females per 100 female population aged 20-69) (excludes agriculture and service). Income Average real income of male elementary school teachers in Deutsche marks as of 1900. Mining Mining employees per 100 employed persons. Manufacturing Manufacturing employees per 100 employed persons. Used only in the city model Urban Urban population per 100 total population. Used only in the Kreis model. Banking employees per 100 population over age 20. Insurance employees per 100 population over age 20. Post, telegraph, and railway employees per 100 population over age 20. Population, in thousands. Used only in the city model. Legitimate infant mortality rate (legitimate deaths under age one per 1,000 legitimate births). Married males/married females. Population born in Kreis per 100 total population. Used only in the Kreis model. Population born in city per 100 total population. Used only in the city model. Cumulative municipal sanitation bond debt per capita in Deutsche marks. Available only for cities. Age-specific death rate for males aged 30-34. Data are available only for Regierungsbezirke. Bank Insurance Communications Population Infant mortality Married sex ratio Kreis born City born Sanitation ASDR NOTES: For details and sources see Galloway et al. (1994, 1995, 1996). Data are available quin- quennially from 1875 to 1910. Vital registration variables are based on 5-year average centered around each quinquennial year. Stillbirths are excluded throughout. There are 36 Regierungsbezirke and 407 Kreise in Prussia. We also examined 54 cities. In general, the German occupational censuses do not lend themselves to calculation of economic sector variables because of a peculiar redefinition of female agricultural laborers that leads to an improbable 2 million increase in the category between 1895 and 1907 (Tipton, 1976:153-158). However, city populations were probably not affected by this problem because there were few agricultural workers in the cities. This is the reason the variable Manufacturing is available only in the cities. Mining is available for both Kreise and cities because virtually all miners were men.

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PATRICK R. GALLOWAY, RONALD D. LEE, AND EUGENE A. HAMMEL TABLE 6-A2 Models Used in the Fertility Analysis 217 Variable Kreis Fertility Model (equation (1)) City Fertility Model (equation (2)) Expected Sign Dependent In dep en dent GMFR Catholic Slav Church Education Health FLFPR Income Mining Urban Bank Insurance Communications Infant mortality Married sex ratio GMFR Catholic Slav Church Education Health FLFPR Income Mining Manufacturing + + + + Bank Insurance Communications Population Infant mortality Married sex ratio + NOTES: In equation (1) two-stage least-squares age specific death rate (ASDR) for males aged 30- 34 is used as an instrument for Infant Mortality. In equation (2) two-stage least-squares Sanitation and ASDR are used as instruments for Infant Mortality.

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218 MACRO EVIDENCE FROM EUROPE AND NEW FINDINGS FROM PRUSSIA TABLE 6-A3 Equation (1~: Summary of Ordinary and Two-Stage Least-Squares Fertility Regression Results for Kreise in Prussia, 1875-1910 (dependent variable is GMFR) Level Variable Expected Sign OLS Change TSLS OLS TSLS Constant Catholic Slav Church Education Health FLFPR Income Mining Urban Bank Insurance Communications Infant mortality + + + Married sex ratio + 189.374** 0.693** 0.348** 258.026** 0.716** 0.137 1.01310.586 -5.488t-5.816 -32.456*-42.767* -0.529t-2.296* -0.0140.032 1.032**1.251 ** 0.034-0.089 -36.0201.850 29.251-48.872 -0.4535.708 -0.052t0.478t 91.828t-107.824 -2.138** -0.283 23.231 ** -9.075** -6.596 -1.235** -0.002 0.107 -1.654** -1.161** 38.721** -7.164** 24.430t -1.153** 0.004 0.757**0.430 -0.385t -55.325**-26.903t -133.466**-66.125* -7.333**-1.799 0.242**1.028** 40.674*-57.928 NOTES: OLS, ordinary least squares. TSLS, two-stage least squares. The unit of analysis is the Kreise. The level regressions use averages of each variable over eight quinquennial periods from 1875 to 1910. The change regressions are fixed-effects models using data for eight quinquennial periods from 1875 to 1910. Estimates for the 407 Kreis dummy variables are omitted. In the level regressions n = 407 and OLS R2 = 0.681. In the change regressions n = 3,256 and OLS R2 = 0.920. **, *, ~ indicate that the coefficient is statistically significant at the 1 percent, 5 percent, and 10 percent levels, respectively, two-tailed test. Age-specific death rate for males aged 30-34 is used as an instrument for Infant Mortality in the two-stage least-squares regressions for both level and change. The two-stage least-squares t statistics are based on the structural residuals (Hall et al., 1992:133-134) and are asymptotically correct. The ordinary least-squares results are discussed at length in Galloway et al. (1994).

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PATRICK R. GALLOWAY, RONALD D. LEE, AND EUGENE A. HAMMEL TABLE 6-A4 Equation (2~: Summary of Ordinary and Two-Stage Least-Squares Fertility Regression Results for Cities in Prussia, 1875-1910 (dependent variable is GMFR) 219 Level Change Expected Variable SignOLSTSLSOLSTSLS Constant 422.365*448.292* Catholic +0.581**0.628**-0.0442.354t Slav +0.2750.2182.010*-1.990 Church +25.98918.053-2.11325.009 Education --4.064-4.589-4.585**-4.809t Health --1.314-1.6187.69396.812** FLFPR --1.264*-0.976-3.571 * *-0.919 Income -0.004-0.004-0.022* *-0.030* * Mining +1.828**1.616*0.161-1.221 Manufacturing +0.761*0.4680.357-0.221 Bank --44.682*-53.788*-11.13954.861t Insurance -17.90123.651-43.001**11.970 Communications --5.276*-6.122t-5.959*-0.045 Population --0.0070.002-0.041 * *0.056 Infant mortality +-0.042-0.1870.337**1.836** Married sex ratio +-193.165-163.150354.038**194.328 NOTES: OLS, ordinary least squares. TSLS, two-stage least squares. The unit of analysis is the city. The level regressions use averages of each variable over eight quinquennial periods from 1875 to 1910. The change regressions are fixed-effects models using data for eight quinquennial periods from 1875 to 1910. Estimates for the 54 city dummy variables are omitted. In level regressions n = 54 and OLS R2 = 0.888. In the change regressions n = 432 and OLS R2 = 0.896. **, *, ~ indicate that coefficient is statistically significant at the 1 percent, 5 percent, and 10 percent levels, respec- tively, two-tailed test. Sanitation and age-specific death rate for males aged 30-34 are used as instruments for Infant Mortality in the two-stage least-squares regressions for both level and change. The two-stage least-squares t statistics are based on the structural residuals (Hall et al., 1992:133- 134) and are asymptotically correct. The ordinary least-squares results are discussed at length in Galloway et al. (1994).

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220 MACRO EVIDENCE FROM EUROPE AND NEW FINDINGS FROM PRUSSIA TABLE 6-A5 Models Used in the Infant Mortality Analysis Infant Mortality Model Expected City (equation (4)) Sign Variable Kreis (equation (3)) Dependent In dep en dent Infant mortality Catholic Slav Education Health FLFPR Income Urban Communications GMFR Kreis born Infant mortality Catholic Slav Education Health FLFPR Income Communications Population GMFR City born Sanitation NOTES: In equation (3) two-stage least squares, Church, Mining, Bank, Insurance, and Married sex ratio are used as instruments for GMFR. In equation (4) two-stage least squares, Church, Mining, Manufacturing, Bank, Insurance, and Married sex ratio are used as instruments for GMFR.

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PATRICK R. GALLOWAY, RONALD D. LEE, AND EUGENE A. HAMMEL TABLE 6-A6 Equation (3~: Summary of Ordinary and Two-Stage Least-Squares Infant Mortality Regression Results for Kreise in Prussia, 1875-1910 (dependent variable is infant mortality rate) 221 Level Change Expected Variable SignOLSTSLSOLSTSLS Constant 656.315**723.051 ** Catholic +0.325**0.4750.1090.639** Slav +0.0870.1320.898**0.925** Education --15.705**-18.071**-0.4831.892 Health --7.386-14.945-43.048**-35.017** FLFPR +2.567**2.364**0.0500.362t Income --0.110**-0.111 **-0.009**-0.007* Urban +-0.256-0.2860.366**0.392** Communications --12.640**-12.368**-5.862**-3.967** GMFR +-0.304**-0.5030.297**0.512** Kreis born --3.418**-3.559**-0.333**-4.10** NOTES: OLS, ordinary least squares. TSLS, two-stage least squares. The unit of analysis is the Kreis. The level regressions use averages of each variable over eight quinquennial periods from 1875 to 1910. The change regressions are fixed-effects models using data for eight quinquennial periods from 1875 to 1910. Estimates for the 407 Kreis dummy variables are omitted. In the level regressions n = 407 and ordinary least-squares R2 = 0.432. In the change regressions n = 3,256 and R2 = 0.922. **, *, ~ indicate that the coefficient is statistically significant at the 1 percent, 5 percent, and 10 percent levels, respectively, two-tailed test. Church, Mining, Bank, Insurance, and Married sex ratio are used as instruments for GMFR in the two-stage least-squares regressions for both level and change. The two-stage least-squares t statistics are based on the structural residuals (Hall et al., 1992:133-134) and are asympototically correct. These results are discussed at length in Galloway et al. (1996).

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222 MACRO EVIDENCE FROM EUROPE AND NEW FINDINGS FROM PRUSSIA TABLE 6-A7 Equation (4~: Summary of Ordinary and Two-Stage Least-Squares Fertility Regression Results for Cities in Prussia, 1875-1910 (dependent variable is infant mortality rate) Level Change Expected Variable SignOLSTSLSOLSTSLS Constant 459.350**455.027** Catholic +0.621t0.609-1.345**-1.296* Slav +-0.737-0.7431.983**1.287 Education --0.0820.1040.2071.954 Health --51.765-51.793-58.008**-52.045** FLFPR +0.9771.002-0.5470.614 Income --0.073**-0.073**0.009*0.014** Communications --7.184-7.084-7.551 * *-3.649 Population +0.053*0.053*-0.053**-0 033t GMFR +-0.198-0.1830.247**0.517** City born --2.215 * *-2.220* *-0.852*-0.289 Sanitation --0.906-0.910-0.434* *-0.287 * NOTES: OLS, ordinary least squares. TSLS, two-stage least squares. The unit of analysis is the city. The level regressions use averages of each variable over eight quinquennial periods from 1875 to 1910. The change regressions are fixed-effects models using data for eight quinquennial periods from 1875 to 1910. Estimates for the 54 city dummy variables are omitted. In the level regressions n = 54 and ordinary least-squares R2 = 0.412. In the change regressions n = 432 and R2 = 0.903. **, *, ~ indicate that the coefficient is statistically significant at the 1 percent, 5 percent, and 10 percent levels, respectively, two-tailed test. Church, Mining, Manufacturing, Bank, Insurance, and Married sex ratio are used as instruments for GMFR in the two-level least-squares regressions for both level and change. The two-stage least-squares t statistics are based on the structural residuals (Hall et al., 1992:133-134) and are asympototically correct. These results are discussed at length in Galloway et al. (1996).

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PATRICK R. GALLOWAY, RONALD D. LEE, AND EUGENE A. HAMMEL ACKNOWLEDGMENTS 223 We are grateful for helpful comments from Barney Cohen, Mark Mont- gomery, Ken Wachter, and two anonymous reviewers on an earlier version of this chapter. The research on which this chapter was based was funded by grants HD25841 and HD07275 from the U.S. National Institute of Child Health and Human Development. REFERENCES Benavente, J. 1989 Social change and early fertility decline in Catalonia. European Journal of Population 5:207-234. Boonstra, O.W.A., and A.M. van der Woude 1984 Demographic transition in the Netherlands, a statistical analysis of regional differences in the level and development of the birth rate and of fertility 1850-1890. A.A.G. Bijdragen 24: 1-57. Brass W., and J.C. Barrett 1978 Measurement problems in the analysis of linkages between fertility and child mortality. Pp. 209-233 in S.H. Preston, ea., The Effects of Infant and Child Mortality on Fertility. New York: Academic Press. Castiglioni, M., G. Dalla Zuanna, and S. La Mendola 1991 Differenze di fecondita fra i distretti del Veneto attorno al 1881. Analisi descrittiva e ipotesi interpretative. Pp. 73-149 in F. Rossi, ea., La Transizione Demografica net Veneto, Alcuni Spunti di Ricerca. Bassano: Infosfera. Coale, A.J., and P. Demeny 1983 Regional Model Life Tables and Stable Populations. New York: Academic Press. Coale, A.J., and R. Treadway 1986 A summary of the changing distribution of overall fertility, marital fertility, and the pro- portion married in the provinces of Europe. Pp. 31-181 in A.J. Coale and S.C. Watkins, eds., The Decline of Fertility in Europe. Princeton, N.J.: Princeton University Press. Coale, A.J., B.A. Anderson, and E. Harm 1979 Human Fertility in Russia since the Nineteenth Century. Princeton, N.J.: Princeton University Press. Crafts, N.F.R. 1984a A cross-sectional study of legitimate fertility in England and Wales, 1911. Research in Economic History 9:89-107. 1984b A time series study of fertility in England and Wales, 1877-1938. Journal of European Economic History 13(3):571-590. 1989 Duration of marriage, fertility and women's employment opportunities in England and Wales in 1911. Population Studies 43: 325-355. Demeny, P. 1968 Early fertility decline in Austria-Hungary: A lesson in demographic transition. Daedalus 97(2):502-522. Fialova, L., P. PavlIk, and P. Veres 1990 Fertility decline in Czechoslovakia during the last two centuries. Population Studies 44:89-106. Flinn, M.W. 1981 The European Demographic System, 1500-1820. Baltimore, Md.: Johns Hopkins Uni- versity Press.

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