Determinants of the Length of Birth Intervals in the Past and Possibilities for Their Study

Introduction and Motives for the Study

Originally, one of the aims of the study of birth intervals was the evaluation of completeness of the studied parish registers. ¹ Among other reasons, this was why this topic was a common and traditional part of historical demographic studies based on the family reconstitution method.

However, the aim of the analysis of birth intervals has moved forward recently from the completeness evaluation mentioned above to an independent research topic. This type of analysis could offer a clearer answer to the hotly discussed question of family size limitation and birth spacing or birth postponement behavior in the past, particularly before and during the fertility transition period. ² The importance of analysis focused specifically on the length of birth intervals is mentioned in many historical demographic works. ³ Despite the importance of this type of analysis and its common usage in many studies, classical approaches of historical demography usually use only simple calculations of length of birth intervals (most often calculated according to birth parity). ⁴ The main reason for this simple approach to analysis may be found, above all, in the significantly demanding and time-consuming calculations. However, as is obvious from the analysis presented below in this article, traditional historical demographic studies are usually unable to cover the whole range of issues related to birth intervals.

Nowadays, the problem of the large databases needed for the analysis and their relatively complicated processing could be at least partly eliminated by using modern statistical software. This is why contemporary statistical and demographic methods have played an increasing role in historical demography recently. ⁵ It opens up the opportunity of using the historical data more effectively to describe it in more depth and also to define potential determinants of the studied process. Although we can find many methods that can be used within historical demography (or in family history or historical studies in general), the most often applied methods are the survival analysis, Cox regression, or logistic regression. The first two approaches are introduced specifically within this article. Both, the survival analysis and the Cox regression, have one important advantage—the ability to work not only with individual life histories (which are often available in historical demography) but also to cope with the so-called incomplete data (records where not all the information is present, i.e., records where the time duration between the initial and studied event is not known completely, though we have at least a knowledge of its minimal potential time duration; these records are defined as “censored” observations. More information is given below in the Main Methods of Analysis section). ⁶ In the meantime, the Cox regression enables us to study complex models incorporating more potential variables concurrently (determinants of the studied process), where the effect of those variables could be described as adjusted for the effect of the other variables (a partial or pure effect may be estimated). One of the latest papers dealing with reproductive behavior in the past using the Cox regression and mentioning the advantages of this method is the work of Sandström and Vikström on the potential effect of sex of a child on the probability of birth of a subsequent child in German families during the nineteenth century. ⁷

In accordance with the mentioned contemporary approaches to historical population studies, one of the objectives of this article is to introduce the most often used methods of analysis together with their practical application to historical data and more specifically to the analysis of potential determinants of birth intervals within Central Europe before the onset of the fertility transition. This article could be taken as one of those contributing to the currently developing approach to historical studies and historical demography that increasingly builds on contemporary methodological tools developed for processing individual observations and for pointing out the importance of this type of data for detailed analysis. ⁸ This could also be understood as proof of the increasing importance of contemporary analytical methods in the field of historical demography and social or historical research in general.

Related Literature and Main Hypotheses of This Article

The classical approach to analysis in historical demography is based on Henry’s family reconstitution method. ⁹ Because of the main aim of the analysis (analysis of natural fertility), Henry’s approach is based on using only complete families (reproduction histories), that is, on using data from families, where women survived within a marriage up to the age of forty-nine (incl.) and where the total number of children was at least six. Moreover, in the analysis, Henry used only records from marriages that lasted at least five years after the wedding. It is clear that such conditions (above all the requirement of completed reproduction and at least six births) radically limit the total number of observations that could be used for the analysis. Moreover, we can assume that the results of such an analysis are limited only to a specific part of the whole population (big families where the reproduction process was completed and families that were not moving, in other words, families where migration played no role).

However, we can find many types of reproduction histories, which could be very useful for analysis and a more detailed description of reproductive behavior in the past but which are traditionally excluded from the analysis—for example, families where the age of the woman was relatively high at the time of marriage (i.e., the potential reproduction period was on average shorter), and thus, it did not enable her to give birth to six or more children. Another example of a family traditionally excluded from analysis under Henry’s approach was a family where the woman died before the age of fifty, although the number of children was higher than six (this could raise the question of whether there was any relationship between the premature death of a woman and a high number of children born within short birth intervals. However, this hypothesis is not discussed within this article).

With the shift in the traditional issues of historical demographic studies, a shift in the approach to the data may also be assumed. The Henry’s data limitation could be explained by the aim to evaluate the data completeness. However, this is usually not the common goal of current studies.

This article is focused on reproductive behavior in the time period before the onset of the fertility transition. This topic is still not fully described for the area of Central Europe, and, in the meantime, it is only possible to compare the results with some other European localities. Maybe surprisingly, various factors influencing fertility behavior could also be found before the fertility transition—breastfeeding habits, sexual behavior, age-related decrease in fecundity, loss of a husband, and so on. As, for example, Timæus and Moultrie ¹⁰ or Van Bavel ¹¹ pointed out, family limitation or birth spacing could also be observed in populations before the onset of the fertility transition. Family limitation may be understood as an intentional limitation on the number of children (births) in a family and birth spacing is then intentional reproductive behavior leading toward longer time intervals between births in a family. Theoretically, as a consequence, birth spacing could lead to family limitation. The above-cited authors also defined birth postponement (or rather conception postponement) as a third theoretical motive for birth control.

The paper from Van Bavel and Kok ¹² could be taken as a typical example of a contemporary historical demographic study of birth intervals based on modern analytical methods. In a similar way to this article, they used data from family reconstructions (from the nineteenth century) and applied the Cox regression with the aim of describing the changes in birth intervals during the studied time period. They proved that lengthening of birth intervals was already occurring before the onset of fertility transition. Moreover, they discussed the possible motives behind the changes in spacing childbirths. In agreement with Moultrie et al., ¹³ Van Bavel and Kok ¹⁴ mentioned that the main reason for the observed reproductive behavior was not only the intentional limitation of family size but rather the spacing and postponement of births. They also studied the effect of religion or family socioeconomic status (SES). Furthermore, the authors pointed out that “In practice, historical-demographic research has focused heavily on parity dependent stopping behaviour at the expense of spacing” ¹⁵ with the aim of emphasizing the importance of the study of birth intervals for a description of fertility behavior changes as well as intentional family size limitation. In applying the Cox regression, Van Bavel and Kok ¹⁶ used the age of mother at birth, length of marriage, birth parity, and the survival status of a previous child as the explanatory variables. Moreover, there was a dummy variable specifying if the studied birth interval was the last one in a family. They worked with the assumption that families with more children could be expected to have on average shorter birth intervals. Also Van Bavel, ¹⁷ using Belgium as an example, pointed out the importance of the study of birth intervals. He argues that spacing the births could be understood as an intentional method of family limitation in historical periods.

The question of birth spacing versus family size limitation is also addressed by Knodel ¹⁸ for Germany, Ewbank ¹⁹ for data from Europe and the United States, and by Reher and Sanz-Gimeno ²⁰ for Spain. However, the latter two papers used rather traditional methods of analysis (e.g., Coale and Trussell’s indices—age-specific marital fertility rates or total marital fertility rate), which means the results are not fully comparable with those obtained using the Cox regression (as it is in this article).

Based on the conclusions of the presented papers, we can state four assumptions related to the analysis of fertility and reproductive behavior. These assumptions will be evaluated within the analytical part of this article.

From demographic, biological, and other scientific and logical reasons, it is natural to assume that birth intervals prolonged with increasing age of mother at birth (holding other variables constant) as a result of the limited and age-related decrease in the ability of a woman’s body to conceive and give birth (age-related decrease in fecundity). Among others, this was previously proved by Henry ²¹ (without standardizing for the potential influence of other factors) and many following researches (usually using the Cox regression where the pure effect of age of mother at birth could be estimated). ²²

As well as in the field of historical demography, the study of family behavior (including the study of birth intervals) based on similar types of data and methods of analysis can also be found in the current demography of developing populations. ³¹ A paper by Moultrie et al. ³² could be taken as an example of this. The authors studied birth intervals in twenty-four African countries using data from the Demographic and Health Surveys (DHS). It can be seen that data from the DHS are often in the same (or similar) structure as data used in historical demography. That is why these two areas of demography have a lot in common and could also share many methodological approaches (as well as problems). In the cited paper, ³³ the description of the process of fertility transition in the studied regions was based on the length of birth intervals, which were studied with regard to the influence of birth parity and age of mother.

Another example from the demography of developing countries can be found in the work of Bhalotra and van Soest. ³⁴ The authors based their study on the use of family histories (as it is common in historical demography) and studied the relationship between the length of birth intervals and level of infant mortality.

In historical populations, as well as in contemporary developing populations, the analysis of birth intervals and factors with a possible influence could be used for the description of the fertility transition as well as other social changes tied to demographic transition. Moultrie et al. ³⁵ connected the pure effect of birth parity (effect of birth parity on the average birth interval adjusted for the age of mother) with intentional limitation of family size related to the process of the fertility transition itself. For the analysis, the event history method (life tables) was used as well as the Brass–Juárez method (particularly applicable to data from sample surveys).

The spheres of historical demography and demography of contemporary developing countries also meet in another paper by Timæus and Moultrie. ³⁶ They also deal with possibilities for defining the intentional family limitation, birth spacing, and birth postponement during the fertility transition. Above all, the third motive for birth control, birth postponement, reaches significant importance in the analysis of contemporary populations after the fertility transition process, when more reliable methods of contraception became available.

From the above, it is clear that the question of birth spacing and family size limitation is still a current and widely discussed topic as well as the methodological approaches to its analysis. These questions are also important in other fields of demographic analysis not only within historical demography.

Goals of This Article

Within this article, the analysis of families living in the town of Jablonec nad Nisou (or “Jablonec” for short) from the seventeenth to nineteenth century is presented (case study in the second part of the article). This town is located in the northern part of the Czech lands, that is, in Central Europe, with a relatively high quality of parish registers and where the population was part Czech and part German. The main aim of this article is a detailed analysis of birth intervals of historical families with respect to current assumptions based on the related literature mentioned above. The analysis is based on contemporary statistical and demographic methods and software. ³⁷ Within the analysis, we aim to evaluate the effects of potential determinants of the length of birth intervals. In the role of explanatory variables, we considered the effect of birth parity, age of mother at birth of a child, age of mother at marriage, total number of births in the family, identifying whether a child was the last born in a family, and the survival status of a previous child.

All the explanatory variables were selected considering the assumptions mentioned previously in this article. All the explanatory variables are available (can be calculated from the data) in the studied data set. Other potential explanatory variables often taken into account (e.g., religion, food prices, breastfeeding practice, and SES of the family) are not available because the information was not usually included in the parish registers. The only exception could be occupations (usually only of the man in a family) which could occasionally be found in the records. However, the information is often missing or could be unreliable or inconsistently recorded. This could be a theme for future studies, but in this article, we do not use occupation as one of the explanatory variables for the analysis.

The conclusions of the analytical part are compared with the results of other traditional historical demographic studies or studies from other localities.

As well as the analytical goal (related to the presented case study), methodological questions are also considered within this article. In the methodological parts, the effect of the traditional strict rules on data limitation in historical demographic analyses (according to Henry) is discussed together with the possible advantages of contemporary analytical methods (above all the Cox regression).

The methodological aspects of the article may be illustrated by using the empirical data from the presented case study. Within the case study, in the data set for Jablonec, nearly 80 percent of all records would not have been used if the analysis was based on Henry’s methodology. Dealing with the analysis below, there could be a discussion of potential loss of data for the historical demographic analysis because of the strict limitations. This is the reason why in this article, we aim to illustrate the effect of described data limitation according to Henry’s methodology ³⁸ and to discuss the question of whether such a limited database might be enriched if the limitations are disregarded. This was done in a practical way where the results based on the limited as well as the complete data set could be compared directly. As a result, this article may raise the questionability of the importance of strict Henry’s data limitation in the application of contemporary analytical methods that are able to deal with incomplete sets of observations (censored data).

Jablonec nad Nisou - Population Characteristics and Data Description

Jablonec is a town located in the northern part of the Czech lands. The first reference to Jablonec was made in the year 1356. From the beginning of the seventeenth century, the town was the center of glass production, especially jewelry. Its production was exported throughout Europe and as well as to countries outside Europe such as the United States, Mexico, and Egypt in the 1830s. At the end of the eighteenth century (1788), there were 265 houses; forty years later (1827), there were 512 houses and 3,126 inhabitants; and another twenty years later (1848), there were 549 houses and 3,651 inhabitants. By the end of the nineteenth century (1900), the number of houses and inhabitants had increased significantly (1,534 houses and 21,091 inhabitants). What is important for the study presented below is the fact that Jablonec was characterized by its high proportion of German inhabitants (about 90 percent at the end of the nineteenth century). ³⁹ This fact was reflected in, among other things, an exceptionally high proportion of premarital conceptions in the locality. The average proportion of premarital conceptions was estimated at around 35 percent from the first births. Moreover, this proportion was generally increasing during the studied period. ⁴⁰

In the parish registers for the studied locality, there is only partial information about the employment of the inhabitants or even their SES. We can derive some idea about the employment structure only from those records, where at least some information was available. From the data set of 2,379 families in the study (not all of them were analyzed in the study below, because repeatedly, one child and childless marriages were excluded as well as families with an unclear year of marriage) for 1,634 (68.7 percent), there was no information about the employment of the men. This means that we have at least some information for only about one-third of the families. From those families where employment is recorded, 31.9 percent worked in industry (above all the glass industry), 31.5 percent worked in agriculture (as peasant, day laborer, or auxiliary force), 27.8 percent of men were craftsmen (miller, shoemaker, etc.), and 5.4 percent were merchants (above all in glass or yarn). According to the records around 3.0 percent of men in the studied families were without a job or beggars, 0.4 percent (men in only three families) were teachers.

What is clear from the brief information about the studied locality is the fact that Jablonec was generally of an urban character and growing relatively rapidly during the nineteenth century. Moreover, from the partial information about employment, we can suppose that around one-third of the men worked in industry, nearly the same proportion in agriculture, and the last third were craftsmen or merchants. This approximate employment structure corresponds with the relatively prosperous period during the studied years supported, above all, by the development of the glass industry and leading to the rapid population increase.

The database used for the analysis comes from the family reconstitution method, which is based on manually excerpted data from parish registers. ⁴¹ The data (not yet in their current extent) were analyzed for the first time in 1992. ⁴² However, that first paper did not contain any more detailed analyses of birth intervals. Later, the data set was studied in 2014–2015 using the survival analysis or Cox regression. ⁴³ Through the application of these methods, it was possible to study the effects of the age of mother at birth of a child, age of mother at marriage, and birth parity for the average length of birth intervals. However, in those studies, the other explanatory variables had not yet been considered; their possible effect was discussed only in a theoretical way in the cited papers.

One of the advantages of the study presented below is a relatively large data set. For all of the marriages (2,366 couples), at least the date of wedding was known (the difference from the above mentioned number of 2,379 is the number of families in the data set where the exact date of marriage was not clear). The earliest wedding occurred in 1650 and the latest one in 1872. However, the last wedding for which there are also records available for at least one child occurred in 1870. So the analysis was not influenced by repeated marriages, where clearly the reproductive behavior follows different rules and regularities, only the first marriages (bachelor/spinster marriages) were used in all the parts of the study. In the database, there were in total 2,007 first marriages.

For the analysis of birth intervals, the data set was reorganized, so that the records concerning children could be studied. There were records of about 10,399 children, where at least the date of birth was known. Because the values of all explanatory variables were not always known for all the children in the data set, for all particular steps of the analysis (for each model of analysis), numbers of analyzed cases were specified separately (see Table 1). Only those children born to women who married between the ages of fifteen and forty-nine and women aged between fifteen and forty-nine at the birth of that child were considered in the analyses.

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Table 1.

Numbers of Observations (Birth Intervals) Used in Particular Parts of the Analysis.

Type of Analysis	Explanatory Variables in the Particular Step of Analysis	Number of Observations in the Analyzed Data Set
		According to Henry’s Methodology	Extended Approach
Descriptive	Age of mother at marriage (Figure 3)	1,304	5,721
Descriptive	Age of mother at birth of a child (Figure 4)	1,433	6,210
Descriptive	Total number of children born in family (Figure 5)	1,433	6,166
Cox regression	All variablesa (Tables 2 and 3)	1,290	5,588

^aAll the variables used in the model of Cox regression: age of mother at marriage, age of mother at birth of the child, total number of children born in a family, survival status of the previous child born in a family, and dummy variable defining the last child in a family.

As stated above, the traditional historical demographic methods are based on Henry’s methodology, and one of the methodological questions of this article is whether the database could be enriched, that is, whether the limitations of the data, defined by Henry, ⁴⁴ could be at least partly relaxed. So that it could be shown what the effect of the Henry’s limitations is, the analysis was repeated on two types of data sets:

The first one is a data set respecting Henry’s methodology. ⁴⁵ From the original data set, only those lengths of birth intervals were used where the reproduction period of the mother was completed, that is, where the mother was at the exact age of fifty still in a marriage (her husband was alive). Moreover, we used only those records where the total number of children born in a family was at least six. We left out the restriction regarding marriage dissolution earlier than five years after the wedding because this fact could influence the age-specific fertility rates but does not influence birth intervals. Results based on this approach are marked as “according to Henry’s methodology” (e.g., in Table 1).

Different numbers of observations in particular steps of the analysis (in Table 1) might be explained by different explanatory variables in those analytical steps, that is, by different variables which may be missing.

However, for both data sets, one important aspect holds in both cases—we have to keep in mind that not children but birth intervals are being studied. This means that also after the birth of the last child in a family, another birth interval starts, although this birth interval is not closed by the birth of another child. In both analyzed data sets, the last birth intervals (time durations after the birth of the last child in a family) should be included, because during this time period, a woman still has the potential of bearing another child. This last interval is not closed by the birth of a child but by the end of the marriage (the last interval is closed on the date of the death of the wife or husband) or by the end of the reproduction period of a woman (fiftieth birthday). In all cases, however, the last interval is a censored observation.

One of the situations we had to deal with was where information about completeness of reproduction was not available, neither information about the death of a wife or a husband (date of the end of marriage). Also, in those cases, the last observation was censored, and the time of censoring was set as the date of birth of the last child in a family. That ensures that this incomplete observation was considered also in the analysis of the time duration after the last birth in a family, that is, in a period where the woman could potentially bear a child (see Figure 1).

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Figure 1.

Explanation of the importance of the time interval after the birth of the last child for the analysis.

Main Methods of the Analysis

First of all, the descriptive analysis was prepared separately for various explanatory variables (age of mother at birth of a child, age of mother at marriage, birth parity, total number of births in a family, reversal birth order, and survival status of a previous child), and finally, all the variables entered into one complex model (Cox regression). That allowed modeling of the pure effects of all the variables adjusted for the different values of the others.

In the analysis, we distinguished between first birth intervals (“marriage–birth”) and birth intervals for children of higher parity (“birth–birth”). In the study below, we concentrate solely on the birth–birth intervals, that is, we did not study the intervals between wedding and the birth of the first child. The length of birth–birth interval was calculated as the difference between the date of birth of the studied child (child of nth parity) and date of birth of a child of previous parity ([n − 1]th parity). The length of the birth interval was expressed in months. This method of calculation is different from Henry’s method. ⁴⁶ Henry divided the calculation of birth–birth intervals into two parts: in the first one, he used only the first four birth intervals for analysis related to the beginning of the reproduction period, and in the second part, the last four birth intervals for analysis of the end of the reproduction period. This calculation did not depend on the total number of children born into a family (but, as mentioned above, Henry considered only families with more than six children).

All the explanatory variables in the analysis presented below were used as categorical ones as follows:

The birth parities were used as individual categories up to the fifth parity. Birth parity six and higher were classified as a separate category (more than 81 percent of children in the data set were born in the fifth and lower parity). The effect of birth parities was confirmed by the first analyses produced using the studied data set. ⁴⁷ Moreover, this variable is considered as one of the most basic ones in studies dealing with birth control before the onset of the fertility transition. ⁴⁸

Only children born to women, who married at age fifteen to forty-nine years, or to women aged between fifteen and forty-nine at birth of a child were included in the analyses. Birth intervals longer than five years were excluded from the analysis because usually it is assumed that such long birth intervals could be tied to missing information about a birth in the family history. ⁵¹ As described above, the interval after the birth of the last child in a family was always considered as a censored observation.

The descriptive statistics presented below were calculated using the survival analysis (procedure Lifetest in the SAS software) stratified according to birth parity, age of a mother at marriage or age of mother at birth of a child, and total number of children born in a family. We present only the most important results below for orientation of the reader within the data set and for better introducing the most important trends or differences according to various explanatory variables.

The survival analysis is rather a simple tool used for analysis of the so-called survival times (failure times, time durations between two defined events). The most common output of the survival analysis is the survival distribution function (survival function). The survival function could be interpreted as a “probability that an experimental unit from the population will have a lifetime that exceeds t.” ⁵² Applied to the study of birth intervals, the estimated survival function, S(t) expresses the probability that a birth interval of a randomly selected child (characterized by values of the stratification variables—birth parity, age of mother at marriage or age of mother at birth of a child, and total number of children born in a family) from the studied data set will exceed a concrete value t: ⁵³

S ( t ) = P ( T > t ) ,

where T is the length of a birth interval for a selected child (measured as the time period between its date of birth and date of birth of a child of (n − 1)th birth parity in the same family). We used the nonparametric Kaplan–Meier method for the estimation of the survival function. This type of calculation is based on the fact that it needs no a priori assumption about the function. More about the survival analysis can be found, for example, in Aalen et al. ⁵⁴ or Hendl. ⁵⁵ After estimation of the survival function, the mean length (or quantiles) of a birth interval for each category of a stratifying variable could be specified. ⁵⁶

As already mentioned above, one big advantage of the survival analysis is the possibility of working with incomplete data (censored observations). The principle of censoring is depicted in Figure 2. In this model example (where the aim is only to explain the principle of censoring), we know the date of birth of a given person, but we do not know the date of his death. If we use the traditional method of historical demography, we cannot use this record for the analysis of mortality (length of life) or more precisely for the analysis of time duration between the birth and the death. The survival analysis can use this record at least partially—as a censored observation (observation with incomplete information). It is possible to use the (partial) information that the studied person lived at the time of another event that happened in his life. For example, we can be sure that the person survived at least until the (last) birth of his or her child. So we do not know the entire duration of life, but we know the minimal reached duration (age at birth of the last child), which could be exceeded. In general, the time of censoring is the last information about the studied person where we know that he or she was still alive. In the model example (see Figure 2), the time of censoring could be the birth of the fourth child in the year 1833 as that is the last available information about the life of the studied person in the example. This type of censoring is called right censoring.

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Figure 2.

Principle of censoring—model example.

The second type of analysis used in this article is the Cox regression (procedure Phreg in the SAS software) or Cox proportional hazards model. The Cox regression could be understood as an extension of the survival analysis (of the Kaplan–Meier method). ⁵⁷ This type of regression “assumes a parametric form for the effects of the explanatory variables, but it allows an unspecified form for the underlying survivor function.” ⁵⁸ In the Cox regression, it is more common to work with the hazard function rather than with the survival function described above (although both these functions in fact represent the same thing). The hazard function (or an age- or time-specific failure rate) could be defined (author’s own symbology) as: ⁵⁹

h ( t ) = lim Δ t → 0 + P ( t ≤ T < t + Δ t | t ≤ T ) Δ t ,

which could be interpreted as the probability that the studied time duration (birth interval) would be longer or equal to t but shorter than t + Δt under the condition that the time duration is at least equal to t.

The main principle of the Cox regression is the assumption of proportional hazards—particular hazard functions are assumed for each value (category) of the explanatory variables. These hazard functions for individual categories are assumed to be proportional to each other (multiplied by a constant, this constant is the estimated parameter). After its estimation, this constant represents the pure effect of a particular value of the explanatory variable. For simplicity, one of the categories of each explanatory variable is taken as a reference category. The effects of the other categories are then multiples of the effect of this reference category. For our study, it is important to keep in mind that higher values of the hazard function (higher multiples of the hazard function related to the reference category) mean shorter average birth intervals (in comparison to the reference category) and vice versa.

Based on the explained principle, in the Cox regression model, the aim is to study the relation between the failure times (in our case the length of birth intervals) and set of explanatory variables (Z). This relation could be formally defined (author’s own symbology) as: ⁶⁰

h ( t , Z ) = exp ( Z × β ) × h 0 ( t ) ,

where β is a vector of parameters representing the effect of explanatory variables Z, and h 0 ( t ) is the baseline hazard function (i.e., a hazard function related to reference categories of all the explanatory variables Z). The hazard ratio, ratio of the two hazard functions defined by different values of Z enables us to express the different influences of particular values of the explanatory variables on the hazard function (their pure effect standardized for the other explanatory variables), that is, on the average length of birth intervals: ⁶¹

h ( t , Z 1 ) h ( t , Z 2 ) = exp( Z 1 × β ) × h 0 ( t ) exp( Z 2 × β ) × h 0 ( t ) = exp( Z 1 × β ) exp( Z 2 × β ) ,

where Z ₁ and Z ₂ are two different vectors of explanatory variables (i.e., these vectors differ in at least one value of the explanatory variables). For illustration, if we suppose that all values of the explanatory variables are the same except for one (Z_n ) and all the other explanatory variables hold constant, then Z_n and Z n * are the two different values of the explanatory variable Z_n , β _n is the parameter representing the effect of variable Z_n , and the hazard ratio can be expressed as: ⁶²

h ( t , Z 1 ) h ( t , Z 2 ) = exp( Z n × β n ) exp( Z n * × β n ) = e Z n × β n e Z n * × β n = e Z n × β n − Z n * × β n = e β n × ( Z n − Z n * ) .

Then, simply, if Z n = Z n * + 1 , we get a special case of the Cox model and the hazard ratio

h ( t , Z 1 ) h ( t , Z 2 ) = e β n × ( Z n − Z n * ) = e β n + 1 = e β n .

The last formula represents the effect of a unit increase in the explanatory variable Z_n (where the other explanatory variables remain constant), and the hazard ratio is also referred to as “relative risk.” ⁶³

In the following text, we will present the values of hazard ratios where the effect of variable value Z_n is compared to the reference value of the same variable (represented above by Z n * ). The value of the hazard ratio could then be interpreted as the relative increase/decrease in the hazard function (risk function) when the explanatory variable reaches value Z_n in comparison with the hazard function of the reference category ( Z n * ).

Selected Results of Importance

The following presentation of the results is divided into two independent parts—the descriptive statistics and the complex Cox regression model. In the descriptive part, the average lengths of birth intervals are presented for particular values of the explanatory variables. However, results in the descriptive part are not adjusted for different values of the other explanatory variables. This fact is eliminated in the Cox regression, where in the complex model, the pure effect of particular categories of the explanatory variables (adjusted for values of the other variables) is estimated. In both parts of the analysis, only the birth–birth intervals were studied, that is, intervals between particular births, not the marriage–birth intervals, that is, intervals from marriage to birth of the first child. The marriage–birth intervals were described already in a previous study. ⁶⁴

Descriptive Statistics

The birth–birth intervals were studied according to all the above-described variables. For the analysis according to birth parity and age of mother at marriage, we could use 5,721 records about children of the first and higher parity when the extended approach was applied to the data and 1,304 records when the strict Henry’s methodology of data limitation was applied (see Table 1; only 22.8 percent of records would be used following Henry’s methodology of data limitation).

When considering the age of mother at marriage together with the birth parity, the mean lengths of the birth–birth intervals are not very different (Figure 3a). Only within particular birth parities are there visible differences according to the age of a woman at marriage. For example, the birth interval between the birth of the first and the second child in a family (first birth parity) and between the birth of the second and the third child (second birth parity) is on average the shortest for women who married at the age of twenty to twenty-nine. However, the differences are only small.

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Figure 3.

(a) Mean length of the birth–birth intervals according to birth parity and age of mother at marriage, Jablonec nad Nisou, seventeenth to nineteenth centuries, extended approach. (b) Mean length of the birth–birth intervals according to birth parity and age of mother at marriage, Jablonec nad Nisou, seventeenth to nineteenth centuries, according to Henry’s methodology.

If the analysis is repeated for the data set limited according to Henry’s methodology, the results are not significantly different from the extended approach to data (Figure 3b). What is clear is the visibly higher variability of the results. This is a consequence of some underrepresented categories present in the limited data set. This holds particularly for the group of women who entered marriage after the age of thirty (see Appendix Table A2). For the other groups of women, birth intervals reach values between twenty-five to thirty months on average.

For the analysis according to birth parity and age of mother at birth of a child, we could use 6,210 records for the extended approach and 1,433 records (23.1 percent) for the Henry’s limitation (see Table 1). The influence of the age of mother at birth of a child to the average length of the birth–birth intervals (Figure 4a and b) seems to be stronger in comparison to the effect of the age of mother at marriage. In accordance to the initial assumption, the average length of birth intervals increases with the age of mother at the birth of a child. This holds for all the birth parities. This fact could be taken as a reflection of decreasing fecundity (ability to procreate and give birth) of women with age. However, in this part of the analysis, the results are not adjusted for values of the other explanatory variables.

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Figure 4.

(a) Mean length of birth–birth intervals according to birth parity and age of mother at birth of a child, Jablonec nad Nisou, seventeenth to nineteenth centuries, extended approach. (b) Mean length of birth–birth intervals according to birth parity and age of mother at birth of a child, Jablonec nad Nisou, seventeenth to nineteenth centuries, according to Henry’s methodology.

Moreover, dealing with the question of data limitation also presented within this article, we can conclude that the results are nearly the same in both approaches. There are only minor differences in the average lengths of birth intervals visible according to birth parities; however, within the particular birth parities, the differences according to age of mother at birth of a child are clear (the obvious lengthening of the birth intervals with age of mother). Because of different data sets (extended or limited ones), the results are not completely the same in the presented graphs (Figure 4a and b)—above all, the group of the first parity (second birth in a family) combined with the lowest age of mothers (under twenty years old) is underrepresented, so the results are not very reliable (see Appendix Tables A3 and A4). For the second age category, the birth interval before the second birth (first parity) was on average 22.7 months, for females aged twenty-five to twenty-nine, it was 25.0 months, and for females aged thirty and older, the time duration was on average 28.9 months (considering the extended approach to data—Figure 4a, Appendix Table A3). According to Henry’s methodology, the age-specific differences in the average birth interval between the first and second birth in a family were nearly the same (they are only slightly shorter which could be caused by the fact that only families with more than six children enter the analysis in this case. This type of family typically has shorter average birth intervals—as is shown later, in Figure 5a and b).

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Figure 5.

(a) Mean length of birth–birth intervals according to birth parity and total number of children born in a family, Jablonec nad Nisou, seventeenth to nineteenth centuries, extended approach. (b) Mean length of birth–birth intervals according to birth parity and total number of children born in a family, Jablonec nad Nisou, seventeenth to nineteenth centuries, according to Henry’s methodology.

According to Henry’s methodology, not all the combinations of different values of birth parity and age of a mother at birth of a child were represented in the data (missing columns in the figures represent those combinations that were not identified in the data—e.g., fourth and higher parity among females under twenty-five years old).

For parities higher than the first one, the average lengths of the birth intervals were nearly the same—for all parities, the most significant difference was proven to be in the average length of birth interval for a woman aged less than thirty years in comparison to a woman aged thirty or over (Figure 4a and b). Except for the first parity, the average birth interval was at least five months longer for females aged thirty and over compared to younger mothers (Appendix Tables A3 and A4). This could correspond to the biological limits of age-related fecundity, which can decrease significantly after the age of thirty. Combinations of higher parities and younger ages are more or less underrepresented again.

If the average lengths of birth intervals are also studied according to the total number of children born in a family, then again the results are similar according to both methodological approaches (Figure 5a and b). For the analysis, there were 6,166 records used according to the extended approach to data limitations and 1,433 records (23.2 percent) according to Henry’s methodology (see Table 1). As previously stated, in accordance with Van Bavel and Kok ⁶⁵ or Van Bavel, ⁶⁶ we expected shorter average birth intervals in families with a higher total number of children (measured as the total number of births in a family not as a total number of children surviving to some particular age).

In the graphs (Figure 5a and b), there is a visible increase in the length of birth intervals with birth parity. This could seem to be opposite to the expected results; however, we can explain it by the ties between the birth parity and age of mother—more often children of higher orders (higher birth parity) are born to older mothers. And as expected and as proved by the results presented above, the average birth intervals are longer for higher ages of mother. That means that the differences in average birth intervals according to birth parity presented in the figures in this part of the analysis are not adjusted for various values of the other explanatory variables (e.g., age of mother at birth of a child in Figure 5a and b). This led us to the use of one complex Cox model below, where the pure effects of the explanatory variables could be studied under the assumption of holding other variables constant (see the next part of the analysis).

Within each birth parity in Figure 5a and b, the average length of birth intervals shortens with increasing total number of births in a family—this is further proof of the importance of using more complex models where the pure effects of explanatory variables can be studied adjusted for the other variables. Of course, because according to Henry’s methodology only families with at least six children were included in the analysis, the results in Figure 5b could be calculated and presented for this group of records only (i.e., there are no data for smaller families). Although there is this data limitation, the main trends in the average length of birth intervals according to the total number of births in families remain nearly the same as in the extended approach to the data (Figure 5a). On average, a birth interval (for all birth parities) was some five to nine months longer in families with six to seven total births in comparison to families with ten and more births (according to the extended approach to data, the main trends and differences are similar, see Appendix Tables A5 and A6).

Complex Model of Cox Regression

The simple descriptive analyses (presented above) are not adjusted for the influence of other variables—there were presented differences according to particular combinations of values of only two selected variables (e.g., birth parity and total number of births in a family in Figure 5a and b) but not adjusted (standardized) for various values of the other possible factors (e.g., age of mother at birth of a child). Moreover, the average length of the birth–birth intervals is assumed to be influenced by survival of a child of previous parity, ⁶⁷ which was not implemented in the previous descriptive statistics. This effect, as well as the effect of being the last child in a family, will be estimated in the following Cox regression model.

The more detailed analysis was done using the Cox regression model presented in this part. The length of birth–birth intervals was considered as the explained variable, and all the other variables (age of mother at marriage, age of mother at birth of a child, total number of children born in a family, survival status of a previous child born in a family, ⁶⁸ identification of the last birth in a family, and birth order/birth parity) were taken as possible explanatory variables.

In the model, a reference parametric schema was used, that is, the hazard ratios represent the effect of particular values of the explanatory variables in comparison to their reference category (see the description of the methods above). The reference category for particular variables is specified in the results presented below together with the interpretation.

It was possible to analyze 5,588 records using the extended approach to data limitations (Table 1). According to the Wald χ² test of significance, all the explanatory variables were shown to be significant for the model at 1 percent level of significance. If the analysis was repeated for the data set limited according to Henry’s methodology, then 1,290 records could be entered into the Cox regression (Table 1). Also in this case, almost all the explanatory variables were shown to be significant in the model at 1 percent level of significance according to Wald’s χ² test. There is only one exception—the variable birth parity was not shown to be statistically significant in the model. However, although a variable is shown to be significant in the model, not all categories of that variable have to be significant too (as will be described below in more detail, see Tables 2 and 3).

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Table 2.

Cox Regression: Maximum Likelihood Estimates of the Parameters (β), Standard Errors and Statistical Significance (p Value) of the Estimates, and Hazard Ratios for Particular Categories to the Reference Category; Jablonec nad Nisou, Seventeenth to Nineteenth Centuries, Extended Approach.

Variable	Value or Category of the Variable	Parameter Estimate (β)	Standard Error of the Estimate	Probability > χ2 (p Value)	Hazard Ratio (to Reference Category)
Age of mother at marriage (reference category = 30 and older)	Under 20 years	−0.72087	.09025	<.0001	0.486
	20–24 Years	−0.39120	.08101	<.0001	0.676
	25–29 Years	−0.12972	.08153	.1116	0.878
Age of mother at birth of the child (reference category = 30 and older)	Under 20 years	1.58983	.25588	<.0001	4.903
	20–24 Years	1.07941	.06859	<.0001	2.943
	25–29 Years	0.65176	.04371	<.0001	1.919
Total number of children born into a family (reference category = 10 and more children)	2–3 Children	−0.48972	.07521	<.0001	0.613
	4–5 Children	−0.63195	.05253	<.0001	0.532
	6–7 Children	−0.54858	.04403	<.0001	0.578
	8–9 Children	−0.30912	.03848	<.0001	0.734
Last child born into a family (reference category = last child)	Not the last child	0.34733	.04150	<.0001	1.415
Birth parity (reference category = 6th and higher parity)	First parity (birth interval before the second child)	−0.18307	.07212	.0111	0.833
	Second parity	−0.11135	.06385	.0812	0.895
	Third parity	−0.06614	.05691	.2452	0.936
	Fourth parity	0.05116	.05365	.3403	1.052
	Fifth parity	0.00576	.05312	.9136	1.006
Survival status of the previous child (reference category = no information about the survival of the child)	Previous child survived the first 12 months of life	0.01352	.03789	.7212	1.014
	Previous child died within the first 12 months of life	0.82127	.03591	<.0001	2.273

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Table 3.

Cox Regression: Maximum Likelihood Estimates of the Parameters (β), Standard Errors and Statistical Significance (p Value) of the Estimates, and Hazard Ratios for Particular Categories to the Reference Category; Jablonec nad Nisou, Seventeenth to Nineteenth Centuries, According to Henry’s Methodology.

Variable	Value or Category of the Variable	Parameter Estimate (β)	Standard Error	Probability > χ2 (p Value)	Hazard Ratio (to Reference Category)
Age of mother at marriage (reference category = 30 and older)	Under 20 years	−1.26735	0.31010	<.0001	0.282
	20–24 Years	−0.90532	0.30064	.0026	0.404
	25–29 Years	−0.81650	0.30145	.0068	0.442
Age of mother at birth of the child (reference category = 30 and older)	Under 20 years	2.95816	1.02516	.0039	19.263
	20–24 Years	1.05636	0.15964	<.0001	2.876
	25–29 Years	0.55072	0.10215	<.0001	1.735
Total number of children born into a family (reference category = 10 and more children)	6–7 Children	−0.71059	0.09385	<.0001	0.491
	8–9 Children	−0.33840	0.06703	<.0001	0.713
Last child born into a family (reference category = last child)	Not the last child	0.71283	0.10033	<.0001	2.040
Birth parity (reference category = 6th and higher parity)	First parity (birth interval before the second child)	0.08992	0.15343	.5578	1.094
	Second parity	0.02566	0.13363	.8477	1.026
	Third parity	0.03410	0.11931	.7750	1.035
	Fourth parity	−0.02707	0.10859	.8031	0.973
	Fifth parity	−0.13569	0.09951	.1727	0.873
Survival status of the previous child (reference category = no information about the survival of the child)	Previous child survived the first 12 months of life	0.11639	0.07651	.1282	1.123
	Previous child died within the first 12 months of life	1.06429	0.07476	<.0001	2.899

The influence of particular categories of explanatory variables could be evaluated using the hazard ratios explained above in the description of methods used. The results for particular variables will be commented separately for a simpler comparison of the results for both methodologies of data limitation (extended approach and Henry’s methodology).

According to the descriptive statistics, almost no differences were found in the average lengths of birth intervals for various values of the age of mother at marriage (representing the approximate start of reproduction). The average birth interval was between twenty-five to thirty months for all birth parities and ages at marriage (according to Henry’s methodology, the results were less stable as a consequence of underrepresentation of some categories; see Appendix Tables A1 and A2). Considering the pure effect of age of a mother at marriage standardized for all values of the other explanatory variables in the Cox regression, younger ages at marriage lead to longer average birth–birth intervals (the hazard function for younger age categories is lower) compared to the reference category (age at marriage of thirty and over), the hazard ratio is lower than one, and lower hazard function leads to longer average birth intervals. For example, in the extended approach, the hazard function of age category of females at marriages under twenty years old is equal to 48.6 percent of the hazard function corresponding with the age category thirty years and over (Table 2), that means approximately a doubling in the length of average birth interval in families where the mother married younger than twenty years old in comparison with families where mothers married older than thirty years (holding other variables constant). These results fully correspond with the fact that the average reproductive period of women, who entered into marriage at a lower age is longer, so those women are able to give birth to children of higher birth parity with longer average birth–birth intervals (Table 2). All the differences among the categories are statistically significant, except for the categories twenty-five to twenty-nine and thirty and years and over (p value equal to .1116)—for the other categories of age at marriage, the difference in average birth intervals is statistically significant (at 1 percent level of significance), see Table 2.

Trends in the results are similar in general when the strict Henry’s methodology of data limitation is used. Again, the birth intervals are on average longer for women who got married at lower ages (Table 3). In this case, the differences among categories are even bigger in comparison to the Cox model applied to data from the extended approach (however, the values of the estimated coefficients are not fully comparable in these two models), for example, the effect of age at marriage equal to twenty years and less in comparison with the age of thirty years and over—the hazard function for the youngest category of females at marriage is equal to 28.2 percent of the hazard function of the oldest category. This means that the hazard function of the highest category of a woman’s age at marriage is 3.55 (i.e., 1/0.282) times higher in comparison with the youngest females. The reason for this extreme difference can be found in Henry’s methodology of data limitation—which limits the data set to only those families where the total number of births is equal to at least six. If a woman got married at the age of thirty or older and, in the meantime, she had six or more children, then it is clear that the birth intervals had to be relatively short. Regarding the variable of age of mother at marriage, the general trend in the values is also confirmed when using the very limited data set (Table 3).

For the variable age of mother at birth of a child, the descriptive statistics have already revealed a clear relationship to the average birth intervals—the birth intervals were shown up to be, on average, longer with increasing age of mother at birth of a child. For the age category of females under twenty years old, the average birth intervals were around twenty months (only data for lower birth parities were represented in this age category). The average birth interval for a female aged twenty to twenty-four years was around twenty-one to twenty-two months (not adjusted for the influence of other variables), and this mean was almost the same using both data sets (limited as well as extended). For the age category of mothers twenty-five to twenty-nine years old, the birth interval was on average around twenty-three to twenty-five months, again the results do not differ significantly for the limited data set. For the oldest category of mothers, thirty years and over, the average birth intervals were around twenty-nine to thirty months in both data sets (Appendix Table A3).

Using the Cox regression, this relation between the age of mother at birth of a child and an average birth interval was confirmed. The results are contrary to the results of the previous variable, age of mother at marriage. The pure effect (adjusted for other variables) of the age at birth of a child shows that lower age at birth of a child means on average shorter average birth–birth intervals and vice versa (Tables 2 and 3). This result could also be tied to the biologically optimal age for conception and relatively rapid onset of births at a lower age. The differences among particular categories of ages at birth are even bigger if Henry’s methodology is used for data limitation (Table 3); however, the standard errors are in this case higher (because of a lower number of cases in some categories, above all in the youngest, due to limitation of the data set).

Using the extended data set for the youngest age category of mothers, the hazard function is almost five times higher than for mothers aged thirty and over (reference category), which means shorter birth intervals (Table 2). There are significant differences among all age categories.

According to the descriptive statistics, the average length of birth intervals decreased with increasing family size (increasing total number of births in the family). In the extended data set, the average birth intervals in families with only two or three children were 26.5 (first parity) or 29.6 months (second parity). In families where four or five children were born, the average birth intervals were from 25.6 months (first parity) to 31.7 months (fourth parity). In families where six or seven children were born, the average birth intervals were around one month shorter in all parities—intervals were from twenty-five (first parity) to thirty-one months (fifth parity). The same also holds for families where eight or nine children were born—the birth intervals were again shorter by around one month than in previous size categories of families (from twenty-three months at first parity), for higher parities, the average shortening was around two months (29.5 months at sixth and higher parity). In families with ten or more births, the average birth intervals were only from 20.5 months (first parity) to 25.8 months (sixth and higher parity). Similar results were also obtained for the limited data set (see Appendix Tables A5 and A6).

In the Cox regression, there is a significant difference between families with less than eight children and bigger families (Table 2). Of course, the results for the data set limited by Henry’s methodology are different, because only three categories of the total number of children in the family are allowed in the model (six to seven children, eight to nine children, and ten and more children). This means that according to this data limitation, a direct comparison of small families (with lower number of children) and big families (with many, e.g., six or eight and more, children) is not possible. However, again the available results are in principle the same—there is a significant difference between families with six or seven births and bigger families (see Table 3): in families where more children were born, the birth intervals were on average shorter. In the extended data set, the difference is especially visible in the comparison between really big families (with eight and more births) and smaller families (with less than six births). For example in families with only two or three total births, the hazard function is 83.5 percent (0.613/0.734, see Table 2) of the hazard function of families with eight or nine children, and only 61.3 percent of the hazard function corresponding to families with ten and more births, that is, the reference category (Table 2). In the limited data set (Table 3), on average, the hazard function of families with six and seven children is only 49.1 percent of the hazard function of families with ten and more births (reference category), this means about half the length of the average birth intervals in the biggest families in comparison to the smaller ones when adjusted for the values of other explanatory variables. This result could lead us to the assumption that bigger families (according to the results families with eight and more children born) could be taken as a specific type of family, where the fecundity was on average higher leading to a higher frequency of pregnancies and a higher number of births during their life. However, this could raise the question of infant and child mortality in this type of family in comparison to families with lower number of births dictated by the limited financial resources of the family or affected by the health status of women after many births. However, this is not the object of this study.

In the descriptive statistics, it turns out that the average birth intervals are longer for higher parities and for higher age of mother at birth of a child. This leads us to the assumption that the last child in a family was probably born with the longest birth interval.

In the Cox regression model for both data sets (Tables 2 and 3), the birth interval before the birth of the last child in a family was significantly longer in comparison to the other birth intervals. The hazard function of a child that is not the last born in a family is circa 1.415 (2.040 according to Henry’s methodology, Tables 2 and 3) times higher than the hazard function related to the last child born in a family (a higher hazard function is related to shorter average birth intervals). This result could again be explained by decreasing fecundity with the approaching end of reproduction of a woman (which does not necessarily correspond to a particular age of women or number of children).

Another variable included in the model is the birth parity (birth order). Although the variable of birth parity itself is a statistically significant explanatory variable in the model, not all the differences among particular categories of this variable are significant. In the extended data set (Table 2), there is a significant difference in the average birth interval for the category of the first parity (birth interval before the birth of the second child in a family) and the reference category (more than sixth parity) at nearly 1 percent level of significance. In this case, the hazard ratio of the lowest category (first parity) is 83.3 percent of the hazard ratio of the reference category (Table 2). In the case of the limited data set according to Henry’s methodology (Table 3), the differences among the categories of birth parity are not statistically significant. This could be caused by the lower number of records in particular categories.

The last included variable, but one of the most important ones, is the survival status of a previous child (child of a previous order in a family). It could be assumed that the effect of this variable would be one of the strongest because of the clear relation to average birth intervals. ⁶⁹ From the analysis (Tables 2 and 3), it turns out that if a previous child survived the first twelve months of life and if we have no information about the survival status of a previous child, there is no significant difference between the categories. In this case, the hazard ratio is around 1. This means that probably most of the cases where we have no information about the survival status of a previous child are cases where a previous child survived the first year of life. On the other hand, if a child of the previous order died within twelve months after birth, the average birth interval before the birth of the next child was more than halved (the hazard ratio for the category “previous child survived the first twelve months” vs. “previous child died within the first twelve months of life” is equal to 1.014/2.273 = 44.6 percent in the extended data set, Table 2). The difference is even more significant in the case of Henry’s methodology of data limitation (Table 3).

In traditional studies, common conclusions state that the higher the birth parity, the longer the average birth–birth interval. ⁷⁰ However, these results are not usually standardized for different values of birth parity, age of mother, and so on. In our model of the Cox regression, birth parity did not show as statistically significant (according to Henry’s methodology of data limitation) or only the difference between the lowest and highest birth parities showed to be statistically significant (extended approach). However, according to the results, the last child in a family (adjusted for the birth order or age of mother and other explanatory variables in the model) was born, on average, with a longer birth interval. The results of our study fully correspond with the limited reproductive period of women.

Discussion and Conclusion

This article consists of an application of selected contemporary analytical methods (the survival analysis and Cox regression) to historical individual data. Thanks to this, the classical methods of historical analysis and their conclusions could be discussed in comparison to more detailed results. In this way, the importance of methodological approaches is revealed. As always, it is important to consider the aim of the study where different methods could be of a particular importance. In this article, through the application of the Cox regression and the survival analysis of large data sets of individual life histories, several new and not yet fully described factors affecting the length of birth intervals in the past were revealed.

Average birth–birth intervals prolonged with higher birth order and the intervals were shorter if a previous child died early after birth. These are the results of classical historical demographic studies. ⁷¹ Using more sophisticated methods, we can study this issue in more detail. It is possible to analyze the pure effect of all variables considered as explanatory ones. Using the Cox regression, it was confirmed that the length of birth–birth intervals was on average shortened with the increasing age of a mother at marriage (effect of limited reproduction period), with a higher number of children born in a family (effect of limited reproduction period as well as the existence of a group of more fertile families threatened by health, social, or financial consequences of a higher number of children) and when a previous child died within twelve months afterbirth (effect of the end of breastfeeding, sexual abstinence after the birth but theoretically also of the reproductive behavior—need for a replacement of the deceased child ⁷² ). On the other hand, the birth–birth intervals prolonged with the age of mother at birth of a child (again the effect of decreasing fecundity with age) and for the last child born in a family (effect of decreasing fecundity with the approaching end of reproduction). These results agree with our initial assumptions.

Moreover, we compared the results calculated for two types of data sets. One of them was limited according to Henry’s methodology, the second one relaxed some of his strict rules—all the families were included in the analysis—not only families with completed reproduction and at least six children. However, in both data sets, the last birth interval (or the time period after the birth of the last child in a family) was included in the analysis and censored by the end of the reproduction period or by the end of the marriage, if the information was available. All the results were nearly the same using both data sets. So we can say that the extension of our database is statistically relevant.

This could be taken as an important result because the size of databases in historical demography is usually not very large and their limited size could cause problems in some types of analysis. In many classical historical studies, only the very limited databases were available and used (data sets with low number of observations), and often, it was also the reason why the more advanced analyses (e.g., with more detailed sorting of data) were not used in these studies. Each possibility of data extension could then be taken as a benefit.

Based on the results, we can confirm, above all, the biological effects acting on the reproductive behavior in the studied locality and time period (e.g., decreasing fecundity with age or with the approaching end of reproduction of a woman, end of breastfeeding in the case of early death of a child, etc.). In the case of infant death of the previous child, we can only theoretically discuss the effect of replacement for the following birth interval, as in the data no intentional family limitation or birth postponement was observable—from the results it seems that the reproductive behavior was influenced, above all, by natural processes. From the studied data, we did not observe any prolongation of birth intervals with increasing birth parity. The longer average interval before the birth of the last child in a family could again be explained by the physiological limitations of female fecundity. On the other hand, this could also be the stimulus for more in-depth study including also the effect of calendar time or sex composition of the children in a family.

Moreover, although we have no information about breastfeeding practices in the studied locality, we can assume that the tradition was probably similar to that in the German villages studied by Knodel. ⁷³ Because the average length of the birth intervals was shown to be similar in Jablonec as in the studied German villages, we can suppose that breastfeeding was rather common in Jablonec for at least several months after the birth. Also, the similarity of the results could be explained by the high proportion of German inhabitants in Jablonec during the studied time period.

Although there is no proof of intentional family limitation or timing of births in the presented analysis, we can suppose that particular differences could be observable in specific socioeconomic groups. However, in the studied data set, there is not enough reliable information about the SES, so this type of analysis was not performed.