Malthus in the Bedroom: Birth Spacing as Birth Control in Pre-Transition England

The original data set, based on family reconstitutions of 26 English parishes, includes 80,704 families and 272,164 births. We begin by restricting the sample to births that occurred in the period 1540–1850, leaving out the thin tails (1536–1539 and 1851–1889). This restriction reduces the number of families to 80,198. Next, we require that the wife had at least two recorded births and that her age was known, between the ages of 15 and 45, at the time of her deliveries. The lower end of the age interval comes naturally: the Church of England did not allow women below the age of 15 to marry, and this is confirmed by the data. The rationale for the upper end is that the sampled women rarely conceived children after age 45 due to menopause. Moreover, the restriction mitigates the potential problem that births recorded as occurring after age 45 may be wrongly recorded.¹ Our restrictions reduce the sample size to 18,220 families.

The sample is then further restricted to families for which wife’s age at marriage can be observed and dates of births (or baptisms) of all recorded family children exist. Prenuptially conceived children are included; however, birth intervals shorter than 40 weeks, which stem from either premature births or potential data entry errors, are excluded. These restrictions ultimately leave us with a total of 15,845 families and 62,223 birth events.² This baseline sample includes 1,208 twin births, which are treated as single events.

In addition to the aforementioned demographic data, our analysis also uses statistics concerning national real wages, crude death rates, and temperatures. Our key explanatory variable when testing for the existence of preventive checks (i.e., parity-independent birth spacing) is living standards measured by national real wages. The real wage series employed in the main analysis is provided by Clark (2007). The wages and prices used to compute the real wages in England are a combination of observations from across the entire country, as discussed in Clark (2007).³ In the duration analyses, the national yearly real wage series is combined with the demographic event data from the year in which the relevant interval started to the year in which the modeled event took place.

Panel a of Fig. 1 illustrates the relationship between average birth intervals and (standardized) real wages in percentiles. The graph demonstrates that periods characterized by higher real wages were associated with shorter birth intervals, suggesting a fertility response to changing economic conditions. Similarly, in illustrating average spacing of births by occupational groups, panel b of Fig. 1 shows that more-affluent social strata (traders, merchants, and gentry) had comparatively shorter birth intervals, suggesting that marital birth spacing was widespread among lower socioeconomic ranks.

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Any analysis that considers birth spacing as a measure of birth control has to address a number of confounding factors that are linked to biology. The key suspects are undernourishment and climatic conditions, both of which can influence the ability to conceive (Bongaarts 1980; Lam and Miron 1996). Both of these factors are also likely to be correlated with real wages through food prices. In further robustness analyses, we use two additional series of data—one of crude death rates and one of surface air temperatures—to identify and control for harvest failure and undernourishment.

Column 1 of Table 3 establishes that the real wage is positively and significantly correlated with the hazard of marriage. This is prima facie evidence of a direct negative effect of living standards on the wife’s age at marriage, supporting the Malthusian hypothesis that delayed marriage was a response to hard times as well as a sign of the existence of a preventive check mechanism operating among the sampled population in pre-transitional England.

Column 2 focuses on the event of giving birth to the first child within marriage (“starting”). The estimates indicate a positive and statistically significant correlation between the real wage and the protogenesic interval. The magnitude of the effects on the events of marriage and starting are very similar: a 1 standard deviation increase in the real wage accelerates time to marriage and to first conception by 23 % and 25 %, respectively. This is consistent with the conventional view that marriage historically marked the onset of a family (i.e., to give birth).

The estimates in column 3 present evidence of pretransitional, parity-independent birth spacing, establishing that an increase in real wages accelerates the timing of the next conception. The magnitude of the impact of the real wage is also economically significant: a 1 standard deviation increase in the real wage accelerates the timing of the next conception by approximately 10 %.¹⁴

Turning to the stopping specification (column 4), we find no statistically significant impact of real wages on the hazard of the last conception. The effect remains statistically insignificant when we consider starting ages other than 15 for the event of stopping and when we split the sample by 50-year subperiods (not reported). These results are perhaps unsurprising: because real wages are largely nontrending across the period under observation, short-term variations in real wages are likely to cancel out over the course of a family life cycle, leaving little room for wages at any point in time to substantially affect the timing of the last birth.¹⁵

In summary, our analyses establish that falling living standards captured by lower real wages led not only to significantly later marriages but also to longer birth intervals within marriage. In our robustness analyses, we explore the impact of some key confounding factors to rule out the possibility that the spacing effects we observe are positive checks rather than preventive checks.

To shed light on the role of socioeconomic factors in historical birth patterns, we subdivided our sampled families into income groups using a categorization proposed by Clark and Cummins (2015). Clark and Cummins used information about male testators to group male occupations according the amount of wealth left in the will. From poorest to richest, these groups are laborers, husbandmen, craftsmen, traders, farmers, merchants, and gentry. Our reference group in the analysis is laborers (the poorest group in the classification scheme). Concerning the hazard of a marriage, apart from craftsmen—who tended to marry later in life than others—none of the groups differ significantly from laborers (Table 3, column 1). When looking at the timing of the first birth, craftsmen—but also farmers—had their firstborns comparatively later in life (column 2).

More interestingly, looking at birth spacing, we find that poorer families had longer birth intervals on average than richer ones: column 3 shows that all six occupational groups included in the model have significantly shorter birth intervals (higher hazard ratios) compared with the reference group (laborers). In particular, we find that the coefficients for the richest groups (traders, farmers, merchants, and gentry) are statistically different from the coefficients of husbandmen and craftsmen; the difference between husbandmen and craftsmen is not statistically significant. Therefore, birth intervals appear to decrease with wealth.

The mechanism causing these differences in birth intervals between rich and poor may have to do with differences in breast-feeding practices. Women in poor families would breast-feed their own children, but the rich could afford to pay a wet nurse, explaining why the more-affluent social groups display a larger hazard of a further birth (Fildes 1987). Differences in the practice of coitus interruptus may also explain the different patterns of birth spacing (Santow 1995).

We also find a large impact of a child death on the next conception, with a child death accelerating the timing of the next conception by some 74 %. Possible reasons for this effect include the interruption of the breast-feeding period (which shortens postpartum amenorrhea) and the attempt to replace the deceased child.

Interestingly, socioeconomic differences also apply in the case of stopping. Column 4 establishes that, on average, laborers stopped later than their more-affluent counterparts and that the gentry were more likely to stop earlier. Husbandmen, craftsmen, traders, and merchants also stopped significantly earlier than laborers. These results are conditional on the mother’s age at marriage, her age at the last birth, and the family size. In fact, we find that a larger family size was associated with a later time of stopping. Therefore, differences in sterility associated with differences in the age at marriage or family size cannot explain the differences in stopping practice across occupational groups. The fact that the rich had more surviving offspring than the poor, as demonstrated by Clark and Hamilton (2006) and Boberg-Fazlic et al. (2011), can thus be ascribed to earlier starting and shorter birth intervals. The earlier stopping pattern among the rich (especially gentry) is consistent with the notion that wealthier families may have had a target number of offspring (for a discussion, see Van Bavel 2004a).

Literacy among wives is also associated with shorter birth intervals and earlier stopping age, even after we control for socioeconomic status. Perhaps literate individuals from the lower socioeconomic ranks imitate the fertility patterns of their higher socioeconomic counterparts. Moreover, couples of low fecundity, captured by a relatively large protogenesic interval, had (as expected) significantly larger birth intervals than couples of high fecundity. Also, the group of couples that gave birth to children within 40 weeks of marriage (which includes couples that conceived their firstborn before marriage) had an overall lower hazard of subsequent births. The latter finding seemingly contradicts the suggestion made by Wrigley et al. (1997:422) in their description of the data’s prevalence of prenuptially conceived births: “It might be expected that such women [giving prenuptially conceived birth] would display higher fertility during the balance of their childbearing life than women whose first child was born more than nine months after marriage, since it might be supposed that women of high fecundity, or perhaps with a greater appetite for sexual activity, would have higher fertility and would be more likely to become pregnant before marriage than others.”

Last, as documented in previous studies, we find that the last birth interval was significantly larger, on average, than the previous intervals. This finding is consistent with the idea that the last birth was sometimes a failed stopping attempt.

Before we proceed to explore the role of parity in detail, it is useful to take a preliminary look at the variable birth order. The coefficient for birth order (Table 3, column 3) is highly statistically significant and suggests that higher parities are associated with shorter spacing. As discussed in the Introduction, this finding may arise from a selection bias stemming from the use of variation in birth spacing across families rather than within them. That is, as we move from lower to higher birth orders, the composition of the sampled families may shift toward a higher share of more-fecund couples, and hence couples of shorter-than-average spacing. As the birth order results of Table 3 indicate, the composition effect may lead us to mistakenly conclude that higher parities were associated with shorter spacing of births. However, given the nature of our data, this issue of selection bias can be addressed by accounting for between-family heterogeneity. To shed light on these matters, the next section explores variation in birth spacing across families as well as within them.

This section is devoted to the question of whether birth spacing depended on the stock of surviving offspring in a family. More specifically, we test the hypothesis that the timing of a successive birth is independent of the number of children already born (e.g., Henry 1953). We conduct the test similar to those in previous studies (e.g., Bengtsson and Dribe 2006; Van Bavel 2004a) by estimating parity fixed effects. In particular, we define net parity as the number of children alive at the start of the interval and include in the model a dummy variable for each net parity. Importantly, to test for parity-specific birth spacing appropriately, we also account for between-couple heterogeneity: that is, the fact that highly fecund couples are able to have shorter birth intervals, on average, and hence can reach higher parities, causing a potential selection bias toward shorter spacing at higher parity. We account for this selection bias by stratifying our sampled birth intervals on the family level.

The findings reported in column 1 of Table 4 show that the speed of a successive conception is significantly lower at parity 2 or higher compared with the reference group (parity 1). In addition, the difference between parity 2 and the remaining (higher) parities is statistically the same. This latter result is consistent with the Cambridge Group’s finding that “birth interval lengths changed very little between parities 2 and 5” (Wrigley et al. 1997:435). Our latter finding would therefore support the natural fertility hypothesis in that the spacing of births (after parity 1) does not appear to depend on parity.

Column 2, instead, reports the results when we account for heterogeneity among the sampled couples, stratifying by family and quarter-century. We stratify also by quarter-century to allow the baseline hazard to vary over time.¹⁶ By using variation in birth spacing within families, we find that the speed of a successive conception decreases monotonically with net parity, meaning that the spacing of births increases monotonically with net parity. For example, the coefficient for “Net parity 2” implies that the time to the successive conception after the second sibling is approximately 52 % lower than after the first sibling; the time to the next conception after the third sibling is 72 % lower compared with the interval after the first sibling; and the time to conception of a further sibling after the sixth child is 94 % lower with respect to the spacing between the first two siblings. These effects are significantly different from each other, as shown in Fig. 2, where we depict the coefficients for net parity with the relative confidence intervals estimated in columns 1 and 2 of Table 4. The figure clearly shows how not accounting for family heterogeneity conceals the positive impact of parity on the spacing of family births. We obtain these findings while accounting for age-related changes in maternal fecundity by controlling, in a time-varying fashion, for the age (and its square) of the mother during the interval. Interestingly, we find that after we account for family heterogeneity, the impact of child death on the successive birth interval increases in size. This finding suggests that unobserved heterogeneity at family level is correlated with child death and estimates not accounting for family heterogeneity provide biased estimates.

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The impact of the real wage on the spacing of births remains highly significant also in the specifications including parity dummy variables. This leaves an important question: Does the effect of wages on births vary with parity? The underlying hypothesis here is that the decision to postpone a birth during hard times may be exacerbated by the presence of other dependent children. We test this hypothesis by interacting the real wage with the parity fixed effects. As shown in column 2 of Table 4, we stratify by family and quarter-century. Column 3 reports the results, establishing that not only are higher parities associated with significantly larger birth intervals but that the size of the demographic response to changing real wages also rises significantly with parity. The coefficients of the interactions show that the impact of real wages on spacing increases up to parity 3 (the interval between the third and fourth sibling) and then stabilizes. The coefficients for the interaction terms imply that if the real wage decreases by 1 standard deviation, the time to the next conception is approximately 8 % lower for the third child (parity 2) and 13 % lower for the fourth child (parity 3) compared with that of the second child (parity 1, the reference group).¹⁷ The fact that the real-wage effect varies across parity seems to suggest that birth spacing was a deliberate decision rather than a biological mechanism.¹⁸

It is also possible to quantify the effects of the real wage and of parities in terms of time. Consider the baseline estimate with parity fixed effects and stratification by family as in column 2 of Table 4. The birth interval associated with the first parity (first two siblings) is 493 days; the birth interval associated with parity 2 (siblings 2 and 3) is 599 days, for a difference of 106 days. This difference increases to 161 days if we consider the birth interval between siblings 3 and 4 with respect to the first interval in the family.¹⁹ As for the real wage, an increase of the real wage by 1.5 standard deviations is associated with the postponement of a conception by about 54 days.²⁰

The estimates shown in column 1 of Table 5 support our previous findings. Within each age group, growing parities are associated with longer birth intervals. Interestingly, we also find that the impact of the real wage on birth spacing is larger and highly significant among young mothers (column 1), suggesting that households responded more strongly to changes in economic conditions during early stages of their life, when they were presumably more financially unstable.²¹

Our evidence of parity-dependent spacing is similar to that observed by Van Bavel (2004a) and others studying settings elsewhere in Europe during later periods: the larger the size of the families, the more the couples strive to postpone the next birth.

The analysis by subperiods suggests that the response in spacing to changes in real wages was most pronounced in the periods 1600–1649 and 1700–1749. This latter finding is consistent with the findings of Kelly and Gráda (2012), who observed a rising impact of wages on birth rates in the early eighteenth century. The point estimate for the subperiod during which we have the strongest preventive check (1600–1649) reveals that a 1 standard deviation increase in the real wage was associated with a 21 % increase in the speed of a successive conception. Again, the coefficients for the parity fixed effects confirm the existence of parity-specific spacing during each of our subperiods.

Because data are unavailable for some parishes for some periods, the composition of parishes in our analysis changes over time. Likewise, the occupational titles of husbands are more frequently reported toward the end of the period under consideration. To the extent that the likelihood of inclusion in the regression sample is correlated with spacing behavior, the estimated relationships may be biased. Although the stratification by quarter-century, parish, or family already accounts for the potential confounding effects of time, location, or family, respectively, we assess the influence of sample selection by focusing on parishes without attrition, and with full occupational coverage. As a further assessment, we investigate the robustness of our results when we control for time fixed effects on a higher resolution than quarter-centuries.²²

The results are reported in Table S3 in Online Resource 1. In column 1, we estimate our model using a subsample containing those 12 parishes with continual coverage across the period 1600–1800.²³ The impact of the real wage on birth intervals remains highly significant and of similar size with respect to the baseline estimate reported in the previous section. In column 2, we include only families in which the husband has an occupational title recorded: our findings are robust to this subsample, also.²⁴

Along similar lines, although the stratification of birth intervals by quarter-century accounts for changes in quarter-century fixed effects, it does not account for potential secular changes affecting both the real wages and the demographic outcomes on a shorter timescale. Column 3 establishes that when accounting for decade fixed effects instead of quarter-century fixed effects (while still stratifying by family), the estimated impact of the real wage on birth intervals remains highly significant both statistically and economically. Thus, the estimated effect of aggregate wages on the hazard of births within families cannot be attributed to secular variations across quarter-centuries. Overall, these specifications indicate that the qualitative results cannot be attributed to sample selection bias.

Another limitation of the data is that the migration of people in or out of the sampled parishes is not detected, which presents a problem if the decision to migrate is correlated with both real wages and actual birth intervals, or if migrants and nonmigrants have different spacing behavior. Although there are, of course, limits to what we can do to deal with the problem of migration, we address the issues in two ways: we account for permanent migration by including a dummy variable indicating those husbands and wives who had a missing birth or death date, and we account for temporary migration by excluding birth intervals lengthy enough to potentially conceal unobserved births. Furthermore, we also follow Ruggles (1999) and restrict our sample to so-called completed marriages, ensuring that the sampled husbands and wives did not terminate the marriage prematurely by migration or death.

Low real wages may induce couples to temporarily leave their parish of residence in search of work. If they give birth and baptize a child while living outside their home-parish, these births will go unobserved in our data and instead appear as an extended birth spacing interval. We address this issue by excluding intervals that are comparatively long. In column 3 of Table 7, we restrict the sample to birth intervals of less than three years, roughly making up the 75th percentile of the sampled intervals. The coefficient on real wages remains highly significant and of the same order of magnitude as the baseline estimate. Column 4 shows the results for an even more restrictive assumption: namely, focusing on birth intervals of less than 2.5 years, which is close to the average length of birth intervals. Once more, we find a significant effect of real wages on spacing.

Ruggles (1999) pointed out that restricting the sample to completed marriages— those marriages in which both spouses survive to the time where the wife reaches age 50—is particularly useful to deal with issues of migration. Not only do completed marriages ensure that the sampled couples are neither permanent immigrants nor permanent emigrants—because we require their birth and death dates to be known—but they also warrant that the couples are healthy enough to not end reproduction prematurely. Column 5 of Table 7 reports the estimates based on the subsample of completed marriages: the coefficient for the real wage is still highly significant and even larger in magnitude than the baseline estimate.²⁵

Is what we observe a biological mechanism rather than deliberate spacing behavior? Two potentially confounding biological factors are undernourishment and climatic conditions, as measured by air temperatures, both of which have been shown to impact fertility (Bongaarts 1980; Lam and Miron 1996). Because both of these factors are also likely to be correlated with real wages (temperatures through crop yields and hence food prices, and undernourishment when real wages are close to subsistence), we need to account for such potentially confounding mechanisms. Although we already established in the baseline analysis that the impact of real wages on spacing is parity-specific, we further address the question of biological influences by accounting for the potential confounding effects of climate and undernourishment.

Accounting for the potential confounding effect of air temperatures (provided by Manley 1953), we find that they are not significantly associated with birth intervals (Table S6, column 1, Online Resource 1). Reassuringly, the effect of the real wage and parity on birth spacing remains highly significant.

To account for the potential biological effects of unobserved correlates of real wages, such as undernourishment, we control for aggregate crude death rates (provided by Wrigley and Schofield 1989). Death rates not only reflect the disease environment—and thus, disease-related infertility—but can also capture episodes of crop failure and famines, and the effect thereof on fecundity. We find that higher death rates increase the time to the next conception (Table S6, column 2, Online Resource 1). However, the effect of the real wage on birth spacing remains highly significant. We reach the same conclusions when including both temperatures and death rates in the model (Table S6, column 3, Online Resource 1).