## Abstract

Fertility has long been declining in industrialised countries and the existence of public pension systems is considered as one of the causes. This paper provides detailed evidence on the mechanism by which a public pension system depresses fertility, based on historical data. Our theoretical framework highlights that the effect of a public pension system on fertility is ex ante ambiguous while its size is determined by the internal rate of return of the pension system. We identify an overall negative effect of the introduction of pension insurance on fertility using regional variation across 23 provinces of Imperial Germany in key variables of Bismarck’s pension system, which was introduced in Imperial Germany in 1891. The negative effect on fertility is robust to controlling for the traditional determinants of the first demographic transition as well as to other policy changes.

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## Notes

The literature explaining the decline in fertility has put relatively more emphasis on labour market institutions affecting female labour supply (e.g. Ahn and Mira 2002), the tax system (e.g. Egger and Radulescu 2012), the interaction between the tax system and family policy (e.g. Apps and Rees 2004), and maternity leave legislation (e.g. Berger and Waldfogel 2004).

*Reichsgesetzblatt*(RGbl) 1899/33.Also refer to the published law in

*Reichsgesetzblatt*(RGbl) 1889/13.After 1900 the definition of old age changed slightly and every worker who reached the age of 65 was automatically classified as invalid.

After 30 to 50 years of contribution, this fraction could increase to about half of a worker’s wage in the lowest category and to about 40 % of a worker’s wage in the middle category (Reichsversicherungsamt 1910). Note that detailed regional information on wages is only available for selected professions.

We analyse a PAYG pension system in which the working generations finance the pensions of the retired generations by their contributions in the same period. In particular, we investigate what is known in the literature as a Bismarckian PAYG pension system in which pensions are proportional to contributions.

Note that this assumption can be relaxed. It does, however, correspond to the fact that at the time when the pension system was introduced, unmarried women were supposed to be working, while married women were still supposed to stay at home and care for the children, which is also reflected by the fact that working women were expected to drop out of the pension system such that the law contained a provision for reimbursement of contributions upon marriage (RGbl 1889/13, 30).

Note that this assumption can easily be relaxed by e.g. assuming a u-shaped time cost of children. This would imply that with a certain number of children the cost of rearing each single one diminishes, because the older children can care for the younger children.

How such transfers from adults to their elderly parents can be enforced is subject of an extended literature about implicit contracts within the family, see e.g. Sinn (2004), Cigno (2006), Cigno et al. (2006). Furthermore, it is possible to assume that the per child transfer decreases with more children without affecting the model results, in which case the total transfer could be written as

*n*_{ t }*b*_{ t+1}(*n*_{ t }). As long as the total intra-family transfer is inelastic with respect to the number of children, \(b_{t+1}+\frac {\partial b_{t+1}}{\partial n_{t}}n_{t}>0\), i.e. total transfers remain increasing with more children, the results of the model are unaffected.^{10}Note that without the intra-family transfers (*b*_{ t }=*b*_{ t+1}=0) the price of a child increases and is always positive. The only effect of excluding such transfers from the model is a stronger income effect.^{11}Population numbers were reported annually until 1895, but afterwards only during census years, i.e. in 1895, 1899, 1900, 1905, 1909, 1910. We use the extrapolated population numbers from Scheubel (2013) for the missing years.^{12}In fact, contribution rates only varied between the four/five contribution categories, but not between provinces and not over time.^{13}Refer to the 1889 law on pension insurance (*Reichsgesetzblatt 1889/13*) and the 1899 revision (*Reichsgesetzblatt 1899/33*).^{14}The CMBR can be computed as \(CMBR=(1-illegitimacy\,\,rate_{t})*\frac {{ Number\,\,of\,\,births}_{t}}{1000}\) for all years.Scheubel (2013) illustrates this by comparing the CMBR to other fertility indices which take into account natural fertility and the age structure of women. As information on age structure is only available for years 1871, 1885, and 1890 while pension insurance was introduced in 1891, we cannot use other fertility measures for the analysis in this paper.

This approach also helps us to reproduce previous findings on the first demographic transition, which shows that our proxies capture the main determinants that have been identified in the literature.

Before 1895 population censuses were conducted almost every year. After 1895 population censuses were conducted in 1899, 1900, 1905, 1909 and 1910.

Women’s wages were lower such that almost only women contributed in the lowest contribution category (Haerendel 2001).

As discussed above, this may be related to the fact that our measure of workers includes those working in mining. Miners’ associations provided pension insurance before the introduction of comprehensive health insurance (Jopp 2013). Hence, any positive correlation between the share of workers and birth rates may be confounded by the negative correlation between the share working in mining and the birth rate.

We refrain from discussing the option of using a random effects model here; it is obvious that we have to control for non-random unobserved province-specific effect. This notion is also confirmed by a simple Hausman test.

There were three major changes to legislation during the period we study: changes to the

*Gewerbeordnungsnovelle*(amendments to the Industrial Code) in 1878 and 1891 and a law banning child labour in 1903 (Boentert 2007). Importantly, the amendments to the Industrial Code did not affect child labour in all areas of production. The 1878 amendment prohibited children below the age of 14 to work in factories. After 1891, this prohibition was extended to workshops and production at home, such as spinning and weaving. The general law from 1903 extended this also to agricultural production. Probably, the changes in 1891 had the comparatively largest impact on household income. However, birth rates only started their sustained decline during the 1900s in all provinces.The appropriate lag of at least 15 years is only given for years 1900 or later. Thus, it should not be surprising to see the expected negative effect mainly for years after 1900.

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## Acknowledgments

We would like to thank Kathrin Weny for valuable research assistance. We are also grateful to Tobias Jopp as well as the editor and the two anonymous referees of this journal for their for helpful comments and suggestions.

## Author information

### Authors and Affiliations

### Corresponding author

## Additional information

*Responsible editor*: Alessandro Cigno

We would like to thank Kathrin Weny for valuable research assistance. We are also grateful to Tobias Jopp as well as to the editor and the two anonymous referees of this journal for their for helpful comments and suggestions. This paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the author and do not necessarily reflect those of the ECB.

## Appendices

### Appendix A: details on the theoretical model

### 1.1 A.1 Second order conditions

In the model of the Bismarckian pay as you go pension system the second derivatives of Eqs. 5, 6 and 7 are given by:

The second-order conditions for a maximum of problem (4) are satisfied since *V*
_{nn} is negative and the following conditions hold true:

This demonstrates that the objective function *V*(*n*
_{
t
},*s*
_{
t
},*b*
_{
t
}) is strictly concave in the decision variables.

### 1.2 A.2 The savings effect of the Bismarckian PAYG pension system

The impact of extending the pension system on savings is given by:

With the negative denominator savings decrease with a higher contribution rate to the PAYG system if the numerator is negative.

In the case of the Bismarckian pension system the numerator is given by

Since the price of a child is positive, *R*
_{
t+1}((1−*τ*)*w*
_{
t
}
*f*
^{′}(*n*
_{
t
}) + *π*
_{
t
})−(*b*
_{
t+1}−Ω_{
t+1}
*τ*
*w*
_{
t
}
*f*
^{′}(*n*
_{
t
}))>0, the numerator is negative if the following condition for the intra-family transfer *b*
_{
t+1} holds: \(\tau w_{t}f^{\prime }(n_{t})<\frac {b_{t+1}}{{\Omega }_{t+1}} <w_{t}f^{\prime }(n_{t})+\pi _{t}\). If this condition holds, savings decrease with a higher contribution rate in the Bismarckian system. The condition is equivalent to: \(-\frac {\partial p_{t+1}^{BIS}}{\partial n_{t}} <b_{t+1}<{\Omega }_{t+1}((1-\tau )w_{t}f^{\prime }(n_{t})+\pi _{t})-\frac { \partial p_{t+1}^{BIS}}{\partial n_{t}}\). Note that the Bismarckian pension decreases in the number of children because the pension is proportional to contributions and income which decreases with more children. Thus, we have according to Eq. 9: \(\frac {\partial p_{t+1}^{BIS}}{ \partial n_{t}}<0.\) We can rewrite the condition for a negative savings effect as \({\Omega }_{t+1}((1-\tau )w_{t}f^{\prime }(n_{t})+\pi _{t})>b_{t+1}+ \frac {\partial p_{t+1}^{BIS}}{\partial n_{t}}>0\) which can be interpreted as follows.

Assume that a higher contribution rate reduces the number of children, i.e. the income effect is larger than the price effect. The second part of the inequality condition means that the loss of intra-family transfer due to fewer children in the second period is higher than the gain of a larger Bismarckian pension. Thus, having fewer children reduces income and decreases consumption in the second period. Then the first part of the condition implies that the discounted reduction of (opportunity) costs for children in the first period is higher than the loss of income in the second period due to fewer children. Hence, a lower number of children increases income and consumption in the first period by more than it reduces consumption in the second period. This implies that the parents react with lower savings in order to re-establish their preferred consumption profile and compensate the negative effect of the contribution rate on the number of children. If saved costs of fewer children in the first period are higher than the income loss in the second period a lower number of children induces lower savings.

###
**Proposition 2**

**Savings effect**
*The introduction or expansion of the PAYG system reduces savings if the lower number of children raises income in the first period to a larger extent than it lowers income in the second period.*

### 1.3 A.3 The effect of a Bismarckian PAYG pension system on the intra-family transfer

The effect of a higher contribution rate on the intra-family transfer is given by:

The numerator can be calculated as:

With *R*
_{
t+1}>Ω_{
t+1} and a positive price of a child, *R*
_{
t+1}((1−*τ*)*w*
_{
t
}
*f*
^{′}(*n*
_{
t
}) + *π*
_{
t
})−(*b*
_{
t+1}−Ω_{
t+1}
*τ*
*w*
_{
t
}
*f*
^{′}(*n*
_{
t
}))>0, the parents reduce the intra-family transfer if the PAYG system is extended: \(\frac {\partial b_{t}}{ \partial \tau }<0.\) The intuition for this result is that a higher contribution rate together with *R*
_{
t+1}>Ω_{
t+1} reduces lifetime income since the contribution contains an implicit tax on wage income. The parents reduce their transfer to the grandparents in order to compensate for this loss in lifetime income. This reduces the old-age consumption of the grandparents.

###
**Proposition 3**

**Effect on intra-family transfer**
*The introduction or expansion of the PAYG system induces the parents to reduce the intra-family transfer to the grandparents.*

### 1.4 A.4 Lack of capital markets

#### 1.4.1 A.4.1 The fertility effect

If we assume that individuals have no possibility to provide for old age by savings the budget constraints in both periods are given by:

where the pension in a Bismarckian system is determined by Eq. 8. Again, the first-order condition (5) holds. The implicit function theorem yields:

and *V*
_{nn}<0 by Eq. 26 and

satisfy the second-order condition. Hence, the fertility response with respect to an introduction or extension of the pension system is determined by the sign of *V*
_{
n
τ
}
*V*
_{bb}−*V*
_{nb}
*V*
_{
b
τ
}:

If *R*
_{
t+1}>Ω_{
t+1}, a higher contribution rate *τ* decreases the marginal price of a child which incites more children:

The second summand on the RHS is again the income effect. A higher contribution rate decreases income in the first period by *w*
_{
t
}(1−*f*(*n*
_{
t
})) and raises pension income in the second period by Ω_{
t+1}
*w*
_{
t
}(1−*f*(*n*
_{
t
})). Reducing the number of children compensates the income loss in period 1 by the expenditure (1−*τ*)*w*
_{
t
}
*f*
^{′}(*n*
_{
t
}) + *π*
_{
t
} per child and decreases the income in period 2 if *b*
_{
t+1}>Ω_{
t+1}
*τ*
*w*
_{
t
}
*f*
^{′}(*n*
_{
t
}), in other words, if the intra family transfer is larger than the Bismarck pension loss due to another child. Smoothing consumption across periods increases utility of the household so that due to the income effect fertility decreases with a higher contribution rate.

Hence, the size of the intra-family transfer determines the income effect and whether it is larger than the first (price) effect in which case fertility decreases with a higher contribution rate.

###
**Corollary**

**Constrained investment effect in a pay as you go Bismarckian pension system**
*In economies with lacking capital markets to provide for old-age the introduction or expansion of a Bismarckian pay-as-you-go pension scheme reduces the number of children if the intra-family transfers are sufficiently large.*

#### 1.4.2 A.4.2 The effect on intra-family transfer

In this case, the effect on intra-family transfer is given by:

With a positive denominator (39) the effect of intra-family transfer by a larger PAYG system depends on the sign of the numerator:

The sign is ambiguous, in particular if *b*
_{
t+1}>Ω_{
t+1}
*τ*
*w*
_{
t
}
*f*
^{′}(*n*
_{
t
}).

### Appendix B: supplementary (online) table on a comparison of estimators

Table 6 presents an OLS model in column (1), our baseline model in column (2) and a first differences estimator in column (3).

A standard OLS model would suffer from several endogeneity issues, such as clustered standard errors and serial, potentially also spatial correlation. Presenting the OLS model (with standard errors robust to at least serial correlation and clustering at the province level) in this context helps to illustrate the importance of controlling for the unobserved fixed effects. In particular, note that the OLS estimates differ in two important respects from our baseline model. First, the coefficients from our baseline model tend to be either overestimated or underestimated by the OLS approach. Second, even though standard errors are adjusted for some clustering as well as for serial correlation, the OLS model sometimes indicates significant estimates while the fixed effects model does not. At the same time, the OLS model is able to indicate the relative size of the different effects fairly well.

In theory, first differencing should yield exactly the same inference as a fixed effects model when the fixed effects model is applied to only two time periods. This is illustrated when comparing columns (2) and (3). The coefficients are the same while standard errors are larger in the model in first differences. This should not be surprising given that the first differences model is less efficient. Losing a degree of freedom in a model with only a small number of cross-sectional observations potentially has a big impact on the precision of the estimates. However, the coefficients in the first differences model are not substantially different from our baseline model and as conjectured.

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Fenge, R., Scheubel, B. Pensions and fertility: back to the roots.
*J Popul Econ* **30**, 93–139 (2017). https://doi.org/10.1007/s00148-016-0608-x

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DOI: https://doi.org/10.1007/s00148-016-0608-x

### Keywords

- Public pension
- Fertility
- Transition theory
- Historical data
- Social security hypothesis
- European fertility decline
- PAYG pension scheme