Analysis of the determinants of fertility decline in the Czech Republic

Abstract

In this paper, we analyze the decline in the total fertility rate (TFR) in the Czech Republic during the economic transition. To identify transition-specific features of this decline, we estimate a Heckman–Walker multistate model of the birth process using data from the 1998 Family and Fertility Survey. We find that the negative effect of transition on TFR is mostly driven by a sharply increased influence of higher education, limited ability to combine employment with childbearing and lack of adequate childcare facilities. We also detect a significant role of the increased use of contraception, motivated by both economic and demographic reasons.

Appendix

1.1 Direction of the effect and marginal effects

Waiting time

First, consider the effect of the covariates on Weibull hazard function

$$h{\left( {t\left| {\theta _{i} } \right.} \right)} = \gamma {\left( {\exp {\left\{ {x\beta + \theta _{i} } \right\}}} \right)}^{\gamma } t^{{1 - \gamma }} $$

Since the first derivative with respect to x β is positive, the sign of the effect will always be equal to the sign of the estimated parameter. For instance, a positive estimated coefficient conveys that an increase in x leads to an increase in the hazard of having a child and, hence, to a reduction in the waiting time between births.

To compute the size of the effect, consider the expected value of a Weibull-distributed random variable

$$E{\left( {T\left| \phi \right.{\left( x \right)}} \right)} = \phi {\left( x \right)}^{{ - 1}} \Gamma {\left( {1 + \gamma ^{{ - 1}} } \right)},$$

where in our case, ϕ(x)=exp {x β+θ _i }. In the presence of unobserved heterogeneity, this expectation modifies to

$$E{\left( {Tx,\theta } \right)} = {\sum\limits_i {\frac{{\pi _{i} }}{{\exp {\left\{ {x\beta + \theta _{i} } \right\}}}}} }\Gamma {\left( {1 + \gamma ^{{ - 1}} } \right)}.$$

Taking the first derivative of E(T∣x,θ) with respect to x, we get

$$\frac{{\partial E{\left( {T\left| {x,\theta } \right.} \right)}}}{{\partial x}} = {\sum\limits_i { - \frac{{\pi _{i} \Gamma {\left( {1 + \gamma ^{{ - 1}} } \right)}}}{{\exp {\left\{ {x\beta + \theta _{i} } \right\}}}}} }\beta .$$

(A1)

As covariates enter E(T x,θ) nonlinearly, the marginal effect at the different levels of one and the same variable will not be the same (e.g., an additional year of schooling for a person with university education will cause a change in waiting time different from that caused by an additional year for a person with only secondary school education). To ensure correct inference, the marginal effects must be calculated for all possible levels of the explanatory variables.

Quit probabilities

Identical inference can be made about changes in quit probabilities. With parameterization

$$p = {\left( {1 + \exp {\left\{ { - x\omega } \right\}}} \right)}^{{ - 1}} ,$$

an increase in the value of the variable will cause an increase in probability of quitting after the realized birth, provided that the corresponding parameter is positive. The marginal effect of the covariates on the expected quit probabilities is

$$\frac{{\partial E{\left( {Px} \right)}}}{{\partial x}} = \frac{{\exp {\left\{ { - x\omega } \right\}}}}{{{\left( {1 + \exp {\left\{ { - x\omega } \right\}}} \right)}^{2} }}\omega .$$

.

Table A1 Estimated coefficients with parameterized quit probabilities: first birth cohort (born 1972–1982)

Table A2 Estimated coefficients with parameterized quit probabilities: second birth cohort (born 1963–1971)

Table A3 Estimated coefficients with parameterized quit probabilities: third birth cohort (born 1954–1962)

Table A4 Test of no increase in the negative effect on timing of births

Table A5 Test of no increase in the negative effect on exit from childbearing