Norway: Fertility & Long Term Earnings
A 2023 study (Reconciling estimates of the long-term earnings effect of fertility by Simon Bensnes, Ingrid Huitfeldt, and Edwin Leuven) evaluates different methodological approaches to estimate the impact of having children on parents' long-term earnings, commonly known as the "child penalty" The authors compare results from three models:
The standard event-study model
An instrumental variable (IV) approach using the success of in-vitro fertilization (IVF) as an instrument (LPR-IV)
A novel event-study IV model that combines the first two approaches (event-IV)
While all three models find substantial child penalties, ranging from 11% to 18%, they lead to very different conclusions as to whether mothers or their partners drive this earnings gap—a key policy question. The event study attributes the entire impact to mothers, while the event-IV model suggests maternal responses account for only about one-fourth of the penalty.
Key Findings
The event study estimates that there are large negative effects on maternal earnings of around 16% but no impact on partners' earnings.
The LPR-IV model finds negligible effects on mothers but an 11% increase in partners' earnings.
The event-IV model falls in between, with a 3% reduction for mothers and a 10% increase for partners, implying a 13% child penalty.
Women time fertility to when their age-earnings profiles flatten. Not accounting for this dynamic selection biases event-study estimates of the counterfactual earnings trajectory.
Adjusting for fertility timing explains half the difference between the event study and event-IV estimates. Other sources of fertility account for the remainder.
Event-IV Approach
The event-IV model addresses the limitations of the other approaches:
Centering time on birth renders the treatment effect invariant to dynamic fertility responses, unlike the LPR-IV model
Adjusting for the timing of the IVF attempt controls for selection into fertility timing
Using IVF success as an instrument addresses the remaining unobserved variable bias
Revisiting Event-Study Assumptions
The study uncovers new insights on the nature of selection into fertility:
Women have children when their earnings growth starts to slow down
Those with later fertility have higher counterfactual earnings trajectories
This violates the parallel trends assumption even if pre-trends are parallel
Adjusting for a linear extrapolation of the pre-trend exacerbates the bias
More flexible event-study estimators allowing for treatment effect heterogeneity do not resolve the bias
Conclusions
The interpretation and policy implications of fertility effects depend on the empirical approach. By accounting for selection in fertility timing and remaining endogeneity, the event-IV model provides a more credible estimate of how parenthood affects mothers' earnings versus their partners.
The paper's insights on dynamic selection into fertility are a broader cautionary tale for event-study designs. They highlight that common intuitions about parallel trend assumptions can be misleading, and pre-trends may not be informative about the sign of selection bias in the treatment period.