Table 4.
Simulation results: Alternative scenarios (percentage point risk differences)
| Scenario | Son Effect |
|
|---|---|---|
| Prospective (δ2) | Cross-sectional () | |
| Base Case | −0.10 (0.04) | −0.44 (0.15) |
| 170 Male Pregnancies Per 100 Female | −0.16 (0.04) | −0.75 (0.14) |
| 110 Male Pregnancies Per 100 Female | −0.01 (0.04) | −0.05 (0.14) |
| 30 % of Pregnancies End in Live Birth | −0.06 (0.04) | −0.24 (0.15) |
| 70 % of Pregnancies End in Live Birth | −0.13 (0.04) | −0.72 (0.15) |
| “High Association” Cases in Figs, 1c and 1d | −0.32 (0.04) | −1.92 (0.13) |
| “Low Association” Case in Fig. 1d | −0.02 (0.04) | 0.08 (0.15) |
| “Threshold Value” Case in Fig. 1c | −0.09 (0.05) | −0.42 (0.14) |
| Positive Correlation Between Fertility and Marriage “Fitness” | −0.10 (0.04) | −0.55 (0.15) |
| Negative Correlation Between Fertility and Marriage “Fitness” | −0.07 (0.04) | −0.31 (0.13) |
Notes: For each scenario indicated, we executed 250 simulations on 250,000 hypothetical couples each time, using base parameters given in column 3 of Table 2, except as indicated in that scenario's label. At the end of the simulation, we estimated a discrete-time, proportional-hazards survival regression on the simulated data set and converted the estimated log odds difference to a percentage-point risk difference, as described in the text and in the notes to Fig. 2. The average risk difference across the 250 simulations is what we report in column 2. We also simulated the process of drawing data on parents with children from a cross-sectional data set like the census, as described in the text and in the notes to Fig. 3, and estimated the difference in risk of having divorced as a function of sex of the first birth, using a linear probability regression. That average risk difference across the 250 simulations is what we report in column 3. In parentheses beneath each risk difference, we report the bootstrap standard error (i.e., the mean squared deviation across the 250 simulations from the reported son effect).