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. Author manuscript; available in PMC: 2021 Aug 1.
Published in final edited form as: Demography. 2020 Aug;57(4):1513–1541. doi: 10.1007/s13524-020-00892-6

Table 5.

Sensitivity of weighted within-twin pair estimates to the presence of residual variation

rz,y
rz,x −0.3 −0.2 −0.1 0.0 0.1 0.2 0.3

−0.3 0.01 0.15 0.27 0.35 0.50 0.63 0.78
−0.2 0.14 0.22 0.29 0.35 0.43 0.51 0.59
−0.1 0.25 0.28 0.32 0.35 0.38 0.42 0.46
0.0 0.32 0.33 0.34 0.35 0.34 0.34 0.32
0.1 0.46 0.42 0.38 0.35 0.32 0.29 0.25
0.2 0.60 0.51 0.43 0.35 0.29 0.22 0.14
0.3 0.77 0.62 0.50 0.35 0.27 0.14 0.01

Note: Alternative weighted within-twin pair estimates for years of schooling were obtained via simulation. In the simulation, we randomly generated an unobserved variable, z, with a pre-specified correlation to years of schooling, x, and age at death, y. We then included this variable in our within-pair model, collected the resulting point estimate for years of schooling, and then averaged across 1,000 replications to obtain stable results. For the sake of reference, the correlation between the householder’s socioeconomic status (measured in terms of SEI) and children’s years of schooling is 0.3, and its correlation with age at death is 0.01.