Fig. A2.

Sensitivity Analyses for Effects of Grandparents’ Education on Grandchildren’s Education under Various Assumptions about Strengths of Unobserved Variables W

Notes: The parameter π can be roughly interpreted as the selection bias, or the correlation between W and A. The parameter θ refers to the intergenerational correlation between W_(t) and W_(t+1). Specifically, I assume that the unobserved variable $W_1=\pi *A_1^{*}+{ϵ}_1$ and $W_3=\theta *W_1^{*}+\pi *A_2^{*}+\pi *Y^{*}+{ϵ}_2$, where $W^{*},A^{*}$, and $Y^{*}$ are standardized variables of W, A, and Y. The values of $\theta ,\pi \in \left[\mathrm{0,1}\right]$. For the sake of simplicity, this figure shows only results from the sensitivity analysis when θ=π. The bias-corrected estimates for each value of the parameters are based on point estimates from 200 simulated samples. The horizontal line refers to the scenario under which the average grandparent effect is zero. The shaded areas refer to 95% confidence intervals. To speed up the computation, the sensitivity results are based on data with complete cases rather than data with missing-data imputation.