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- Since the parameters estimated in the two steps are based on different samples (HRS in the first step and CogEcon in the second), ˆ R is exactly zero (Murphy and Topel (1985), page 377). Now, consider each derivative in the two matrices. In the first-step probit log likelihood Aging and Strategic Learning Joanne W. Hsu contribution of each person: lnfi1 = F(θ1, x1i) = yilnΦ(xT i θ1) + (1 − yi)ln(1 − lnΦ(xT i θ1)) (21) ∂lnfi1 ∂ˆ θ1 = ∂lnfi1 ∂xi ˆ θ ∂xi ˆ θ ∂ˆ θ1 = statascore ∗ xi. (22)
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