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- It is assumed that γ follows a normal distribution with mean ðœ‡ðœ‡Î³ and variance-covariance matrix Ωγ. Then, the asymptotic distribution ðœ†ðœ† Ì‚ of can be expressed as: ðœ†ðœ† Ì‚~ð‘ð‘�ðœ†ðœ† + Î ðœ‡ðœ‡Î³, Σ2ð‘†ð‘†ð‘†ð‘†ð‘†ð‘† + ΠΩγΠ′� (C.3) Following Conley et al. (2012), we implement the simplest form of priors for γ, that is, γ~ð‘ð‘(0, ð›¿ð›¿2) and computed the 95% confidence intervals for ðœ†ðœ† for different values of ð›¿ð›¿. Under the assumption that priors are correct, this approach provides valid inference and robustness with respect to normal 2SLS approach. The second method is the Union Confidence Interval (UCI), which allows us to analyse the robustness of the estimations in case of a direct relationship between the instrumental variables (parent’s age of decease) and the outcome variables.
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- Methodology described in Conley et al. (2012) Union of Confidence Intervals. Hours of formal care The γ-Local-to-Zero (LTZ) approximation bounds are drawn for different values of δ under the assumption that γ~N(0, δ2). All the reported bounds are for the 95% confidence intervals generated with robust standard errors. The Union for Confidence Intervals (UCI) bounds are drawn for different values of δ, which define the support of γ (i.e., the true direct effect of parents’ age of decease on TTD). Dash lines around the 2SLS estimation represent the upper and confidence intervals or the respective tests. The solid red line represents the value λ = 0. The solid black line in the γ-Local-to-Zero (LTZ) approximation represents the 2SLS class size effect estimate. Estimations performed using the command plausexog from STATA. -1500000 -1000000 -500000 0 ï¬ 0 2 4 6 8 ï¤
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- Methodology described in Conley et al. (2012) Union of confidence intervals. Length of stay at hospital -1500000 -1000000 -500000 0 ï¬ 0 2 4 6 8 ï¤
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- Methodology described in Conley et al. (2012) Union of Confidence Intervals. Length of stay at nursing home -1500000 -1000000 -500000 0 ï¬ 0 2 4 6 8 ï¤
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- Point Estimate (LTZ) CI (LTZ) Methodology described in Conley et al. (2012) Local to Zero Approach. Length of stay at hospital -400000 -200000 0 Effect of the instrument 0 2 4 6 8 ï¤
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- Point Estimate (LTZ) CI (LTZ) Methodology described in Conley et al. (2012) Local to Zero Approach. Number of consultations -400000 -200000 0 Effect of the instrument 0 2 4 6 8 ï¤
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