Slides_Econ140A_2SLS

Slides_Econ140A_2SLS - Goals 2SLS Two-stage least squares...

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9/14/2011 1 2SLS Two-stage least squares Copyright Dick Startz 1 Goals Instrumental variables again Intuition on variance Optimal instrument Two-stage least squares (2SLS) interpretation Simultaneous equations Structural Reduced form Identification Copyright Dick Startz 2 Instrumental variable ? is an instrumental variable if it is correlated with ? and uncorrelated with the error term 1. ? = ?? + 𝜀 2a. plim 1 ? ∑? 2 = ? 𝑧 2 2b. plim 1 ? ∑ ?? = ? 𝑧𝑥 3. plim 1 ? ∑?𝜀 = 0 4. E(? ? 𝜀 ? 𝜀 ? ? ? ) = 𝜎 2 ? ? 2 , ? = ? 0, ? ≠ ? Copyright Dick Startz 3 Instrumental variable (IV) estimator ? 𝐼𝑉 = ∑?? ∑?? ? 𝐼𝑉 = ∑? ?? + 𝜀 ∑?? = ? ∑?? ∑?? + ∑?𝜀 ∑?? ? 𝐼𝑉 = ? + 𝜀 1 × ? 1 ∑?? + ⋯ + 𝜀 ? × ? ? ∑?? plim ? 𝐼𝑉 = ? Copyright Dick Startz 4 Asymptotic variance 𝑎?? var ? 𝐼𝑉 = plim ? 𝐼𝑉 − ? 2 = plim 𝜀 1 × ? 1 ∑?? + ⋯ + 𝜀 ? × ? ? ∑?? 2 = 1 ? 2 plim 1 1 ? ∑?? 2 plim 𝜀 1 2 ? 1 2 + 𝜀 1 𝜀 2 ? 1 ? 2 + ⋯ 𝑎?? var ? 𝐼𝑉 = 1 ? 2 1 ? 𝑧𝑥 2 𝜎 2 × ? × ∑?
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