Section_10

Section_10 - Section 10 Econ 140 GSIs Hedvig Tarso Xiaoyu 1...

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Unformatted text preview: Section 10 - Econ 140 GSIs: Hedvig, Tarso, Xiaoyu * 1 Binary Dependent Variables ( Y i = 1 or Y i = 0 ) 1.1 General model • Y i = β + β 1 X 1 i + ... + β k X ki + u i • E [ Y | X 1 ,...,X k ] = 1 × Pr ( Y = 1 | X 1 ,...,X k ) + 0 × Pr ( Y = 0 | X 1 ,...,X k ) • Pr ( Y = 1 | X 1 ,...,X k ) = F ( β + β 1 X 1 + ... + β k X k ) , where F ( . ) is the cumulative distribution function 1.2 Interpretation • Predicted probabilities: c Pr ( Y = 1 | X 1 ,...,X k ) = F ( b β + b β 1 X 1 + ... + b β k ) • E ect of a change in a regressor (example: in X 1 ) : INFERENCE HERE! e ect = c Pr ( Y = 1 | X 1 + Δ X 1 ,X 2 ,...,X k )- c Pr ( Y = 1 | X 1 ,X 2 ,...,X k ) * continuous variable: e ect = ∂ c Pr ( Y =1 | X 1 ,...,X k ) ∂X 1 = b β 1 .f b β + b β 1 X 1 + ... + b β k X k , where f ( . ) is the density function * discrete variable: e ect = c Pr ( Y = 1 | 1 ,X 2 ,...,X k )- c Pr ( Y = 1 | ,X 2 ,...,X k ) 1.3 Estimation • Nonlinear Least Squares (NLLS): b β NLLS = argmin...
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Section_10 - Section 10 Econ 140 GSIs Hedvig Tarso Xiaoyu 1...

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