segura 2013 -- el problema fundamental de la medición de impacto - v2 - 11 agosto 2013

Evaluación de Impacto: Introducción // @JackFlash

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𝑦𝑖 𝑖

𝑖 = 1,2, … , 𝑁


𝐷𝑖 =

1 𝐷𝑖 = 0


𝑌𝑖𝑗 𝑗 = {0,1}

𝑗 = 1

𝑗 = 0

𝑌𝑖1:

𝑌𝑖0:


𝐷𝑖∀𝑖 = 1,2,… , 𝑛 𝑛

𝐷𝑖 = 1

𝐷𝑖 = 0

𝑌𝑖(𝐷𝑖)

𝑌𝑖(𝐷𝑖 = 1) = 𝑌𝑖(1)

𝑌𝑖(𝐷𝑖 = 0) = 𝑌𝑖(0)

𝜏𝑖 = 𝑌𝑖(1) − 𝑌𝑖(0)


𝑌𝑖(1) 𝑌𝑖(0)

𝑌𝑖(1) 𝐷𝑖 = 1 𝑌𝑖(0)

𝐷𝑖 = 0

𝑌𝑖(1) 𝐷𝑖 = 0

𝑌𝑖(0) 𝐷𝑖 = 1

𝑌𝑖 = 𝐷𝑖𝑌𝑖(1) + 𝐷𝑖𝑌𝑖(0) = {𝑌𝑖(1) ⟷ 𝐷𝑖 = 1

𝑌𝑖(0) ⟷ 𝐷𝑖 = 0


𝜏𝑖 = 𝑌𝑖(1) − 𝑌𝑖(0)

𝜏𝐴𝑇𝐸 = 𝐸(𝜏𝑖) = 𝐸[𝑌𝑖(1) − 𝑌𝑖(0)]

𝜏𝐴𝑇𝐸

𝑌𝑖 = 𝛽0 + 𝜏𝑖𝐷𝑖 + 𝜇𝑖

𝜏𝑖 = 𝑌𝑖(1) − 𝑌𝑖(0)

𝑌𝑖(0) = 𝐸[𝑌𝑖(0)] + 𝜇𝑖 = 𝛽0 + 𝜇𝑖


𝜏𝐴𝑇𝑇 𝜏𝐴𝑇𝑈


𝐸[𝑌𝑖(0)|𝐷𝑖 = 0] ≅ 𝐸[𝑌𝑖(0)|𝐷𝑖 = 1]

𝜏𝐴𝑇𝑇


𝑌4𝑌3𝑌4 − 𝑌3

𝑌3

𝑌2 𝑌0


𝐸[𝑌𝑖(0)|𝐷𝑖 = 0] ≅ 𝐸[𝑌𝑖(0)|𝐷𝑖 = 1]

𝜏𝐴𝑇𝑇

𝐸[𝑌𝑖(0)|𝐷𝑖 = 1] − 𝐸[𝑌𝑖(0)|𝐷𝑖 = 0] == 0

𝐷𝑖 = 1 𝐷𝑖 = 0


𝑌𝑖 = 𝛽0 + 𝛽1𝐷𝑖 + 𝜇𝑖

𝑌𝑖𝐷𝑖 𝐷𝑖 = 1 𝐷𝑖 = 0

𝜇𝑖𝐷𝑖


𝐸[𝑌𝑖(0)|𝐷𝑖 = 1] == 𝐸[𝑌𝑖(0)|𝐷𝑖 = 0]

𝐷𝑖𝜇𝑖

𝐸[𝜇𝑖|𝐷𝑖] = 0

𝜇𝑖




𝛽1

�̂�1𝑝𝑙𝑖𝑚→ 𝛽1

𝐸[�̂�1] = 𝛽1


» 𝐷𝑖 = 1

» 𝐷𝑖 = 0

𝐷𝑖 = 1

𝐷𝑖 = 0

𝑌𝑖 𝑍𝑖 = 0


𝐸[𝑌𝑖(0)|𝐷𝑖 = 1] = 𝐸[𝑌𝑖(0)|𝐷𝑖 = 0]


𝜏𝐴𝑇𝑇𝐸[𝑌𝑖(0)|𝐷𝑖 = 1] − 𝐸[𝑌𝑖(0)|𝐷𝑖 = 0]


𝐸[𝑌𝑖(0)|𝐷𝑖 = 1] = 𝐸[𝑌𝑖(0)|𝐷𝑖 = 0]


𝐷𝑖 𝐷𝑖 = 1 𝐷𝑖 = 0

𝛽1 �̂�1

𝐸[𝑢𝑖|𝐷𝑖] = 0

𝐸[𝑢𝑖|𝐷𝑖] ≠ 0


𝑢𝑖

𝐸[𝑢𝑖|𝐷𝑖] ≠ 0

β̂′ = [�̂�0, �̂�1] . 𝑒. ¬𝐵𝐿𝑈𝐸


𝐷𝑖 𝑢𝑖β̂′ �̂�1𝐸[�̂�1] ≷ 𝛽1

�̂�1

𝐷𝑖𝑌𝑖 𝜏𝐴𝑇𝑇

𝑋𝑖 𝑖 = 1,… , 𝑛 𝜏𝐴𝑇𝑇

𝑌𝑖 = 𝛽0 + 𝛽1𝐷𝑖 + 𝛽2𝑋𝑖 + 𝑢𝑖


𝑋𝑖

𝑋𝑖

𝑌𝑖 = 𝛽0 + 𝛽1𝐷𝑖 + ∑ 𝛽𝑘𝑋𝑖𝑘𝐾𝑘 + 𝑢𝑖

𝐾


𝑋𝑖



𝜇𝑖 = 𝛽2𝑋𝑖 + 𝑢𝑖 𝜇𝑖′𝜇𝑖 ≫ 𝑢𝑖

′𝑢𝑖

𝐸[�̂�1] ≷ 𝛽1


�̂�1 𝛽1

- 𝐷𝑖𝑋𝑖

- 𝑋𝑖




�̂�1

𝐶𝑜𝑟𝑟(𝐷𝑖 , 𝑋𝑖) > 0 𝐶𝑜𝑟𝑟(𝐷𝑖 , 𝑋𝑖) < 0

𝛽2 > 0 𝐸[�̂�1] > 𝛽1 𝐸[�̂�1] < 𝛽1𝛽2 < 0 𝐸[�̂�1] < 𝛽1 𝐸[�̂�1] > 𝛽1

𝛽1


𝐸[𝑌𝑖(0)|𝐷𝑖 = 1] = 𝐸[𝑌𝑖(0)|𝐷𝑖 = 0]


𝐸[𝑌𝑖(0)|𝐷𝑖 = 0]

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