Barreras de Entrada a la Universidad en Chile

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𝑌𝑖 = 𝛼 + 𝛽0𝑇𝑖 + 𝑓(𝑟𝑖) + 𝜀𝑖

𝑌𝑖 𝑌𝑖 = 1| 𝑖 𝑌𝑖 = 0| 𝑖

𝛼

𝑇𝑖 𝑇𝑖 = 1|𝑖

𝑇𝑖 = 0| 𝑖

𝑟𝑖

𝑇𝑖

𝑇𝑖

𝑟𝑖 𝑇𝑖

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𝑇𝑖

𝑇𝑖

𝑌𝑖 = 𝛼 + 𝛽0𝑇𝑖 + 𝛽1𝑟𝑖 + 𝛽2𝑟𝑖2 + 𝛽3𝑟𝑖

3 + 𝛽4𝑟𝑖𝑇𝑖 + 𝛽5𝑟𝑖2𝑇𝑖 + 𝛽6𝑟𝑖

3𝑇𝑖 + 𝜀𝑖

𝑟𝑖

𝛽0

𝑇𝑖

𝛼

𝑟𝑖

𝑇𝑖

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𝛽0

𝛽0

𝑟𝑖 𝑇𝑖

𝑇𝑖

𝛽0

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𝐷1,𝑖

𝐷1,𝑖 = 1

𝐷1,𝑖 = 1

𝐷1,𝑖 = 1

𝐷1,𝑖 = 1

𝐷1,𝑖 = 1

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𝑇𝑖

𝑌𝑖 = 𝛼 + 𝛽0𝑇𝑖 + 𝛽1𝐷1,𝑖 + 𝛽2𝐷1,𝑖𝑇𝑖 + 𝑓(𝑟𝑖) + 𝜀𝑖

𝛼

𝛽1

𝐷1,𝑖 = 1

𝛽0 + 𝛽2 𝐷1,𝑖 = 1

𝑓(𝑟𝑖)

𝐷1,𝑖

𝐷1,𝑖𝑇𝑖

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𝐸(𝑌𝑖 |𝑇𝑖, 𝐷𝑖 = 1) = 𝛼 + 𝛽0 + 𝛽1 + 𝛽2 + 𝑓(𝑟𝑖)

𝐸(𝑌𝑖 |𝑇𝑖 = 0; 𝐷𝑖 = 1) = 𝛼 + 𝛽1 + 𝑓(𝑟𝑖)

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𝛽1

𝛽2

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𝛽1 𝛽2

𝛽2

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𝑅2

𝑇𝑖

𝑟𝑖

𝑟𝑖 𝑥 𝑇𝑖

𝑟𝑖2

𝑟𝑖2𝑥 𝑇𝑖

𝑟𝑖3

𝑟𝑖3𝑥 𝑇𝑖

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𝑅2

𝑟𝑖

𝑟𝑖 𝑥 𝑇𝑖

𝑟𝑖2

𝑟𝑖2𝑥 𝑇𝑖

𝑟𝑖3

𝑟𝑖3𝑥 𝑇𝑖

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𝑅2

𝐷1

𝛽0

𝛽2

𝛽1

𝛽1 + 𝛽2

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