Question: Take the heteroskedastic nonparametric binary choice model Y m(X)e e j X N 0,2 (X) Y Y 1 Y

Take the heteroskedastic nonparametric binary choice model Y ¤

Æm(X)Åe e j X »N

¡

0,¾2 (X)

¢

Y Æ Y ¤1

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Y ¤

È 0

ª

.

The observables are {Yi ,Xi : i Æ 1, ...,n}. The functionsm(x) and ¾2(x) are nonparametric.

(a) Find a formula for the response probability .

(b) Arem(x) and ¾2(x) both identified? Explain.

(c) Find a normalization which achieves identification.

(d) Given your answer to part (c), does it make sense to “allow for heteroskedasticity” in the binary choice model? Explain?

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