Homework 8

Arellano (2000), "Discrete Choices with Panel Data"

Arellano and Honore (2000)

(Due 4/16)

You need to type and email me your answers.

  1. Show MATH is a sufficient statistic for $\eta _{i}$ on page 6 in Arellano (2000).

  2. Derive equation (23) on page 6 in Arellano (2000).

  3. Show equation (95) on page 46 in Arellano and Honore (2000).

  4. Show equation (96) on page 47 in Arellano and Honore (2000).

  5. Explain "the maximum score estimator of Manski (1987) is not root-n consistent and not asymptotically normal," on page 9 in Arellano (2000).

  6. If we know that $\widehat{\theta }$ converges to some $\theta _{0},$ then it makes sense to ask how rapidly it converges. Define the root-n consistency. Hint: we say $\widehat{\theta }$ is root-n consistent for $\theta _{0}$ if
    MATH
    what is $b_{n}?$

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