From "Victor Waters" To statalist@hsphsun2.harvard.edu Subject st: Not Directly Stata Related, But Please Help Date Wed, 12 Mar 2008 17:55:06 -0500

```Apologies for question not directly related to STATA.

If you think I should not have posted this here, please tell me where

My question is about deriving a formula in Cameron and Trivedi
Microeconometrics 2005.

On page 763 the following equations and text appears.

-------------------------
y_it = gamma y_i,t-1 + alpha_i + epsilon_it,    i = 1 to N, t=2, .. T

Cor(y_it, y_i,t-1) = Cor [gamma y_i,t-1 + alpha_i + epsilon_it,  y_i,t-1]

= gamma + Cor [ alpha_i ,  y_i,t-1]

= gamma + (1- gamma) /  1 + (1- gamma) sigma_epsilon ^2 / (1 + gamma)
sigma_alpha ^2),    (22.33)

where the second equlaity assume cor [epsilon_it, y_i,t-1] = 0 and the
third equality is obtained after some
algerbra for the special case of randome effects with epsilon_ii iid [
0, sigma_epsilon ^2] and alpha_i iid
[0, sigma_alpha ^2]

------------------------

In the next page they say that when gamma = 0. Cor (y_it, yi, t-1)
simplifies to

sigma_alpha^2 / (sigma_alpha ^2 _ sigma_epsilon ^2)

The last line suggests that may be extra parentheses are needed in the
denominator of 22.33.

I thought that I understood this material, but I am frutstated that I
cannot derive 22.33. It doesn't seem all that complicated,
but my inability to derive it makes me suspect that I did not
understand this material as well as I should.

I will appreciate it if you could help me.

Best regards,

Victor Waters
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```