## GMM regarding logistic regression

Consider the binary logit model for the choice between two alternatives, 0 and 1. We take the simplest case with a single regressor, so the probability that individual i chooses alternative 1 is πi(β) = exi β/(1 + exi β), with β to be estimated. We observe the xi and di , with di = 1 if individual i chooses alternative 1 and di = 0 otherwise. A little useful result is ∂π/∂z = π(1 − π) when π = ez/(1 + ez) (check). And don’t forget the chain rule. We condition on x (as usual in regression although often not stated explicitly) so we have E(di − πi | xi ) = 0.

a)  Give two moment conditions of your choice for estimating β. Why are they valid? What is arguably the simplest moment condition?
(b)  With two moment conditions we do GMM for estimating β. Choose the unit matrix for your weight matrix. What is the first-order condition from which βˆ follows?
(c)  Elaborate the general formula for the estimated asymptotic variance of βˆ for the specific case of your estimator.
(e)  Elaborate the general form of the J-test for this case.

hi I also want to ask why the following condition is considered in the linear regression

Consider adding the moment condition based on E(x_i^2*yi). What is it? Discuss how useful adding this moment condition is.

### QUIZ

When using the free-cash flow model, cash flows are discounted at the weighted average cost of capital (WACC) and when using the dividend discount model, dividends are discounted at….

### Dixie’s Daughter’s Book Quiz Assignment

Dixie’s Daughter’s Book Quiz Assignment Directions: After reading Dixie’s Daughters:  The United Daughters of the Confederacy and the Preservation of Confederate Culture:   please answer the following questions about the book.  ….

### Its 4 page essay

PLEASE READ INSTRUCTIONS CAREFULLY Purpose: To write a response to Gloria Anzaldua’s “How to Tame a Wild Tongue,” a chapter in her book Borderlands/La Frontera. In your response, you should….