95% CI for WTP

[a.tran@sydney.edu.au]

Hi Michiel,
Good morning!
Could you please teach/share with me how to calculate 95% CI for WTP? If it is hard to share here (typing equations, and etc), your guidance on the chapter/paper would be greatly appreciated.

Thank you and all the best,
Anh

[Michiel Bliemer]

It is easy to calculate for an MNL model, but much harder for a mixed logit model. If you use Apollo for model estimation, you can simply run .deltaMethod with the relevant WTP to get the outcome automatically.

The Delta method should be applied.

Suppose you would like to compute WTP = beta1/beta2, where beta2 is the cost coefficient.

Step 1: From the parameter estimates, obtain the following values:
* beta1 - estimated coefficient
* beta2 - estimated coefficient
* se(beta1) - standard error
* se(beta2) - standard error
* cov(beta1,beta2) - covariance
The first four are standard output in a results table, the last is obtained from the covariance matrix (which is also output of model estimation).

Step 2: Compute the following:
* w = beta1/beta2
* var(beta1) = se(beta1)^2
* var(beta2) = se(beta2)^2

Step 3: Compute se(WTP) using the Delta method formula, see for example equation (10) in our paper:
https://www.sciencedirect.com/science/a ... 1513001707
se(WTP) = (1/beta2) * sqrt[ var(beta1) - 2*w*cov(beta1,beta2) + w^2 * var(beta2) ]

Step 4: Compute 95% confidence interval:
lowerbound = w - 1.96 * se(WTP)
upperbound = w + 1.96 * se(WTP)
CI = [lowerbound, upperbound]

Michiel