Driscoll-Kraay standard error for panel logit

[Jasmine Xu]

Hi,

I am trying to estimate a structural logit model using panel data. Because my data is suspected to have cross-cluster correlation, I am thinking to use Driscoll-Kraay standard error.
I am aware that using Driscoll-Kraay standard error in logit is admitting the model is mispecified. However, I would like to start here, and then proceed to perhaps bootstrapping standard error.

My question is what is the formula for Driscoll-Kraay standard error using information matrix (jacobian and hessian of the likelihood function)? I have been looking for this for a long time, I am really appreciate it if anyone can point me to any learning material.

I am aware of the formula using residuals, then can I also use this formula for logit and use the residuals calculated as 1-predicted probability or 0-predicted probability?

[Jeff Wooldridge]

Jasmine: First, you are not admitting the logit model is misspecified if you compute D-K standard errors. You simply have not modeled either spatial correlation or serial correlation. The D-K standard errors exist so that you don't have to.

Regrettably, I don't think D-K is computed for nonlinear models. It wouldn't be hard to do because it proceeds by averaging the score (gradient) of the log-likelihood across the cross section for each t, to created a single time series. Then, one applies a Newey-West HAC to the resulting time series.

[Jasmine Xu]

Dear Prof Jeff Wooldridge,

Thanks for your suggestions!

About the mispecification, is it because the model might be consistent with QML even with serial correlation and cross-cluster correlation? I was thinking that serial correlation and cross-cluster correlation mean violation of the iid assumption of ML.

I have tried to implement D-K standard error in panel logit with a simple self-defined likelihood function. I am now proceeding to implement it for my complete likelihood function in which I use finite mixture model and the types of individuals are fixed across time:

So here I am bit confused how I should treat `cluster` and `time` dimension when I am trying to get the score vectors because now the each contribution to the total likelihood function is not coming from each observation but each cluster.