Inference for Pooled Default Logit Models with Shared Macro Variables

Summary

The document raises an inference problem in pooled firm-year logistic regression when the outcome is a default indicator and macroeconomic predictors are identical across firms within each year. Because observations share the same time-level predictors, ordinary model-based uncertainty estimates may not account for dependence associated with common year effects. The question considers Huber sandwich standard errors and Fama–MacBeth estimation as possible approaches.

It asks whether the sandwich estimator should replace the Hessian in Newton–Raphson maximum-likelihood estimation, and whether Fama–MacBeth can be adapted from ordinary least squares to maximum likelihood. No answer or empirical analysis is included, so the document does not resolve these methodological choices or establish which variance estimator is appropriate. It is useful as a statement of the problem and candidate methods, but researchers need additional guidance on clustering, time dependence, and inference for nonlinear panel models before applying a procedure.

Key ideas

• The setting is pooled firm-year logit estimation of default using macro variables shared across firms within a year.
• Shared time-level predictors raise concerns about dependence in standard errors.
• The question considers Huber sandwich standard errors and Fama–MacBeth inference.
• It asks whether a sandwich estimator changes Newton–Raphson estimation or only its uncertainty calculation.
• No answer is provided, so the document does not establish a recommended estimator.

Tags

# Standard errors clustered along the time dimension in pooled panel logit model


# Standard errors clustered along the time dimension in pooled panel logit model












I'm trying to estimate a logit model on pooled panel data set (unit of observation is firm-year). My dependant variable is default indicator and I have several macro variables as independant variables. These are going to be identical for all firms in a given year, so i need something to correct for this effect.

I saw that one can use Huber sandwich estimate or Fama MacBeth standard errors. I'm using Newton-Raphson to run MLE. If I go with Huber sandwich estimator, should I use it in stead of standard Hessian in the NR algorythm? On the other hand, since Fama MacBeth approach was developed for OLS, is it possible to use the same approach with MLE?

If anyone has hands-on experience with these issues, any thought would be much appreciated.

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