Pooled Probit with Cluster Robust Standard Errors

[Tobias Cagala]

Dear all,

My question concerns STATA's cluster option for MLE.

I estimate a model with Pooled Probit and panel data of individual decisions. Assuming independence between individuals, I cluster on the individual level. The data generating process is such that y_it affects x_it+1, so I can only assume contemporaneous exogeneity.

Does clustering provide correct standard errors if I only include contemporaneous explanatory variables in the model?

Thanks

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In the section about inference under cluster sampling (13.8.4), Wooldridge (2002) assumes that "for each group or cluster g, f(y_g|x_g; \theta) is a correctly specified conditional density of y_g given x_g". After redefining the cluster index with i and using the index g for units within the cluster, Wooldridge points out that it is not necessary to assume that "D(y_ig|x_i1,...,x_iGi) = D(y_ig|x_ig)", which is analogous to contemporaneous exogeneity. In a nutshell, I am not sure if the assumption that f(y_g|x_g; \theta) is correctly specified holds if I only include contemporaneous explanatory variables.

[Jeff Wooldridge]

I cover this explicitly in Section 15.8.1 in 2e of my book. You just have to assume the probit model is correct for the variables you actually condition on, so strict exogeneity is not needed. Clustering gives the proper inference. JW

[Tobias Cagala]

Thank you for the clarification. That is very helpful.