Cluster standard error _versus_ fixed effects

Question

I am working with experimental data -correspondence test in the rental housing market-. On which ground can I choose between:

1. F.E. for the region where the apt is and cluster s.e. on the day the application to the apt was sent
2. cluster s.e. on region where the apt is and F.E. for the day the application was sent (day is too much, perhaps, better w-e or month)?

More in general.

On what ground can I choose whether to control for a variable or to cluster the s.e. on that variable?

The first option changes the estimate of the coefficients while the second changes the estimate of the s.e.'s....both of them should be used when I suspect there is something which is substantially non observable.

So, I know the practical difference between option 1 and 2, but on what ground do I choose?

Answer 1

Is the cluster something you're not really interested in - just an irritant? Use clustered standard errors. E.g. if you've got kids in classrooms, and want to know their mean score on a test, you can use clustered standard errors.

Is the cluster something you're interested in or want to remove? E.g. if you've got kids in classrooms, and you want to make one classroom the reference, use fixed effects. The mean in the fixed effects model will be the mean of the classroom that was the reference category. Any between classroom effects are removed.

If you wanted to look at (say) teacher experience and test scores, you can't use fixed effects, because when you use control for classroom, you control for all differences between classes, including teacher experience.

Answer 2

You adjust for clustering at the level at which your experimental treatment is assigned. If your treatment is randomized by day of application, cluster by day. If your treatment is randomized by region, cluster by region.