Hi, I am trying to identify the impact of race on unemployment (due to COVID-19) from April to December 2020. Using data from the U.S. Household Pulse Survey, I created a pooled cross-sectional dataset comprising 9 waves (1 wave per month) with each wave made up of a different set of individuals. My regression specification is as follows:

logit Unemployed i.Black i.Asian i.Hispanic c.Month c.BlackxMonth c.AsianxMonth c.HispanicxMonth, robust

where Unemployed is a binary variable (1=Unemployed, 0 otherwise). My independent variables are dummy variables for Black, Asian and Hispanic, 'Month' is a continuous variable to measure the change in probability of unemployment from April to December for the reference group (White, non-Hispanic) and the interaction variables measure the differential in this change between a given group and the reference group.

As I am using a pooled cross-sectional dataset, I am unable to address the problem of unobserved individual heterogeneity in the way that is done when panel data is used (i.e. fixed effects). I was previously advised to aggregate the dataset at the state level, and run a fixed effects model. However, this will only account for unobserved state heterogeneity. As such, is there another method I can use to address this problem?

In addition, I will be grateful if anyone can recommend further validity and robustness checks (such as a test for autocorrelation/spatial correlation) for my model. Thank you