I am running a regression on a Cross section time series data set (cross sectional dominant) that has the following characteristics:
- 1,200 cross sections (6 countries * 200 products). Each country - product combination is one cross section
- 30 consecutive months of data in each cross section
- Total of 36,000 observations
- Some independent variables vary by country, others by product, but most are the same data in each country - product combination
- the products are not particularly correlated with each other, but the product time series move similarly across countries
- normalized the dependent variable
I first built the model in OLS (proc reg in SAS), but then included an intercept based on the average of the dependent variable in each country - product cross-section. While I only get one coefficient for this variable, effectively I'm running a fixed effects regression (please correct me if wrong).
As a next step I wanted to see if the t-values of my independent variables hold up under robust standard errors (I have about 50 variables in the model without multi collinearity). I thus ran proc surveyreg. The robust t-values dropped 50% on average. On one variable of interest the t-value dropped from a classical t-value of 14 to a robust t-value of 1.5. This variable varied by product, but not across countries. For another variable of interest the t-value dropped from 2 to 1, this variable had the same data in each cross section. The way I specified the clusters is across the products, so each cluster has 180 observations (30 months * 6 countries).
Believe this means there is evidence of heteroskedasticity. Would appreciate if you could help with path forward here:
- Since my t-values are still above 1 with robust standard errors, can I still make inferences based on the results of my model?
- Is the problem that my cross-sections are too different from each other and I am not accounting for these differences enough?
- Will switching to mixed effects solve the problem - proc mixed?
Help much appreciated. Thanks, Michael