Nathaniel

You cannot use fixed effect analysis with cross sectional data as all the degrees of freedom are used up at the higher  level by the dummies. 

The Hausman test does not distinguish between FE and RE - it actually tests whether the  cross sectional element of a  time varying variable is different to its longitudinal effect, There are other ways ( Mundlak specification and within - between models random effects) besides fixed effect of tackling potential endogeneity - all of this is covered in the papers I cited.

Dear Badreldin,

A simple answer is "yes" - by using the time series data to estimate values at the time of the cross-section then comparing these with the cross-sectional data. But it really depends upon your research question.

Maybe you could use a panel data. This structure of data combines both dimensions (times-series and cross-sectional) at the same time. In this case, you need to use different regression approaches, such as fixed-effects model and Pooled OLS. A good book could be "Introductory Econometrics" by Wooldridge.

I too think you could use a repeated measures panel study in which time series element is time varying data and the cross-sectional data is time invariant

have a look at 

https://www.researchgate.net/publication/233756428_Explaining_Fixed_Effects_Random_Effects_Modeling_of_Time-Series_Cross-Sectional_and_Panel_Data

and its follow up

https://www.researchgate.net/publication/299604336_Fixed_and_Random_effects_making_an_informed_choice

there are a lot of resources here - see panel models

http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#multipleresp

Article Explaining Fixed Effects: Random Effects Modeling of Time-Se...

Article Fixed and Random effects models: making an informed choice

Nathaniel

You cannot use fixed effect analysis with cross sectional data as all the degrees of freedom are used up at the higher  level by the dummies. 

The Hausman test does not distinguish between FE and RE - it actually tests whether the  cross sectional element of a  time varying variable is different to its longitudinal effect, There are other ways ( Mundlak specification and within - between models random effects) besides fixed effect of tackling potential endogeneity - all of this is covered in the papers I cited.