The model is not quite appropriate.The model advanced by Fama and MacBeth (1973) passed most empirical tests of their paper and became a standard methodology in financial literature as it possessed clarity and simplicity. However, their procedure does not properly account for errors of estimation and non-independence among cross sectional residuals. This omission may result to false inference when used to validate hypothesis based on the approximated parameters. The two mathematicians jointly recognize the existence of the errors in their procedure. This is due to an early attempt to increase precision.
Cross sectional and time series data are a special case of panel data that are in one dimension.