Unlike some direct methods, information on free carrier dynamics in GaAs-like semiconductors from time-resolved picosecond excitation-correlation (PEC) luminescence spectra can be obtained provided a theoretical model of the PEC signal is available. In this paper, we present our calculations of the time- and energy-resolved PEC luminescence due to spontaneous radiative recombination of free electron-hole pairs, excited by picosecond laser pulses. Our calculations show that the PEC luminescence line shape and its time evolution can depend critically on the conditions of carrier density decay, hot carrier cooling, density dependent band gap renormalization, broadening of energy states, (k) over right arrow (versus no-(k) over tilde) conservation, etc., incorporated in the theory.