Networks in the brain operate in an excitation-inhibition (EI) balanced state. Altered EI balance underlies aberrant dynamics and impaired information processing. Given its importance, it is crucial to establish non-invasive measures of the EI balance. Previous studies have suggested that relative EI balance can be inferred from the spectrum of the population signals such as Local Field Potentials (LFP), Electroencephalogram (EEG) and Magnetoencephalography (MEG). This idea exploits the fact that in most cases excitatory and inhibitory synapses have quite different time constants. However, it is not clear to what extent spectral slope of population activity is related to the network parameters that define the EI balance e.g. excitatory and inhibitory conductance. To address this question we simulated two different types of recurrent networks and measured spectral slope for a wide range of parameters. Our results show that the slope of the spectrum cannot predict the ratio of excitatory and inhibitory synaptic conductance. Only in a small set of simulations a change in the spectral slope was consistent with the corresponding change in the synaptic weights or inputs to the network. Thus, our results show that we should be careful in interpreting the change in the slope of the population activity spectrum.