Single-cell expression profiling is destructive, giving rise to only static snapshots of cellular states. This loss of temporal information presents significant challenges in inferring dynamics from population data. Here we provide a formal analysis of the extent to which dynamic variability from within individual systems (“intrinsic noise”) is distinguishable from variability across the population (“extrinsic noise”). Our results mathematically formalise observations that it is impossible to identify these sources of variability from the transcript abundance distribution alone. Notably, we find that systems subject to population variation invariably inflate the apparent degree of burstiness of the underlying process. Such identifiability problems can be remedied by the dual-reporter method, which separates the total gene expression noise into intrinsic and extrinsic contributions. This noise decomposition, however, requires strictly independent and identical gene reporters integrated into the same cell, which can be difficult to implement experimentally in many systems. Here we demonstrate mathematically that, in some cases, the same noise decomposition can be achieved at the transcriptional level with non-identical and not-necessarily independent reporters. We use our result to show that generic reporters lying in the same biochemical pathways (e.g. mRNA and protein) can replace dual reporters, enabling the noise decomposition to be obtained from only a single gene. Stochastic simulations are used to support our theory, and show that our “pathway-reporter” method compares favourably to the dual-reporter method.