Many closed-loop, continuous-control brain-machine interface (BMI) architectures rely on decoding via a linear readout of noisy population neural activity. However, recent work has found that decomposing neural population activity into correlated and uncorrelated variability reveals that improvements in cursor control coincide with the emergence of correlated neural variability. In order to address how correlated and uncorrelated neural variability arises and contributes to BMI cursor control, we simulate a neural population receiving combinations of shared inputs affecting all cells and private inputs affecting only individual cells. When simulating BMI cursor-control with different populations, we find that correlated activity generates faster, straighter cursor trajectories, yet sometimes at the cost of inaccuracies. We also find that correlated variability can be generated from either shared inputs or quickly updated private inputs. Overall, our results suggest a role for both correlated and uncorrelated neural activity in cursor control, and potential mechanisms by which correlated activity may emerge.