This paper considers identifying effective cortical connectivity from scalp EEG. Recent studies use time-varying multivariate autoregressive (TV-MAR) models to better describe the changing connectivity between cortical regions where the TV coefficients are estimated by Kalman filter (KF) within a state-space framework. We extend this approach by incorporating Kalman smoothing (KS) to improve the KF estimates, and the expectation-maximization (EM) algorithm to infer the unknown model parameters from EEG. We also consider solving the volume conduction problem by modeling the induced instantaneous correlations using a full noise covariate. Simulation results show the superiority of KS in tracking the coefficient changes. We apply two derived frequency domain measures i.e. TV partial directed coherence (TV-PDC) and TV directed transfer function (TV-DTF), to investigate dynamic causal interactions between motor areas in discriminating motor imagery (MI) of left and right hand. Event-related changes of information flows around beta-band, in a unidirectional way between left and right hemispheres are observed during MI. A difference in inter-hemispheric connectivity patterns is found between left and right-hand movements, implying potential usage for BCI.