Identification of structural vector autoregressions through higher unconditional moments

This paper pursues two objectives. First, we determine the sufficient condition for local, statistical identification of SVAR processes through the third and fourth unconditional moments of the reduced-form innovations. Our findings provide novel insights when the entire system is not identified, as they highlight which subset of structural parameters is identified and which is not. Second, we elaborate a tractable testing procedure to verify whether the identification condition holds, prior to the estimation of the structural parameters of the SVAR process. To do so, we design a new bootstrap procedure that improves the small-sample properties of rank tests for the symmetry and kurtosis of the structural shocks.