Infinite-variance, alpha-stable shocks in monetary SVAR

This paper outlines a theory of what might be going wrong in the monetary SVAR (structural vector autoregression) literature and provides supporting empirical evidence. The theory is that macroeconomists may be attempting to identify structural forms that do not exist, given the true distribution of the innovations in the reduced-form VAR. This paper shows that this problem occurs whenever (1) some innovation in the VAR has an infinite-variance distribution and (2) the matrix of coefficients on the contemporaneous terms in the VAR's structural form is nonsingular. Since (2) is almost always required for SVAR analysis, it is germane to test hypothesis (1). Hence, in this paper, we fit <italic>α</italic>-stable distributions to the residuals from 3-lag and 12-lag monetary VARs, and, using a parametric-bootstrap method, we reject the null hypotheses of finite variance (or equivalently, <italic>α</italic> = 2) for all 12 error terms in the two VARs. These results are mostly robust to a sample break at the February 1984 observations. Moreover, ARCH tests suggest that the shocks from the subperiod VARs are homoskedastic in seven of 24 instances. Next, we compare the fits of the <italic>α</italic>-stable distributions with those of t distributions and a GARCH(1,1) shock model. This analysis suggests that the time-invariant <italic>α</italic>-stable distributions provide the best fits for two of six shocks in the VAR(12) specification and three of six shocks in the VAR(3). Finally, we use the GARCH model as a filter to obtain homoskedastic shocks, which also prove to have <italic>α</italic> > 2, according to ML estimates.