Applied macroeconomists interested in identifying the sources of business cycle fluctuations typically have no more than 40 or 50 years of data at a quarterly frequency. With sample sizes that small, identification may not be possible even with correctly specified representations of the data. In this article, I investigate whether small samples are indeed a problem for some commonly used statistical representations. I compare three—a vector autoregressive moving average (VARMA), an unrestricted state space, and a restricted state space—that are all consistent with the same prototype business cycle model. The statistical representations that I consider differ in the amount of a priori theory that is imposed, but all are correctly specified. I find that the identifying assumptions of VARMAs and unrestricted state space representations are too minimal: the range of estimates for statistics of interest for business cycle researchers is so large as to be uninformative.
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