Measuring persistence in aggregate output: ARMA models, fractionally integrated ARMA models and nonparametric procedures

Econometric issues in the estimation of persistence in macro-economic time series are considered. In particular, the relative merits of estimates based on ARMA models, ARFIMA models and nonparametric procedures are investigated. It is shown that ARFIMA models are inappropriate for the purpose of estimating persistence. Furthermore, some of the criticism leveled in the literature against the use of ARMA models for estimating long run properties is put into perspective. Methodological issues arising in the estimation of ARMA models that are relevant to estimation of persistence are discussed. It is shown how overparameterization of an ARMA model may lead to severely downward biased estimates of persistence. The theoretical results are employed to explain some of the findings in Campbell and Mankiw (1987a) and Christiano and Eichenbaum (1990). The methodological aspects of the paper are also relevant for the problem of estimating the value of a spectral density at any given frequency. An empirical study confirms persistence estimates reported in Campbell and Mankiw (1987a), and shows that ARMA models as well as nonparametric procedures give very similar estimates of persistence if properly applied.