Maximum likelihood estimation of structural VARFIMA models

This paper considers the maximum likelihood estimation of a class of structural vector autoregressive fractionally integrated moving-average (VARFIMA) models. The structural VARFIMA model includes the fractional cointegration model as one of its special cases. We show that the conditional likelihood Durbin–Levinson (CLDL) algorithm of Tsay (2010a) is a fast and reliable approach to estimate the long-run effects as well as the short- and long-term dynamics of a structural VARFIMA process simultaneously. In particular, the computational cost of the CLDL algorithm is much lower than that proposed in Sowell (1989) and Dueker and Startz (1998). We apply the CLDL method to the Congressional approval data of Durr et al. (1997) and find that the long-run effect of economic expectations on Congressional approval is at least 0.5718, which is over twice the estimate of 0.24 found in Table 2 of Box-Steffensmeier and Tomlinson (2000). This paper also tests the divided party government hypothesis with the CLDL algorithm.     

The long memory autoregressive distributed lag model and its application on Congressional approval

This paper considers the instrumental variables (IV) estimation of the autoregressive distributed lag (ADL) model consisting of fractionally integrated regressors and errors, while allowing for part of the regressors to be endogenous. The idea of Liviatan (1963) and that of Tsay (2007) are combined to construct consistent and asymptotically normally distributed multiple-differenced two-stage-least-squares (MD-TSLS) and MD generalized method of moments (MD-GMM) estimators for the long memory ADL model. The simulations show that the performance of the MD-GMM estimator is especially excellent even though the sample size is 100. The IV estimators are applied to the data of Durr, Gilmour, and Wolbrecht (1997) on Congressional approval. As compared to the 0.08 estimate of the long-run effect of presidential approval on Congressional approval based on the scalar ADL model of De Boef and Keele (2008), a stronger support for the divided party government hypothesis is found for a class of the vector ADL model which generates a corresponding long-run impact equal to 0.26 or higher.