Bayesian Model Selection and Forecasting in Noncausal Autoregressive Models

Abstract

In this paper, we propose a Bayesian estimation and prediction procedure for noncausal autoregressive (AR) models. Specifically, we derive the joint posterior density of the past and future errors and the parameters, which gives posterior predictive densities as a byproduct. We show that the posterior model probability provides a convenient model selection criterion and yields information on the probabilities of the alternative causal and noncausal specifications. This is particularly useful in assessing economic theories that imply either causal or purely noncausal dynamics. As an empirical application, we consider U.S. inflation dynamics. A purely noncausal AR model gets the strongest support, but there is also substantial evidence in favor of other noncausal AR models allowing for dependence on past inflation. Thus, although U.S. inflation dynamics seem to be dominated by expectations, the backward-looking component is not completely missing. Finally, the noncausal specifications seem to yield inflation forecasts which are superior to those from alternative models especially at longer forecast horizons.JEL Classification: C11, C32, C52, E31

Autoregression-based estimation of the new Keynesian Phillips curve

“…Moreover, in this case, endogeneity of such an instrument is not reliably revealed by Hansen's (1982) J test. Noncausality of in ‡ation found by Lanne and Saikkonen (2011a) and Lanne et al (2011) thus indicates that using lags of in ‡ation as instruments as is commonly done in the previous literature, is likely to yield misleading results. Lanne and Saikkonen (2011b) also found noncausality very common in a comprehensive data set compirising more than 300 macroeconomic and …nancial time series, which suggests that …nding valid additional instruments for the estimation of the NKPC 2 may be challenging.…”

“…Also, Whelan (2005a, 2007), and Nason and Smith (2008a), inter alia, have found little evidence of forward-looking in ‡ation dynamics in analyses based on estimated NKPCs for the U.S. On the other hand, the recent results of Lanne and Saikkonen (2011a) and Lanne et al (2011) based on so-called noncausal autoregressive (AR) models suggest that the persistence in the U.S. in ‡ation results from agents'forward-looking behavior rather than dependence on past in ‡ation. The NKPC estimation results of Galí and Gertler (1999), and Galí 1 et al (2005), to name but a few, also lend support to the NKPC in the U.S.…”

Has US inflation really become harder to forecast?

“…Therefore, following Lanne and Saikkonen (2008), we specify Student's t-distribution for t . In addition to these authors, also Lanne et al (2009Lanne et al ( , 2010 have shown this distribution to …t U.S. in ‡ation series well.…”

“…Speci…cally, they claim that before 1983, PC models were superior to the univariate autoregressive (AR) model, but after 1984, the situation has reversed.We argue that SW's benchmark model is not the appropriate univariate model, especially in the 1970-1983 period, but, in fact, in ‡ation dynamics are better captured by a noncausal, instead of a conventional causal AR model. This claim is backed up by the …ndings of Lanne and Saikkonen (2008) and Lanne et al (2009) for the CPI in ‡ation and Lanne et al (2010) for the GDP price in ‡ation.…”

“…However, as shown by Lanne and Saikkonen (2008), and Lanne et al (2009Lanne et al ( , 2010, the errors of AR models estimated for U.S. in ‡ation series are not well characterized as Gaussian, but exhibit excess kurtosis. In those papers, Student's t-distribution is assumed for the errors and it turns out to provide a good …t.…”