In a new paper, coauthored with Jim Nason, we estimate a version of the StockWatson (SW) unobserved components (UC) model of inflation jointly with the MankiwReis sticky information (SI) law of motion. Jim and I innovate on these models by adding timevarying persistence to the inflation gap of the SWUC model in the form of a timevarying parameter AR(1) or AR(2) and to the SI model we let the frequency of forecast updating be timevarying. These timevarying parameters (TVPs) are assumed to follow independent random walks. As is standard in the SWUC model, the innovations to trend and gap inflation are afflicted with stochastic volatility (SV) that follow log random walks.
Our estimates (filtered and smoothed) of SV in the inflation trend are here, they display a pattern known from Stock & Watson (2007, JMCB):
The joint model is estimated on real time U.S. GNP/GDP inflation and the associated average inflation predictions of the Survey of Professional Forecasters (SPF) on a sample running from 1968Q4 to 2014Q2. We estimate the joint model using a particle filter algorithm. The estimates show the data prefer a joint model with a TVPAR(1) inflation gap.
Here are estimates of our timevarying AR(1) coefficients, again filtered and smoothed, indicating substantial variation in inflation gap persistence as in Cogley and Sargent (2005, RED):
The joint model with timevarying inflation gap persistence also produces less sticky average SPF inflation predictions than with a fixed coefficient AR(1) inflation gap. We also find the SV of trend inflation exhibits negative comovement with the timevarying frequency of SI forecast updating while the SV and timevarying persistence of gap inflation often show positive comovement. Thus, the average SPF respondent is most sensitive to the impact of permanent shocks on the conditional mean of inflation.
Finally, here are the estimates of our stickiness parameter, represented as a weight on sticky vs current information. A value near zero is thus consistent with forecasts close to rational expectations:
The paper is here: pdf
Slides are here: pdf (This is an updated version of our talk at the NBER SI) A shorter set of slides is here: pdf
