Constructing the Term Structure of Uncertainty from the Ragged Edge of SPF Forecasts
with Todd E. Clark (FRB Cleveland), and Gergely Ganics (Central Bank of Hungary)
Abstract: We develop a model that permits the estimation of a term structure of both expectations and forecast uncertainty for application to professional forecasts such as the SPF. Our approach exactly replicates a given data set of predictions from the SPF or a similar forecast source without measurement error. Extending some previous work, our model includes not only fixed-horizon forecasts but also fixed-event forecasts, including at horizons beyond the fixed-horizon maximum, and it accommodates variation over time in the available horizons of fixed-event forecasts. The model casts a decomposition of multi-period forecast errors into a sequence of forecast updates that may be partially unobserved, resulting in a multivariate unobserved component model with stochastic volatility. In addition, we bring the density forecast information contained in the SPF's probability bins for fixed-event forecasts to bear on the term structure of uncertainty through entropic tilting. This application of entropic tilting allows us to treat the SPF's subjective point and density forecasts commensurately.
In our empirical analysis, examples of quarterly fan charts of point forecasts and uncertainty bands around those forecasts show that the model's estimates of uncertainty vary over time. Over the full sample, incorporating information in the SPF's subjective probability bins through entropic tilting does not improve anymore on the baseline model estimates, but in some subsamples, tilting to the bin information improves the accuracy of both point and density forecasts. We conclude by applying our estimates to construct SPF-based fan charts with calendar year forecasts like those published by the Federal Reserve.
Indeterminacy and Imperfect Information
with Thomas A. Lubik (FRB Richmond) and Christian Matthes (U Indiana)
(Fully revised: April 2022)
Abstract: We study equilibrium determination in an environment where two types of agents have different information sets: Fully informed agents observe histories of all exogenous and endogenous variables. Less informed agents observe only a strict subset of the full information set and need to solve a dynamic signal extraction problem to gather information about the variables they do not directly observe. Both types of agents know the structure of the model and form expectations rationally. In this environment, we identify a new channel that generates equilibrium indeterminacy: Optimal information processing of the less informed agent introduces stable dynamics into the equation system that lead to self-fulling expectations. For parameter values that imply a unique equilibrium under full information, the limited information rational expectations equilibrium is indeterminate. We illustrate our framework with monetary policy models where an imperfectly informed central bank follows an interest rate rule.
Forecasting with Shadow-Rate VARs
with Andrea Carriero (Queen Mary University of London, U Bologna), Todd Clark (Federal Reserve Bank of Cleveland), Massimiliano Marcellino (Bocconi, IGIER and CEPR)
Measuring Uncertainty and Its Effects in the COVID-19 Era
Older working papers
On the Reliability of Output Gap Estimates in Real Time
Abstract: Real-time estimates of the Output Gap — defined as the cyclical component of GDP — have previously been shown to be unreliable, since they are subject to large revisions when new data comes in. However, this result has so far only been derived for constant parameter models. This paper uses statistical models where the volatility of shocks to trend and cycle can vary over time. In this case, output gap estimates derived from data vintages going back to the 1970s are much closer to “final” estimates derived from all available sample data. The final estimates not only fall mostly within the credible intervals generated by the real-time data. When generated from a model with stochastic volatility, these credible sets are also tighter, at least over low-volatility periods.
Discreet Commitments and Discretion of Policymakers with Private Information
This papers presents general methods to compute optimal commitment and discretion policies, when a policymaker is better informed about the realization of some shocks than the public. In this situation, public beliefs about the hidden information emerge as additional state variables, managed by the policymaker.
Under commitment, policy is additive in two components: The optimal policy, as if the government shared the public's information set and the systematic manipulation of that information set. Even under discretion, belief management imparts history dependence.
Illustrated in a New Keynesian economy with time-varying output targets of the policymaker, belief management improves outcomes compared to symmetric information. At the margin, the policymaker tries to be intransparent about policy objectives by engineering disturbances which lower public beliefs about the persistence of output targets.