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Working Papers


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Forecasting with Shadow-rate VARs

with Andrea Carriero (Queen Mary University of London), Todd Clark (Federal Reserve Bank of Cleveland), Massimiliano Marcellino (Bocconi, IGIER and CEPR)

  • draft: html (FRB Cleveland WP with supplementary appendix)
  • slides: pdf
Abstract

Interest rate data are an important element of macroeconomic forecasting. Projections of future interest rates are not only an important product themselves, but also typically matter for forecasting other macroeconomic and financial variables. A popular class of forecasting models are linear Vector Autoregressions (VARs) that include shorter- and longer-term interest rates. However, in a number of economies, at least shorter-term interest rates have now been stuck for years at or near their effective lower bound (ELB), with longer-rates drifting toward the constraint as well. In such an environment, linear forecasting models that ignore the ELB constraint on nominal interest rates appear inept.
To handle the ELB on interest rates, we model observed rates as censored observations of a latent shadow-rate process in an otherwise standard VAR setup. The shadow rates are assumed to be equal to observed rates, when above the ELB.  Point and density forecasts for interest rates (short-term and long-term) constructed from a shadow-rate VAR for the US since 2009 are superior to predictions from a standard VAR that ignores the ELB. For other indicators of financial conditions and measures of economic activity and inflation, the accuracy of forecasts from our shadow-rate specification is on par with a standard VAR that ignores the ELB. 

Addressing COVID-19 Outliers in BVARs with Stochastic Volatility

with Andrea Carriero (Queen Mary University of London), Todd Clark (Federal Reserve Bank of Cleveland), Massimiliano Marcellino (Bocconi, IGIER and CEPR)

Revised: April 5 2021 

  • supplementary results: pdf

Abstract: 
Incoming data in 2020 posed sizable challenges for the use of VARs in economic analysis: Enormous movements in a number of series have had strong effects on parameters and forecasts constructed with standard VAR methods. We propose the use of VAR models with time-varying volatility that include a treatment of the COVID extremes as outlier observations. Typical VARs with time-varying volatility assume changes in uncertainty to be highly persistent. Instead, we adopt outlier-adjusted stochastic volatility (SV) models for VAR residuals that combine transitory and persistent changes in volatility. In addition, we consider the treatment of outliers as missing data. Evaluating forecast performance over the last few decades in quasi-real time, we find that outlier-augmented SV schemes do at least as well as a conventional SV model and outperform standard homoskedastic VARs.  Our best-performing model features stochastic volatility, fat tails, and an occasional outlier state.  Point forecasts made in 2020 from heteroskedastic VARs are much less sensitive to outliers in the data, and the outlier-adjusted SV models generate more reasonable gauges of forecast uncertainty than a standard SV model.  Treating outliers as missing data also generates better-behaved forecasts than the conventional SV model. However, since uncertainty about the incidence of outliers is ignored in that approach, it leads to strikingly tight predictive densities.

Measuring Uncertainty and Its Effects in the COVID-19 Era

with Andrea Carriero (Queen Mary University of London), Todd Clark (Federal Reserve Bank of Cleveland), Massimiliano Marcellino (Bocconi, IGIER and CEPR)


Abstract:

We measure the effects of the COVID-19 outbreak on macroeconomic and financial uncertainty, and we assess the consequences of the latter for key economic variables. We use a large, heteroskedastic vector autoregression (VAR) in which the error volatilities share two common factors, interpreted as macro and financial uncertainty, in addition to idiosyncratic components. Macro and financial uncertainty are allowed to contemporaneously affect the macroeconomy and financial conditions, with changes in the common component of the volatilities providing contemporaneous identifying information on uncertainty. We also consider an extended version of the model, based on a latent state approach to accommodating outliers in volatility, to reduce the influence of extreme observations from the COVID period. The estimates we obtain yield very large increases in macroeconomic and financial uncertainty over the course of the COVID-19 period. These increases have contributed to the downturn in economic and financial conditions, but with both models, the contributions of uncertainty are small compared to the overall movements in many macroeconomic and financial indicators. That implies that the downturn is driven more by other dimensions of the COVID crisis than shocks to aggregate uncertainty (as measured by our method).

Indeterminacy and Imperfect Information

with Thomas A. Lubik and Christian Matthes 

(Revised August 2020)
  • draft: pdf
  • older working paper draft: pdf and its supplementary appendix: pdf
  • slides: pdf
  • Video of ESWC talk: YouTube (first 30min; recorded Jul 2020)

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 a monetary policy problem where an imperfectly informed central bank follows an interest rate rule. 
 

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

Abstract: 

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.


Three Essays on the Determinants of Output, Inflation and Interest Rates (2007, Study Center Gerzensee) 


Ph.D. Thesis. University of Lausanne, 18 October 2007 (Dissertation Committee)