Working Papers

My research is also posted at IDEAS, SSRN, GoogleScholar, ResearcherID, ORCID.

Codes can also be found at GitHub. Below you also find GitHub links to individual projects.

Constructing Fan Charts from the Ragged Edge of SPF Forecasts

with Todd E. Clark (FRB Cleveland), and Gergely Ganics (Banco de España)

Abstract: We develop models that take point forecasts from the Survey of Professional Forecasters (SPF) as inputs and produce estimates of survey-consistent term structures of expectations and uncertainty at arbitrary forecast horizons. Our models combine fixed-horizon and fixed-event forecasts, accommodating time-varying horizons and availability of survey data, as well as potential inefficiencies in survey forecasts. The estimated term structures of SPF-consistent expectations are comparable in quality to the published, widely used short-horizon forecasts. Our estimates of time-varying forecast uncertainty reflect historical variations in realized errors of SPF point forecasts, and generate fan charts with reliable coverage rates.

Parts of this paper were earlier circulated under the title “Constructing the Term Structure of Uncertainty from the Ragged Edge of SPF Forecasts.”

Shadow-Rate VARs

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

Abstract: VARs are popular for forecasting and structural analysis, but ill-suited to handle occasionally binding constraints, like the effective lower bound on nominal interest rates. We extend the VAR framework by modeling interest rates as censored observations of a latent shadow-rate process, and propose an efficient sampler for Bayesian estimation of such ``shadow-rate VARs.'' We find benefits to including both actual and shadow rates serve as explanatory variables.  Historical shadow-rate estimates indicate that the FOMC would have set the funds rate much lower than it could during recent ELB episodes.  In historical forecast accuracy, when compared to a standard VAR, shadow-rate VARs generate superior predictions for interest rates and deliver some gains for macroeconomic variables.   Our structural analysis of shocks to financial conditions show strong differences in the reaction of interest rates depending on whether the ELB binds or not, with implications for the response of economic activity to the shocks.

Among others, the paper has been presented at NBER SI 2023. Earlier versions of this paper were also earlier circulated under the title “Forecasting with Shadow-Rate VARs.”

What Is the Predictive Value of SPF Point and Density Forecasts?

with Todd E. Clark (FRB Cleveland), and Gergely Ganics (Banco de España)

Abstract: This paper presents a new approach to combining the information in point and density forecasts from the Survey of Professional Forecasters (SPF) and assesses the incremental value of the density forecasts.  Our starting point is a model, developed in companion work, that constructs quarterly term structures of expectations and uncertainty from SPF point forecasts for quarterly fixed horizons and annual fixed events. We then employ entropic tilting to bring the density forecast information contained in the SPF's probability bins to bear on the model estimates.  In a novel application of entropic tilting, we let the resulting predictive densities exactly replicate the SPF's probability bins. Our empirical analysis of SPF forecasts of GDP growth shows that tilting to the SPF's probability bins can visibly affect our model-based predictive distributions.  Yet in historical evaluations, tilting does not offer consistent benefits to forecast accuracy relative to the model-based densities that are centered on the SPF's point forecasts and reflect the historical behavior of SPF forecast errors.  That said, there can be periods in which tilting to the bin information helps forecast accuracy.

Parts of this paper were earlier circulated under the title “Constructing the Term Structure of Uncertainty from the Ragged Edge of SPF Forecasts.”

Older working papers

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)


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).

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.

Correct variance for estimated Sharpe Ratios