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 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.

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)

Abstract: Interest rate data are an important element of macroeconomic forecasting. Not only are projections of future interest rates an object of interest themselves, but also they matter for forecasting other macroeconomic and financial variables. A popular class of forecasting models is linear vector autoregressions (VARs) that include shorter- and longer-term interest rates. However, in a number of economies, shorter-term interest rates have by now been stuck at or near their effective lower bound (ELB) for years, with longer-term rates drifting toward the constraint as well. In such an environment, linear forecasting models that ignore the ELB constraint on nominal interest rates can be problematic along various dimensions. Instead, we model nominal interest rates as censored observations of a latent shadow-rate process and relate their dynamics to other economic variables in a so-called ``shadow-rate VAR.'' We consider specifications where both actual and shadow interest rates, or only shadow interest rates, matter for forecasting. Our empirical application studies the performance of point and density forecasts generated by shadow-rate VARs for US data since 2009. In comparison to a standard VAR, shadow-rate VARs generate superior predictions for short- and long-term interest rates. By ignoring the ELB, the standard VAR can generate a negative-rate outlook which influences its economic forecasts in ways that can be similar to a shadow-rate VAR. On balance, across measures of economic activity and inflation, the accuracy of forecasts from our shadow-rate specifications is on par with a standard VAR.

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).

Older working papers

On the Reliability of Output Gap Estimates in Real Time

  • slides (pdf, 2019)

  • draft (pdf, 2014)

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