Precision-based sampling for state space models that have no measurement error (2023, Journal of Economic Dynamics and Control)
earlier draft: pdf (revised June 2023)
online appendix: pdf
replication code: https://github.com/elmarmertens/ABCprecisionsampler
Abstract: This article presents a computationally efficient approach to sample from Gaussian state space models. The method is an instance of precision-based sampling methods that operate on the inverse variance-covariance matrix of the states (also known as precision). The novelty is to handle cases where the observables are modeled as a linear combination of the states without measurement error. In this case, the posterior variance of the states is singular and precision is ill-defined. As in other instances of precision-based sampling, computational gains are considerable. Relevant applications include trend-cycle decompositions, (mixed-frequency) VARs with missing variables and DSGE models.
Stochastic Volatility in Bayesian Vector Autoregressions (2023, Oxford Research Encyclopdia)
with Todd E. Clark (Federal Reserve Bank of Cleveland)
Abstract: Vector autoregressions with stochastic volatility are widely used in macroeconomic forecasting and structural inference. The stochastic volatility component of the model conveniently allows for time variation in the variance-covariance matrix of the model's forecast errors. In turn, that feature of the model generates time variation in predictive densities. The models are most commonly estimated with Bayesian methods, most typically Markov Chain Monte Carlo methods such as Gibbs sampling. Recently developed equation-by-equation methods enable the estimation of models with large variable sets at much lower computational cost than the standard approach of estimating the model as a system of equations. The Bayesian framework also facilitates the accommodation of mixed frequency data, non-Gaussian error distributions, and non-parametric specifications. With recent advances, researchers are also addressing some of the framework's outstanding challenges, particularly the dependence of estimates on the ordering of variables in the model and reliable estimation of the marginal likelihood, which is the fundamental measure of model fit in Bayesian methods.
Indeterminacy and Imperfect Information (2023, Review of Economic Dynamics)
with Thomas A. Lubik (FRB Richmond) and Christian Matthes (U Indiana)
replication codes: https://github.com/elmarmertens/LMMREDcode
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.
Addressing COVID-19 Outliers in BVARs with Stochastic Volatility (2022, in press, Review of Economics and Statistics)
A Time Series Model of Interest Rates With the Effective Lower Bound (2021, Journal of Money, Credit, and Banking)
Supplementary appendix: pdf
replication files: GitHub
Updated estimates through 2023:Q3 (using FRED data available on Aug 23 2023) : Real-rate trend, shadow rate. (The usual disclaimer applies; none of the estimates or related material necessarily represents the views of the Deutsche Bundesbank, the Eurosystem, the Board of Governors of the Federal Reserve System or the Federal Open Market Committee.)
Abstract: Modeling nominal interest rates requires taking account of their effective lower bound (ELB). We propose a flexible time-series approach that includes a ``shadow rate'' -- a notional rate identical to the actual nominal rate except when the ELB binds. We apply this approach to a trend-cycle decomposition of interest rates and macroeconomic variables that generates competitive interest-rate forecasts. Our estimates of the real-rate trend edged down somewhat in recent decades, but not significantly so. We identify monetary policy shocks from shadow-rate surprises and find they were particularly effective at stimulating economic activity during the ELB period.
Inflation and Professional Forecast Dynamics: An Evaluation of Stickiness, Persistence and Volatility (2020, Quantitative Economics)
with James M. Nason
This paper studies the joint dynamics of U.S. inflation and a term structure of average inflation predictions taken from the Survey of Professional Forecasters (SPF). We estimate these joint dynamics by combining an unobserved components (UC) model of inflation and a sticky-information forecast mechanism. The UC model decomposes inflation into trend and gap components, and innovations to trend and gap inflation are affected by stochastic volatility. A novelty of our model is to allow for time-variation in inflation-gap persistence as well as in the frequency of forecast updating under sticky information. The model is estimated with sequential Monte Carlo methods that include a particle learning filter and a Rao-Blackwellized particle smoother. Based on data from 1968Q4 to 2018Q3, estimates show that (i) longer horizon average SPF inflation predictions inform estimates of trend inflation; (ii) inflation gap persistence is countercyclical before the Volcker disinflation and acyclical afterwards; (iii) by 1990 sticky-information inflation forecast updating is less frequent than it was earlier in the sample; and (iv) the drop in the frequency of the sticky-information forecast updating occurs at the same time persistent shocks become less important for explaining movements in inflation. Our findings support the view that stickiness in survey forecasts is not invariant to the inflation process.
Modeling Time-Varying Uncertainty of Multiple-Horizon Forecast Errors (2020, Review of Economics and Statistics)
with Todd E. Clark, Michael W. McCracken
supplementary appendix: pdf
We estimate uncertainty measures for point forecasts obtained from survey data, pooling information embedded in observed forecast errors for different forecast horizons. To track time-varying uncertainty in the associated forecast errors, we derive a multiple-horizon specification of stochastic volatility. We apply our method to forecasts for various macroeconomic variables from the Survey of Professional Forecasters. Compared to simple variance approaches, our stochastic volatility model improves the accuracy of uncertainty measures for survey forecasts.
Measuring the Level and Uncertainty of Trend Inflation (2016, Review of Economics and Statistics)
replication data: Harvard Dataverse (html)
Firmly-anchored inflation expectations are widely viewed as playing a central role for the conduct of monetary policy. This paper presents estimates of trend inflation, based on information contained in monthly data on realized inflation, survey expectations, and the term structure of interest rates. In order to assess whether inflation expectations are anchored, a time-varying volatility of trend shocks is estimated as well. There is quite some commonality in inflation- and survey-based estimates of trend inflation, but yield-based trend estimates embed a highly persistent component orthogonal to trend inflation. Trimmed-mean inflation rates and survey forecasts are most indicative of trend inflation.
Managing Beliefs about Monetary Policy under Discretion (2016, Journal of Money, Credit, and Banking)
replication code: zip
In models of monetary policy, discretionary policymaking is typically constrained in its ability to manage public beliefs. However, when a policymaker possesses private information, policy actions serve as signals to the public about unobserved economic conditions and belief management becomes an integral part of optimal discretion policies. My paper derives the optimal time-consistent policy for a general linear-quadratic setting.
The optimal policy is illustrated in a simple New Keynesian model, where analytical so- lutions can be derived as well. In this model, imperfect information about the policymaker’s output target leads to lower policy losses.
Trend Inflation in Advanced Economies (2015, International Journal of Central Banking)
with Christine Garnier and Edward Nelson
We derive estimates of trend inflation for fourteen advanced economies from a framework in which trend shocks exhibit stochastic volatility. The estimated specification allows for time variation in the degree to which longer-term inflation expectations are well anchored in each economy. Our results bring out the effect of changes in monetary regime (such as the adoption of inflation targeting in several countries) on the behavior of trend inflation. Our estimates represent an expansion of those in the previous literature along several dimensions. For each country, we employ a multivariate approach that pools different inflation series in order to identify their common trend. In addition, our estimates of the inflation gap (that is, the difference between trend and observed inflation) are allowed to exhibit considerable persistence—a treatment that affects the trend estimates to some extent. A forecast evaluation based on quasi-real-time estimates registers sizable improvements in inflation forecasts at different horizons for almost all countries considered. It remains the case, however, that simple random-walk forecasts of inflation are difficult to outperform by a statistically significant amount.
Stock Prices, News, and Economic Fluctuations: Comment (2014, American Economic Review)
with Andre Kurmann
web appendix (pdf)
Replication Files (zip)
Beaudry and Portier (2006) propose an identification scheme to study the effects of news shocks about future productivity in Vector Error Correction Models (VECM). This comment shows that their methodology does not have a unique solution, when applied to their VECMs with more than two variables. The problem arises from the interplay of cointegration assumptions and long-run restrictions imposed by Beaudry and Portier (2006).
Are Spectral Estimators Useful for Long-Run Restrictions in SVARs? (2012, Journal of Economic Dynamics and Control)
No, not really. In response to concerns about the reliability of SVARs, one proposal has been to combine OLS estimates of a VAR with non-parametric estimates of the spectral density. But as shown here, spectral estimators are no panacea for implementing long-run restrictions. They can suffer from small sample and misspecification biases just as VARs do. As a novelty, this paper uses a spectral factorization to ensure a correct representation of the data's variance. But this cannot overcome the basic small sample issues, which arise when trying to estimate long-run properties from relatively short samples of time-series data.
Structural Shocks and the Comovements between Output and Interest Rates (2010, Journal of Economic Dynamics and Control)
WP version incl. appendix: pdf
Stylized facts on U.S. output and interest rates have so far proved hard to match with DSGE models. But model predictions hinge on the joint specification of economic structure and a set of driving processes. In a model, different shocks often induce different comovements, such that the overall pattern depends as much on the specified transmission mechanisms from shocks to outcomes, as well as on the composition of these driving processes. I estimate covariances between output, nominal and real interest rate conditional on several shocks, since such evidence has largely been lacking in previous discussions of the output-interest rate puzzle.
Conditional on shocks to neutral technology and monetary policy, the results square with simple models, like the standard RBC model or a textbook version of the New Keynesian model. In addition, news about future productivity help to explain the overall counter-cyclical behavior of the real rate.
A sub-sample analysis documents also interesting changes in these pattern. During the Great Inflation (1959--1979), permanent shocks to inflation accounted for the counter-cyclical behavior of the real rate and its inverted leading indicator property. Over the Great Moderation (1982--2006), neutral technology shocks were more dominant in explaining comovements between output and interest rates, and the real rate has been pro-cyclical.
Predictability in Financial Markets: What do Survey Expectations Tell Us? (2009, Journal of International Money and Finance)
There is widespread evidence of excess return predictability in financial markets. For the foreign exchange market a number of studies have documented that the predictability of excess returns is closely related to the predictability of expectational errors of excess returns. In this paper we investigate the link between the predictability of excess returns and expectational errors in a much broader set of financial markets, using data on survey expectations of market participants in the stock market, the foreign exchange market, the bond market and money markets in various countries. The results are striking. First, in markets where there is significant excess return predictability, expectational errors of excess returns are predictable as well, with the same sign and often even with similar magnitude. This is the case for foreign exchange, stock and bond markets. Second, in the only market where excess returns are generally not predictable, the money market, expectational errors are not predictable either. These findings suggest that an explanation for the predictability of excess returns must be closely linked to an explanation for the predictability of expectational errors.