Gary Koop

Working Papers

• Working Paper

  Predictive Density Combination Using a Tree-Based Synthesis Function

  Tony Chernis Niko Hauzenberger Florian Huber Gary Koop James Mitchell
  11.21.2023 | WP 23-30
  Bayesian predictive synthesis (BPS) provides a method for combining multiple predictive distributions based on agent/expert opinion analysis theory and encompasses a range of existing density forecast pooling methods. The key ingredient in BPS is a “synthesis” function. This is typically specified parametrically as a dynamic linear regression. In this paper, we develop a nonparametric treatment of the synthesis function using regression trees. We show the advantages of our tree-based approach in two macroeconomic forecasting applications. The first uses density forecasts for GDP growth from the euro area’s Survey of Professional Forecasters. The second combines density forecasts of US inflation produced by many regression models involving different predictors. Both applications demonstrate the benefits – in terms of improved forecast accuracy and interpretability – of modeling the synthesis function nonparametrically.
  
  Topics: Econometrics, modeling, and forecasting
  
• Working Paper

  Incorporating Short Data into Large Mixed-Frequency VARs for Regional Nowcasting

  Gary Koop Stuart McIntyre James Mitchell Aubrey Poon Ping Wu
  05.08.2023 | WP 23-09
  Interest in regional economic issues coupled with advances in administrative data is driving the creation of new regional economic data. Many of these data series could be useful for nowcasting regional economic activity, but they suffer from a short (albeit constantly expanding) time series which makes incorporating them into nowcasting models problematic. Regional nowcasting is already challenging because the release delay on regional data tends to be greater than that at the national level, and "short" data imply a "ragged edge" at both the beginning and the end of regional data sets, which adds a further complication. In this paper, via an application to the UK, we develop methods to include a wide range of short data into a regional mixed-frequency VAR model. These short data include hitherto unexploited regional VAT turnover data. We address the problem of the ragged edge at both the beginning and end of our sample by estimating regional factors using different missing data algorithms that we then incorporate into our mixed-frequency VAR model. We find that nowcasts of regional output growth are generally improved when we condition them on the factors, but only when the regional nowcasts are produced before the national (UK-wide) output growth data are published.
  
  Topics: Econometrics, modeling, and forecasting, State and local economies
  
• Working Paper

  Bayesian Modeling of Time-Varying Parameters Using Regression Trees

  Niko Hauzenberger Florian Huber Gary Koop James Mitchell
  01.11.2023 | WP 23-05
  In light of widespread evidence of parameter instability in macroeconomic models, many time-varying parameter (TVP) models have been proposed. This paper proposes a nonparametric TVP-VAR model using Bayesian additive regression trees (BART). The novelty of this model stems from the fact that the law of motion driving the parameters is treated nonparametrically. This leads to great flexibility in the nature and extent of parameter change, both in the conditional mean and in the conditional variance. In contrast to other nonparametric and machine learning methods that are black box, inference using our model is straightforward because, in treating the parameters rather than the variables nonparametrically, the model remains conditionally linear in the mean. Parsimony is achieved through adopting nonparametric factor structures and use of shrinkage priors. In an application to US macroeconomic data, we illustrate the use of our model in tracking both the evolving nature of the Phillips curve and how the effects of business cycle shocks on inflationary measures vary nonlinearly with movements in uncertainty.
  
  Topics: Business cycles, Econometrics, modeling, and forecasting
  
• Working Paper

  Tail Forecasting with Multivariate Bayesian Additive Regression Trees

  Todd E. Clark Florian Huber Gary Koop Massimiliano Marcellino Michael Pfarrhofer
  07.12.2022 | WP 21-08R
  We develop multivariate time series models using Bayesian additive regression trees that posit nonlinearities among macroeconomic variables, their lags, and possibly their lagged errors. The error variances can be stable, feature stochastic volatility, or follow a nonparametric specification. We evaluate density and tail forecast performance for a set of US macroeconomic and financial indicators. Our results suggest that the proposed models improve forecast accuracy both overall and in the tails. Another finding is that when allowing for nonlinearities in the conditional mean, heteroskedasticity becomes less important. A scenario analysis reveals nonlinear relations between predictive distributions and financial conditions.
  
  Topics: Econometrics, modeling, and forecasting
  
• Working Paper

  Using Stochastic Hierarchical Aggregation Constraints to Nowcast Regional Economic Aggregates

  Gary Koop Stuart McIntyre James Mitchell Aubrey Poon
  03.03.2022 | WP 22-06
  Recent decades have seen advances in using econometric methods to produce more timely and higher-frequency estimates of economic activity at the national level, enabling better tracking of the economy in real time. These advances have not generally been replicated at the sub–national level, likely because of the empirical challenges that nowcasting at a regional level presents, notably, the short time series of available data, changes in data frequency over time, and the hierarchical structure of the data. This paper develops a mixed– frequency Bayesian VAR model to address common features of the regional nowcasting context, using an application to regional productivity in the UK. We evaluate the contribution that different features of our model provide to the accuracy of point and density nowcasts, in particular the role of hierarchical aggregation constraints. We show that these aggregation constraints, imposed in stochastic form, play a key role in delivering improved regional nowcasts; they prove to be more important than adding region-specific predictors when the equivalent national data are known, but not when this aggregate is unknown.
  
  Topics: Econometrics, modeling, and forecasting, International economics
  
• Working Paper

  Forecasting US Inflation Using Bayesian Nonparametric Models

  Todd E. Clark Florian Huber Gary Koop Massimiliano Marcellino
  03.02.2022 | WP 22-05
  The relationship between inflation and predictors such as unemployment is potentially nonlinear with a strength that varies over time, and prediction errors may be subject to large, asymmetric shocks. Inspired by these concerns, we develop a model for inflation forecasting that is nonparametric both in the conditional mean and in the error using Gaussian and Dirichlet processes, respectively. We discuss how both these features may be important in producing accurate forecasts of inflation. In a forecasting exercise involving CPI inflation, we find that our approach has substantial benefits, both overall and in the left tail, with nonparametric modeling of the conditional mean being of particular importance.
  
  Topics: Inflation, Econometrics, modeling, and forecasting
  
• Working Paper

  Reconciled Estimates of Monthly GDP in the US

  Gary Koop Stuart McIntyre James Mitchell Aubrey Poon
  01.10.2022 | WP 22-01
  In the US, income and expenditure-side estimates of GDP (GDPI and GDPE) measure "true" GDP with error and are available at a quarterly frequency. Methods exist for using these proxies to produce reconciled quarterly estimates of true GDP. In this paper, we extend these methods to provide reconciled historical true GDP estimates at a monthly frequency. We do this using a Bayesian mixed frequency vector autoregression (MF-VAR) involving GDPE, GDPI, unobserved true GDP, and monthly indicators of short-term economic activity. Our MF-VAR imposes restrictions that reflect a measurement-error perspective (that is, the two GDP proxies are assumed to equal true GDP plus measurement error). Without further restrictions, our model is unidentified. We consider a range of restrictions that allow for point and set identification of true GDP and show that they lead to informative monthly GDP estimates. We illustrate how these new monthly data contribute to our historical understanding of business cycles and we provide a real-time application nowcasting monthly GDP over the pandemic recession.
  
  Topics: Econometrics, modeling, and forecasting, Business cycles
  
• Working Paper

  Tail Forecasting with Multivariate Bayesian Additive Regression Trees

  Todd E. Clark Florian Huber Gary Koop Massimiliano Marcellino Michael Pfarrhofer
  03.22.2021 | WP 21-08
  We develop novel multivariate time series models using Bayesian additive regression trees that posit nonlinear relationships among macroeconomic variables, their lags, and possibly the lags of the errors. The variance of the errors can be stable, driven by stochastic volatility (SV), or follow a novel nonparametric specification. Estimation is carried out using scalable Markov chain Monte Carlo estimation algorithms for each specification. We evaluate the real-time density and tail forecasting performance of the various models for a set of US macroeconomic and financial indicators. Our results suggest that using nonparametric models generally leads to improved forecast accuracy. In particular, when interest centers on the tails of the posterior predictive, flexible models improve upon standard VAR models with SV. Another key finding is that if we allow for nonlinearities in the conditional mean, allowing for heteroskedasticity becomes less important. A scenario analysis reveals highly nonlinear relations between the predictive distribution and financial conditions.
  
  Topics: Econometrics, modeling, and forecasting
  
• Working Paper

  A New Model of Inflation, Trend Inflation, and Long-Run Inflation Expectations

  Joshua C.C. Chan Todd E. Clark Gary Koop
  10.19.2015 | WP 15-20
  This paper adds to the growing literature which uses survey-based long-run forecasts of inflation to estimate trend inflation.
  
  Topics: Inflation, Econometrics, modeling, and forecasting