Oesterreichische Nationalbank (Jubiläumsfonds)
CONTENT OF THE PROJECT: In this project we develop a flexible multivariate econometric framework and use it to model the interaction between macroeconomic quantities and the term structure of interest rates. The recent literature on yield curve dynamics has highlighted different forms of parameter change to be of relevance. To cope with this inherent uncertainty with respect to how coefficients behave over time we propose methods for automatically selecting adequate state equations in time-varying parameter vector autoregressive regression (TVP-VAR) models in a data-driven manner.
The TVPs are assumed to depend on a set of observed and unobserved covariates, also known as effect modifiers. As unobserved covariates, we consider a set of low dimensional latent factors that follow a random walk, alongside Markov switching indicators that allow for abrupt structural breaks. Our model nests several alternatives commonly used in the literature on modeling macroeconomic and financial time series. To choose between state equations, we use a hierarchical Bayesian global-local shrinkage prior on the most flexible specification.
The resulting model works well in terms of predictive accuracy but, more importantly, can be used to shed light on how the yield curve (parameterized by its slope, curvature and level factor) changes if other factors (such as fiscal policy, economic uncertainty or the state of the business cycle) are altered. Our approach is not only applicable to long time series but also specifically tailored for short time series such as the ones available for the Eurozone.
RESEARCH RESULTS: Our general model rests upon innovations presented in several independent methodological papers that are briefly described below. These papers explicitly deal with the role of uncertainty along various dimensions within flexible Bayesian time series frameworks. These time series models are then used to model and forecast the term structure of interest rates in the Eurozone and in the United States.
The first paper, “Dynamic Shrinkage Priors for Large Time-Varying Parameter Regressions Using Scalable Markov Chain Monte Carlo Methods” (still under review), proposes a new dynamic shrinkage prior which reflects the empirical regularity that TVPs are typically sparse (i.e. time variation may occur only episodically and only for some of these coefficients). Moreover, a scalable MCMC algorithm is developed which is capable of handling very high dimensional TVP regressions or TVP vector autoregressions. In an application involving the term structure of interest rates in the Eurozone, we find our dynamic shrinkage prior to effectively pick out small amounts of parameter change and our methods to forecast well.
The second paper on “Combining Shrinkage and Sparsity in Conjugate Vector Autoregressive Models” proposes a straightforward means of postprocessing posterior estimates of a conjugate Bayesian VAR to effectively perform equation-specific covariate selection. Compared with existing techniques using shrinkage alone, our approach combines shrinkage and sparsity in both the VAR coefficients and the error variance-covariance matrices, greatly reducing estimation uncertainty in large dimensions while maintaining computational tractability.
In the third paper, entitled “Fast and Flexible Bayesian Inference in Time-Varying Parameter Regression Models”, we write the time-varying parameter regression model involving K explanatory variables and T observations as a constant coefficient regression model with KT explanatory variables. In contrast with much of the existing literature which assumes coefficients to evolve according to a random walk, the paper introduces a hierarchical mixture model on the time-varying parameters. The resulting model closely mimics a random coefficients specification which groups the TVPs into several regimes. econometric methods based on a singular value decomposition of the KT regressors. These flexible mixtures allow for time-varying parameters that feature a small, moderate or large number of structural breaks. The paper develops computationally efficient Bayesian econometric methods based on a singular value decomposition of the KT regressors.
In macroeconomics, most researchers compress information using linear methods such as principal components to summarize information embodies in huge datasets in forecasting applications efficiently. Machine learning techniques describing large datasets with relatively few latent factors have gained relevance in the last years in various areas. The fourth paper “Real-Time Inflation Forecasting Using Non-Linear Dimension Reduction Techniques”, shows that using such approaches potentially improves real-time inflation forecasts for a wide range of competing model specifications. The paper indicates that point forecasts or simpler models are hard to beat (especially at the one-month-ahead horizon). But we find that more sophisticated modelling techniques that rely on non-linear dimension reduction do particularly well for density forecasts. Among all the techniques considered, the results suggest that the Auto-encoder, a particular form of a deep neural network, produces the most precise inflation forecasts (both in terms of point and density predictions).
The first four papers developed techniques that led to the fifth paper, entitled “General Bayesian Time-Varying Parameter VARs for Modeling Government Bond Yields”. This paper outlines a VAR model with time-varying parameters and stochastic volatility which treats the nature of parameter dynamics as unknown. Coefficients can evolve according to a random walk, a Markov switching process, observed predictors, or depend on a mixture of these. Observed predictors can be proxies for fiscal policy shocks, recession indicators or measures of economic uncertainty. To decide which form is supported by the data and to carry out model selection, we adopt Bayesian shrinkage priors. Our estimation strategy revolves around specifying suitable shrinkage priors that allow us to shrink coefficients associated with irrelevant effect modifiers towards zero. These priors are capable of endogenously selecting the appropriate law of motion for the parameters and, since the TVPs depend linearly on the effect modifiers, also allows for combinations of different law of motions. Moreover, the model enables the researcher to drill into the driving forces of parameter time-variation. This feature is important if the researcher is interested in investigating why relations between variables in a VAR change over time, and to what extent these changes are explained by the observed effect modifiers. Model estimation is carried out through a computationally efficient Markov chain Monte Carlo algorithm.
Hauzenberger N., Huber F. & Koop G. (2020): Dynamic Shrinkage Priors for Large Time-Varying Parameter Models, submitted for publication to Studies in Nonlinear Dynamics and Econometrics, still under Review
Hauzenberger N., Huber F. & Onorante L. (2021): Combining Shrinkage and Sparsity in Conjugate Vector Autoregressive Models, Journal of Applied Econometrics, 36 (3), 304-327, doi: 10.1002/jae.2807
Hauzenberger N., Huber F., Koop G. & Onorante L. (2021): Fast and Flexible Inference in Time-Varying Parameter Regression Models, Journal of Business & Economic Statistics, 40 (4), 1904-1918, doi: 10.1080/07350015.2021.1990772
Hauzenberger N., Huber F. & Klieber K. (2022): Real-Time Inflation Forecasting Using Non-Linear Dimension Reduction Techniques, International Journal of Forecasting, 39 (2), 901-921, doi: 10.1016/j.ijforecast.2022.03.002
Fischer, M.M., Hauzenberger, N., Huber, F. & Pfarrhofer M. (2023): General Bayesian Time-Varying Parameter VARs for Predicting Government Bond Yields, Journal of Applied Econometrics, 38(1), 69-87, http://dx.doi.org/10.1002/jae.2936
To assess whether our methods pay off relative to simpler alternatives (which are nested in our general framework), we apply the model to analyze the US term structure of interest rates and carry out a thorough predictive exercise, and show that our techniques produce favorable point and density forecasts. The performance is specific to the information set used in the underlying TVP-VAR and appears to be more pronounced for density forecasts. The forecasting exercise illustrates that our approach produces very competitive forecasts without increasing the risk of overfitting, while providing a framework to trace the sources of time-variation. After showing that our model works well out-of-sample, we model the relationship between the level, slope and curvature of the term structure of bond yields. Assuming that these three factors depend on a set of latent and observed covariates we detect several interesting patterns in abrupt and gradual time-variation patterns in long-run cross-variable relations. These changes appear to be specific to the monetary regime, the state of the business cycle and the fiscal policy stance.