Nowcasting in a pandemic using non-parametric mixed frequency VARs

Florian Huber, Gary Koop, Luca Onorante, Michael Pfarrhofer, Josef Schreiner

Working Paper Series

Nowcasting in a pandemic using non-parametric mixed frequency VARs

No 2510 / January 2021

Disclaimer: This paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB.

Abstract

This paper develops Bayesian econometric methods for posterior inference in non-parametric mixed frequency VARs using additive regression trees. We argue that regression tree models are ideally suited for macroeconomic nowcasting in the face of extreme observations, for instance those produced by the COVID-19 pandemic of 2020. This is due to their exibility and ability to model outliers. In an application involving four major euro area countries, we nd substantial improvements in nowcasting performance relative to a linear mixed frequency VAR.

JEL: C11, C32, C53, E37

KEYWORDS : Regression tree models, Bayesian, macroeconomic forecasting, vector

autoregressions

ECB Working Paper Series No 2510 / January 2021

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Non-technical summary

Mixed Frequency VARs have been a standard tool for producing timely, high frequency nowcasts of low frequency variables for several years. With the arrival of the COVID-19 pandemic of 2020 the need for such nowcasts has become even more acute. However, conventional linear MF-VARs nowcast poorly during the pandemic due to their inability to e ectively deal with the extreme observations that have occurred.

This paper develops a mixed frequency, Bayesian additive vector autoregressive tree (MF- BAVART), which is a non-parametric model using additive regression trees. We argue that regression tree models are ideally suited for macroeconomic nowcasting in the face of extreme observations, for instance produced by the COVID-19 pandemic of 2020, due to their exibility and ability to model outliers.

MF-BAVART can be cast as a non-linear state space model. We develop an approximate MCMC algorithm where the parameters de ning the conditional mean of the VAR are drawn using a standard BART algorithm and, conditional on these, the states are drawn using a linear approximation. This linear approximation is taken from the machine learning literature on black-box models and we use simulations to show that it also works well for a DGP that closely matches the evolution of GDP during the pandemic.

In a nowcasting application involving four major countries in the European Union (EU), we nd substantial improvements in nowcasting performance relative to a linear mixed frequency VAR. Our nowcasting exercise shows that MF-BAVART, with few exceptions, forecasts better than the linear MF-VAR at all times in our sample, but particularly big nowcasting bene ts occur during the pandemic. We show how and why this occurs by providing a detailed comparison of nowcast densities in the rst six months of 2020.

The techniques outlined in this paper can be applied to any non-linear and non-parametric learner commonly used in the literature. Our focus on using BART is motivated by its strong performance in various applications as well as its exibility in handling outliers. As a fruitful avenue for further research one could assess how di erent learners perform and then combine them using Bayesian model averaging techniques.

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• Introduction

Mixed frequency vector autoregressions (MF-VARs) have enjoyed great popularity in recent years as a tool for producing timely high frequency nowcasts of low frequency variables. A common practice (see, e.g., Schorfheide and Song, 2015)1 is to choose a quarterly macroeconomic variable such as gross domestic product (GDP) and a set of monthly variables and model them together in a VAR so as to produce monthly nowcasts of GDP. The fact that statistical agencies release data such as GDP with a delay, whereas appropriately chosen monthly variables are released with less of a delay further enhances the benets of the MF-VAR. Nowcasts can be updated in a timely fashion.

The pandemic lockdown of 2020 has further increased the need for timely, high frequency nowcasts of economic activity. And the increasing availability of a variety of high frequency (i.e., monthly, weekly or daily) and quickly released data (i.e., some variables are released almost instantaneously) presents rich opportunities for the mixed frequency modeler. However, the pandemic also poses challenges to the conventional, linear, MF-VAR. During the pandemic, we have seen values of variables that are far from the range of past values. Linear time series econometric methods seek to nd average patterns in past data. If current data is very dierent, using such patterns and linearly extrapolating them may be highly questionable.

This has led researchers to try to develop new VAR frameworks for nowcasting during the pandemic. For instance, Schorfheide and Song (2020) nd that the model developed in Schorfheide and Song (2015) nowcasts poorly, but that if they estimate their MF-VAR using data through 2019 and then produce conditional forecasts for the rst half of 2020, improvements were obtained. In essence, the extreme data in the rst half of 2020 caused estimates of the full sample MF-VAR coecients to change in a manner which led to poor forecasts. Lenza and Primiceri (2020) propose an alternative VAR-based approach which allows the error covariance matrix to have a mixture distribution. In essence, the pandemic is treated as a large variance shock and pandemic observations are, thus, drastically downweighted in the model estimation. They conclude: "Our results show that the ad-hoc strategy of dropping these observations may be acceptable for the purpose of parameter estimation. However, disregarding these recent data is inappropriate for forecasting the future evolution of the economy, because it vastly underestimates uncertainty." Thus, although Schorfheide and Song (2020) and Lenza and Primiceri (2020) adopt very dierent approaches, they end up with similar advice: discard the pandemic observations when estimating the model.

1A few other recent MF-VAR references adopting similar strategies include Eraker et al. (2015), Ghysels (2016), Brave et al. (2019) and Koop et al. (2020).

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