## 1 Introduction

^{1}We attempt to advance this line of work in several directions, offering both methodological and macroeconomic policy contributions.

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^{3}Second, our approach allows for nonlinearities between financial conditions and the real economy. Third, we are able to examine macroeconomic tail risk in a mutually consistent manner from both the short-run perspective, which has been the focus of the literature, and from the long-run perspective.

^{4}Finally, we investigate trends in downside output growth tail risk and the effect of policy frameworks by focusing on changes in model parameters and the role of economic shocks.

## 2 Model for simulation of predictive distributions

^{5}We use a mean-adjusted threshold vector autoregression with the threshold variable potentially dependent on (the lags of) all endogenous variables. The regime switch is thus linked explicitly to the macroeconomic variables, allowing for the regime to be path-dependent. An additional benefit is that the parameters of the predictive distribution of output growth (the mean, variance, skewness and kurtosis) can be directly linked to macroeconomic entities. These include regime-specific steady states and regime-specific shock volatilities together with the regime probabilities dependent on macroeconomic variables.

## 3 Data and estimation

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^{7}As usual in the literature, the short-term measure of macroeconomic risk is conditional on data in period \(t - 4\): the 10th percentiles are taken from the predictive output growth distribution four periods ahead. More specifically, we take all simulated paths of output growth and look at the 10th percentile at a distance of four quarters.

## 4 Estimates of risk measures

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## 5 Analysis of short-run risk

^{9}As such Eq. (4) can provide useful information on the effect of structural shocks on short-run risk rather than directly on effects of structural shocks on a particular macroeconomic variable. Finally, note that to account for the fact that the moments are estimated quantities, the confidence intervals for the model parameters are bootstrapped; the procedure is described in Appendix B.4.

^{10}Similarly to moments the employed structural shocks in (4) are also estimated quantities. Unfortunately, the confidence bands of shock estimates are not available, which could in principle result in biased estimates in (4).

^{11}As an example, consider a frequently analyzed monetary policy tightening scenario (e.g., Duprey and Ueberfeldt 2020; Loria et al. 2023; Jung and Lee 2019). Research studies commonly find that tighter monetary conditions shift the left tail of the output growth distribution leftward; in a way that exceeds the shift of the mean. However, this could be a consequence of several distinct factors: (i) increased conditional variance, (ii) a more negative conditional skewness, or (iii) fatter tails of the conditional output growth distribution.

### 5.1 Monetary policy shocks

^{12}Depending on the specific form of the policymakers’ loss function, broadening the focus from the mean to the entire output growth distribution implies different monetary policy actions. Regarding the even moments (variance and kurtosis), the specification in (4) with separated easing and tightening shocks reported in Appendix C.1 implies that both the tightening shock and (even more so) the easing shock result in a decrease of kurtosis in the short run. The benchmark specification implies only a minor impact as the effect is not symmetric. This points to a potentially important policy message that runs counter the arguments for interest rate smoothing. If monetary policy reacts immediately to shocks without excessive smoothing, fat-tailedness of the output growth distribution is reduced. This is beneficial as it reduces the probability of periods featuring very low output growth.

### 5.2 Financial shocks

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### 5.3 Shocks and long-run risk

^{14}This argument draws on structural shocks and is thus more informative in regard of nonsystematic component of the policies. A supplementary argument based on the systematic component of policies is presented in the next section.

## 6 Analysis of long-run risk

^{15}Figure 4 plots the three counterfactuals we examine: fixed steady states, fixed reduced-form shock volatilities and fixed autoregressive parameters. For example, the first counterfactual shows what the 10th percentile would be if the steady states in both regimes were kept unchanged over time. The second and third counterfactuals conduct the same exercise, fixing the regime-specific shock volatilities and the regime-specific short-run dynamics, respectively. Comparing the counterfactual with the factual then indicates whether the specific feature (subset of parameters) contributed to the observed profile of tail risk, and in what way.

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^{17}We focus on the two equations because the interest rate served as an instrument of conventional monetary policy, whereas the spread served as an unconventional monetary policy instrument after the interest rate hit the zero lower bound.

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