The present study employs nonlinear regression models to analyse the relationship between the difference in yield on short-term German government bonds and the ECB's deposit rate, as well as the deposit rate itself. The aforementioned variables are positively correlated, and the difference can be described by a concave function depending on the deposit rate. To achieve a more comprehensive modelling, a methodology for determining thresholds is introduced, and additional economic indicators are considered as explanatory variables. In conclusion, it has been determined that the incorporation of an inflation limit, situated in close proximity to the target value as stipulated by the ECB, in conjunction with the volatility exhibited by the EURIBOR, is the most significant factor contributing to the enhancement of explanatory power. This approach yielded an R-squared of 0.6, without using lagged variables. The exclusion of lagged variables is predicated on the objective of the research, which is to elucidate the factors contributing to excess returns, as opposed to making predictions about future returns. The utilization of only same-day data was imperative to ensure optimal interpretability.

We analyse potential mismeasurement of the Harmonised Index of Consumer Prices (HICP) at the upper level of aggregation, focusing on two sources of measurement error: the choice of index formula (representativity component) and the reliability of weights (data vintage component). HICP weights are annually updated based on national accounts data, which at the time of use have preliminary status. The use of final data is expected to yield more reliable weights and, thus, a better estimate of inflation. With national accounts vintage data, we calculate bias and inaccuracy metrics in order to analyse mismeasurement at the upper level of aggregation in the HICPs for Germany, France, Italy, Spain and the Netherlands, as well as for the country group, over the period from 2012 to 2021. For the representativity component, the data availability allows an additional analysis of the period until 2024. Measured in terms of annual HICP rates, the total upper-level aggregation bias falls short of one-tenth of a percentage point. Further, the representativity component, which captures the fact that a Laspeyres-type index such as the HICP suffers from a systematic overestimation of inflation due to the disregard of changes in consumption patterns, and the data vintage component are both found to contribute to overall bias. The contribution of both the representativity and the data vintage components amounts to quite similar shares. However, during the recent high inflation period around 2022 and 2023, the representativity component reveals a significantly higher bias compared to previous years.

Bayesian Additive Regression Trees (BART) have been shown to be a flexible, non-parametric regression approach that captures non-linear interactions between covariates and response variables. Building on a multivariate extension of the BART framework, we propose a non-linear vector autoregressive model, which we refer to as the Seemingly Unrelated Bayesian Additive Vector Autoregressive Tree (SUBAVART).

Through a comprehensive Monte Carlo study, we demonstrate that the estimated generalized impulse responses converge to their underlying true values for linear as well as non-linear data generating processes. This indicates that the SUBAVART correctly recovers both the dynamic structure and the error covariance matrix of the true model, highlighting its flexibility with respect to the complexity of the data.

To induce sparsity in the model, we incorporate a Dirichlet prior over the splitting variables, which effectively shrinks the predictor space by selecting only the most relevant (lagged) variables for building the trees.

The multivariate extension enables us to incorporate various (structural) identification methods beyond the order-dependent recursive Cholesky decomposition to identify macroeconomic shocks, including for instance identification based on external instruments.

We illustrate the usefulness of the model in an empirical application on monetary policy shocks.