Abstract This paper analyses possibly time-varying shock transmission in structural vector autoregressive (VAR) models when the reduced-form VAR coefficients are time-invariant and the shocks are identified through non-Gaussianity. To check for possible time-variation in the impulse responses, we propose Wald tests for two situations: (1) homoskedastic and (2) heteroskedastic structural shocks with changes in the unconditional variances. For the latter case, the challenge is to ensure that the test does not indicate time-varying impulse responses if the changes are due only to changes in the variances of the shocks. To illustrate the usefulness of the tests, they are applied to an empirical model of the crude oil market. They support time-varying shock transmission reflected in impulse response functions that change over time.

Abstract Different proxy variables used in fiscal policy SVARs lead to contradicting conclusions regarding the size of fiscal multipliers. Our analysis suggests that the conflicting results may stem from violations of the proxy exogeneity assumptions. We propose a novel approach to include proxy variables into a Bayesian non-Gaussian SVAR, tailored to accommodate potentially endogenous proxies. Using our model, we find that increasing government spending is more effective in stimulating the economy than reducing taxes.

Abstract This paper extends difference-in-differences to settings with continuous treatments. Specifically, the average treatment effect on the treated (ATT) at any level of treatment intensity is identified under a conditional parallel trends assumption. Estimating the ATT in this framework requires first estimating infinite-dimensional nuisance parameters, particularly the conditional density of the continuous treatment, which can introduce substantial bias. To address this challenge, we propose estimators for the causal parameters under the double/debiased machine learning framework and establish their asymptotic normality. Additionally, we provide consistent variance estimators and construct uniform confidence bands based on a multiplier bootstrap procedure. To demonstrate the effectiveness of our approach, we apply our estimators to the 1983 Medicare Prospective Payment System (PPS) reform studied by Finkelstein (2008), reframing it as a DiD with continuous treatment and nonparametrically estimating its effects.

Abstract This study presents a model that enables automatic trend detection in Bayesian vector autoregressions (BVARs). The proposed model features cyclical components that follow a stationary VAR and trend components that evolve as a random walk. We employ a spike-and-slab prior on the variance of shocks in the trend component, allowing for the automatic identification of stochastic trends and, if present, their estimation within the same Gibbs sampling procedure. A marginal likelihood comparison provides evidence in favor of the proposed model over standard BVARs. Furthermore, out-of-sample forecasting exercises demonstrate that our model significantly enhances predictive accuracy, particularly for highly persistent variables and longer-horizon forecasts. These results remain robust across models of different sizes, including small, medium, and large.

Summary Impulse responses and forecasts are central concepts for policymakers. They are also sufficient statistics to solve many important macroeconomic problems, from policy counterfactuals to policy evaluation, and offer a promising alternative to the standard structural modelling approach. In this work, we discuss and extend recent progress on the use of these sufficient macro statistics for policy evaluation. We illustrate the methods by evaluating the performance of the European Central Bank over 1999–2023.

Summary We consider forecast comparison in the presence of instability when this affects only a short period of time. We demonstrate that global tests do not perform well in this case because they were not designed to capture very short-lived instabilities, and their power vanishes altogether when the magnitude of the shock is very large. We then discuss non-parametric approaches that are more suitable to detect such situations. We illustrate these results in a Monte Carlo exercise and in a comparison of the nowcast of the quarterly US nominal GDP from the Survey of Professional Forecasters against a naive benchmark of no growth, over a period that includes the GDP instability brought by the COVID-19 crisis. We recommend that forecasters do not pool the sample, but exclude the short periods of high local instability from the evaluation exercise.

Summary Although health affects many economic outcomes, its dynamics are still poorly understood. We use k-means clustering, a machine learning technique, and data from the Health and Retirement Study to identify health types during middle and old age. We identify five health types: the vigorous resilient, the fair-health resilient, the fair-health vulnerable, the frail resilient, and the frail vulnerable. They are characterized by different starting health and health and mortality trajectories. Our five health types account for 84% of the variation in health trajectories and are not explained by observable characteristics, such as age, marital status, education, gender, race, health-related behaviours, and health insurance status, but rather by one’s past health dynamics. We also show that health types are important drivers of health and mortality heterogeneity and dynamics. Our results underscore the importance of better understanding health type formation and of modelling it appropriately to properly evaluate the effects of health on people’s decisions and the implications of policy reforms.

Summary We evaluate the distributional effects of a minimum wage introduction based on a dataset with a moderate sample size, but a large number of potential covariates. In this context, the selection of relevant control variables at each distributional threshold is crucial to test hypotheses about the impact of the continuous treatment variable. To this end, we use a post-double-selection logistic distribution regression approach, which allows for uniformly valid inference about the target coefficients of our low-dimensional treatment variables across the entire outcome distribution. Our empirical results show that the minimum wage replaced hourly wages below the minimum threshold, increased monthly earnings in the lower-middle segment, but not at the very bottom of the distribution, and did not significantly affect the distribution of working hours.