# Research

## Working Papers

Multivariate Distribution Regression, 2021
This paper introduces multivariate distribution regression (MDR), a semi-parametric approach to estimate the joint distribution of outcomes conditional on covariates. The method allows studying complex dependence structures and distributional treatment effects without making strong, parametric assumptions. I show that the MDR coefficient process converges to a Gaussian process and that the bootstrap is consistent for the asymptotic distribution of the estimator. Methodologically, MDR contributes by offering the analysis of many functionals of the multivariate CDF, including counterfactual distributions. Compared to copula models, MDR (i) requires comparably weaker assumptions and (ii) achieves the same accuracy in simulation studies. Finally, I analyze shifts in spousal labor supply in response to a health shock. I find that if low-income individuals receive disability insurance benefits, their spouses respond by increasing their labor supply. The opposite holds for high-income households, likely because they can afford to work fewer hours and look after their partner.
Slides, Functions (R), Simulations (R)

Assessing the Demand Effects of Discounts on Swiss Train Tickets, (with Martin Huber and Hannes Wallimann), 2021
We assess the demand effects of discounts on train tickets issued by the Swiss Federal Railways, the so-called supersaver tickets’, based on machine learning, a subfield of artificial intelligence. Considering a survey-based sample of buyers of supersaver tickets, we use causal machine learning to assess the impact of the discount rate on rescheduling a trip, which seems relevant in the light of capacity constraints at rush hours. Assuming that (i) the discount rate is quasi-random conditional on our rich set of characteristics and (ii) the buying decision increases weakly monotonically in the discount rate, we identify the discount rate’s effect among always buyers’, who would have traveled even without a discount, based on our survey that asks about customer behavior in the absence of discounts. We find that on average, increasing the discount rate by one percentage point increases the share of rescheduled trips by 0.16 percentage points among always buyers. Investigating effect heterogeneity across observables suggests that the effects are higher for leisure travelers and during peak hours when controlling several other characteristics.

Physician Induced Demand and Financial Incentives – Evidence from a Large-Scale Fee Changes (with Tamara Bischof), 2019
This paper analyzes how physicians adapt their provision of medical services when financial incentives change. Exploiting a plausibly exogenous and large-scale reform, we find that physicians are not immune to monetary incentives in a fee-for-service system. We isolate two response channels: substitution and volume expansion. We find that providers provide more (fewer) services that gained (lost) attractiveness. Further, physicians increase consultations, especially after substantial revenue losses. Finally, volume expansion is the main driver of aggregate cost changes whereas substitution is of limited importance for aggregate costs. This finding encourages the use of value-based payment.

The Distributional Effects of Marital Status and Children: Evidence from Large Administrative Panel Data, 2018
In this paper, I study the effects of marital status and children on the income distribution using unique tax panel data. I control for unobserved heterogeneity by including individual fixed effects when estimating the mentioned effects. Using counterfactual analysis I am able to calculate the effects at the unconditional quantiles of income. My main findings are threefold. First, there is considerable heterogeneity in the income effects for women but not for men. High-income women are less negatively affected by marriage and divorce. Second, marriage and divorce do not only significantly affect labor income but also total income. The heterogeneity of the effects for women is robust to the choice of the income aggregate. Finally, only looking at couples I find that being married and having children increase the income gap between men and women whereas the effect of divorce goes the opposite way.

## Work in Progress

Heterogeneity in Returns to Wealth – Evidence from Swiss Administrative Data (with Marc Brunner and Armando Näf), 2021
In this paper, we address how returns on financial assets vary across the population. Exploiting rich administrative data, we can neatly describe the heterogeneity across all parts of the distribution of wealth. We find compelling evidence that the rich benefit from higher returns. Likely, this is due to two different effects that have been called \textit{scale dependence} and \textit{type dependence}. The former is due to an observed positive correlation between net worth and returns. The latter describes a high persistence of returns for each individual, most possibly due to better information and market access advantages. In our first set of results, we find evidence that both channels play an essential role. Conceptually, this paper contributes by investigating the interaction of type and scale dependence. As returns are persistent, we identify low and high-type investors across the distribution of returns. Thus, modeling the latter allows us to document the scale dependence for many different types. We find that net worth has a larger positive effect on returns for high types, highlighting a previously undocumented channel through which wealth inequality reinforces itself.

Censored Distribution Regression (with Blaise Melly)
When researchers aim to estimate the effect of explanatory variables on duration, the most popular approach is the Cox proportional hazard estimator. This estimator is very flexible concerning the baseline hazard but restricts the covariates’ effect to be constant over time. Distribution regression is a generalization of the Cox model that naturally allows the coefficients to change with time. Typically, survival times are censored, making the inclusion of time-varying effects challenging. This paper introduces a novel censored distribution regression estimator based on maximum likelihood estimation (CDR-MLE) that overcomes this difficulty. We assume that the censoring time is independent of the event time conditional on the covariates, which is the standard type of censoring in the literature. The CDR-MLE estimator is numerically identical to the Kaplan-Meier estimator when the covariates include only a constant and converges to the Cox coefficients when the coefficients are time-constant. It consistently estimates the conditional survival distribution for discrete, continuous, and mixed duration. We show weak convergence of the censored distribution regression coefficient process and the conditional distribution process to centered Gaussian processes. In addition, we complement the literature by providing undiscovered links to an existing estimator. Simulation studies show the good finite-sample properties of the CDR-MLE estimator. Finally, we apply our estimator to unemployment duration data and find that a longer benefit duration has little effect on short unemployment spells but a strong and significant effect on long-term unemployment.

Predicting Swiss Healthcare Costs using Machine Learning (with Dino Collati), 2021