## Three essays in econometrics: heterogeneity across outcomes, time and physicians

This thesis consists of three essays in econometrics. The first part of the thesis, consisting of chapters one and two, treats novel estimators aiming at distributional effects. In the first chapter, I introduce a methodology to estimate the joint distribution of multiple outcome variables. The second chapter incorporates censoring, a prevalent challenge when analyzing duration data, into distribution regression methods. Finally, the third chapter analyzes a reform in the health care sector.

Chapter 1 introduces Multivariate Distribution Regression (MDR), a semi-parametric approach to model the joint distribution of several outcome variables. Typically, researchers are interested in the effects on multiple outcomes when the latter are correlated (see Patton, 2012, for an overview). For instance, this is the case for the impact of a crisis on asset prices. Asset prices co-move tightly as they depend on common factors such as market cycles. A shock on one price index may thus affect many other indices. In addition, the effect could vary across the distribution of the prices – a peculiarity that MDR accounts for. Essentially, MDR estimates the impact of interest at every point of the outcomeâ€™s distribution.

MDRâ€™s most obvious advantage is its flexibility. Existing methods, such as copula models, typically impose a parametric form of the dependence structure across outcomes (i.e. Klein et al., 2019). In contrast, MDR does not require equally restrictive, parametric assumptions. Thus, the effects estimated using MDR describe the underlying mechanisms more accurately. Further, MDR generalizes two well-known estimators: (i) the empirical multivariate cumulative CDF by allowing for covariates and (ii) univariate Distribution Regression (DR) by considering multiple outcomes. Building on earlier work in the field (Chernozhukov et al., 2013), I establish that MDR consistently estimates the regression coefficient process. Further, I show that coefficients are well-behaved and converge to a Gaussian process, with the bootstrap being a consistent tool to assess the asymptotic distribution.

To illustrate the usefulness of MDR, I estimate the effect of disability insurance benefits on labor supply responses among Swiss households. Generally, receiving these benefits is related to lower incentives to supply labor (i.e. Autor et al., 2016). Autor et al. (2019) find that spouses increase their labor supply once their partner is disabled. My results indicate that spouses of low-income partners do respond as suggested by Autor et al. (2019). Yet, among average to high-income households, the need to compensate for the financial loss appears less immediate.

In Chapter 2, co-authored with Blaise Melly, we incorporate censoring into the univariate DR model. The resulting estimator, censored distribution regression (CDR), allows studying how the covariatesâ€™ effects vary over time. From a theoretical perspective, CDR represents a generalization of three existing estimators. In particular, CDR simplifies (i) to the Kaplan-Meier estimator in the absence of covariates Kaplan and Meier (1958), (ii) to distribution regression in the absence of censoring, and (iii) to Coxâ€™s proportional hazard estimator in the absence of heterogeneity (Cox, 1972). As our main results, we establish weak convergence of the coefficient process to a Gaussian process.

The standard tool to analyze duration data is Coxâ€™s proportional hazard model, which assumes time-constant effects. On many occasions, this assumption seems too restrictive. For instance, job search behavior differs during unemployment. In this context, we apply the CDR estimator to estimate the effect of potential benefit duration (PBD) on unemployment spells. Search models suggest that faced with the upcoming exhaustion of benefits, individuals intensify their search efforts and lower their target wages (Krueger and Mueller, 2016; Marinescu and Skandalis, 2021). Our results indicate that PBD has a negligible effect for short-term unemployed but a strong and significant effect for the long-term unemployed. This is in line with an increased likelihood of finding a job once the benefits are close to exhaustion.

In Chapter 3, co-authored with Tamara Bischof, we address how physicians respond to changes in their financial incentives. We exploit plausibly exogenous changes in the fee structure for medical services in the outpatient sector. The tariff partners, the health care providers and insurances, failed to reach an agreement on how to reform the outdated tariff scheme TARMED. In response, the federal government set the new fees, causing a revenue loss of up to 40% for single physicians. Previous research suggests that physicians may respond in two different ways: Faced with a revenue loss, physicians can (i) substitute from low-paying to more attractive services and (ii) increase their overall health care supply (i.e. Clemens and Gottlieb, 2014; McGuire and Pauly, 1991; Yip, 1998). Our main goal is to disentangle these two channels and to quantify their relative importance.

Our results are threefold. (i) We find that providers raise (lower) the volume of services that have become relatively more (less) attractive. (ii) Physicians increase their overall volume of services and treat more patients when they lose a significant share of their revenue. (iii) Finally, a comparative exercise indicates that volume expansions are far more important than substitution responses. In particular, a revenue loss of 5% leads to an increase in the overall supply of roughly 3% whereas we do not observe a significant rise in substitution responses. Concerning policy implications, our results suggest (i) that gradual fee changes may prevent strong and costly reactions due to more considerable revenue losses. (ii) Further, policy-makers could directly incentivize physicians to provide services that are of high value for consumers.