<div>Dynamic treatment regimes (DTRs) are often considered for the medical care of chronic diseases and complex conditions. They consist of multistage treatment decisions, each based on the individual's health information and their treatment and response history. In this dissertation, we consider this setting with binary responses (i.e., either respond favorably or unfavorably to a treatment) and highlight one type of heterogeneity, specifically the existence of subgroups of patients who respond favorably to only a distinct subset of study treatments. </div><div>Currently, most works employ model-free approaches to find the optimal DTR. In contrast, we propose a model-based approach, which focuses more on describing heterogeneity in treatment responses. We first consider the scenario when baseline covariates are not included. A mixture of mixed logit models is proposed along with an EM alogorithm to estimate these subgroup proportions and the probabilities of a favorable response. We describe how an optimal dynamic treatment regime can be determined given the model information. We also discuss the necessary identifiability conditions (i.e., what sets of parameters are necessary for DTR determination). </div><div><div>Then, we extend the proposed model to incorporate baseline covariates. Specifically, we include certain baseline covariates in the logistic model for the probabilities of a favorable response and develop a multivariate Bernoulli model to incorporate the remaining covariates in the determination of subgroup proportions. Furthermore, time effects are considered in the model to allow for a potential overall decline in response effectiveness over time. </div><div>In each setting, simulation studies are performed to demonstrate the effectiveness of the proposed method in both parameter and DTR estimation. We also compare our approach with another competing method, Q-learning, and provide the scenarios when our mixture model outperforms Q-learning in terms of finding the optimal DTR.</div></div>

This thesis investigates the impacts of user choice in Swedish elderly care on quality and cost as well as the impact of marketisation on the Covid-19 death toll. In the last three decades welfare service provision in Sweden has been increasingly marketised. Since 2009, Swedish municipalities have been able to introduce user choice in elderly care and it has been widely adopted in home care. To investigate the impact of introducing user choice, new insights from econometrics literature is used to estimate a staggered Difference-in-Difference model, using panel data for the years 2003-2019 and the 290 Swedish municipalities. The impact of marketisation on the Covid-19 death toll is estimated through Ordinary Least Squares using a cross-sectional data set. There are three main findings of this thesis. (i) The impact on quality and cost of the introduction of user choice has had heterogeneous effects across adoption groups, calendar time, and exposure length of treatment, and hence, the standard Difference- in-Difference approach is likely to provide biased estimates in this setting. (ii) The introduction of user choice has no clear effect on non-contractible quality measured by mortality rate and fall accidents, nor on cost. However, user choice has increased subjective quality, as measured by user satisfaction. (iii) A higher degree of marketisation in home care is associated with a higher Covid-19 death toll amongst those which had home care.

This thesis consists of four self-contained essays. The first essay concerns educational choice and the returns to college in Sweden. I apply a recently introduced econometric framework that allows for self selection and treatment effect heterogeneity. I also examine the influence of cognitive and noncognitive ability on college choice and the returns to college. Essays two through four concern different aspects of intergenerational income mobility. In the second essay, we study the impact on mobility estimates from heterogeneous income profiles and, more specifically, life-cycle bias. We use nearly career-long income measures for both fathers and sons to give a detailed account of this bias and assess recent methods to deal with it. In the third essay, we present a simple model of intergenerational transmission and use it to analyze the dynamic behavior of the intergenerational income elasticity following structural changes. We find that past structural frameworks, for example in the form of past policies or institutions, matter for current trends in mobility. The fourth essay provides a cross-country perspective on intergenerational income mobility. We construct comparable data sets for Sweden and the UK and account for country differences in the role of parental income for various productivity traits of children. Finally, we examine whether such differences can explain the country difference in intergenerational income mobility.