In Chapter 1 of this thesis we examine two key empirical questions in public economics by exploiting the 2009 Polish tax reforms. First, we estimate the degree of substitution between employment and self-employment tax bases – on the extensive margin. In particular, we quantify the impact of changes in the differential in rates of taxation between the two tax bases on the propensity of taxpayers to declare any positive level of employment or self-employment income. Second, we contribute to the literature on elasticities of taxable income on the intensive margin – the responsiveness of taxable income to changes in marginal tax rates – by providing estimates which are more likely to be robust to changes in year-to-year income dynamics than previous estimates.

To identify these effects, we exploit variation in marginal and total tax rates around the 2009 reforms which occurs independently of an individual’s position in the income distribution as a result of joint reporting with a spouse. At the same time, to obtain the extensive-margin responses, we exploit the uniqueness of the 2009 Polish tax reforms, which left the tax schedule un-changed for some types of self-employment while changing the tax schedule for the employed. The baseline estimates of the intensive-margin elasticities are around 0.2-0.3 for the employed and around 0.5-0.7 for the self-employed. The estimates jointly make possible the decomposition of the deadweight losses of the tax reform into intensive and extensive-margin responses, with the contribution of the extensive margin found to be around 7% of the total.

In Chapter 2, we examine the optimal non-linear taxation in an environment in which individuals have the option of engaging in either employment or self-employment activity. We build on the estimates from Chapter 1 to calibrate an extension of the classic Mirrleesian model which allows for extensive-margin transitions between employment and self-employment. The results help rationalise the preferential tax treatment of self-employment income versus employment income given in certain tax systems. They also illustrate the ways in which the possibility of extensive-margin transitions between tax bases moderate the incentive to give such preferential treatment. Based on the parameterisation here, the presence of the extensive-margin ap- pears to have a limited impact on the optimal marginal and total tax rates faced by the employed and self-employed. This, together with the earlier decomposition of deadweight losses in Chapter 1 by types of response, points towards a limited role of the extensive margin as a consideration for optimal-tax design, at least as far as the employment and self-employment tax bases are concerned.

Chapter 3 turns to a fundamental question in health economics: how do health states change over the life-cycle, and how does the risk of adverse health-shocks change over the life-cycle? Most economic models of individuals’ behaviour over the life-cycle, to the extent to which they incorporate a measure of health risk, assume a simplified unidimensional measure of health. We contribute to this literature by estimating a flexible dynamic factor model of health and health risk over an individual’s life using the rich health data from the Health and Retirement Study (HRS). We find that the many potentially collinear health indicators found in the HRS can broadly be summarized into four underlying factors. Three of these correspond to what may be termed subjective health measures, such as self-reported mobility, while a fourth corresponds to objective measures, including the number of overnight hospital stays, doctor visits and medical spending. The persistence of these underlying factors and the variance of their shocks are estimated as parameters of a vector auto-regressive process. We obtain results about the deterministic evolution of the health factors with age, the level of risk relating to each health measure, as well as heterogeneity by level of education. These are intended as building blocks of an ongoing project concerning the optimal design of disability insurance, given the health risks faced by individuals.