Essays in dynamic optimal taxation: working experience, unemployment scarring and poverty

This thesis investigates the design of optimal tax systems in dynamic environments. The first essay characterizes the optimal tax system where wages depend on stochastic shocks and work experience. In addition to redistributive and efficiency motives, the taxation of inexperienced workers depends on a second-best requirement that encourages work experience, a social insurance motive and incentive effects. Calibrations using U.S. data yield higher expected optimal marginal income tax rates for experienced workers for most of the inexperienced workers. They confirm that the average marginal income tax rate increases (decreases) with age when shocks and work experience are substitutes (complements). Finally, more variability in experienced workers' earnings prospects leads to increasing tax rates since income taxation acts as a social insurance mechanism. In the second essay, the properties of an optimal tax system are investigated in a dynamic private information economy where labor market frictions create unemployment that destroys workers' human capital. A two-skill type model is considered where wages and employment are endogenous. I find that the optimal tax system distorts the first-period wages of all workers below their efficient levels which leads to more employment. The standard no-distortion-at-the-top result no longer holds due to the combination of private information and the destruction of human capital. I show this result analytically under the Maximin social welfare function and confirm it numerically for a general social welfare function. I also investigate the use of a training program and job creation subsidies. The final essay analyzes the optimal linear tax system when there is a population of individuals whose perceptions of savings are linked to their disposable income and their family background through family cultural transmission. Aside from the standard equity/efficiency trade-off, taxes account for the endogeneity of perceptions through two channels. First, taxing labor decreases income, which decreases the perception of savings through time. Second, taxation on savings corrects for the misperceptions of workers and thus savings and labor decisions. Numerical simulations confirm that behavioral issues push labor income taxes upward to finance saving subsidies. Government transfers to individuals are also decreased to finance those same subsidies.

Stress Inversion Using LiDAR Tunnel Deformation Measurements

Far-field stresses are those present in a volume of rock prior to excavations being created. Estimates of the orientation and magnitude of far-field stresses, often used in mine design, are generally obtained by single-point measurements of stress, or large-scale, regional trends. Point measurements can be a poor representation of far-field stresses as a result of excavation-induced stresses and geological structures. For these reasons, far-field stress estimates can be associated with high levels of uncertainty. The purpose of this thesis is to investigate the practical feasibility, applications, and limitations of calibrating far-field stress estimates through tunnel deformation measurements captured using LiDAR imaging. A method that estimates the orientation and magnitude of excavation-induced principal stress changes through back-analysis of deformation measurements from LiDAR imaged tunnels was developed and tested using synthetic data. If excavation-induced stress change orientations and magnitudes can be accurately estimated, they can be used in the calibration of far-field stress input to numerical models. LiDAR point clouds have been proven to have a number of underground applications, thus it is desired to explore their use in numerical model calibration. The back-analysis method is founded on the superposition of stresses and requires a two-dimensional numerical model of the deforming tunnel. Principal stress changes of known orientation and magnitude are applied to the model to create calibration curves. Estimation can then be performed by minimizing squared differences between the measured tunnel and sets of calibration curve deformations. In addition to the back-analysis estimation method, a procedure consisting of previously existing techniques to measure tunnel deformation using LiDAR imaging was documented. Under ideal conditions, the back-analysis method estimated principal stress change orientations within ±5° and magnitudes within ±2 MPa. Results were comparable for four different tunnel profile shapes. Preliminary testing using plastic deformation, a rough tunnel profile, and profile occlusions suggests that the method can work under more realistic conditions. The results from this thesis set the groundwork for the continued development of a new, inexpensive, and efficient far-field stress estimate calibration method.