Tejas, Tavish. Essays on hypothesis testing and optimization under uncertainty with applications to financial economics and taxation. Retrieved from https://doi.org/doi:10.7282/t3-fwjv-9559
DescriptionThe first essay of my dissertation addresses the quantification of probabilistic uncertainty. I develop a new statistical test that uses the Hellinger distance for distinguishing probability distributions based on data and I show that the errors of this test can be used to create a set of competing probability distributions that are difficult to separate from a benchmark distribution. The test does not require distributions to share the same support (mutual absolute continuity), and this allows a larger set of probabilistic specifications to impact economic decision making under uncertainty. I explore the connections between the Hellinger distance and the error probabilities of likelihood ratio tests by obtaining an equivalence between controlling the Hellinger distance and constraining the testing error. In addition, I show that the error probabilities of likelihood ratio tests decrease exponentially as the Hellinger distance between competing distributions increases by deriving a large deviation principle for locally asymptotically normal sequences of likelihood ratios. I also provide new interpretations of certain probability metrics and show that they can be used to quantify Arrow's measure of risk premium in economics and the market price of risk in finance. In the second essay of my dissertation, I extend the classical consumption-investment model in frictionless markets to accommodate incentives that exclude a fixed amount of capital gains from taxation. Such incentives are present around the world and limits on their use vary significantly across countries, within countries, and across various asset classes. The main result of my analysis is a characterization of consumption-investment decisions in the presence of these capital gains tax incentives. I expand the model by allowing uncertainty about tax rates to reflect the present condition of tax policy in the United States. I also examine the implications of increasing the limit on the use of such incentives and find that in some cases, doing so may result in decreasing investments or have no effect on consumption-investment decisions. As an application, I estimate the model parameters using United States housing market data and obtain results that may be of practical importance for policymakers.