Studies On Stochastic Dominance Tests And Their Applications

In uncertainty decision making,Stochastic Dominance(SD)theory has always been one of the most important analytical tools,and it plays an irreplaceable role in related research directions in finance,economics,statistics,and decision science.This thesis focuses on SD tests and a series of application scenarios in the evaluation problem of SD theory.As portfolios' evaluation tool that has complementary advantages with Mean-Variance theory(MV),the biggest motivation for us to study the SD efficiency test is to maximize the selection of efficient investment portfolios in the financial market.This is regarded as the evaluation application of the SD efficiency test in finance.We only need to replace the moment condition in the SD efficiency test statistic to satisfy the SD optimality criterion,then the way of constructing an SD efficiency test can be similarly used to establish a general SD test.Meanwhile,the SD test,which is the main theoretical contribution of this thesis,can also be applied to the evaluation questions in economics,and it is in contrast with the test results of other existing SD tests.Aiming to the application of SD theory in evaluation problems,from the perspective of economics,we try to build corresponding theoretical frameworks in the analysis of inequality measurement and poverty alleviation policy,wage polarization and economic states' transition,and the combination evaluation in welfare economics by introducing the analytical paradigm of SD theory,and use the SD tests to establish a complete analysis system from theory to empirical research.In this thesis,the above four questions are studied under the framework of SD theory,and the main contributions of each chapter are as follows.In Chapter 2,for a given portfolio,we propose an SD efficiency test based on an Adjusted Gaussian Quasi-likelihood Ratio statistic(AQLR)for evaluating the efficient portfolios,and the AQLR statistic is also suitable for building an SD test,and this test will be used for empirical studies in Chapters 3 and 4.In Chapter 3,we respectively use the Gini index,Theil index,and Atkinson index to measure the inequality of the consumption gap of household expenditure items,and then conduct SD tests on the distributions of these consumption items in different years,thus a fact that the effect of SD tests on the measure of inequality is consistent with the results of the above three indices can be confirmed.At the same time,with the perspective of SD theory,the idea of investigating poverty-returning issues from the "crossover" situation of low-income groups in the cumulative distribution functions' curves is proposed.In Chapter 4,we find the intrinsic link between the polarization of manufacturing wages and the transition of manufacturing states and measure the degree of manufacturing wages' polarization by SD tests,thus we could identify the specific stage of development of China manufacturing industry.In Chapter 5,we study the influence of enrollment expansion of higher education on the welfare of Chinese urban households.This is the application of the SD combination evaluation method in welfare economics.The specific research results are as follows:In Chapter 2,aiming at the moment equality condition proposed by Post and Versijp(2007),we deduce a modification moment condition with economics meaning by the KKT method.Then,using quadratic statistic and absolute value statistic,we develop a multivariate test for SD efficiency when the population is known(see the Theorem 2.1),and develop a multivariate test for SD efficiency when we just know the observed sample by an AQLR statistic(see the Theorem 2.2),and we show that the above two SD efficiency tests are sufficient and necessary criteria.By introducing the recommended moments selection(RMS)procedure,we can finish the parameters' estimation and statistical inference involved in the above SD efficiency tests,and we give numerical simulation examples to illustrate the effectiveness of the SD efficiency test.Besides,we can similarly build an SD test based on an AQLR statistic,and we compare the AQLR method's results to other SD tests' results in the empirical research of Chapter 3 and Chapter 4,we find that the AQLR test can effectively judge SD relations.In Chapter 3,depending on the Gini index,the Theil index and the Atkinson index,we use the 2012-2017 household consumption data to calculate the consumption gaps on education-culture-entertainment and health-care.It shows that:(1)For the education-culture-entertainment expenditure,the inequality of the rural and urban residents' consumption gap is shrinking;(2)For the health care expenditure,the inequality of the rural residents' consumption gap is also shrinking,but the inequality of urban residents' consumption gap has further expanded.Finally,taking the poorer Gansu province as an example,we test the trend on the above two expenditures of rural residents by our AQLR method,Wald method,Anderson's maximal t value method,and Davidson and Duclos' maximal t value method,and we find the proportions of these two expenditures of rural residents in their total consumption are increasing,which are consistent with the calculation results of the above-mentioned inequality indices.This shows that the poverty alleviation policy recently implemented nationwide has achieved results,and the SD criterion can effectively analyze the poverty problem in the same way as the above three inequality measure indices,and the AQLR method has obvious test results.In Chapter 4,inspired by the theory of Convergence and Synergetics,we propose the hypothesis of the equilibrium state of the manufacturing,which aims to establish a link between the income of manufacturing workers and the state of development of the manufacturing industry.Introducing an analytical framework for measuring the degree of polarization of income distribution by SD method,the polarization of the income distribution is quantified measurement using the Kolmogorov-Smirnov-type test(KS)and our AQLR method.Based on the above theory,we measure the degree of polarization of China's urban manufacturing income distribution from 2007 to 2016.The results show that China's manufacturing industry is generally in a relatively stable equilibrium state.In the meantime,in the context of a large accumulation of technology,China's manufacturing industry has shown a trend of the transition to the next technological breakthrough point.In Chapter 5,we study the problem of combination evaluation of SD and discuss the causes and special cases of the failure of the combination evaluation problem by the classical SD tests.By introducing the Utopia Index model based on stochastic dominance theory,we study the influence of enrollment expansion of higher education on the welfare of Chinese urban households.Based on the data about urban households in China Household Finance Survey(CHFS)in 2013,we partition those households into different classifications according to the period of the head of those households accepts higher education,and convert the household income into equivalent-welfare.By the calculation of the Utopia Index for the equivalent-welfare of different households,we find that:(1)from the perspective of all urban households,the younger the households,the higher the welfare level;(2)for urban households who have received higher education,in addition to the households who started their higher education before 1977,the law that younger households have higher welfare level is held;(3)from the perspective of urban households' welfare growth,as the velocity of enrollment expansion in higher education tends to be stable,the quality of higher education in China has begun to increase steadily after the quality of higher education decline in a certain period of time.Finally,using the Chinese Household Income Project(CHIP2013)data to implement a robustness verification,the results show that the above conclusions are robust.