Abstract
摘要:本計畫希望提出對Central Dominance 的檢定,本計畫中的Central Dominance 包含三個比較分配的觀念: Central Dominance , Portfolio Dominance 和Ranged Central Dominance。對於上述三個隨機優越的概念,我們分別提出檢定的方法,檢定的統計量。利用拔靴法我們提出檢定統計量的critical value,我們並進一步利用模擬衡量檢定統計量的效果。
Central Dominance,Portfolio Dominance 和Ranged Central Dominance 雖然是非常相關的三個比較分配的觀念,但是檢定方法上都有各自的難處,彼此有關卻又不盡相同。因此,我們會先從Central Dominance 著手,預計一年的時間完成這個部份。利用我們在 Central Dominance 上累積的經驗,我們希望能再各花一年的情況下,進一步克服Portfolio Dominance 和Ranged Central Dominance。
最後,我們希望應用我們前面在理論計量上的突破,把成果分別應用於公共財政和投資上。隨機優越(Stochastic Dominance)的檢定被廣泛應用於公共財政和投資上,許多論文也都刊登於頂尖的學術期刊。我們希望,我們在理論計量上的突破也能進一步帶動在
實證上的新發現。
Abstract: In this project, we consider testing central dominance, a concept first proposed by Gollier (1995) to characterize a relation between two distribution functions. Compared with sto chastic dominance that provides a preference ordering of risks, central dominance implies a deterministic comparative statics of change in decision when risk changes. We propose a test and analyze the asymptotic properties of the proposed test statistics.
Further, we extend our work related to central dominance to portfolio dominance proposed by Gollier (1997). Compared with central dominance providing an unambiguous comparative statics of a change in the portion on risky assets when the return distribution of the risky asset changes, portfolio dominance providing the condition for the risk-averse investor to change in the portion on risky assets regardless of the level of the risk-free asset when the return distribution of the risky asset changes.
Finally, we will derive a new concept, called ranged central dominance. The so-called ranged central dominance is the condition for the risk-averse investor to change in the portion on risky assets within a range of value of the risk-free asset when the return distribution of the risky asset changes. Note that ranged portfolio dominance collapses into portfolio dominance when the range of the value of the risk-free asset happens to be the domain of it. Thus, ranged portfolio dominance is a weaker condition of portfolio dominance and can be applied to more cases in the real world.
The proposed tests for CD, portfolio dominance and ranged central dominance are applied to problems in public …nance using the income distribution data from Canadian Family Expenditure Survey in the years of 1974, 1978, 1982, 1986, and 1990. We intend to test whether the income distributions in 1978 and 1990 central dominate, respectively, those in 1974 and 1986. If our null hypotheses are not rejected, this implies that the optimal income tax rates in 1978 and 1990 should have been lower than what they were, had the government maximized an increasing and concave social welfare function. We also intend to empirically test portfolio dominance and ranged central dominance.
Further, the proposed tests for CD, portfolio dominance and ranged central dominance are applied to investment problems using the return distribution of the stock market data. Adopting daily returns in each year, we intend to test whether the distribution of daily returns in one year is dominated by that of the next year. If our null hypotheses are not rejected, this implies that the risk-averse investors should increase her portion on the risky assets. We also intend to empirically test portfolio dominance and ranged central dominance.
Keyword(s)
central dominance
contact set
functional inequality
stochastic dominance
portfolio dominance.