Applications of Statistical and Economic Analysis in Finance and Health Industry by Xuan Sun Program in Statistical and Economic Modeling Date:_______________________ Approved: ___________________________ Kent P. Kimbrough, Supervisor ___________________________ Surya Tokdar ___________________________ Edward Tower Thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Program in Statistical and Economic Modeling in the Graduate School of Duke University 2015 i v ABSTRACT Applications of Statistical and Economic Analysis in Finance and Health Industry by Xuan Sun Program in Statistical and Economic Modeling Date:_______________________ Approved: ___________________________ Kent P. Kimbrough, Supervisor ___________________________ Surya Tokdar ___________________________ Edward Tower An abstract of a thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Program in Statistical and Economic Modeling in the Graduate School of Duke University 2015 Copyright by Xuan Sun 2015 Abstract This paper intends to present my summary of internship and some academic individual and team projects, including a quantitative and statistical analysis of some important Macro factors and financial models, and a data analysis project in drug cost reduction. The first chapter discusses the mechanism and impact of pass-through from the dynamics of RMB exchange in China, and the method I used here is the basic econometrics regression analysis. The result is significant and coincides with our common sense when we make investment decisions. The second chapter is about the revised CCAPM model. Through a modified distribution of error terms, CCAPM model will show an improved explanation power. The third chapter is a data analysis project of drug cost reduction. I used Bayesian method to explore the relationship between drug cost and other predictors, and the result gives us advice on designing health plans to minimize the cost. iv Contents Abstract .......................................................................................................................................... iv List of Tables ................................................................................................................................ vii List of Figures ............................................................................................................................. viii 1. Introduction ............................................................................................................................... 1 2. Mechanism and impact of pass-through from the dynamics of RMB exchange ............. 2 2.1 Theoretical Review ........................................................................................................... 2 2.2 Data collection and predictors selection ....................................................................... 3 2.3 Model Building ................................................................................................................. 4 2.4 Econometrics Analysis ..................................................................................................... 5 2.5 Conclusion ......................................................................................................................... 8 3. A statistical analysis of CCAPM Model ............................................................................... 10 3.1 Model and Methodology ............................................................................................... 10 3.2 Data and Goodness of Fits ............................................................................................ 12 3.3 Empirical Result .............................................................................................................. 14 3.4 Conclusion Remarks ...................................................................................................... 16 4. Data Analysis Project: Drug Cost Reduction ...................................................................... 17 4.1 Data Description ............................................................................................................. 17 4.2 Methodology ................................................................................................................... 18 4.3 Results and Summary .................................................................................................... 24 4.4 Discussion ........................................................................................................................ 27 v References ..................................................................................................................................... 29 vi List of Tables Table 1: Result of ADF Test ......................................................................................................... 5 Table 2: Result of Co-integration Test ........................................................................................ 7 Table 3: CCAPM VS. CCAPM-AEPD using total consumption growth ............................ 15 Table 4: CCAPM VS. CCAPM-AEPD (nondurable total consumption growth) ............... 15 Table 5: Bayesian Full Model ..................................................................................................... 25 Table 6: Ridge Regression .......................................................................................................... 25 Table 7: Lasso Regression .......................................................................................................... 25 Table 8: BMA ................................................................................................................................ 26 Table 9: Marginal Posterior ........................................................................................................ 26 vii List of Figures Figure 1: Frequentist: Potential outliers and influential observations ................................ 19 Figure 2: Bayesian: potential outliers and influential observations ..................................... 20 Figure 3: Checking Multi-Colinearity ...................................................................................... 21 Figure 4: Ridge Regression ........................................................................................................ 22 Figure 5: Lasso Regression ......................................................................................................... 22 Figure 6: BMA .............................................................................................................................. 23 Figure 7: BMA2 ............................................................................................................................ 24 viii 1. Introduction In this paper, there are three projects related with statistical and economic analysis. The first one is my individual project during my summer intern in 2014. It is a macro econometric analysis about the mechanism and dynamics of RMB exchange rate, and I did this project for my intern supervisor to research some macro factors the company is following. The second one is a team project for a MBA course (Fixed Income and Speculative Strategies) taught by Prof. Breeden at Fuqua School of Business. The other two team-members are Duke Economics MA students: Mengyang Lin and Jin Cao. This project is generally about a statistical analysis of CCAPM model. The third project is my individual course project for a PHD Statistics course (Linear Models) taught by Prof. Merlise at Department of Statistical Science. This one is generally an application of Bayesian Data Analysis techniques in health industry. 1 2. Mechanism and impact of pass-through from the dynamics of RMB exchange Exchange rate and price level are two core variables in an open macro-economy, these two variables are closely related with other economic variables in the macro- economy, influencing the behaviors of manufacturers and consumers of the economy. Since China had conducted the reform of the RMB exchange rate system in 2005, the related monthly data of this thesis are selected from January 2006 to December 2012, and this chapter is centered on conducting practical analysis of the impact of dynamics of RMB exchange rate on CPI, PPI, CCI, and M2, which help us understand analyze the pass-through effect of the change of RMB exchange rate on price, consumers’ expectations about the whole economy and the inflation rate. 2.1 Theoretical Review From many theoretical papers, the model of the price of imported goods are described as follows: ** PEMCtt= θ t (1) Where Pt refers to the price of imported goods expressed in domestic currencies; Et refers to the exchange rate; θ * refers to the ratio of cost addition for exporters; and * MCt refers to the marginal cost for exporters. 2 * If we define the demand of importers as Dt , and define the competing pressure Pc of importers as , where Pc refers to the price given by the competitors of * Ett MC importers. Then, θ * can be expressed as: α **⎡⎤Pc t β (2) θ = ⎢⎥* D ⎣⎦Ett MC Substituting (2) into (1): 1*1*−−αααβ Ptt= EPMC t ct D (3) Make a log transformation to (2), we get: Ptctt=(1−αααβ )ecPDt + (1− ) + + (4) This is the basic theoretical model for the dynamics of the exchange rate. 2.2 Data collection and predictors selection In order to explore the relationship between the exchange rate and price level, several other predictors are selected.