ECON 7818-001 Mathematical Statistics for Economists
ECON 7818 Syllabus, fall 2003 Mathematical Statistics for Economists. Professor: Jose J. Canals-Cerda. Office: Econ 103 Phone/Voicemail: 303-492-7869 E-mail: [email protected] Class meets on Tuesday and Thursday 2:00 p.m. to 3:15 p.m. Classroom: EDUC 143 (The information in this syllabus is subject to change). Course Objectives. The course is designed as a rigorous introduction to advanced statistics and econometrics. Registration in the class e-mail list. Please send me a brief email message containing your name and the subject "ECON7818 Student". Be aware that most of the course announcements, solutions to homework, and exams, etc., will be done using e-mail. Thus, it is important that you send this email to me as soon as possible. How to contact me. Office Hours: My office hours are Tuesdays and Thursdays from 12:20 p.m. to 1:20 p.m. You can make an appointment if you want to talk to me at any other time (by e-mail, phone or in person). Students with Disabilities. The University abides by Section 504 of the Rehabilitation Act of 1973, which stipulates that no student shall be denied the benefits of an education "solely by reason of a handicap." Disabilities covered by law include but are not limited to learning disabilities and hearing, sight or mobility impairments. If you have specific physical, psychiatric or learning disabilities and require accommodations, please let me know early in the semester so that your learning needs may be appropriately met. You will need to provide documentation of your disability to the Disability Services Office in Willard 322 (phone 303-492-8671). Exams. There will be two midterms administered during the semester and one final exam. I will provide you also with problem sets but they will not be graded. The course paper. One of the requirements of this class is a paper. The course paper will replicate published research. This work will require the use of statistical or econometrics computer packages. You are not required to use a specific package. You can access computer packages like SAS, R, LIMDEP, STATA OR GAUSS, among others. With the exception of R that is free, you can buy most of these products from the University at a reasonable student discount price. Most of these statistical packages are also available in the computer labs located in the Economics building. During the semester we will spend some time teaching SAS, and I will only answer questions about this statistical package. I encourage you to work in groups of 3 students. You should plan to start your paper as soon as possible. You may be required to present the paper in class. The quality of your presentation will be an important determinant of your grade. This applies also to the clarity of your programs. The final draft of the paper will consist of an introduction describing and motivating the interest of the paper in a simple way, as well as a road map with a short description of the different sections of the paper. The paper should have a section describing the data, a section describing the econometric methodology, a section with results and a final section presenting the conclusions. If necessary, the paper may include one or several appendixes. In particular, the programs used for the statistical work should be included in an appendix. Grading. The Final grade for this class is based on your performance in midterms (me1, me2), a final exam (fe) and the research paper (rp). Your final grade will be computed using the following formula: 0.25* rp + 0.05*me1 + 0.10*Max(me1,fe) + 0.05*me2 + 0.10*Max(me2,fe) + 0.45*fe Important Dates. October 9: First Midterm Exam. October 16: First draft of research paper due. November 13: Second Midterm Exam. December 11: Final draft of research paper due. The Final Exam date will be scheduled by the University Administration. Texts and Other Materials. Recommended book: Amemiya, Takeshi (1994): "Introduction to Statistics and Econometrics." Harvard University Press. You may also find the following book useful: Rice, John A. : “Mathematical Statistics and Data Analysis.” Wadsworth & Brooks/Cole Advanced Books & Software Pacific Grove, California. For learning sas: Cody and Smith: “Applied Statistics and the SAS Programming Language.” Prentice Hall Ed. (4 th edition). (This is a book for learning sas). Course Outline. What follows represent a tentative list of subjects to be covered in class. Chapter 1: Introduction to Regression analysis. Introduction to regression analysis. Omitted variables. Endogeneity. The Linear probability model. Chapter 2: Probability Theory. Axioms of Probability. Conditional Probability and Independence. Chapter 3: Random variables and probability distributions. Definitions. Discrete Random Variables. Continuous Random Variables. Distribution Function. Change of Variables. Normal Random Distribution. Chapter 4: Moments. Expected Value. Higher Moments. The Moment Generating Function. Covariance and Correlation. Conditional Mean and Variance. Chapter 5: Large sample theory Modes of convergence. Laws of Large Numbers and Central Limit Theorems. Chapter 6: Point Estimation Introduction. Properties of Estimators. Least Squares Estimators. Chapter 7: Maximum Likelihood and Method of moments. Introduction. Properties of Maximum Likelihood and Method of Moments Estimation. Chapter 8: Interval Estimation and Test of Hypothesis. Introduction. Confidence Intervals. Test of Hypothesis. Constrained Least Squares Estimators. Test of Hypothesis in the Linear Regression Framework. Chapter 9: Advanced econometric models. Generalized Least Square. Nonlinear Regression model. Qualitative Response Models.