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Course No. Course title : : Number of credits Number of Lectures – Tutorials – Practical Faculty Name : : : MPE 171 Quantitative Methods (Statistics and Introduction to Econometrics) 4 46 – 6 – 4 Subir Sen Course outline The course is aimed at familiarising students with the understanding and application of probability and mathematical-statistics concepts on which statistical and econometric analyses of economic data are based. An understanding of probability theory and statistical inference is a key a foundation to later courses in econometrics, and are also important for advanced micro and macro-economic courses. Specific learning objectives includes stating, interpreting, and assessing the assumptions required for appropriate use and interpretation of estimators and estimation results; how to derive statistical properties of random variables, functions of random variables, and functions of sample data; the characteristics of different probability distributions and major advantages and limitations of using these distributions for statistical or econometric models; and the basic properties of the least squares estimator in the general linear model (single equation econometric models) context and an introduction to estimation issues that arise when basic assumptions underlying the model are violated. Emphasis is also given to learning by doing and hence part of the learning objectives will involve use of the MINITAB and EXCEL spreadsheet packages. In the practical sessions, students will be exposed to using these software(s) for summarising and plotting data, basic probability theory, testing hypotheses, correlation analysis and regression. After completion of the course, students are expected to use the concepts and techniques learned in assignments and term paper. Evaluation Procedure 1 Term paper: 2 minor tests: 1 major test (end semester): 25% 30% (15% each) 45% Details of course content and allotted time Topic Introduction What is Statistics? What is Econometrics? Descriptive Statistics: (a) Data types; Tabular and Graphical Methods of data grouping and display (b) Numerical Measures of Data: Five Measures of Central Tendency, Dispersion and useful measures of Allotted time (hours) Lectures Tutorials Practical 4 0 2 Topic Dispersion, Other Measures of location – percentiles and quartiles; Measures of Distribution Shape Probability Theory Probability concepts, types and basic rules, Conditional probability and independence, Bayes Theorem Random Variables Discrete and Continuous random variables; probability mass function, probability density function; Expectation of a random variable and some special expectations mean, variance, moment generating functions; Multiple random variables: Joint probability distribution of discrete and continuous variables, properties of multiple variables, conditional distributions and expectations, covariance and correlation Special Distributions The Binomial and related distributions, Poisson distribution, Geometric & Hyper-geometric distributions; Uniform distribution, Normal distribution, Exponential distribution; Gamma, Chi-square and Beta distributions Sampling & Statistical Inferences Statistics and parameters, Types of sampling – nonrandom and random or probability sampling; Sampling with and without replacement; Types of Probability sampling – simple random sampling, stratified random sampling, systematic sampling, cluster sampling; Sampling distributions - t and F distributions; Student’s Theorem; Ordered Statistics – Quantiles Estimation Point estimate, interval estimate; Properties of estimators – unbiased, consistency, minimum variance, efficiency, sufficiency; Estimation of model parameters – mean, proportion, variance, difference of means, ratio of variances Hypothesis Testing: Introduction to hypothesis testing procedure, simple and composite hypothesis, Type I and type II errors and the power function; Neyman-Pearson Theorem; Parametric tests- t-test, χ2- test, F-test; ANOVA – one way & two way; Non Parametric Tests – Sign test, Wilcoxon signed rank Test; Mann-Whitney-Wilcoxon test, Kurskal- Wallis Test; Measures of Association – rank correlation & Kendall’s tau Allotted time (hours) Lectures Tutorials Practical 2 1 1 4 1 2 6 1 1 8 1 0 6 0 0 8 1 0 Topic Additional Topics on Testing and Bayesian Statistics Sufficiency, likelihood ratio test, subjective probability and simple Bayesian procedures Introduction to Regression Analysis Theoretical constructs and empirical observable; inference problems in non-experimental sciences; uses of econometric models; Specification of simple linear regression model, least square method of estimation, classical assumptions, general and confidence approach to hypothesis testing. Total Allotted time (hours) Lectures Tutorials Practical 4 0 0 4 1 2 46 6 4 Suggested readings Text Books: 1. Introduction to Mathematical Statistics, 6th Ed. R. V. Hogg, J W. McKean and A. T. Craig, Prentice-Hall (2008). 2. Econometrics, 1st Ed. J Woolridge, Cengage / South-Western Thomson Learning (2009). Supplementary Books: 1. Introduction to the Theory of Statistics, 3rd Ed. A. M. Mood, F. A. Graybill and D. C. Boes, McGraw Hill (1974). 2. Basic Statistics, 2nd Ed. A. L. Nagar and R. K. Das, Oxford University Press (1997). (for Basic Statistics Review) 3. Statistics for Business and Economics, 1st Ed. D. R. Anderson, D. J. Sweeney and T. A. Williams, Cengage / South-Western Thomson Learning (2002). (for problems and numerical examples) 4. Basic Econometrics, 4th Ed. D Gujarati, Tata McGraw Hill (2000) The term paper involves the following tasks: Stage 1: One page essay describing any economic or business problem; the context in which it occurs, and application of statistical technique either to identify or to resolve the problem. Stage 2: A two page outline of the statistical concept addressed / applied in the paper preferably in own words. The reason why the particular technique is undertaken for the economic problem identified. Five articles/ research works from referred journals that are relevant to your topic should be read for and referred to in this assignment. Stage 3: Turn in a paper consisting of 15-20 double spaced typed pages. Not more than 5 pages may be used to review related literature. The rest of the term paper should be devoted to developing an statistical / economic model (if so or the selected economic problem) selected in Stage I. The assumptions, objectives and policy implications that can be derived from the model should be clearly stated. All term papers are to be presented in class. Presentations should be of about 15 to 20 minutes per student.