# Econometrics and Data Analysis I

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1 Econometrics and Data Analysis I Yale University ECON S131 (ONLINE) Summer Session A, 2014 June 2 July 4 Instructor: Doug McKee Teaching Fellow: Yu Liu Classroom: Online Class Hours: MWF, 11:00am 12:00pm Instructor Office Hours (online): MWF, 12:00pm 1:00pm TF Office Hours (online): TBD Course Description This course teaches how to evaluate quantitative information and how to use data to answer quantitative questions in the social sciences. We will cover three main areas: 1. The first area, probability, provides a foundation for modeling uncertainties, such as the uncertainties faced by financial investors, insurers, and individuals in everyday life. We will study the mechanics of probability (manipulating some probabilities to get others) and the use of probability to make judgments about uncertain events. 2. The second area, statistics, provides techniques for interpreting data, such as what a marketing department might know about past consumer purchases. Statistical methods permit us to use small amounts of information to answer larger questions. 3. The third area, linear regression, is an area of statistics dedicated to estimating the relationships between two or more variables. For example, we might be interested in estimating the demand for health insurance as a function of the price, insurance policy attributes and consumer attributes. The prerequisites for this course are introductory microeconomics and familiarity with single variable calculus. In most econometrics classes, mathematical methods are introduced and then applied to a few examples. This class turns that around. We will focus on substantive questions first and then introduce mathematical methods that will help us answer them. By the end of the class, you will have acquired several concrete skills. Specifically, you will: 1. Understand the strengths and weaknesses of different methods. 2. Be able to choose appropriate methods to answer real-world questions. 3. Understand the math behind methods like linear regression and hypothesis testing. 4. Understand the intuition behind these methods. 5. Be able to apply these methods to analyze real data with a powerful statistical analysis package (Stata) 1

4 Schedule PART I: PROBABILITY (M1) Monday, June 2: Probabilities and Events Read: SW, Chapter 1 Probability hand-out Optional: Freedman et al, Chapters Course overview Terminology and concepts: experiments, outcomes, and events Probabilities and chance Multiple events, probability rules, and Venn diagrams Probability tables Conditional probability: definition and intuition (M2) Wednesday, June 4: Random Variables Read: SW, Optional: Freedman et al, Chapter 14 Probability trees Independence and information sets Terminology of random variables Expected values Variance and standard deviation Covariance and independence (M3) Friday, June 6: Binomial and Normal Random Variables Due: Problem Set 1 Read: SW 2.4 Binomial distribution hand-out Optional: Freedman et al, Chapter 15 Calculating Binomial probabilities Expected Value and variance of Binomial random variables Calculating Normal probabilities Sums of Normal random variables and standardizing 4

5 PART II: STATISTICS (M4) Monday, June 9: Sample Statistics and Estimation Read: SW , 3.1 Optional: Freedman et al., Chapter 20 Sample and populations: Overview Estimating a population mean and the law of averages Estimating and using variances, covariances, and correlations Normal approximations and the Central Limit Theorem Distribution of sample sums and sample means Standard errors Introduction to Stata (M5) Wednesday, June 11: Sampling and Confidence Intervals Read: SW 3.3 Optional: Freedman et al., Chapters 21 and 23 Sampling and surveys Accuracy of sample statistics Confidence intervals for sample estimates Confidence intervals for averages (M6) Friday, June 13: Hypothesis Testing Due: Problem Set 2 Read: SW 3.2, 3.4, 3.6 Optional: Freedman et al., Chapter 27 Null hypotheses and alternatives p-value mechanics for means and proportions Interpretation and communication of results One-sided vs. two-sided tests Small sample situations and t-tests Differences in means tests 5

6 (M7) Monday, June 16: Randomized Experiments Due: Problem Set 3 Read: SW 3.5 Angrist and Pischke, Chapters 1 2 (online) Interpreting observational and experimental data Wednesday, June 18: MIDTERM EXAM PART III: REGRESSION (M8) Friday, June 20: Introduction to Regression Analysis Due: Part 1 of Big Empirical Project Read: SW Chapter 4 Optional: Allison, Chapters 1 and 5 Mechanics of simple regression Correlation vs. slope Interpreting regression estimates Doing regression in Stata R 2 and goodness-of-fit (M9) Monday, June 23: Statistical Inference in Regression Read: SW Chapter 5 Hypothesis testing and statistical significance Confidence intervals Prediction (M10) Wednesday, June 25: Multiple Regression Read: SW Chapter 6 Optional: Allison, Chapters 2 and 3 Mechanics of multiple regression Interpreting multiple regression results Confounding variables Intervening variables Dummy regression variables 6

7 Model building and avoidable mistakes (M11) Friday, June 27: Model Building in Practice Read: SW Chapters 8 9 Optional: Allison, Chapters 7 and 8 Developing regression models Interpreting and using results Model building using real data (M12) Monday, June 30: Joint Hypothesis Testing Due: Problem Set 4 Read: SW Chapter 7 Joint hypothesis testing Regression F-test Restricted and Unrestricted models Tests of linear restrictions in regression models The linear probability model (M13) Wednesday, July 2: Difference-in-Differences Due: Empirical Project Read: SW Angrist and Pischke, Chapter 5 (online) Natural experiments and regression Strategies for identifying effects of a policy Extending diff-in-diff with a regression Thursday, July 3: FINAL EXAM 7

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