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EC 331. 01&02 ECONOMETRICS I Fall 2011 Lecture notes Chapters 1-2-3

EC 331. 01&02 ECONOMETRICS I Fall 2011 Lecture notes Chapters 1-2-3. Brief Overview of the Course. This course is about using data to measure causal effects. In this course you will:. Review of Probability and Statistics (SW Chapters 2, 3). The California Test Score Data Set.

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EC 331. 01&02 ECONOMETRICS I Fall 2011 Lecture notes Chapters 1-2-3

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  1. EC 331. 01&02ECONOMETRICS IFall 2011 Lecture notesChapters 1-2-3

  2. Brief Overview of the Course

  3. This course is about using data to measure causal effects.

  4. In this course you will:

  5. Review of Probability and Statistics(SW Chapters 2, 3)

  6. The California Test Score Data Set

  7. Initial look at the data:(You should already know how to interpret this table) • This table doesn’t tell us anything about the relationshipbetween test scores and the STR.

  8. Question: Do districts with smaller classes have higher test scores? Scatterplot of test score v. student-teacher ratio What does this figure show?

  9. We need to get some numerical evidence on whether districts with low STRs have higher test scores – but how?

  10. Initial data analysis: Compare districts with “small” (STR < 20) and “large” (STR ≥ 20) class sizes: 1. Estimation of  = difference between group means 2. Test the hypothesis that  = 0 3. Construct a confidence interval for 

  11. 1. Estimation

  12. 2. Hypothesis testing

  13. Compute the difference-of-means t-statistic:

  14. 3. Confidence interval

  15. What comes next…

  16. Review of Statistical Theory

  17. (a) Population, random variable, and distribution

  18. Population distribution of Y

  19. (b) Moments of a population distribution: mean, variance, standard deviation, covariance, correlation

  20. Moments, ctd.

  21. Random variables: joint distributions and covariance

  22. The covariance between Test Score and STR is negative: so is the correlation…

  23. The correlation coefficientis defined in terms of the covariance:

  24. The correlation coefficient measures linear association

  25. (c) Conditional distributions and conditional means

  26. Conditional mean, ctd.

  27. (d) Distribution of a sample of data drawn randomly from a population: Y1,…, Yn

  28. Distribution of Y1,…, Ynunder simple random sampling

  29. (a) The sampling distribution of

  30. The sampling distribution of , ctd.

  31. The sampling distribution of when Yis Bernoulli (p = .78):

  32. Things we want to know about the sampling distribution:

  33. The mean and variance of the sampling distribution of

  34. Mean and variance of sampling distribution of , ctd.

  35. The sampling distribution of when n is large

  36. The Law of Large Numbers:

  37. The Central Limit Theorem (CLT):

  38. Sampling distribution of when Y is Bernoulli, p = 0.78:

  39. Same example: sampling distribution of :

  40. Summary: The Sampling Distribution of

  41. (b) Why Use To Estimate Y?

  42. Why Use To Estimate Y?, ctd.

  43. Calculating the p-value, ctd.

  44. Calculating the p-value with Y known:

  45. Estimator of the variance of Y:

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