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Introduction to Econometrics

Introduction to Econometrics. The Statistical Analysis of Economic (and related) Data. 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).

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Introduction to Econometrics

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  1. Introduction toEconometrics The Statistical Analysis of Economic (and related) Data

  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 relationship between test scores and the STR.

  8. 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. 2 random variables: joint distributions and covariance

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

  23. The correlation coefficient is 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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