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

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&02ECONOMETRICS IFall 2011 Lecture notesChapters 1-2-3

This course is about using data to measure causal effects.

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.

Question: Do districts with smaller classes have higher test scores? Scatterplot of test score v. student-teacher ratio

What does this figure show?

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

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 

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

Moments, ctd. standard deviation, covariance, correlation

R standard deviation, covariance, correlationandom variables: joint distributions and covariance

The standard deviation, covariance, correlationcovariance between Test Score and STR is negative:

so is the correlation…

The standard deviation, covariance, correlationcorrelation coefficientis defined in terms of the covariance:

The correlation coefficient measures standard deviation, covariance, correlationlinear association

(c) Conditional distributions and conditional means standard deviation, covariance, correlation

Conditional mean, ctd. standard deviation, covariance, correlation

Distribution of Y population: 1,…, Ynunder simple random sampling

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

The sampling distribution of when population: n is large

The population: Law of Large Numbers:

The population: Central Limit Theorem (CLT):

Same example population: : sampling distribution of :

(b) Why Use To Estimate population: Y?

Why Use To Estimate population: Y?, ctd.

Calculating the p-value with population: Y known:

What is the link between the population: p-value and the significance level?

Comments on this recipe and the Student population: t-distribution

Summary: population:

Let population: ’s go back to the original policy question: