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

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

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

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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.

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

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

Compute the difference-of-means t-statistic:

(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

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

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

(a) The sampling distribution of population:

The sampling distribution of , ctd. population:

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 :

Summary: The Sampling Distribution of population:

(b) Why Use To Estimate population: Y?

Why Use To Estimate population: Y?, ctd.

Calculating the p-value, ctd. population:

Calculating the p-value with population: Y known:

Estimator of the variance of population: Y:

Computing the p-value with estimated population: :

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

At this point, you might be wondering,... population:

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

Comments on Student t distribution, ctd. population:

Comments on Student t distribution, ctd. population:

Comments on Student t distribution, ctd. population:

The Student-t distribution – summary population:

Confidence intervals, ctd. population:

Summary: population:

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