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 PowerPoint PPT Presentation


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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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Ec 331 01 02 econometrics i fall 2011 lecture notes chapters 1 2 3

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


Brief overview of the course

Brief Overview of the Course


This course is about using data to measure causal effects

This course is about using data to measure causal effects.


In this course you will

In this course you will:


Review of probability and statistics sw chapters 2 3

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


The california test score data set

The California Test Score Data Set


Initial look at the data you should already know how to interpret this table

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.


Ec 331 01 02 econometrics i fall 2011 lecture notes chapters 1 2 3

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

What does this figure show?


Ec 331 01 02 econometrics i fall 2011 lecture notes chapters 1 2 3

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

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 


1 estimation

1. Estimation


2 hypothesis testing

2. Hypothesis testing


Compute the difference of means t statistic

Compute the difference-of-means t-statistic:


3 confidence interval

3. Confidence interval


What comes next

What comes next…


Review of statistical theory

Review of Statistical Theory


A population random variable and distribution

(a) Population, random variable, and distribution


Population distribution of y

Population distribution of Y


B moments of a population distribution mean variance standard deviation covariance correlation

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


Moments ctd

Moments, ctd.


R andom variables joint distributions and covariance

Random variables: joint distributions and covariance


The covariance between test score and str is negative

The covariance between Test Score and STR is negative:

so is the correlation…


The correlation coefficient is defined in terms of the covariance

The correlation coefficientis defined in terms of the covariance:


The correlation coefficient measures linear association

The correlation coefficient measures linear association


C conditional distributions and conditional means

(c) Conditional distributions and conditional means


Conditional mean ctd

Conditional mean, ctd.


D distribution of a sample of data drawn randomly from a population y 1 y n

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


Distribution of y 1 y n under simple random sampling

Distribution of Y1,…, Ynunder simple random sampling


A the sampling distribution of

(a) The sampling distribution of


The sampling distribution of ctd

The sampling distribution of , ctd.


The sampling distribution of when y is bernoulli p 78

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


Things we want to know about the sampling distribution

Things we want to know about the sampling distribution:


The mean and variance of the sampling distribution of

The mean and variance of the sampling distribution of


Mean and variance of sampling distribution of ctd

Mean and variance of sampling distribution of , ctd.


The sampling distribution of when n is large

The sampling distribution of when n is large


The law of large numbers

The Law of Large Numbers:


The central limit theorem clt

The Central Limit Theorem (CLT):


Sampling distribution of when y is bernoulli p 0 78

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


Same example sampling distribution of

Same example: sampling distribution of :


Summary the sampling distribution of

Summary: The Sampling Distribution of


B why use to estimate y

(b) Why Use To Estimate Y?


Why use to estimate y ctd

Why Use To Estimate Y?, ctd.


Calculating the p value ctd

Calculating the p-value, ctd.


Calculating the p value with y known

Calculating the p-value with Y known:


Estimator of the variance of y

Estimator of the variance of Y:


Computing the p value with estimated

Computing the p-value with estimated:


What is the link between the p value and the significance level

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


At this point you might be wondering

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


Comments on this recipe and the student t distribution

Comments on this recipe and the Student t-distribution


Comments on student t distribution ctd

Comments on Student t distribution, ctd.


Comments on student t distribution ctd1

Comments on Student t distribution, ctd.


Comments on student t distribution ctd2

Comments on Student t distribution, ctd.


The student t distribution summary

The Student-t distribution – summary


Confidence intervals ctd

Confidence intervals, ctd.


Summary

Summary:


Let s go back to the original policy question

Let’s go back to the original policy question:


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