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&02ECONOMETRICS IFall 2011 Lecture notesChapters 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


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 


1. Estimation


2. Hypothesis testing


Compute the difference-of-means t-statistic:


3. Confidence interval


What comes next…


Review of Statistical Theory


(a) Population, random variable, and distribution


Population distribution of Y


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


Moments, ctd.


Random variables: joint distributions and covariance


The covariance between Test Score and STR is negative:

so is the correlation…


The correlation coefficientis defined in terms of the covariance:


The correlation coefficient measures linear association


(c) Conditional distributions and conditional means


Conditional mean, ctd.


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


Distribution of Y1,…, Ynunder simple random sampling


(a) The sampling distribution of


The sampling distribution of , ctd.


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


Things we want to know about the sampling distribution:


The mean and variance of the sampling distribution of


Mean and variance of sampling distribution of , ctd.


The sampling distribution of when n is large


The Law of Large Numbers:


The Central Limit Theorem (CLT):


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


Same example: sampling distribution of :


Summary: The Sampling Distribution of


(b) Why Use To Estimate Y?


Why Use To Estimate Y?, ctd.


Calculating the p-value, ctd.


Calculating the p-value with Y known:


Estimator of the variance of Y:


Computing the p-value with estimated:


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


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


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, ctd.


The Student-t distribution – summary


Confidence intervals, ctd.


Summary:


Let’s go back to the original policy question:


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