Introduction to Econometrics

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Introduction toEconometrics

• The Statistical Analysis of Economic (and
  related) Data

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Brief Overview of the Course
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This course is about using data to measure causal
effects.
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In this course you will
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Review of Probability and Statistics(SW Chapters
2, 3)
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The California Test Score Data Set
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Initial look at the data(You should already
know how to interpret this table)

• This table doesnt tell us anything about the
  relationship between test scores and the STR.

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

• What does this figure show?

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We need to get some numerical evidence on whether
districts with low STRs have higher test scores
but how?
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Initial data analysis Compare districts with
small (STR lt 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 ?

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1. Estimation
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2. Hypothesis testing
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Compute the difference-of-means t-statistic
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3. Confidence interval
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What comes next
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Review of Statistical Theory
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(a) Population, random variable, and distribution
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Population distribution of Y
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(b) Moments of a population distribution mean,
variance, standard deviation, covariance,
correlation
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Moments, ctd.
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2 random variables joint distributions and
covariance
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The covariance between Test Score and STR is
negative
so is the correlation
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The correlation coefficient is defined in terms
of the covariance
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The correlation coefficient measures linear
association
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(c) Conditional distributions and conditional
means
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Conditional mean, ctd.
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(d) Distribution of a sample of data drawn
randomly from a population Y1,, Yn
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Distribution of Y1,, Yn under simple random
sampling
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(a) The sampling distribution of
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The sampling distribution of , ctd.
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The sampling distribution of when Y is
Bernoulli (p .78)
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Things we want to know about the sampling
distribution
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The mean and variance of the sampling
distribution of
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Mean and variance of sampling distribution of
, ctd.
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The sampling distribution of when n is large
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The Law of Large Numbers
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The Central Limit Theorem (CLT)
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Sampling distribution of when Y is Bernoulli,
p 0.78
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Same example sampling distribution of

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Summary The Sampling Distribution of
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(b) Why Use To Estimate ?Y?
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Why Use To Estimate ?Y?, ctd.
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Calculating the p-value, ctd.
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Calculating the p-value with ?Y known
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Estimator of the variance of Y
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Computing the p-value with estimated
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What is the link between the p-value and the
significance level?
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At this point, you might be wondering,...
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Comments on this recipe and the Student
t-distribution
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Comments on Student t distribution, ctd.
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Comments on Student t distribution, ctd.
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Comments on Student t distribution, ctd.
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The Student-t distribution summary
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Confidence intervals, ctd.
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Summary
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Lets go back to the original policy question