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Introduction to Econometrics

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Introduction to. Econometrics. The Statistical Analysis of Economic (and related) Data ... (You should already know how to interpret this table) ... – PowerPoint PPT presentation

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Title: Introduction to Econometrics


1
Introduction toEconometrics
  • The Statistical Analysis of Economic (and
    related) Data

2
Brief Overview of the Course
3
This course is about using data to measure causal
effects.
4
In this course you will
5
Review of Probability and Statistics(SW Chapters
2, 3)
6
The California Test Score Data Set
7
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.

8
Do districts with smaller classes have higher
test scores? Scatterplot of test score v.
student-teacher ratio
  • What does this figure show?

9
We need to get some numerical evidence on whether
districts with low STRs have higher test scores
but how?
10
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 ?

11
1. Estimation
12
2. Hypothesis testing
13
Compute the difference-of-means t-statistic
14
3. Confidence interval
15
What comes next
16
Review of Statistical Theory
17
(a) Population, random variable, and distribution
18
Population distribution of Y
19
(b) Moments of a population distribution mean,
variance, standard deviation, covariance,
correlation
20
Moments, ctd.
21
(No Transcript)
22
2 random variables joint distributions and
covariance
23
The covariance between Test Score and STR is
negative
so is the correlation
24
The correlation coefficient is defined in terms
of the covariance
25
The correlation coefficient measures linear
association
26
(c) Conditional distributions and conditional
means
27
Conditional mean, ctd.
28
(d) Distribution of a sample of data drawn
randomly from a population Y1,, Yn
29
Distribution of Y1,, Yn under simple random
sampling
30
(No Transcript)
31
(a) The sampling distribution of
32
The sampling distribution of , ctd.
33
The sampling distribution of when Y is
Bernoulli (p .78)
34
Things we want to know about the sampling
distribution
35
The mean and variance of the sampling
distribution of
36
(No Transcript)
37
Mean and variance of sampling distribution of
, ctd.
38
The sampling distribution of when n is large
39
The Law of Large Numbers
40
The Central Limit Theorem (CLT)
41
Sampling distribution of when Y is Bernoulli,
p 0.78
42
Same example sampling distribution of

43
Summary The Sampling Distribution of
44
(b) Why Use To Estimate ?Y?
45
Why Use To Estimate ?Y?, ctd.
46
(No Transcript)
47
(No Transcript)
48
Calculating the p-value, ctd.
49
Calculating the p-value with ?Y known
50
Estimator of the variance of Y
51
Computing the p-value with estimated
52
What is the link between the p-value and the
significance level?
53
At this point, you might be wondering,...
54
Comments on this recipe and the Student
t-distribution
55
Comments on Student t distribution, ctd.
56
Comments on Student t distribution, ctd.
57
(No Transcript)
58
Comments on Student t distribution, ctd.
59
The Student-t distribution summary
60
(No Transcript)
61
Confidence intervals, ctd.
62
Summary
63
Lets go back to the original policy question
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