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Introduction to Econometrics

- What do I expect of you before you come to

class? - Print out the slides.
- Read the chapter(s), and as you read, write down

on the slides any questions you have. - Therefore, when I am lecturing, I do not expect

it to be the first time you are hearing about a

concept. - If you dont do this, it will seem like I am

going really, really fast. - And if this approach to teaching, which places

high demand on your pre-class preparation,

doesnt suit you, I wont be offended if you take

Eco205 from someone else.

Announcements

- Read Chapters 4 and 5 for Tuesday (see syllabus)
- Remember to attend lab today
- Please bring the Stata lab book with you
- Lab assignments will be due (which means sending

an email with the requested work to both your TA

and me) by 1000 on the Tuesday following lab. - Please write the subject line in your email as

follows 205 Lab01 mafoley

Yesterday in the news

- AFFORDABLE HOMES VITAL TO HEALTH AND EDUCATIONAL

ACHIEVEMENTS OF AMERICA?S CHILDREN - First-Ever Comprehensive Look at the Impact of

Housing on Health and Education Reveals the Link

Between Decent, Affordable Homes and a Brighter

Future for America?s Families - In-Depth Research Makes Strong Case for Elevating

Housing on the National Agenda - This research analysis presents evidence that

children of homeowners and their families achieve

better physical and mental health outcomes

compared to renters, including fewer long-term

illnesses, as well as lower blood pressure and

depression levels. Approximately 85 percent of

homebuyers reported that homeownership made them

feel better about themselves. These findings

point to a strong correlation between

homeownership and overall health and well-being.

Since much of the benefits of homeownership

appear to be tied to the stability it provides,

it is possible that similar benefits may be

achieved through more stable forms of rental

housing. - Source www.enterprisecommunity.org/about/media/ne

ws_releases/documents/2007/july/media2520housing_

impacts_press_release.pdf

Introduction toEconometrics

- The Statistical Analysis of Economic (and

related) Data

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 doesnt tell us anything about the

relationship between test scores and the STR.

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 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 ?

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.

(No Transcript)

2 random variables joint distributions and

covariance

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 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,, Yn under simple random

sampling

(No Transcript)

(a) The sampling distribution of

The sampling distribution of , ctd.

The sampling distribution of when Y is

Bernoulli (p .78)

Things we want to know about the sampling

distribution

The mean and variance of the sampling

distribution of

(No Transcript)

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.

(No Transcript)

(No Transcript)

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.

(No Transcript)

Comments on Student t distribution, ctd.

The Student-t distribution summary

(No Transcript)

Confidence intervals, ctd.

Summary

Lets go back to the original policy question

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