New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

ECON 300 Week 3 Notes

by: Patricia Soto

ECON 300 Week 3 Notes ECON 300

Patricia Soto
GPA 3.89

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Week 3 Notes
Irina Horoi
Class Notes
25 ?




Popular in Econometrics

Popular in Economcs

This 4 page Class Notes was uploaded by Patricia Soto on Sunday January 31, 2016. The Class Notes belongs to ECON 300 at University of Illinois at Chicago taught by Irina Horoi in Winter 2016. Since its upload, it has received 43 views. For similar materials see Econometrics in Economcs at University of Illinois at Chicago.


Reviews for ECON 300 Week 3 Notes


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 01/31/16
ECON  300     Week 3 Y = βo + β1x+ u Y: dependent variable, predicting variable, left hand side variable (lhs),  y is a function of x • Ex. Y = test scores X: independent variable, (variables that can effect y), right hand side variable • Ex. X = class size U: error term, (captures ALL other things that affect y, note: it’s not in the model) • Ex. Teacher quality Suppose we have two values of x that differ by Δx (Δ= change/difference) • Δy =β1Δx if the unobserved factors that affect y are the same for both values of x β1: slope (constant slope, linear function), the linear slope parameter means that the effect on y of a one unit change in c is the same regardless of the level of x βo: Intercept parameter, tells use the value of y when x = 0. We are interested in β1 as a causal parameter! This depends on our assumptions about the error term u. Two primary assumptions about u that would allow us to interpret β1 as a causal parameter. • E(u) = 0 (The mean of the distribution of unobservable factors is centered on 0. Ex. Avg teacher quality = 0) • E(u|x) = E(u) ( The mean value doesn’t depend on x at all because it’s independent on x. There’s no relationship between u and x.) • Therefore, E(u)=0 (zero conditional mean assumption) Taking the conditional expectation of y: E(y|x) = E(βo+β1x +u|x) =E(βo|x) + E(β1x|x) + E(u|x) =βo + β1x + 0 => E(y|x) = βo + β1x E(y|x) = y1 E(y|x) =y2 ECON  300     The relationship defined above only tells us about the mean or average value of y based on what we know about x. st 1 to estimate Y = βo + β1x+ u we need data! i | x | y 1| 20| 85 2| 23| 83 …….. n|n|n Yi = βo + β1xi+ ui = indicates estimate To derive βo, β1 • E(u) = 0 • Cor(x,u) =0 => E[(x -µx)(u-µu)] = E(xu -xµ - uµx -µxµu) = E(xu) – E(xuµ_ - E(ux) – E(µx) (Note: µu= E (u) = 0 = E(x) *E(u)st 0 using our 1 equation, E (u) = 0, => E (Y-β1x-βo) = 0 o Implies => 1/n *Σ( Yi - βo -β1xi) = 0 o 1/n* Ybar (Ybar = average y) nd 2 equation: E[x(y-β1x - βo)] = 0 Taking the first equation: 1/n *Σ( Yi - βo -β1xi) = 0 You can simplify to: = ybar – 1/n βo - β1xbar = 0 Then rearrange for βo. Taking the 2 nd equation: E[x(y-β1x - βo)] = 0 • 1/nΣxi(yi-βo -β1x) = 0 Aside: will need to use these properties: • Σxi(xx-xbar) = Σ(xi – xbar)^2 • Σxi(yi-ybar) = Σ(xi-x)(yi-ybar) Going back to the second equation: Plug in for βo => Σxi(yi-(ybar-β1xbar)-β1xi)=0 If we multiply top and bottom by 1/n then => β1 = Cor(xy)/ Var(x) To solve for βo plug β1 into the original second equation Example: True population model for education attainment and annual salary is this: Annual Salary = βo + β1education + u We need data on salary + years of schooling/ We got 6 people to tell us that: ECON  300     Observation Salary $ Education (year) 1 45000 15 2 50000 17 3 60000 17 4 30000 13 5 45000 14 6 45000 17 β1 = Σ(educai – educ-bar)(salary – salary-bar)/ (Σ (educ- educ-bar)^2 mean salary (salary-bar) = 45,833.33 mean education (educ-bar) = 15.5 Observation (educai- educ- (salaryi-salary- Column 2*3 bar) bar) 1 -.5 -833.33 416.67 2 1.5 4166.67 1250 3 1.5 14166.67 21250 4 -2.5 -15833.33 39583.33 5 -1.5 -833.33 1250 6 1.5 -833.33 -1250 Σ(educi-educ-bar)(sali-sal-bar) = 67500 (numerator) Σ(educi-educ-bar)^2 (denominator) Observation (educi-educ-bar)^2 1 .25 2 2.25 3 2.25 4 6.25 5 2.25 6 2.25 Now you need to sum all of them up to get = 15.5 β1 = 67500/15/5 = $4354.84 COOL. YOU GUYS WE JUST REGRESSED X ON Y. • SO WHAT DOES THIS MEAN? o For every additional year of schooling you gain $4354.84 annual salary then without the extra year. (my interpretation) o β1 is interpreted as an additional year of education is associated with an average increase in annual salary of $4354.84 ECON  300     The estimated values of the slope + intercept are ordinary least squares (OLS). To see why: Yi = βo +βixi If we take our real values of y and subtract Yi we get the residuals (ui) • Ui = yi – yi = yi - βo - β1x  


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Allison Fischer University of Alabama

"I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over $600 per month. I LOVE StudySoup!"

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.