Lecture+8+Simple+Regression

Lecture+8+Simple+Regression - Lecture 8, ECON 123A, Fall...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 8, ECON 123A, Fall 2011 Dale J. Poirier 8-1 Lecture 8 Simple Regression 2.1 Definition of the Simple Regression Model Questions: C A state implements tough new penalties on drunk drivers. What is the effect on highway fatalities? C A school district cuts the size of its elementary school classes. What is the effect on its students’ standardized test scores? C You successfully complete one more year of college classes. What is the effect on your future earnings?
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Lecture 8, ECON 123A, Fall 2011 Dale J. Poirier 8-2 Generic question: What is the effect of changing a variable x on another variable y? C Linear regression is one vehicle for answering this question. C Ultimately our aim is to estimate the causal effect on y of a change in x. C The place to begin is with the joint distribution of y and x.
Background image of page 2
Lecture 8, ECON 123A, Fall 2011 Dale J. Poirier 8-3 C Suppose a researcher gets to observe x and then wishes to predict y, using a general function g(x). B What function g( @ ) should the researcher use? < The answer depends on the criteria employed to judge the quality of predictions. < One popular criterion is: choose g( @ ) so as to minimize the expected squared error of prediction. B Property CE.6 provided the answer: the population regression function E(y * x) is the optimal function, i.e.,
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Lecture 8, ECON 123A, Fall 2011 Dale J. Poirier 8-4 C This predictive motivation leads us to adopt y * x as our distribution of interest , and in particular its mean E(y * x) . B Define B So B The next theorem tells us that u and x have a special relationship involving the mean-independence concept introduced in Lecture 2.
Background image of page 4
Lecture 8, ECON 123A, Fall 2011 Dale J. Poirier 8-5 Theorem: Suppose E(y * x) exists. Define u = y - E(y * x). Then: (a) E(U * X) = 0 (2.6) (b) U is mean-independent of X. (c) Cov(X, U) = 0 (d) E(U) = 0
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Lecture 8, ECON 123A, Fall 2011 Dale J. Poirier 8-6 C Suppose we believe This gives rise to the simple linear regression model C In (2.1) u is mean-independent of x by definition . It is not an additional assumption. (2.1)
Background image of page 6
Lecture 8, ECON 123A, Fall 2011 Dale J. Poirier 8-7
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Lecture 8, ECON 123A, Fall 2011 Dale J. Poirier 8-8 Example 2.1: Suppose that soybean yield is determined by the model so that y = yield and x = fertilizer. The agricultural researcher is interested in the effect of fertilizer on yield, holding other factors fixed. This effect is given by $ 1 . The error term u contains factors such as land quality, rainfall, and so on. The coefficient $ 1 measures the effect of fertilizer on yield, holding other factors fixed: ) yield = $ 1 ) fertilizer. (2.3)
Background image of page 8
Lecture 8, ECON 123A, Fall 2011 Dale J. Poirier 8-9 Example 2.2: A model relating a person’s wage to observed education and other unobserved factors is If wage is measured in dollars per hour and educ is years of education, then $ 1 measures the change in hourly wage given another year of education, holding all other factors fixed. Some of those factors include labor force experience, innate ability, tenure with current employer, work ethic, and innumerable other things.
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 76

Lecture+8+Simple+Regression - Lecture 8, ECON 123A, Fall...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online