Lecture 7 Prof. Arkonac's Slides (Ch 5.3 - Ch 6.3) for ECO 4000

# Lecture 7 Prof. Arkonac's Slides (Ch 5.3 - Ch 6.3) for ECO 4000

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

Introduction to Multiple Regression ECO 4000, Statistical Analysis for Economics and Finance Fall 2010 Lecture 7 Prof: Seyhan Erden Arkonac, PhD 1

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

View Full Document
Where we stopped last time, and what will we do today? Regression when X is a binary (dummy) variable (i.e. X=0 or X=1) Heteroskedasticity and Homoskedasticity (variance of the error term is constant? Or not?) The theoretical foundation of the OLS (not in detail!) Omitted variable bias THE MULTIPLE REGRESSION MODEL 2
3 Regression when X is Binary (Section 5.3) Sometimes a regressor is binary: X = 1 if small class size, = 0 if not X = 1 if female, = 0 if male X = 1 if treated (experimental drug), = 0 if not Binary regressors are sometimes called “dummy” variables. So far, 1 has been called a “slope,” but that doesn’t make sense if X is binary. How do we interpret regression with a binary regressor?

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

View Full Document
4 Interpreting regressions with a binary regressor Y i = 0 + 1 X i + u i , where X is binary ( X i = 0 or 1): When X i = 0, Y i = 0 + u i the mean of Y i is 0 that is, E ( Y i | X i =0) = 0 When X i = 1, Y i = 0 + 1 + u i the mean of Y i is 0 + 1 that is, E ( Y i | X i =1) = 0 + 1 so : 1 = E ( Y i | X i =1) – E ( Y i | X i =0) = population difference in group means
5 Example : Let D i = 1 if 20 0 if 20 i i STR STR OLS regression : TestScore = 650.0 + 7.4 D (1.3) ( 1.8 ) Tabulation of group means : Class Size Average score ( Y ) Std. dev. ( s Y ) N Small ( STR ≤ 20) 657.4 19.4 238 Large ( STR > 20) 650.0 17.9 182 Difference in means: small large YY = 657.4 – 650.0 = 7.4 Standard error: SE = 22 sl ss nn = 19.4 17.9 238 182 = 1.8

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

View Full Document
6 Summary: regression when X i is binary (0/1) Y i = 0 + 1 X i + u i 0 = mean of Y when X = 0 0 + 1 = mean of Y when X = 1 1 = difference in group means, X =1 minus X = 0 SE( 1 ˆ ) has the usual interpretation t -statistics, confidence intervals constructed as usual This is another way (an easy way) to do difference-in-means analysis The regression formulation is especially useful when we have additional regressors ( as we will very soon )
7 Heteroskedasticity and Homoskedasticity, and Homoskedasticity-Only Standard Errors (Section 5.4) What…? Consequences of homoskedasticity Implication for computing standard errors What do these two terms mean? If var( u | X = x ) is constant – that is, if the variance of the conditional distribution of u given X does not depend on X then u is said to be homoskedastic . Otherwise, u is heteroskedastic .

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

View Full Document
To understand heteroskedasticity better; Wage i = β 0 + β 1 Male i + u i Wage i = β 0 + u i for women Wage i = β 0 + β 1 + u i for men For women, u i is the deviation of the i th woman’s wage from the population mean wage for women (β 0 ) and for men, u i is the deviation of the i th man’s wage from the population mean wage for men (β 0 1 ) The following 3 statements are the same: “The variance does not depend on the regressor Male”= “the variance of wage is the same for men as it is for women” = “error term is homoskedastic” 8
9 Example : hetero/homoskedasticity in the case of a binary regressor (that is, the comparison of means) Standard error when group variances are unequal : SE = 22 sl ss nn Standard error when group variances are equal : SE = 11 p s where 2 p s = ( 1) ( 2 s s l l n s n s (SW, Sect 3.6) s p = “pooled estimator of 2 ” when 2 l = 2 s

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 05/05/2011 for the course ECON 4000 taught by Professor Arkonac during the Spring '11 term at CUNY Baruch.

### Page1 / 71

Lecture 7 Prof. Arkonac's Slides (Ch 5.3 - Ch 6.3) for ECO 4000

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

View Full Document
Ask a homework question - tutors are online