12_MultivariateA_handout

# 12_MultivariateA_handout - Multivariate OLS 73-261...

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Multivariate OLS 73-261 Econometrics September 1, 2010 Wooldridge 3.1-3.2, 6.3

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p. 2 © CMU / Y. Kryukov 73-261 1.2 Multivariate OLS Announcements Homework 1 – due next Wednesday Recitation this Friday Quiz – based on this week More GRETL
p. 3 © CMU / Y. Kryukov Plan New topic: Multiple independent variables Basics (Wooldridge 3.1-3.2) Selection of variables (6.3) Mean & variance of the estimates (3.3-3.4) Matrix notation – optional as of this year Simpler notation, easier derivation But requires linear algebra It usually is the graduate school material We will show just a bit for those who know it 73-261 1.2 Multivariate OLS

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p. 4 © CMU / Y. Kryukov Multiple independent variables Closer fit = Better prediction D ( Q ) also depends on income, substitutes, etc. “Ceteris paribus” effects: How much does education increase wage? wage = β 0 + 1 years-of-education ? But wage is also affected by ability, … … and able people tend to get more education Is education just a “signal” of ability? Need effect of education given same ability How do we separate the two effects? wage = 0 + 1 years-of-education + 2 ability 73-261 1.2 Multivariate OLS
p. 5 © CMU / Y. Kryukov Population equation y = β 0 + 1 x 1 + 2 x 2 + u y = wage x 1 = years of education x 2 = ability, e.g. SAT score, IQ test, etc. More generally: y = 0 + 1 x 1 + + k x k + u What does Math call [ 1 x 1 +… + k x k ]? It’s the . . . . . . . . . . . . . . .: . . . . = x 0 0 + x 1 1 +… + x k k Note that we assume x 0 1 , so 0 is part of the β vector 73-261 1.2 Multivariate OLS

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p. 6 © CMU / Y. Kryukov The equation – matrix notation
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12_MultivariateA_handout - Multivariate OLS 73-261...

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