# Motivation (2 pages)

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# Motivation

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## Motivation

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Lecture 12

Lecture number:
12
Pages:
2
Type:
Lecture Note
School:
Cornell University
Course:
Econ 3120 - Applied Econometrics
Edition:
1
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Econ 3120 1st Edition Lecture 12 Outline of Current Lecture I Goodness of Fit II Unbiasedness Current Lecture III Motivation Motivation Multiple regression allows us to account for more than one factor in explaining our dependent variable y Consider the familiar example of the relationship between schooling and wages Suppose we have data on the SAT score of the individual while she was in high school We might be interested in estimated a relationship of the form log wage 0 1educ 2SAT u Or to take a simple model from macroeconomics suppose we want to estimate the determinants of a country s growth rate We may model the growth rate of a country from 1980 2000 as a function of per capita income in 1980 and income inequality as measured by the Gini coefficient growthrate 0 1inc80 2Gini u A multivariate model with two independent variables x1 and x2 takes the form y 0 1x1 2x2 u In this case 1 represents the change in the y for a one unit change in x1 holding all other factors x2 and u fixed This is the partial derivative of y with respect to x1 holding x2 and u fixed Our x 0 s don t have to be separate variables they can actually be f unctions of the same variable For example suppose we are studying the relationship between household consumption and income and we model the relationship as follows cons 0 inc 2inc2 u 1 In this case the effect of income on consumption depends on both 1 and 2 inc cons u constant 1 2inc The general form of the multivariate model with k independent variables is y 0 1x1i 2x2i kxki ui 1 Note that I use the notation x ji for observation i and variable x j while Wooldridge uses xi j Analogous to the bivariate model the key assumption is the independence of the error term and the regressors independent variables E u x1 x2 xk 0 This implies that u must be independent of and uncorrelated with all of the explanatory variables x j If u is correlated with any of these variables the assumption does not hold and our estimates will be unbiased more on this

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