lect12_2010 - Introduction to Econometrics Econ 322 Fall...

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1 / 20 Introduction to Econometrics Econ 322 Fall, 2010 Lecture 12: Simple Linear Regression IV October 13, 2010
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Topics Covered triangleright Topics Covered What if X is a binary variable? Determining Performance of the Regression Reporting Regression Results The determinants of Earnings (revisited) Improving our Model Improving our Model (cont) Omitting a relevant variable in the SLRM Omitting a relevant variable in the SLRM (cont) Omitting a relevant variable in the SLRM (cont) Omitted Variable Bias Our Example Correcting Omitted Variable Bias 2 / 20 1. Binary variables 2. Regression statistics 3. Reporting the regression results 4. Omitted variable bias
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What if X is a binary variable? Topics Covered triangleright What if X is a binary variable? Determining Performance of the Regression Reporting Regression Results The determinants of Earnings (revisited) Improving our Model Improving our Model (cont) Omitting a relevant variable in the SLRM Omitting a relevant variable in the SLRM (cont) Omitting a relevant variable in the SLRM (cont) Omitted Variable Bias Our Example Correcting Omitted Variable Bias 3 / 20 square Sometimes we want to look into the effect a discrete (or binary) variables has on the dependent variable. square For example, suppose we want to see what effect gender has on hourly earnings. square Consider the following variable: female i = braceleftBigg 1 if individual i is female 0 if individual i is not female
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Binary Variables (cont) Topics Covered triangleright What if X is a binary variable? Determining Performance of the Regression Reporting Regression Results The determinants of Earnings (revisited) Improving our Model Improving our Model (cont) Omitting a relevant variable in the SLRM Omitting a relevant variable in the SLRM (cont) Omitting a relevant variable in the SLRM (cont) Omitted Variable Bias Our Example Correcting Omitted Variable Bias 4 / 20 square This variable (female) is an example of a binary variable as it can take only one of two possible values (0 or 1). square Consider the regression earnings i = β 0 + β 1 female i + epsilon1 i . square How do we interpret β 1 ? square Before we interpreted β 1 as β 1 = E bracketleftbigg Δ earnings Δ Female bracketrightbigg square This interpretation doesn’t make much sense in this case. So consider the following interpretation:
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Binary Variables (cont) Topics Covered triangleright What if X is a binary variable? Determining Performance of the Regression Reporting Regression Results The determinants of Earnings (revisited) Improving our Model Improving our Model (cont) Omitting a relevant variable in the SLRM Omitting a relevant variable in the SLRM (cont) Omitting a relevant variable in the SLRM (cont) Omitted Variable Bias Our Example Correcting Omitted Variable Bias 5 / 20 1. what is the expected earnings for a female? This is 2. what is the expected earnings for a male? This is square From these two statements we see that 1. is the expected wage of males (the base group) 2. is the difference in expected earnings between females and males. i.e.
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Binary Variables (cont)
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