Understanding Dummy Variables in Regression Analysis, Study notes of Economic Analysis

Download Understanding Dummy Variables in Regression Analysis and more Study notes Economic Analysis in PDF only on Docsity! 1 Chapter 7, Dummy Variable Dummy variable can only take values 1 and 0. It is categorical, that means the numbers 1 and 0 have no numerical meanings (we cannot say 1 is greater than 0). In this chapter we use dummy as regressor. Chapter 17 (covered in eco411) shows how to use dummy as the dependent variable. First let’s use wage data and consider a simple regression 𝑤𝑎𝑔𝑒 = 𝛽0 + 𝛽1𝐷 + 𝑢 (1) where 𝐷 = 0 for male, and 𝐷 = 1 for female. For dummy variable, you have to be clear 𝐷 = 0 is for which group (called base group). Later all comparisons are made relative to the base group. You can report the frequency of 𝐷 using tab D. The key to understand the dummy-variable-model is to discuss: when = 0, 𝑤𝑎𝑔𝑒 = _____________________. If we take expectation we get ___________________ when = 1, 𝑤𝑎𝑔𝑒 = _____________________. If we take expectation we get ___________________ So 𝛽0 can be interpreted as ________________________; and 𝛽1 can be interpreted as____________________ This result suggests that we can conduct the two-sample t test (the comparison of means test, stata command: ttest wage, by(D)) using the simple regression (1) that involves dummy. Now consider a multiple regression 𝑤𝑎𝑔𝑒 = 𝛽0 + 𝛽1𝐷 + 𝛽2𝑥 + 𝛽3(𝐷 ∗ 𝑥) + 𝑢 (2) For example x can be exper, and 𝐷 ∗ 𝑥 is the interaction term (product of) x and dummy. Let’s discuss again: when 𝐷 = 0, _________________________________________________________________________________________ when 𝐷 = 1, _________________________________________________________________________________________ 𝛽0 can be interpreted as _________________________________________________________; 𝛽1 can be interpreted as _________________________________________________________; 𝛽2 can be interpreted as _________________________________________________________; 𝛽3 can be interpreted as _________________________________________________________; How to show 𝛽1 and 𝛽3 in graph?