1. Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Chapter 13 Panel Data

2. 13-2 Learning Objectives Understand the Nature of Panel Data Employ Pooled Cross-Section Analysis Estimate Panel Data Models

3. 13-3

4. 13-4 The Nature of Panel Data

5. 13-5 The Nature of Panel Data

6. 13-6 Pooled Cross-Section Analysis Pooled cross-section analysis is when more than one time- period of cross-sectional data are estimated in the same model.

7. 13-7 Pooled Cross-Section Analysis With Year Dummies Adding year dummy variables (for n-1 years) starts to control for the fact that there are different time periods in these data.

8. 13-8 First-Differenced Data

9. 13-9 First-Differenced Data

10. 13-10 First-Differenced Data In theory, this works because: First-differencing the data removes the time-invariant component from the error term because. Doing so generates unbiased estimates because, which is correlated with the independent variables, is removed through the differencing. Notes: In first-differenced models, it is impossible to estimate marginal effects for two types of independent variables 1)Those that are constant across time periods, such as gender, years of education, marital status, and race, because all of the first- differenced values equal. 2)Those that increase by a fixed amount over time, such as years of age, work experience, etc., because all of the first-differenced values will equal the same fixed value.

11. 13-11 Fixed-Effects Models

12. 13-12 Fixed-Effects Models

13. 13-13 Fixed-Effects Models In theory, this works because: Differencing the data remove the time-invariant component from the error term because. Doing so increases the efficiency of our estimates by exploiting the panel nature of our data to control for an unobserved component of the error term. Notes: In fixed-effects models, it is impossible to estimate marginal effects for two types of independent variables 1)Those that are constant across time periods, such as gender, years of education, marital status, and race, because all of the first- differenced values equal. 2)Those that increase by a fixed amount over time, such as years of age, work experience, etc., because all of the first-differenced values will equal the same fixed value.

14. 13-14 Random-Effects Models

15. 13-15 Random-Effects Models

16. 13-16 Random-Effects Models In theory, this works because: Quasi-differencing the data in this case does not remove the time-invariant component from the error term, but that does not cause bias because the are not correlated with the error term. This process does, however, increase efficiency because it accounts for the fact that the individual values are related to each other over time. Note: Random effects model, we note that it will generally be considered inappropriate for economic applications, because in nearly all of the economic cases that we encounter the time invariant component of the error term, will be correlated with one or more the independent variables, rendering the fixed- effects model more appropriate.