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Chapter 10 Regression with Panel Data

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2 Regression with Panel Data (SW Chapter 10)

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3 Notation for panel data

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4 Panel data notation, ctd.

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5 Why are panel data useful?

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6 Example of a panel data set: Traffic deaths and alcohol taxes

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7 U.S. traffic death data for 1982:

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8 U.S. traffic death data for 1988

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9 Why might there be higher more traffic deaths in states that have higher alcohol taxes?

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10 These omitted factors could cause omitted variable bias.

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11 Example #2: cultural attitudes towards drinking and driving:

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12 Panel Data with Two Time Periods (SW Section 10.2)

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15 Example: Traffic deaths and beer taxes

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16 FatalityRate v. BeerTax:

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17 Fixed Effects Regression (SW Section 10.3)

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20 The regression lines for each state in a picture

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22 Summary: Two ways to write the fixed effects model n-1 binary regressor form

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23 Fixed Effects Regression: Estimation

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24 1. n-1 binary regressors OLS regression

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25 2. Entity-demeaned OLS regression

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26 Entity-demeaned OLS regression, ctd.

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27 Entity-demeaned OLS regression, ctd.

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28 Example: Traffic deaths and beer taxes in STATA

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29 Example, ctd. For n = 48, T = 7:

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30 By the way… how much do beer taxes vary?

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33 Regression with Time Fixed Effects (SW Section 10.4)

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34 Time fixed effects only

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35 Two formulations for time fixed effects

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36 Time fixed effects: estimation methods

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38 Combined entity and time fixed effects

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39 The Fixed Effects Regression Assumptions and Standard Errors for Fixed Effects Regression (SW Section 10.5 and App. 10.2)

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40 A. Extension of LS Assumptions to Panel Data

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41 Assumption #1: E(u it |X i1,…,X iT, i) = 0

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42 Assumption #2: (X i1,…,X iT,Y i1,…,Y iT ), i =1,…,n, are i.i.d. draws from their joint distribution.

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43 Assumption #5: corr(u it,u is |X it,X is, i) = 0 for t s

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44 Assumption #5 in a picture:

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45 What if Assumption #5 fails: so corr(u it,u is |X it,X is, i) 0?

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46 B. Standard Errors

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47 Sampling distribution of fixed effects estimator, ctd.

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48 Sampling distribution of fixed effects estimator, ctd.

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49 Case I: when u it, u is are uncorrelated

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50 Case II: u it and u is are correlated – so Assumption 5 fails

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51 Case II: Clustered Standard Errors

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52 Comments on clustered standard errors:

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53 Comments on clustered standard errors, ctd.

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54 Comments on clustered standard errors, ctd.

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55 Implementation in STATA

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56 Case II: treat uit and uis as possibly correlated

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57 Try adding year effects:

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59 Fixed Effects Regression Results Dependent variable: Fatality rate

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60 Summary: SEs for Panel Data in a picture:

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61 Application: Drunk Driving Laws and Traffic Deaths (SW Section 10.6)

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62 Drunk driving laws and traffic deaths, ctd.

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69 The drunk driving panel data set

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70 Why might panel data help?

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73 Empirical Analysis: Main Results

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74 Digression: extensions of the n-1 binary regressor idea

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75 Summary: Regression with Panel Data (SW Section 10.7)

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