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**Regression with Panel Data**

Chapter 10 Regression with Panel Data

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**Regression with Panel Data (SW Chapter 10)**

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**Notation for panel data**

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**Panel data notation, ctd.**

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**Why are panel data useful?**

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

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**U.S. traffic death data for 1982:**

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**U.S. traffic death data for 1988**

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

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**These omitted factors could cause omitted variable bias.**

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

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

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**Example: Traffic deaths and beer taxes**

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**FatalityRate v. BeerTax:**

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**Fixed Effects Regression (SW Section 10.3)**

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**The regression lines for each state in a picture**

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

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**Fixed Effects Regression: Estimation**

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**1. “n-1 binary regressors” OLS regression**

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**2. “Entity-demeaned” OLS regression**

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**Entity-demeaned OLS regression, ctd.**

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**Entity-demeaned OLS regression, ctd.**

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**Example: Traffic deaths and beer taxes in STATA**

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

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

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**Regression with Time Fixed Effects (SW Section 10.4)**

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**Time fixed effects only**

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**Two formulations for time fixed effects**

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**Time fixed effects: estimation methods**

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**Combined entity and time fixed effects**

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

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**A. Extension of LS Assumptions to Panel Data**

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**Assumption #1: E(uit|Xi1,…,XiT,i) = 0**

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**Assumption #2: (Xi1,…,XiT,Yi1,…,YiT), i =1,…,n, are i. i. d**

Assumption #2: (Xi1,…,XiT,Yi1,…,YiT), i =1,…,n, are i.i.d. draws from their joint distribution.

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**Assumption #5: corr(uit,uis|Xit,Xis,i) = 0 for t s**

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**Assumption #5 in a picture:**

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**What if Assumption #5 fails: so corr(uit,uis|Xit,Xis,i) 0?**

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B. Standard Errors

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**Sampling distribution of fixed effects estimator, ctd.**

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**Sampling distribution of fixed effects estimator, ctd.**

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**Case I: when uit, uis are uncorrelated**

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**Case II: uit and uis are correlated – so Assumption 5 fails**

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**Case II: Clustered Standard Errors**

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**Comments on clustered standard errors:**

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**Comments on clustered standard errors, ctd.**

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**Comments on clustered standard errors, ctd.**

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**Implementation in STATA**

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**Case II: treat uit and uis as possibly correlated**

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**Try adding year effects:**

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**Fixed Effects Regression Results Dependent variable: Fatality rate**

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**Summary: SEs for Panel Data in a picture:**

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

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**Drunk driving laws and traffic deaths, ctd.**

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**The drunk driving panel data set**

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**Why might panel data help?**

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**Empirical Analysis: Main Results**

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**Digression: extensions of the “n-1 binary regressor” idea**

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

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