cn7 - PANEL DATA (Ch. 10) The recommended exercise...

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PANEL DATA ( C h . 1 0 ) The recommended exercise questions from the textbook: Chapter 10: All except (10.6), (10.10). [1] What are panel data? Panel data consists of the observations on the same n entities at two or more time periods T. If the data set contains observations on the variables X and Y, then the data are denoted ( , ), 1,. .., .., it it X Y i n and t T = = , where the first subscript, i, refers to the entity being observed, and the second subscript, t, refers to the date at which it is observed. Balanced panel Vs. unbalanced panel. • Balanced panel: Variables are observed for each entity and each time period. • Unbalanced panel: Some missing data for at least one time period. We consider the analysis of balanced panel. But extension to unbalanced is straightforward. Panel-1
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[2] Revisiting Omitted Variables Biases Issue: Do alcohol taxes help decrease traffic deaths? Data: fatality.wf1 48 U.S. states (excluding Alaska and Hawaii): N = 48. 1982 -1988: T =7. fatality rate = # of traffic accident deaths per 10,000 people. beertax = tax per a case of beer ($). Estimation results for the 1982 data: n FatalityRate = 2.01 + 0.15BeerTax (0.15) (0.13) Estimation results for the 1988 data: n FatalityRate = 1.86 + 0.44BeerTax (0.11) (0.13) Panel-2
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Panel-3
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What is going on here? Consider a simple multiple regression model (for a given time t): Y it = β 0 + β 1 X it + β 2 Z i + u it , i = 1, . .. , N, where Z i is a time-invariant regressor. 1 What do β 1 and β 2 measure? β 1 measures the partial effect of X it on Y it with Z i held constant. Similarly, β 2 measures the partial effect of Z i on Y i with X it held constant. If you estimate Y it = α 0 + α 1 X it + error it instead? 11 2 cov( , ) ˆ var( ) it i p it XZ X αβ β →+ Each state would have a different level of preference for alcohol (say, Z i = Pal). Pal (Z) and Beertax (X) could be positively related: cov( , ) it i X Z >0. Pal (Z) would have a positive partial effect on FatalityRate ( β 2 > 0). Thus, 1 ˆ α could be positive even if the true β 1 is negative. How could we control Pal using panel data? Panel-4
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[3] Panel Data with Two Time Periods Two equations for 1982 and 1988: FatalityRate i,1988 = β 0 + β 1 BeerTax i,1988 + β 2 Z i + u i,1988 . FatalityRate i,1982 = β 0 + β 1 BeerTax i,1982 + β 2 Z i + u i,1982 . FatalityRate i,1988 – Fatality i,1982 = β 1 (BeerTax i,1988 –BeerTax i,1982 ) + (u i,1988 -u i,1982 ). (1) No Z i in (1)! OLS on (1) will yield a consistent estimator of β 1 . Actual estimation results for (1): n 1988 1982 Fatality Fatality = -0.072 – 1.04(BeerTax 1988 – BeerTax 1982 ) (0.065) (0.36) Panel-5
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Comments on the before-and-after estimation results. As real beer tax increases by $1 per case, the traffic fatality rate falls by 1.04 deaths per 10,000 people. This is a big effect, because mean traffic fatality rate is approximately two. • This before-and-after approach works well if T = 2. What should we do if T > 2?
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cn7 - PANEL DATA (Ch. 10) The recommended exercise...

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