Ch. 10 Panel Data - PANEL DATA(Ch 10 The recommended...

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1 | Panel PANEL DATA (Ch. 10) The recommended exercise questions from the textbook: • Chapter 10: All except (10.6), (10.9) and (10.10) of the 2 nd ed; all except (10.6), (10.9) and (10.11) of the 3 rd ed. [1] What are panel data? • Panel data consist of observations on the same n entities at two or more time periods T . The data are denoted ( , ), 1,..., 1,..., it it X Y i n and t T , where “ i ” refers to the entity, and “ t ” refers to the time.
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2 | Panel • 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 the unbalanced cases is straightforward.
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3 | Panel [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 ($).
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4 | Panel • Estimation results for the 1982 data: FatalityRate = 2.01 + 0.15BeerTax (0.15) (0.13) • Estimation results for the 1988 data: FatalityRate = 1.86 + 0.44BeerTax (0.11) (0.13)
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5 | Panel
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6 | Panel • What is going on here? • Consider a simple multiple regression model (for a given time t ): Y it = 0 + 1 X it + 2 Z i + u it , i = 1, ... , N , where Z i is a time-invariant regressor. • What do β 1 and β 2 measure? β 1 = partial effect of X it on Y it with Z i held constant. 2 = the partial effect of Z i on Y i with X it held constant. • If you estimate Y it = 0 + 1 X it + error it instead? 1 1 2 cov( , ) ˆ var( ) it i p it X Z X • Candidates of Z ?
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7 | Panel • Each state has 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 ( 2 >0). 1 ˆ could be positive even if the true β 1 is negative.
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8 | Panel [3] Panel Data with Two Time Periods • Two equations for 1982 and 1988: FatalityRate i ,1988 = 0 + 1 BeerTax i ,1988 + 2 Z i + u i ,1988 . FatalityRate i ,1982 = 0 + 1 BeerTax i ,1982 + 2 Z i + u i ,1982 . FatalityRate i ,1988 FatalityRate i ,1982 = 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 .
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