Lecture_15__Prof._Arkonac's_Slides_(Ch_10_Panel_Data)

Lecture_15__Prof._Arkonac's_Slides_(Ch_10_Panel_Data) -...

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Panel Data I & II (Fall 2010) Lecture 15 Prof: Seyhan Erden Arkonac, PhD 1
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2 Regression with Panel Data A panel dataset contains observations on multiple entities (individuals), where each entity is observed at two or more points in time. Hypothetical examples : Data on 420 California school districts in 1999 and again in 2000, for 840 observations total. Data on 50 U.S. states, each state is observed in 3 years, for a total of 150 observations. Data on 1000 individuals, in four different months, for 4000 observations total.
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3 Notation for panel data A double subscript distinguishes entities (states) and time periods (years) i = entity (state), n = number of entities, so i = 1,…, n t = time period (year), T = number of time periods so t =1,…, T Data: Suppose we have 1 regressor. The data are: ( X it , Y it ), i = 1,…, n , t = 1,…, T
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4 Panel data notation, ctd. Panel data with k regressors: ( X 1 it , X 2 it ,…, X kit , Y it ), i = 1,…, n , t = 1,…, T n = number of entities (states) T = number of time periods (years) Some jargon… Another term for panel data is longitudinal data balanced panel : no missing observations (all variables are observed for all entites [states] and all time periods [years])
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5 Why are panel data useful? With panel data we can control for factors that: Vary across entities (states) but do not vary over time Could cause omitted variable bias if they are omitted are unobserved or unmeasured – and therefore cannot be included in the regression using multiple regression Here’s the key idea: If an omitted variable does not change over time, then any changes in Y over time cannot be caused by the omitted variable.
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6 Example of a panel data set: Traffic deaths and alcohol taxes Observational unit: a year in a U.S. state 48 U.S. states, so n = of entities = 48 7 years (1982,…, 1988), so T = # of time periods = 7 Balanced panel, so total # observations = 7 48 = 336 Variables: Traffic fatality rate (# traffic deaths in that state in that year, per 10,000 state residents) Tax on a case of beer Other (legal driving age, drunk driving laws, etc.)
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Fatality rate = 2.01 + 0.15 Beer tax (1982 data) (0.15) (0.13) not significant even at 10% Fatality rate = 1.86 + 0.44 Beer tax (1988 data) (0.11) (0.13) significant at 1% (t=3.43) Higher beer taxes are associated with more traffic deaths!!! 7
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8 U.S. traffic death data for 1982: Higher alcohol taxes, more traffic deaths?
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9 U.S. traffic death data for 1988 Higher alcohol taxes, more traffic deaths?
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10 Why might there be higher more traffic deaths in states that have higher alcohol taxes? Other factors that determine traffic fatality rate: Quality (age) of automobiles driven in the state Quality of roads (state highways are in good repair?) “Culture” around drinking and driving (hard to measure!) Density of cars on the road (most driving is rural or urban?)
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If these factors remain constant over time in a given state…. Use Panel Data …. Why? Even though we can not measure these factors we can hold them constant by using OLS regression with Fixed Effects 11
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12 These omitted factors could cause omitted variable bias.
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Lecture_15__Prof._Arkonac's_Slides_(Ch_10_Panel_Data) -...

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