Econ 281 Regression with Panel Data

# Econ 281 Regression with Panel Data - Regression with Panel...

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1 Regression with Panel Data Introduction to Econometrics Econ 281

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2 Regression with Panel Data (SW Chapter 10) 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.
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 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])
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 number 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 Others (legal driving age, drunk driving laws, etc.)
7 Cross-Sectional Regressions Let’s run our usual regression first By usual we mean we run our regressions by year

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8 U.S. traffic death data for 1982: Higher alcohol taxes, more traffic deaths?
9 U.S. traffic death data for 1988 Higher alcohol taxes, more traffic deaths?

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## This note was uploaded on 09/25/2010 for the course ECON 281 taught by Professor Habermalz during the Winter '08 term at Northwestern.

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Econ 281 Regression with Panel Data - Regression with Panel...

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