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Lecture+6+Regression+with+panel+data

Lecture+6+Regression+with+panel+data - WhatisPanelData...

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1 Lecture 6 Regression with panel data What is Panel Data? Panel data are data collected by following the same group of survey subjects over time. A panel dataset contains observations on the same group of survey subjects repeatedly over time. Panel data is also called longitudinal data Examples : Data on 1000 students, observed every year in 6 year, for 6,000 observations total. Data on 50 U.S. states, each state is observed in 3 years, for a total of 150 observations. Data on 5000 firms, in ten years, for 50,000 observations total. Notation for panel data A double subscript distinguishes subjects and time periods. i = subjects, n = number of subjects, so i = 1,…, n t = time period (year, month, quarter etc), 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 n = number of subjects T = number of time periods In total, we have n T observations. Why are panel data useful? With panel data, one observes the survey units multiple times, so can control for fixed effects (or fixed factors, or characteristics) of survey units even when they are unobserved or unmeasured, i.e., fixed factors are that: Vary across survey units but for the same unit, they stay constant over time For example, innate ability, risk aversion, or state/firm unobserved characteristics that can be considered fixed over time. Could cause omitted variable bias if they are omitted

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2 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, so one can look at changes in Y to get away from the omitted variable bias. Examples of a panel data set: 1. Drunk driving and alcohol taxes Observational unit: a U.S. state in a year 48 U.S. states, so n = of entities = 48 7 years (1982,…, 1988), so T = # of time periods = 7 So total # observations = 7 × 48 = 336 Variables: Drunk driving rate (# drunk driving caught in that state in that year, per 10,000 state residents) Alcohol tax Other (legal driving age, average age, percentage of single males etc.)
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