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Understanding Panel Data Analysis: Fixed vs. Random Effects Models

Panel data analysis allows researchers to observe behavior across entities over time, controlling for unobservable variables influencing the outcomes. This method benefits from fixed effects models, which capture entity-specific characteristics, and random effects models, which assume variation between entities is random and uncorrelated with independent variables. Utilizing these approaches, researchers can examine relationships between estimations and outcomes, improving the understanding of complex data structures over time, such as analyzing fatality rates influenced by various usage metrics across multiple states.

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Understanding Panel Data Analysis: Fixed vs. Random Effects Models

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  1. Panel Data Analysis

  2. INTRO • Panel Data is where you observe behavior of entities across time. • Allows to control for unobservable variables that change over time but not entity • Allows to control for unobservable variables across entities • xtsetentity time

  3. xtlinefatalityrate, (ov)

  4. Fixed Effect Models

  5. Eq 2 Dummy Variables xi: regfatalityratesb_useagei.fipsi.year predict yhat separate yhat, by(fips) separate yhat, by(year) twoway connected yhat1-yhat56 sb_useage|| lfitfatalityratesb_useage, clwidth(thick) clcolor(black) twoway connected yhat1983-yhat1997 sb_useage|| lfitfatalityratesb_useage, clwidth(thick) clcolor(black)

  6. Eq 1 n entity-specific intercepts aregfatalityratesb_useage, absorb(state) aregfatalityratesb_useage year2…year10, absorb(state)

  7. Eq 1 n entity-specific intercepts xtsetfips year xtregfatalityratesb_useage, fe

  8. xtregoptions fe: fixed effects Explores relationship between estimations and outcomes within an entity. Assumes each entity has own characteristics that may influence yhat to control for. re: random effects Variation across entities is assumed to be random and uncorrelated with the independent variables included in the model be: between effects pa: population-average

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