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Unformatted text preview: REGRESSIONS WITH PANEL DATA Read (Stock and Watson, Chapter 10) Panel data notes (see additional notes folder Panel on Sakai) on WHAT IS PANEL DATA? Panel data is a combination of cross section Panel and time series data and Panel data is also called longitudinal data EXAMPLES OF PANEL DATA The relationship between the number of The traffic fatalities in 50 states over 7 years traffic The relationship between the demand for The water and price in 5 municipalities observed over 4 years Canadian foreign aid to 10 developing Canadian countries observed over 6 years countries PANEL DATA: ADVANTAGES 1. More observations resulting in more 1. efficient estimation efficient 2. Multicollinearity is less severe 3. The Omitted Variable Bias problem is 3. less i.e. allows us to control for omitted variable bias variable PANEL DATA: LIMITATIONS 1. Attrition TYPES OF PANEL DATA Balanced panel: no missing observations Unbalanced panel: has missing observations CLASSICAL POOLING Step 1: Combine all the observations Step constituting the panel dataset constituting Step 2: Estimate the regression by OLS and Step obtain a single intercept and slope obtain CLASSICAL POOLING: PROBLEMS Commonly the fit is very poor (as measured Commonly by R-squared or Adjusted R-squared) by FIXED EFFECTS REGRESSION A better alternative to classical pooling Allows the intercepts to vary among the Allows different cross section units different Involves introducing several binary (or Involves dummy) variables. dummy) Better fit (as measured by R-squared or Better Adjusted R-squared) Adjusted FIXED EFFECTS REGRESSION: TYPES Individual fixed effects regression Time fixed effects regression 2-way fixed effects regression INDIVIDUAL FIXED EFFECTS REGRESSION Example of a panel dataset with 4 cross section Example units observed over 3 years (i.e. a balanced panel) units In an individual fixed effects regression we In include only 3 binary variables. Note that one of the binary variables must be excluded to circumvent the binary variable trap problem as explained in the Study Notes. explained TIME EFFECTS REGRESSION See Notes 2-WAY FIXED EFFECTS REGRESSION See Notes ...
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