# Pooled Cross Sections and Panel Data I

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Pooled Cross Sections and Panel Data I
Econometrics 2 Pooled Cross Sections and Panel Data I Pooled Cross Sections and Panel Data

Pooled Cross Sections and Panel Data: Overview
Observations over individual units and time: Wooldridge chapters 13 and 14. Pooling independent cross sections across time (13.1-2). Panel data: Following the same individual units across time: Two-period panel data (13.3-4) General case: Two or more periods Fixed effects estimation (13.5, 14.1) Random effects estimation (14.2) Four lectures to cover these chapters. Exercises 2 and 3. Pooled Cross Sections and Panel Data

Data structures and definitions
Cross section (”tværsnit”): Observations on a set of variables in a given period, t, for individual units i=1,2,…,n: Usually think of the cross section as a random sample from some population at time t Two period case: Period 1 cross section: Period 2 cross section: How are the period 1 and period 2 cross sections related? Independent cross sections: Two independently drawn random samples: (In general) different individual units in period 1 and period 2. Panel data: Same n individuals appear in period 1 and in period 2. Pooled Cross Sections and Panel Data

Pooling independent cross sections across time
Independent cross sections for two periods: Pooled (”sammenstykkede”) data: One extreme: Estimating pooled model: Other extreme: Treat the data in each cross section separately: ”Partial pooling”: Combine the cross sections but allow the coefficients of some variables to change between cross sections. Pooled Cross Sections and Panel Data

Pooling independent cross sections
Allow the coefficients of some of the variables to change over time: A special case of structural change Use dummy variables (W ch. 7): Time dummies (e.g. year dummies) Two periods: Need one dummy variable, usually for second period: Usually: Allow intercept to change Other coefficients allowed to change as well: Interaction terms. Pooled Cross Sections and Panel Data

Pooling independent cross sections: Testing
Testing: Is constant over time? Usual t-test for in Allow all coefficients to change over time: No gain from pooling the cross sections Fully interacted regression: F-test for Easy implementation of F-statistic: SSRs from pooled and separate regressions (”Chow test”) Pooled Cross Sections and Panel Data

Pooling independent cross sections
Wage regression: Example 13.2 Two independent cross sections: 1978-CPS, 1985-CPS Data on wage, educ, exper, expersq, union, female for 1,084 workers. Define time dummy y85. Use 1978-cross section as reference group. Question: Has the return to education and/or the gender wage gap changed between 1978 and 1985. Include above variables and y85, y85*educ, y85*female Data in CPS78_85.in7, analyze in PcGive. Chow test of overall regression. Is it of interest in this case? Why not? Pooled Cross Sections and Panel Data

Policy analysis with pooled cross sections
Example 13.3: Effect of the location of a garbage incinerator on house prices. Hypothesis: Having an incinerator nearby lowers the price of a house. Data: Prices and characteristics of houses in different distances to the incinerator. Two cross-sections: 1978 and 1981. Before and ”after” the incinerator was built in 1981. Pooled Cross Sections and Panel Data

Policy analysis with pooled cross sections
Naive approach: Use 1981 cross section to estimate the model price is the price of a house, nearinc is a dummy variable that takes the value 1 if the house is located near the incinerator. OLS estimates using 1981 cross section: Is this a ”good” estimate of the causal effect on house prices of locating the incinerator nearby? NO! Incinerator may have been located near houses that were already cheap in 1978. OLS estimates using 1978 cross section: Pooled Cross Sections and Panel Data

Policy analysis with pooled cross sections
Difference-in-differences approach: House prices have gone up between 1978 and 1981 for most houses. Whether nearby and far away from the location of the incinerator. Relevant question: Has the change been bigger for houses far from the incinerator? Need to look at differences in space (nearby/far away) of differences in time (between 1978 and 1981): Diff-in-diff. Regression implementation: Pooled Cross Sections and Panel Data

Policy analysis with pooled cross sections
Model: Common change over time Pre-incinerator difference in prices Change in price due to incinerator Test of the hypothesis that nearby incinerator lowers house prices: Pooled Cross Sections and Panel Data

Policy analysis with pooled cross sections: Example 13.3
Coefficient Standard error Model as above -12 7.5 0.17 Full set of ”controls” -14 5 0.67 Pooled Cross Sections and Panel Data

Quasi-experiments and natural experiments
Mimic controlled experiments in science by finding something that happened ”naturally” to one group of people, but not to another. Treated group: Houses nearby the location of the incinerator. Control group: Houses far away. Comparing groups before and after the ”treatment”: Building the incinerator Pooled Cross Sections and Panel Data

Pooled Cross Sections and Panel Data
Next time Panel data: Observations over time for the same individual units. W sec : Two-period panels No exercises this week! Will start next week. No Econometrics 2 lecture on Thursday. IV supplementary course starts Friday, 14-16, in Bisp 214 Pooled Cross Sections and Panel Data