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Econometrics 2

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

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Econometrics 2

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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. Policy analysis with pooled cross sections: Example 13.3 Pooled Cross Sections and Panel Data

  13. 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

  14. Next time • Panel data: Observations over time for the same individual units. • W sec. 13.3-13.4: 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

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