Econometrics 2 Observations over individual units and time: - - PowerPoint PPT Presentation

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Pooled Cross Sections and Panel Data 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: Twor 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.

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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.

1 11 12 1 1

( , , ,..., ), 1,2,...,

i i i i k

y x x x i n =

1 2

( , , ,..., )

it it it itk

y x x x

2 21 22 2 1 1 1 2

( , , ,..., ), 1, 2,...,

i i i i k

y x x x i n n n n = + + +

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.

1 2 1 1 1 2

( , , ,..., ), 1,2,..., , 1,....,

it it it itk

y x x x i n n n n = + +

ˆ

pooled

y X u β β = + →

1 1 1

ˆ , 1,2,..., y X u i n β β = + = →

2 2 1 1 1 2

ˆ , 1, 2,..., y X u i n n n n β β = + = + + + →

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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.

2 1 if individual is in the period 2 sample = 0 if individual is not in the sample in period 2

i

d i i =

1 1

2 ...

i i i k ik i

y d x x u β δ β β = + + + + +

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”)

1 1 1 1 2 2

2 2 ...

i i i i i i k ik i

y d x d x x x u β δ β δ β β = + + + + + +

1 1 1 1 2 2 2 2

2 2 2 ... 2

i i i i i i i i k ik k i ik i

y d x d x x d x x d x u β δ β δ β δ β δ = + + + + + + + + +

1

β

1

δ =

1

...

k

δ δ δ = = = =

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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.

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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

• f locating the incinerator nearby?

NO! Incinerator may have been located near houses that

were already cheap in 1978.

OLS estimates using 1978 cross section:

1nearinc

price u γ γ = + +

• 101

31 nearinc price = −

• 83

19 nearinc price = −

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:

1 1

81 81 price y nearinc y nearinc u β δ β δ = + + + ⋅ +

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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:

1

β =

1 1

81 81 price y nearinc y nearinc u β δ β δ = + + + ⋅ +

δ =

1

δ =

1 1 1

: 0 vs. : H H δ δ = <

Pooled Cross Sections and Panel Data 12

Policy analysis with pooled cross sections: Example 13.3

0.67 5

• 14

Full set of ”controls” 0.17 7.5

• 12

Model as above Standard error Coefficient

1 1 1

: 0 vs. : H H δ δ = <

1

ˆ δ

2

R

1 1

81 81 price y nearinc y nearinc u β δ β δ = + + + ⋅ +

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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

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