Topic 1: Panel data models

 These are Models that Combine Cross-section and Time-Series Data  In panel data the same cross-sectional unit industry, firm, country is surveyed over time, so we have data which is

Dr Pham Thi Bich Ngoc

Hoa Sen University

ngoc.phamthibich@hoasen.edu.vn

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 Learn and use STATA?

http://www.ats.ucla.edu/stat/stata/

 Introductory Economics: A Modern Approach

- Jeffrey M Wooldridge (2012)

 “Economic Analysis of Cross section and

Panel data” - Jeffrey M Wooldridge (2010)

 These are Models that Combine

Cross-section and Time-Series Data

 In panel data the same cross-sectional unit

(industry, firm, country) is surveyed over

time, so we have data which is pooled over

space as well as time.

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YEU TO CHU THE VA YEU TO THOI GIA

I : ID (DOANH NGHIEP, INDIVIDUAL, HOUSEHOLD, COUNTRY, INDUSTRY

T : TIME (DAY, WEEK, QUATER, YRYEAR

ID / YEAR / WAGE / EDU / EXP / MARRIED KHOA 2010 7 12 6 0

KHOA 2011 8 12 7 0

KHOA 2012 8 12 8 0

PHUONG 2010 5 12 1 0

PHUONG 2011 5 13 3 0

file excel BT1

If all the cross-sectional units have the same number of time series observations the panel is balanced, if not it is

T T

Nt it

t t

N i

N i

y y

y y

y y

y y

y y

y y

y y

y y

2 1

2 2

22 12

1 1

21 11

Time series

Cross section

- a matrix of balanced panel data observations on variable y,

N cross-sectional observations, T time series observations

1 Panel data can take explicit account of specific heterogeneity (“individual” here meansrelated to the microunit)

individual-2 By combining data in two dimensions, panel datagives more data variation, less collinearity andmore degrees of freedom

3 Panel data is better suited than cross-sectional

example it is well suited to understanding

transition behaviour – for example companybankruptcy or merger; the effects of technologicalchange, or economic cycles

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 Grunfeld and Griliches [1960]

◦ i = 10 firms: GM, CH, GE, WE, US, AF, DM, GY, UN,

 yit = Real per capita GDP

1 ln( ) ln( )

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 LWAGE = log of wage = dependent variable in regressions

 EXP = work experience

WKS = weeks worked

OCC = occupation, 1 if blue collar,

IND = 1 if manufacturing industry

SOUTH = 1 if resides in south

SMSA = 1 if resides in a city (SMSA)

 Pooled OLS

 Difference in Difference, First Differences

(FD), Between Effects, Fixed Effects (FE),

Random Effects (RE), and Hausman test

 Two stages Least Square (2SLS)

David Roodman, 2009 " How to do xtabond2: An introduction to

difference and system GMM in Stata ," Stata Journal , StataCorp LP, vol

9(1), pages 86-136, March.

David Roodman, 2006 " How to Do xtabond2: An Introduction to

"Difference" and "System" GMM in Stata ," Working Papers 103, Center

for Global Development.

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A Pooled OLS

(Pooled Cross Section)

 Often loosely use the term panel data to refer to any data set that has both a cross- sectional dimension and a time-series

 We may want to pool cross sections just to

get bigger sample sizes

 We may want to pool cross sections to

investigate the effect of time

 We may want to pool cross sections to

investigate whether relationships have

changed over time

coi taatat ca cac quan sat thoi gian nhu 1 quan sat binh thuong

thoi gian la tong hop cac bien co den nen kinh te.

• Suppose y is firm output and x is a number of employees

• We have i = 1…n firms and t = 1…T time periods (year)

• A simple econometric model:

ϵit is a random error term: E (ϵit ) ~ N (0, σ2)

Assumptions: intercept and slope coefficients are constant across time and firms and that the error term captures

differences over time and over firms???

it it

Pooled regression by POLS may result in heterogeneity bias :

Pooled regression:

yit= a0+ a1xit+ uit

True model: Firm 1

True model: Firm 2

True model: Firm 3

True model: Firm 4

 reg depvar [indepvars] [i.year]

B Fixed Effects Model

(One Way) Fixed Effects Model: (individual effects)

If each group (firm) to have its own intercept:

HOW?  create a set of dummy (binary) variables, one for

each firm, and include them as regressors

 This form of estimation is also known as Least Squares

Dummy Variables (LSDV)

it it

i

y  0  1  

it it

N

i

it i

it a D a x

0

Fixed Effects Estimation:

STATA: reg depvar [indepvars] i.id

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(Two Way) Fixed Effects Model: (individual + time effects)

 allow the intercept to vary across the different time periods (Two Way Fixed Effects):

it it

T

t

it i N

i

it i

0

STATA: reg depvar [indepvars] i.id i.year

Fixed Effects/Within:

 discards all variation between individuals and uses only

variation over time within an individual

) (

)

(

1 0

0i i it i it it i

it y a a a x x e e

it i

it i

C Random Effects Model

 Previously we’ve assumed that ui was

correlated with the x ’s, but what if it’s not?

 OLS would be consistent in that case, but composite error will be serially correlated

 Need to transform the model and do GLS

to solve the problem and make correct inferences

 End up with a sort of weighted average

of OLS and Fixed Effects – use

u

x x

y y

1 0

2 1 2 2

2

 If θ = 1, then this is just the fixed effects

estimator

 If θ = 0, then this is just the OLS estimator

 So, the bigger the variance of the

unobserved effect, the closer it is to FE

 The smaller the variance of the unobserved

effect, the closer it is to OLS

We assume that:

regressor)of

t independen(both

0)

()

(

n)correlatiogroup

across(no

if0)

(

ation)autocorrel

(noor

if0)

(

)components two

ofnce(independe

,,0

)(

tic)homoscedascomponents

(both )

(

)

(

0)

()

(

2 2

2 2

i

j

i

js it

j it

it

v i

it i

x e E x

u

E

j i

u

u

E

j i

s t

e

e

E

j t i u

Choosing between Fixed Effects (FE) and Random Effects (RE)

1 With large T and small N there is likely to be little

difference, so FE is preferable as it is easier to compute

2 With large N and small T, estimates can differ significantly

If the cross-sectional groups are a random sample of the

population RE is preferable If not the FE is preferable

3 If the error component, vi , is correlated with x then RE is biased, but FE is not

4 For large N and small T and if the assumptions behind RE hold then RE is more efficient than FE

 Test for Var(ui) = 0 , that is

◦ If Ti=T for all i, the Lagrange-multiplier test

statistic (Breusch-Pagan, 1980) is:

◦ For unbalanced panels, the modified Breusch-Pagan

LM test for random effects (Baltagi-Li, 1990) is:

◦ Alternative one-side test:

ˆ

1 ~ (1) ˆ

it

i i i t i

 Fixed effects estimator is consistent under H0and H1; Random effects estimator is efficient

under H0, but it is inconsistent under H1.

 Hausman Test Statistic

Tests for the statistical significance of the difference

between the coefficient estimates obtained by FE and by

RE, under then null hypothesis that the RE estimates are efficient and consistent, and FE estimates are inefficient

Hausman test:

STATA: hausman FE RE

 The data in WAGEPAN.RAW are from Vella and

Verbeek (1998) Each of the 545 men in the sample worked in every year from 1980 through 1987

 Some variables in the data set change over time:

three important ones

 Other variables do not change: race and education

are the key examples If we use fixed effects (or

first differencing), we cannot include race,

education, or experience in the

equation

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 We use three methods: pooled OLS, random

effects, and fixed effects

 In the first two methods, we can include educ and

race dummies (black and hispan), but these drop

out of the fixed effects analysis

 The time-varying variables are exper, exper2,

union, and married “exper” is dropped in the FE

analysis (but exper2 remains) Each regression also contains a full set of year dummies