SERIAL CORRELATION
In Panel data
Chapter 5(Econometrics Analysis of Panel data -Baltagi)
Shima Goudarzi
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As We assumed the stndard model:
and
(No Matter how far t is from s)
The regression disturbances are homoscedastic with the
same variance across time and individuals.
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� This assumption cannot be always true
For example in Investment, Consumption a shock affects
the behavioral relationship for at least the next few periods.
� Using the routine solution results in:
consistent but inefficient estimates of regression coefficients
and biased standard errors.
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Serial Auto regression AR(1) in νit
(Willis- Lillard 1978)
� They generalized the error component model to the
serially correlated case, by assuming that
lρl<1
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Baltagi and Li (1991) applied the Prais-Winstten transformation
matrix ,to transform disturbances into serially uncorrelated
classical errors.
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First step :They suggest estimating � from Within
esiduals �� it as :
-for large T
-for small T
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Second step: Estimating , by substituting OLS residuals ��
in this equation:
Then, Estimating and From
Where
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Empirical Application AR(1)
Lillardand Weiss(1979) used the panel earnings data on
American scientists over the decade 1960-70 to analyze the
covariance structure of earnings over time .
Ln Yit = Xit β+ Uit
Yit : real annual earnings of the ith person in the tth year
x : dependent variables like ,experience ,gender,
employment in private industry .
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μi Represents unmeasured characteristics such as ability and work on the
relative earning of scientists (individual effects).
Represents the effect of omitted variables which affect the growth of
earning like learning ability.
Transitory but serially correlated differences, represents the rate of
deterioration of the effect of random shock εit on which persists over a
year.
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They used the Maximum likelihood to estimate the
parameters of the residual and then applied GLS to
estimates β.
By comparing the actual and predicted covariances, we see that
their specification is quite successful in predicting the pattern.
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Serial Auto regression AR(2) in νit
The transformation can allow also for AR(2) process on the νit
where
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The matrix C defined
The first step is transforming the data by the C Matrix
And then obtain GLS on model by computing .
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Unequally Spaced Panels with AR(1) Disturbances
(Baltagi 1991)
Sometimes panels cannot be collected every period due to
lack of resources or cut in data.
� Panel daily data from stock market that is unequally
spaced when the market closes on holidays.
� Housing resale data when the pattern of resale for each
house occurs at different time periods.
In this paper Baltagi and Wu tried to estimate an unequally
spaced panel data regression model with Random effect and
AR(1)disturbances.
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Random
Effect(GLS)
Random Effect GLS with
AR(1)
β1 0.11(0.011) 0.095(0.008)
β2 0.308(0.017) 0.32(0.026)
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Random Effect and AR(1) and locally best invariant test(LBI
- The Baltagi –Wu LBI statistics: 0.95
- Durbin-Watson for : 0.68
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Jointly test of Serial Correlation and Individual Effects
Remainder disturbances AR(1) process
or MA(1) process
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Extensions
Other extensions include
� The fixed effect model with MA(q)Remainder
disturbances and also the treatment of Autoregressive
moving average ARMA(p,q) case on the νit.
� Extension to the two-way model with serially correlated
disturbances
� Chamberlain (1982, 1984) allows for arbitrary serial
correlation and heteroskedastic patterns by viewing each
time period as an equation and treating the panel as a
multivariate.
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Refrences:
-Becketti, S.,W. Gould, L. Lillard and F.Welch, 1988, The panel study of income dynamics after fourteen years: An evaluation, Journal of Labor Economics 6, 472–492
-Berry, S., P. Gottschalk and D. Wissoker, 1988, An error components model of the impact of plant closing on earnings, Review of Economics and Statistics 70, 701–707
Baltagi, B.H. and Q. Li, 1995, Testing AR(1) against MA(1) disturbances in an error component model,
Journal of Econometrics 68, 133–151.
-Econometric Analysis of Panel Data, 4th Edition ,Badi H.Baltagi,2008,Wiley
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