Panel Data Course Lecture 3

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Panel Data CourseLecture 3

• Trinity Term 2006
• Dr David Rueda

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Today

• From last week Summary of the Parks Method.
• Panel-Corrected Standard Errors.
• Temporal Dynamics in TSCS/Panel Data.
• Stata Session.

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The Parks Method (1)

• We can set up the following assumptions for our
  TSCS/Panel model
• Within units, the error variance is constant
  (within-unit homoscedasticity but across-unit
  heteroscedasticity).
• Errors between units are correlated but only
  contemporaneously and the correlation doesnt
  vary over time.
• The error correlation within units is constant
  over time.
• The Parks method is designed to deal with data
  when these assumptions are reasonable.
• Because the assumptions are reasonable (or,
  rather, because people think they are), it has
  been a popular method in comparative politics.
• There are two parts to the Parks method one
  dealing with serial correlation, the other with
  contemporaneous (spatial) correlation and
  panel-level heteroscedasticity.

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The Parks Method (2)

• You can see Beck and Katz (1995) for the details.
  But, in practical terms
• The Parks method cant be estimated at all unless
  T gt N.
• It is not a good idea to use it unless T is
  significantly larger than N.
• Problems?
• See Beck and Katz (1995), they show that the
  Parks method has serious problems for data
  usually analyzed in TSCS context.
• The Parks method may yield standard errors that
  are too small (up to 600 percent) and therefore
  overconfident results.
• They recommend using Parks only when T is very
  large relative to N.

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Panel-Corrected Standard Errors

• Beck and Katz (1995) as T ? 8, the Parks method
  is fine. But
• With the kind of data we normally deal with in
  political science, this method tends to
  underestimate standard errors.
• The solution? Deal with serial correlation first,
  and then correct for heteroscedasticity.
• To do PCSEs, therefore, we must get rid of serial
  autocorrelation or make sure that there is none.
• In the absence of serial autocorrelation, OLS
  gives us consistent estimates of ß. But the
  standard errors could be better.
• The intuition behind this approach is to use OLS
  estimates of the ß, but to correct the estimates
  of the standard errors using the information
  contained in the residuals.
• (The way we correct for panel-specific
  heteroscedasticity is quite similar to the use of
  Whites heteroscedasticity-consistent estimator
  in time series.)

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Panel-Corrected Standard Errors

• How do we do it?
• Where E is the TxN matrix of OLS residuals, (X)
  is the Kroenecker product operator, and It is an
  identity matrix of size T.
• When the data fit the conditions of the method
  (panel-level heteroscedasticity and
  contemporaneous spatial correlation, but no
  temporal autocorrelation), pcses are better than
  Parks.
• The question is if the data fit the conditions.

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Temporal Dynamics in TSCS/Panel Data

• Two options (1) the static and (2) the dynamic
  options.
• (1) Treat the model as static, and the temporal
  correlation as a problem.
• We assume it just prevents valid estimation and
• We assume that it has no substantively interest
  effect.
• In this option, the method is to estimate ? and
  to then use this estimate to whiten the errors.
• (2) Include a dynamic specification of the model
  by including a lagged dependent variable into the
  model
• This may get rid of the error autocorrelation but
  more importantly..
• We may have substantive reasons to care about the
  amount of influence previous values have. And we
  can calculate long-term effects.

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Stata Session (1)

• The Stata commands
• xtgls is the general command for estimating
  GLS-based TSCS models.
• Options (to come after the model variables).
• panel() indicates the type of panel (unit)
  variability. The options are
• iid independent, common-variance panels
  yielding a single estimate of s2.
• heteroscedastic uncorrelated units, each with
  its own variance estimate.
• correlated heteroscedastic, spatially
  correlated panels).
• corr() indicates the withinunit temporal
  correlation. Options
• independent gives estimates with no temporal
  correlation.
• ar1 gives estimates with common AR(1) errors
  estimates a single value of ?.
• psar1 gives panel-specific AR(1) error
  estimates.

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Stata Session (2)

• xtpcse estimates models with panelcorrected
  standard errors.
• corr is the same as for xtgls
• xtpcse will automatically do a Prais-Winsten
  regression to deal with temporal correlation if
  either of the two AR options are specified.
• hetonly is the same as panel(heteroscedastic)
  option in xtgls.
• independent is the same as panel(independent)
  option in -xtgls-.
• The default is for heteroscedastic,
  spatiallycorrelated panels.
• xtregar estimates fixed and randomeffects
  models with AR(1) error structures.
• Some tests
• xttest2 used after xtgls or xtreg, fe
  implements a BreuschPagan test for crossunit
  correlation. It tests whether the cross-unit
  correlations are identically zero.
• xttest3 is a modified Wald statistic that tests
  the null hypothesis of homoscedastic panels.

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Stata Session (3)

• See computer class notes.
• See Stata file in Student_Shared folder
  (cps3.do).
• It is annotated with explanations of commands and
  procedures.