Panel Data Course Lecture 4

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Panel Data CourseLecture 4

• Trinity Term 2006
• Dr David Rueda

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Today

• More on Temporal Dynamics in TSCS/Panel Data.
• First Difference Estimators.
• Arellano and Bond.
• Random Coefficient Models.
• Stata Session.

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More on Temporal Dynamics in TSCS/Panel Data (1)

• From last week
• Two options (1) the static and (2) the dynamic
  options.
• (1) Treat the model as static, and the temporal
  correlation as a problem.
• (2) Include a dynamic specification of the model
  by including a lagged dependent variable into the
  model
• We can take the models that we did last week a
  little farther. Imagine we have a model that has
  both unit-effects and a lagged dependent
  variable.
• What happens if we estimate this model with OLS.
  In other words, we estimate
  where

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More on Temporal Dynamics in TSCS/Panel Data (2)

• Note we are assuming that the errors mean is 0
  and that there is no serial correlation.
• Lets look at the lagged dependent variable in
  more detail
• You can see that both uit and Yit-1 contain ai.
  Which means
• That in our OLS model one of our independent
  variables is correlated with the error terms
  which means we will have biased and inconsistent
  estimates of F and ß.
• Possible solutions?

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First Difference Estimators (1)

• Anderson and Hsiao (1981) difference the series
  to get rid of the cross-sectional effects
• which is the same as
• Using first differences we get rid of the unit
  effects.
• But the correlation between the independent
  variables and the errors is still a problem
  (Yit-1 and uit-1 are still correlated).

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First Difference Estimators (2)

• This can be resolved through the use of
  instrumental variables
• Use a set of variables Z to predict the X that is
  a problem.
• The Z variables need to be highly correlate to X
  but uncorrelated to uit.
• Since there is no serial correlation
  (assumption), ?Yit-2 and Yit-2 are correlated
  with ?Yit-1 and Yit-1 but uncorrelated with ?uit.
  
• So we can either use ?Yit-2 or Yit-2 as the Z
  (instrument for ?Yit-1).

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Arellano and Bond

• Since we are assuming that the errors mean is 0
  and that there is no serial correlation
• ?uit is uncorrelated with all Yit and Xit for t-2
  and earlier.
• Therefore all these variables (Yit-2, Yit-3,
  and Xit-2, Xit-3, ) can be used as instruments
  for ?Yit-1.
• See Wawro 2002 for details.
• Strengths of Arellano and Bond
• Your instruments get better as N is larger.
• The model can be applied to more complex lags of
  Y.
• Weaknesses
• Same problem as fixed effect model?
• It is not possible to estimate the effect of time
  invariant factors.
• Observations are dropped. Why?
• For the lags we are using as instruments, we lose
  the first observation, etc.

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Random Coefficient Models (1)

• We will not get into this in great detail. Some
  intuitions.
• Back to the main model
• We have been assuming a common effect for all
  units.
• We could assume instead a unit specific effect
• We could then use the usual F test to check if
  the unit specific model is a better
  specification.
• This method (comparing the two models above and
  choosing the most appropriate one) is, in a way,
  an all-or-nothing approach.
• Instead we could compromise and find a way in
  between. This is what a random coefficient model
  does.
• What random coefficient models do is to produce
  estimates that are a combination of the
  unit-specific and the pooled estimates.

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Random Coefficient Models (2)

• Steins Shrinkage estimator
• The linear combination of the unit-specific and
  pooled OLS estimators is determined by the F test
  itself.
• GLS Shrinkage estimators
• The error term is considered to have the usual
  variability of uit but also the variability due
  to the differences in ß across units.
• The estimates are a combination of the pooled OLS
  ones and of a weighted combination of the
  unit-specific estimates (the units with the
  lowest variance are the most influential).
• In Stata 8, we can estimate a Hildreth-Houck
  random coefficient model
• See stata session.
• In Stata 9 there are other options (xtmixed).

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Stata Session

• See computer class notes.
• See Stata file in Student_Shared folder
  (cps4.do).
• It is annotated with explanations of commands and
  procedures.