Damodar Gujarati

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CHAPTER 17

• PANEL DATA REGRESSION MODELS

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PANEL DATA REGRESSION MODELS

• Panel data regression models are based on panel
  data, which are observations on the same
  cross-sectional, or individual, units over
  several time periods.
• A balanced panel has the same number of time
  observations for each cross-sectional unit.
• Panel data have several advantages over purely
  cross-sectional or purely time series data. These
  include
• (a) Increase in the sample size
• (b) Study of dynamic changes in cross-sectional
  units over time
• (c) Study of more complicated behavioral models,
  including study of time-invariant variables

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PANEL DATA REGRESSION MODELS

• However, panel models pose several estimation and
  inference problems, such as heteroscedasticity,
  autocorrelation, and cross-correlation in
  cross-sectional units at the same point in time.
• The fixed effects model (FEM) and the random
  effects model (REM), also known as the error
  components model (ECM), are commonly used methods
  to deal with one or more of these problems.

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FIXED EFFECTS MODEL (FEM)

• In FEM, the intercept in the regression model is
  allowed to differ among individuals to reflect
  the unique feature of individual units.
• This is done by using dummy variables, provided
  we take care of the dummy variable trap.
• The FEM using dummy variables is known as the
  least-squares dummy variable model (LSDV).
• FEM is appropriate in situations where the
  individual-specific intercept may be correlated
  with one or more regressors, but consumes a lot
  of degrees of freedom when N (the number of
  cross-sectional units) is very large.

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WITHIN-GROUP (WG) ESTIMATOR

• An alternative to LSDV is to use the within-group
  (WG) estimator.
• Here we subtract the (group) mean values of the
  regressand and regressor from their individual
  values and run the regression on the
  mean-corrected variables.
• Although it is economical in terms of the degrees
  of freedom, the mean-corrected variables wipe out
  time-invariant variables (such as gender and
  race) from the model.

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RANDOM EFFECTS MODEL (REM)

• In REM we assume that the intercept value of an
  individual unit is a random drawing from a much
  larger population with a constant mean.
• The individual intercept is then expressed as a
  deviation from the constant mean value.
• REM is more economical than FEM in terms of the
  number of parameters estimated.
• REM is appropriate in situations where the
  (random) intercept of each cross-sectional unit
  is uncorrelated with the regressors.
• Unlike in FEM, time-invariant regressors can be
  used in REM.

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FIXED EFFECTS OR RANDOM EFFECTS?

• If it assumed that ei and the regressors are
  uncorrelated, REM may be appropriate, but if they
  are correlated, FEM may be appropriate.
• In the former case we also have to estimate fewer
  parameters.
• The Hausman test can be used to decide between
  FEM and REM
• The null hypothesis underlying the Hausman test
  is that FEM and REM do not differ substantially.
• The test statistic has an asymptotic (i.e., large
  sample) ?2 distribution with df equal to number
  of regressors in the model.
• If the computed chi-square value exceeds the
  critical chi-square value for given df and the
  level of significance, we conclude that REM is
  not appropriate because the random error term are
  probably correlated with one or more regressors.
• In this case, FEM is preferred to REM.

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ATTRITION

• Some specific problems with panel data model need
  to be kept in mind
• The most serious problem is the problem of
  attrition, whereby for one reason or another,
  members of the panel drop out over time so that
  in the subsequent surveys (i.e., cross-sections)
  fewer original subjects remain in the panel.
• Also, over time subjects may refuse or be
  unwilling to answer some questions.