#### Transcript Dynamic Panel Data: Challenges and Estimation

```Dynamic Panel Data:
Challenges and Estimation
Ass. Prof. of Economics
Outline
1. Problemo:
Bias of dynamic fixed effect models
– Within estimator
– First differenced estimator
2. Consistent estimators
1. Hsiao estimator
2. Arellano-Bond estimator
PROBLEMO
Models of the dynamics of investment
• Where Iit is investment, Kit is capital.
• ct is the year-specific constant of the equation,
and yit=Iit/Kit is the investment rate (= growth
of capital – depreciation rate).
Dataset
• 703 publicly traded UK firms for which there is
consecutive annual data from published
company accounts for a minimum of 4 years
between 1987 and 2000.
Autoregressive model
• hi is an individual effect, potentially correlated
with the yi.
• Covariates xi can be added to this
specification.
First-differenced estimator
• The first-differenced specification does not
satisfy A3.
• Indeed, there is a negative correlation
between lagged changes in y and changes in v
(the residual).
• This is called “mean reversion.” Individuals
that are lucky in one period will see a decline
in y in the next period.
• Downward bias in the estimator of a.
Within-estimator
• The within-transformed specification also
does not satisfy A3 because the within
transformation of the lagged dependent is
correlated with the within-transformation of
the residual.
• Simulation results indicate that in general the
within estimator is biased downward.
OLS with dummies
• We assume throughout that T is small and N is
going to infinity.
• In this case, the vector of coefficients in OLS
with dummies is increasing in size, thus OLS
with dummies is not a consistent estimator of
the coefficients.
• Positive correlation between the fixed effect
and the lagged dependent variable.
Notes
• Random effects models are not affected by
the bias.
• With random effects, the OLS estimator, or
any WLS/GLS gives a consistent estimator of
the coefficients.
CONSISTENT ESTIMATORS:
HSIAO AND ARELLANO-BOND
Assumptions
• The residuals vit are not correlated across
time. Hence the residuals do not have an
AR(1) structure.
• Corr(vit,vit’)=0 if t is diff. from t’.
• Assume that we have at least T>=3 time
periods.
Hsiao approach
• Any instrument correlated with Dyit-1 and
uncorrelated with vit will give a consistent 2SLS
estimator.
• A candidate is yit-2.
• With T>3, there are more candidates: twice, k-th time
lagged dependent, difference of the lagged dependent.
Arellano-Bond
• Acknowledge that
– there are more than one instrument for T>3.
– there is serial correlation of the residuals of the
first-differenced equation.
• Hence 2SLS is not efficient.
• GMM estimator of Holtz-Eakin, Newey and
Rosen (1988), and Arellano and Bond (1991).
Moment conditions
• Matrix of instruments.
• And moment conditions.
• With:
GMM estimator
• The asymptotically efficient consistent
estimator of the model minimizes the GMM
criterion.
• Where WN is the inverse of the variancecovariance matrix of the moments.
• Estimated as:
Implementation
CONCLUSIONS
Conclusions
• A negative effect of the lagged dependent
variable can rise suspicion that ‘mean reversion’