12.4 A Dynamic Panel Data Model
- z1 =
panlag
(z, a,{, T})
- yields the lagged (or trimmed) variables of the dataset z
- {output, beta} =
pandyn
(z, p, IVmeth{, T})
- computes 1-st stage GMM estimate of a dynamic linear model with p
lags of the dependent variables
|
A dynamic panel data model is given by
 |
(12.5) |
For such a model the within-group estimator is not applicable.
Therefore, Arrelano and Bond (1991) suggest to estimate the
model using a GMM estimation procedure. The idea is to estimate
the differenced model
 |
(12.6) |
where
is the difference operator such that
by using the instruments:
 |
(12.7) |
In general, it is possible to construct different GMM estimators
using the instruments from (12.7).
Arrelano and Bond (1991) suggest several instrumental variable
matrices which are also implemented in
XploRe
. (For details on the
different methods see Xplore Learning Guide, Section 12.5.) In our
example we have a panel with
. In this case we only use
,
and
as
instruments for lagged differences:
To continue our UIP example we rewrite our model in dynamic form
as
 |
(12.8) |
We include the one-period lag of the exchange index growth rate
as an additional regressor. To estimate equation (12.8) we
use the
XploRe
quantlet
pandyn
with the general syntax
{output,beta} = pandyn(z,p,IVmeth {,T})
where z is the data set, p the number of lagged
dependent variables, IVmeth the method for constructing the
instrument matrix and T the number of period covered in the
data set. Note that the T is only needed if the panel is
balanced. For the UIP data we just type
pandyn(z1,1,1)
to get the following output table:
[ 1,] "====================================================="
[ 2,] "GMM-Estimation of the Dynamic Fixed-Effect Model: "
[ 3,] "y(i,t) = y(i,t-1)'gamma + x(i,t)'beta + a(i) + e(i,t)"
[ 4,] "====================================================="
[ 5,] "PARAMETERS Estimate SE t-value"
[ 6,] "====================================================="
[ 7,] "beta[ 1 ]= 0.5454 0.2085 2.617"
[ 8,] "beta[ 2 ]= -0.1357 0.1842 -0.737"
[ 9,] "Lag [ 1 ]= 0.2896 0.0846 3.424"
[10,] "====================================================="
[11,] "N*T= 362 N= 16 DF= 2 "
[12,] "R-square (Levels): 0.1513 "
[13,] "Hansen's J-statistic (p-val): 0.2848 "
[14,] "Instruments according to method: 1 "
[15,] "====================================================="
As in the static model,
turns out to be insignificant on
conventional levels and in line with results from the static fixed
effects model
is now significantly different from zero
on the 5% level. Moreover, the coefficient of the lagged
dependent variable
is significant and about the
same magnitude as in the test for autocorrelation in the static
model. Now that we account for first order autocorrelation the
parameters are estimated more precisely. These estimates support
the evidence in favor of UIP theory.