Dynamic Panel Models
The aim of this type of model is to introduce some dynamic effects into the standard panel model, which is done through the inclusion of a lagged dependent variable among the regressors. The justification for this form of model can be the partial adjustment model among others: y
* it y it
 
0
 
1
 y it

1
 x it

( y
* it
 u it
 y it

1
)
Where y * is the desired level of y . By substituting the expression for y * into the other equation we obtain the following estimating equation: y it
 
0
 
( 1
 
) y it

1
 
1 x it
  u it
Unfortunately there is a problem with trying to estimate this type of model, as the lagged dependent variable will be correlated with the error term (in small samples).
To overcome this an instrumental variable technique can be used, such as Generalised
Method of Moments (GMM), where the instruments can be lagged values of the variables in the original models. There are two approaches to dynamic panel models, the most common is the Arellano-Bond dynamic panel, where individual or fixed effects are accounted for by differencing the data. The second approach is the
Arellano-Bovver approach, which differs to the former by allowing the fixed effects through orthogonal deviations.
Although dynamic panel models have been widely used over the recent past, especially in finance where it is assumed adjustment is slow, such as dividend models, there are a number of criticisms of these models.
1) The dynamic structure is very basic, with a single lagged dependent variable, which is unlikely to capture the real dynamics of the model.
2) They do not account for the stationarity or otherwise of the data.
3) These models are restricted to the case where N>T, i.e. they need a reasonably long cross section relative to the time series.
4) The methods for accounting for the unobserved heterogeneity tend to be limited.
5) There is some evidence that the standard errors associated with the
Arellano-Bond approach may not be reliable under some circumstances.
However despite some misgivings, they are more popular in the literature than the panel cointegration models, which as yet have not been as widely published as the dynamic panel models.

Panel Unit Root Tests
These type of unit root tests have the advantage that they increase the power of the tests relative to the standard ADF tests encountered previously. They differ mainly in the assumptions regarding the nature of the hypotheses being tested, as some test for a common unit root process, whereas others for an individual unit root process. As with
ADF tests, alternative panel unit root tests also make different assumptions about the way in which autocorrelation is removed, using either lags or adjusted standard errors.
Although there are various versions of each, the two main test are the Levine Lin test for a common unit root and the Im Pesaran and Shin test for an individual unit root process:
Levin and Lin Test (LL)
 y it
 z
 
 y i , t fixed /

1
 p i 
L

1
 iL
 y i , t

L random effect
 z
  u it
Im Pesaran and Shin Test (IPS)
 z
 y it

  i y i , t

1 fixed /

L p i 

1
 iL
 y i , t

L random effect
 z
   u it
The main difference between the tests is that the LL assumes the unit root is common to all the cross sections in the model, whereas the IPS test assumes they can differ.
Both tests assume that different lag lengths can be used across the different cross sections. The hypotheses also differ, as the alternative hypothesis in the LL test is that all individual cross sections are stationary, whereas with the IPS test the alternative is that at least one is stationary. These differences can produce different results depending on the relative values for N (number of cross sections ) and T (number of time series).
There are a number of panel cointegration tests available, including an Engle-
Granger based test, termed the Pedroni test and a Johansen ML type test called the
Fisher test, which requires the same inputs as the standard Johansen test, in terms of the lag length and interpretation of the cointegrating vectors.