lagging one period of the dependent variable in panel data, what model could I use?

[David Wong]

Dear everyone,

Greetings. I am a new guy here. I have one question regarding my panel data.
Particularly, I plan to run one model in fixed effect:

Yt = c + aXt + bZt + ε

where Yt is the dependent variable which is continuous;
Xt is one independent variable which is continuous;
Zt is one independent variable which is continuous.

Initially, I tried use xtreg , fe r. The coefficients of Xt and Zt are significant and the sign are fitting my expectation.
However, I assume that Yt-1 should also influence Yt. Therefore, I consider to include Yt-1 in another model.

As far as know, there is a dynamic panel model ( Arellano and Bond 1991) which would be helpful. Its Stata code:

xtabond depvar indepvars, lags(p) maxdep(q) twostep vce(robust) pre(varlist) endogenous(varlist) inst(varlist)

However, in my model, we do not have endogenous, pre-determined or instrument variable as it is very unlikely that Yt has any influence neither on Xt nor Zt, i.e. no reverse causality. Therefore, I just hope to lag one period of my dependent variable Yt.

My model turns to be:

Yt = c + dYt-1 + aXt + bZt + ε


Here is the question:" Should I do Sargan test after the estimation?" Thank you so much.


Reference:
Arellano, M., and S. Bond. 1991. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58: 277-297.

[Attaullah Shah]

When you include lagged dependent variable in your regression, As shown in (Bond, 2002), the individual effects are assumed to be stochastic. If so, these effects will be correlated with the lagged dependent variable . In such a case, the OLS estimator of alphas and betas are inconsistent and the estimators of alpha are biased upward because the lagged variable is positively correlated with the error term. Within Group estimator can remove this inconsistency by transforming the variables such that observations are expressed as deviations from group means. The transformation removes the individual effects. However, such transformation invites a correlation between the error term -e,i,t-1/T-1 and the lagged dependent variable and the resultant estimate of alpha is heavily biased downward. OLS and the Within Group estimates are biased in opposite directions and help in evaluating a candidate consistent estimate that will lie between the two. Instead of using the Within Group estimate, the firm specific effects can also be removed with taking the first difference of the equation.

However, in this model too the differenced error term and the differenced lagged dependent variable are correlated. To overcome this weakness, Anderson and Hsiao (1982) developed a model (AH 2SLS) where two period differenced or two periods lagged dependent variables are used as instruments for the first difference of the lagged dependent variable. The instruments are correlated with lagged dependent variable but uncorrelated with it difference error term. However, AH 2SLS method does not use all possible moment conditions. Further precision in the estimates can be obtained through a method of Generalized Methods of Moments (GMM), a technique suggested by (Arrelano and Bond, 1991). Under this method, all available moments can be used by using the orthogonality conditions which are present between the lagged values of dependent variable and error terms. Arrelano and Bond, (1991) GMM is also called difference GMM.

For your second question, yes we have to test for the validity of the instruments and for over-identifying restriction. I would suggest xtabond2 (from SSC) doing all these as this program has lots of features for GMM and system GMM.

[David Wong]

Dear Attaullah,

I am sorry that I am unable to reply in time. Your answer really help and I understand now. Thank you so much for your kind help.

Best regards,
David