# Re: st: dynamic panel data, system GMM and fixed effect

 From "V. Sarafidis" <[email protected]> To [email protected] Subject Re: st: dynamic panel data, system GMM and fixed effect Date 21 Sep 2005 10:34:38 +0100

Hi Andrea,

I am not sure this is a meaningful thing to do.

If you put fixed effects in first-differences then you imlicitely assume that your initial model equals to

y(i,t) = a(i) + a(i)*t + g*L.y(i,t) + b*X(i,t) + u(i,t)

Taking first-differences on the above leads to having fixed effects in the resulting model. But this specification is a bit awkward.

Perhaps if you want to allow for some heterogeneity you may use time fixed effects or individual-specific trends (which resembles closer your model). xtabond2 will work I believe provided N is not extremely large. But at the end of the day, if your slope coefficients are truly heterogeneous I don't think you can rescue the situation in this way - rather you need to model this heterogeneity explicitely.

I am not sure actually on this but maybe someone else in this list is able to say something: if heterogeneity in the slope coefficients is regarded to be fixed, would an xtabond command with multiplicative dummies make sense?

I.e. if you run the following model

y(i,t) = a(i) + g*L.y(i,t) + Dummy(i)*L.y(i,t)+ b*X(i,t) + Dummy(i)*X(i,t) + u(i,t)

then you first-differences equation becomes

Dy(i,t) = g*DL.y(i,t) + g1*Dummy(i)*DL.y(i,t)+ b*DX(i,t) + b1*Dummy(i)*DX(i,t) + Du(i,t)

Then you would need to use gmm instruments for DL.y(i,t) as well, I suppose, although questions arise as to the properties of your multiplicative dummy coefficients.

Vasilis

On Sep 21 2005, sistoand80 wrote:

Dear all, I've a panel of 20 regions and 7 years (1998-2004)and I try to estimate a dynamic panel model as

yit = a*l.yit + b*(Xit) + uit.

My problem is that i've a heterogeneous panel. I tested for homogeneity constraints through a F-test but results showed that i could impose homogeneity on "a" and "b" only if fixed effect are included in the estimates.

Standard approach for estimate DPD is to take the first difference to remove fixed effect (xtabond). However, this procedure imposes a high degree of homogeneity, so that with heterogeneous panel, this seems to lead to inconsistent estimate as a big portion of the variance of y is explained by fixed effect.

If a include fixed effect in xtabond, the command drop these dummy as it takes the first-difference. I've try to run a system of gmm (xtabond2) including fixed effect from the level equation.

However, I don't know if this procedure is correct.
Could anyone help me?
Is a system of GMM consistent in presence of fixed effect?

I've to run a dynamc fixed effect model (xtivreg)? Is a dynamicFE a consistent way to estimate such a dynamic panel (heterogeneity, N>T, etc.)?

Best,
Andrea Sisto,
PHD student
University of Eastern Piedmont

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