System GMM and Fixed effects generate contradictory results

[Maria Schmidt]

Dear all,

I have an unbalanced panel data set of N=240 entities over 17 years with nearly 1,200 observations.

Using Stata version 14.1, I am running system GMM (xtabond2) and a fixed effects (xtreg, fe) regression to determine the effect of x and its lagged values on y, but am getting contradictory results.

1) GMM
Here is my GMM syntax:

xtabond2 y L.y L2.y L3.y L(0/3).x cvar1 cvar2 cvar3 cvar4 cvar5 yr*, gmmstyle(L.y, collapse) gmmstyle(L.(x cvar1 cvar2 cvar3 cvar4 cvar5), collapse) ivstyle (yr*, equation(level)) twostep robust orthogonal

When running system GMM, I get the following relationship between my independent and dependent variable:
L0.x -> positive effect on y (p<0.10)
L1.x -> negative effect on y (p<0.01)
L2.x -> positive effect on y (p<0.05)
L3.x -> negative effect on y (p<0.10)
Number of instruments = 125, Number of groups = 145.

The model seems to be properly identified as:
AR(1): p=0.001, AR(2): p=0.172
Sargan test of overid. restrictions: chi2(95) = 303.22 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(95) = 107.95 Prob > chi2 = 0.172
(Robust, but weakened by many instruments.)

If I exclude L2.y L3.y from the model, only the effect of L1.x on y remains significant.
Depending on whether I add or delete some control variables, L0.x-L3.x gain or lose on their significance.

I do not know whether this could play a role for GMM, but my independent variable in t is highly correlated with its own values in t-1 (correlations between 0.8 and 0.96). The same applies to the dependent variable (correlations between 0.95 and 0.99).

2) Fixed effects
To prove the robustness of my GMM results, I am running the same regression in fixed effects. For this purpose, I have created lagged values of my independent variable x (L1.x-L3.x) for fixed effects.

Here is my fixed effects syntax without control variables:

xtreg y L1.x L2.x L3.x, fe

And here is my fixed effects syntax with control variables:

xtreg y L1.x L2.x L3.x cvar1 cvar2 cvar3 cvar4 cvar5 yr*, fe

With or without my control variables, I am getting the following results:
L1.x -> positive effect on y (p<0.001)
L2.x, L3.x -> negative n.s.

If I am running individual regressions for each of the lagged values of independent variables (e.g. syntax: xtreg y L3.x, fe), I get a positive significant effect of each lagged value on y.


So whereas GMM suggests that the lagged values of x influence y positive in L0 and L2 and negative in L1 and L3, fixed effects show only positive effects of x and its lagged values on y.


Therefore I would like to kindly ask for your advice:

1. What could be the reason for the results discrepancy between GMM and fixed effects?
2. Do you see any misspecification in my GMM or fixed effects models, which could be responsible for this discrepancy?
3. What could I do to verify, which results are correct?

I would be very grateful to receive any comments.

Thank you very much in advance!

Kind regards,
Maria

[Phil Bromiley]

You get different results because you're estimating very different models. With a lagged dv, the parameters on the x's depend only on the variation in x that is not included in the lagged dv. It is quite likely that much of the variability in x is lost with the lagged dv. That doesn't mean you shouldn't use the lagged dv, but recognize the parameters have very different meanings.

[Maria Schmidt]

Dear Phil,

thank you very much for your answer! It helps me a lot.

As I am primarily interested on the effect of X on Y and do not expect the lagged value of Y to be of crucial importance for the model, do you think I should then go for the fixed effects instead of system GMM in my analysis? What would be an appropriate way to figure out, which model fits the best?

Thank you very much in advance!

Kind regards,
Maria