Laglimits in system GMM

[Guest]

Hello everyone,

I am estimating whether there is a threshold above which financial development has a negative effect on economic growth. My variables of interest are prcredtiBI and prcreditBI2 (quadratic term). The data are split in 5 year periods 1961-1965 , 1966-1970 etc. All explanatory variables are initial values , meaning explanatory variables take the first value in each period (1961, 1996 etc). Economic growth is calculated as (Yt-Yt-5)/5.

I am using system GMM and when I use lag 2 and more as instruments I obtain significant results for my variables of interest prcreditBI and prcreditBI2. Nevertheless, when I estimate the same model using all available lags I lose the significance of either the quadratic term or the linear term variable. I want to know if it is correct to use the second lag and more as instruments? Can someone please explain if using lag 2 and more is correct?

xtabond2 gr lgrowth prcreditB prcreditB2 log_trade log_govsize log_school linfl td* if period<9, gmm(L.
> ( lgrowth prcreditB prcreditB2 log_trade log_govsize log_school linfl) , lag(2 .) ) iv(td*) two robust
> ar(3)
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
td4 dropped due to collinearity
td9 dropped due to collinearity
td10 dropped due to collinearity
td11 dropped due to collinearity
Warning: Number of instruments may be large relative to number of observations.
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.
Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: Country_ Number of obs = 567
Time variable : period Number of groups = 117
Number of instruments = 148 Obs per group: min = 1
Wald chi2(14) = 292.37 avg = 4.85
Prob > chi2 = 0.000 max = 8
------------------------------------------------------------------------------
| Corrected
gr | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lgrowth | -.7689202 .3082432 -2.49 0.013 -1.373066 -.1647746
prcreditB | 6.905971 2.156115 3.20 0.001 2.680063 11.13188
prcreditB2 | -4.228281 1.353518 -3.12 0.002 -6.881127 -1.575434
log_trade | -.1900365 .4802487 -0.40 0.692 -1.131307 .7512337
log_govsize | -2.145452 1.069133 -2.01 0.045 -4.240915 -.0499899
log_school | 1.897029 .4945887 3.84 0.000 .927653 2.866405
linfl | -.3022494 .1936457 -1.56 0.119 -.681788 .0772891
td1 | -.0600677 .7960421 -0.08 0.940 -1.620282 1.500146
td2 | .6802363 .7777636 0.87 0.382 -.8441524 2.204625
td3 | .0154354 .5971205 0.03 0.979 -1.154899 1.18577
td5 | -2.372172 .4649549 -5.10 0.000 -3.283467 -1.460878
td6 | -1.526232 .4668291 -3.27 0.001 -2.4412 -.6112635
td7 | -2.051561 .4730705 -4.34 0.000 -2.978762 -1.12436
td8 | -1.754049 .5397025 -3.25 0.001 -2.811847 -.6962519
_cons | 12.7255 3.329272 3.82 0.000 6.200247 19.25075
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(td1 td2 td3 td4 td5 td6 td7 td8 td9 td10 td11)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(2/10).(L.lgrowth L.prcreditB L.prcreditB2 L.log_trade L.log_govsize
L.log_school L.linfl)
Instruments for levels equation
Standard
td1 td2 td3 td4 td5 td6 td7 td8 td9 td10 td11
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL.(L.lgrowth L.prcreditB L.prcreditB2 L.log_trade L.log_govsize
L.log_school L.linfl)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -3.45 Pr > z = 0.001
Arellano-Bond test for AR(2) in first differences: z = -1.71 Pr > z = 0.086
Arellano-Bond test for AR(3) in first differences: z = 0.25 Pr > z = 0.804
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(133) = 167.65 Prob > chi2 = 0.023
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(133) = 87.61 Prob > chi2 = 0.999
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(98) = 84.08 Prob > chi2 = 0.841
Difference (null H = exogenous): chi2(35) = 3.53 Prob > chi2 = 1.000

[Guest]

Can someone help please? It is urgent

[Al litu]

You got any explanations?
i also need to know this.
Can you?

[Sebastian Kripfganz]

You might find the following presentation slides useful:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.

[Al litu]

Model 2: LGDPPC = β₀+ β₁ LGDPPC _{i t-1} + β2PI_it-1 + β3LFDI_it-1 + β₄(PI*LFDI) + β₅LTO_it + β₆LCAP_it + β₇LLAB_it + ε_it

Model 3: LGDPPC = β₀+ β₁ LGDPPC _{i t-1} + β2PI_it-1 + β3LFDI_it-1 + β₄(PI _it-1*LFDI _it-1) + β₅LTO_it + β₆LCAP_it + β₇LLAB_it + ε_{it
hI, My panel suggests me to consider two of my focus variables as indegenous. PI and FDI. Now, I want to know if i take their lag and if I want to show their interaction term also, then should i take interaction of the lagged version or I can show interaction without the lagged version?
I am using two step system GMM but I do not want to use time dummy. If i do not use time dummies, then the model is invalid?I have 90 countries and 20 years of data.
WHich model is ok? MODEL 1 or 2? should i take the lagged version when showing interaction? or not?
IF i take conside PI and FDI as endogenous the may i SHow this in equation like this?}β2PI_it-1 + β3LFDI_it-1 ?

[Sebastian Kripfganz]

Lagging regressors because they are deemed endogenous is a very bad empirical practice. This usually leads to model misspecification, which might even be worse than the initial endogeneity problem. If the variables are endogenous, you should instead choose appropriate instruments.

Why do you "not want" to use time dummies? In such macroeconomic applications, there are hardly good reasons for not including time dummies, as they capture unobserved global variables which often have a relevant influence.

[Al litu]

Thank you for your reply.
I did not include those as endogenous in my model in stata. I considered only the lag1 of dependent variable as endogenous and used 2 lag of that as instrument aslo. But as panels are urging, I asked here first.

Actually, I estimated my result without time dummies; I do not have enough knowledge about it, so i excluded it. Now I am at a loss as I have estimated and explained my result already.You are true, as I am not getting any justification.