SEM, systemGMM, checking the causal link from poverty to GDP growth

[Taka Sakamoto]

Dear Statalisters:

I am analyzing the potential effects of poverty and income inequality on economic growth. When I use SEM to check the link, I get the results below, suggesting that social market economies (SMEs) reduces poverty, and then poverty reduces GDP growth through indirect effects via consumption and gross capital fixed formation. It is customary to use system-GMM in economics to examine the causal link from inequality to GDP growth to deal with reverse causality. So, I enter the command attached below to estimate the effects of poverty, I get a null result, which I think happens because the system-GMM does not take into account the indirect effects. Besides, the test results suggest that my GMM model is not good.

I would like to ask what kind of steps I can make from here. I'm new to both SEM and system-GMM. I thank you in advance for your time and help. If something is unclear, I'll explain it.

Thank you.

Taka Sakamoto

My SEM results look like this:

Then, I enter the following command:

xtabond2 gdpgrow l.koenpov50disposable l.inflation  l.gfcfgrow l.hfcegrow l.ltotsshead2 l.tradeopen l.lrgdpopc if id~=10, gmm(gdpgrow koenpov50disposable inflation  gfcfgrow hfcegrow ltotsshead2 , lag(2 2) collapse eq(diff)) gmm(gdpgrow koenpov50disposable inflation  gfcfgrow hfcegrow, lag(2 2) collapse eq(level)) iv(l.lrgdpopc l.tradeopen ,eq(level)) two robust small

And I get the GMM results:

. xtabond2 gdpgrow l.ikoenpov50disposable l.inflation  l.gfcfgrow l.hfcegrow l.ltotsshead2 l.tradeopen
> l.lrgdpopc if id~=10, gmm(gdpgrow ikoenpov50disposable inflation  gfcfgrow hfcegrow ltotsshead2 , lag
> (2 2) collapse eq(diff)) gmm(gdpgrow ikoenpov50disposable inflation  gfcfgrow hfcegrow, lag(2 2) coll
> apse eq(level)) iv(l.lrgdpopc l.tradeopen ,eq(level)) two robust small
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.

Dynamic panel-data estimation, two-step system GMM

Group variable: id                              Number of obs      =       474
Time variable : year                            Number of groups   =        18
Number of instruments = 14                      Obs per group: min =         1
F(7, 17)      =     53.29                                      avg =     26.33
Prob > F      =     0.000                                      max =        37

Corrected
gdpgrow  Coefficient  std. err.      t    P>t     [95% conf. interval]

ikoenpov50disposable
L1.    .0952777   .2081635     0.46   0.653    -.3439088    .5344642

inflation
L1.   -.4408443   .1306032    -3.38   0.004     -.716393   -.1652956

gfcfgrow
L1.    .0567349   .0259194     2.19   0.043     .0020497    .1114201

hfcegrow
L1.    .1746356   .1303227     1.34   0.198    -.1003212    .4495924

ltotsshead2
L1.   -.5971171    1.76011    -0.34   0.739    -4.310624     3.11639

tradeopen
L1.    .0009009   .0155505     0.06   0.954    -.0319078    .0337096

lrgdpopc
L1.   -2.951766   1.690673    -1.75   0.099    -6.518774    .6152423

_cons    37.37254   6.274231     5.96   0.000     24.13507    50.61001

Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L2.(gdpgrow ikoenpov50disposable inflation gfcfgrow hfcegrow ltotsshead2)
collapsed
Instruments for levels equation
Standard
L.lrgdpopc L.tradeopen
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL2.(gdpgrow ikoenpov50disposable inflation gfcfgrow hfcegrow) collapsed

Arellano-Bond test for AR(1) in first differences: z =  -3.13  Pr > z =  0.002
Arellano-Bond test for AR(2) in first differences: z =  -2.42  Pr > z =  0.015

Sargan test of overid. restrictions: chi2(6)    =  17.88  Prob > chi2 =  0.007
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(6)    =  11.61  Prob > chi2 =  0.071
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group:     chi2(1)    =   7.21  Prob > chi2 =  0.007
Difference (null H = exogenous): chi2(5)    =   4.40  Prob > chi2 =  0.494
gmm(gdpgrow ikoenpov50disposable inflation gfcfgrow hfcegrow ltotsshead2, collapse eq(diff) lag(2 2))
Hansen test excluding group:     chi2(0)    =   0.00  Prob > chi2 =      .
Difference (null H = exogenous): chi2(6)    =  11.61  Prob > chi2 =  0.071
gmm(gdpgrow ikoenpov50disposable inflation gfcfgrow hfcegrow, collapse eq(level) lag(2 2))
Hansen test excluding group:     chi2(1)    =   7.21  Prob > chi2 =  0.007
Difference (null H = exogenous): chi2(5)    =   4.40  Prob > chi2 =  0.494
iv(L.lrgdpopc L.tradeopen, eq(level))
Hansen test excluding group:     chi2(4)    =  10.89  Prob > chi2 =  0.028
Difference (null H = exogenous): chi2(2)    =   0.72  Prob > chi2 =  0.699