Hi Statalisters,

I ran xtabond2 command to study the dynamic relationship between institutions and per capita carbon emissions and carbon intensity. The main difference between the two regressions below is the dependent variable. The dependent variable in the first regression is per capita carbon emissions, while in the second is the carbon intensity of energy use.

Code:
qui xtabond2 lpccarb L.lpccarb lrgdp c.lrgdp#c.lrgdp  lenguse lpopden indus period3-period31, gmm(L.(lpccarb) L.(lrgdp lrgdp2  lpopden lenguse indus), collapse lag(1 4) ortho) iv(i.year lenguse lpopden, equation(level)) robust twostep small ortho

margins , dydx(lrgdp) at((p10) lrgdp) at((p25) lrgdp) at((p50) lrgdp) at((p75) lrgdp) at((p90) lrgdp)
Warning: cannot perform check for estimable functions.

Average marginal effects                        Number of obs     =      2,953
Model VCE    : Corrected

Expression   : Fitted Values, predict()
dy/dx w.r.t. : lrgdp

1._at        : lrgdp           =    7.722011 (p10)

2._at        : lrgdp           =    8.404015 (p25)

3._at        : lrgdp           =    9.261054 (p50)

4._at        : lrgdp           =    10.13737 (p75)

5._at        : lrgdp           =    10.63512 (p90)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lrgdp        |
         _at |
          1  |   .3619309   .1424492     2.54   0.011     .0827356    .6411262
          2  |   .2485135   .1102424     2.25   0.024     .0324425    .4645846
          3  |   .1059876   .0753118     1.41   0.159    -.0416209    .2535961
          4  |  -.0397445   .0579482    -0.69   0.493    -.1533208    .0738318
          5  |  -.1225195   .0631338    -1.94   0.052    -.2462595    .0012204
------------------------------------------------------------------------------
Code:
qui xtabond2 co2int L.co2int lrgdp lrgdp2 frleg frleg2 c.frleg#c.lrgdp lpopden indus  period3-period31, gmm(L.( co2int lrgdp lrgdp2 frleg c.frleg#c.frleg  lpopden indus), collapse lag(1 4) ortho ) iv( period3-period31  frleg frleg2  c.frleg#c.lrgdp  lpopden  , equation(level)) robust twostep small ortho

margins , dydx(lrgdp) at((p10) lrgdp) at((p25) lrgdp) at((p50) lrgdp) at((p75) lrgdp) at((p90) lrgdp)
Warning: cannot perform check for estimable functions.

Average marginal effects                        Number of obs     =      2,944
Model VCE    : Corrected

Expression   : Fitted Values, predict()
dy/dx w.r.t. : lrgdp

1._at        : lrgdp           =    7.723423 (p10)

2._at        : lrgdp           =    8.404617 (p25)

3._at        : lrgdp           =     9.26136 (p50)

4._at        : lrgdp           =    10.13833 (p75)

5._at        : lrgdp           =    10.63704 (p90)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lrgdp        |
         _at |
          1  |   1.207137    .459612     2.63   0.009     .3063144     2.10796
          2  |   1.207137    .459612     2.63   0.009     .3063144     2.10796
          3  |   1.207137    .459612     2.63   0.009     .3063144     2.10796
          4  |   1.207137    .459612     2.63   0.009     .3063144     2.10796
          5  |   1.207137    .459612     2.63   0.009     .3063144     2.10796
------------------------------------------------------------------------------
I use margins command to understand how the marginal effect of institutions affect the Environmental Kuznets Curve relationship or how the inclusion of institutions affects the impact of income on carbon emissions.
When I ran margins command, I don't know why do I get same dy/dx for carbon intensity at different percentiles? However, that's not the case with per capita carbon emissions (see margins results from the first equation).

#1. Am I running the wrong postestimation command?

#2. Why is the marginal effect of institutions on EKC relationship same at different percentiles for carbon intensity?

#3. Can someone also help me with the interpretation of margins command? I read that it's not a unit change but in fact a small change in x affecting y. Please correct me if I am wrong.

Thank you.

Ritika