Hello, I am bit unsure of whether my interpretaion of the coefficients is correct:
The following are my STATA commands, dependant variable is delta of log gdp per capita (real) and Im interested in corruption (CPI_est_scale) and interaction term of corruption between democracy (c.polyarchy_scale)

xtabond2 d_ln_gdp_pc l.d_ln_gdp_pc c.CPI_est_scale##c.polyarchy_scale d_money_supply cap_pop openess educ_yrs d_ln_pop i.year_group, gmm(l.d_ln_gdp_pc c.cc_est_scale##c.polyarchy_scale d_money_supply cap_pop openess educ_yrs d_ln_pop) iv(i.year_group, eq(level)) twostep robust

margins, dydx(CPI_est_scale) atmeans at(polyarchy_scale=(0(.5)6))
marginsplot
graph export output/gmm_CPI_est_margins.pdf, replace


this is my STATA output:
Dependant Variable Annual Growth rate of real GDP per capita (1)
Lagged Real GDP/Capita Growth 0.446***

(0.0745)
Corruption (CPI) ( -0.0760*

(0.0364)
Democracy -0.0631**
(0.0219)
CorruptionCPIxDemocracy 0.0192*

(0.00878)
Delta Money Supply 0.000771

(0.00111)
Capital Per capita 0.00000481

(0.00000471)
Economic Freedom -0.00160

(0.00188)
Educational Attainment -0.00150

(0.00678)
Population Growth -0.649**

(0.208)
0.year_group 0
(.)
1.year_group 0
(.)
2.year_group 0.0995***
(0.0135)
3.year_group 0.0317*
(0.0133)
4.year_group 0
(.)
Bureocratic (GE)
Bureocratic (GE) x Demorcacy
_cons 0.430*



Autocorrell-p-values

Hansen J-statistic (p-value)		 (0.172)




(0.037)




(0.200)

Robust







N 331
Robust Standard errors in parentheses
* p < 0.05, ** p < 0.01, *** p < 0.001


Is it correct to intepret these results as follows: At the mean level of democracy of 3.418, the marginal effect of () corruption on economic growth is equal to d (growth rate of real GDP per capita) / d CPI= -0.076+3.418*0.0192= -0.0104, which implies that increasing the corruption score by one standard deviation (1.399), decreases economic growth by 1.45 percentage points? And given theis marginal effects equation: d (growth rate of real GDP per capita) / d CPI= -0.076+DEMOCRACY*0.0192= -0.0104, from a level of 3,96=DEMOCRACY the marginal effect of corrutpion on economic growth rate is positive so greater corruption increaes growth rate of GDPPC? Thanks for any help