Strange results of difference GMM using pgmm in R

Question

I am running three regressions to identify the effect of immigration in Germany using, ols, first differences and the difference GMM model from Arellano and Bond. I use a regional approach and compare the unemployment rate and the foreign share in Germany. I use the pgmm function of the plm package and I want to use the three and four year lagged values of the foreign-share of the districts of instrumental variables.

The results confuse me, because the effect of a higher share of foreigners is ten times higher in the GMM model. I wonder if I have done anything wrong in the description of the instrumental variables within the GMM function. I have found no similar effect of the foreign share in my literature.

1. My results are the following

Table 2
The effects of immigrants for the unemployment rate in Germany 

                      OLS             DIFF           GMM

Foreign share           0.040***    0.056*          0.530***
    
Average age native  0.420***    0.150***    0.003
    
Average age foreign -0.114***   0.123***    0.158***

In the following is that code that I have used to compute the three regressions:

ols=plm(Arbeitslosenquote~Ausländeranteil+Durchschnittsalter_Inländer+Durchschnittsalter_Ausländer,effects="time",model="pooling",data=newjoin,index=c("Kreise","Jahr"),pooling=TRUE)
      
first_difference=plm(Arbeitslosenquote~Ausländeranteil+Durchschnittsalter_Inländer+Durchschnittsalter_Ausländer,data=newjoin,model="fd",effects="time",index=c("Kreise","Jahr"),robust=TRUE)
                  
GMM=pgmm(formula=unemployment_rate~foreign_share+mean_age_natives+mean_age_foreignes| lag(foreign_share,3:4),
         data=my_data,model="twosteps",index=c("Kreise","Jahr"),
         effect="twoways",time.dummies=TRUE,transformation="d",robust=TRUE)