Fama MacBeth vs. Pooled OLS

Question

I have an unbalanced panel of monthly bond returns and would like to regress them on several possible return-drivers. There is cross-sectional correlation in the residuals. In this case, Peterson shows that there are two ways to estimate the model (Peterson (2009): Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches):

• Fama MacBeth (by using the pmg() function in R): In the first step, pmg() runs cross sectional regressions for every single month. In the second step the average over the estimates is taken. The standard deviations of the cross-sectional regression estimates are used to generate the sampling Errors for these estimates.

Fama_MacBeth<-pmg(R~SIZE+MOMENTUM+VOLA+Rating+Value+Duration+Liquidit, data=Data_Z, index=c("Date","ISIN"))

• Pooles OLS with standard Errors clustered by time

OLS_Pooling<-plm(R~SIZE)+MOMENTUM)+VOLA)+Value+Rating+Duration+Liquidity, data=Data_Z, model='pooling', index=c('ISIN', 'Date'))

Pooling_Test<- coeftest(OLS_Pooling, vcov=function(x) vcovHC(x, cluster="time", type="HC1"))

My results below are quite different for Pooled OLS and Fama MacBeth. I know that some degree od deviation is normal, but in my case even some positive and negativ signs are different.

 Dependent variable:     
                    ----------------------------
                                         R      
                     coefficient       mean     
                         test         groups    
                      Pooled OLS   Fama MacBeth 
                         (1)            (2)     
------------------------------------------------
Beta.DEF               -0.093         0.061*    
                       (0.061)        (0.034)   
                                                
SIZE                   -0.131***      -0.043**   
                       (0.020)        (0.017)   
                                                
MOMENTUM               -0.007         0.008    
                       (0.054)        (0.014)   
                                                
VOLA                   -0.257***      -0.022    
                       (0.051)        (0.017)   
                                                
Value                  -0.128***      0.019***   
                       (0.023)        (0.007)   
                                                
Rating                 0.180***      -0.013***  
                       (0.015)        (0.003)   
                                                
Duration               0.073***       0.021*    
                       (0.017)        (0.012)   
                                                
Liquidity              0.004*       0.027***   
                       (0.002)        (0.005)   
                                                
Constant              -2.386***      -1.432***  
                       (0.140)        (0.099)   
                                                
------------------------------------------------
Observations                          335,369   
R2                                     0.378    
================================================
Note:                *p<0.1; **p<0.05; ***p<0.01

Do you have any suggestion how to deal with these results? Any idea what went wrong?