Dear Statalist participants,

I am running a panel data modeling in the municipality level of aggregation, as all my variables are in municipality-level. As my dependent variable presents a high portion of zero-valued observations, I am using the PPML estimator to run my regressions. My key explanatory variables are IndVar1, IndVar2 and IndVar3 and the others are control variables. As expected, in the main results in regression (1), IndVar3 e IndVar4 are captured by the year fixed effects, because they do not show variation through the years, and Var2 is captured by the region fixed effects, because it does not vary within the places, just through the years. I would like to run some robustness analysis. Discussing with my Ph.D. colleagues, one of them told me to modify the level of aggregation and verify the stability of the estimations. I searched in the literature and did not find such sensitivity analysis for a robustness check. The lowest level is the municipality. The second is the microregion, which contains many municipalities, and so on: Municipality < Microregion < Mesoregion < State < Region < Country(or no region fixed effect). I observe the following results, keeping the cluster in the municipality with
Code:
vce(cluster code_mun)
:

Code:
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                              (1)             (2)             (3)             (4)             (5)             (6)             (7)   
                     Municipality     Microregion      Mesoregion           State          Region            None            None   
------------------------------------------------------------------------------------------------------------------------------------
IndVar1                     0.518+          0.520+          0.542*          0.544*          0.292**         0.455***        0.421***
                           (0.27)          (0.27)          (0.24)          (0.22)          (0.10)          (0.08)          (0.07)   
IndVar2                                                                                                                    -0.662***
                                                                                                                           (0.03)   
IndVar3                                     0.159           0.205           0.263           0.690*          0.531+          0.537+  
                                           (0.80)          (0.41)          (0.24)          (0.27)          (0.31)          (0.31)   
ln(IndVar4)                                 1.167***        1.147***        1.149***        1.063***        0.966***        0.966***
                                           (0.07)          (0.07)          (0.05)          (0.07)          (0.05)          (0.05)   
ln(IndVar5)                 1.361          -0.018          -0.048          -0.133**        -0.085+         -0.017          -0.016   
                           (6.80)          (0.09)          (0.07)          (0.05)          (0.05)          (0.04)          (0.04)   
ln(IndVar6)                 0.152           0.716***        0.750***        0.700***        0.662***        0.916***        0.909***
                           (0.54)          (0.17)          (0.11)          (0.11)          (0.11)          (0.08)          (0.07)   
Constant                  -10.046         -23.446***      -23.916***      -23.337***      -22.264***      -24.636***      -19.747***
                          (39.15)          (3.58)          (2.40)          (2.38)          (1.91)          (2.02)          (2.18)   
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Observations                22995           22995           22995           22995           22995           22995           22995   
Pseudo-R-sqr                 0.88            0.79            0.74            0.71            0.68            0.67            0.66   
Log Pseudo-Lik.          -5607.27        -9809.12       -11853.13       -13362.15       -14539.46       -15119.41       -15511.41   
Regional FE                   Yes             Yes             Yes             Yes             Yes              No              No   
Year FE                       Yes             Yes             Yes             Yes             Yes             Yes              No   
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Standard errors in parentheses
+ p<0.10, * p<0.05, ** p<0.01, *** p<0.001
In general lines, I can observe stability in the coefficients as I modify the level of aggregation. The coefficients might change in the level of statistical significance, but the signs and the magnitude keep the standards.

My questions are:

1- What I am testing if I realize this sensitivity analysis?
2- Do you think it is a good method for sensitivity analysis of robustness check?
3- If question 1 is yes, should I keep the cluster in the muncipality level or change according to each level of aggregation?
4- Would you recommend some literature using similar method?
5- As I expand the level of aggregation, the Log Pseudo-Likelyhood and the Pseudo R2 show that the models decreases the explanation power. Why does it happen?
6- When I expand the level of aggregation, IndVar3 and IndVar4 are not captured by place fixed effects anymore. Why does it happen?

Thank you in advance.