Hi,

I'm currently modeling the public-private wage gap in Brazil. The work revolves around estimating Mincer earning equations for all Brazilian States for a set of years, based on public surveys that we have here, of course controlling (through a dummy) if the person is a public employee or not.

With they average pay gap estimated by the first set of equations I'm looking to how this pay gap behaves along other macro variables. After literature research and testing some models I have the following model:

xtdpdgmm l(0/3).gap pibg l(0/2).desemp, collapse model(diff) gmm(gap, l(2 4)) gmm(pibg, l(0 3)) gmm(desemp, l(0 6)) teffects two vce(robust)

Reporting only the coefficients and p-values in []

Fitting full model:
Step 1 f(b) = .00116484
Step 2 f(b) = .13189159

Group variable: uf Number of obs = 297
Time variable: year Number of groups = 27

Moment conditions: linear = 25
Obs per group: min = 11
nonlinear = 0 avg = 11
total = 25 max = 11

(Std. Err. adjusted for 27 clusters in uf)
------------------------------------------------------------------------------
| WC-Robust
gap | Coef. [P>|z|]
-------------+----------------------------------------------------------------
gap |
L1. | .4221597 [0.002]
L2. | .0809683 [0.525]
L3. | .1240309 [0.187]
|
pibg | .227904 [0.018]
|
desemp |
--. | 1.070113 [0.212]
L1. | -.0882452 [0.922]
L2. | 2.114248 [0.071]
|
year |
2006 | .0397795 [0.170]
2007 | .0089088 [0.671]
2008 | .0144458 [0.608]
2009 | .0381506 [0.119]
2010 | .0383212 [0.143]
2011 | .0269762 [0.289]
2012 | .0734528 [0.026]
2013 | .0696775 [0.010]
2014 | .1018182 [0.006]
2015 | .0931151 [0.032]
|
_cons | -.1425435 [0.551]
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(diff):
L2.gap L3.gap L4.gap
2, model(diff):
pibg L1.pibg L2.pibg L3.pibg
3, model(diff):
desemp L1.desemp L2.desemp L3.desemp L4.desemp L5.desemp L6.desemp
4, model(level):
2006bn.year 2007.year 2008.year 2009.year 2010.year 2011.year 2012.year
2013.year 2014.year 2015.year
5, model(level):
_cons


Sargan-Hansen test of the overidentifying restrictions
H0: overidentifying restrictions are valid

2-step moment functions, 2-step weighting matrix chi2(7) = 3.5611
Prob > chi2 = 0.8287

2-step moment functions, 3-step weighting matrix chi2(7) = 3.8972
Prob > chi2 = 0.7915

Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1: z = -3.9248 Prob > |z| = 0.0001
H0: no autocorrelation of order 2: z = 1.3064 Prob > |z| = 0.1914
H0: no autocorrelation of order 3: z = 0.7208 Prob > |z| = 0.4711
H0: no autocorrelation of order 4: z = 0.6962 Prob > |z| = 0.4863
H0: no autocorrelation of order 5: z = -1.1282 Prob > |z| = 0.2592


Where 'gap' is the pay gap between public and private employees; 'pibg' is the growth rate of the real GDP and 'desemp' is the level of unemployment. Other variables and model specifications were tested and this one is the one that seems more reliable. Coefficients for are significant and with the expected signal

Taking into account the reduced number of instruments, overidentifying tests and ABAR tests the seems to be ok.

So what's my concern. The model seems to be well specified only when I include lags 2 and 3 of the dependent variable, and even if they are non significant if I remove them the fitting tests worsen a lot.

My doubt is: is there any problem to keep these parameters on the model even if they are non significant if they improve (a lot) the moment conditions?

Thank you!