Hello!

For a university project, I am investigating the impact of income inequality on economic growth. To do this, I have regressed the average five-year growth rates of GDP per capita (agr) on the Gini coefficient (ginid) and a number of control variables, which include the natural logarithm of the value for output at the beginning of each period (gdpL1).

I believe a dynamic panel data estimator model must be estimated in order to achieve this, since average growth rates are calculated by subtracting the natural logarithm of the value of output at the start of the five-year period (gdpL1) from the natural logarithm of the value of output at the end of the five-year period (gdp). I have thus used the following code in order to obtain systems-GMM estimators:

Code:
xtabond2 agr ginid gdpL1 schl invrt pli, gmmstyle (ginid gdpL1 schl invrt pli, lag(0 0) eq(level) collapse) gmmstyle (ginid gdpL1 schl invrt pli, lag(1 1) eq(diff) collapse) twostep robust small
This has yielded the following results for me:

Code:
Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: cid                             Number of obs      =       600
Time variable : period                          Number of groups   =       123
Number of instruments = 11                      Obs per group: min =         2
F(5, 122)     =     34.48                                      avg =      4.88
Prob > F      =     0.000                                      max =         6
------------------------------------------------------------------------------
             |              Corrected
         agr |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       ginid |  -6.311882    1.13181    -5.58   0.000    -8.552413   -4.071352
       gdpL1 |  -.3207819   8.090252    -0.04   0.968    -16.33624    15.69468
        schl |  -23.85938   7.747925    -3.08   0.003    -39.19717   -8.521588
       invrt |   .9996619   .3860444     2.59   0.011     .2354484    1.763875
         pli |  -2.560345   .5779149    -4.43   0.000    -3.704385   -1.416305
       _cons |   310.9364   73.78493     4.21   0.000     164.8717     457.001
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L.(ginid gdpL1 schl invrt pli) collapsed
Instruments for levels equation
  Standard
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.(ginid gdpL1 schl invrt pli) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -4.43  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =  -5.54  Pr > z =  0.000
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(5)    =  10.57  Prob > chi2 =  0.061
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(5)    =   7.86  Prob > chi2 =  0.164
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(0)    =   0.00  Prob > chi2 =      .
    Difference (null H = exogenous): chi2(5)    =   7.86  Prob > chi2 =  0.164
  gmm(ginid gdpL1 schl invrt pli, collapse eq(level) lag(0 0))
    Hansen test excluding group:     chi2(0)    =   0.00  Prob > chi2 =      .
    Difference (null H = exogenous): chi2(5)    =   7.86  Prob > chi2 =  0.164
  gmm(ginid gdpL1 schl invrt pli, collapse eq(diff) lag(1 1))
    Hansen test excluding group:     chi2(0)    =   0.00  Prob > chi2 =      .
    Difference (null H = exogenous): chi2(5)    =   7.86  Prob > chi2 =  0.164
The issue I have spotted is that, plainly, there is a problem of autocorrelation in first-differences as per the statistically significant test for AR(2). However, I noticed that the test statistic for AR(2) has an absolute value that is larger than that of AR(1), which seems peculiar to me since one might expect negative first-order serial correlation in first-differences.

I was therefore wondering if there was anything about my code which might explain this peculiarity, or if it is instead a problem with the specification itself.

Many thanks in advance!