xtabond 2: dynamic model and coefficient changes

[Zahrina Adani]

Hello everyone, I need some help regarding dynamic and static panel data.

So, I have done my regression using two way fixed effect estimator. I want to see the impact of trade openness on income inequality. I use TradeToGDP as the openness measure.

xtreg Gini TradeToGDPLowIncome TradeToGDPMiddleIncome TradeToGDPHighIncome IncomeTax Inflation AgricultureEmp FDI_Inflow_Net i.Years, fe

and this gives me:

Fixed-effects (within) regression Number of obs = 1,136
Group variable: Country1 Number of groups = 76

R-sq: Obs per group:
within = 0.1246 min = 1
between = 0.0058 avg = 14.9
overall = 0.0031 max = 27

F(33,1027) = 4.43
corr(u_i, Xb) = -0.4614 Prob > F = 0.0000

----------------------------------------------------------------------------------------
Gini | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
TradeToGDPLowIncome | -.06155 .0161868 -3.80 0.000 -.093313 -.0297869
TradeToGDPMiddleIncome | .0199004 .0081096 2.45 0.014 .0039871 .0358138
TradeToGDPHighIncome | .0199616 .0089076 2.24 0.025 .0024825 .0374408
IncomeTax | .0293793 .0152064 1.93 0.054 -.0004598 .0592184
Inflation | .0006822 .0010576 0.65 0.519 -.001393 .0027575
AgricultureEmp | .1802943 .034233 5.27 0.000 .1131196 .247469
FDI_Inflow_Net | 3.99e-12 2.23e-12 1.79 0.074 -3.92e-13 8.37e-12
|
Years |
1992 | -.3466778 .9122989 -0.38 0.704 -2.136861 1.443505
1993 | -.2133869 .919033 -0.23 0.816 -2.016784 1.59001
1994 | .8066799 .8812392 0.92 0.360 -.9225551 2.535915
1995 | 1.299737 .8665922 1.50 0.134 -.4007569 3.00023
1996 | .5405956 .8596357 0.63 0.530 -1.146247 2.227439
1997 | 1.383839 .8623544 1.60 0.109 -.3083392 3.076017
1998 | 1.800655 .8567846 2.10 0.036 .1194068 3.481903
1999 | 2.10394 .8548144 2.46 0.014 .4265573 3.781322
2000 | .9132993 .8602804 1.06 0.289 -.7748087 2.601407
2001 | 1.508731 .858822 1.76 0.079 -.1765157 3.193977
2002 | 1.882481 .8448652 2.23 0.026 .2246215 3.54034
2003 | 2.1945 .8515699 2.58 0.010 .5234848 3.865516
2004 | 2.133066 .8355123 2.55 0.011 .4935601 3.772573
2005 | 1.812517 .8373152 2.16 0.031 .1694726 3.455561
2006 | 2.070935 .8499631 2.44 0.015 .4030726 3.738798
2007 | 1.837156 .855111 2.15 0.032 .1591915 3.51512
2008 | 1.395048 .8527779 1.64 0.102 -.2783381 3.068434
2009 | 1.628369 .8362036 1.95 0.052 -.0124939 3.269232
2010 | 1.221273 .8387296 1.46 0.146 -.4245468 2.867092
2011 | .4981045 .8497077 0.59 0.558 -1.169257 2.165466
2012 | .7187541 .8564171 0.84 0.402 -.9617731 2.399281
2013 | 1.13784 .863204 1.32 0.188 -.5560051 2.831685
2014 | 1.024986 .8635313 1.19 0.236 -.6695011 2.719473
2015 | 1.10972 .8693817 1.28 0.202 -.5962473 2.815687
2016 | .0624701 .890913 0.07 0.944 -1.685748 1.810688
2017 | -.6174582 1.016741 -0.61 0.544 -2.612586 1.377669
|
_cons | 30.61958 1.2186 25.13 0.000 28.22835 33.01081
-----------------------+----------------------------------------------------------------
sigma_u | 9.2271905
sigma_e | 2.7934134
rho | .9160447 (fraction of variance due to u_i)
----------------------------------------------------------------------------------------
F test that all u_i=0: F(75, 1027) = 104.46 Prob > F = 0.0000


then, since I wanted to see the dynamic model as well, I regressed the variables above including Gini lagged 1 with xtabond2

xtabond2 Gini l.Gini TradeToGDPLowIncome TradeToGDPMiddleIncome TradeToGDPHighIncome IncomeTax Inflation AgricultureEmp AgricultureEmp,gmm(l.Gini, collapse) iv(TradeToGDPLowIncome TradeToGDPMiddleIncome TradeToGDPHighIncome IncomeTax Inflation AgricultureEmp AgricultureEmp, equation(level)) robust

Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
AgricultureEmp dropped due to collinearity
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate robust weighting matrix for Hansen test.
Difference-in-Sargan statistics may be negative.

Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: Country1 Number of obs = 979
Time variable : Years Number of groups = 63
Number of instruments = 44 Obs per group: min = 1
Wald chi2(7) = 39.37 avg = 15.54
Prob > chi2 = 0.000 max = 27
----------------------------------------------------------------------------------------
| Robust
Gini | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
Gini |
L1. | -.0211976 .203964 -0.10 0.917 -.4209597 .3785644
|
TradeToGDPLowIncome | .0082909 .0090827 0.91 0.361 -.0095108 .0260927
TradeToGDPMiddleIncome | -.0299092 .0152892 -1.96 0.050 -.0598755 .0000572
TradeToGDPHighIncome | -.0448108 .0168887 -2.65 0.008 -.0779121 -.0117096
IncomeTax | -.0626523 .054567 -1.15 0.251 -.1696017 .0442971
Inflation | .0013642 .0046243 0.30 0.768 -.0076992 .0104276
AgricultureEmp | .1927797 .0848601 2.27 0.023 .0264569 .3591025
_cons | 39.04371 7.929515 4.92 0.000 23.50215 54.58527
----------------------------------------------------------------------------------------
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/.).L.Gini collapsed
Instruments for levels equation
Standard
_cons
TradeToGDPLowIncome TradeToGDPMiddleIncome TradeToGDPHighIncome IncomeTax
Inflation AgricultureEmp AgricultureEmp
GMM-type (missing=0, separate instruments for each period unless collapsed)
D.L.Gini collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -1.52 Pr > z = 0.129
Arellano-Bond test for AR(2) in first differences: z = -0.45 Pr > z = 0.649
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(36) = 53.66 Prob > chi2 = 0.029
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(36) = 31.97 Prob > chi2 = 0.661
(Robust, but can be weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(35) = 31.96 Prob > chi2 = 0.616
Difference (null H = exogenous): chi2(1) = 0.02 Prob > chi2 = 0.900
iv(TradeToGDPLowIncome TradeToGDPMiddleIncome TradeToGDPHighIncome IncomeTax Inflation AgricultureEmp AgricultureEmp, eq(level))
Hansen test excluding group: chi2(30) = 23.43 Prob > chi2 = 0.797
Difference (null H = exogenous): chi2(6) = 8.54 Prob > chi2 = 0.201

My question is, how can I justify the change of the coefficient in the dynamic model? in the static model I only have TradeToGDPLowIncome which is negative while in the dynamic model it becomes positives. For the TradeToGDPMiddleIncome and TradeToGDPHighIncome it's the other way around. Could somebody please help me why this is happening? And what should I do with my analysis?

Thanks a lot in advance

[Sebastian Kripfganz]

Your results are not comparable because you do not have time dummies in your dynamic model. (When specifying time dummies, note that there is a bug in xtabond2 that yields incorrect degrees of freedoms for the overidentification tests when some of these dummies are reported as omitted. You should either specify the dummies manually without factor notation or use the xtdpdgmm command instead; see below.)

More on GMM estimation of linear dynamic panel data models:
XTDPDGMM: new Stata command for efficient GMM estimation of linear (dynamic) panel models

[Zahrina Adani]

Your results are not comparable because you do not have time dummies in your dynamic model. (When specifying time dummies, note that there is a bug in xtabond2 that yields incorrect degrees of freedoms for the overidentification tests when some of these dummies are reported as omitted. You should either specify the dummies manually without factor notation or use the xtdpdgmm command instead; see below.)

More on GMM estimation of linear dynamic panel data models:
XTDPDGMM: new Stata command for efficient GMM estimation of linear (dynamic) panel models

Dear Sebastian, thank you for your reply. So I can use the XTDPDGMM to introduce the time dummies instead of the xtabond2?

[Sebastian Kripfganz]

xtdpdgmm has the option teffects that automatically adds the relevant time dummies.

[Zahrina Adani]

xtdpdgmm has the option teffects that automatically adds the relevant time dummies.

Dear Sebastian,

I have tried your xtdpdgmm and teffects. Thank you. I still a have question though.
As you see above that I regressed both the dynamic and static models, and found only TradeToGDPLowIncome and Agriculture Employment that are significant in static model. In the dynamic model they became insignificant. Does it mean that Trade To GDP doesn't actually have an impact on income inequality? I'm still confused when I encounter a result when the variables become insignificant after regressing in dynamic model. Thanks in advance.

[Sebastian Kripfganz]

The coefficient of the lagged dependent variable is close to 1. This means that a large amount of variation is explained by history dependence rather than the other explanatory variables. It is not uncommon in these situations that explanatory variables lose statistical significance, in particular if they are themselves highly persistent such that their effect becomes hard to distinguish from the the autoregressive part.

In any case, your number of instruments appears to be too high which could also effect the precision of your estimates.