My data is structured as follows
Code:
* Example generated by -dataex-. For more info, type help dataex
clear
input int(id year) float y byte x1 float(x2 x3 x4)
4 2002 . 0 . . .
4 2003 . 0 . . .
4 2004 77.5 0 1.1184173 . 2.397895
4 2005 69.23 0 1.2320774 .03 2.484907
4 2006 69.64 0 1.198828 .09 2.397895
4 2007 69.05 0 1.168271 .03 2.484907
4 2008 71.25 0 .9770876 .01 2.397895
4 2009 68.75 0 .9854457 .01 2.397895
4 2010 69.05 1 .8685386 .01 2.484907
4 2011 71.43 1 .9251 .01 2.564949
4 2012 65.85 1 .8766528 .01 2.564949
4 2013 68.6 1 .9305043 -.12 2.564949
4 2014 70.93 1 .9707114 .01 2.6390574
4 2015 74.47 1 1.0396616 .01 2.397895
4 2016 68.75 1 .9870396 .02 2.397895
4 2017 76.92 1 .9896186 .02 2.397895
4 2018 75.68 1 1.042021 .02 2.397895
4 2019 73.38 1 1.0807108 .02 2.397895
4 2020 72.29 1 1.139076 .02 2.397895
4 2021 48.8 1 1.1821591 .02 2.397895
4 2022 . 1 . . .
end
When I type this code
Code:
xtabond2 y l.y l2.y i.x1 x2 x3 x4 year*, gmm(y, laglimits(6 9) collapse) gmm(x4, laglimits(0 0) eq(level) collapse) gmm( x1, laglimits (1 6)) iv(x2) iv(x3) iv( year*, eq(level)) twostep rob
Code:
Dynamic panel-data estimation, two-step system GMM ------------------------------------------------------------------------------ Group variable: id Number of obs = 56230 Time variable : year Number of groups = 8009 Number of instruments = 76 Obs per group: min = 1 Wald chi2(7) = 305279.82 avg = 7.02 Prob > chi2 = 0.000 max = 18 ------------------------------------------------------------------------------ | Corrected y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- y | L1. | .6579452 .1257772 5.23 0.000 .4114264 .904464 L2. | .203073 .1159586 1.75 0.080 -.0242018 .4303477 | 1.x1 | 1.731265 .6617663 2.62 0.009 .4342269 3.028303 x2 | -.181484 .059002 -3.08 0.002 -.2971259 -.0658422 x3 | 6.685274 .6702776 9.97 0.000 5.371554 7.998994 x4 | 2.542435 .9939581 2.56 0.011 .5943129 4.490557 year | .1915175 .0268854 7.12 0.000 .138823 .244212 _cons | -382.9742 55.254 -6.93 0.000 -491.2701 -274.6784 ------------------------------------------------------------------------------ Instruments for first differences equation Standard D.x3 D.x2 GMM-type (missing=0, separate instruments for each period unless collapsed) L(1/6).x1 L(6/9).y collapsed Instruments for levels equation Standard year x3 x2 _cons GMM-type (missing=0, separate instruments for each period unless collapsed) D.x1 D.x4 collapsed DL5.y collapsed ------------------------------------------------------------------------------ Arellano-Bond test for AR(1) in first differences: z = -3.06 Pr > z = 0.002 Arellano-Bond test for AR(2) in first differences: z = -0.44 Pr > z = 0.661 ------------------------------------------------------------------------------ Sargan test of overid. restrictions: chi2(68) = 74.56 Prob > chi2 = 0.274 (Not robust, but not weakened by many instruments.) Hansen test of overid. restrictions: chi2(68) = 74.73 Prob > chi2 = 0.269 (Robust, but weakened by many instruments.) Difference-in-Hansen tests of exogeneity of instrument subsets: GMM instruments for levels Hansen test excluding group: chi2(55) = 54.86 Prob > chi2 = 0.480 Difference (null H = exogenous): chi2(13) = 19.87 Prob > chi2 = 0.098 gmm(y, collapse lag(6 9)) Hansen test excluding group: chi2(63) = 62.68 Prob > chi2 = 0.488 Difference (null H = exogenous): chi2(5) = 12.06 Prob > chi2 = 0.034 gmm(x4, collapse eq(level) lag(0 0)) Hansen test excluding group: chi2(67) = 74.71 Prob > chi2 = 0.242 Difference (null H = exogenous): chi2(1) = 0.02 Prob > chi2 = 0.877 gmm(x1, lag(1 6)) Hansen test excluding group: chi2(2) = 1.84 Prob > chi2 = 0.399 Difference (null H = exogenous): chi2(66) = 72.89 Prob > chi2 = 0.262 iv(x2) Hansen test excluding group: chi2(67) = 74.64 Prob > chi2 = 0.244 Difference (null H = exogenous): chi2(1) = 0.10 Prob > chi2 = 0.756 iv(x3) Hansen test excluding group: chi2(67) = 74.72 Prob > chi2 = 0.242 Difference (null H = exogenous): chi2(1) = 0.02 Prob > chi2 = 0.899 iv(year, eq(level)) Hansen test excluding group: chi2(67) = 72.87 Prob > chi2 = 0.291 Difference (null H = exogenous): chi2(1) = 1.86 Prob > chi2 = 0.173
Code:
xtabond2 y l.y l2.y l3.y i.x1 x2 x3 x4 year*, gmm(y, laglimits(6 9) collapse) gmm(x4, laglimits(0 0) eq(level) collapse) gmm( x1, laglimits (1 6)) iv(x2) iv(x3) iv( year*, eq(level)) twostep rob
Code:
Dynamic panel-data estimation, two-step system GMM ------------------------------------------------------------------------------ Group variable: id Number of obs = 48584 Time variable : year Number of groups = 6865 Number of instruments = 75 Obs per group: min = 1 Wald chi2(8) = 290706.28 avg = 7.08 Prob > chi2 = 0.000 max = 17 ------------------------------------------------------------------------------ | Corrected y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- y | L1. | .6406586 .1225116 5.23 0.000 .4005402 .8807771 L2. | .1945418 .1598152 1.22 0.223 -.1186903 .5077739 L3. | .0162681 .1021677 0.16 0.873 -.183977 .2165131 | 1.x1 | 1.616271 .6009242 2.69 0.007 .4384809 2.79406 x2 | -.1789571 .0708278 -2.53 0.012 -.317777 -.0401372 x3 | 6.718723 .800452 8.39 0.000 5.149866 8.28758 x4 | 3.199218 1.119148 2.86 0.004 1.005728 5.392707 year | .2022503 .0304903 6.63 0.000 .1424904 .2620103 _cons | -405.5231 62.75726 -6.46 0.000 -528.5251 -282.5211 ------------------------------------------------------------------------------ Instruments for first differences equation Standard D.x3 D.x2 GMM-type (missing=0, separate instruments for each period unless collapsed) L(1/6).x1 L(6/9).y collapsed Instruments for levels equation Standard year x3 x2 _cons GMM-type (missing=0, separate instruments for each period unless collapsed) D.x1 D.x4 collapsed DL5.y collapsed ------------------------------------------------------------------------------ Arellano-Bond test for AR(1) in first differences: z = -2.88 Pr > z = 0.004 Arellano-Bond test for AR(2) in first differences: z = -0.22 Pr > z = 0.829 ------------------------------------------------------------------------------ Sargan test of overid. restrictions: chi2(66) = 74.83 Prob > chi2 = 0.214 (Not robust, but not weakened by many instruments.) Hansen test of overid. restrictions: chi2(66) = 76.21 Prob > chi2 = 0.183 (Robust, but weakened by many instruments.) Difference-in-Hansen tests of exogeneity of instrument subsets: GMM instruments for levels Hansen test excluding group: chi2(53) = 59.37 Prob > chi2 = 0.255 Difference (null H = exogenous): chi2(13) = 16.84 Prob > chi2 = 0.207 gmm(y, collapse lag(6 9)) Hansen test excluding group: chi2(61) = 68.55 Prob > chi2 = 0.237 Difference (null H = exogenous): chi2(5) = 7.66 Prob > chi2 = 0.176 gmm(x4, collapse eq(level) lag(0 0)) Hansen test excluding group: chi2(65) = 76.07 Prob > chi2 = 0.164 Difference (null H = exogenous): chi2(1) = 0.15 Prob > chi2 = 0.703 gmm(x1, lag(1 6)) Hansen test excluding group: chi2(1) = 1.69 Prob > chi2 = 0.193 Difference (null H = exogenous): chi2(65) = 74.52 Prob > chi2 = 0.196 iv(x2) Hansen test excluding group: chi2(65) = 76.20 Prob > chi2 = 0.161 Difference (null H = exogenous): chi2(1) = 0.01 Prob > chi2 = 0.926 iv(x3) Hansen test excluding group: chi2(65) = 76.08 Prob > chi2 = 0.164 Difference (null H = exogenous): chi2(1) = 0.13 Prob > chi2 = 0.714 iv(year, eq(level)) Hansen test excluding group: chi2(65) = 75.80 Prob > chi2 = 0.169 Difference (null H = exogenous): chi2(1) = 0.41 Prob > chi2 = 0.522
1- To my understanding, the coefficients on the yit-1 and yit-2 should be significant to justify including them in the model. However, as can be seen, including the yit-2 improves the various specification tests but causes yit-1 coefficent to become insignificant. Can you advise me on which estimation procedure is more valid?
2- The past values of some predetermined variables (i.e., x2) are endogenous to the current period, which causes the various specification tests to faill. For instance, when I type:
Code:
xtabond2 y l.y l2.y i.x1 x2 x3 x4 year*, gmm(y, laglimits(6 9) collapse) gmm(x4, laglimits(0 0) eq(level) collapse) gmm( x1, laglimits (1 6)) gmm(x2, eq(level) collapse) iv(x3) iv( year*, eq(level)) twostep rob
Code:
------------------------------------------------------------------------------ Arellano-Bond test for AR(1) in first differences: z = -4.79 Pr > z = 0.000 Arellano-Bond test for AR(2) in first differences: z = 1.78 Pr > z = 0.076 ------------------------------------------------------------------------------ Sargan test of overid. restrictions: chi2(85) = 102.61 Prob > chi2 = 0.094 (Not robust, but not weakened by many instruments.) Hansen test of overid. restrictions: chi2(85) = 120.07 Prob > chi2 = 0.007 (Robust, but weakened by many instruments.) Difference-in-Hansen tests of exogeneity of instrument subsets: GMM instruments for levels Hansen test excluding group: chi2(54) = 54.31 Prob > chi2 = 0.462 Difference (null H = exogenous): chi2(31) = 65.76 Prob > chi2 = 0.000 gmm(y, collapse lag(6 9)) Hansen test excluding group: chi2(80) = 99.36 Prob > chi2 = 0.070 Difference (null H = exogenous): chi2(5) = 20.70 Prob > chi2 = 0.001 gmm(x4, collapse eq(level) lag(0 0)) Hansen test excluding group: chi2(84) = 119.19 Prob > chi2 = 0.007 Difference (null H = exogenous): chi2(1) = 0.88 Prob > chi2 = 0.348 gmm(x1, lag(1 6)) Hansen test excluding group: chi2(19) = 40.52 Prob > chi2 = 0.003 Difference (null H = exogenous): chi2(66) = 79.54 Prob > chi2 = 0.122 gmm(x2, collapse eq(level) lag(1 .)) Hansen test excluding group: chi2(67) = 76.26 Prob > chi2 = 0.205 Difference (null H = exogenous): chi2(18) = 43.81 Prob > chi2 = 0.001 iv(x3) Hansen test excluding group: chi2(84) = 119.95 Prob > chi2 = 0.006 Difference (null H = exogenous): chi2(1) = 0.11 Prob > chi2 = 0.735 iv(year, eq(level)) Hansen test excluding group: chi2(84) = 120.07 Prob > chi2 = 0.006 Difference (null H = exogenous): chi2(1) = 0.00 Prob > chi2 = 0.971
Code:
gmm(x2, collapse)
Code:
iv(x2)
Code:
xtabond2 y l.y l2.y i.x1 x2 x3 x4 year*, gmm(y, laglimits(6 9) collapse) gmm(x4, laglimits(0 0) eq(level) collapse) gmm( x1, laglimits (1 6)) gmm(x2,laglimits(4 6) eq(level) collapse) iv(x3) iv( year*, eq(level)) twostep rob
Code:
Dynamic panel-data estimation, two-step system GMM ------------------------------------------------------------------------------ Group variable: id Number of obs = 56230 Time variable : year Number of groups = 8009 Number of instruments = 78 Obs per group: min = 1 Wald chi2(7) = 303225.28 avg = 7.02 Prob > chi2 = 0.000 max = 18 ------------------------------------------------------------------------------ | Corrected y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- y | L1. | .6855261 .1228667 5.58 0.000 .4447118 .9263404 L2. | .1885715 .1139641 1.65 0.098 -.0347939 .411937 | 1.x1 | 1.751948 .6706459 2.61 0.009 .4375064 3.06639 x2 | .9491019 .3190374 2.97 0.003 .3238 1.574404 x3 | 5.325703 .7414402 7.18 0.000 3.872507 6.778899 x4 | 1.965658 1.01822 1.93 0.054 -.0300161 3.961332 year | .1390683 .0297333 4.68 0.000 .0807922 .1973444 _cons | -278.4076 60.88738 -4.57 0.000 -397.7446 -159.0705 ------------------------------------------------------------------------------ Instruments for first differences equation Standard D.x3 GMM-type (missing=0, separate instruments for each period unless collapsed) L(1/6).x1 L(6/9).y collapsed Instruments for levels equation Standard year x3 _cons GMM-type (missing=0, separate instruments for each period unless collapsed) DL(4/6).x2 collapsed D.x1 D.x4 collapsed DL5.y collapsed ------------------------------------------------------------------------------ Arellano-Bond test for AR(1) in first differences: z = -3.25 Pr > z = 0.001 Arellano-Bond test for AR(2) in first differences: z = -0.30 Pr > z = 0.768 ------------------------------------------------------------------------------ Sargan test of overid. restrictions: chi2(70) = 73.89 Prob > chi2 = 0.352 (Not robust, but not weakened by many instruments.) Hansen test of overid. restrictions: chi2(70) = 74.18 Prob > chi2 = 0.344 (Robust, but weakened by many instruments.) Difference-in-Hansen tests of exogeneity of instrument subsets: GMM instruments for levels Hansen test excluding group: chi2(54) = 54.35 Prob > chi2 = 0.461 Difference (null H = exogenous): chi2(16) = 19.83 Prob > chi2 = 0.228 gmm(y, collapse lag(6 9)) Hansen test excluding group: chi2(65) = 62.18 Prob > chi2 = 0.576 Difference (null H = exogenous): chi2(5) = 12.00 Prob > chi2 = 0.035 gmm(x4, collapse eq(level) lag(0 0)) Hansen test excluding group: chi2(69) = 74.07 Prob > chi2 = 0.316 Difference (null H = exogenous): chi2(1) = 0.11 Prob > chi2 = 0.738 gmm(x1, lag(1 6)) Hansen test excluding group: chi2(4) = 3.81 Prob > chi2 = 0.432 Difference (null H = exogenous): chi2(66) = 70.37 Prob > chi2 = 0.334 gmm(x2, collapse eq(level) lag(4 6)) Hansen test excluding group: chi2(67) = 73.30 Prob > chi2 = 0.279 Difference (null H = exogenous): chi2(3) = 0.88 Prob > chi2 = 0.831 iv(x3) Hansen test excluding group: chi2(69) = 73.89 Prob > chi2 = 0.322 Difference (null H = exogenous): chi2(1) = 0.29 Prob > chi2 = 0.588 iv(year, eq(level)) Hansen test excluding group: chi2(69) = 73.70 Prob > chi2 = 0.327 Difference (null H = exogenous): chi2(1) = 0.48 Prob > chi2 = 0.488
Please feel free to comment on any asepct of the presented estimation even it is not related to my questions.
looking forward to your feedback
Thank you
0 Response to Questions on the validity of a dynamic model of the Second-Order [using XTABOND2 command]
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