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Dear Sebastian,
Sorry for more questions, however I am a little bit confused after I run more regressions with different specifications. In my selected model11 which I put in post #14, all the regressors were treated as endogeneous. I developed new models with some regressors treated as predetermined instead of endogeneous and used MMSC to compare all the models including model11. Based on the results below, models which treated some regressors as predetermined seems more reasonable than model11. Can I select the the most reasonable model based on only MMSC results or is it a theoretical issue to classify regressors as endogeneous or predetermined? I am concerned about the issue because significancy of variables changes in a way to change the interpretation of results.
Code:xtdpdgmm L(0/2).TOBINSQ_w L(0/3).( ESGSCORE ) SIZE_w ROA_w LEV_w, model(fod) collapse gmm( TOBINSQ_w , lag(1 .)) gmm( ESGSCORE , lag(1 .)) gmm( SIZE_w , lag(1 .)) gmm( LEV_w , lag(1 .)) gmm( ROA_w , lag(1 .)) teffects two vce(r) overid
Code:xtdpdgmm L(0/2).TOBINSQ_w L(0/3).( ESGSCORE ) SIZE_w ROA_w LEV_w , model(fod) collapse gmm( TOBINSQ_w , lag(1 .)) gmm( ESGSCORE , lag(1 .)) gmm( SIZE_w , lag(1 .)) gmm( LEV_w , lag(1 .)) gmm( ROA_w , lag(1 .)) gmm(ESGSCORE, lag(0 0)) teffects two vce(r) overid
Code:xtdpdgmm L(0/2).TOBINSQ_w L(0/3).( ESGSCORE ) SIZE_w ROA_w LEV_w , model(fod) collapse gmm( TOBINSQ_w , lag(1 .)) gmm( ESGSCORE , lag(1 .)) gmm( SIZE_w , lag(1 .)) gmm( LEV_w , lag(1 .)) gmm( ROA_w , lag(1 .)) gmm(ESGSCORE SIZE_w, lag(0 0)) teffects two vce(r) overid
Code:xtdpdgmm L(0/2).TOBINSQ_w L(0/3).( ESGSCORE ) SIZE_w ROA_w LEV_w , model(fod) collapse gmm( TOBINSQ_w , lag(1 .)) gmm( ESGSCORE , lag(1 .)) gmm( SIZE_w , lag(1 .)) gmm( LEV_w , lag(1 .)) gmm( ROA_w , lag(1 .)) gmm(ESGSCORE SIZE_w LEV_w, lag(0 0)) teffects two vce(r) overid
Code:xtdpdgmm L(0/2).TOBINSQ_w L(0/3).( ESGSCORE ) SIZE_w ROA_w LEV_w , model(fod) collapse gmm( TOBINSQ_w , lag(1 .)) gmm( ESGSCORE , lag(1 .)) gmm( SIZE_w , lag(1 .)) gmm( LEV_w , lag(1 .)) gmm( ROA_w , lag(1 .)) gmm(ESGSCORE SIZE_w LEV_w ROA_w, lag(0 0)) teffects two vce(r) overid
Code:xtdpdgmm L(0/2).TOBINSQ_w L(0/3).( ESGSCORE ) SIZE_w ROA_w LEV_w , model(fod) collapse gmm( TOBINSQ_w , lag(1 .)) gmm( ESGSCORE , lag(1 .)) gmm( SIZE_w , lag(1 .)) gmm( LEV_w , lag(1 .)) gmm( ROA_w , lag(1 .)) gmm(ESGSCORE LEV_w ROA_w, lag(0 0)) teffects two vce(r) overid
Code:estat mmsc model16 model15 model14 model13 model12 model11
Code:Andrews-Lu model and moment selection criteria Model | ngroups J nmom npar MMSC-AIC MMSC-BIC MMSC-HQIC -------------+---------------------------------------------------------------- . | 440 33.5487 50 16 -34.4513 -173.4017 -90.4955 model16 | 440 33.5487 50 16 -34.4513 -173.4017 -90.4955 model15 | 440 34.6032 51 16 -35.3968 -178.4339 -93.0893 model14 | 440 32.0787 50 16 -35.9213 -174.8717 -91.9656 model13 | 440 28.7788 49 16 -37.2212 -172.0848 -91.6170 model12 | 440 28.5757 48 16 -35.4243 -166.2011 -88.1718 model11 | 440 27.3939 47 16 -34.6061 -161.2962 -85.7053Comment
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If the models with some variables treated as predetermined still pass all the specification tests, then they should deliver more efficient estimates. You could of course stick to the classification as endogenous variables if you have good theoretical reasons why these variables should be endogenous and not predetermined. The model selection criteria are only a tool to help you make a decision, not to completely replace your own judgement.
The benefit of classifying variables as predetermined is certainly that the extra instrument is typically stronger than the instruments used under the endogeneity classification.Comment
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Dear Sebastian,
I am trying to understand the difference between predetermined and endogenous variables. I have read some articles regarding this issue. Based on these readings I have classified my variables as follows:
1) My dependent variable (TOBIN'S Q-which measures the financial performance of the company) and the main regressor (ESGSCORE-which measures the sustainability performance of the company) are endogeneous, because the firm with a high financial performance may also achieve a high performance in sustainability or vice versa may also be valid.
2) My control variables SIZE, LEVERAGE and ROA are all predetermined because they are influenced by the past performance of the company.
Is my logic true for classifying variables as predetermined and endogenous?Comment
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I am not familar with that particular literature, but this sounds reasonable.Comment
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Dear Sebastien,
I am trying to follow you London 2019 presentation to see if my system GMM passes post-estimation tests. As I understand it, the code below is assessing whether the inclusion of levels is valid (is this the stationarity assumption of system GMM as per Roodman (2009). If so, then if levels are not valid, then a non-linear estimation as per Ahn and Schmidt (1995) is more appropriate since it doesn't require the stationarity assumption? In any case, I am struggling to understand exactly what the final matrix for 'excluding' and 'difference' is trying to show - is it that if the p values in the difference column are still above 5% significance, then levels were appropriate, or am I misunderstanding the test? Would really appreciate your help so I can understand this properly.
NB I believe that since fod is used below, the lag 0 corresponds to the second lag as in xtdpdgmm, but would instead be (1 .) in xtabond2?
Code:. quietly xtdpdgmm growth_rate l.gini_disp l.EFW l.ln_Income l.ln_pl_i l.fyr_sch_sec l.myr > _sch_sec, model(fod) gmm(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), la > g(0 .) collapse) two w(ind) teffects . estimates store fod . quietly xtdpdgmm growth_rate l.gini_disp l.EFW l.ln_Income l.ln_pl_i l.fyr_sch_sec l.myr > _sch_sec, model(fod) gmm(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), la > g(0 .) collapse) gmm(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), lag(0 > 0) collapse diff model(level)) two w(ind) teffects . estat overid fod Sargan-Hansen difference test of the overidentifying restrictions H0: additional overidentifying restrictions are valid 2-step moment functions, 2-step weighting matrix chi2(6) = 8.8463 Prob > chi2 = 0.1824 2-step moment functions, 3-step weighting matrix chi2(6) = 9.4235 Prob > chi2 = 0.1511 . xtdpdgmm growth_rate l.gini_disp l.EFW l.ln_Income l.ln_pl_i l.fyr_sch_sec l.myr_sch_sec > , model(fod) gmm(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), lag(0 .) c > ollapse) gmm(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), lag(0 0) colla > pse diff model(level)) two w(ind) teffects overid note: standard errors can be severely biased in finite samples Generalized method of moments estimation Fitting full model: Step 1 f(b) = .00056772 Step 2 f(b) = .68611491 Fitting reduced model 1: Step 1 f(b) = 2.106e-17 Fitting reduced model 2: Step 1 f(b) = .62188557 Fitting reduced model 3: Step 1 f(b) = .58474151 Fitting no-level model: Step 1 f(b) = .49432499 Group variable: ncountry Number of obs = 708 Time variable: period Number of groups = 112 Moment conditions: linear = 87 Obs per group: min = 1 nonlinear = 0 avg = 6.321429 total = 87 max = 11 ------------------------------------------------------------------------------ growth_rate | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- gini_disp | L1. | -.0032421 .0004287 -7.56 0.000 -.0040824 -.0024019 | EFW | L1. | .0076495 .0012811 5.97 0.000 .0051386 .0101604 | ln_Income | L1. | -.026949 .0030902 -8.72 0.000 -.0330057 -.0208923 | ln_pl_i | L1. | .0062677 .0025666 2.44 0.015 .0012372 .0112981 | fyr_sch_sec | L1. | .0087229 .005542 1.57 0.115 -.0021393 .0195851 | myr_sch_sec | L1. | .0000241 .0062299 0.00 0.997 -.0121863 .0122344 | period | 1970 | -.0044333 .0036187 -1.23 0.221 -.0115259 .0026593 1975 | -.0078899 .0039663 -1.99 0.047 -.0156638 -.0001161 1980 | -.02762 .0051465 -5.37 0.000 -.037707 -.017533 1985 | -.0207805 .0057611 -3.61 0.000 -.0320721 -.0094889 1990 | -.0149447 .0062097 -2.41 0.016 -.0271154 -.0027739 1995 | -.0189019 .0066239 -2.85 0.004 -.0318844 -.0059194 2000 | -.027381 .0066834 -4.10 0.000 -.0404802 -.0142818 2005 | -.0128459 .0072379 -1.77 0.076 -.0270319 .0013402 2010 | -.0173122 .0075533 -2.29 0.022 -.0321163 -.002508 2015 | -.036889 .0080391 -4.59 0.000 -.0526452 -.0211327 | _cons | .3523914 .0330178 10.67 0.000 .2876778 .417105 ------------------------------------------------------------------------------ Instruments corresponding to the linear moment conditions: 1, model(fodev): L.gini_disp L1.L.gini_disp L2.L.gini_disp L3.L.gini_disp L4.L.gini_disp L5.L.gini_disp L6.L.gini_disp L7.L.gini_disp L8.L.gini_disp L9.L.gini_disp L.EFW L1.L.EFW L2.L.EFW L3.L.EFW L4.L.EFW L5.L.EFW L6.L.EFW L7.L.EFW L8.L.EFW L9.L.EFW L10.L.EFW L11.L.EFW L.ln_Income L1.L.ln_Income L2.L.ln_Income L3.L.ln_Income L4.L.ln_Income L5.L.ln_Income L6.L.ln_Income L7.L.ln_Income L8.L.ln_Income L9.L.ln_Income L10.L.ln_Income L11.L.ln_Income L.ln_pl_i L1.L.ln_pl_i L2.L.ln_pl_i L3.L.ln_pl_i L4.L.ln_pl_i L5.L.ln_pl_i L6.L.ln_pl_i L7.L.ln_pl_i L8.L.ln_pl_i L9.L.ln_pl_i L10.L.ln_pl_i L11.L.ln_pl_i L.fyr_sch_sec L1.L.fyr_sch_sec L2.L.fyr_sch_sec L3.L.fyr_sch_sec L4.L.fyr_sch_sec L5.L.fyr_sch_sec L6.L.fyr_sch_sec L7.L.fyr_sch_sec L8.L.fyr_sch_sec L9.L.fyr_sch_sec L10.L.fyr_sch_sec L11.L.fyr_sch_sec L.myr_sch_sec L1.L.myr_sch_sec L2.L.myr_sch_sec L3.L.myr_sch_sec L4.L.myr_sch_sec L5.L.myr_sch_sec L6.L.myr_sch_sec L7.L.myr_sch_sec L8.L.myr_sch_sec L9.L.myr_sch_sec L10.L.myr_sch_sec L11.L.myr_sch_sec 2, model(level): D.L.gini_disp D.L.EFW D.L.ln_Income D.L.ln_pl_i D.L.fyr_sch_sec D.L.myr_sch_sec 3, model(level): 1970bn.period 1975.period 1980.period 1985.period 1990.period 1995.period 2000.period 2005.period 2010.period 2015.period 4, model(level): _cons . estat overid, difference Sargan-Hansen (difference) test of the overidentifying restrictions H0: (additional) overidentifying restrictions are valid 2-step weighting matrix from full model | Excluding | Difference Moment conditions | chi2 df p | chi2 df p ------------------+-----------------------------+----------------------------- 1, model(fodev) | 0.0000 0 . | 76.8449 70 0.2688 2, model(level) | 69.6512 64 0.2932 | 7.1937 6 0.3033 3, model(level) | 65.4910 60 0.2921 | 11.3538 10 0.3306 model(level) | 55.3644 54 0.4230 | 21.4805 16 0.1608Last edited by Tegh Summy; 20 Feb 2020, 15:36.Comment
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estat overid shows two tests. The first is the Sargan-Hansen test for a model that is EXCLUDING a certain set of instruments. The null hypothesis is that the model is correctly specified without these instruments. If you do not reject the null hypothesis (p-value sufficiently large), then the second test can be used to evaluate the DIFFERENCE in the Sargan-Hansen tests from the models without and with the respective instruments. The null hypothesis is that adding the respective instruments still leaves the model correctly specified.
Thus, while you are primarily interested in the DIFFERENCE test, not rejecting the EXCLUDING test is a prerequisite for the applicability of the second test.
In your example, the last row jointly tests all the instruments for the level model. The model appears to be correctly specified without those instruments (p-value of the EXCLUDING test is sufficiently high). Adding the levels instruments still does not lead to a rejection of the DIFFERENCE test at the conventional significance levels, implying that you could carry on the analysis with these instruments (although not with too much confidence given that the p-value is still relatively small).
If you were rejecting the levels instruments, then indeed the Ahn-Schmidt estimator with nonlinear moment conditions might be the best alternative.
Note that your overall number of instruments is large relative to the number of groups. You could restrict the number of lags that you use for the FOD model, in particular given the unbalanced nature of your data set, e.g. lag(0 6) instead of lag(0 .).
I am not sure if I understand your question correctly. With xtdpdgmm, the lags used as instruments are exactly as you specify them. Thus, lag(0 .) for variable L.gini_disp creates all available lags of gini_disp starting from 1 (because of the lag operator in front of gini_disp; i.e. all available lags of L.gini_disp starting from 0). That is different when you use xtabond2, where misleadingly the lags of gini_disp would start from 0 (i.e. 1 forward lead of L.gini_disp) if specified as above (which turns the instruments invalid).Originally posted by Tegh Summy View PostComment
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Ah okay thanks - so in the example above it suggests that the inclusion of levels as instruments is sufficient.
Thanks for this, in fact it gives more comfortable sargan-hansen values. I do have one more question on this though if you wouldn't mind explaining to me:Originally posted by Sebastian Kripfganz View Post
In the above example, I am a little unsure since the 2-step matrix implies a rejection of the null, yet the 3-step doesn't. I presume this is more an issue of weak instruments used.Code:Sargan-Hansen test of the overidentifying restrictions H0: overidentifying restrictions are valid 2-step moment functions, 2-step weighting matrix chi2(64) = 67.9986 Prob > chi2 = 0.3427 2-step moment functions, 3-step weighting matrix chi2(64) = 83.7050 Prob > chi2 = 0.0498
Also, what exactly is the difference in what is being tested for by:Code:estat overid
I thought the former tests for overall identification of the model, while the latter tests for whether the inclusion of levels is valid under the mean stationarity assumption of system GMM?Code:estat overid, difference
Last edited by Tegh Summy; 21 Feb 2020, 09:11.Comment
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Weak, highly collinear, or too many instruments could lead to a poor estimation of the weighting matrix which would be reflected in the observed differences from the 2-step and 3-step version of the Sargan-Hansen test. It might be helpful to use the iterated GMM estimator in this case.
estat overid tests all overidentification restrictions of the model. estat overid, difference tests different subsets such as the level instruments only. In particular if you have many instruments and still a relatively small sample size, the overall Sargan-Hansen test might not be able to detect violations of the validity for a small subset of instruments.Comment
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Dear Sebastian,
What should be the minimum number of t with which a system gmm can be applied?Comment
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But is this not just a work around? I am struggling to understand how the igmm iterations allows a weakly identified instruments to now pass the overidentification test? Seems oddOriginally posted by Sebastian Kripfganz View Post
I see, so this doesn't solve endogeneity issues then since the second lag is needed as the first instrument, assuming all variables are endogenous. If your endogenous variable is specified as l.X1, then if FOD is specified under xtdpdgmm, (0 .) takes the second lag, but if first differences is specified in xtdpdgmm, then (1 .) takes the second lag - and similarly (1 .) in xtabond2 takes the second lag. Or have i misunderstood the slides?Originally posted by Sebastian Kripfganz View PostLast edited by Tegh Summy; 21 Feb 2020, 12:09.Comment
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Dear Sebastian,
I am still trying to find the most reliable model specification using xtdpdgmm command. Actually I have tried nearly 30 models and now trying to decide between the 2 models below. The only difference between these 2 models is the classification of the variable "ESGSCORE". Theory is not clear about the issue. And also according to MMSC results the first model has higher value for AIC and the second model has higher values for BIC and HQIC. What would you suggest me to decide between these 2 models?
Code:. xtdpdgmm L(0/2).TOBINSQ_w L(0/3).( ESGSCORE ) SIZE_w ROA_w LEV_w i.ICBIC, model(fod) collapse gmm( TOBINSQ_w , lag(1 .)) gmm( ESGSCORE , > lag(1 .)) gmm( SIZE_w , lag(1 .)) gmm( LEV_w , lag(1 .)) gmm( ROA_w , lag(1 .)) gmm(SIZE_w LEV_w ROA_w, lag(0 0)) iv(i.ICBIC, model(le > vel)) teffects two vce(r) overid small Generalized method of moments estimation Fitting full model: Step 1 f(b) = .00752046 Step 2 f(b) = .07087966 Fitting reduced model 1: Step 1 f(b) = .04897409 Fitting reduced model 2: Step 1 f(b) = .05377945 Fitting reduced model 3: Step 1 f(b) = .05632305 Fitting reduced model 4: Step 1 f(b) = .06589232 Fitting reduced model 5: Step 1 f(b) = .05520447 Fitting reduced model 6: Step 1 f(b) = .06314406 Fitting reduced model 7: Step 1 f(b) = .0568395 Fitting reduced model 8: Step 1 f(b) = .0568395 Fitting no-level model: Step 1 f(b) = .0568395 Group variable: ID Number of obs = 2164 Time variable: YEAR Number of groups = 440 Moment conditions: linear = 60 Obs per group: min = 1 nonlinear = 0 avg = 4.918182 total = 60 max = 7 (Std. Err. adjusted for 440 clusters in ID) ------------------------------------------------------------------------------ | WC-Robust TOBINSQ_w | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- TOBINSQ_w | L1. | .708244 .0751168 9.43 0.000 .5606108 .8558772 L2. | -.0915846 .0504549 -1.82 0.070 -.1907478 .0075786 | ESGSCORE | --. | -.0109863 .0083649 -1.31 0.190 -.0274265 .0054539 L1. | .0066849 .0083482 0.80 0.424 -.0097226 .0230923 L2. | .0004879 .0015732 0.31 0.757 -.0026041 .0035799 L3. | -.0017218 .0010791 -1.60 0.111 -.0038427 .0003991 | SIZE_w | .0032791 .0311532 0.11 0.916 -.0579488 .0645071 ROA_w | .0229559 .005887 3.90 0.000 .0113856 .0345262 LEV_w | .5195704 .4081103 1.27 0.204 -.2825224 1.321663 | ICBIC | 15 | -.468148 .2004594 -2.34 0.020 -.8621274 -.0741685 20 | -.2059732 .1803947 -1.14 0.254 -.5605178 .1485714 30 | -.5782991 .2395053 -2.41 0.016 -1.049019 -.1075796 35 | -.6183523 .2099517 -2.95 0.003 -1.030988 -.2057169 40 | -.264506 .1729662 -1.53 0.127 -.6044508 .0754387 45 | -.0447206 .1819766 -0.25 0.806 -.4023743 .3129331 50 | -.4910032 .2061424 -2.38 0.018 -.8961519 -.0858546 55 | -.4529933 .1955252 -2.32 0.021 -.8372752 -.0687114 60 | -.526652 .1942312 -2.71 0.007 -.9083906 -.1449133 65 | -.5785641 .2094078 -2.76 0.006 -.9901305 -.1669978 | YEAR | 2013 | -.0316305 .0316193 -1.00 0.318 -.0937746 .0305136 2014 | .0392972 .0328588 1.20 0.232 -.0252829 .1038773 2015 | .0163137 .0398006 0.41 0.682 -.0619097 .0945371 2016 | .0167137 .0392525 0.43 0.670 -.0604325 .0938599 2017 | .0829173 .0380593 2.18 0.030 .0081163 .1577183 2018 | -.0032769 .0469364 -0.07 0.944 -.0955248 .0889711 | _cons | .7578736 .5269252 1.44 0.151 -.2777359 1.793483 ------------------------------------------------------------------------------ Instruments corresponding to the linear moment conditions: 1, model(fodev): L1.TOBINSQ_w L2.TOBINSQ_w L3.TOBINSQ_w L4.TOBINSQ_w L5.TOBINSQ_w L6.TOBINSQ_w L7.TOBINSQ_w L8.TOBINSQ_w 2, model(fodev): L1.ESGSCORE L2.ESGSCORE L3.ESGSCORE L4.ESGSCORE L5.ESGSCORE L6.ESGSCORE L7.ESGSCORE L8.ESGSCORE 3, model(fodev): L1.SIZE_w L2.SIZE_w L3.SIZE_w L4.SIZE_w L5.SIZE_w L6.SIZE_w L7.SIZE_w L8.SIZE_w 4, model(fodev): L1.LEV_w L2.LEV_w L3.LEV_w L4.LEV_w L5.LEV_w L6.LEV_w L7.LEV_w L8.LEV_w 5, model(fodev): L1.ROA_w L2.ROA_w L3.ROA_w L4.ROA_w L5.ROA_w L6.ROA_w L7.ROA_w L8.ROA_w 6, model(fodev): SIZE_w LEV_w ROA_w 7, model(level): 15bn.ICBIC 20.ICBIC 30.ICBIC 35.ICBIC 40.ICBIC 45.ICBIC 50.ICBIC 55.ICBIC 60.ICBIC 65.ICBIC 8, model(level): 2013bn.YEAR 2014.YEAR 2015.YEAR 2016.YEAR 2017.YEAR 2018.YEAR 9, model(level): _cons . estat serial, ar(1/3) Arellano-Bond test for autocorrelation of the first-differenced residuals H0: no autocorrelation of order 1: z = -5.0045 Prob > |z| = 0.0000 H0: no autocorrelation of order 2: z = 0.0935 Prob > |z| = 0.9255 H0: no autocorrelation of order 3: z = 0.6493 Prob > |z| = 0.5161 . estat overid Sargan-Hansen test of the overidentifying restrictions H0: overidentifying restrictions are valid 2-step moment functions, 2-step weighting matrix chi2(34) = 31.1870 Prob > chi2 = 0.6062 2-step moment functions, 3-step weighting matrix chi2(34) = 34.5633 Prob > chi2 = 0.4409 . estat overid, difference Sargan-Hansen (difference) test of the overidentifying restrictions H0: (additional) overidentifying restrictions are valid 2-step weighting matrix from full model | Excluding | Difference Moment conditions | chi2 df p | chi2 df p ------------------+-----------------------------+----------------------------- 1, model(fodev) | 21.5486 26 0.7131 | 9.6384 8 0.2913 2, model(fodev) | 23.6630 26 0.5952 | 7.5241 8 0.4813 3, model(fodev) | 24.7821 26 0.5313 | 6.4049 8 0.6020 4, model(fodev) | 28.9926 26 0.3114 | 2.1944 8 0.9745 5, model(fodev) | 24.2900 26 0.5594 | 6.8971 8 0.5478 6, model(fodev) | 27.7834 31 0.6323 | 3.4037 3 0.3335 7, model(level) | 25.0094 28 0.6273 | 6.1777 6 0.4036 8, model(level) | 25.0094 28 0.6273 | 6.1777 6 0.4036 model(fodev) | . -9 . | . . . model(level) | 25.0094 18 0.1247 | 6.1777 16 0.9861 estimates store model1Code:. xtdpdgmm L(0/2).TOBINSQ_w L(0/3).( ESGSCORE ) SIZE_w ROA_w LEV_w i.ICBIC , model(fod) collapse gmm( TOBINSQ_w , lag(1 .)) gmm( ESGSCORE, > lag(1 .)) gmm( SIZE_w , lag(1 .)) gmm( LEV_w , lag(1 .)) gmm( ROA_w , lag(1 .)) gmm(ESGSCORE SIZE_w LEV_w ROA_w, lag(0 0)) iv(i.ICBIC > , model(level)) teffects two vce(r) overid small Generalized method of moments estimation Fitting full model: Step 1 f(b) = .00792192 Step 2 f(b) = .07787653 Fitting reduced model 1: Step 1 f(b) = .05702261 Fitting reduced model 2: Step 1 f(b) = .05746492 Fitting reduced model 3: Step 1 f(b) = .06223917 Fitting reduced model 4: Step 1 f(b) = .07500942 Fitting reduced model 5: Step 1 f(b) = .06466674 Fitting reduced model 6: Step 1 f(b) = .06844919 Fitting reduced model 7: Step 1 f(b) = .06126709 Fitting reduced model 8: Step 1 f(b) = .06126709 Fitting no-level model: Step 1 f(b) = .06126709 Group variable: ID Number of obs = 2164 Time variable: YEAR Number of groups = 440 Moment conditions: linear = 61 Obs per group: min = 1 nonlinear = 0 avg = 4.918182 total = 61 max = 7 (Std. Err. adjusted for 440 clusters in ID) ------------------------------------------------------------------------------ | WC-Robust TOBINSQ_w | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- TOBINSQ_w | L1. | .7022894 .0689522 10.19 0.000 .5667719 .8378069 L2. | -.0820685 .0472527 -1.74 0.083 -.1749382 .0108012 | ESGSCORE | --. | -.004424 .0021132 -2.09 0.037 -.0085774 -.0002707 L1. | -.0000922 .0009929 -0.09 0.926 -.0020437 .0018592 L2. | -.0001361 .001209 -0.11 0.910 -.0025121 .00224 L3. | -.0018211 .0010012 -1.82 0.070 -.0037889 .0001467 | SIZE_w | .0067991 .0293538 0.23 0.817 -.0508923 .0644905 ROA_w | .0213136 .0050915 4.19 0.000 .0113068 .0313203 LEV_w | .5400862 .3757136 1.44 0.151 -.1983346 1.278507 | ICBIC | 15 | -.5031778 .2080399 -2.42 0.016 -.9120557 -.0942998 20 | -.2366629 .1931924 -1.23 0.221 -.6163598 .143034 30 | -.6249097 .2402844 -2.60 0.010 -1.09716 -.1526589 35 | -.6516954 .2130733 -3.06 0.002 -1.070466 -.2329248 40 | -.2823403 .1854318 -1.52 0.129 -.6467847 .082104 45 | -.0626127 .1953937 -0.32 0.749 -.446636 .3214106 50 | -.5298647 .2097636 -2.53 0.012 -.9421305 -.1175989 55 | -.4716376 .2045576 -2.31 0.022 -.8736716 -.0696036 60 | -.5526683 .2043407 -2.70 0.007 -.9542759 -.1510607 65 | -.61627 .215013 -2.87 0.004 -1.038853 -.1936873 | YEAR | 2013 | -.0266645 .028777 -0.93 0.355 -.0832224 .0298933 2014 | .0453585 .0288974 1.57 0.117 -.011436 .102153 2015 | .0122681 .0340743 0.36 0.719 -.0547009 .0792371 2016 | .0106376 .0343315 0.31 0.757 -.056837 .0781122 2017 | .0859826 .0359496 2.39 0.017 .0153278 .1566374 2018 | .0081361 .0420546 0.19 0.847 -.0745173 .0907895 | _cons | .7646082 .5119804 1.49 0.136 -.2416292 1.770846 ------------------------------------------------------------------------------ Instruments corresponding to the linear moment conditions: 1, model(fodev): L1.TOBINSQ_w L2.TOBINSQ_w L3.TOBINSQ_w L4.TOBINSQ_w L5.TOBINSQ_w L6.TOBINSQ_w L7.TOBINSQ_w L8.TOBINSQ_w 2, model(fodev): L1.ESGSCORE L2.ESGSCORE L3.ESGSCORE L4.ESGSCORE L5.ESGSCORE L6.ESGSCORE L7.ESGSCORE L8.ESGSCORE 3, model(fodev): L1.SIZE_w L2.SIZE_w L3.SIZE_w L4.SIZE_w L5.SIZE_w L6.SIZE_w L7.SIZE_w L8.SIZE_w 4, model(fodev): L1.LEV_w L2.LEV_w L3.LEV_w L4.LEV_w L5.LEV_w L6.LEV_w L7.LEV_w L8.LEV_w 5, model(fodev): L1.ROA_w L2.ROA_w L3.ROA_w L4.ROA_w L5.ROA_w L6.ROA_w L7.ROA_w L8.ROA_w 6, model(fodev): ESGSCORE SIZE_w LEV_w ROA_w 7, model(level): 15bn.ICBIC 20.ICBIC 30.ICBIC 35.ICBIC 40.ICBIC 45.ICBIC 50.ICBIC 55.ICBIC 60.ICBIC 65.ICBIC 8, model(level): 2013bn.YEAR 2014.YEAR 2015.YEAR 2016.YEAR 2017.YEAR 2018.YEAR 9, model(level): _cons . estat serial, ar(1/3) Arellano-Bond test for autocorrelation of the first-differenced residuals H0: no autocorrelation of order 1: z = -5.3793 Prob > |z| = 0.0000 H0: no autocorrelation of order 2: z = 0.1777 Prob > |z| = 0.8589 H0: no autocorrelation of order 3: z = 0.5930 Prob > |z| = 0.5532 . estat overid Sargan-Hansen test of the overidentifying restrictions H0: overidentifying restrictions are valid 2-step moment functions, 2-step weighting matrix chi2(35) = 34.2657 Prob > chi2 = 0.5034 2-step moment functions, 3-step weighting matrix chi2(35) = 35.8556 Prob > chi2 = 0.4282 . estat overid, difference Sargan-Hansen (difference) test of the overidentifying restrictions H0: (additional) overidentifying restrictions are valid 2-step weighting matrix from full model | Excluding | Difference Moment conditions | chi2 df p | chi2 df p ------------------+-----------------------------+----------------------------- 1, model(fodev) | 25.0899 27 0.5694 | 9.1757 8 0.3277 2, model(fodev) | 25.2846 27 0.5585 | 8.9811 8 0.3439 3, model(fodev) | 27.3852 27 0.4432 | 6.8804 8 0.5496 4, model(fodev) | 33.0041 27 0.1969 | 1.2615 8 0.9960 5, model(fodev) | 28.4534 27 0.3879 | 5.8123 8 0.6682 6, model(fodev) | 30.1176 31 0.5112 | 4.1480 4 0.3863 7, model(level) | 26.9575 29 0.5740 | 7.3082 6 0.2933 8, model(level) | 26.9575 29 0.5740 | 7.3082 6 0.2933 model(fodev) | . -9 . | . . . model(level) | 26.9575 19 0.1056 | 7.3082 16 0.9669 estimates store model2Code:. estat mmsc model2 model1 Andrews-Lu model and moment selection criteria Model | ngroups J nmom npar MMSC-AIC MMSC-BIC MMSC-HQIC -------------+---------------------------------------------------------------- . | 440 34.2657 61 26 -35.7343 -178.7714 -93.4269 model2 | 440 34.2657 61 26 -35.7343 -178.7714 -93.4269 model1 | 440 31.1870 60 26 -36.8130 -175.7633 -92.8572Comment
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I agree. The iterative GMM estimator is not a substitute for the removal of weak instruments.Originally posted by Tegh Summy View Post
Even without weak instruments, the two-step GMM estimator might be sensitive to the chosen weighting matrix, in particular when the sample size is small. This is the situation, when the iterative GMM estimator is most useful.
Please see my comment #27 in the following Statalist discussion:Originally posted by Tegh Summy View Post
XTDPDGMM: new Stata command for efficient GMM estimation of linear (dynamic) panel modelsComment
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There is no clear answer to this question. Both pass the specification tests and yield very similar results. You can choose either of them, depending on whether you prefer more robust results (by imposing weaker assumptions on the variables) or more efficient results (by imposing stronger assumptions).Originally posted by Sinem Ates View PostComment
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Apologies this still isnt 100% clear to me from that post. I think the inclusion of bodev in that post may be confusing matters for me. So, from my understanding of how the two commands differ, codes (1) & (2) should specify System GMM with orthogonal deviations and first-differences respectively. (3) & (4) are the same but with xtdpdgmm. (5) includes bodev. All I think avoid the endogeneity problem by taking second lags and the levels equation doesn't change for any of them.Originally posted by Sebastian Kripfganz View Post
Code:xtabond2 Y1 L.Y1 X1 i.year, orthogonal twostep gmmstyle(L.Y1 L.X1, laglimits(1 4) equation(diff), gmmstyle(L.Y1 L.X1, laglimits(0,0) iv(i.year, equation(level))
Code:xtabond2 Y1 L.Y1 X1 i.year, twostep gmmstyle(L.Y1 L.X1, laglimits(1 4) equation(diff), gmmstyle(L.Y1 L.X1, laglimits(0,0) iv(i.year, equation(level))
Code:xtdpdgmm Y1 L.Y1 X1, model(fodev) gmm(L.Y1 L.X1, laglimits(1 4), gmmstyle(L.Y1 L.X1, laglimits(0,0) diff model(level) teffects twostep w(ind))
Code:xtdpdgmm Y1 L.Y1 X1, model(diff) gmm(L.Y1 L.X1, laglimits(1 4), gmmstyle(L.Y1 L.X1, laglimits(0,0) diff model(level) teffects twostep w(ind))
However, as you have mentioned in previous posts, the addition of iv instruments in xtabond2 triggers a bug and hence, incorrect estimates. Thus, xtdpdgmm is preferable to xtabond2Code:xtdpdgmm Y1 L.Y1 X1, model(fodev) bodev gmm(L.Y1 L.X1, laglimits(0 3), gmmstyle(L.Y1 L.X1, laglimits(0,0) diff model(level) teffects twostep w(ind))
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But, when I run this, I get a different number of instruments to that in xtabond2: 81 vs 87; is that part of the bug? When specified with (0 .) instead for the xtdpdgmm command, they both then have 87 instruments? When I estimate it also with (1,6) lags for both xtabond2 and xtdpdgmm (as opposed to the (1 .) in the below example) and they have equal instruments.Originally posted by Sebastian Kripfganz View Post
Code:. xtdpdgmm growth_rate l.gini_disp l.EFW l.ln_Income l.ln_pl_i l.fyr_sch_sec l.myr_sch_se > c, model(fod) gmm(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), lag(1 .) > collapse) gmm(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), lag(0 0) co > llapse diff model(level)) two w(ind) teffects note: standard errors can be severely biased in finite samples Generalized method of moments estimation Fitting full model: Step 1 f(b) = .0004639 Step 2 f(b) = .61873748 Group variable: ncountry Number of obs = 708 Time variable: period Number of groups = 112 Moment conditions: linear = 81 Obs per group: min = 1 nonlinear = 0 avg = 6.321429 total = 81 max = 11 ------------------------------------------------------------------------------ growth_rate | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- gini_disp | L1. | -.0028221 .000591 -4.78 0.000 -.0039804 -.0016639 | EFW | L1. | .0101077 .0017127 5.90 0.000 .0067508 .0134646 | ln_Income | L1. | -.0299243 .0036129 -8.28 0.000 -.0370055 -.0228432 | ln_pl_i | L1. | .0061707 .0033557 1.84 0.066 -.0004064 .0127477 | fyr_sch_sec | L1. | .0107652 .0058304 1.85 0.065 -.0006622 .0221927 | myr_sch_sec | L1. | .0013427 .0074306 0.18 0.857 -.0132211 .0159065 | period | 1970 | -.0039494 .0039993 -0.99 0.323 -.0117878 .0038891 1975 | -.0066799 .0053048 -1.26 0.208 -.0170772 .0037173 1980 | -.025354 .006897 -3.68 0.000 -.0388718 -.0118362 1985 | -.0194735 .0077691 -2.51 0.012 -.0347007 -.0042463 1990 | -.0149665 .0086307 -1.73 0.083 -.0318824 .0019494 1995 | -.0224494 .0100823 -2.23 0.026 -.0422104 -.0026884 2000 | -.0328859 .0100959 -3.26 0.001 -.0526735 -.0130983 2005 | -.0196653 .0109115 -1.80 0.072 -.0410515 .001721 2010 | -.0258266 .011566 -2.23 0.026 -.0484955 -.0031576 2015 | -.0454088 .0122855 -3.70 0.000 -.0694879 -.0213298 | _cons | .3448211 .0389346 8.86 0.000 .2685107 .4211316 ------------------------------------------------------------------------------ Instruments corresponding to the linear moment conditions: 1, model(fodev): L1.L.gini_disp L2.L.gini_disp L3.L.gini_disp L4.L.gini_disp L5.L.gini_disp L6.L.gini_disp L7.L.gini_disp L8.L.gini_disp L9.L.gini_disp L1.L.EFW L2.L.EFW L3.L.EFW L4.L.EFW L5.L.EFW L6.L.EFW L7.L.EFW L8.L.EFW L9.L.EFW L10.L.EFW L11.L.EFW L1.L.ln_Income L2.L.ln_Income L3.L.ln_Income L4.L.ln_Income L5.L.ln_Income L6.L.ln_Income L7.L.ln_Income L8.L.ln_Income L9.L.ln_Income L10.L.ln_Income L11.L.ln_Income L1.L.ln_pl_i L2.L.ln_pl_i L3.L.ln_pl_i L4.L.ln_pl_i L5.L.ln_pl_i L6.L.ln_pl_i L7.L.ln_pl_i L8.L.ln_pl_i L9.L.ln_pl_i L10.L.ln_pl_i L11.L.ln_pl_i L1.L.fyr_sch_sec L2.L.fyr_sch_sec L3.L.fyr_sch_sec L4.L.fyr_sch_sec L5.L.fyr_sch_sec L6.L.fyr_sch_sec L7.L.fyr_sch_sec L8.L.fyr_sch_sec L9.L.fyr_sch_sec L10.L.fyr_sch_sec L11.L.fyr_sch_sec L1.L.myr_sch_sec L2.L.myr_sch_sec L3.L.myr_sch_sec L4.L.myr_sch_sec L5.L.myr_sch_sec L6.L.myr_sch_sec L7.L.myr_sch_sec L8.L.myr_sch_sec L9.L.myr_sch_sec L10.L.myr_sch_sec L11.L.myr_sch_sec 2, model(level): D.L.gini_disp D.L.EFW D.L.ln_Income D.L.ln_pl_i D.L.fyr_sch_sec D.L.myr_sch_sec 3, model(level): 1970bn.period 1975.period 1980.period 1985.period 1990.period 1995.period 2000.period 2005.period 2010.period 2015.period 4, model(level): _consCode:. xtabond2 growth_rate l.gini_disp l.EFW l.ln_pl_i l.ln_Income l.fyr_sch_sec l.myr_sch_se > c i.period, twostep orthogonal gmmstyle(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec > myr_sch_sec), laglimits(1 .) collapse equation(diff)) gmmstyle(l.(gini_disp EFW ln_Inco > me ln_pl_i fyr_sch_sec myr_sch_sec), laglimits(0 0) collapse equation(level)) ivstyle(i > .period, equation(level)) Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, pe > rm. Warning: Two-step estimated covariance matrix of moments is singular. Using a generalized inverse to calculate optimal weighting matrix for two-step estimati > on. Difference-in-Sargan/Hansen statistics may be negative. Dynamic panel-data estimation, two-step system GMM ------------------------------------------------------------------------------ Group variable: ncountry Number of obs = 708 Time variable : period Number of groups = 112 Number of instruments = 87 Obs per group: min = 1 Wald chi2(20) = 1157.80 avg = 6.32 Prob > chi2 = 0.000 max = 11 ------------------------------------------------------------------------------ growth_rate | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- gini_disp | L1. | -.0024912 .0003266 -7.63 0.000 -.0031314 -.001851 | EFW | L1. | .0084917 .0012756 6.66 0.000 .0059916 .0109918 | ln_pl_i | L1. | .00124 .0021368 0.58 0.562 -.0029481 .005428 | ln_Income | L1. | -.0121744 .0024858 -4.90 0.000 -.0170466 -.0073023 | fyr_sch_sec | L1. | .0060619 .0050967 1.19 0.234 -.0039274 .0160513 | myr_sch_sec | L1. | -.0085779 .0047785 -1.80 0.073 -.0179435 .0007878 | period | 1950 | 0 (empty) 1955 | 0 (omitted) 1960 | 0 (omitted) 1965 | .0158533 .0061104 2.59 0.009 .0038771 .0278295 1970 | .0141804 .0051209 2.77 0.006 .0041436 .0242171 1975 | .0125153 .0051383 2.44 0.015 .0024444 .0225862 1980 | -.0025692 .0046551 -0.55 0.581 -.0116931 .0065547 1985 | .0093397 .0037981 2.46 0.014 .0018956 .0167838 1990 | .0169863 .0037924 4.48 0.000 .0095534 .0244193 1995 | .0134741 .002298 5.86 0.000 .0089701 .0179781 2000 | .0083086 .0025524 3.26 0.001 .003306 .0133112 2005 | .0228808 .0019733 11.59 0.000 .0190131 .0267484 2010 | .0196544 .0022434 8.76 0.000 .0152575 .0240513 2015 | 0 (omitted) | _cons | .1731173 .0296145 5.85 0.000 .1150739 .2311607 ------------------------------------------------------------------------------ Warning: Uncorrected two-step standard errors are unreliable. Instruments for orthogonal deviations equation GMM-type (missing=0, separate instruments for each period unless collapsed) L(1/13).(L.gini_disp L.EFW L.ln_Income L.ln_pl_i L.fyr_sch_sec L.myr_sch_sec) collapsed Instruments for levels equation Standard 1950b.period 1955.period 1960.period 1965.period 1970.period 1975.period 1980.period 1985.period 1990.period 1995.period 2000.period 2005.period 2010.period 2015.period _cons GMM-type (missing=0, separate instruments for each period unless collapsed) D.(L.gini_disp L.EFW L.ln_Income L.ln_pl_i L.fyr_sch_sec L.myr_sch_sec) collapsed ------------------------------------------------------------------------------ Arellano-Bond test for AR(1) in first differences: z = -3.67 Pr > z = 0.000 Arellano-Bond test for AR(2) in first differences: z = -0.83 Pr > z = 0.404 ------------------------------------------------------------------------------ Sargan test of overid. restrictions: chi2(66) = 131.35 Prob > chi2 = 0.000 (Not robust, but not weakened by many instruments.) Hansen test of overid. restrictions: chi2(66) = 79.13 Prob > chi2 = 0.129 (Robust, but weakened by many instruments.) Difference-in-Hansen tests of exogeneity of instrument subsets: GMM instruments for levels Hansen test excluding group: chi2(60) = 70.54 Prob > chi2 = 0.166 Difference (null H = exogenous): chi2(6) = 8.58 Prob > chi2 = 0.198 gmm(L.gini_disp L.EFW L.ln_Income L.ln_pl_i L.fyr_sch_sec L.myr_sch_sec, collapse eq(le > vel) lag(0 0)) Hansen test excluding group: chi2(60) = 70.54 Prob > chi2 = 0.166 Difference (null H = exogenous): chi2(6) = 8.58 Prob > chi2 = 0.198 iv(1950b.period 1955.period 1960.period 1965.period 1970.period 1975.period 1980.period > 1985.period 1990.period 1995.period 2000.period 2005.period 2010.period 2015.period, e > q(level)) Hansen test excluding group: chi2(56) = 70.28 Prob > chi2 = 0.095 Difference (null H = exogenous): chi2(10) = 8.85 Prob > chi2 = 0.547Last edited by Tegh Summy; 23 Feb 2020, 10:22.Comment
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