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  • Problem With Xtabond2 In Dynamic Panel Data With Lagged Dependent Variables

    Dear Stata users,

    By running xtabond2 I am using the System twostep GMM approach to estimate my dynamic panel data model. My dataset consists of 146 countries with observations from 1960-2010. The data set is unbalanced, hence certain gaps exist between years for some countries.

    The point is to estimate the effect of a country being democratic (dummy = 1 if democracy, else 0) on Ln ofGDP pr. capita. Since the model is dynamic I also use three lags of Ln GDP pr. capita as independent variables. My linear regression model takes the form:
    yc,t = β1Dc,t + β2yc,t-1 + β3yc,t-2 + β3yc,t-3 + αc + µt + ɛc,t
    Dc,t is the dummy for democracy and my coeffecient of interest.

    When I estimate the linear regression model by a fixed effect model with year dummies I run the following command:
    xtreg LnGDP Democ L.LnGDP L2.LnGDP L3.LnGDP i.year, fe vce(robust)
    I get a coefficient on the democracy dummy of β1 = 0,0056, hence 0,56 pct. growth following a democratic transition all else equal.
    When I estimate the linear regression model by a two-step system GMM with year dummies I run the following code:

    xtabond2 LnGDP Democ L.LnGDP L2.LnGDP L3.LnGDP i.year, ///
    gmm(Democ, lag(1 2) collapse eq(diff)) ///
    gmm(L.LnGDP L2.LnGDP L3.LnGDP, lag(1 4) collapse eq(diff)) ///
    gmm(L.LnGDP L2.LnGDP L3.LnGDP, lag(1 4) collapse eq(level)) ///
    iv(i.year) twostep robust


    I hereby instrument by two lags of the democracy dummy as first-difference and four lags of each lagged dependent variable both as level and first-difference. I obtain the following results:
    Reg. on: LnGDP Coef. Corrected std. Err. z P>|<| [95% Conf. Interval]
    Democ 0.03710 0.0118498 3.13 0.002 0.0138786 to 0.060329
    LnGDP:
    L1. 1.14025 0.0285374 39.96 0.000 1.084313 to 1.196177
    L2. -0.10163 0.030588 -3.32 0.001 -0.1615781 to -0.0416753
    L3 -0.01509 0.0250936 -0.60 0.547 -0.0642785 to 0..0340866
    My question is: How can it be that the coefficient on Democ is 0.03710 and hereby almost ten times as large as the coefficient obtained by the fixed effect model above? I tried different lags of both Democ and LnGDP in the gmmstyle but the coefficient is not reduced significantly. Am I setting up the year dummies by Ivstyle in a wrong way?

    Thank you in advance.

  • #2
    First of all, you are using different estimators and there is nothing here that guarantees that the estimates have to be close to each other.

    Second, the coefficients of your lagged dependent variable some up to approximately unity. This could imply that the mean stationarity assumption required for the level moment conditions is violated. With the fixed-effects estimator, this strong persistence could imply that even with 50 time periods there might still be a large dynamic panel bias ("Nickell bias").

    Regarding time dummies, my comment #4 in the following topic (and the referenced links therein) might be of interest: [https://www.statalist.org/forums/for...01603]xtabond2 and deeper lags[/URL].
    https://www.kripfganz.de/stata/

    Comment


    • #3
      Thank you for your answer.
      The reason for my concern is comparing my results to the academic paper: "Democracy does cause growth" by D.Acemoglu, S. Naidu P. Restrepo and J. Robinson (http://www.nber.org/papers/w20004.pdf). When using four lags of the dependent variable, they obtain a coefficient of β1 of 0,00875 whereas I get 0,0258 when using same amount of lags - hence adding another lag as dependent variable in the xtabond2 code in my previous post.
      As i read in the other threat on your comment #4, the degrees of freedom in the Hansen test might be incorrect in the presence of omitted variables. In my case it does exactly say "omitted" for the years 1961, 1962 and 1963 since I instrument by three lagged dependent variables in my GMMstyle. Could the larger coefficient be a result of the fact that my year dummies are interpreted in the wrong way by xtabond2?

      Regarding the Nickell bias the makes sense! I will make sure to include that when considering the fixed-effects estimator.

      Thank you in advance.

      Comment


      • #4
        I figured out the problem and there is no need for further help.
        Best regards.

        Comment


        • #5
          Hi my dynamic model is
          Gender Inequality Index(GII) = a+GIIt-1+bFDI+ (ControlV)+U
          My control variables are 7. I have used all the control variables and my main explanatory variable as the strictly exogenous ivstyle instruments. Is this correct. I have read somewhere that we can treat all the regressors in ivstyle but i still don't understand why?


          Code: xtabond2 GII lag_GII log_FDIinflowreal NaturalresourceRent Generalgovernmentexpenditure GDPGrowth Schoolsecondaryfemale UrbanPopulationControl polity2 Fertilityrate Y*, gmm(GII, lag (0 5) collapse) iv( log_FDIinflowreal NaturalresourceRent Generalgovernmentexpenditure GDPGrowth Schoolsecondaryfemale UrbanPopulationControl polity2 Fertilityrate Y*, equation(level)) nodiffsargan two
          > step robust orthogonal small

          Dynamic panel-data estimation, two-step system GMM
          ------------------------------------------------------------------------------
          Group variable: countrycode Number of obs = 239
          Time variable : Year Number of groups = 49
          Number of instruments = 24 Obs per group: min = 1
          F(17, 48) = 22.88 avg = 4.88
          Prob > F = 0.000 max = 9
          ----------------------------------------------------------------------------------------------
          | Corrected
          GII | Coef. Std. Err. t P>|t| [95% Conf. Interval]
          -----------------------------+----------------------------------------------------------------
          lag_GII | .4063319 .1660706 2.45 0.018 .0724247 .7402392
          log_FDIinflowreal | .0052016 .004571 1.14 0.261 -.0039891 .0143923
          NaturalresourceRent | .0001336 .0007056 0.19 0.851 -.0012852 .0015523
          Generalgovernmentexpenditure | -.0011517 .0027406 -0.42 0.676 -.0066621 .0043588
          GDPGrowth | .0000538 .0011326 0.05 0.962 -.0022235 .0023311
          Schoolsecondaryfemale | -.0015661 .0005599 -2.80 0.007 -.0026918 -.0004405
          UrbanPopulationControl | .0002386 .000501 0.48 0.636 -.0007687 .0012459
          polity2 | .0029176 .00107 2.73 0.009 .0007662 .005069
          Fertilityrate | .0172748 .0121555 1.42 0.162 -.0071655 .0417151
          Year | -.0002603 .0066672 -0.04 0.969 -.0136656 .013145
          Yeardummy1 | .1047832 .1552767 0.67 0.503 -.2074215 .4169879
          Yeardummy17 | -.006658 .0432925 -0.15 0.878 -.0937034 .0803874
          Yeardummy18 | -.0006796 .0359611 -0.02 0.985 -.0729842 .071625
          Yeardummy19 | -.0071339 .0330241 -0.22 0.830 -.0735332 .0592655
          Yeardummy20 | -.0066488 .0261336 -0.25 0.800 -.0591938 .0458963
          Yeardummy21 | .0021421 .0180578 0.12 0.906 -.0341655 .0384498
          Yeardummy22 | .0005937 .0097345 0.06 0.952 -.0189789 .0201663
          _cons | .8149224 13.41294 0.06 0.952 -26.15361 27.78345
          ----------------------------------------------------------------------------------------------
          Instruments for orthogonal deviations equation
          GMM-type (missing=0, separate instruments for each period unless collapsed)
          L(0/5).GII collapsed
          Instruments for levels equation
          Standard
          log_FDIinflowreal NaturalresourceRent Generalgovernmentexpenditure
          GDPGrowth Schoolsecondaryfemale UrbanPopulationControl polity2
          Fertilityrate Year Yeardummy1 Yeardummy2 Yeardummy3 Yeardummy4 Yeardummy5
          Yeardummy6 Yeardummy7 Yeardummy8 Yeardummy9 Yeardummy10 Yeardummy11
          Yeardummy12 Yeardummy13 Yeardummy14 Yeardummy15 Yeardummy16 Yeardummy17
          Yeardummy18 Yeardummy19 Yeardummy20 Yeardummy21 Yeardummy22 Yeardummy23
          Yeardummy24
          _cons
          GMM-type (missing=0, separate instruments for each period unless collapsed)
          DL.GII collapsed
          ------------------------------------------------------------------------------
          Arellano-Bond test for AR(1) in first differences: z = -1.70 Pr > z = 0.090
          Arellano-Bond test for AR(2) in first differences: z = 0.43 Pr > z = 0.669
          ------------------------------------------------------------------------------
          Sargan test of overid. restrictions: chi2(6) = 18.25 Prob > chi2 = 0.006
          (Not robust, but not weakened by many instruments.)
          Hansen test of overid. restrictions: chi2(6) = 5.55 Prob > chi2 = 0.475
          (Robust, but weakened by many instruments.)

          Comment


          • #6
            The instruments in your ivstyle() option are implicitly assumed to be uncorrelated with the unobserved country-specific effects. This is effectively a random-effects assumption, which is unlikely to hold. The following presentation might be helpful:
            https://www.kripfganz.de/stata/

            Comment

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