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  • Coefficients from a Dynamic Panel Data Model of Economic Growth

    Hello all,

    I am having difficulties with the interpretation of the regression results from estimating a growth regression in a dynamic panel data set-up, estimated using Stata's xtabond and xtabond2 commands. (i'm using difference GMM and system GMM estimators by Arellano-Bond and Arellano-Bover/Blundell-Bond respectively).
    For my thesis I am interested in the effect of a set of regressors X on growth. My specification is a follows:
    Ln(Y_i,t) = a*Ln(Y_i,t-1) + b*X_i,t + e_i,t
    • Y measures income per capita
    • X is the independent variable of interest, which represents a percentage where 1% is written as 0.01 for example.
    My difficulty lies in the interpretation of coefficient b, therefore I would like to ask for your help.
    - Is it correct that b represents the effect on the growth rate(as the lagged income per capita is also incorporated in the model)?
    - Also if the outocome is for example 0.5 how do i calculate the actual effect?
    - How do i calculate the rate of convergence in this model if stata reports 0.990 as coefficient for the lagged income variable?


    Thanks in advance, your help is much appreciated!

    Maarten


  • #2
    - It is less a question of whether to interpret b as an effect on the growth rate or the level (because they are interrelated) but more importantly to interpret it as a short-run effect as opposed to a long-run effect. b measures the short-run effect of your regressor X on the output growth rate (in percentage points) or the output level (in percent). In the context of short-run dynamics I nevertheless prefer the interpretation as an effect on the growth rate.

    - What do you mean by "the actual effect"? As said before, b measures a short-run effect. A corresponding long-run effect on the output level (here the distinction is important!) can be obtained as b / (1-a), where 1-a is the rate of convergence. You can compute this long-run effect for instance with the postestimation command nlcom.
    https://twitter.com/Kripfganz

    Comment


    • #3
      Hi Sebastian,

      Thanks for your reply, and the clarification on short-run vs long-run effects. This is something I will consider for the discussion of my results.


      To be more clear on the second question.
      I can now see that from the specification it follows that I am estimating the effect on economic growth:

      Ln(Y_i,t) - Ln (Y_i,t-1) = (a - 1)*Ln(Y_i,t-1) + b*X_i,t + e_i,t


      After running the model, the estimate for b is 0.07. My difficulty lies in the interpretation of this 0.07. Does this mean that if x is changed by 1 (=100% in my case, as x is measured as share of GDP), then the growth rate is 7% higher?


      Thanks in advance,
      Maarten


      Comment


      • #4
        Be careful with % and %-points. As both the growth rate and your regressor x are measured in percent, the effect is measured in percentage points (on both sides).

        Depending on the economic content of your regressor x, a 100 percentage points increase is most likely not "marginal" (taking marginal effects literally). I rather suggest to interpret b=0.07 as follows: A 10 percentage points increase in x leads to an 0.7 percentage points increase in the output growth rate (conditional on all other regressors, in particular the initial level of income per capita).
        https://twitter.com/Kripfganz

        Comment


        • #5
          Thanks again Sebastian! very helpful

          Comment


          • #6
            Hello all,
            I'm trying to estimate the same growth regression model with a dynamic panel data set-up and I have a problem in the interpretation of the coefficient on the lagged dependent variable.
            My model is Ln(Y_i,t) = a*Ln(Y_i,t-1) + b*X_i,t + e_i,t
            I can rewrite it as
            Ln(Y_i,t) - Ln (Y_i,t-1) = (a - 1)*Ln(Y_i,t-1) + b*X_i,t + e_i,t but I think I have to run in Stata the first one. So, How can I interpret the coefficient "a"? Is this the rate of convergence or is "a-1"? Then, in many papers I find the lambda estimate reported in the output regressions as the real rate of convergence. So, the ultimate question is: how can I calculate the rate of convergence starting from the coefficient on the lagged dependent variable?

            Thanks in advance, your answer would be very grateful and helpful
            Vito

            Comment


            • #7
              Hello all,
              I'm trying to estimate the same growth regression model with a dynamic panel data set-up and I have a problem in the interpretation of the coefficient on the lagged dependent variable.
              My model is Ln(Y_i,t) = a*Ln(Y_i,t-1) + b*X_i,t + e_i,t
              I can rewrite it as
              Ln(Y_i,t) - Ln (Y_i,t-1) = (a - 1)*Ln(Y_i,t-1) + b*X_i,t + e_i,t but I think I have to run in Stata the first one. So, How can I interpret the coefficient "a"? Is this the rate of convergence or is "a-1"? Then, in many papers I find the lambda estimate reported in the output regressions as the real rate of convergence. So, the ultimate question is: how can I calculate the rate of convergence starting from the coefficient on the lagged dependent variable?

              Thanks in advance, your answer would be very grateful and helpful
              Vito

              Comment


              • #8
                Neither nor. The rate of convergence is \( 1 - a \), which should be a positive number. Intuitively, if \( a = 1 \) and therefore \( 1 - a = 0 \) there is no convergence because the growth rate of the dependent variable does not depend on the previous period's state of the economy. I \( a = 0 \) and therefore \( 1 - a = 1 \) the economy adjusts immediately and completely to any deviation from the long-run relationship (i.e. there is no dynamic adjustment process becaue we are in the steady state in every period).
                https://twitter.com/Kripfganz

                Comment


                • #9
                  Thank you Sebastian,
                  but I don't understand the reason why the rate of convergence should be 1-a and not a-1 in the second equation. Indeed, the latter permits me to have a negative coefficient when it occurs. It's not the same using the first one. Moreover, I always find in many papers that the implied lambda is the rate of convergence, which is given by this formula: β*t=exp(-λ*t)-1. What is this?
                  And then, is it correct to use the first equation in the command xtabond2 or is it better to use the second? xtabond2 differences the equation in GMM procedure and I'm not sure, using the second equation, whether it is appropriate to differenciate the dependent variable twice.
                  Thanks in advance,
                  VM

                  Comment


                  • #10
                    Hello everyone, I work on a similar problem but have little experience with econometrics so far. My question is:

                    Why do you use Ln(Y_i,t) instead of Y_i,t ? - Is this somehow given by Stata and would I get false results simply using Y_i,t instead?

                    Thanks you
                    Andreas

                    Comment


                    • #11
                      I am estimating the dynamic panal data based growth equation Ln(Y_i,t) = a*Ln(Y_i,t-1) + b*X_i,t + e_i,t.

                      What I don't understand is how to calculate the speed of convergence. Can anyone please help?

                      Comment


                      • #12
                        @vitosky: Usually you should use the first equation, as otherwise the question would be why your are interest in a twice-differenced dependent variable (changes the interpretation of the model)

                        @Naujoks: Ln has the advantage that you can norm variables of different units, and when all your variables (dependent and independent) are in ln or shares you can directly interpret the coefficients as elasticities

                        Comment


                        • #13
                          Dear All,

                          i am trying to estimate the random effect (pitt and lee 1981) and true random effect (Greene 2005) model in SFA with weakly balanced panel data. but when i add any dummy variable stata gives only coefficients without any standard error or probability value.

                          further i tried to run GLS model with xtreg y x1 x2 x3, re, stata gave error message (insufficient observation) but there are 15000 observations.

                          can anyone help me in this regard? any guidance will be highly appreciated.

                          Regards

                          Comment


                          • #14
                            Hello All, I am estimating the dynamic panal data based growth equation Ln(Y_i,t) = a*Ln(Y_i,t-1) + b*X_i,t + e_i,t.

                            With i=22 and t=20. But, what I don't know is how to put the per capita income data for the initial year of each i in the data table. Can anyone please help?

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