Panel Data - Trade coefficient

[Derek Liam]

Hi All,

I'm using a panel data set for 30 countries over 24 time periods (years) in Stata.
I want to research the impact of increasing trade between two specific large countries on thirty nearby small countries' growth.
After dropping insignificant control variables, I am left with my main independent variable of interest and three control variables.
My dependent variable is the real growth rate of GDP per capita for each of the 30 countries.
My independent variable of interest is the log of trade growth between the two large countries. The three control variables are: Capital Investment, Inflation and World GDP per capita growth rate.
The hausman test indicates I should account for fixed effects. Due to the presence of heteroskedasticity and serial correlation in my model, I am using the fe vce (robust) command.
My main concern is the large coefficient on the main independent variable of interest - the log of trade growth between the two large countries.
I think lagged variables of the independent variable of interest are important to use but I’m also I’m getting quite large coefficients on lag1 and lag2 variables.
lag3 variable was insignificant so I dropped it so I’m only including only the lag1 and lag2 variables now.
The second xtreg below includes the lagged variables, the first xtreg does not.

xtreg  gdppcgrowth lntradeAB capitalinv worldgrowthrate inflation, fe vce (robust)

Fixed-effects (within) regression               Number of obs      =       720
Group variable: countryn                        Number of groups   =        30

R-sq:  within  = 0.2581                         Obs per group: min =        24
       between = 0.0745                                        avg =      24.0
       overall = 0.2341                                        max =        24

                                                F(4,29)            =     13.26
corr(u_i, Xb)  = -0.0766                        Prob > F           =    0.0000

                              (Std. Err. adjusted for 30 clusters in countryn)
------------------------------------------------------------------------------
             |               Robust
 gdppcgrowth |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   lntradeAB |   6.548358    1.58085     4.14   0.000     3.315158    9.781559
  capitalinv |    .005364   .0015468     3.47   0.002     .0022005    .0085275
worldgrowt~e |   .7311719   .1602057     4.56   0.000     .4035145    1.058829
   inflation |  -.0030991   .0007019    -4.42   0.000    -.0045346   -.0016636
       _cons |  -.3775184   .6862688    -0.55   0.586    -1.781096    1.026059
-------------+----------------------------------------------------------------
     sigma_u |  1.7330239
     sigma_e |  4.4820809
         rho |  .13005877   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. 
. xtreg  gdppcgrowth  lntradeAB capitalinv  worldgrowthrate inflation  lntradeABlag1 lntradeABlag2, fe vce (robust)

Fixed-effects (within) regression               Number of obs      =       660
Group variable: countryn                        Number of groups   =        30

R-sq:  within  = 0.2867                         Obs per group: min =        22
       between = 0.0159                                        avg =      22.0
       overall = 0.2316                                        max =        22

                                                F(6,29)            =     14.50
corr(u_i, Xb)  = -0.0835                        Prob > F           =    0.0000

                              (Std. Err. adjusted for 30 clusters in countryn)
------------------------------------------------------------------------------
             |               Robust
 gdppcgrowth |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   lntradeAB |   6.169046    1.73935     3.55   0.001     2.611675    9.726417
  capitalinv |   .0036179   .0011013     3.29   0.003     .0013654    .0058704
worldgrowt~e |   .5928987    .143695     4.13   0.000     .2990095     .886788
   inflation |  -.0325204   .0061145    -5.32   0.000     -.045026   -.0200148
lntradeABl~1 |   3.946839   .8017647     4.92   0.000     2.307046    5.586632
lntradeABl~2 |     3.3768   1.696444     1.99   0.056    -.0928162    6.846417
       _cons |   .3204642   .6301695     0.51   0.615    -.9683772    1.609306
-------------+----------------------------------------------------------------
     sigma_u |  1.9016914
     sigma_e |  3.5790648
         rho |  .22016318   (fraction of variance due to u_i)
------------------------------------------------------------------------------

Does anyone agree that the large coefficient on the main independent variable of interest is a problem? Does anyone see something that I have done wrong that may have caused this issue?


Best Regards,
Derek

[Clyde Schechter]

From a statistical point of view I don't see any problem here. The model has no inherent mis-specification, and the code seems correct. The output shows nothing worrisome. As for whether your primary variable coefficients are too large, it is impossible to comment on them without knowing the units in which everything is measured. Log-transformed variables tend to be pretty small, so they often require large coefficients in order to scale up to the level of a variable like per capita GDP, which is often a very large number.

That said, I assume you have some reason for thinking this number is too big and can't be right. I certainly think you should continue inquiring into that. But I think it will be more fruitful for you to consult an economist/econometrician about this: perhaps your model is not a good one and something about your choice of variables is causing lntradeAB to capture variance that should really be attributed to something you have omitted from the model. That's a subject matter issue, not a statistical one.

[Phil Bromiley]

There might be a problem if some of the rhs variables figure into the calculation of gdp. I assume you're trying to examine a real economic effect, not an accounting identity.
Note also that you have a logged value on tradeAB so your intuitive understanding of the size of the effect could be way off.