[elena mengo]

Hello everyone,

thanks for your help yesterday. I am still struggling with this analysis because I was expecting different results. Indeed according to my literature reviews, with the addition of the quadratic term I should have an inverted U-shaped relationship and with my data I do not obtain this. Furthermore the relationship between fdi and pollution was supposed to be positive which yesterday was not the case. I changed my data and I used fdi inflows as percentage of gdp and I run a new regression; this time seems to work better

------------------------------------------------------------------------------
co2 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
gdp | -.000071 .0000332 -2.14 0.032 -.000136 -5.92e-06
gdp2 | 2.71e-09 1.39e-09 1.95 0.051 -1.68e-11 5.43e-09
fdi | .0030663 .0085254 0.36 0.719 -.0136432 .0197758
trade | -.0016979 .0030044 -0.57 0.572 -.0075864 .0041906
_cons | 7.629662 .6228844 12.25 0.000 6.408831 8.850493
-------------+----------------------------------------------------------------
sigma_u | 1.6634221
sigma_e | .62703764
rho | .87558303 (fraction of variance due to u_i)

However, I still do not understand the negative coefficient od gdp....there are several missing data in my observations, could this be a possible explanation?

[Koen Crolla]

He Elena,

I came across your question and I am also studying the effect of gdp and trade on carbon emissions. Are you interested in keeping in touch, so we can discuss some of the results we found?
Greetings Koen

[elena mengo]

Hi Koen!

Sure we can keep in touch! I really need someone to confront my results with. So far as I mentioned above I got coefficients that I was not expecting according to previous literature on the topic.
I can send you my e-mail if you wish.

Elena

[Koen Crolla]

yes please, my mail is [email protected]

[elena mengo]

Mine is [email protected]

[Clyde Schechter]

Well, the literature you have reviewed may suggest an inverted U-shaped relationship between CO2 emissions and GDP, but there is nothing even remotely like that in your data. Just look at some simple graphs (run this code):

use diss2, clear
replace country = lower(subinstr(country, " ", "_", .))
levelsof country, local(countries) clean


foreach c of local countries {
 graph twoway line co2 gdp if country == "`c'", sort name(`c', replace) ///
  title("`c'")
}

graph combine `countries', altshrink nocopies xcommon

There is, if anything, in some of your countries, an upright U-shaped relationship. But none of them exhibit an inverted U-relationship, and some don't look particularly quadratic at all. So for some reason your data are truly inconsistent with what you have gleaned from your reviews. You will need to consider the sources of these data and possible selection biases or other errors that might account for this if you really believe the findings in the literature are correct and should apply to your context.

Your regression output is, in fact, an upright U-shaped relationship with a turning point at 13,106. (Pasted from Results window showing commands and output):

. xtreg co2 c.gdp##c.gdp fdi trade

Random-effects GLS regression                   Number of obs     =        187
Group variable: cnt_2                           Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 0.0424                                         min =         16
     between = 0.1982                                         avg =       18.7
     overall = 0.0807                                         max =         21

                                                Wald chi2(4)      =       5.80
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.2143

------------------------------------------------------------------------------
         co2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         gdp |   -.000071   .0000332    -2.14   0.032     -.000136   -5.92e-06
             |
 c.gdp#c.gdp |   2.71e-09   1.39e-09     1.95   0.051    -1.68e-11    5.43e-09
             |
         fdi |   .0030663   .0085254     0.36   0.719    -.0136432    .0197758
       trade |  -.0016979   .0030044    -0.57   0.572    -.0075864    .0041906
       _cons |   7.629662   .6228844    12.25   0.000     6.408831    8.850493
-------------+----------------------------------------------------------------
     sigma_u |  1.6634221
     sigma_e |  .62703764
         rho |  .87558302   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. display as text "Turning point = " %5.0f = -_b[gdp]/(2*_b[c.gdp#c.gdp])
Turning point = 13106

The coefficient of gdp in the context of a quadratic just locates the parabola on the horizontal axis: its sign says nothing about the right-side-up or upside-downess of the parabola. The coefficient of the squared term determines whether the graph is an upright or inverted parabola.

[elena mengo]

Thanks Clyde, I thought indeed that there might be something wrong with the data although I took them from the world bank database which is supposed to be reliable so I might try to investigate the how the explanatory variables influence the emission of CO2 for every country in isolation from the others even though you already have showed that in none of the countries there is the kind of relationship I am expecting. Do you know which code do I have to type in order to do that?