Trying to understand the role of FE on individual actors

[Paola Bertolini]

Dear all,

I am currently using a static dataset featuring a group of individuals performing an action with intensity from 0.01 to 1. Each individual has been allocated to a group and I have some information about individuals' demographic and personal features.

I am interested into assessing the role of group participation into individual decision making.

For this reason, I run a simple xtreg, fe . I then collected the FE for each group, created a quantile distribution and then plotted the quantile distribution against the average action of individuals for each group.

The result is contained in this picture: https://ibb.co/wsdBKrn

My question is: am I allowed to think that there is a positive association between the group's influence (as captured by the FE) and the average action of individuals belonging to that group? Is that a trivial result?

thank you all for your much appreciated support. This forum is helping me on so many dimensions.

[Carlo Lazzaro]

Paola:
to get helpful replies, you should share via CODE delimiters (please see the FAQ) what you coded and what Stata gave you back (graphs included). Thanks.

[Paola Bertolini]

Dear Carlo,

Many thanks for the kind reply. I tried to edit my message but apparently the edit window (if I understand) lapsed. So I will report the code down here:

Suppose I have a group of individuals i=1,..,,n organized in k=1,...K groups. Each group has size N_k
I can't control group allocation but I am currently assuming they have been imposed from outside the model. This is a static dataset. Each individual can perform an action y_i = [0.01,1]. I also have information about origin neighborhood, ethnic origin, age.

The commands I run are

g age2 = age^2

xtset groups

xtreg y_i neighborhood ethnic_origin age age2, fe robust

predict groups_fe, u

Unfortunately, my competences with STATA do not allow me to proceed further with this software. I pass to matlab the vector of residuals "groups_fe", the vector "y_i" and the vector of group size N_k.

Last, I plot the scatterplot given by variables groups_fe and variable (y_i/N_k).

The above produces the picture: https://ibb.co/wsdBKrn

Thank you!

[Carlo Lazzaro]

Paola:
thanks for clarifying.
Please consider what follows as a tentative reply, as I am not clear with what you're after:

. use "https://www.stata-press.com/data/r18/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtreg ln_wage c.age##c.age i.union, fe vce(cluster idcode)

Fixed-effects (within) regression               Number of obs     =     19,229
Group variable: idcode                          Number of groups  =      4,150

R-squared:                                      Obs per group:
     Within  = 0.0978                                         min =          1
     Between = 0.0461                                         avg =        4.6
     Overall = 0.0587                                         max =         12

                                                F(3, 4149)        =     225.93
corr(u_i, Xb) = 0.0183                          Prob > F          =     0.0000

                             (Std. err. adjusted for 4,150 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0324229   .0051058     6.35   0.000     .0224129     .042433
             |
 c.age#c.age |  -.0002752   .0000818    -3.37   0.001    -.0004355   -.0001149
             |
     1.union |   .1054165   .0098217    10.73   0.000     .0861607    .1246723
       _cons |   .9942539   .0782432    12.71   0.000     .8408553    1.147652
-------------+----------------------------------------------------------------
     sigma_u |  .42293457
     sigma_e |  .26192667
         rho |  .72278248   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. predict fe, u

. bysort idcode: gen wanted=_N/union

. twoway (scatter wanted fe)

.

Possibly off topic here, I recommend you to use -fvvarlist- notation to create categorical variables and interactions.
Notably, the highest payoff with -fvvarlist- is earned when using -margins- and/or -marginsplot- after any regression commands.

[Paola Bertolini]

Dear Carlo,

thank you for the splendid availability. What you pictures captures the technical realization of what I was after, thanks. In terms of the purpose of this array of commands, I wish to obtain a representation of the influence of group effects on individual decision making. From the picture I enclosed earlier (replicated with your code) it appears that a positive relationship exists between intensity of individual action and group fixed effect. Would this be a possible statement, or I am achieving this outcome out of some trivial mechanical reason?

I find comforting that a relationship does not appear to exist in your example.

thank you!

[Carlo Lazzaro]

Paola:
yes, you're right: a a relationship does not appear to exist in my example.
Is there any interactions between predictors that you can exploit to investigate the existence of a potential relationship between individual action (the regressand?) and group membership?

[Paola Bertolini]

Hi and thank you for your comment.

Unfortunately, I don't have much else in my dataset at the moment (there are bits of information that have been collected by another team which will made available at a later date). I was tempted to think that the positive relationship I observe is precisely due to a peer effect. Teams have the opportunity to communicate before acting, therefore it seems to me that the relationship is potentially very meaningful.

thanks,

[Carlo Lazzaro]

Paola:
most depends, I guess, on what the literature in your reserach field tells about this issue.

[Paola Bertolini]

Hi Carlo,

Apologies for the delay in coming back. I hoped I could get the second part of the data to elaborate a bit further on the previous results, but these are lagging behind. In the meantime, thanks again for the great support. It means a lot to me,

Paola