I can not find any control variables that are significant

[Guest]

Dear statalist community

I am trying to find the relationship between public spending (dependent variable) and the amount of immigration (independent variable). The format is in panel data.
Right now I am doing a robustness test, finding control variables that might affect dependent variable. I am doing an FE test.
However, I think the result is too good because the first simple specification gives me p-value of 0.000. Also, after adding the control variables, none of them seem to be significant and important.

I would like to ask whether...
1. Is this strange?
2. If this is not strange, how can I interpret the coefficient of control variables as they are not really significant at all
3. (This is not really related but I'm just not sure) How can I interpret the coefficient of year dummy variable?

Here are my results
[specification 1] without control variable

. xi: xtreg govexp_gdp migrant_pop  i.year, fe

i.year _Iyear_1990-2010 (naturally coded; _Iyear_1990 omitted)


Fixed-effects (within) regression Number of obs = 163

Group variable: country Number of groups = 35


R-sq: within = 0.2436 Obs per group: min = 1

between = 0.0196 avg = 4.7

overall = 0.0019 max = 5


F(5,123) = 7.92

corr(u_i, Xb) = -0.7451 Prob > F = 0.0000


------------------------------------------------------------------------------

govexp_gdp | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

migrant_pop | .4818744 .1003668 4.80 0.000 .2832044 .6805443

_Iyear_1995 | .1822943 .5228856 0.35 0.728 -.8527256 1.217314

_Iyear_2000 | -1.286386 .5284281 -2.43 0.016 -2.332377 -.2403948

_Iyear_2005 | -1.169919 .5584982 -2.09 0.038 -2.275432 -.0644057

_Iyear_2010 | -.4115732 .5954315 -0.69 0.491 -1.590193 .7670469

_cons | 15.59851 .8436665 18.49 0.000 13.92853 17.2685

-------------+----------------------------------------------------------------

sigma_u | 4.4247688

sigma_e | 1.929498

rho | .84022677 (fraction of variance due to u_i)

------------------------------------------------------------------------------

F test that all u_i=0: F(34, 123) = 10.84 Prob > F = 0.0000


[specification 2] : adding control variable called gdpcap
.

xi: xtreg govexp_gdp migrant_pop gdpcap  i.year, fe

i.year _Iyear_1990-2010 (naturally coded; _Iyear_1990 omitted)


Fixed-effects (within) regression Number of obs = 163

Group variable: country Number of groups = 35


R-sq: within = 0.2436 Obs per group: min = 1

between = 0.0194 avg = 4.7

overall = 0.0018 max = 5


F(6,122) = 6.55

corr(u_i, Xb) = -0.7444 Prob > F = 0.0000


------------------------------------------------------------------------------

govexp_gdp | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

migrant_pop | .4789815 .1104045 4.34 0.000 .2604246 .6975383

gdpcap | 1.83e-06 .0000284 0.06 0.949 -.0000545 .0000581

_Iyear_1995 | .1769877 .5314915 0.33 0.740 -.8751528 1.229128

_Iyear_2000 | -1.289436 .5327061 -2.42 0.017 -2.343981 -.2348909

_Iyear_2005 | -1.189522 .6386239 -1.86 0.065 -2.453742 .0746979

_Iyear_2010 | -.4384528 .7300596 -0.60 0.549 -1.883679 1.006773

_cons | 15.59788 .8471609 18.41 0.000 13.92084 17.27492

-------------+----------------------------------------------------------------

sigma_u | 4.4198834

sigma_e | 1.937357

rho | .83883391 (fraction of variance due to u_i)

------------------------------------------------------------------------------

F test that all u_i=0: F(34, 122) = 10.45 Prob > F = 0.0000


[specification 3] : adding control variable called gdpcap, pop65
. xi: xtreg govexp_gdp migrant_pop gdpcap pop65 i.year, fe

i.year _Iyear_1990-2010 (naturally coded; _Iyear_1990 omitted)


Fixed-effects (within) regression Number of obs = 163

Group variable: country Number of groups = 35


R-sq: within = 0.2438 Obs per group: min = 1

between = 0.0160 avg = 4.7

overall = 0.0010 max = 5


F(7,121) = 5.57

corr(u_i, Xb) = -0.7467 Prob > F = 0.0000


------------------------------------------------------------------------------

govexp_gdp | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

migrant_pop | .4814699 .1116231 4.31 0.000 .2604826 .7024573

gdpcap | 4.75e-06 .0000325 0.15 0.884 -.0000596 .0000691

pop65 | .0457717 .2422359 0.19 0.850 -.4337981 .5253415

_Iyear_1995 | .132254 .5837644 0.23 0.821 -1.023462 1.28797

_Iyear_2000 | -1.370131 .6844093 -2.00 0.048 -2.725099 -.015162

_Iyear_2005 | -1.345254 1.044199 -1.29 0.200 -3.412521 .7220138

_Iyear_2010 | -.6426634 1.305842 -0.49 0.624 -3.227923 1.942596

_cons | 14.94983 3.533554 4.23 0.000 7.954223 21.94543

-------------+----------------------------------------------------------------

sigma_u | 4.4414601

sigma_e | 1.9450592

rho | .83907768 (fraction of variance due to u_i)

------------------------------------------------------------------------------

F test that all u_i=0: F(34, 121) = 9.45 Prob > F = 0.0000


Thank you
Guest

[Clyde Schechter]

1. Is it strange? Well, it's not something that happens very often, because most phenomena are complicated and have lots of confounding variables. But it doesn't mean there's anything wrong.

2. How do you interpret the control variables? Well, if they are really "control" variables, you don't interpret them at all, no matter what their coefficients turn out to be. By calling them "control" variables you are saying that they aren't of direct interest and are included in the analysis only because they may exert influences on the outcome variable that overlap with or interfere with the influence of your main independent variable(s) and you need to adjust for them to avoid omitted variable bias. But they don't require explanation in their own right.

To me, the most important thing we learn from looking at the three different models is that the variables gdpcap and pop65 really don't do very much in the model. I say that without even looking at their p-values. The relevant fact is that their exclusion or inclusion in the model makes essentially no impact on the estimated coefficient for your main variable, migrant_pop. That is a direct demonstration that there is no omitted variable bias if you leave them out, because when you "correct" the omitted variable bias by including them, nothing changes!

3. The interpretation of the year variables is that they estimate year-specific shocks to govexp_gdp that apply equally to all of your countries. Again, these are included just to deal with any omitted variable bias that might arise from omitting them. Since you don't show a model that omits them, we can't really say how much omitted variable bias there might actually be, Another approach is to compare those coefficients to the coefficient of your main predictor, migrant_pop. But migrant_pop is, I imagine, a continuous variable, and you have not given any information about its scale. So it isn't really possible to say, based on what is shown, whether the influences of these year-specific shocks are just a trivial rounding error compared to variation coming from migrant_pop, or whether they are appreciable. You might want to look into that: does a difference in migrant_pop of realistic size translate into a much larger effect on govexp_gdp than any of the year variables' coefficients (in which case the year variables are not really contributing much to the model)? Or are the year variables at least a noticeable contribution relative to that?

Added: By the way, there is no need to use xi: here. If you just drop -xi:- from your commands, these particular regressions will have proper specification of factor variable notation (-help fvvarlist- to learn about this). In recent versions of Stata, nearly all estimation commands accept factor-variable notation, and this, in turn, feeds into the wonderful -margins- command for estimating predicted values and marginal effects in complicated models. Using -xi:- prevents you from using -margins- and -marginsplot-. So -xi:- should be used only in those few commands and situations where factor-variable notation is not supported. (Most of those commands are old and their functionality has been incorporated into newer commands that do allow factor-variable notation, and the other situations requiring the use of -xi:- are sufficiently exotic that most Stata users will never encounter them.) So it wouldn't hurt you to almost forget you ever heard of -xi-.

[Guest]

Dear Clyde Schechter

Thank you very much! I have read a lot of your answers in statalist and all of them are very useful. I am grateful that you answer my question.

Guest