# Reasons for high standard error (no collinearity)

After running a least squares regression, I have the problem that one of my regressors has a really high standard error while the coefficient on this variable is very close to zero. After checking variance inflation measure I am quite sure that it is not a multicollinearity issue.

        Coef.   Std. Err.
X1     .911         .193
X2     .286         .089
X3    -.166         .082
X4     .016         .044
X5    -.024         .787


The VIF on variable X5 is 2.82. It strikes me as unusual that a variable with such a small coefficient has such a large standard error.

What else are potential (econometric) explanations for one single standard error being that high?

I have panel data with 92 units over 10 years (strictly balanced). I am running a Fixed Effects 2SLS in Stata using xtivreg, where variable X1 is endogenous, and X2-X5 are exogenous. I checked the VIF with Fixed-Effects-transformed variables. I used both conventional Standard Errors, as well as clustering on the country level, the issues of a high standard error on the one variable stayed the same.

summary statistic for variables:

                  Obs        Mean    Std. Dev.      Min.       Max.
Y |        920        .822        .197        .25          1
X1 |        920        .817        .061       .582       .948
X2 |        920        9.44        1.06       6.71       11.8
X3 |        920        26.0        1.72       22.1       30.5
X4 |        920        3.80        .248       2.77       4.37
X5 |        920        .241        .023       .189       .291

• stats.stackexchange.com/questions/242762/… This may serve your purposes. – shenflow Feb 22 '18 at 9:57
• But that does not explain why the standard error for only one variable is so high... – Tartan Leaves Feb 22 '18 at 13:17
• All it means is that the coefficient for $x5$ is rather imprecisely estimated. This may, or may not, have anything to do with its rather restricted variability relative to the other $x$. – mdewey Feb 22 '18 at 15:04
• +1. Think about the theoretical model you are constructing. You are not saying what the variables are exactly, but the answer probably lies right there. – shenflow Feb 22 '18 at 16:46
• Thanks for the comments! I thought there may be econometric issues, like collinearity, I hadn't thought of. – Tartan Leaves Feb 22 '18 at 17:18

Second, the variance of the predictor is inversely related to the standard error of the predictor's effect estimate (have a look at the formula for the standard error of the regression coefficient estimate in OLS--$(X'X)^{-1}$ appears in the formula). X5 has very little variability relative to the other predictors in the model and so it makes sense that its standard error is larger.