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?

*Some additional information*:

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 `

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#### Best Answer

First of all, a VIF of 2.82 is not that small–your standard error is around 67% larger than it would be without collinearity.

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.

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