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I have a regression as follows:

$$ y = \alpha + \mu L + \beta_1 x + \beta_2 x^2 + \varepsilon $$

where L is a dummy, and x is a control variable.

Both $x$ and $x^2$ are significant when I run the regression. I create a matching sample using $L$, $x$ and $x^2$. The results of the regression on matched sample has significance for $x^2$ only and the significance of $x$ disappears.

Would you help me interpreting this result?

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  • $\begingroup$ Your question title said matching doesn't affect the significance of coefficients, but your question text said it does. What are you trying to ask? $\endgroup$
    – Noah
    Commented Apr 29 at 13:04
  • $\begingroup$ @Noah you are right. I modified the title. Issue is that it changes the significance for the first degree, but not the second degree. I was wondering how to interpret this. $\endgroup$ Commented Apr 30 at 12:49

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A matched sample is smaller than an unmatched sample, so the variance of coefficient estimates will be larger after matching, leading to larger p-values. It doesn't matter, though; you should not interpret the value or significance of coefficients on covariates in the model if your goal is to estimate a treatment effect. These coefficients may be horribly confounded or subject to other biases even if including the covariate is necessary for unbiased estimation of the treatment effect. You should neither report nor examine the significance of any coefficients in your outcome model other than that on treatment, and it is always safer to use g-computation to interpret your treatment effect.

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