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I've created the following model:

log(consumption) = a + b*log(GDP) + c*log(GDP(-1)) + d*log(consumption(-1)) 

The slope coefficients are all statistically significant, however the intercept has a p-value of 0.1085. How important is this and how will it affect my model?

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    $\begingroup$ The p-value hasn't affected your model at all. Could you clarify the sense in which you intend us to understand "important"? $\endgroup$
    – whuber
    Mar 16, 2019 at 16:20
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    $\begingroup$ Sorry, should have been clearer. I mean to ask, should I reject this model on the grounds that the intercept is not significantly significant? $\endgroup$ Mar 16, 2019 at 16:29
  • $\begingroup$ I saw some researches were they discard the intercept term if it's not significant $\endgroup$ Mar 16, 2019 at 16:29
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    $\begingroup$ How you deal with p-values depends on the purpose of your analysis, so it's essential that you include that information in your post. Since the effect of the constant term can be profound--it looks like you have a time series model in terms of logarithms, so at each time step the exponential of the intercept will multiply the consumption estimate, causing it to have an exponentially greater effect over time--so it would be foolish, without much more consideration, to assume that what "some researches" might have done would be appropriate for you. $\endgroup$
    – whuber
    Mar 16, 2019 at 16:34

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The intent of your question is not entirely clear. But, if you ask if you could/should reestimate the model without the intercept, if it is not significant, then have a look at When is it ok to remove the intercept in a linear regression model? and you will understand that the answer is NO, almost surely. If you don't have a very good, specific reason to omit the intercept, don't do it. One reason: Imagine the true value of the intercept nonzero, but small. Then its estimate will be nonsignificant with large probability, but omitting the intercept will then destroy the unbiasedness of all the other coefficient estimates.

There are other reasons, discussed in many other posts at this site. See Should I keep or eliminate an insignificant confounding variable? or Should control variables be included in model if statistically insignificant?. While this posts is about predictors, not the intercept, much the same applies.

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