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I am estimating a model which gives me significant parameter estimates for my variables of interest. However, when I use the log version of the model log(dependent)=log(independent), I don't get significant estimates at the 95% confidence level.

I am replicating two other studies, and the authors do get significant results under both specifications.

Can someone please explain why does this happen and what does it mean? Any way of solving the problem?

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    $\begingroup$ You're testing different hypotheses. Broadly speaking, both approaches do test whether $X$ has an effect on $Y$ but the nature of that effect is very different in the two models so it's not a surprise that you're getting different results. I guess my question would be: what is the substantive reason for conducting both tests? What are you trying to learn/prove by doing this? It seems to me you should use whichever model makes more sense in the context of the application, but not both. $\endgroup$ – Macro Aug 21 '13 at 14:02
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    $\begingroup$ Actually, there is no reason to worry. If estimate is insignificant than simply you cannot be certain that estimate differs from zero. In most cases p>0.05 means nothing, e.g. you can neither accept nor decline the hypothesis. I'd better recommend you to compare estimates, but not p-values. Most likely that 95% confidence interval of your estimates contain the estimates taken from other studies. That is enough to say that all studies are consistent. $\endgroup$ – O_Devinyak Aug 21 '13 at 14:02
  • $\begingroup$ Detail: Best to avoid expressions such as "significant estimates at the 95% confidence level". All too easy to forget to mention "confidence" and then many will be confused and some will suspect you don't understand. In any case, simpler to say significant at the 5% level (and better to give P-values). $\endgroup$ – Nick Cox Aug 21 '13 at 14:19
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    $\begingroup$ There isn't really any "problem" to solve here. $\endgroup$ – Peter Flom Aug 21 '13 at 15:10
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    $\begingroup$ Well, your two models ask different questions and get different answers. That's not a problem. And your model was run on different data than other authors' so that's not a problem, either. $\endgroup$ – Peter Flom Aug 21 '13 at 15:58

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