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If the mills ratio of a Heckman selection model (with/without exclusion restriction) is not significant, shall I prefer to estimate my model with OLS instead? Or is it better to use the estimates from the heckman model although there seems to be no sample selection?

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    $\begingroup$ Pedants' corner: The ratio in question is named after J.P. Mills. Thus Mills ratio, Mills' ratio and Mills's ratio are all correct renderings. But any use of the apostrophe is dangerous as it tends to be copied in the wrong place. So I suggest "Mills ratio" and this seems to be the commonest correct rendering in the literature. $\endgroup$ – Nick Cox May 2 '13 at 9:27
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In this case you would have no selection problem, so you could use OLS on the non-censored observations. This can be tested by what you did. So you are correct, see e.g. also wikipedia

"so testing the null that the coefficient on $\lambda$ is zero is equivalent to testing for sample selectivity."

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