<p>A major concern with the use of non-probability samples is their lack of representativeness that, if not accounted for properly, may lead to large bias in survey estimates. Non-probability samples involve subjective methods for sample selection, so that inclusion probabilities are unknown and it is not possible to apply the traditional randomization theory for inference on the population parameters. In this paper, the uncertainty in survey estimates resulting from the non-identifiability of the sampling design acting in the non-probability sample, as well as its reduction due to availability of extra-sample information, is discussed. Next, the effect of non-identifiability on survey estimates accuracy is evaluated. Finally, an application to real enterprise data from Italy is performed.</p>