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According to the book I am using, Introductory Econometrics by J.M. Wooldridge, there are 5 Gauss-Markov assumptions necessary to obtain BLUE.

However, by looking in other literature, there is one of Wooldridge's assumption I do not recognize, i.e. the so-called "Random Sampling" assumption according to which "We have a random sample of n observations $(x_{i1}, x_{i2}, \dots, x_{ik}, y_i): i= 1, \dots, n)$ following the population model".

I am trying to figure out how to test this assumption on my data, knowing that my supervisor is looking for a proof more solid than simply saying my data was obtained randomly.

Could you please help on this? I am using Stata for any statistical tests.

P.S. I am aware of the 6th assumption (normality of errors) in order to obtain valid statistical inference.

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    $\begingroup$ The sample won't (can't) tell you how it was produced in the same way that you can't tell whether 1, 0, 1, 0, 0 are just numbers I made up or the results of a series of coin tosses (tails 1, heads 0). $\endgroup$ – Nick Cox Dec 21 '18 at 10:39
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    $\begingroup$ No such implication on my part. The point is that the sampling credentials of data are to be sought in how they were sampled (measured, produced), not in what they are or seem like. If one does not know, then that underlines the ignorance of the researcher; it doesn't establish the innocence of the data. $\endgroup$ – Nick Cox Dec 21 '18 at 10:53
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    $\begingroup$ You could estimate autocorrelation to check whether there is significant correlation / dependence between your observations, and that's as far as you can go. $\endgroup$ – user2974951 Dec 21 '18 at 10:56
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    $\begingroup$ The detail depends on whether on your definition random sampling implies independence. $\endgroup$ – Nick Cox Dec 21 '18 at 11:05
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    $\begingroup$ So that's important information not in the question. There are at least three matters to address. 1. What is your population? 2. In what sense would your sampling design ideally produce a random sample? 3. Consideration of the implications of selective response (non-response). The same questions and difficulties arise for a large fraction of social science studies. $\endgroup$ – Nick Cox Dec 21 '18 at 14:24

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