Endogenous instruments in IV 2SLS regression in Stata

If I am looking at an ivreg2 equation where:

ivreg2 y1 x2 x3 x4 (x1 = x5 x6)


and I know that x5 and x6 are endogenous variables (i.e. they are motivated by latent, unmeasurable characteristics) and there are no other viable alternatives, does IV 2sls work? Is it biased? Inconsistent?

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One of the prime assumptions of instrumental variables is the exclusion restriction---essentially, it states that the instrument(s) must be exogenous and not directly related to your outcome $y$ (they can only impact $y$ indirectly by changing your endogenous variable $x_1$). If you don't have any exogenous variables, then you don't have any candidates for instruments. As a result, IV will not deliver unbiased or consistent results.