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I have one linear regression with a set of explanatory variables and an other set of instrument variables.

In my constrained regression, one of the coefficient for a given variable is constrained to be equal to one.

The moment conditions are not valid for the unconstrained regression according to the J-stat. While, they are for the constrained regression.

Is it theoretically possible ? Or is the consequence of a spurious regression ? The Philipps-Ouliaris reject the null hypothesis of noncointegration between my endogenous explanatory variable and the instruments I put instead with a p-value between 5 and 10%.

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