Suppose I have a likelihood maximisation problem
$$ \hat{\theta} = \max L_n(\theta;y) $$
where $\theta = [\theta_1, \theta_2, ...., \theta_k]^T$.
What if I would estimate instead estimate the maximisation problem leaving out a parameter
$$ \hat{\theta_{-k}} = \max L_n(\theta_{-k};y) $$
but a loop over each value of $\theta_k$ and pick the specification with the highest likelihood. Would this be identical to estimating the problem jointly?