where formula_19 is what the estimated coefficient vector would be if "x" were not correlated with "u". In this case, it can be shown that formula_19 is an unbiased estimator of formula_21 If formula_22 in the underlying model that we believe, then OLS gives a coefficient which does "not" reflect the underlying causal effect of interest. IV helps to fix this problem by identifying the parameters formula_23 not based on whether formula_24 is uncorrelated with formula_25, but based on whether another variable formula_26 is uncorrelated with formula_25. If theory suggests that formula_26 is related to formula_24 (the first stage) but uncorrelated with formula_25 (the exclusion restriction), then IV may identify the causal parameter of interest where OLS fails. Because there are multiple specific ways of using and deriving IV estimators even in just the linear case (IV, 2SLS, GMM), we save further discussion for the Estimation section below.