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This paper proposes a new strategy to identify causal effects. Instead of finding a conventional instrumental variable correlated with the treatment but not with the confounding effects, we propose an approach which employs an instrument correlated with the confounders, but which itself is not causally related to the direct effect of the treatment. Utilizing such an instrument enables one to estimate the confounding endogeneity bias. This bias can then be utilized in subsequent regressions first to obtain a "binding" causal effect for observations unaffected by institutional barriers that eliminate a treatment's effectiveness, and second to obtain a population-wide treatment effect for all observations independent of institutional restrictions. Both are computed whether the treatment effects are homogeneous or heterogeneous. To illustrate the technique, we apply the approach to estimate sheepskin effects. We find the bias to be approximately equal to the OLS coefficient, meaning that the sheepskin effect is near zero. This result is consistent with Flores-Lagunes and Light (2010) and Clark and Martorell (2014). Our technique expands the econometrician's toolkit by introducing an alternative method that can be used to estimate causality. Further, one potentially can use both the conventional instrumental variable approach in tandem with our alternative approach to test the equality of the two estimators for a conventionally exactly identified causal model, should one claim to already have a valid conventional instrument.