Final answer:
The extent of the bias in OLS estimators from excluding relevant predictor variables depends on the correlation between included and excluded predictor variables. Lurking variables, if correlated with included predictors, can introduce bias. Proper experimental design or controlling for all relevant variables is essential to reduce this bias.
Step-by-step explanation:
If one or more of the relevant predictor variables are excluded, then the resulting OLS estimators are biased. The extent of the bias depends on the degree of the correlation between the included and the excluded predictor variables. When significant predictor variables are not included in an OLS regression model the omitted variables may contain information that explains the variability in the response variable. If the excluded variables are correlated with the included variables, this omission can lead to erroneous findings because the effects of the omitted variables are incorrectly attributed to the variables that are included in the model. Lurking variables are an example of the kinds of variables that can introduce bias when not included in a model. If these lurking variables have a significant connection with both the predictor and response variables, their absence in the analysis can result in a misestimated relationship between the included predictors and the response.
It is essential in research to isolate the explanatory variable through experimental design, using random assignment where possible to balance the presence of lurking variables across treatment groups. This helps in determining a cause-and-effect relationship between the explanatory and response variables. However, in non-experimental observational studies where random assignment isn't feasible controlling for all relevant predictor variables becomes critical to reduce bias in OLS estimators.