Dropping a variable:

One of the  'simplest'  methods is  to drop one of the collinear variables. Thus as  shown earlier  in our consumption expenditure illustration, when we drop the variable wealth, we obtain  the result that incoine is highly significant whereas in the original model. income was insignificant. The problem here is that by dropping variables arbitrarily from the model wc are exposed to the risk of specrficaiion birrs, which arises from the incorrect specification of the model for analysis. Thus  if economic  theory says that both income and wealth should'have an impact on consumption then dropping one of  them is  a misspecification of  the model and g'  2s rise  to error. Specification error or bias usually leads to biased~stimates  of the coefficients. Therefore although convenient, this approach has a serious drawback since the remedy may be worse than the disease in some situations. Whereas multicollinearity may prevent precise estimation of the parameters of the model, omitting a variable may seriously mislead us as to the true values of the parameters. We note that with specification error the estimates can be potentially biased. So what you gain from lower standard errors of remaining variables may not be worth paying the price of biased estimates.