An economist estimates the regression model yi= ?0 + ?1x1i + ?2x2i + ?i. The estimates of the parameters ?1 and ?2 are not very large compared with their respective standard errors

But the size of the coefficient of determination indicates quite a strong relationship between the dependent variable and the pair of independent variables. Having obtained these results, the economist strongly suspects the presence of multicollinearity. Since his chief interest is in the influence of X1 on the dependent variable, he decides that he will avoid the problem of multicollinearity by regressing Y on X1 alone. Comment on this strategy.

If Y is, in fact, strongly influenced by X2, dropping it from the regression equation could lead to serious specification bias. Instead of dropping the variable, it is preferable to acknowledge that, while the group as a whole is clearly influential, the data do not contain information to allow the disentangling of the separate effects of each of the explanatory variables with some degree of precision.