Suppose your goal is to estimate the elasticity of demand for blueberries. Your model of blueberry demand is lnQt = a – blnPt + et, where Qt is the quantity of blueberries bought and sold in month t and Pt is the price of blueberries in month t. (The reason for entering the variables in logs is that we are interested in estimating the elasticity of demand rather than the slope of the demand curve. The reason for the minus sign, which is not essential, is that because we think demand depends negatively on price, it makes the equation easier to interpret.) You are considering trying to estimate b by an ordinary least squares regression of lnQt on a constant and lnPt.
a. The condition for a regression to give us a good estimate of the impact of the independent variable on the dependent on is that the residual is not systematically correlated with the independent variable. Is there likely to be a systematic correlation between et and lnPt? (Hint: Your answer should involve supply and demand diagrams and discussing the effects of shifts of one or both curves)