Question

Next, suppose you add the unemployment rate, as a variable, to the regression model above and obtain the following estimates:

SALES = 5.987-0.876(PRICE)-0.045(UNEMPLOYMENT RATE)

B) What does this imply about the omission of the unemployment rate from the model above?  In other words, given the coefficient on PRICE went from -1.034 to -0.876, what was the nature of the omitted variable bias?

Answer 1

This is an instance of model specification bias where the term unemployment rate has a coefficient of -0.045 but also the coefficient of Price went up from -1.034 to -0.876. Hence, this suggests that the variable unemployment rate affects both the dependent variable Sales as well as the independent variable Price.

However, since the coefficient alone by its size i.e. -0.045 does not seem significant enough(although there are specific hypothesis tests to check this but apt information is not available in this case). Such coefficients can be tested for significance and hence can be questioned about the inclusion of the model.