Suppose that you observed several key characteristics of a random sample of firms in your industry. You know that the semi-partial correlation of firm Productivity (Y) with R&D (Z) investment holding amount of Labor (X) fixed is positive. Furthermore, suppose you know that the covariance of R&D investment and amount of labor is positive. How will the coefficient on Labor when you run the regression of Productivity on Labor and R&D investment relate to the coefficient on Labor when you run a regression of Productivity on just Labor?
A) It'll be equal to
B) It'll be greater than
C) It'll be less than
D) There is not enough information to determine.

Question

Quizplus · Accepted Answer

The semi-partial correlation of firm Productivity (Y) with R&D (Z) investment holding amount of Labor (X) fixed is positive, which means that when the amount of Labor is held constant, R&D investment has a positive effect on productivity. The covariance of R&D investment and amount of labor is positive, which means that when there is an increase in R&D investment, the amount of labor also tends to increase. Therefore, the coefficient on Labor when you run the regression of Productivity on Labor and R&D investment will be less than the coefficient on Labor when you run a regression of Productivity on just Labor because some of the effect of Labor on Productivity is explained by the variation in R&D investment.

Suppose That You Observed Several Key Characteristics of a Random