Suppose you have many observations of the price of refrigerators, with other characteristics including their energy cost as well as whether or not they are stainless steel. Now, suppose you ran the standard linear regression of price on energy cost: Price_i = β₀ + β₁ Energy Cost_i + U_i and got an estimate of β₁. Now, suppose you know that stainless steel refrigerators are more popular (i.e., sell for higher prices holding all other characteristics constant) and tend to be in more energy efficient (i.e., lower energy cost) refrigerator models. What should you expect your estimate of β₁ in the following regression Price_i = β₀* + β₁*Energy Cost_i + β₂* Stainless Steel_i + U_i to be? A) β₁* β₁ C) β₁* = β₁ D) You cannot tell from the information given.

Question

Suppose you have many observations of the price of refrigerators, with other characteristics including their energy cost as well as whether or not they are stainless steel. Now, suppose you ran the standard linear regression of price on energy cost: Price_i = β₀ + β₁ Energy Cost_i + U_i and got an estimate of β₁. Now, suppose you know that stainless steel refrigerators are more popular (i.e., sell for higher prices holding all other characteristics constant) and tend to be in more energy efficient (i.e., lower energy cost) refrigerator models. What should you expect your estimate of β₁ in the following regression Price_i = β₀* + β₁*Energy Cost_i + β₂* Stainless Steel_i + U_i to be? A) β₁* < β₁ B) β₁* > β₁ C) β₁* = β₁ D) You cannot tell from the information given.

Quizplus · Accepted Answer

Stainless steel refrigerators are more popular and tend to be in more energy efficient refrigerator models. So, including the stainless steel indicator variable in the regression will capture some of the variation in price that was previously attributed to energy cost. This will lead to a smaller coefficient on energy cost in the new regression.

Suppose You Have Many Observations of the Price of Refrigerators