The interpretation of the slope coefficient in the model $\ln \left( Y _ { i } \right) = \beta _ { 0 } + \beta _ { 1 } \ln \left( X _ { i } \right) + u _ { i }$
is as follows:
A) a 1 % change in X is associated with a $\beta _ { 1 } \%$ change in Y .
B) a change in X by one unit is associated with a $\beta _ { 1 }$ change in Y .
C) a change in X by one unit is associated with a 100 $\beta _ { 1 } \%$ change in Y .
D) a 1 % change in X is associated with a change in Y of 0.01 $\beta _ { 1 }$

Question

The interpretation of the slope coefficient in the model $\ln \left( Y _ { i } \right) = \beta _ { 0 } + \beta _ { 1 } \ln \left( X _ { i } \right) + u _ { i }$
is as follows:
A) a  1 %  change in  X  is associated with a $\beta _ { 1 } \%$ change in  Y .
B) a change in  X  by one unit is associated with a $\beta _ { 1 }$ change in  Y .
C) a change in  X  by one unit is associated with a 100 $\beta _ { 1 } \%$ change in  Y .
D) a  1 %  change in  X  is associated with a change in  Y  of  0.01 $\beta _ { 1 }$

Quizplus · Accepted Answer

A 1% change in X is associated with a β1% change in Y.

The Interpretation of the Slope Coefficient in the Model ln⁡(Yi)=β0+β1ln⁡(Xi)+ui\ln \left( Y _ { i } \right) = \beta _ { 0 } + \beta _ { 1 } \ln \left( X _ { i } \right) + u _ { i }ln(Yi​)=β0​+β1​ln(Xi​)+ui​

The Interpretation of the Slope Coefficient in the Model $\ln \left( Y _ { i } \right) = \beta _ { 0 } + \beta _ { 1 } \ln \left( X _ { i } \right) + u _ { i }$