Consider the regression model ln Y; = a + BC; + €; where Y; is annual income and C₂ is a dummy for being a college graduate. (a) Solve for Y in the above expression, differentiate with respect to C₁, and derive an expression for that shows why the slope coefficient in the "semilog model" can be interpreted as the percent increase in annual income associated with being a college graduate. (b) Consider instead In Y₁ = y + pln X; + v; where Y; is annual income and X; is parental income. Solve for Yi, differentiate with respect to X₁, and derive an expression for P. What do economists call parameters like p? (c) Take the original model and modify as follows: In Y₁ = a + BC₁ + 8 (C₂F;) + €; where F; is a dummy for being female. Interpret the parameters in this case in terms of differences in means.

Consider the regression model ln Y; = a + BC; + €; where Y; is annual income and C₂ is a dummy for being a college graduate. (a) Solve for Y in the above expression, differentiate with respect to C₁, and derive an expression for that shows why the slope coefficient in the "semilog model" can be interpreted as the percent increase in annual income associated with being a college graduate. (b) Consider instead In Y₁ = y + pln X; + v; where Y; is annual income and X; is parental income. Solve for Yi, differentiate with respect to X₁, and derive an expression for P. What do economists call parameters like p? (c) Take the original model and modify as follows: In Y₁ = a + BC₁ + 8 (C₂F;) + €; where F; is a dummy for being female. Interpret the parameters in this case in terms of differences in means.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter4: Estimating Demand

Section: Chapter Questions

Problem 8E

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