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Consider the regression model In Y₁ = a + BC₁ + €; where Yį 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 + 3Ci + 8 (CiFi) + €i where Fi is a dummy for being female. Interpret the parameters in this case in terms of differences in means.

Consider the regression model In Y₁ = a + BC₁ + €; where Yį 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 + 3Ci + 8 (CiFi) + €i where Fi is a dummy for being female. Interpret the parameters in this case in terms of differences in means.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Consider the regression model ln Y₁ = a + BC; +e; where Yį is annual income and C₁ 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 X₂ + v₂ where Y is annual income and X, is parental income. Solve for Yi, differentiate with respect to Xi, 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 + 3C₁ + 8 (CiFi) + €; where Fi is a dummy for being female. Interpret the parameters in this case in terms of differences in means.
Transcribed Image Text:Consider the regression model ln Y₁ = a + BC; +e; where Yį is annual income and C₁ 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 X₂ + v₂ where Y is annual income and X, is parental income. Solve for Yi, differentiate with respect to Xi, 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 + 3C₁ + 8 (CiFi) + €; where Fi is a dummy for being female. Interpret the parameters in this case in terms of differences in means.
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