Econ 340 homework 4-3 Maribel. Perez

Econ 340 Home Work Assignment 4 Department of Economics Cal State Fullerton 1. Consider the following dummy variable regression function where food expenditure is a function of disposable income. i i i i e D b X b b Y     3 2 1 (1) Here Y is food expenditure, X is income and D = 1 if female and D = 0 if male. (a) Using the data set (foodexpenditure.xls) provided in the blackboard, estimate the regression function to examine whether food expenditure is different across genders. Interpret your estimated results: explain if food expenditures are different between males and females. Also comment on the statistical significance of your findings. (10) ŷi= 1506.24 +.0589x-228.98 D i The condition under which female’s expenditure is higher than males’ starting food expenditure isβ2>0, withβ2 be positive. Based on the information provided -228.98<0 and it is negative therefore, food expenditure is different across genders, with females having a lower food expenditure compare to males. (b) To allow interactions between X and D estimate the following regression function. (10)

i i i i i i e D X b D b X b b Y      ) ( 4 3 2 1 ŷi = 1432.57+ 0.06xi- 67.89Di - 0.006Dixi (2) (c) Interpret the estimated results you have found in equation (2). Are the rates of increase in food expenditure due an increase in income are different between males and females? Explain. (10) Males Di = 0 Yi = 1432.57 + 0.06xi - 67.89(0) - 0.006xi(0) = 1432.57 + 0.06xi Females Di = 1432.57 + 0.06xi - 67.89(1) - 0.006(1)xi =1364.67 + 0.054xi Our theoretical condition is the circumstance in which female food spending increases faster than male food expenditure if the projected value B3 is positive,B3 > 0.However, if B3 is negative, -0.06, female food expenditure will increase at a lower rate than male food expenditure. As a result, as income rises, female food expenditure rises at a lower rate than males'. 2. I have uploaded data set (school teachers.xls) of the mean salary of school teachers for all states in the USA. I have also categorized the entire USA into 3 regions: region 1 (Northeast and North central states), region 2 (Sothern states), and region 3 (Western states). Since there are 3 categories (region 1, region 2, and region 3), so there must be 2 dummy variables here.  1 D 1 for region 1 =0 for region 2 and region 3  2 D 1 for region 2 =0 for region 1 and region 3. Therefore both dummy variables are zero for region 3. And thus region 3 is our base category. Here annual salary is the dependent variable and per student (pupil) spending (pps) is the independent variable. (a) Formulate a dummy variable regression model of the annual salary of school teachers with government spending as the regressor to see which region has the

(d) Estimate the regression model you developed in part (c) and interpret your results. (10) For Region 1: the model gives: Ŷi = 14625.33 + 2.94xi- 3950.6 * 1 - 5040.1 * 0 + 0.58 * 1 * xi + 1.12 * 0 * xi = 14625.33 + 2.94xi - 3950.6 * 1 + 0.58 * 1 * xi = 10674.73 + 3.52 xi For Region 2: the model gives: Ŷi = 14625.33 + 2.94xi- 3950.6 * 0 - 5040.1 * 1 + 0.58 * 0 * xi + 1.12 * 1 * xi = 14625.33 + 2.94xi - 5040.1 * 1 + 1.12 * 1 * PPS = 9525.85 + 4.06xi For Region 3: the model gives: Ŷi = 14625.33 + 2.94xi- 3950.6 * 0 - 5040.1 * 0 + 0.58 * 0 * xi + 1.12 * 0 * xi = 14625.33 + 2.94xi When we compare the slope coefficient to one another, Region 2 has the highest salary increase when government spending increases. 3. Consider the following dummy-variable regression model for the annual salary of engineers on the basis of race. Here, i Y is annual salary, i X is years of training/education after the job, i Z is years of experience, and i D = 1 if the engineer is white and i D = 0 if the engineer is non-white. i i i i i e D b Z b X b b Y      4 3 2 1 (1) (a) Write down the equation of expected (fitted) salary for both white and non-white engineers. (5) White Engineers: Yi=b1+b2xi+b3Zi+b4(1)+ei =(b1+b4)+b2xi+b3zi Non-white Engineers= Yi=b1+b2xi+b3Zi+b4(0)+ei =b1+b2xi+b3zi (b) State the condition under which non-white engineers will not start with a higher salary than white. (5)

the condition under which non-white engineers will not start with a higher salary than white is when b4 is greater or equal to 0. (c) Assume that non-white engineers start with higher salary than white engineers. Write down the model that will allow you to investigate whether or not the gap in salary increases or decreases with the increase in years of education and experience. (10) The engineer who is white: Yi=b1+b2xi+b3zi+b4Di+B5xiDi+b6ziDi+ei=(b1+b4)+ (b2+b5)xi+(b3+b6)zi The engineer who is non-white: Yi=b1+b2xi+b3Zi+ei With non-white engineers start with a higher salary than white engineers by b4 greater than equal to 0. The gap is (b1+b4)+(b2+b5)xi+(b3+b6)zi-9b1+b2xi+b3zi+ei)=b4+b5xi+b6zi (d) Write down the condition under which the gap in salary will not decrease with the increase in years of experience. Write down the condition under which the white engineers will catch up with the increase in years of training/education. (10) The gap in salary will not decrease with the increase in years of experience when the coefficient b6 (the interaction term between experience and race) is statistically significantly different from zero, indicating that the effect of experience on salary differs for white and non-white engineers. The condition under which white engineers will catch up with the increase in years of training/education is when the coefficient b5 (the interaction term between education and race) is statistically significantly positive, suggesting that the effect of education on salary is more pronounced for white engineers, leading to a narrowing of the salary gap with increased education.