7310AFE Econometric Methods Assignment

Question 1 [15 marks]

The MBA program at a large university is facing a pleasant problem – too many applicants. The current admissions policy requires students to have completed at least three years of work experience and an undergraduate degree with a score of at least 75% on their MBA admission test. Up until three years ago, the school admitted any applicant who met these requirements. However, because the program recently converted from a two-year (four-semester) program to a one-year (three-semester) program, the number of applicants has increased substantially. The dean, who teaches statistics courses, wants to raise the admissions standards by developing a method that more accurately predicts how well an applicant will perform in the MBA program. She believes that the primary determinants of success are:

• undergraduate grade point average (GPA)
• MBA Admissions Test (MAT) score
• number of years of work experience.

She randomly samples students who have completed the MBA and records their MBA program GPA, as well as the three variables listed above. These data are recorded and stored in the first four columns of the file MBA.wf1. Develop a model and test to decide which primary determinants should be used to select which applicants to admit.

After considering the results of the initial study, the dean realised that she may have omitted an important variable – the type of undergraduate degree completed. She returned to her sample of students and recorded the type of undergraduate degree completed, using the following codes: 1 = BA; 2 = BCom; 3 = BEng or BSc; 4 = Other (including no undergraduate degree). These data are provided in the fifth column of the data file. Can the dean conclude that the type of undergraduate degree completed is a factor in determining how well a student will perform in the MBA program?

Question 2 [15 marks]

The State of West Bengal is one of India's largest rice producers, accounting for about 20% of rice production. Rice occupies three-quarters of the entire agricultural area in the lower Ganga Plains. The Rice.xlsx data file includes data from 352 observations of 44 paddy farmers in West Bengal, India, between 2000 and 2007. The data file contains the following variables.

Ar: hectares planted (land)
Fe: kilograms of fertilizer
Lb: person-days of hired and family labour
Pd: tonnes of freshly threshed rice

Treat the data set as one sample with N= 352 and answer the following questions.

(a) Estimate the following production function and report the results, interpret the estimates, and comment on the statistical significance of the estimates.

(b) Using 5% level of significance, test the hypothesis that the elasticity of substitution with respect to land is equal to the elasticity of production with respect to labour. (c) Using 10% level of significance, test the hypothesis that the production function exhibits constant returns to scale. That is

(d) Using a 5% level of significance, jointly test the two hypotheses in parts (b) and (c).

(e) Re-estimate the model in part (a) with (i) Fe omitted, (ii) Lb omitted, and (iii) Ar omitted. In each case discuss the effect of omitting a variable on the estimates of the remaining two elasticities.

(f) In each case given in part (e), check to see if the RESET test has picked up the omitted variable.

Question 3 [20 marks]

Imagine that you are an Economist working for an economic consultancy firm. Your current assignment involves investigating whether lotteries function as a regressive tax that adversely affects the poor and uneducated. Despite the fact that lotteries are a significant source of revenue for governments, there have been claims that they disproportionately impact disadvantaged groups. To explore this issue, you carried out a survey with a random selection of 100 adults and inquired about their lottery ticket expenditures. Additionally, you conducted interviews to gather information on various socioeconomic factors. The data from this research is stored in the

Expenditure_Survey.xlsx

file.

The aim of this analysis was to assess the validity of the following claims:

(a) People with relatively less education spend a higher amount on lotteries compared to those with relatively more education.

(b) Older individuals purchase more lottery tickets than younger individuals.

(c) People with a larger number of children spend more on lotteries than those with fewer children.

(d) People who are relatively poor spend a larger proportion of their income on lotteries than those who are relatively wealthy.

Based on the analysis, what inferences can be drawn? Comment on all your estimations and examine any potential problems with the regression model assumptions. Present any diagnostic test findings that you believe are more relevant. When presenting your estimation findings, follow the "Reporting Estimation Results" format outlined in your lecture slides.

Produce a 200-word report that either supports or opposes the notion that lotteries are a levy on the impoverished and uneducated, based on your research, to be published by a newspaper.