Section A. (35 marks)
Question 1. (20 marks)
Consider the following consumption function:
y_t=α+βx_t+ϵ_t
Where y_t is consumption , x_t is disposable income, and ϵ_tis an i.i.d. random error with distribution ϵ_t (0,ϵ^2 ).
a. What is the economic meaning of α.
b. Derive Least Square estimator of α.
c. List the assumptions for consistency of the OLS estimators in a multiple liner regression model.
d. Prove that β ^ is an unbiased estimator of β. (Let β ^=β+∑w_t ϵ_t,w_t=((x_t-x ´ ))/(∑(x_t-x ´ )^2 )
e. What are the differences (if any) between an unbiased and a consistent estimator?
Question 2. (15 marks)
It was argued in class that it is not possible to test the exogeneity assumption if the number of instruments is equal to the number of endogenous variables.
Show that if we try to apply the overidentification restrictions test in such scenario, we would get an R^2 equal to zero always.
Use the following simple linear regression model with one endogenous regressor, x,
y=β_0+β_1 x+u
and a single instrumental variable, z, for your proof.
Section B. (65 marks)
The following part of the assignment is to be presented in the form of a clear report including graphs and tables. Make sure you indicated clearly question numbers. You are expected to answer the questions straightforwardly (i.e., no ‘Abstract’, ‘Introduction’ etc. needed). Your answers must be short, clear and concise. Any lengthy unclear off-topic attempt will cause you penalty
Where regression output is needed, this should be presented in a clearly labelled and referenced table. The reader should be able to understand to which table, and numbers within that table, the answer refers to. . For reporting numerical results, you are advised to round the numbers at the fourth decimal place.
All inference is to be carried out at the 5% significance level.
Eviews or Stata could be used for this coursework. You should also submit your Evies workfiles / Stata do files to Moodle for inspection purposes. Please keep in mind that this is an individual project. Any plagiarism will be detected and appropriately penalised.
The datasets for the coursework are available on Moodle ( pizza.dat for Question 3; savings.dat for Question 4)
Coursework will only be marked, if submitted electronically on Moodle. You do not have to submit a hard copy. The deadline is as stated on Moodle and relates to the electronic submission.
The University regulations on plagiarism and unfair practice must be observed.
Collaboration is not allowed.
Question 3 (30 marks)
Consider the following pizza expenditure function:
Pizza=c+αAge+βIncome+ϵ_t
The data file pizza.dat includes additional information about the pizza expenditure problem. The dummy variable FEMALE=1 for females; 0 otherwise. The variables HS, COLLEGE, and GRAD are dummy variables indicating level of educational attainment. HS=1 for individuals whose highest degree is a high school diploma. COLLEGE=1 for individuals whose highest degree is a college diploma. GRAD=1 if individuals have a graduate degree. If HS, COLLEGE, and GRAD are all 0, the individual did not complete high school.
What is an intercept dummy variable? How to interpret the coefficient of a intercept dummy?
Include gender (FEMALE) as an explanatory variable and estimate the pizza expenditure function. What is the effect of including this dummy variable? Is gender a relevant explanatory variable?
Include HS, COLLEGE, GRAD as explanatory variables and estimate the pizza expenditure function. What is the effect? Is level of educational attainment is a significant explanatory variable?
Test the hypothesis that separate regression equations for males and females are identical, against the alternative that they are not. Use the 5% level of significance and discuss the consequences of your findings.
Question 4 (35 marks)
There are 50 observations on savaings(y), income(x), and averaged income (z) in savings.dat
Estimate a least square regression of savings on income. Present and nterpret regression results
Estimate the relation between savings(y) and income(x) using the instrumental variables estimator, with instrument z, using econometric software designed for instrumental variables, or two-stage least squares, estimation. Interpret your results
Carry out the Hausman test (via an artificial regression) for the existence of correlation between x and the random disturbance e. Outline the steps of Hausman test and interpret your results.
Use two least squares regressions to obtain the IV estimates in part (b). Compare the estimates, standard errors, and t-statistics to those in part (b) and comment on the differences.
F
(Fail) 0 No answer has been attempted or evidence of unfair practice.
1 – 9 The work presented for assessment may be incomplete and/or irrelevant and demonstrates a serious lack of comprehension and/or engagement with the set task. Attainment of the learning outcomes is minimal and assessment criteria are not addressed.
10 – 19 Misunderstanding or misinterpretation of the set task, providing a short and/or largely irrelevant response. Consequently, no learning outcomes are met in full although there may be minimal attainment in relation to one or two.
20 - 29 Minimal understanding of the set task and will partially have met some of the learning outcomes. Little knowledge and understanding of the field of study relevant to the task. Limited ability shown to communicate simple econometrics concepts. Significant difficulties in report’s structure and organisation detract from the clarity and meaning overall. Demonstrates some ability to describe and report but very little evidence is available to indicate an ability to engage in critical evaluation and reflection. No real evidence of linking experiment’s results to econometrics theory.
30 – 39 Partial understanding of the set task and some of the associated learning outcomes met at a basic level. Inaccuracies, errors and misconceptions are evident in important areas and elements of the assessed work may be irrelevant to the task. If attempted, the presentation of arguments and more complex ideas may be confused and clumsily expressed. Some enquiry and analysis relevant to the task attempted but outcomes may be simplistic and/or unconvincing. Demonstrates limited knowledge of the discipline. The work is largely descriptive and arguments, if attempted, are rarely substantiated. Some weak evidence of linking theory to set tasks.
D
(Third) 40 - 49 Demonstrates a basic understanding of the set task and an ability to have met the associated learning outcomes and addresses the assessment criteria at a threshold level. Displays a basic knowledge and understanding of many aspects of the field of study relevant to the task. Reproduction of information received from elsewhere (e.g. programme materials). Errors and misconceptions will be evident but these are outweighed by the degree of knowledge and understanding demonstrated overall.
Generally, the work is appropriately structured although key points may not be logically sequenced. Some limited analysis and enquiry relevant to the task/discipline included and has intermittent success in presenting and commenting on results. A limited ability to critically evaluate and reflect. Although some critical reflection is evident, the balance within the work is likely to be in favour of description and factual presentation. Connections are made between econometric theory and results, but not always in a completely appropriate manner.
C
(Lower Second) 50 - 59 A secure understanding of the set task and an ability to have met the associated learning outcomes and address the assessment criteria at a satisfactory level. Displays a sound knowledge and understanding of most key aspects of the field of study relevant to the task and there is some evidence of an ability to apply such knowledge. Some evidence of independent thinking beyond programme notes. Overall, the structure and format of the work are appropriate. Occasional faults in the presentation of work, but overall, these do not detract from the clarity of expression. Arguments are usually substantiated. The experiments results are mostly correctly related to basic econometric theory.
B
(Upper Second) 60-69 Demonstrates a full understanding of the set task and an ability to have met the learning outcomes and address the assessment criteria at a good level. A detailed knowledge and thorough understanding of key aspects of the field of study relevant to the task are shown. There is clear evidence of an ability to apply such knowledge and, in some contexts, to extend and transform it. Discussion of complex concepts is often tackled successfully and there is evidence of independent thinking. Displays an ability to communicate information, ideas and concepts clearly and succinctly. Work is well presented and the format appropriate. Key points are appropriately organised and the writing style is fluent and arguments are well articulated. Detailed analysis and critical enquiry relevant to the task/discipline is undertaken by making use of appropriate techniques and has considerable success in presenting and commenting on outcomes. There is linkage between theory and practice. Examples referred to indicate a breadth and depth of individual reading and investigation that extend beyond the sources provided. Arguments are clearly considered and substantiated. Good connections between econometric theory and the results of the project, with most relevant theory covered.
A
(First) 70 – 79 Demonstrates a full and detailed understanding of the set task and an ability to have met the learning outcomes and address the assessment criteria at a very good level.
A detailed knowledge and systematic understanding of key aspects of the field of study relevant to the task are evident. There is strong evidence of an ability to extend, transform and apply such knowledge. The student also demonstrates an ability to engage in confident discussion of complex concepts. Independent thinking and original insights are also present in the report. Ability shown in communicating information, complex ideas and concepts in a coherent and succinct manner. The standard of presentation is high and the format appropriate. Key points are logically organised and in written work, the style is lucid and mature. Detailed and thorough knowledge of discipline. An ability to engage in critical evaluation of concepts/arguments/data and to make appropriate and informed judgements is shown. Arguments are well developed, sustained and substantiated.
80 - 89 Beyond the above, a full and detailed understanding of the set task and an ability to have met the learning outcomes and address the assessment criteria at an excellent level is displayed.
90 - 100 Beyond the above, demonstrates a full and detailed understanding of the set task and an ability to have met the learning outcomes and address the assessment criteria at an outstanding and exceptional level.
Learning Outcomes:
Ordinary least squares estimator
Multiple linear regression model
Hypothesis testing
Instrumental Variables
Understanding Model Predictions