ECONOMIC STUDIES
BU31002
ECONOMETRICS: 2024-2025
ASSIGNMENT 3
Assignment 3 contributes 20% to the overall module assessment and consists of workshop questions W1 to W3 only [marks sum to 100]. The assignment should be submitted via Turnitin by 11:45am on Friday 22 November and will form. the basis for the tutorial in Week 11 (Friday 29 November 13:00-14:00 or 14:00-15:00, depending on tutorial group) by which time you will have received a grade for your work.
WORKSHOP
The workshop for this assignment to be held on Friday 15 November will provide an opportunity to estimate a number of simple linear regression models and perform. a variety of statistical inference procedures. You should note that computer output alone will not be accepted or acceptable as answers to the workshop part of the assignment - indeed there is no need to present any computer output at all if you so wish, though you may want to keep a copy for your own records. Instructions for saving results to a file (which can be printed at the end of the session) are given in Section II.A.3 of the course computer manual.
For the purpose of the exercise, you should continue to work with the EAEF data set assigned to you in the first workshop (see Table at the end of this document). If you did not save the data set in the first session then you will have to download it again from the Blackboard VLE (see Workshop 1 instructions for personal assignment of data sets). Otherwise you should simply load your data file. Instructions are given in Section II.B.1 of the manual.
In the first workshop, you worked with the educational attainment variable S (highest grade completed as of 1994; i.e. years of schooling) and the ability variable ASVABC. We will go on in this workshop to also explore the determinants of earnings as measured by the hourly wage rate variable EARNINGS (current hourly earnings in $ reported at 1994 interview)
The gender of each respondent is recorded in the data set by the dummy variable MALE which takes a value of 1 for men and 0 for women. Each sample consists of 325 observations on men and 245 observations on women (570 observations in total). Find the average earnings of the whole sample and of each gender separately by issuing the following commands in the Command window:
summarize EARNINGS MALE [ ]
summarize EARNINGS MALE if MALE== 0[ ]
summarize EARNINGS MALE if MALE== 1[ ]
(where the summary statistics for MALE should confirm that first sub-sample consists solely of women and the second solely of men). Keep a record of your findings for future reference.
Regress EARNINGS on a constant (see Section II.C) by typing
regress EARNINGS [ ]
(Stata automatically includes a constant (named _cons) in the regression model). Note that the intercept is equal to the sample mean level of earnings of the whole sample and that the R2 value for the regression is equal to zero (cf. Assignment 1).
Assume that the relationship between earnings and gender is given by the model:
EARNINGSi = β1 + β2 MALEi + ei; i = 1, ... .570
Estimate this model by regressing EARNINGS against the gender dummy MALE.
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W1(a) Write down the estimated regression equation that you obtain. Interpret the regression coefficients in the light of the values that you have obtained for the average earnings of men and women in your sample. [8 marks]
(b) Formally test whether the coefficient on MALE is significantly different from zero. Remember to state clearly the null hypothesis being tested and its alternative, the steps involved in the test procedure and any conclusions that you may reach. Is there any evidence that the earnings of males are different from that of females? [15 marks]
(c) How would you modify the specification of the hypotheses in (b) if you wanted to test for the existence of wage discrimination against women? [6 marks]
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Note that the statistical tables do not give critical values of the t distribution on 568 degrees of freedom. You should use the critical values of the t distribution on 120 degrees of freedom instead. These will provide a conservative basis for the conduct of the various hypothesis tests and the construction of confidence and prediction intervals.
Next consider the econometric model:
EARNINGS= β1 + β2 S + e; i = 1, ... .570
where b1 and b2 are unknown parameters or coefficients, and e is a disturbance term. Estimate this model to obtain a fitted relationship of the form.
EARNINGS = b1 + b2 S
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W2 (a) Write down the estimated regression equation that you obtain and interpret the regression results. Comment on the value of R2. [10 marks]
(b) State and interpret: (i) the standard error of the response coefficient on S and (ii) the standard error of the regression (SER – denoted Root MSE in Stata output). [8 marks]
(c) Formally test whether or not an additional year of schooling will raise hourly earnings by $1. Remember to state clearly the null hypothesis being tested and its alternative, the steps involved in the test procedure and any conclusions that you may reach. [15 marks]
(d) Calculate a 99% confidence interval for the regression coefficient on S. Interpret the interval that you obtain. [10 marks]
(e) What relationship is there between the conclusion that you obtained in (c) and the confidence interval that you constructed in (d)? [6 marks]
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In the first workshop, you estimated a simple linear regression model in which educational attainment (S) were determined as a function of ability (ASVABC):
S = b1 + b2 ASVABC
Re-run this regression.
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W3(a) Write down the estimated regression equation. Predict the number of years of schooling of an individual with the mean level of ability in your sample. [7 marks]
(b) Calculate a 95% confidence interval for your prediction. Interpret this interval.
[10 marks]
(c) Suppose you were to predict the educational attainment of an individual with some level of ability that was not equal to the mean in your sample. Would the 95% confidence interval for this prediction be narrower, wider or the same as that calculated in (b)? Explain your answer. [5 marks]
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Optional workshop exercises
The remaining exercises allow you to further explore the properties of the simple regression model. You do not have to hand in answers to these exercises as part of the assignment though you may do so if you would like feedback on your work. (You will certainly get more from the exercises if you maintain some record of your results whether you submit it or not).
W4. A researcher chooses to denote gender using the dummy variable FEMALE which takes a value of 1 for women and 0 for men. Create this variable from the existing gender dummy variable by typing the command:
gen FEMALE=1-MALE
and then run a regression of EARNINGS on FEMALE. What is the relationship between the results that you obtain and those that you found in W1? Does it make any substantive difference to the results that you obtain as to whether the gender dummy variable in the model is specified as MALE or FEMALE? Can you explain your findings?
W5. (Difficult) A researcher argues that schooling determines intellectual ability, rather than vice versa, and therefore specifies the model:
ASVABCi = δ1 + δ2 Si + ei; i = 1, ... .570
Estimate this model to obtain a fitted relationship of the form.
ASVABC = d1 + d2 S
Finally, invert the fitted relationship to give:
S = d2/d1 + d2/1 ASVABC
Do you get the same results as those that you obtained from the original regression of schooling on intellectual ability? Can you explain your findings? (Hint: calculate the product of b2 from W3 and d2. What is this value equal to? Why?)
Instructions for printing your log file (if you have created one) are given in Section II.A.3. Finally, you will need to logout (see Section I).