QUESTIONS
(a) Investigate the main question of the Project by using descriptive statistics only; e.g. by appropriate use of means, medians, variances, graphs, etc. Don’t forget that you need to investigate this in terms of both outcome variables ‘salary’ and ‘professional’. There is no word limit for this question, but your answer needs to be presented within two A4 sides (so, all tables, graphs and discussions need to be presented within two A4 sides, i.e. one full page). The assigned weight of this part will be revealed in due course, but this will be worth around 10-15% of the overall mark of the Project.
(b) In this part you need to investigate the main question of the Project by using regression anal- ysis (i.e. appropriate MLR models). Don’t forget that you need to investigate this in terms of both outcome variables, ‘salary’ and ‘professional’. That is, you will need two separate MLR models, one using ‘salary’ as the dependent variable, and one using ‘professional’ as dependent variable. So, in this part, you need to investigate whether Economics graduates are expected to ‘earn more/less’ relative to each of the other subjects, and whether Economics graduates are more/less likely ‘to get into professional roles’, holding other variables fixed (i.e. if Eco- nomics graduates had the same tariff scores, the same socio-economic background, etc. with the graduates of the other subjects).
Here are some important instructions/notes. Please read these very carefully:
• The dependent variable salary must be used in a logarithmic form (i.e. the natural log of salary). Note that the professional dependent variable is binary (taking value 0 for ‘non-professional’ and 1 for ‘professional’). We still haven’t seen examples of using a binary dependent variable, but we will see an example on the live lecture of Week 11, to explain how to interpret the coefficients in such models.
• Your main explanatory variable (i.e. subject) is categorical, so it needs to be added in the MLR model in the form of dummy variables. We will see examples of how to include categorical variables in the MLR model using dummy variables in the material of Week 9 (both on the Asynchronous lecture notes/videos and on the Synchronous sessions).
• In your discussion of your results, you need to provide an appropriate interpretation of the coefficients of the subject-related dummy variables. You also need to conduct hypothesis testing, to test: (i) whether there is statistical evidence that the mean salary of Economics graduates differs from the mean salary of graduates of each of the other subject, holding the other variables fixed (you can do this by using the p-values); (ii) whether there is evidence of joint significance of the subject dummy variables (this is done by an F -test, which will be covered in the material of Week 10).
• It is up to you to decide which other explanatory variables you add to your model. Note that categorical variables (such as degree class or region, need to be added in form of dummies variables). For each explanatory variable that you add, you need to offer a short justification on why it is important for these variables to be included in the model (about 100-150 words for each). Also, for the variables that you decide not to add, you also need to provide justification as to why these were not added (about 50-100 words for each).
• Note that variables tariff and age must be included in the model.
– For tariff , you need to decide whether you use it in its linear form, or whether you include a quadratic term / replace it by the natural log of tariff . Your choice needs to be justified within your justifications above.
– For the variable representing the graduates’ age, it must be included in the model as a quadratic function (i.e. add both age and age2). You also need to provide two graphs, one for predicted salary against age, and one for the predicted probability of getting into professional employment against age. Then, based on these graphs, you need to discuss the relationship between age and salary/professional (in about 200-250 words overall).
• Your ‘salary’ regression model needs to be tested for violation of MLR5 (i.e. whether there is a heteroskedasticity problem). If there is evidence of heteroskedasticity, then the standard errors presented in your regressions must be made ‘robust to heteroskedasticity’. Please note that testing for heteroskedasticity and correcting the standard errors, will be covered in the material of Week 12. Also note that in your ‘professional’ regression model, heteroskedasticity robust standard errors must be used.
• Note that all your regression results need to be presented in one or two tables. There are Stata commands that create such tables automatically. I will prepare a video, showing how to do this, using the example of the Experience/Wage relationship.
• The assigned weight of this part will be revealed in due course, but you can expect that this will be worth around 50% of the overall mark of the Project.
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