Apr 19, 2024

### Assignment Task

This exam’s questions touch on the true story of the Steamboat Ladies.

Up until 1904, women at Trinity College Dublin could study and pass exams, but could not graduate and obtain a degree. After campaigning, they obtained the right to graduate with a degree in 1904. In contrast, at Oxford and Cambridge, women could study and pass exams but could not graduate and obtain a degree until 1907. They could, however, study in one of those two universities and graduate from Trinity College Dublin between 1904-1907 due to a special arrangement between these three universities. Over 1904-1907, about 720 women from Oxford and Cambridge, the so-called Steamboat Ladies, obtained degrees from Trinity Dublin. The name comes from the means of transport commonly used by these women to travel to Dublin.

Question: An important question in the economics of education is that of separating the value of a degree and the value of the accumulated knowledge obtained in university on later life employment outcomes. We will be trying to identify causal effects in relation to this question in the context of the Steamboat ladies.

Data: After some elaborate effort, someone managed to put together a dataset. The dataset includes all women who studied in Oxford, Cambridge, and Trinity at any time between 1900 and 1911. It contains the following information: Wage ( Y) 20 years after finishing university studies (continuous variable), year of finishing university studies, university at which a person studied, an indicator ( D) for whether the person obtained a degree (1=Yes, 0=no). After 1907, you may assume that women only receive degrees from the universities they studied in.

1. To obtain the effect of a degree separate from the effect of accumulated knowledge from university, someone proposes running a simple regression. They tell you to only use data for women studying at Oxford and Cambridge between 1904-1907. They then tell you to run a regression with Wage Y on the left hand side and the degree indicator D on the right hand side. Do you think this will produce the desired degree signalling effect clean of the effect of accumulated knowledge from university?

2. A second person comes along and tells you they have another idea. They tell you to only use data for women who finished their studies at Oxford and Cambridge between 1900-1907. They also tell you to drop from the analysis women who finished their studies between 1904-1907 and did not go to Trinity by steamboat to obtain a degree. They then tell you to run a regression with Wage Y on the left hand side and the degree indicator D on the right hand side. Do you think this will produce the desired degree signalling effect clean of the effect of accumulated knowledge from university? Explain.

3. A last person comes along and tells you they have yet another idea. They tell you to only use data for women studying at Oxford and Cambridge but to drop all data for women who finished their studies between 1904-1907. They then tell you to run a regression with Wage Y on the left hand side and the degree indicator D on the right hand side. Do you think this will produce the desired degree signalling effect clean of the effect of accumulated knowledge from university? Explain.

Ultimately, regardless of what assumptions you made and what you wrote in a-c, you decide none of these strategies are good ideas.

Unfortunately, when you look into the data, you realise that the data for women who studied at Oxford and Cambridge between 1904-1907 and took the steamboat to obtain a degree at Trinity is corrupted and cannot be used. The good news though is that you are informed convincingly that women who finished their studies at Oxford and Cambridge between 1904-1907 and did not take the steamboat to obtain a degree at Trinity are plausibly a random selection of all women finishing their studies at Oxford and Cambridge between 1904-1907 (do not use this information in your answers to a-c).

Upon thought, you draw from your knowledge about Difference-in- Differences to try to answer the question at hand. You decide on a three period model: pre-1904, 1904-1907, post 1907. You further decide to take women who studied at Cambridge and Oxford as one group, and those who studied at Trinity to be the other group.

4. Set up a Difference-in-Differences model capable of identifying the effect of a degree clean of the effect of accumulated knowledge from university. You may use all periods or a subset of periods, that is your choice, but you need to justify your choice. Also explain precisely what is identified by the causal parameter in your model

5. Propose a FE evaluation approach for this model and write down the estimating equations.

6. What assumptions are necessary to identify the causal effect of interest in this model? Give examples in which these assumptions are violated.

7. Eureka, you found a fix to the data for women who finished their studies at Oxford and Cambridge between 1904-1907 and took the steamboat to obtain a degree at Trinity is corrupted. Upon thinking, you realise that you can now also write a model which produces different effects of obtaining a degree, depending on whether that degree was obtained from Trinity, or from Oxford or Cambridge. Explain why that is the case and augment your model in d. with an interaction term to identify the different effects by degree conferring institutions. Also explain precisely what is identified by each causal parameter in your model.

8. You are starting to feel very confident, so you decide out of curiosity to try using a different approach to estimating the relevant causal effect. You decide to take an instrumental variable approach. More precisely, you only use the data for Oxford and Cambridge between 1900-1907. You define as Z an indicator equal to 1 if you finished your studies between 1904-1907, and equal to 0 if finished prior to You then define D as equal to 1 if you obtain a degree and 0 otherwise. Using this information and ignoring all aspects of time in the model, propose an estimator that can still give you a valid causal estimate of the value of the degree.

9. Discuss the necessary assumptions required to obtain a causal effect from this model and describe the interpretation of the causal parameter. You should give examples of how the assumptions could be violated in the current context. You may also want to give an opinion on whether you think the assumptions are credible in this

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