Section A

The questions in this section are based on the work presented in Fetzer, T. (2021) Subsidising the Spread of Covid-19:  Evidence from the UK’s Eat- Out- To-Help- Out Scheme.  Economic Journal, ueab074, https://doi.org/10.1093/ej/ueab074.  You were asked to read this paper before this examination. Some relevant tables are reproduced in the Appendix. In your answers you can also refer to other material in the above article.

1.  Briefly describe the circumstances which allow the author to consider a diference-in- diference research design to answer the question of whether or not the Eat-Out-to-Help- Out (EOHO) scheme caused higher covid infection rates.  [No technical language, max 150 words.] [10 MARKS]

2. The author says that he is concerned about reverse causality.  Briefly explain what the concern is.  [No technical language, max 50 words.] [5 MARKS]

3.  Describe briefly the key features of the data.  [Max 50 words] [4 MARKS]

4.  Equation (1) of the paper is the author’s Base Model. A well-established framework for estimating treatment efects is Easy Wooldridge (13.16). Is the author’s (1) fundamentally the same or does  it difer  in any substantial way?   If the  latter,  briefly explain  how. Explain how the treatment dummy varies over time and geographic location. [No technical language, max 50 words.] [6 MARKS]

5. The regression results presented in Table 1 suggest that the efect of the EOHO scheme was a 10% increase in Covid cases. Do you agree? [5 MARKS]

6.  How does the author go about providing evidence to justify the parallel trends assumption? [max 150 words] [5 MARKS]

7.  How does the author  use  rainfall data to strengthen the causal  interpretation of the results?  [ max 200 words.] [10 MARKS]

8. Would you judge the EOHO scheme a success? [max 150 words.] [5 MARKS]

Section B

9.  In the simple regression model

y = ↵ + βx + u  where Cov(u,x) = 0,

a very simple way to derive the OLS estimator in the population is to run the Covariance Operator through the model:

Cov(y,x) = ↵Cov(1,x)+ βCov(x,x)+ Cov(u,x).

The estimator requires Cov(u,x) = Cov(1,x) = 0. Explain why can we write Cov(1,x) = 0.

[Hint:  In general, the definition of the covariance Cov(W,Z) is E{[W − E(W)][(Z − E(Z)]}.] [3 MARKS]

10.  Consider the following regression models relating log real hourly wage (log w) to age (a), whether the individual has a 1st class degree (D1  = 1), or an upper second (D2  = 1), or

otherwise (D3  = 1), and whether the individual has a PG degree (P = 1) or not. log w = ↵ + βa +(100γ)(a/10)2 + 61 D1 + 62 D2 + 63 P + u,    q = 1, 2.

u is an error term that satisfies the usual exogeneity assumptions.  The index q denotes the type of UG degree undertaken; either

q = 1: Science, Technology, Engineering and Maths (STEM), or

q = 2: Law, Economics, and Management (LEM).

The model is estimated for q = 1, 2 separately.

This model, amongst others, was estimated by Walker, Ian and Yu Zhu, “Diferences by degree:  Evidence of the net financial rates of return to undergraduate study for England and Wales,” Economics of Education Review, 2011, 30 (6), 1177 to 1186. They use LFS data 2005-2009.  The following was taken from their Table 5a.  To answer this question you do not need to look at their paper.

STEM

LEM

(a)  (6 points)  Consider the following 3 statements:

S1  Instead of specifying the age-squared variable as  (a/10)2  you re-estimate the

regression with a2 .  The estimate and standard error for the STEM regression would be –0.00110 (0.00007).

S2  In neither model is a quadratic in age justified on the evidence given.

S3 The model is misspecified (“wrong”) because there should also be a term 64 D3 . State whether each statement is TRUE or FALSE. If it is false, write one sentence explaining why.

(b)  (5 points)  It is clear that the relationship between E(log w) and age is a quadratic.

Compute the age at which E(log w) is a maximum for men who obtain a first class degree and complete a PG degree for both subject groups.  Does your calculation change for men who get a lower second or worse (and therefore do not qualify for a PG degree)? Explain why in one sentence.

(c)  (6 points)  Compute

E(log w|a = 25,q = 2) − E(log w|a = 25,q = 1)   and E(log w|a = 65,q = 2) − E(log w|a = 65,q = 1).

Express your answers as percentages. Comment briefly.

(d)  (6 points)  Someone suggests that E(log w|a,q = 2) − E(log w|a,q = 1) is a con- stant.  How would you amend the model above so that this is imposed upon the model?  Make sure you define any new variables/parameters.  [Hint:  another com- monly used greek symbol for a regression parameter is λ .] [23 MARKS]

b) Without estimating the above model, make an argument why you think that rt  does (or does not) granger-cause vt .  [Max. 150 words] [5 MARKS]