Section A

The questions in this section are based on the work presented in Devereux, P.J and Hart R.A. (2010) Forced to be rich? Returns to compulsory schooling in Britain, The Economic Journal, 120, 1345-1364. You were asked to read this paper before this examination so that you could answer these questions. Relevant tables are reproduced in the Appendix.

1.  Summarise the findings of the paper, in particular emphasising how the authors’ results compare to previous empirical findings on the returns to an additional year of schooling on earnings. (max 100 words) [5 MARKS]

2.  Describe the change in legislation that underpins the authors’ Regression Discontinuity estimation strategy. (max 50 words) [5 MARKS]

3. Just because everyone was supposed to have one more year of schooling,  it does not follow that this happened. Is there any evidence in the paper that everyone did have one more year of schooling? (max 100 words) [5 MARKS]

4.  In Section 3 (Pooled GHS Results and Comparison to Oreopolous (2006)) you can find Table 2 (replicated in the Appendix to this exam paper). [25 MARKS]

(a)  Using either their  notation,  or the  notation of the  lecture slides,  explain why a

typical estimate in columns (7–9) multiplied by a typical estimate in columns (1–3) is approximately the same as a typical estimate in columns (4–6). (max 150 words)

(b) As an example, in Row 1 cols(2,5,8), the estimates satisfy this relationship: 0.019 ⇤ 0.506 ⇡ 0.010.  In words, explain exactly how these three estimates are interpreted in the context of the causal chain from legislation to earnings. (max 150 words)

(c)  In assesing whether an instrument is valid, only one of the 3 conditions is testable. Use Table 2 to assess whether this one condition holds. (max 50 words)

(d)  Comment on how, qualitatively, the results in this section difer from those presented in Oreopolous (2006). (max 100 words)

9.  Consider the following regression

y = β0 + 6d + β1T + TdT + u,

where d is a time dummy for after the treatment occurs, and T is a dummy for whether treated. After 4 appropriate exogeneity assumptions have been imposed:

E(y|d = 0,T = 0) = β0

E(y|d = 0,T = 1) = β0 + β1

E(y|d = 1,T = 0) = β0 + 6

E(y|d = 1,T = 1) = β0 + 6 + β1 + T.

Which of the following statements are true?

S1 T is the DiD estimator in the population.

S2 β0   is what would have been the efect of being treated, except it happens in the “before” period d = 0.

S3 6 is a macro efect, but only for the control group.

If a statement is false, write it out again underlining the corrected word(s).  Otherwise, write “Sx is true” . [8 MARKS]

10. The simplest returns-to-education model is a regression of log earnings y on years-of- schooling x1 :

y = β0 + β1 x1 + u.

When estimating the regression using a sample of data from the BHPS/US, the investi- gator’s OLS estimate of β1  is 0.08.  However, it is well known that ability x2  should also be included in the regression.  He has a variable called ‘IQ’ in his dataset which can act as an excellent proxy for ability.  Before he re-estimates his amended earnings regression, he decides to estimate

x2  = 60 + 61 x1 + e,

just to see what is happening with the two RHS variables.  His OLS estimate of 61   is positive, large and statistically significant.  What do you think will happen to the OLS estimate of β1  in

y = β0 + β1 x1 + β2 x2 + u?

S1 The new estimate of β1  will go up by a significant amount.

S2 The new estimate of β1  will go down by a significant amount.

S3 The new estimate of β1  will hardly change.

S4 There is not enough information to say what will happen to new estimate of β1 .

Which one of these statements is correct? Justify your answer using the OVB formula.  [7 MARKS]

11.  Consider the following model

y = β0 + β1 x + u,               (1)

where x is endogenous:

Cov(x,u)  0.

We know that the IV estimator is given by:

Cov(z,y)

β1  =                                                     (2)

a) Write down 3 conditions that the variable z must satisfy to be a valid instrument. [6 MARKS]

b)  Using these 3 conditions, starting with  Equation  (1), show  how  Equation  (2) is arrived at. [5 MARKS]

12.  Consider the time-series of real GDP and the Consumer Price Index (CPI) for the UK from 1960 onwards.

a)  Sketch a rough time-series graph for the GDP and the CPI for the UK. Ensure that you label your time-series plot. [4 MARKS]

b) A colleague runs a regression with GDPt  as the dependent variable and CPIt  as the explanatory variable.  He reports that he has found clear evidence that higher price levels cause higher GDP. What has your colleague found in his regression output and do you support his conclusion? (max 150 words) [5 MARKS]