EC902/907 Midterm, 17 November 2021

1.   We are planning an RCT and, given the available information on sample size   and the standard deviation of the outcome variable, we expect the standard   error of our estimate to be around 10. If the true effect was around 40, how    likely it is that we obtain an estimate which is statistically different from zero at the 5% level?

a.   About 50%

b.   About 5%

c.   About 97.5%

d.   It is not possible to answer the question given the available information

2.   In a randomized controlled trial, if the standard deviation of the outcome variable becomes four times larger, standard errors tend to be:

a.   twice as large

b.   50% smaller

c.    four times as large

d.   four times smaller

3.   Randomization inference

We conduct an RCT with 4 participants, and we randomly assign 2                   individuals to the treatment group and 2 to the control group. We observe    that the outcome for the two treated individuals is equal to 3 and 2, and the outcome for the two non-treated individuals is equal to 1 and 0. Using            Fisher’s Exact Test, the p-value under the null hypothesis that the treatment has no effect is equal to:

a.    1/6

b.   2/6

c.    3/6

d.   4/6

4.   Warwick students’ grade point average (GPA) is on average 65, and the          standard deviation is around 10. If we take random samples of 100 students, the sample mean will be 95% of the time:

a.    between 64 and 66

b.    between 63 and 67

c.    between 60 and 70

d.    between 55 and 75

5.   Imagine that we are planning an RCT. If the true effect was around 4, how likely it is that we obtain an estimate which is statistically different from zero at the 5% level?

a.   More than 5%

b.   Exactly 5%

c.   Less than 5%

d.   Exactly 4%

6.   Using data for May 2020 from Understanding Society, a large-scale panel        survey representative of the UK population, we observe that individuals who work from home often or always have a lower probability of reporting that    they had contracted COVID (4.0%) than the rest of the population (4.7%).      The point estimate is equal to -0.7 percentage points, with standard error       equal 0.4 percentage points.

If we give face value to this estimate, would you say that the impact of the “working from home” is:

a.   statistically significant at standard levels and economically large

b.   not    statistically    significant    at    standard    levels    but    potentially economically large

c.    not statistically significant at standard levels nor economically relevant

d.   statistically significant at standard levels but economically small

7.   Using data from Understanding Society, a large-scale panel survey                      representative of the UK population, for May 2020, we observe that                   individuals who work from home often or always have a lower probability of reporting that they had contracted COVID (4.0%) than the rest of the                 population (4.7%). The point estimate is equal to -0.7 percentage points, with standard error equal 0.4 percentage points. How should we interpret this        estimate?

a.   Itcapturesthecausalimpactof“workingfromhome”ontheprobability of contracting COVID

b.   It provides an upper bound of the causal impact of the “working from home” (i.e. the true effect is even more negative than -0.7), if we assume that individuals working from home have other features that makes it

less likely that they contract COVID

c.    It provides a lower bound of the causal impact of the “working from home”  (i.e.  the  true  effect  is  larger  than  -0.7  and  it  could  even  be positive), if we assume that individuals working from home have other features that makes it less likely that they contract COVID

d.   None of the above

8.   Using data from Understanding Society, a large-scale panel survey   representative of the UK population, for May 2020, we observe that individuals who work from home often or always have a lower probability of reporting that they had contracted COVID (4.0%) than the rest of the                 population (4.7%). The point estimate is equal to -0.7 percentage points, with standard error equal 0.4 percentage points. In this analysis, would it be a         good idea to control for age?

a.   Bad control, because it is correlated with the probability of working

from home                                                                                                                   b.   Good  control,  because  it  is  predetermined  and  it  might  affect  the

probability of contracting COVID

c.    Good  control,  because  it  is  predetermined  and  it  cannot  affect  the probability of contracting COVID

d.   Bad control, because it is correlated with the probability of contracting COVID

9.   Using data from Understanding Society, a large-scale panel survey                      representative of the UK population, for May 2020, we observe that                   individuals who work from home often or always have a lower probability of reporting that they had contracted COVID (4.0%) than the rest of the                 population (4.7%). The point estimate is equal to -0.7 percentage points, with standard error equal 0.4 percentage points.

The database also includes information on the “frequency with which      individuals take public transportation” . If we want to estimate the causal impact of “working from home”, would it be a good idea to include this    additional variable as a control.

a.   No, it is a bad control because it might be affected by working from home

b.   Good control, because it is correlated with the variable “working from home” and it might affect the probability of contracting COVID

c.    Good control, because it is not correlated with the variable “working from home” and it might affect the probability of contracting COVID

d.   Bad control, because it is not correlated with the variable “working from home”

10. Using data from Understanding Society, a large-scale panel survey                      representative of the UK population, for May 2020, we observe that                   individuals who work from home often or always have a lower probability of reporting that they had contracted COVID (4.0%) than the rest of the                 population (4.7%). The point estimate is equal to -0.7 percentage points, with standard error equal 0.4 percentage points.

Sometimes COVID is asymptomatic, and some people may be unaware that  they had COVID. How would this affect our estimates of the impact of             working from home on the probability of contracting COVID? (note: thing     carefully whether this is going to introduce random measurement error or, alternatively, whether it will affect more the group with a higher covid rate)

a.   The estimate will suffer an attenuation bias

b.   The estimate will be still consistent but less precise

c.    The estimate will be subject to an upwards bias

d.   The estimate will be a lower bound of the true effect

11. Using data from Understanding Society, a large-scale panel survey                      representative of the UK population, for May 2020, we observe that                   individuals who work from home often or always have a lower probability of reporting that they had contracted COVID (4.0%) than the rest of the                 population (4.7%). The point estimate is equal to -0.7 percentage points, with standard error equal 0.4 percentage points.

The variable “working from home” might be subject to measurement error. Let us assume that this measurement error was random. How would this    affect their estimate?

a.   The estimate will suffer an attenuation bias

b.   The estimate will be still consistent but less precise

c.    The estimate will be subject to an upwards bias

d.   The estimate will be a lower bound of the true effect

12. A randomized controlled trial (RCT) was conducted in Denmark in April and  May 2020 to analyze the impact of mask recommendation on SARS-CoV-2       infections. The RCT assessed whether recommending surgical mask use           outside the home reduces wearers' risk for SARS-CoV-2 infection in a setting where masks were uncommon and not among recommended public health     measures. In the control group, participants were just encouraged to follow   social distancing measures but there was no mask recommendation. In the     treatment group, in addition to a recommendation for social distancing            measures, participants were encouraged to wear a mask when outside the      home among other persons together with a supply of 50 surgical masks and   instructions for proper use. Around 4862 participants completed the study.    Infection with SARS-CoV-2 occurred in 1.8% of participants in the treatment  group, compared to 2.1% in the control group. The between-group difference was equal to -0.3 percentage points, with standard error equal to 0.4 percentage points. Would you say that this estimate is?

a.   statistically significant at standard levels and “economically” large

b.   not     statistically     significant     at     standard     levels     but     potentially “economically” large

c.    not statistically significant at standard levels nor “economically” relevant

d.   statistically significant at standard levels but “economically” small

13. A randomized controlled trial (RCT) was conducted in Denmark in April and  May 2020 to analyze the impact of mask recommendation on SARS-CoV-2       infections. The RCT assessed whether recommending surgical mask use           outside the home reduces wearers' risk for SARS-CoV-2 infection in a setting where masks were uncommon and not among recommended public health     measures. In the control group, participants were just encouraged to follow   social distancing measures but there was no mask recommendation. In the     treatment group, in addition to a recommendation for social distancing            measures, participants were encouraged to wear a mask when outside the      home among other persons together with a supply of 50 surgical masks and   instructions for proper use. Around 4862 participants completed the study.    Infection with SARS-CoV-2 occurred in 1.8% of participants in the treatment  group, compared to 2.1% in the control group. The between-group difference was equal to -0.3 percentage points, with standard error equal to 0.4                 percentage points.

Would you include in the analysis as a control variable a dummy indicating    whether some family member of the participant got infected with SARS-CoV- 2 during the intervention?

a.   Bad control, because it might be caused by the participant being infected

b.   Good   control,   because   it   is   predetermined   and   it   might   affect  the probability of contracting COVID

c.    Good  control,  because  it  is  predetermined  and  it  cannot  affect  the probability of contracting COVID

d.   Bad control, because it is not correlated with the probability of contracting COVID

14. In a paper published in 2019, several authors estimate the effect of minimum wages on low-wage jobs using 138 prominent state-level minimum wage               changes between 1979 and 2016 in the United States, using data from several      million workers. At which level would it make sense to cluster standard errors in this paper:

a.   individual level

b.   state level

c.    state * year level

d.   individual * year level