EC220 PAST PAPER NOTES
Q1: MT CONTENTS
DISCUSSING CAUSAL RELATIONSHIP
Would you interpret the effect as causal?
- Plausible story about confounders
- Reverse causality
Size of effect
- Compare 𝛽̂0 and 𝛽̂0 + 𝛽̂1 for a binary variable -> percentage difference in effect
OVB
- OVB = 𝛽 𝑆 − 𝛽 𝐿 = relationship of omitted in long × relationship between omitted and not-
omitted -> can infer relationship between omitted and not-omitted
Interaction
We would like to test whether pensioners are more likely to make the donation when they
receive the flyer
- Test coefficient on interaction
To include or not to include a variable
- To include:
o Confounder – even if not statistically significant
o Good control – explain the residuals – improve precision
o If not statistically significant, may still be able to make causal claim – maybe the
variation in this variable is not enough such that precision is not enough
- Not to include:
o Bad control which is a result of the outcome – would reintroduce selection bias
o Multicollinearity – would enlarge standard error and make the estimates volatile
Hardest causal question: 2021ST
Researchers would like to analyse whether consumers reacted to the disaster by reducing their
consumption of BP branded petrol during the oil spill. An observation is a particular petrol
station. Non-BP stations in BP zip codes are not used in the sample.
⇒ 𝐵𝑃𝑖 = 1 if the petrol station is in a BP zip code and sells BP oil
𝑃𝑟𝑖𝑐𝑒𝑖 = 𝛼 + 𝛽𝐵𝑃𝑖 + 𝑢𝑖
Define the treatment, the control group, the outcome, and the counterfactuals implicit in the
regression
, - Treatment is placed on control group to get the average treatment effect of interest
So treatment is on petrol stations
Treatment: the station sells BP petrol and therefore is exposed to potential
consequences of the oil spill
- Control group is the group of observations that are not treated
Control group: non-BP stations in non-BP zip codes that are not exposed to potential
consequences of the oil spill
- Counterfactuals: the average price of petrol sold at BP stations (the treated) over the
period, had the oil spill not happened
- Outcome: the average price of petrol sold at a station (treated + control) over the period
Balance check
- Run regression before the treatment to check whether there are any difference in the
outcomes before the treatment
- If there were statistically and economically significant differences, the concern would be
that there are systematic differences between the treatment and control groups, and
these differences might still explain any differences after the treatment
- If we cannot find any evidence for such differences, we are more confident that the
treatment and control groups are similar
- Discuss the significance -> conclude that the treatment and control groups are on average
likely to be similar
IV
Discuss the IV procedure
𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑓 𝑍 𝑜𝑛 𝑌
- Wald estimator: 𝛽̂ 𝐼𝑉 = 𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑓 𝑍 𝑜𝑛 𝑋
- The randomly assigned Z is assumed to affect Y only through X alone. That means the
effect of X is attributed exclusively to X, and we need to correct for the fact that some
offered the lottery doesn’t comply, while a few of those who were not initially offered
were treated. We adjust by rescaling the effect of Z, which will give us the effect of actual
treatment.
o The effect of Z on X = treated/lottery winner – treated/non-lottery winner
IV effect not significant, why?
- Reason 1: weak first stage
- Reason 2: IV assumptions may fail (discuss in depth)
Elasticity
ΔPrice
- = Δquantity
- Can be calculated from estimates
Q1: MT CONTENTS
DISCUSSING CAUSAL RELATIONSHIP
Would you interpret the effect as causal?
- Plausible story about confounders
- Reverse causality
Size of effect
- Compare 𝛽̂0 and 𝛽̂0 + 𝛽̂1 for a binary variable -> percentage difference in effect
OVB
- OVB = 𝛽 𝑆 − 𝛽 𝐿 = relationship of omitted in long × relationship between omitted and not-
omitted -> can infer relationship between omitted and not-omitted
Interaction
We would like to test whether pensioners are more likely to make the donation when they
receive the flyer
- Test coefficient on interaction
To include or not to include a variable
- To include:
o Confounder – even if not statistically significant
o Good control – explain the residuals – improve precision
o If not statistically significant, may still be able to make causal claim – maybe the
variation in this variable is not enough such that precision is not enough
- Not to include:
o Bad control which is a result of the outcome – would reintroduce selection bias
o Multicollinearity – would enlarge standard error and make the estimates volatile
Hardest causal question: 2021ST
Researchers would like to analyse whether consumers reacted to the disaster by reducing their
consumption of BP branded petrol during the oil spill. An observation is a particular petrol
station. Non-BP stations in BP zip codes are not used in the sample.
⇒ 𝐵𝑃𝑖 = 1 if the petrol station is in a BP zip code and sells BP oil
𝑃𝑟𝑖𝑐𝑒𝑖 = 𝛼 + 𝛽𝐵𝑃𝑖 + 𝑢𝑖
Define the treatment, the control group, the outcome, and the counterfactuals implicit in the
regression
, - Treatment is placed on control group to get the average treatment effect of interest
So treatment is on petrol stations
Treatment: the station sells BP petrol and therefore is exposed to potential
consequences of the oil spill
- Control group is the group of observations that are not treated
Control group: non-BP stations in non-BP zip codes that are not exposed to potential
consequences of the oil spill
- Counterfactuals: the average price of petrol sold at BP stations (the treated) over the
period, had the oil spill not happened
- Outcome: the average price of petrol sold at a station (treated + control) over the period
Balance check
- Run regression before the treatment to check whether there are any difference in the
outcomes before the treatment
- If there were statistically and economically significant differences, the concern would be
that there are systematic differences between the treatment and control groups, and
these differences might still explain any differences after the treatment
- If we cannot find any evidence for such differences, we are more confident that the
treatment and control groups are similar
- Discuss the significance -> conclude that the treatment and control groups are on average
likely to be similar
IV
Discuss the IV procedure
𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑓 𝑍 𝑜𝑛 𝑌
- Wald estimator: 𝛽̂ 𝐼𝑉 = 𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑓 𝑍 𝑜𝑛 𝑋
- The randomly assigned Z is assumed to affect Y only through X alone. That means the
effect of X is attributed exclusively to X, and we need to correct for the fact that some
offered the lottery doesn’t comply, while a few of those who were not initially offered
were treated. We adjust by rescaling the effect of Z, which will give us the effect of actual
treatment.
o The effect of Z on X = treated/lottery winner – treated/non-lottery winner
IV effect not significant, why?
- Reason 1: weak first stage
- Reason 2: IV assumptions may fail (discuss in depth)
Elasticity
ΔPrice
- = Δquantity
- Can be calculated from estimates
