Assumptions Flashcards
(49 cards)
What is the SUTVA assumption?
The potential outcomes of an individual i do not depend on the treatments received by other individuals.
ATT Defintion
Mean difference in observed outcomes and counter factual for treatment group
ATC defintion
Mean difference in observed outcomes and counter factual for control group
ATE defintion
Mean effect in the entire population, whether or not they actually participate
Mean Independence Assumption (MIA) and what does it mean if it holds?
E[Y0|D = 0] = E[Y0 |D = 1] and E[Y1|D = 0] = E[Y1|D = 1].
If it holds, data is generated from experiment and potential outcomes are independent of treatment.
Perfect balance between treated and untreated
What happens to the treatment effects under randomisation? And why?
DIM = ATT (No BB) = ATE (No BB or DTE) = ATC
What are some issues with experiments, and threats to internal validity?
They can be costly, impractical and sometimes impossible.
Threats to internal validity:
Hawthorne effect - People react to being observed
John Henry effect - People react to be in control group
What is the CIA?
The CIA is when the potential outcomes are independent of treatment given X is controlled for
What is the CMIA, and what does it mean if it holds?
If it holds, the selection bias disappears after conditioning on the observed characteristics X, as the treatment is as good as random. They will, on average, have the same potential outcomes.
E[Y0|D = 1, X] = E[Y0|D = 0,X]
What are the 2 assumptions to calculate the treatment effect from observational data?
E[Y1|D = 1, X] = E[Y1|D = 0, X]
E[Y0|D = 1, X] = E[Y0|D = 0, X]
Different types of individuals based on the potential treatments
Always Takers: D(1) = 1 and D(0) = 1
Never Takers: D(1) = 0 and D(0) = 0
Compilers: D(1) = 1 and D(0) = 0
Defiers: D(1) = 0 and D(0) = 1
What are 2 assumptions for making calculations on ‘Always takers’ etc?
No defiers
Instruments are independent of treatment
What makes a valid instrument?
- Has a causal effect on treatment (First Stage)
- It’s as good as randomly assigned
- It effects outcomes only through treatment (Exclusion Restriction)
Benefits of the 2SLS
1) Allows use of multiple instruments
2) Controls for exogenous variables
2) Controls for observable characteristics X
What do the elements in this regression mean?
M_Hat[A] = alpha + rhoD[a] + gamma[alpha] + e[alpha]
M - Mortality Average
Rho - Estimate of the jump exactly at the threshold
Gamma - Slope coefficient
D[a] - treatment dummy
a - running variable
Why might a simple linear model produce misleading estimates? Regression discontinuity
If relationship between 2 variables is not linear
If relationship between variables is not the same on each side of the discontinuity.
What identification assumptions need to be made for an estimate to be causal? RD
- Independence of potential outcomes either side of the discontinuity
- No OVB in the estimating equation, implies rho is causal
- No other ‘jumps’ at D (threshold)
How do you test the causal estimate assumptions? RD
2 possible tests
- See if other observable characteristics are balanced either side of the discontinuity
- Ensure that there is no manipulation of the running variable. (If no manipulation, density of a would be smooth around DC)
What is manipulation?
Manipulation is when the variable X is chosen -> ideally we would like it to be something like age
Pros and cons of Narrower bands for Band width
Pros - Less likely to be misspecified, closer to true estimate of rho
Cons - Means less data and less precise estimate
What is the difference between standard error and standard deviation?
Standard error is the difference in how much the mean would vary if it were measured from lots of different samples.
Standard deviation is a measure of how much observations vary from one another.
What is the relationship between Regression and CEF, and what would be saturated model mean?
Regression is an approximation for the CEF. If the regression model is saturated, the regression should have the same number of parameters as the CEF has values. (Another way of estimating a naive comparison of means)
CEF: E[Y|D]
CEF is just an average -> does not mean its causal
Baseline Bias
Difference in average outcome, in absence of treatment, between the treated and untreated.
E[Y0|D=1] - E[Y0|D=0]
DTE Bias
The benefit of the treatment (causal effect), for those who are treated and untreated is not the same.
If positive the treated gain more.
(1-pi){ E[Y1-Y0|D=1] - E[Y1-Y0|D=0]}
Where pi is the proportion of sample who getting treated
