ECON 474 - Midterm 1 Vocab

Stable unit treatment value assumptions (SUTVA) assumptions

1) No interference - my treatment does not affect your outcome
2) No hidden treatment versions - treatment is well-defined (one “aspirin” is the same as another)

Assignment Mechanism - Randomized Experiment

Assignment is completely random, independent of potential outcomes

Assignment Mechanism - Unconfounded (Ignorable) Assignment

assignment depends on observed covariates but not on potential outcomes

Assignment Mechanism - irregular (confounded) assignment

assignment is correlated with potential outcomes

stratified randomized experiment

Research design that divides participants into distinct, homogeneous subgroups based on key background characteristics before randomly assigning them to treatment or control groups

Paired Randomized experiment

Match units on observed characteristics, randomly assign one in each pair to treatment. Improves power when the matching variable predicts outcomes

Internal validity

study correctly identifies casual effects for the study population

External validity

findings generalize to the broader population of interest

OLS Assumption: Exogeneity

X should not be related the factors in the error term, on average

OLS Assumption: Idependent and identically distributed (I.D.D.)

Independent - one observation should not influence another observation
Identically Distributed - all observations come from the same underlying pop. dist.

OLS Assumption: Variation on the regressor

X must vary across observations

OLS Assumption: Finite fourth moments

X and the error term cannot have extremely heavy-tailed distributions that make their 4th moments infinite

Type 1 error

When you reject a true null hypothesis

Type 2 error

When you fail to reject a false null hypothesis

Power

1 - B; probability that the test correctly rejects H0 when H1 is true

Observational study: Unconfoundedness assumption

There are no unobservable factors that simultaneously determine treatment and potential outcomes

Observational study: Overlap Assumption

within every subclass defined by xi, we must have both treated and control units to make a comparison. If a subclass contains only one group, the treatment effect is not identified there.

norm.diff formula

caliper matching

Match only if propensity scores differ by less than a threshold

Balancing score

A balancing score b(X) is any function of X such that D ⊥ X | b(X). Balance is about whether the groups have enough similar characteristics that regression or matching can credibly adjust for the gap

Balancing Score: Finest

X itself. Conditioning on X trivially balances X.

Balancing Score: Coarsest

It throws away as much information as possible while still balancing.

Balancing Score: In between

any function of X that is at least as fine as p(X) also works, meaning p(X) can be recovered from it. For example, (p(X), one extra covariate) is a balancing score.

norm diff defintion

Measures how many standard deviations apart the group means are, indicating how much the covariate distributions overlap.

t-stat - two sample, unequal variances

t = (X̄₁ − X̄₀) / √(s₁²/n₁ + s₀²/n₀)

t-stat - beta hat

t = β̂ / se(β̂)

(Y(0), Y(1)) L treatment | X

potential outcomes statistically independent of treatment holding covariates fixed

Block-level standard error

Weight of each block

n1 - number of treated individuals in a block, N1 - total number of treated peopel across all blocks

Overall standard error

Overall avg treatment effect on the treated

Average treatment effect across the entire population

Sum of squared residuals

p-value

Assuming null is true, what is the probability of getting a test statistic at least as extreme as the one observed?

propensity score

P(Di = 1 | X1 = x) - the probability that a person gets a treatment, given their characteristics

When are ATE and ATT equal

when treatment status is determined using random assignment

The logic behind using a propensity score

Suppose you want to know if textbooks improve test scores. You can’t always compare a student who doesn't use textbooks with one who does because they might be different kinds of students with different aptitudes and circumstances that impact their scores. If you take 2 students who both had the same probability of being assigned, you take out how the other factors impact them, and you are able to just look at the effects.

Robust to specification