Instrumental Variables

Question 1

Instrument

Answer 1

The variable that helps explain the effect of the treatment on the outcome often represented by Z

Question 2

Non-compliance

Answer 2

The mismatch between the units assigned to treatment and the units that actually took up treatment

Question 3

One-sided non-compliance

Answer 3

When some units assigned to treatment do not take up treatment OR some units assigned to the control take up treatment

Question 4

Two-sided non-compliance

Answer 4

When some units assigned to treatment do not take up the treatment AND some units assigned to the control take up the treatment

Question 5

Intent to Treat (ITT)

Answer 5

The Causal effect of the treatment assignment is ignored by defiers and other people who di not comply with their treatment status

Question 6

Local Average Treatment Effect (LATE)

Answer 6

Measures the average causual effects for units who treatment status is tenriely determined by the instrument. It is more accurate when you mostly have compliers but varies with the particular instrument of Zi. Can only measure if you meet all four of the identification assumptions.

Question 7

Why use IV?

Answer 7

IV tries to solve a similar problem to reverse causality: how do we know that the treatment in causing the outcome when it also contributes to the treatment. By adding another variable (Z), that produces an exogenous or random variation in D, we then can focus on D’s effect on Y exclusively through Z.

Question 8

Binary Instrument (Zi)

Answer 8

Zi = 1 if unit i is assigned to receive the treatment
Zi = 0 if unit i is assigned to receive the control

Question 9

Potential Treatment Status

Answer 9

Diz = 1 if unit i takes the treatment given Zi = z
Diz = 0 if unit i DOES NOT take the treatment given Zi = z

Question 10

Observed Treatment

Answer 10

Di = Zi * Di1 + (1-Zi) * Di0
Di = Di1 if Zi = 1
Di = Di0 if Zi = 0

Question 11

Compliers

Answer 11

Units who take the treatment when assigned to it and don’t take it if they weren’t assigned to it
Di1 > Di0 (ie Dio = 0 and Di1 = 1)

Question 12

Always Takers

Answer 12

Units who always take the treatment whether or not they were assigned to it
Di1 = Di0 = 1

Question 13

Never Takers

Answer 13

Units who never take the treatment whether or not they were assigned to it
Di1 = Di0 = 0

Question 14

Defiers

Answer 14

Units who take the treatment when they were NOT assigned to it and don’t take the treatment when they were assigned to it
Di1 < Di0 (ie Dio = 1 and Di1 = 0)

Question 15

Identification Assumptions

Answer 15

Exogeneity of the instrument, Exclusion Restriction, First stage relationship, and monotonicity

Question 16

Exogeneity of the Instrument

Answer 16

The assignment of the instrument has to be randomly assigned, which allows for measuring the intent to treat effect

Question 17

Exclusion Restriction

Answer 17

The instument has no direct effect on the outcome, once the value of the instrument is fixed. The instrument only affects the result through treatment. Can’t just assume that random assignment of the instrument is enough to explain why exclusion works – also need to provide a rationale for why excluding the instrument enables the treatment to affect the results. Also can’t test this assumption, so gotta use your own logic

Question 18

First-Stage Relationship

Answer 18

The instrument must have an effect on the treatment, or that being assigned to the treatment actually enables people to take up the treatment. Can test this by regressing the treatment on the instrument

Question 19

Monotonicity

Answer 19

The instrument has a uniform effect on the treatment, thus, ruling out the existence of any defiers