Significance of DD variable in a DDD specification

[Surya Singh]

Hello,

I am running a triple differences regression comparing a treatment group (ex: mothers) and control group (ex: women of childbearing age) where I have a repeated cross section of individuals and staggered policy introduction from 1990-2011 across 50 states where 25 states have implemented a policy sometime during 1990-2011. My specification is as follows:

y_it = B₀ + B₁X_i + B₂Z_j + B₃(state_j) + B₄(year_t) + B₅ (policy_i) + B₆(eligibility_i) + B₇(policy_i * eligibility_i) + e_i


X_i = individual-level covariates (i.e. income, marital status, etc.)
Z_j = state-level covariates (i.e. unemployment rate)
state_j = state fixed effects
year_t = year fixed effects
Policy_i = 1 for individuals living in a state after the introduction of the policy and = 0 otherwise
Eligibility_i = 1 for individuals in the treatment group (ex: mothers) = 0 for individuals in the control group (ex: women of child-bearing age)
and B₇ on the interaction between policy*eligibility is my DDD coefficient.

This specification follows Baum (2003) (http://www.sciencedirect.com/science...2753710300037X).
I wanted to ask what does the policy variable represent in the DDD specification and would we expect it to be significant or insignificant in a DDD specification? Baum (2003) states that it represents state-specific, year-specific effects; however, he does not state whether it should be significant or insignificant or whether it does not matter so I'm a little confused on the meaning of the DD variable in the context of a DDD specification.

Thanks for any help!

Surya

[Clyde Schechter]

The coefficients of the policy_i variables don't actually mean very much at all in this model. They represented the expected value of y - B₀ when all of the following are true:

1. X_i = 0
2. Z_j = 0
3. j is the reference state (the state for which no indicator variable is included)
4. t is the reference year
5. Eligibility_i = 0
6. policy is policy_i.

Generally speaking there won't be any such observations. In fact, in many situations, it would not even be possible in principle for there to be any such observations. They might or might not be "significant", but you shouldn't care either way.

[Surya Singh]

The coefficients of the policy_i variables don't actually mean very much at all in this model. They represented the expected value of y - B₀ when all of the following are true:

1. X_i = 0
2. Z_j = 0
3. j is the reference state (the state for which no indicator variable is included)
4. t is the reference year
5. Eligibility_i = 0
6. policy is policy_i.

Generally speaking there won't be any such observations. In fact, in many situations, it would not even be possible in principle for there to be any such observations. They might or might not be "significant", but you shouldn't care either way.

Ah ok, that makes sense. Thanks Clyde!