Hi. Welcome to Causal Inference 2,

the sequel to Causal Inference 1.

In Causal Inference 1,

we focused on the identification and estimation of a few basic estimands,

namely average treatment effects or effects the treatment on the treated.

So, throughout almost all of causal inference 1,

we assumed that; one,

treatment assignment was unconfounded, given measured covariates.

Two, each study participant could be exposed to

either the control condition or the treatment condition with positive probability,

and three we made the stable unit treatment value assumption.

At the end, we examined attempts to access

the plausibility of the unconfoundedness assumption and

the extent to which the unconfoundedness assumption

could be violated without reversing the conclusions of the study.

Now, going forward, there are a number of

interesting and important questions that scientists would

like to address that require additional considerations.

First, how does the cause produce the effect.

Presumably, because operates by

activating intermediate pathways between it and the effect.

Addressing this issue necessitates the formulation of new estimands,

and to identify these extensions of the unconfoundedness assumption previously discussed.

A second issue is how to compare different treatment regimens.

For example, a researcher might wish to know if administering a treatment once a

week is superior to administering the same treatment every other week.

In a randomized study where the investigator can assign

subjects to different regimens, this is straightforward.

But in an observational study where the investigator compares

participants who took treatment every week versus every other week,

treatment status in any given week can depend on previous treatment status,

how well the participant has reacting to previous treatments,

and other characteristics of the participant.

These matters are addressed in the literature on longitudinal causal inference.

Again, new estimands and extensions of the unconfoundedness assumption are needed.

Third issue, we have assumed each subject has

a positive probability of receiving treatment or not.

This doesn't cover the case of experiments in which a subject's assignment depends

on a cut off score that he or she may exceed or not exceed.

As an example, consider the case where a researcher wants to know the effect of

a remedial reading program for school-aged children on subsequent reading ability.

Well, the best way to study this would be to randomly

assign children to either receive or not receive the program,

suppose the researcher can only conduct or has access to the study in which

all children below the cutoff are assigned to the remedial reading program,

and all children and above are not assigned to the program.

This might occur if the investigator who conducted the study was prohibited and on

ethical grounds from denying access to the program for children below the cut off.

This set-up has come to be called the regression discontinuity design.

Forth, the SUTVA assumption.

Remember that Stable Unit Treatment Value Assumption

is violated when there are multiple versions of the treatment,

and or interference amongst units.

For example, if an aspirin is administered in gel or capsule form,

and the dosage differs in the different forms,

or if the effect of a given dosage depends on the form,

these are multiple versions of the treatment.

Intuitively, this needs to be taken into account in order to achieve valid inferences.

Interference amongst unit occurs when an outcome of unit i is affected

not only by i's treatment's assignment but by the treatment assignment of other units,

call them i prime.

Examples are common when outcomes may depend on social interactions among units as in

the transmission of infectious diseases

and when individual behaviors are influenced by other individuals.

Fifth, one might ask if it sometimes possible to

identify and estimate treatment effects when it is

not possible to observe all confounders.

To that end, economists long ago proposed

a clever and intuitive idea of exploiting longitudinal and clustered

study designs in conjunction with modelling

assumptions to neutralize the effects of the unobserved confounders.

These give rise to so-called 'fixed effects' regression models.

Given the substantial use of these models in the social sciences,

we examine them more carefully.

Using the literature on longitudinal causal inference,

we give conditions under which coefficients of

the fixed effects models admitted interpretation as a treatment effect.

Unfortunately, the conditions are usually very unrealistic.

For the clustered case,

in order to coefficients admit and interpretation as in effect,

it is necessary to assume no interference among units.

Again, often unreasonable for cluster sharing a common fixed effect.