The causal network shown below represents one possible hypothesis for the link between school expenditures and student performance. It involves some educational policy variables (expenditures, class size, teacher compensation) and some other potentially important variables.
The variables in rectangles are potentially measurable. The variable in the gray circle is “latent,” that is, a theoretical player which isn’t directly measured.
1 Intervening to set the level of expenditure erases all the other causal inputs to expenditure and thus blocks all the backdoor pathways that would otherwise exist.You convince the Federal Government to do an experiment where they independently set the level of expenditure. Show that the backdoor pathways through the non-policy variables are blocked.
2 The latent variable and the family income and education variables are thought to contribute to test scores. This additional variation can obscure that due to the action of the policy variables. By adjusting for the non-policy variables, you reduce unexplained variance and thereby make it easier to detect the possible relationships among the policy variables.Even if the backdoor pathways are blocked, as in (1), explain why it would help to use the non-policy variables as covariates.
3 Option (b) effectively studies a relationship with no unblocked backdoor pathways. In the medical literature, this is called an “intent to treat analysis.” The correlation between increment and outcome may be hard to detect because of all the other sources of variation in outcome, but it definitely will be about the causal relationship through the policy variables.Hard to believe that parents and local officials would allow school expenditures to be set–randomly!–by the Federal government. So the experiment in (1) is not going to happen. However, the government might be able to set up a program to incrementally increase expenditures and award the increase randomly to school districts. In studying the results, the government statisticians have access to the record of the randomly generated increment: call this increment. Which would be a better way of assessing whether there is a causal connection between expenditures through the policy variables to student outcome: