Question

d.) note that the outcome of interest is a function of , and thus balance on is critical for valid causal inference. if units are matched or partitioned into subgroups according to their true propensity scores, are these subgroups expected to be balanced, on average, in terms of ? why or why not? choose the best answer.

Answer 1

Yes, the subgroups are expected to be balanced, on average, in terms of X5 because the outcome of Y is still a function of X5.

The true data-generating mechanism for the simulated data is given below.

Y = 4Z - 0.8X1 - 3X2 + 6X4 + X5 + error

We see that the outcome of interest Y is a function of X5, and thus balance on X5 is critical for valid causal inference. The units are matched or partitioned into subgroups according to their true propensity scores. We need to determine if these subgroups are expected to be balanced, on average, in terms of X5 or not, and the reason behind it.

We can conclude from the above statements that the outcome of Y is still a function of X5.

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