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5

You construct the policy dummy the way you first describe it, i.e. create a column of zeroes. Then for each firm you replace this with ones if a firm is in the treatment group AND it is in the post-treatment period. Something like this $$ \begin{array}{ccccc} \text{firm} & \text{time} & \text{treated} & \text{post} & \text{policy} \\ \hline ...


3

The simple answer to your question is, unfortunately "no". Without a control group and without longitudinal data you have no way of figuring out the effect of the treatment. You can compare treatments to each other - since you appear to have data on several treatments - but what those comparisons will mean will depend, in part, on how treatments were ...


3

This makes no sense to do because the average outcome of the healthy patients is meant to stand in for the average outcome of the sick patients had they not received treatment (which is not observed due to the fundamental problem of causal inference/unbearable lightness of being). Without some additional strong assumptions, there is not much else you can do ...


2

$E[Y_{0i}|D=1]$ is not observable because we cannot know the counterfactual, i.e. what outcome the individual would have if they did not receive the treatment as they always get the treatment (D=1). What randomisation does is guarantee that the treatment assignment is statistically independent of potential outcomes, therefore: $E[Y^*_0]=E[Y^*_0|D=1]=E[Y^*_0|...


2

No, you do not have marginal independence, not even under restrictive parametric assumptions. Let's ignore $X$ and let Y = g(U) be linear, so that $$Y = \beta D + U. $$ Furthermore, let $D \sim Unif[0, 1]$, and $D = I(U > 0.5)$. Then $E[Y_1] = \beta + 0.5$, but $$E[Y_1|D = 1] = \beta + E[U|U > 0.5] = \beta + 0.75, $$ so $D$ is not independent ...


2

One thing you want to think about is the distribution of missingness or "missingness mechanism." See the figure below from Schafer & Graham (2002). Your missing data are missing at random (MAR) if the missingness is unrelated to the missing data itself, but missing not at random (MNAR) if the missingness is related to the missing data itself. For ...


1

Based on your causal diagram, it appears that "selection variables" refers to confounders, not factors related to selection into the sample. This distinction is important because the items included in the different inverse probability weights is important. Briefly, to answer your question, I would not use any of the approaches you listed. The analysis and ...


1

You mention several treatments so you can compare them and tell which if any is better than the others but you have no direct comparison with no treatment so that comparison is ruled out. If there is historical data and the effect of your treatment is very strong then the historical control might be enough. If your treatment for Ebola virus disease leads to ...


1

Rubin explains in his great free book, Basic Concepts of Statistical Inference for Causal Effects in Experiments and Observational Studies (pdf), what's called "The fundamental problem of causal inference" (see, e.g., p. 4). I'd suggest starting form there. In short: the only way to truly assess a causal effect is to compare things that don't really exist - ...


1

In the absence of more detailed information, it seems like you are interested in "structural equation models", or SEM. This is a broad class of multivariate methods that incorporate latent constructs into a regression framework, often specified through path diagrams similar to yours. (That said, you actually have most of the arrows pointed in the wrong ...


1

You can interact treatment and control variables in the matched sample. There are a few reasons one might do this. One would be simply to adjust for the control variables beyond the adjustment afforded by the matching (i.e., as Ho, Imai, King, & Stuart, 2007, recommend). To do this, you would center your control variables before interacting them with the ...


1

Firstly you could compute a correlation matrix with the Y (dependent) in the first column and all the Xs (predictors). Look along the first row or column and eliminate the Xs that have low pairwise correlation with Y. So that may give you an initial reduction in the number of predictor variables. Regardless of whether you do this first step or not, you ...


1

First of all, it is necessary to identify the outcome(s). In the case you describe, if the variables that differ in distribution between treated and non-treated are also associated with the potential outcomes (i.e. the outcomes in case of treatment and non-treatment respectively), they are confounders. This means that, if you don't control for them, you can'...


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