New answers tagged

10

Neither. An estimator is consistent for some parameter, so in this case the answer is Yes, $\hat\gamma_2$ is consistent for $\beta_2$ No, $\hat\gamma_2$ is not consistent for $\gamma_2$ (or for $\beta_0$ or lots of other things). In this case, the causal assumptions suggest you'd be more interested in whether it was consistent for $\gamma_2$, but you still ...


2

Causal interpretation of the one-equasion regression is indeed derived from the strict exogeneity of all the variabes: $E(\varepsilon|X)=0$. Consistency of an estimator is proven under this assumption, I do not think there is a need to discuss it. This however, is derived from other assumption: that we fully know structural model (DGP). This assumption is ...


6

Here's a partial answer for when the underlying model is actually linear. Suppose that the true underlying model is $$Y = \alpha + \beta X + v.$$ I'm making no assumptions about $v$, though we have that $\beta$ is THE effect of $X$ on $Y$. A linear regression for $\beta$, which we will denote as $\tilde{\beta}$ is simply just a statistical relationship ...


2

Thank you for including a causal diagram! Answer: Simply regress $Y$ on $T$ like this: $$Y=aT+b.$$ There is no backdoor path from $T$ to $Y,$ so you don't need to condition on anything. In fact, if you want the full causal effect of $T$ on $Y,$ you need to NOT condition on $x_2.$ You have a mediation situation, so there are other numbers in which you might ...


1

No. Matching methods in this case have the same fragility as regression. They do not automagically control for any endogeneity sources. In assessment of treatment effect, both matching and regression base on the same Conditional Independence Assumption (CIA) (Angrist and Pishke, 2008), which is: $$ \{Y_{0i}, Y_{1i} \} \perp \! \! \! \perp c_i | X_i $$ As ...


6

Following up on Dimitriy's comment, which I agree with. There are (at least) three sources of uncertainty when performing a propensity score matching analysis: 1) the estimation of the PS, 2) the matching, and 3) sampling variability. I have been writing a review of uncertainty estimation after matching so I'll briefly share those findings here. The way ...


0

The innovation of the synthetic control method (Abadie et al. 2010) is that it enables estimating the factor model that allows unobserved common factors (lambda) to vary across unit (mu) with fairly reasonable assumptions (equation 1 in the paper). Choosing a synthetic control in this manner is, of course, not feasible because μ1,...,μJ+1 are not observed. ...


1

Take note of the comments by @DimitriyV.Masterov. Difference-in-differences works well with repeated cross-sections data. Your equation would look something like the following: $$ y_{ist} = \alpha + \gamma S_s + \lambda A_{t} + \delta (S_s \times A_{t}) + \theta X_{ist} + \epsilon_{ist} $$ where $y_{ist}$ denotes movie $i$ in society $s$ at time period $t$. ...


1

It's true that there are several sources of uncertainty in propensity score matching. One is sampling from the superpopulation (which is true of most statistical analyses and is the usual justification for sampling distributions and confidence intervals), but two others are the uncertainty in estimating the propensity score and the uncertainty due to ...


2

The most straightforward way would be to specify a caliper. A caliper is the maximum distance two units can be apart from each other before they are not allowed to be matched. Any treated units that do not receive a match because there are no remaining units within their caliper are left unmatched and discarded. The tighter the caliper, the more units are ...


1

But then my question really would be, why beer consumption, which...does have an...effect on fatalities, would not be part of the error term u? The error term in the linear model is not interpreted to contain quite "...all factors affecting fatalities other than beer tax" (although you can see why it's not unreasonable for make this initial claim ...


0

A random-effects model does not control for unobserved invariant unit-level heterogeneity ($\alpha_i$ in your excerpt from Verbeek). If your intention is to make causal claims from the model and you have reasons to believe that $\alpha_i$ is correlated with the causal variable of interest, your model will be rejected by the scientific community because it ...


0

Let's say I run a model of Depression (Y) as a function of Drug use (X), and I have somehow magically controlled for all other variable that might be correlated with both X and Y, and the beta for drug use is positive. Does that mean drug use causes depression? Maybe, but it might also be that depression causes drug use. In fact both of these causal ...


0

Ideally, the covariates used for matching should be measured contemporaneously for both treatment and control groups, before the treatment has started, but as close to the start as possible. If the covariates used for matching make the treatment assignment ignorable (loosely speaking, the treatment group and control groups are similar to each other on ...


3

Ah, I see you are studying Pearl's Causal Inference in Statistics: A Primer, co-written with Glymour and Jewell. Excellent choice! Theorem 4.3.2 says that if $\tau$ is the total effect of $X$ on $Y$, which is $ab$ in this case, then, for any evidence $Z=e,$ we have $$E[Y_{X=x}|Z=e]=E[Y|Z=e]+\tau(x-E[X|Z=e]).$$ So, in our case, if we want to compute $E[Y_1-...


4

SVM can be used to generate predicted values, which can be used as estimates of propensity scores or potential outcomes, just like any other supervised machine learning method. It is not special in that regard. These predicted values can be used to estimate causal effects when other assumptions about the data-generating process are known. In addition, ...


1

There are two qualities on which matched samples should be assessed: covariate balance and remaining (effective) sample size. Covariate balance is the degree to which the covariate distributions are the same between the treatment groups in the matched sample. Remaining sample size is the number of units remaining after discarding unmatched units. Covariate ...


2

You are right that there is a problem. At the extreme, suppose no-one ever went off treatment. Survival time would be identical to time on treatment, giving an apparently infinite benefit even if the true benefit was zero. Doing better than this still requires some information about how treatment length ends up being the way it is. This is partly a solved ...


1

In the same way we don't know the form of the outcome model (which is why we use propensity score matching in the first place), we don't know whether regression completely removes all confounding in a matched sample. Matching makes it more plausible for confounding to be removed by regression; this is the main thesis of Ho, Imai, King, and Stuart (2007), the ...


3

That's some amazing balance! There are a few things you should know about genetic matching with MatchIt. These are due to the fact that MatchIt calls the function GenMatch in the Matching package, which has a different syntax from matchit(). First, by default, it performs matching with replacement, which is not true of nearest neighbor matching. To perform ...


1

In dagitty, when you indicate that a variable $A$ is "adjusted", you indicate that you will definitely adjust/control for it in the analysis. Dagitty will then tell you whether and how you can still estimate a causal effect of the variable of interest $E$ from this analysis via adjusting for additional variables or using an instrumental variable. ...


0

Here are a few suggestions: Falsification/placebo test. As suggested in the first answer. If you have an alternative outcome that you know is not affected by treatment then you can assess the credibility of your primary results; e.g, if the main outcome is income after treatment then income before treatment is an ideal candidate. Covariate balance. If you ...


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