Econometrıcs II (ENG) — Ünite 7 Soru-Cevap

It means that, it seeks to determine whether a change in one variable causes a change in another variable.

All causal inference methods aim to identify the causal impact of treatment using a control group which will give us an average outcome as close as possible to the counterfactual’s outcome if we had observed it.

Treatment (i.e., intervention, policy, or program, etc.) could be a change in the legislation, construction of new schools in some regions of a country, a training program, and so on.

Counterfactual helps us to find out the trend of the treatment group in the post-treatment period if they had not received the treatment.

It is the difference between the expected value of outcome for the treated units under treatment and the expected outcome of treated units under no treatment, both in the post-treatment period.

The fundamental problem of causal inference occurs because the counterfactual cannot be observed.

If we have more than one time period in the pre-treatment period, we can only observe if the parallel trends between control and treatment groups exist in the pre-treatment period.

 We can run diagnostic tests to check if there is a parallel trend between treatment and control groups before the treatment

This implies that there would be no anticipation of the treatment by treated units so that treatment will

not have any impact on the observed outcomes of treated units in the pre-treatment period.

This assumption implies that the treatment being taken by the treated units should not have a spillover effect on the control (untreated) units. In other words, we should be only observing the two potential outcomes that exist for each group: their potential outcomes under treatment and under no treatment.

In the canonical DiD, we assume that all treated units are treated at the same time. We can instead run more general regression model if there is a staggered adoption of treatment as below which is called the “two-way fixed effects model (TWFE).

Staggered adoption means that treatment assignments for different units happen in different time periods. In other words, not all units receive the treatment at the same time but rather at different time periods.

In a regression model, we can include dummy variables for the periods before and after the treatment for each unit, then we will be able to understand the average treatment effect on the treated at different periods after the treatment.

Goodman-Bacon (2021) shows that the TWFE estimate is a weighted sum of average treatment effects that are found comparing different groups with each other according to their treatment adoption timing

It’s meaning that the intensity of treatment is the same for all treated units.

It is very useful to estimate a treatment effect as it is pretty straightforward to eliminate the selection bias in RDD.

In RDD, researchers benefit from arbitrary thresholds that determine treatment assignment. In other words, the probability of treatment jumps at the threshold, the point at which we expect to have a discontinuity in the treatment assignment. 

There are two types of regression discontinuity design, namely Sharp RDD and Fuzzy RDD.

In the Sharp RDD, treatment probability jumps at c from 0 to 1. In other words, all units that are below c are definitely assigned to a control group and all units above c are surely in the treatment group. Thus, in the Sharp RDD, we have perfect compliance. However, in the Fuzzy RDD, treatment probability still jumps at the cutoff point c but it is not a jump of the probability of treatment assignment from zero to one. In other words, there is ‘imperfect compliance’ in the case of Fuzzy RDD.

If the relationship between the outcome variable and the running variable is not linear, then there is a risk of interpreting a spurious relationship wrongly as a causal effect.