Announcement

Collapse
No announcement yet.
X
  • Filter
  • Time
  • Show
Clear All
new posts

  • Heteroscedasticity and Synthetic Control Method (SCM)

    Dear all,

    My question: is there an alternative synthetic control method package to synth and synth_runner that controls for heteroscedasticity?

    Background: I am using the commands synth and synth_runner for an analysis with one and several treated units. I was asked how the Synthetic Control Method (SCM) deals with heteroscedasticity and after reading up on the topic I found out that heteroscedasticity can occur when the variation of the transitory shocks is different between the treated and untreated unit or over time.
    I also found a paper from David Powell (Imperferfect Synthetic Controls) in which he proposes a way for inference in SCM which controls for heteroscedasticity. However, this is a paper without a corresponding software package.

    Thanks for any help.
    Best,
    Michael

  • #2
    Michaell, heteroskedasticity is related to statistical inference. To my knowledge, inference in SCM is design-based (aka permutation inference) rather than sampling-based, so we won't get standard errors as in linear regressions. One of the pioneers of SCM, Alberto Abadie, published a review paper in Journal of Economic Literature in 2020 and gives zero word on heteroskedasticity. Just not sure whether heterosk is a valid issue or not here.

    Comment


    • #3
      Thank you Fei,

      You are right in that the comparison of the synthetic control with the observed unit and the following permutation test for inference does not have an error term and therefore no heteroscedasticity in the sense we know it from regression analysis.

      However, when solving the minimization problem, i.e when estimating the weights for the synthetic control that is where there could be an error term and hence heteroscedasticity.

      The weights estimation can be described in a linear factor model of the form:

      Y_jt = delta_t + theta_t * Z_j + lambda_t * mu_j + epsilon_jt

      (this is equation (10) in the AbadieĀ“s paper you are referring to). The epsilon in this model is referred to as transitory shocks by Abadie and that is where heteroscedasticity can occur. In other words, if the variation of the transitory shocks is different between the treated unit and the donor pool units then we have heteroscedasticity.

      As far as I understand it this kind of heteroscedasticity can lead to a rejection or non-rejection of weights for individual donor pool units, which could mean that as a result the synthetic control values would be biased in one way or another.

      Does anyone know how to deal with this issue in Stata? or is my way of thinking wrong and transitory shocks do not bias anything?

      Best,
      Michael

      Comment


      • #4
        Michaell, thanks for your interpretation. I see your point now. Abadie suggests only putting control units that are similar enough to the treated unit to the donor pool, because SCM assumes that all units share the same underlying linear factor model. The heterosk issue occurs when control units are not sufficiently similar to the treated, and even worse the whole underlying model may differ beyond just error structure. So I think one solution, according to Abadie, is to cautiously select donor pool units and attempt to avoid this issue from the very beginning.

        Comment


        • #5
          Thanks a lot for this answer. It makes so much more sense to me now. Very helpful.
          Last edited by Michaell Keller; 25 Nov 2021, 06:28.

          Comment


          • #6
            Michael Keller I saw your message to me on stack.

            I can send you a brief excerpt of Stata code to do this, if you'd like. I'm sort of doing an analysis like this right now.

            Comment

            Working...
            X