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I hope the group will be able to help on the following. I have the following policy-evaluation problem: stock exchange A reduced their trading costs after period X (say, after 2008), thus managing to spur their trading activity. Estimation of the actual effect is however impossible because of the lack of a counterfactual. Neighbouring exchange B, with similar characteristics and a similar trend in trading activity, does not apply any such or other confounding policies after the treatment period, thus representing a natural candidate as a control group.

While this setup seems perfect for a difference-in-differences estimation, I am left with an excruciating doubt: in both the treatment and the control groups I have a sample of 1. Can one use the argument that if the series are stationary and ergodic, one can estimate a Conditional Average Treatment Effect on the Treated (that is, a treatment effect on the sample of the treated, in this case exchange A?).

I haven't found similar applications, and perhaps for a reason...

Waiting for your expert comments!

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If you have a single treatment group $(i=1)$ and a single control group $(i=2)$ for many time periods before and after treatment it is perfectly acceptable to use a diff-in-diff methodology. (So on net, you'd need: $T >= 2, I >=2, n >=4$ ) Additional control groups will help with the robustness and persuasiveness but are not required.

However, if you have only a single sample (n=1), then you cannot reasonably do a diff-in-diff examination, and I think that should be very clear.

Plug: You may want to consider the Economics StackExchange for Diff-in-Diff approaches, it is pretty discipline-specific.

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  • $\begingroup$ SE standing for? $\endgroup$ – Stafanko Dec 10 '18 at 16:58
  • $\begingroup$ It is clear, to me. What I was asking was slightly different, that is: if one has a long enough time series, can one exploit time series property (such as ergodicity, that is the fact that the mean over time would be equal to the cross-sectional mean of all possible unrealised alternatives) to run the evaluation? $\endgroup$ – Stafanko Dec 10 '18 at 17:09
  • $\begingroup$ As I haven't found such applications, i believe the answer would be "no", but tried to throw a pebble in the pond. $\endgroup$ – Stafanko Dec 10 '18 at 17:09

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