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I'm currently doing the statistical part of my final thesis and I am having troubles with correctly interpreting my regressions results. The models I am using (with the plm package in R) are pretty simple:

(1) Ln(Emissions) ~ Treatment + Post + Treatment*Post + TimeFE

(2) Ln(Emissions) ~ Treatment + Post + Treatment*Post + TimeFE + IndustryFE

(3) Ln(Emissions) ~ Treatment + Post + Treatment*Post + TimeFE + InstallationFE

with

  • Ln(Emissions)...natural log of emissions in 1,000 metric tons (on installation-level)
  • Treatment...a dummy indicating installations in the treatment group (dummy = 1) or the control group (dummy = 0)
  • Post...a dummy indicating post-treatment observations (since the treatment is staggered - for some installations post-treatment starts one period later than for the others - the treatment dummy remains in the estimations with time fixed effects and is not omitted)
  • Treatment*Post...Interaction term -> the estimated coefficient is what I am interested in
  • TimeFE...Time fixed effects
  • IndustryFE...Industry fixed effects
  • InstallationFE...Installation fixed effects

I have installation-level data on yearly emissions (balanced panel with n=~450, T=9, ~4,000 installation-year observations). During my period of observation a treatment (a law affecting just the treatment group) occurs...therefore I am utilizing the 3 models describe above to derive an estimate of a possible treatment effect. I have checked various (working) papers to figure out how to correctly derive the economic magnitude of the effect from my regression estimates but I am still looking for a way that is (at least to me) intuitive and understandable.

For the first specification I derive the following estimates:

Treatment: -0.417**

Post: 1.127***

Treatment x Post: -0.258**

TimeFE_2008: 3.862***

TimeFE_2009: 3.849***

TimeFE_2010: 3.851***

TimeFE_2011: 3.689***

TimeFE_2012: 3.598***

TimeFE_2013: 2.832***

TimeFE_2014: 2.417***

TimeFE_2015: 2.467***

TimeFE_2016: 2.451***

(*, and *: significant at the 5%, 1% and 0.1% level)

The estimates in the other specifications are similar (in terms of magnitude and significance).

Does anyone know how to usefully interpret the estimate of treatment*post in terms of its "economic magnitude"? (in the kind of "The estimated coefficient implies a reduction in emissions for treatment installations of about 12% subsequent to the treatment")

One approach I have in mind is to take the average of the absolute (not ln-transformed) emissions in the treatment group in the pre-treatment period and compare them with (1) the post-treatment estimates of the treatment group and (2) the post-treatment estimates of the treatment group without considering the estimate on the interaction term between treatment and post: Effect = (Mean of the yearly post-treatment estimates for the treatment group ignoring the estimate on the interaction of Post and Treatment MINUS Mean of the yearly post-treatment estimates for the treatment group taking into account the estimate on the interaction between Post and Treatment) DIVIDED BY (Mean of the yearly pre-treatment estimates for the treatment group)

Thanks!!

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