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Does standardizing of a dependent variable within the identifying group make sense?

The following working paper (Deforestation slowdown in the Legal Amazon; Prices or Policies?, pdf) uses a standardized dependent variable to analyze the effect of general policy change in Brazil on deforestation.

Standardization is done as as follows:
$$ Y^{new}_{it} = \frac{Y_{it} - \overline{Y_i}}{sd(Y_{it})} $$

The authors argue, this serves to "consider relative variations in deforestation increments within municipalities". The authors use hereby a FE estimation (page 12) for panel data. Including a Post-policy-dummy for each following year after the a new law.

  • How should coefficients be interpreted if the dependent variable was standardized in this way?
  • Is standardization not unorthodox as it gives higher values to observations where the group/municipality experienced lower variations over time?
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the answer at the link below maybe of some help for the first question. Standardized dependent variable and non standardized independent varaible

On the second question: Intuitively, you would want to give higher weight to groups where the standard deviation is lower since then it means that the values dont jump around too much for that group and hence is more representative of the true value.

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