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I am running an impact evaluation to investigate the impact of a specific program on several indicators x. These indicators have values between 0 and up to 10000, and a high standard deviation.

For my purpose, I'd like to create one index for each indicator each that takes into account the initial level of the indicator x in the base year (year=0) and the change between the base year and the post-intervention year (year=1), for each observation (household). The index should be constructed from two components, the initial level wi and the change diffi, with wi and diffi each being normalized (0 to 1) and wi X diffi making the indicator. At least, thats how it was done in a previous paper, where the variables, however, had logical limits, i.e. months per year etc.

A total loss of the initial value between year 0 and year 1 (i.e. diffi=-100%) should be 0 and a gain of 100% or more (.e. diffi >= 100%) should be 1. I cannot simply focus on the change itself, as initial levels determine the "impact" of the change on the household (outcome variables are measures for food security in a drought-affected developing country).

Do you have any suggestions?

Lukas Borkowski
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This sounds like a candidate for a log-transform of the diff variable. That way you'll be effectively measuring the percentage change in the variable. The losses will be transformed to negative values and the gains will be positive. If you felt that the percentage change was still impacted by the initial value, you could also use that as an offset term or as a predictor in your model.

Mike Nute
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  • By predictor you mean I should use the initial level of x in year=1 as additional explanatory variable in my regression model? Well, I cannot do that in all of my models as I am estimating the ATT using a specific Stata command (psmatch2) that allows to include the additional variable in the equation to estimate the propensity score, but it is not possible to include additional explanatory variables to estimate the ATT on the outcome variable. Hence, I need to construct an integrated index, based on wi and diff. – Lukas Borkowski Aug 13 '13 at 18:54
  • I just meant if you thought that the percent change would vary depending on the initial value, then you could use it as one of the explanatory variables. But it's not strictly necessary, just use a log transform of the difference between the year=1 value and the year=0 value, and that could be an effective index. – Mike Nute Aug 14 '13 at 07:22