Marginal Effects, Normalization, and Percentage Changes

[Jared Greathouse]

Consider the following

clear *
u "http://fmwww.bc.edu/repec/bocode/s/scul_basque.dta", clear

qui xtset
local lbl: value label `r(panelvar)'

loc unit ="Basque Country (Pais Vasco)":`lbl'


loc int_time = 1975

qui xtset
cls

g treat = cond(`r(panelvar)'==`unit' & `r(timevar)' >= `int_time',1,0)

cls
xtdidreg (gdp) (treat), group(id) time(year)

preserve
    qui su year if treat==1

    
    tempvar _XnormVar _xXnormVar
            
    loc pretreatm1 = r(min)-1
    
    qui g `_XnormVar' = gdp if year== `pretreatm1'
    
    
    qbys id: egen `_xXnormVar' = max(`_XnormVar')
    
    qui replace gdp = 1*gdp/`_xXnormVar'

xtdidreg (gdp) (treat), group(id) time(year)
restore

The first DD regression gives the levels effect of terrorism in the Basque Country.

The second regression does the same, but it follows code from Wiltshire 2022 Justin Wiltshire where he remarks (page 6) that this formula

normaliz[es the outcome] for each i and all its donor pool units to the final pre-treatment period for i (Y 0 jt i = 100 ×Yjt/YjT0i) to ensure the estimated marginal treatment effects, τˆie, are measured in deviations from a common null just prior to treatment, in units that are meaningfully comparable such that their average, ˆτ e, retains maximum interpretability

My question is, is this marginal treatment effect equivalent to the percentage change? Put differently, does the second DD regression imply that terrorism, on average, decreased Basque GDP by 23.5% compared to what it otherwise would've been had terrorism not happened?