Interpreting Log transformed ITSA model

[Andrew Adkins Second]

This question might not be so much as a programming question as an interpretation question.

I have a sample dataset as follows:

* Example generated by -dataex-. For more info, type help dataex
clear
input byte id str8 date byte month_num int year byte seq float(oc_per10000 ec_per10000) byte period
1 "Jan 2022"  1 2022  1  632.7574 4.2058268 0
1 "Feb 2022"  2 2022  2 572.58765 4.0631905 0
1 "Mar 2022"  3 2022  3   633.962  4.245679 0
1 "Apr 2022"  4 2022  4 605.58405 3.6853316 0
1 "May 2022"  5 2022  5  616.6671 4.1147165 0
1 "Jun 2022"  .    .  .         .         . .
1 "Jul 2022"  7 2022  6  596.7175  5.263053 1
1 "Aug 2022"  8 2022  7  620.8705  5.038163 1
1 "Sep 2022"  9 2022  8  571.1929 4.3138437 1
1 "Oct 2022" 10 2022  9  577.1292  4.168524 1
1 "Nov 2022" 11 2022 10  560.5041 4.1477256 1
2 "Jan 2022"  1 2022  1  632.7574 4.2058268 0
2 "Feb 2022"  2 2022  2 572.58765 4.0631905 0
2 "Mar 2022"  3 2022  3   633.962  4.245679 0
2 "Apr 2022"  4 2022  4 605.58405 3.6853316 0
2 "May 2022"  5 2022  5  616.6671 4.1147165 0
2 "Jun 2022"  .    .  .         .         . .
2 "Jul 2022"  7 2022  6  596.7175  5.263053 1
2 "Aug 2022"  8 2022  7  620.8705  5.038163 1
2 "Sep 2022"  9 2022  8  571.1929 4.3138437 1
2 "Oct 2022" 10 2022  9  577.1292  4.168524 1
2 "Nov 2022" 11 2022 10  560.5041 4.1477256 1
end

* Declare data to be time-series data
tsset id monthly

* sort by ID and time
sort id monthly

di monthly("2022m7","YM")

*log for percentage point change;
gen logec_per10000=ln(ec_per10000)
gen logoc_per10000=ln(oc_per10000)

*ITSA initial model;
itsa ec_per10000, single treat(1) trperiod(750) posttrend replace
*test for autocorrelation;
actest ,lags(9) 
*ITSA final model;
itsa ec_per10000, single treat(1) trperiod(750) posttrend replace force
*ITSA Log;
itsa logec_per10000, single treat(1) trperiod(750) posttrend fig replace force

My question is how to interpret the coefficients on the log transformed itsa for _t (pre-trend), _b[_t]+_b[_x_t2022m7] (post-trend), and _x_t2022m7 (change in trend).

1. When you log transform the dependent variable, is taking the natural log the appropriate method?
2. Do I have to further exponentiate the coefficients to interpret it as a monthly growth rate? (i.e., (exp(coef)-1)*100)?

Thanks,

[Jared Greathouse]

1: yes. 2: Yes, I believe so.

Why not just use the real growth rate?

[Andrew Adkins Second]

1: yes. 2: Yes, I believe so.

Why not just use the real growth rate?

It’s an interpretation thing—our field prefers interpretation as percent growth rather than real rate since it’s more interpretable I suppose. Two follow up questions:

1. how do you interpret the real growth rate?
2. Similarly, how would you interpret the coefficient on log transformed dependent variable from itsa if it's capturing volume per 10000?

thanks,

[Jared Greathouse]

The second question doesn't change, it's take just the % change in the rate.

Real growth rate is just the percentage change in growth rate after the intervention- I think! I'd really need to ask a microeconomist who works with growth rates more

[Andrew Adkins Second]

The second question doesn't change, it's take just the % change in the rate.

Real growth rate is just the percentage change in growth rate after the intervention- I think! I'd really need to ask a microeconomist who works with growth rates more

Apologies if the questions are rudimentary but using the link you provided, I derive a monthly growth rate:

 
 . gen g_ecper1000 = D.logec_per10000  
 *Re-estimate ITSA model; itsa g_ecper1000, single treat(1) trperiod(750) posttrend replace

1. How would you interpret the coefficient on the term for _t, for example assuming the coefficient is 0.0250218.
2. My intention is to say something to the effect that the monthly volume decreased by X% leading up to the intervention and so forth in terms of interpretation
3. Alternatively, since I have gaps, can I just use logec_per10000 as my Y then use (exp(coef)-1)*100) to interpret this as a volume decrease by X%?