# Change vs Difference

I have data on "share in labor employed in manual occupations" for two years (i.e. 1980 and 2005) and looking to create the following dependent variable:

change in the share of labor employed in manual occupation over the period 1980-2005

Which is the appropriate method based on the definition in bold above?

1. Share in 2005 - Share in 1980

2. (Share in 2005 - Share in 1980)/(Share in 1980)

My best guess: given that I am dealing with "shares", method 1 would be appropriate.

1 gives you the percentage point (p.p.) difference, 2 gives you the percentage difference.

There is no rule that says that if you're dealing with shares, you have to use 1. The reason 1 is preferred is that, when the measurement unit is in percentage, things get confusing quickly (e.g. going from a 2% to a 1% interest rate is a 50 percent reduction in the interest rate, but of course only a 1 p.p. reduction).

In your case, 2 could be meaningful, though. For example, "the share in labor employed in manufacturing decreased by half". A compromise could be to express the change in percentage points to avoid confusion, and then add the percentage change if it is meaningful (e.g. the labor share decreased by 20 p.p., a reduction of 50%).

• +1, but I am not sure that 1 is actually preferred. You see the option 2 being applied quite often in the papers (especially in policy literature), even though you are right it can be deceiving if a person does not pay attention to the original percentages (although this does not just hold for percentages but ordinary numbers as well increase in car accidents from 1 to 2 is 100% change)
– 1muflon1
Commented Jan 3, 2021 at 21:25
• I guess the message really is, always provide the full picture / think about what is the correct way to present it in a particular case. I do have the sense that percentage point is seen as more correct (see f.e. the Wikipedia page for p.p.), but I'm sure it depends on convention too. Commented Jan 3, 2021 at 23:58
• No I agree it is not more correct mathematically, but in policy evaluation studies you will see it more often because although this will sound sad it is easier to publish and you will get more exposure when you report large positive result. Although this being said since there is no correct way how to present 1 or 2 it is not duplicitous to use 2 to make numbers look nicer - in the end as long as the readers are careful it should not matter as same information is conveyed
– 1muflon1
Commented Jan 4, 2021 at 0:01