Constraints on Statements about Larger GDP in LCU
It's a holiday in Somalia, it's tough, kid, but it's life.
Imagine you want to declare that the GDP in your developmental examplar is undervalued by some large percentage. You can do it in two ways.
At first, you can declare that the purchasing power in the selected place is far higher due to a mix of degeneracy of rich countries and economic theories like a Ricardo–Viner–Harrod–Balassa–Samuelson–Penn–Bhagwati effect. It’s a respectful idea and it’s far harder to check because these types of comparisons are very hard if not impossible. We are not talking about it here.
The second is to declare that an official government is undercounting GDP in local currency units. It’s an argument à la Bramal about how the government doesn’t understand how exactly good they are having it because they don’t collect proper statistics about large sectors of economy whatever it’s services, real estates or “informal economy” at large.
We will concentrate on the second idea here. The fundamental check on these kinds of exercises is not exactly obvious and people rarely apply it. It based on two trivial ideas that (1) the government knows relatively well how much money it collects in taxes (2) richer countries collect more taxes and you shouldn’t end up in Somalia by tax collection after you decide that you are so much richer. (1) is not exactly true because you have a different levels of government, weird semi-government structures (Iran is famous for it) which makes an aggregation harder, but it’s generally doable.
Imagine that
t: Official tax collection as a share of official GDP (e.g., 0.2 for 20%).
Y: Official GDP (reported value).
g: Rate by which GDP is underreported (e.g., 0.1 for 10%)
r: Real tax collection rate as a share of GDP
\(r = \frac{t \cdot Y}{Y \cdot (1 + g)} = \frac{t}{1 + g}\)
[r = t / (1 + g)]
Now you can plug your g and check your peers.
For example, if you are collecting 23% of GDP as taxes (as defined by IMF), but you decide that your GDP is undervalued by 50% in LCU, you can look at countries that collect 15% of GDP as taxes. If you think that it’s 100%, you can think about finding yourself with Somalia, Ethiopia, and Sudan with 7% of GDP.
It’s especially relevant for leftwing people and institutionalists who think that countries generally should be collecting more taxes as they get richer and it’s a way how they are getting richer in general.