Questions on comparing GDP between various countries What is the difference between OER vs PPP? What fundamentally drives them? Shouldnt an arb opportunity exist and wouldnt that difference then go away? My understanding of OER is the official nominal exchange rate that is quoted by banks and is used by travelers to exchange money. PPP is an estimated exchange rate that is a function of the same good that is sold in different countries (causes being difference in costs/living standards). Is PPP the "real" exchange rate? For a given product, say a hamburger and OER rates of A:B of 10:1, let's say that we can buy 5 hamburgers in A at 20 units of A currency for a total value of 100 A dollars. If we bring them to B and in B, hamburgers are worth 3 units B currency, then our 5 hamburgers are now worth 15 B. If we use the OER to convert back to A, then we would have 150 A of value. Shouldn't this arb go away?
GDP numbers (nominal or real) from various countries are usually reported in their own currency. If one wanted to compare GDP between countries, one would have to use an exchange rate to convert to some common currency. What exchange rate should be used (OER vs PPP... and are there others?) and which GDP (nominal vs real) should be used? My intuition is that OER is usually use and its on nominal GDP (since real is usually indexed but its still possible to compare real by taking inflation and exchange rates into account based on difference between the two years that real GDP are indexed to?)
How do interest rates and inflation affect currency strength (in general?)?


Apologies if these are simple macro concepts. I have a limited understanding
Answer to question 1:

OER is an actual price set by the government. The real exchange rate or RER (That´s how people typically call it) is a ratio of prices of goods, as you mention. 

The arbitrage does not go away because the goods in the RER calculation are not completely tradable. The PPP among tradable goods is closer to 1 (meaning the PPP exchange rate among tradable goods is closer to the OER). You can´t trade hamburgers, they get cold, mushy....

Moreover, goods and services are not the only thing being traded across countries. You also trade capital. So a country that is in vogue for international investors will see lots of demand for its capital, raising the price of everything denominated in its exchange rate. So its goods and services look expensive, but its not that things are in disequilibrium its just a disequilibrium in the goods and services part of the balance of payments, that is balanced by another disequilibrium in the capital part of the balance of payments.

Answer to question 2:

Use nominal GDP, in Dollars or in PPP Dollars. Use dollars if you care about dollars, for example if you want to figure out the likely market size for your good which is produced in the US. Use PPP dollars if you care about local living conditions. PPP adjusted (per capita) GDP is a good way to figure out (economic) living conditions.

Answer to question 3:

High rates should imply higher returns to investors that provide liquidity to the local economy, so they should be connected with a more appreciated currency. High inflation lowers the expected future value of the currency, so it should make holding the currency less desirable instead. This should lead to a more depreciated currency.

However, the answer quickly gets more complicated if you add expectations and monetary policy to the mix. For example, an increase in interest rates that will lead to an expectation of a slowdown in the economy and very low future rates might depreciate the currency; high inflation that will lead to an expectation of a big monetary policy contraction raising interest rates, might appreciate the currency.