Relative purchasing power parity

Relative Purchasing Power Parity is an economic theory which predicts a relationship between the inflation rates of two countries over a specified period and the movement in the exchange rate between their two currencies over the same period. It is a dynamic version of the absolute purchasing power parity theory. A reason for the prominence of this concept in economic research is the fact that most countries publish inflation data normalized to an arbitrary year, but not absolute price level data. Suppose that the currency of Country A is called the A$(A-dollar) and the currency of country B is called the B$. The exchange rate between the two countries is quoted as , so country A can be regarded as the "home country". The theory states that if the price in country A of a basket of commodities and services is (measured in A$), then the price of the same basket in country B will be (still measured in A$), where C is a unitless and time-invariant constant. That is, one price level is always a constant multiple of the other. To measure in B$, divide by the exchange rate (now measured in B$). The last identity can be rewritten for t=1 as and because C is time-invariant, this has to hold for all periods, so This can be further transformed to which is the "exact formulation" of the Relative Purchasing Power Parity. Using the common first-order Taylor approximation to the logarithm for close to , this can be written linearly as where lowercase letters denote natural logarithms of the original variables. Using the first-order approximation again on the definition of the inflation rate from t=1 to t=2 allows us to finally rewrite the equation as which implies that the value of A$relative to B$ should depreciate (nominally) by (approximately) the same amount that the inflation in country A exceeds inflation in country B. This is quite intuitive, as an agent in country A with a constant real income stream would ceteris-paribus have a higher purchasing power for goods from country B after one period has passed, but the exchange rate adjusts exactly to offset this advantage by making the currency of country B nominally more expensive.