If the Phillipine peso falls in value against the USD by 5% in a year, but the domestic inflation rate in the Phillipines is 10%, compared to 2% in the USA, the nominal exchange rate has fallen (by 5%), but the real exchange rate has risen by 3%.
Could anyone help me explain why "the real exchange rate has risen by 3%."?
A Word of caution: it is not the RER that rises or falls. It is currencies. A currency (in this case the PH peso) either appreciates or depreciates relative to another. The PH peso appreciates in real terms when the cost of a PH basket of godos falls relative to the cost of the same basket in the US, when both baskets are expressed in the same currency. Let P be the Price index for PH and P* be the Price index for US. If E is defines as the number of dollars that must be given up in Exchange for one PH peso, then the RER can be defined as:
This indicates the number of PH baskets that must be given up in exchange to obtain a similar basket of US godos. If this number raises then the PH peso has appreciated in real terms vis-avis the US dollar.
Taking percentage changes and ignoring second order terms: