The Big Mac Index is a popular measure of the degree of undervaluation or overvaluation of a certain currency with respect to US dollar (or any other world currency). It is based on the purchasing power parity theory.
Although originally designed by The Economist magazine as a light-hearted introduction to the exchange rate economics, it has been published regularly since then. Moreover, in the recent years, the Big Mac Index has been used as an argument in different debates in prominent magazines. For example, in a 2010 article, The Economist was arguing that the Chinese Yuan is still undervalued by 49%. The prestigious magazine Forbes also used the Big Mac index to argue that the official CPI in US under-reported the inflation.
There are many limitations of the Big Mac Index (such as, the focus a single good). However the most important issue probably refers to the issue of how nontradables (namely those goods and services that can sold only locally and thus cannot be internationally traded) are treated in the construction of the Big Mac Index.
Theoretically, the local price of the Big Mac should include both the prices of tradables and nontradables. Due to the international trade, we could expect that the prices of tradable are equal across countries. However we would also expect that the prices of non-tradables are different. Moreover, it is generally acknowledged that the price of nontradables increases with the level of income per capita, see the study here. That is why we should expect that the bigger the difference between the income level per capita in a certain country and, let’s say, United States, the bigger the differences in the price of nontradables. In the end, the differences in the prices of Big Mac could largely reflect not only the different income per capita between the countries in question, but also the share of nontradables that are part of the Big Mac Index.
This issue becomes more significant when emerging economies like China or India are compared to the US in terms of Big Mac Index. These aspects are discussed by Yang in his paper on the relevance of the Big Mac Index for the evaluation of the Renminbi, see here.
In the end, we can agree that the Big Mac Index has its value, however, things go wrong when people start using this index for more serious purposes.