Theoretical Description and Empirical Evidence over the Validity of Ppp and the Law of One Price as Its Building Block

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CARDIFF BUSINESS SCHOOL| PURCHASING POWER PARITY AND THE LAW OF ONE PRICE |

Against all odds
Despite being severely criticised for more than three decades the Purchasing Power Parity and its building block - the Law of One Price still play vital role in economics

Introduction
Would you believe in the law of gravity if quite often objects that should stay firmly on the ground were instead flowing weightlessly in the air even though they were not supposed to? Probably not. However, if physicians were economists they would simply attribute it to a marginal error in their calculations and still accept it as a valid law. Among the considerable amount of examples the Purchasing Power Parity (PPP) and its building block – the Law of One Price (LOP) seem to stand out the most due to their fundamental importance for modern economics. Officer (1986) even argues that without the imposition of LOP, there would not even be the traditional "pure theory" of international trade. “Without this law, much of the “monetary theory”, too, would have to be reconstructed” (Officer, 1986). In this essay the Law of One Price and the theory of Purchasing Power Parity (PPP) will be presented. First, a theoretical definition of PPP will be given with short explanation what makes it so important for the contemporary economics and finance. Second, a definition of the LOP will be made as a building block of the PPP. A discussion built around the statement of Isard (1977) that “In the assumed absence of transport costs and trade restrictions, perfect commodity arbitrage insures that each good is uniformly priced (in common currency units) throughout the world – the “law of one price” prevails” will follow with reference to some key empirical research. Some support the law whereas other go as far as suggesting dismissal or at least reformulation of the law. Due to the vast amount of research on the topic this essay will attempt to only summarise and present the findings very briefly. In conclusion the essay will show that even if the law of one price is true, we have no way of verifying it except for a small class of goods or in specific context. The “theory-data gap”— between the specifications which allow the theory to apply and the conditions under which the relevant data can be collected in the real world—is much too large, and shows no signs of becoming smaller. What is Purchasing Power Parity (PPP)?

The concept of purchasing power parity (PPP) can be traced back to as early as 16th-century writings of scholars from the University of Salamanca in Spain (Officer, 1982, cited in Rogoff, 1996). Yet, the definition of PPP as we use it in modern economics is relatively new and is usually credited to Gustav Cassel (1918). The idea behind it is fairly straight forward and intuitive: when measured in common currency, the monies of different countries should have the same purchasing power and be able to purchase the same basket of goods (Reinert et.al., 2009). Stated otherwise - if the market arbitrage enforces broad parity in prices across a sufficient range of individual goods (the law of one price, which is discussed further down), then there should also be a high correlation in aggregate price levels (Rogoff, 1996). To illustrate it with a simplified example the PPP states that in the “long run”, if £100 can buy a certain basket of goods in UK, then, after converting it into US Dollars, the sum should be able to buy approximately the same basket of goods overseas in the United States. While few empirically literate economists take PPP seriously as a short-term proposition, most instinctively believe in some variant of purchasing power parity as an anchor for long-run real exchange rates. Absolute and Relative form

To describe the relationship between exchange rates and national price levels economists usually use one of the two main conditions of PPP – absolute or relative. The first states that the spot exchange rate is determined by the...
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