Essay: PPP hypothesis

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  • Subject area(s): Economics essays
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  • Published on: November 7, 2018
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Where denotes the real exchange rate between the two countries. In its weaker relative form, it only requires:

Clearly, the absolute version implies the relative, but not vice versa. Unlike the absolute which requires the real exchange rate of the goods to be in parity, the relative only require that it is constant over time. If the LOP were to hold for each individual good, it must be that it then holds for a basket of goods. Even if deviations from the LOP occur, it may be that they cancel out when aggregated. In the original Casselian view of PPP this basket refers to the general price level of a country, which is measured by the Consumer Price Index (CPI) as a weighted sum of prices. In its absolute form, the PPP hypothesis requires:

Or if we were to take its logarithmic form:

Where and are the logs of the price levels for the domestic and foreign countries respectively. In its absolute form, PPP requires that nominal exchange rates be equal to the price differentials of two identical baskets. However, one glaring problem is that the composition of these baskets and their weightings can very immensely between countries, despite being conceptually similar.

Heterogeneous baskets are less of a concern if we were to believe that price impulses effect all goods in the baskets homogenously. This is, however, unlikely to be the case. There have been efforts to construct an international standardised CPI. The most notable is the “International Comparison Programme” (ICP) by Summers and Heston (1991), which reports absolute PPP estimates using a constructed common basket of goods. However, this is less valuable empirically due to its infrequency and availability for only a few select countries. Sarno and Taylor (2002) argue that the degree of extrapolation used by the ICP makes these estimates partially artificial, and thus less reliable.

There are also other indices related problems, especially in the context of a time series analysis. One is how to address changes in weights, or the introduction and/or removal of goods. In order to account for possible constant differentials between price levels much of the literature focuses on examining PPP in its relative form:

In its relative form, PPP requires that changes in the growth of exchange rates are offset by changes in the growth of price level differences. In other words, whereas absolute PPP is concerned with price level differentials, relative PPP focusses on inflation differentials of the two countries. A second problem is that CPI portrays prices that are relative to its base year value, and test using it only examine deviations of exchange rates and price level differentials from said year. Therefore, unless we are to assume that PPP held over some base period, there is no way to estimate its deviation from the absolute PPP condition. As a result, any empirical work using price indices can only test for relative, and not absolute, PPP. (Crownover et al., 1996)

Relative PPP is the focus of the majority of empirical work done in this field. This is due to the use of price indices as its logarithmic changes roughly equates to its inflation.

1.2 Empirics of PPP

PPP is an almost century old concept. Despite its deceptively simple formulation it has remained a challenge to conclusively identify its existence. In order to appreciate its complexity, it is important to review it empirical history. With each new iteration of econometric techniques there is a wave of research as we are better able to model the dynamics of PPP.

Stage 1: Simple PPP

Early works of PPP testing, through the 1970s, attempted to model Cassel’s (1922) view that PPP was a tendency for exchange rates to revert to PPP that was subject to short run deviations. However, at this point in time there was no theoretical or statistical tools to distinguish between short and long run real effects. Unable to fully model the dynamics, this first stage short run modelling of absolute PPP was usually characterised as:

Where is an error term, or alternatively:

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