在上面的方程中,,,,的自然对数,、和分别。考虑运输成本和其他错误的价格指数,我们可以允许等式的右边是任何固定不变,它可能不等于名义汇率的开始时期。因此,越来越多的经济学家倾向于进一步扩大上述条件,一个变量测试实际汇率的稳定方程(3 – 1),并代表名义汇率分别为开始和结束的时期。和分别为国内外价格水平。通过自然日志方程和进一步转变我们的差异:。尽管上述方程与传统理论不同,它需要国内外价格指数对称,相对价格,另一方面应该成正比的汇率。所以它仍然是一个严格的形式的购买力平价,不是完全远离传统的购买力平价理论。
In the equation above, , , , are the natural logarithms of , , , and respectively. Consider transportation costs and other errors in price indices, we may allow the right hand side of the equation to be any fixed constant, it may not equal to the nominal exchange rate at the beginning of the period. Therefore, more and more economists tend to enlarge the above conditions further, to a single variable testing the stationary of the real exchange rate In equation (3-1) , and represent the nominal exchange rate at the beginning and the end of the period respectively. and are the domestic and foreign price levels respectively. By taking natural log differences of equation and transforming further we get: .Although the above equation is different from the traditional theory, it requires domestic and foreign price index symmetry, and on the other hand relative prices should be proportional to the exchange rates. So it is still a strict form of purchasing power parity, not completely away from the traditional purchasing power parity theory.