After Engel and Granger (1987) proposed two-step cointegration test theory, a large number of empirical tests were put forward to testify the long term PPP condition. Taylor (1988) enlarged the constraints and tested whether there was a cointegration relationship between the nominal exchange rate and the relative price. The conclusion from his study did not support long-term PPP condition. Diebold et al. (1991) and Cheung, Lai (1993) reached the same conclusion in their studies: their test using co-integration theory does not support long-term PPP condition either. These findings not only led to the development of PPP theory, but also promoted the progress of the quantitative methodology. A basic consensus that the PPP does not hold over a long period is that unit root and co-integration tests have low efficiency (i.e. accepting the false null hypothesis), which led to a potential study to improve the efficiency of tests. So the researchers expanded the sample in two ways to solve this problem: (1) the use of large-span of long-term historical data; (2) using multi-country cross-time series data analysis techniques that is the panel data approach (panel datum.). Both these two methods have their own shortcomings. Also the conclusions of these two tests are not same.
Researches on PPP began to focus on the deviation of the PPP. The key point turns from the test of PPP condition to the decision making of real exchange rate and the rate of convergence to the deviation of the PPP (Enge1, 1996).