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There are a lot of studies that test Ballasa  –Samuelson hypothesis also known as Harrod-BalassaSamuelson effect directly via the effect of productivity, one possible explanation is that PER Capita GDP is not  good explanation for productivity (.i.e. Labor productivity) differences; an increase (decrease) in relative efficiency  of the distribution sector with respect to foreign countries induces depreciation (appreciation) of the exchange rate. After we obtained the number of co-integrated vectors we continue further to see whether the CV tells us something about the long run relationship into the model, likelihood ratio test of exactly identified restrictions test confirms that constant is insignificant variable therefore we can confirm that there is long-run relationship in which the changes in Exchange rate are positively correlated with the changes of ratio of German Consumer Price Index (CPI) to the UK Retail Price Index (RPI). In order to test for relative PPP to support the theoretical relationship between the variables, restrictions are put on the PPP knowing that PPP and that downward movement in the series indicates increase of UK price level relative to German price level. In each EC model there is an EC mechanism and coefficient on the co integrating vector measures the rate per period at which one of the endogenous variables adjusts. In the first equation the error correction mechanism is highly significant and negative. If the system is out of equilibrium, alteration in the change of the exchange rates will be downward (everything else ceteris paribus) compensating around 68% of the  disequilibrium per year. In the second equation error correction mechanism is also highly significant but positive meaning that if the system is in disequilibrium changes of change in the ratio of German CPI relative to UK Retail Price index will rise offsetting 15% of the disequilibrium per year until the equilibrium rate of exchange rate will be achieved. Model implies  German Labor productivity to UK Labor productivity  ratio doesn’t have significant influence on explaining on relative change on prices not even on theexchange rate contrary to Pugh, Beachil study

Empirical Testing of Balassa-Samuelson Hypothesis with German and UK Data