This paper analyses the efficient market hypothesis. It proposes a new method of testing the efficient market hypothesis based on the idea of Shiller (1979). Using a GARCH model, we test whether the excess volatility in the German and US sovereign debt markets is an indication of inefficient markets during different periods. The results indicate that omitting structural breaks may lead to wrong results. We find that although both debts were efficient during some periods and inefficient during other periods of time. Taking all periods together the financial markets appear to be inefficient. Hence, the general outcome was that both financial markets are not efficient markets.