The findings of a recent European Central Bank report into household wealth have inflamed public opinion in Germany. In 2010, the average net wealth of German households – all assets minus all liabilities – stood at €195,000 (£168,000). In the southern member states, the figures were surprisingly high: €291,000 in Spain, €275,000 in Italy, €153,000 in Portugal, €148,000 in Greece and, wait for it, €671,000 in Cyprus. It makes it look as if the German people have been asked to rescue southerners who are often richer than their rescuers. "The poverty lie", says the front page of this week's Der Spiegel. Are German citizens right to be annoyed? The answer is yes, but they have chosen the wrong target.

The answer to why some southerners appear richer than Germans is straightforward: housing. The systems through which European nations meet their housing needs differ widely, reflecting history, politics, and social custom. Germans and Austrians tend to rent their houses. Spaniards, Italians, Greeks, Cypriots and others have very high percentages of owner occupation. With steadily higher inflation in the periphery during the last 15 years, plus outright housing speculation in Spain and Cyprus, the value of houses has risen, making southerners appear richer.

Households also have debts, though, which must be serviced out of income. How do southerners compare with Germans in this respect? Judging by the ratio of household debts to assets, Germans appear to be worse off than southerners, which is quite natural, since southerners have overvalued houses and so large assets. But when it comes to servicing debts, things are very different. The ratio of household debts to income is 37% in Germany, but 114% in Spain, 50% in Italy, 134% in Portugal, 47% in Greece and 157% in Cyprus. Not so rich in the periphery, then.

Low net wealth in Germany has nothing to do with Germans being taken for a ride by southerners, but reflects the failure of the European monetary union. For about 15 years German governments have been following a strict policy of very low wage increases, thus holding inflation below that of other EMU countries, and even below the inflation target of the ECB. By doing so, Germany has kept the prices of its exports low, creating an enormous advantage for its exporters within the EMU.

Peripheral enterprises have thus found it difficult to compete against German enterprises, and eurozone markets have become dominated by German industry. However, in the domestic German economy it has been another story. Since wage increases have been low, demand has been weak, incomes have been rising slowly, and inequality has increased greatly. Most German people have been counting the pennies and, as we know, have not accumulated substantial wealth. Their main benefit has been relatively low unemployment on the back of strong exports.

Meanwhile, the German export juggernaut has caused mayhem in the rest of the EMU. Peripheral countries, unable to compete, have accumulated huge public and private debts. Indebtedness masked their inherent weakness for a while by boosting domestic consumption and, in some countries, leading to a housing bubble. But then the global crisis arrived and the essential failure of peripheral Europe became evident. The southerners have found themselves sitting on overvalued houses while holding large debts that they can hardly service. Riches indeed.

Germany's plan to fix this mess has made things even worse. Peripheral countries have been forced to cut wages to increase their competitiveness as well as adopting austerity. Inevitably, the result is deep recession and rising unemployment. The apparently rich southerners are now teetering on the edge of depression, their incomes falling and the value of their houses declining. Their wealth is disappearing and yet their debts persist and are becoming more and more difficult to service. If Germany forces southerners to commit some of their putative wealth to meeting the costs of the crisis, for example, by having a "haircut" on bank accounts, as has happened in Cyprus, the result will be accelerated economic devastation.

The German public is right to be annoyed at how things have turned out in the eurozone. But it should seek the real culprit, which is the German policy of keeping wages low, suppressing domestic demand and increasing exports. That is the cause of income tightness, and even poverty, in Germany. If Germans want an effective answer, they should not seek to punish the imaginary rich of the south even further but instead aim for higher wages, boosting domestic demand and reducing the weight of exports. Now, that is a fight worth fighting.

• This article was amended on 17 April 2013. It originally stated that average net wealth in a list of southern eurozone countries was much higher than in Germany. In two of those countries, Greece and Portugal, the figure is actually lower than in Germany. This error, introduced in editing, has now been corrected.