The European Central Bank rarely misses an opportunity to criticise governments over excessive deficits or failure to reform.

But there is one subject, much closer to its heart, on which the ECB has chosen to stay suspiciously silent. It is the story of the Bank of Italy, one of the ECB's shareholders, sliding ever deeper into a mud of allegations relating to the handling of recent takeover bids in the Italian banking sector.

It was always tacitly assumed that Antonio Fazio, governor of the Bank of Italy, discouraged foreign takeovers in the Italian banking sector. But what used to be a vague suspicion has turned into something more concrete after the embarrassing leak in July of a telephone conversion between Mr Fazio and the chairman of Banca Popolare Italiana. This conversation came just minutes after Mr Fazio had given the go-ahead for BPI's takeover bid for Banca Antonveneta, another Italian bank. The other bidder was ABN Amro, a Dutch bank. Further transcripts suggested Mr Fazio had overruled his own inspectors, who had spotted some problems with BPI's bid.

Since the publication of the transcripts, Mr Fazio has been facing calls for his resignation. Last week, three well-known Italian economists - Alberto Alesina of Harvard University, Guido Tabellini of Milan's Bocconi University and Luigi Zingales of the University of Chicago - called for an urgent change to the central bank's statutes.

But this is not an entirely Italian affair. It has implications for the eurozone at large. Most economists and central bankers would agree that integrated financial markets are a prerequisite for a single currency to function properly. The reason is that money needs to flow through the system as efficiently as possible. The European Union is still struggling to create a fully fledged single market for banking and financial services. IfMr Fazio, who is also a governor of the ECB, has protected domestic banks against foreign takeovers, he has acted to the detriment of the eurozone, in breach of his responsibilities.

Unlike most other central banks, the Bank of Italy is not a fully state-owned institution. Its shareholders are commercial banks. Article three of its statutes says public institutions and public-owned enterprises must constitute a majority of its shareholders. There used to be no conflict as long as most banks were state-owned. But after a series of bank privatisations in the 1990s, the majority shareholders are now in the private sector. This is in apparent breach of the Bank's own statutes.

The problem is that the Bank of Italy is not just a central bank but also a banking regulator. This essentially means the Bank of Italy regulates its majority shareholders. It does not take a conspiratorial mind to detect conflicts of interest in this arrangement.

Mario Monti, the former European competition commissioner, has proposed four reforms for the Bank of Italy: changes to its shareholding structure; changes to the way its management takes decisions; changes to its regulatory functions; and the abolition of the life-long term of office for the central bank governor.

Because of the lifetime tenure rule, Mr Fazio is answerable to nobody. The excuse for the life-long appointment was to guarantee the governor's independence. But this is clearly overkill. One could easily achieve that goal with a fixed-term appointment, as is the case in many other central banks.

A lifelong appointment is nothing but an extreme form of restrictive labour market practice. Considering that central bankers are among the loudest advocates of labour market flexibility, this smacks of hypocrisy. The truth is that central banks are among the least reformed bureaucracies in Europe and the banking sector they control is one the most protected industries.

As life-long governor of the Bank of Italy, Mr Fazio is by extension also a life member of the governing council of the ECB, which sets interest rates for the eurozone. As the Bank of Italy is a participant of the European System of Central Banks and a shareholder in the ECB, it follows that Italy's commercial banks are indirectly also the shareholders of the ECB.

This is a problem that affects the rest of the eurozone much more directly than would appear at first sight. It constitutes a serious malfunctioning of Europe's central banking system. This should be of great concern to the ECB. It is possible ECB officials are holding behind the scenes talks with the Bank of Italy. But the ECB's public silence on this affair is deafening.

Mr Fazio's loyal supporters have tried to deflect attention by insisting that the real scandal was the invasion of privacy Mr Fazio and other bankers suffered. This is nonsense. These published transcripts have greatly served the public interest because they have given us a unique insight into the close-knit world of banking regulation in Italy.

There is an unspoken rule among central bankers that you never criticise one of your own. Recently, I was listening to a discussion panel chaired by a former central banker and including a current central banker. The former central banker said to the current central banker: "No matter what you are going to say, I shall agree with you."

This is the spirit of central banking, and I suspect it is also the reason for the silence from Frankfurt.