LONDON (Reuters) - The new Italian government’s latest budget proposals have caused consternation in markets and irritation in Brussels - yet many at the heart of euro policymaking will quietly feel a dose of market discipline is a precisely what’s needed to rein Rome in.

Let the bond vigilantes loose, is how thinking goes. A surge in Italian government borrowing costs and steep drop in the country’s banking stocks have the power to change even the most ambitious budget mathematics and force Italy’s coalition leaders to roll back their plans.

“If they do crazy things, let the market play its role. Market discipline exists, as we have seen,” one policymaker put it recently.

Sounds good in theory. But it may also be a case of “careful what you wish for”. At what point does market discipline in Italy and its related political fallout infect the rest of the euro area and undermine the single currency?

A paper by Guido Tabellini, professor of economics at Bocconi University, published by the Center for Economic Policy Research in July, found that efforts to impose market discipline work “very imperfectly”, even if the economic fundamentals are relatively sound.

“The larger the outstanding debt, the higher the risk that market discipline degenerates into a debt run,” Tabellini wrote, and a crisis of confidence in one euro zone country was likely to spread to others.

“The resilience of the euro area is not much higher than that of its weakest member. For this reason, reforms that increase the vulnerabilities of the weaker countries may be counter-productive for all,” he found.

Italy’s economic fundamentals are not particularly sound, and its outstanding debt is huge. While there’s been relatively little spillover to date from the turmoil in Italian markets, the recent history of euro crises shows it’s dangerous to assume that will remain the case indefinitely.

The scars of 2010-2012 are healing but run deep.

Greece - with an economy almost a tenth the size of Italy’s - was the epicenter of that euro crisis. And yet the financial contagion associated with risk of an unprecedented euro exit ripped through Ireland, Italy, Spain and Portugal - eventually forcing ECB president Mario Draghi to do “whatever it takes” and fire up the bank’s money printing presses to calm the storm.

Italian bond yields hit 7.45 percent in 2011 and the spread over Germany topped 550 basis points. We’re not back there yet, but the 10-year yield is near 3.50 percent and the spread over Germany is 300 bps, both the highest in years.

Since Italy’s general election in May, the country’s stock market has lost 18 percent and bank stocks have plunged 30 percent. Wider contagion has been pretty limited, but at this stage it cannot be blindly dismissed.

SPILLOVER

Goldman Sachs has constructed a model that shows that since 2010, on days when there’s been an equivalent 100 bps rise in Italian yields, Spanish yields rise by around 40 bps, while safe-haven flows push German yields down by around 20 bps.

In equities, this results in Spanish, French and German markets falling 3.5 to 5 percent, and U.S., UK and Japanese stocks falling between 2 and 3 percent.

More broadly, Spanish financial conditions tighten by around 40 bps, and U.S., UK and Japanese conditions tighten by around 20 bps. Thanks to the fall in the euro’s exchange rate and Bund yields, German financial conditions ease by around 15 bps.

(Graphic: Italy contagion scenarios - reut.rs/2OBrIo0)

(Graphic: Italian market contagion 2010-present - reut.rs/2OBlk00)

Spillovers in the 2010-13 period were obviously greater than the years since, but the analysis shows that meaningful moves in Italian bonds do move other markets. Some more than others.

Given how heavily invested Italian banks are in the country’s sovereign bonds, the correlation between BTP futures and euro zone banking stocks is particularly strong.

This week, the simple daily correlation between the two reached 0.76, matching levels seen in May and closing in on the crisis peaks of 0.85 to 0.90 in 2011 and 2012. The highest possible correlation between two asset classes or markets is 1.0.

(Graphic: Italian bonds v euro zone banks correlation - reut.rs/2OwtSFw)

At the root of the current volatility is the budget standoff between Rome and Brussels. Italian government sources told Reuters on Wednesday that next year’s deficit target remains 2.4 percent of gross domestic product, falling to 2 percent in 2021, maybe even lower.

But growth in Italy has been chronically low for years, nowhere near strong enough to prevent the country’s debt-to-GDP ratio from rising. Are these forecasts enough to bring the ratio down to a rate acceptable to Brussels?

Punishment from Brussels over the deficit might not keep Italian politicians up at night, but market forces would. Rising bond yields would damage growth even more, and the perfect storm of weak growth and higher debt funding costs could push the debt-to-GDP ratio to 130 pct even higher.

That would bring the rating agencies back into play. Italy could be downgraded, maybe even by three notches to junk. “The wider connotations of falling down this path don’t bear thinking about,” says Steve Barrow at Standard Bank.

(The opinions expressed here are those of the author, a columnist for Reuters.)