Renzi has staked his leadership on a referendum on constitutional reform in October which is aimed at reforming the Senate and supposed to make it easier to govern in Italy. Deadlock in the lawmaking process is a persistent bugbear between the lower and upper houses of parliament in Italy which has made reform (of the labor market as well as the constitution) a slow, tortuous process at a time when the recession-hit economy needed it most.
Although Italy emerged from almost two years of economic contraction in May 2015, it could still be vulnerable to a political shock should the referendum fail; Renzi has threatened to resign if the referendum goes against him, leading to more political upheaval when growth has only recently returned.
Gross domestic product (GDP) expanded by 0.3 percent in the first quarter of 2016 from the previous quarter, and 1 percent from the same period last year. The European Commission expects growth of 1.1 percent in 2016 and 1.3 percent in 2017.
With the economy seeing a fragile recovery, the constitutional referendum is the next "risk event" to watch, Fabio Fois from Barclays said in a note on Monday.
"Without Senate reform, Italy faces the risk of political upheaval, which would be extremely negative for the implementation of those structural reforms (in addition to those already implemented) that are still needed to boost growth," Fois remarked.
"As PM Renzi has stated on many occasions, should the Senate reform be rejected, he will step down and potentially also leave politics. At that point, with about 18 months to go before the next round of national elections, it would likely be very difficult for a care-taker government to implement either the electoral system or the institutional reforms needed to avoid a hung Parliament at the next general election, as happened in 2013."
"While we are aware that the situation may change as the date of the referendum approaches, the surprisingly negative outcome predicted by the early polls may indicate that the referendum has already become charged by other political motivations. We recommend that polls on the referendum and general elections be followed closely together."
More worrying for Italy is the specter of debt and its fragile banking system. Banking stocks have suffered from investor concerns over the amount of government bonds and non-performing loans (NPLs) held by various Italian lenders. The Bank of Italy has said that the latest data available shows there were just over 340 billion euros ($385.3 billion) worth of NPLs on Italian banks' balance sheets at the end of the third quarter of 2015. In addition, government debt remains stubbornly high. The country's debt pile remains the second highest in Europe after Greece (at 132.7 percent of GDP).
Iain Stealey, Portfolio Manager at JPMorgan Asset Management, told CNBC Europe's "Squawk Box" on Monday that Italy had turned a corner economically and that investors should give the country time to focus on growth and reducing its debt pile.
"I think the concern that they've got is that austerity doesn't work. So a couple of years ago the buzzword was 'austerity' and they thought they could try to fix the debt problem that way and that hasn't worked and now they want to try to grow their way out of it and that's the best way to get your debt levels down – and Italy does appear to have turned the corner."
"If you think that they went through a period of a year and a half without growing at all, which is remarkable for such a large economy and such a big player within Europe and they have started to come through that, we're starting to see growth and it's not just real growth, it's nominal growth too – if you can get that high, that's when you can really start bringing your debt burden down."
Stealey added that Italy needed to be given the benefit of the doubt and time to work off its debt.
"We all know it takes time, it takes years to get through these debt burdens," he said.
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