* Negative rate has not yet forced core banks to lend
* Euro slightly weaker, money market rates low and stable
* Government debt costs fall but some warn of bond bubble
* Hunt for yield so far helping peripheral banks
By Marius Zaharia
LONDON, July 1 (Reuters) - The European Central Bank's move a month ago to start charging banks for keeping spare cash on overnight deposit has not yet reanimated euro zone money markets although it is helping to keep short-term rates low and steady.
Fully functioning money markets would make the ECB's ultra-easy monetary policy more effective. If banks cannot get funding in the market they will not lend to businesses and consumers as the central bank intends, spurring economic growth across the 18-country currency bloc.
Take-up at the ECB's weekly offerings of unlimited one-week loans to banks remains high, however, suggesting banks in the euro zone's wealthier northern states are still wary of lending to cash-starved peers in the south.
"Will (negative deposit rates) encourage lending? We haven't seen much of that," said Antonio Garcia Pascual, chief euro area economist at Barclays. "Banks in the core remain risk-averse and they don't want exposure to the periphery."
The daily average turnover in overnight bank-to-bank lending markets since the ECB cut its deposit rate to -0.1 percent on June 5 was 27.3 billion euros, just a tad above the 26.5 billion average for 2014, Reuters calculations show.
On Tuesday, banks took 97 billion euros from the ECB in one-week loans, compared with 115 billion euros maturing.
The minor drop reflects the fact that banks needed more liquidity in the previous week for quarter-end window dressing rather than improved access to market funding, analysts said, and this year has seen smaller weekly take-ups.
The negative deposit rate has had some impact elsewhere.
The euro is trading below $1.37, above where it was when the ECB met on June 5 but down from over $1.39 before the ECB flagged the cut in May. A weaker euro helps exporters and prevents further downward pressure on inflation, which is already running well below target at just 0.5 percent.
The negative rate has also effectively removed the risk of spikes in money market rates, which would be akin to tighter, potentially growth-crippling monetary policy conditions. Since the June ECB meeting, the average overnight Eonia bank-to-bank lending rate has been 0.05 percent, compared with an average of 0.21 percent in 2014 before the meeting.
Societe Generale's head of fixed income and forex strategy, Vincent Chaigneau, said some banks have already lent cash at a negative rate and that Eonia might soon turn negative for the first time in its history.
He said this penalty would eventually push cash-rich banks to take more risk and lend to their weaker peers.
"There is still fragmentation in the system ... and it's not going to disappear overnight," Chaigneau said. "But I do believe that excess liquidity has become more undesirable and in time that will have an impact."
The money that banks in the euro zone have beyond what they need for their day-to-day operations stood at almost 170 billion euros on Tuesday.
Another impact of the negative deposit rate has been a move lower in borrowing costs for euro zone governments. While some of those countries would welcome this after years of struggling with unsustainable costs, some analysts warn of a bond bubble.
Hyun Song Shin, an economic adviser to the Bank for International Settlements, said pension funds and other long-term investors are taking ever bigger risks to maximise returns and could be laying the ground for renewed turmoil when money becomes more expensive around the world.
This hunt for yield, whether sustainable or not, is helping peripheral euro zone banks look healthier on paper.
Traders said stronger banks have been more willing to park some of their excess cash in Italian and Spanish T-bills rather than in German ones, which have negative yields. They buy those assets from peripheral banks.
Since the ECB flagged the move in May, yields on Italian three-month T-bills have fallen some 40 bps to 0.16 percent, with a similarly large move in Spanish and Portuguese T-bills. In comparison, German three-month T-bill yields have fallen 9 bps to minus 0.03 percent.
"The main avenue for the money to go to the peripheral banks is through asset sales. Peripheral banks will continue to deleverage and they can use the money to pay back the ECB," said Gianluca Ziglio, an analyst with Sunrise Brokers. (Editing by Nigel Stephenson and Catherine Evans)