* Bank cuts rate for second month in a row
* Chile economy gradually slowing, demand cooling
* Inflation has fallen below central bank's target
By Anthony Esposito
SANTIAGO, Nov 19 (Reuters) - Chile's central bank cut its key interest rate by a quarter of a percentage point to 4.50 percent on Tuesday, the second reduction in as many months, to try to stimulate a cooling economy.
Chilean market watchers had been fairly evenly split on whether the bank would hold the rate steady or follow up last month's surprise 25-basis-point reduction with another cut.
"Domestically, economic activity has continued to evolve at a moderate pace, in line with the scenario depicted in the last Monetary Policy Report," the bank said in its statement.
"Third-quarter data and revised figures of earlier quarters confirm the slowdown of all the components of final demand, as was projected."
The bank cut the rate to 4.75 percent from 5.0 percent on Oct. 17, citing slower world growth, less favorable terms of trade, and expectations for cooling domestic demand.
Since then, domestic demand, an important driver of the economy, has continued to slow. It expanded by 1.3 percent in the third quarter, compared with the year-before quarter, versus growth of 4.1 percent in the second quarter of 2013 and 8.3 percent in the third quarter of 2012.
Annual inflation has also fallen well below the central bank's 2 to 4 percent target range.
"Inflation is behaving moderately and market expectations foresee that it will gradually normalize toward 3 percent within the next 24 months," the bank said.
Earlier this month, the bank left the door open to more interest rate cuts, saying the timing of any future monetary policy moves will depend on how economic conditions evolve at home and abroad.
"Undoubtedly the central bank has started a rate-cut cycle, and regardless of whether it continues to cut in December or January, it probably won't end the cycle until the rate reaches 4 percent," said Pablo Correa, chief economist with Santander Chile.
Interest rates closer to 4 percent were more suited to Chile's economic growth, he added. The bank has forecast 2013 growth of between 4 and 4.5 percent in the top copper exporter.
In central bank polls last week, traders and analysts said they saw a cut to 4.25 percent within six months.
But a stronger-than-expected growth spurt in the third quarter and a wide current account deficit had led some analysts to believe the bank would hold the key rate steady on Tuesday.