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* American Airlines up on smaller-than-expected Q3 loss forecast

* Tesla rises on record China-made vehicle sales in September

NEW YORK, Oct 12 (Reuters) - U.S. stocks finished lower on Tuesday, with investors jittery in the run up to third-quarter earnings, while a jump in Tesla shares helped support the market.

Adding to investor caution, the Federal Reserve is expected to release minutes on Wednesday from its last policy meeting, which market participants will scour for hints about when the U.S. central bank could begin tapering its massive bond-buying program.

Earnings unofficially kick off this week with results from JPMorgan Chase & Co on Wednesday and other banks to follow. JPMorgan's shares were down on the day, while the S&P 500 banks index was also down.

Analysts expect to see strong U.S. profit growth for the third quarter, but investors are worried about how supply chain problems and higher prices will affect Corporate America as businesses emerge from the coronavirus pandemic. A number of companies have warned of issues heading into the reporting period.

"For the most part, institutional portfolio managers are of the view - let's see what earnings look like and how much of a negative impact is being seen from shortages, higher rates and supply chain bottlenecks," said Michael James, managing director of equity trading at Wedbush Securities in Los Angeles.

"A lot of those factors are currently reflected where equity prices are now."

According to preliminary data, the S&P 500 lost 10.79 points, or 0.25%, to end at 4,350.40 points, while the Nasdaq Composite lost 20.27 points, or 0.14%, to 14,465.93. The Dow Jones Industrial Average fell 121.37 points, or 0.35%, to 34,374.69.

Tesla advanced after data showed the electric vehicle maker sold 56,006 China-made vehicles in September, the highest since it started production in Shanghai about two years ago. The company's shares provided the biggest boost to the S&P 500 and the Nasdaq.

Shares of American Airlines Group rose after the company estimated a smaller-than-expected adjusted loss for the third quarter and signaled improved bookings for the rest of the year.

MGM Resorts surged in the wake of Credit Suisse's upgrade of the companies stock to "outperform" from "neutral."

Investors also weighed comments from Fed Vice Chair Richard Clarida, who said the central bank has all but met its employment goal for reducing its bond buying program.

On the economic front, U.S. data showed the labor market remained tight, with a record number of Americans quitting their jobs and job vacancies numbering more than 10 million, stoking inflation fears as employers hike wages to attract and retain workers.

Wednesday's consumer price index report will attract attention from investors seeking clues about inflation. (Additional reporting by Devik Jain, Shreyashi Sanyal in Bengaluru and Federica Urso in Gdansk; Editing by Saumyadeb Chakrabarty, Arun Koyyur and David Gregorio)