By Herbert Lash

NEW YORK, April 15 (Reuters) - A desire by investors for more investment products contributes to excessive complexity in the U.S. stock market, the U.S. securities regulator in charge of analyzing the stock market's structure said on Tuesday.

The argument that some market participants are continuously seeking to outperform each other through faster and new technology is incomplete, said Gregg Berman, an associate director at the Securities and Exchange Commission.

While the argument has merit, the desire of investors for new products to invest in, such as the explosion in the number of exchange-traded funds and similar products, has required an unavoidable increase in the market's complexity, Berman said.

This complexity also is driving the need for more and faster technologies, Berman told a New York conference about trading.

The speech comes at a time "high-frequency trading" faces fresh scrutiny by law enforcement and securities regulators after an explosive new book by author Michael Lewis that alleges the market is rigged in favor of the tech-savvy traders.

The book portrays a marketplace heavily reliant on expensive technology at the expense of investors who cannot afford to keep pace with the spiraling arms race.

Also on Tuesday, Nobel economics winner Joseph Stiglitz in a paper presented at a Federal Reserve conference in Atlanta again questioned the social value of high-frequency trading.

Berman acknowledged the market is complex, but so is society he said, pointing to the capabilities of his smart phone. But he asked whether the market is too complex or whether it's driven by a desire for more products, like his phone and its countless apps.

"What does it mean for something to be too complex? I consider a system to be too complex if it has more complexity, more moving parts, more stuff - than is required to meet the desires of its users," Berman said.

After a long analysis of stock quote cancellations, which he said debunked many misconceptions about their usage, Berman found that an increase in quotations has been driven by rising usage of ETFs and related arbitrage activity.

"These products require market participants to engage in a lot of active quoting and cancelling if investors want to receive fair prices when they buy or sell these products," he said.

The result is greater complexity. "More linkages are created and more speed, and certainly more computing power is needed to continue to ensure prices stay in line," he said.

Berman emphasized that he did not find the increase in ETFs worrisome or problematic. His observations came after a study of order cancellations over a 21-month period by staff using the SEC's Market Information and Data Analysis System, or MIDAS.

(Reporting by Herbert Lash; Editing by Cynthia Osterman)