State Treasurer John Chiang laid out a plan Tuesday to create a public bank for marijuana merchants in open defiance of what he called an “out of step” Trump administration fixing to take the hose to California’s sizzling new herbal trade.

Chiang said he and California Attorney General Xavier Becerra have initiated “a methodical and disciplined” cost-benefit analysis to determine whether a public bank would work in California amid the threat of a federal crackdown.

The move comes 30 days after California’s recreational market officially began, creating a financial windfall for marijuana merchants and illuminating a serious problem. Store owners, growers and distributors are being forced to use cash because most banks won’t open accounts for them while the federal government still considers marijuana illegal.

The lack of banking also complicates the state’s efforts to collect taxes from the industry. Every month, thousands of business owners head to the tax collector’s office with piles of cash in shopping bags and suitcases.

“We are contending with the emergence of a multibillion-dollar cannabis industry that needs banking services, and a private banking industry that is stymied by federal law in meeting the needs of the new industry,” said Chiang, who is running for governor. “The current administration is out of step with the will of the people, not only those in California, but the 29 states that have legalized either or both medicinal and recreational-use cannabis.”

Industry leaders estimate that 70 percent of the more than 1,600 recreational and medical dispensaries in the state are still paying employees, suppliers and California’s new 15 percent cannabis tax in cash.

As revenues inevitably increase, they will be lugging larger stacks of 50s and 100s to the tax collector, a situation that everyone agrees makes businesses vulnerable to thievery, violent crime, money laundering and extortion.

The plan, recommended by an 18-member Cannabis Banking Working Group that Chiang set up last year, is to conduct a feasibility study. The treasurer’s office would figure out the costs, benefits and risks of such a system while the attorney general’s office would determine legal and regulatory ramifications.

The studies would make recommendations by the end of the year on the structure and funding of such a bank as well as issues like lending standards, the clearing of checks, insurance, interbank transfers, and whether the bank would be brick-and-mortar or entirely online.

Chiang said his goal is to make sure the industry is fully above board and “regulated to prevent sales to minors, to protect the public’s health and safety, and ensure cannabis businesses behave as legitimate, tax-paying members of our economy.”

The move comes less than a month after U.S. Attorney General Jeff Sessions rescinded an Obama administration request not to prosecute cannabis businesses in states where the drug is legal. The decision would allow federal prosecutors to override state marijuana laws and file criminal charges.

“The recent action taken by Attorney General Sessions threatens us with new national divisiveness and casts into turmoil a newly established industry that is creating jobs and tax revenues,” Chiang said. “Until the slow, clunking machinery of the federal government catches up with the values and will of the people it purportedly serves, states like California will continue to both resist, and more importantly, to lead.”

Chiang, who is working with 19 other states that have legalized medicinal or recreational marijuana, said the feasibility study could provide a framework for other jurisdictions.

It’s not known whether a single public bank can solve a problem that affects so many in the recreational cannabis industry, which is expected to top $5 billion in sales this year.

“I am not convinced that a public bank in California will solve the problems, but it definitely won’t hurt,” said Hezekiah Allen, executive director of the California Growers Association, an advocacy group for more than 1,000 marijuana farmers, business owners and patients around the state. “The problem is antiquated laws at the federal level. Congress must solve that issue, and it is incumbent on everyone who cares about public safety here in our state to call on our government on Washington, D.C., to provide relief.”

California wouldn’t be the first to establish a public bank. Chiang said the first public bank was established in Genoa, Italy, in the early 15th century “to eradicate certain bad practices of bankers.”

North Dakota founded one in 1919 after private banks failed to properly promote agriculture, commerce and industry, he said.

Chiang isn’t the only one trying to solve the cash-only problem. Oakland and San Francisco also have brought up the idea of a public bank. Last week, state Sen. Bob Hertzberg, D-Van Nuys, introduced legislation that would allow state-chartered banks, credit unions and other financial institutions to open accounts and issue checks for marijuana retailers.

Chiang urged California in November to hire armored cars to help pick up the taxes, which industry experts predict will top $1 billion a year. But many courier services are fearful of being targeted by the federal Drug Enforcement Administration, and nothing has been done.

Peter Fimrite is a San Francisco Chronicle staff writer. Email: pfimrite@sfchronicle.com Twitter: @pfimrite