President Reagan was right when he suggested the other day that it would be more proper if House Speaker Jim Wright were investigated by an independent counsel instead of the House ethics committee.

This suggestion is being resisted on the grounds that the proposed outside investigation would be longer, more costly, and supposedly more political.Perhaps the most telling objection is that there's no legal authority for an investigation of the House Speaker by an independent counsel of the kind set up by law to look into allegations of wrongdoing by officers of the executive branch. The Justice Department has challenged the constitutionality of that law.

But the objections are way off base, and the case for assigning an independent counsel to investigate Wright is compelling.

To begin with, the House ethics committee now conducting the investigation - which it undertook reluctantly - is composed of six Democrats and six Republicans. This even division is supposed to prevent partisan domination. But it also creates the potential for a deadlock.

Then, again, there's also the possibility that Republican members of the committee might go easy on Wright, even though he's a Democrat, simply because the House Speaker is so powerful.

As The Los Angeles Times recently noted in arguing for the investigation of Wright by an independent counsel, the tiny staff of the House ethics committee is "inadequate for the task ahead."

What about legal barriers to an independent investigation? They can be overcome simply by not using the challenged law but instead having the independent counsel appointed by the House ethics committee.

Perhaps the strongest argument for an independent investigator is the indication that the House committee may not be doing as thorough a job as necessary. The ethics committee is looking into six possible violations of House rules by Wright, but the investigation evidently needs to probe even wider and deeper judging from new allegations about Wright that the committee has failed to mention so far.

The latest allegations concern the marketing of the Texas Democrat's book, "Reflections of a Public Man." It seems that the book was sold in mass quantities to lobbyists and political cronies in such a way as to circumvent House rules against excessive outside income.

For example, Fort Worth developer Gene Payte, who bought thousands of dollars worth of the book, told the New York Times "I couldn't give him any money. There are rules against that. So I bought his book." Similar mass purchases were also made by the Teamsters union, a board member of the National Education Association, the president of a university that received Wright's help in winning federal grants, and several Washington lobbyists. Scripps Howard News Service adds that a $2,000 order came from an insurance company as a substitute for a speaking fee.

House rules limit such fees - and gifts from anyone with a direct interest in legislation. Investigators should determine whether Wright's publishing venture was just an honest exercise in bad judgment or an unethical scheme to launder improper payments through his publisher.

In any event, the more the public learns about House Speaker Wright's financial dealings, the clearer becomes the need for an independent investigation by a special counsel.