There’s no doubt that increased trade has weakened the American manufacturing base, just as it has strengthened the services sector. This agreement, however, should not significantly increase imports of manufactured goods to the United States. Six of the 11 other nations in the TPP already have free-trade agreements with us. And the other five face only minimal tariffs.

A second myth is that the TPP would degrade labor and environmental standards and raise drug costs. But the accord includes protections directly drawn from the International Labor Organization, with strong enforcement mechanisms. As for the environment, there is nothing new in the TPP that would affect existing dispute-resolution mechanisms. Finally, it is far from certain that new protections for drug companies would lead to higher drug costs.

A third myth is that the TPP is flawed because it won’t prevent countries from competing unfairly by devaluing their currencies to stimulate exports. This criticism is shortsighted. When the Federal Reserve, having lowered its key interest rate to nearly zero, began extensive bond-buying in 2009, the trading value of the dollar fell against most other currencies. There was severe criticism from Europe and Asia that we were unfairly depreciating the dollar to improve our trade position. Of course, the Fed’s sole goal was to revive spending and investment here. Now, both the European Central Bank and the Bank of Japan have initiated their own versions of extreme monetary easing. And, in response, the trading value of the dollar has risen against the euro and the yen. But the eurozone and Japan aren’t trying to start a trade war any more than we were. We should hope their monetary policies succeed in spurring growth, because then their demand for American exports will rise. What’s more, China, widely seen as the main culprit in currency manipulation, isn’t part of the TPP. The International Monetary Fund should remain the venue for challenging what are judged to be illegitimate government interventions to drive down their currencies.

The benefits of the TPP are many. It would further open the 12-nation region to trade in services and agriculture, two sectors in which the United States historically runs large trade surpluses. Better protection of American intellectual property will help industries, from high-tech manufacturing to Hollywood, in which Asian piracy has been rampant.

Free trade leads to greater overall prosperity. The gains from free trade need to be widely shared, but defeating the TPP would not solve America’s problems with inequality. Instead, it would further rattle our allies. “Further” is the key word here, as there already are rising doubts about American reliability — the result of the debt-ceiling crises, government shutdowns, the failure to follow through on threats in Syria and, most recently, the letter addressed to Iran from 47 senators. If the TPP fails, countries that, rightly or wrongly, see Washington as ineffective will pay America less heed.