The phrase refers to a pattern where nonstop fares are roughly $45 lower on routes serviced by Southwest Airlines than those that are not, according to a University of Virginia study. Low-cost carrier Southwest recently revealed that it plans to start selling tickets for service to Hawaii next year.
But Hawaiian Airlines' Dunkerley said he believes the "Southwest Effect" to be most prominent on less competitive routes. He explained that Hawaiian already competes with many other carriers, especially on flights departing from major airports like Los Angeles.
"It's a very competitive marketplace. Adding one more competitor into that marketplace is unlikely to have the kind of effect of adding a competitor when a carrier is sitting on a monopoly, for example," he said.
The CEO said that Hawaiian has a lot of confidence in its business model.
"There is no carrier that is better positioned than we are and we think that doesn't change when United adds capacity, as they're intending to do in 2018, and it won't change when Southwest or any other carrier comes in," Dunkerley said.
Hawaiian shares, however, have fallen 30 percent so far this year. But Dunkerley said investors should focus on the stock's longer-term gains. The shares have surged 198 percent in the last three years.
Dunkerley said that, in the past, Hawaiian has responded well to increased competition in service to the vacation hotspot.
"What we're looking at now is far from unprecedented. Two, three years ago, we had at that time Alaska Airlines move in very aggressively into the marketplace. When the dust settled, our market share went up and our margins went up," Dunkerley said.
— CNBC's Leslie Josephs contributed to this report.