Actually, no. A higher "domain authority" doesn't have anything to do with your actual search engine rankings. Moz is a third-party company, and their "Domain Authority" score doesn't enter at all into the ranking calculations of Google, Bing, Baidu, or any other search engine.
It is merely Moz's "best guess" at what the search engines might be looking at. You can possibly use it as a rough guide if you need something to reassure yourself you're on the right track, but it certainly isn't something anyone who knows what they're doing needs to obsess over.
Increasing your "domain authority" may or may not have any effect on your actual search rankings. One expert whose opinion I trust once equated "domain authority" with throwing darts at a wall while blindfolded.
This is not intended as a specific knock on Moz. They offer a lot of useful advice, especially for those who are getting started with SEO. It's just that I don't place a whole lot of stock in any
third party rankings that purport to give you a scientific-sounding numeric "ranking" of your site's status or effectiveness.