There are plenty of case studies proving that regular links coming in from relevant websites in your niche are important to ranking. When it comes to local that is much harder to do as typically local sites are low authority and most folks wont link back to you from their websites.
In other words if you are a roofing company you want high authority dofollow links coming in from sites talking about roofing. Even better if your page on your site is talking about Roof Repairs and there are sites also talking about Roof Repairs linking to your Roof Repair page you are Golden especially if those links are also dofollow and high authority. (Like LinkDaddy® Links)
When it comes to local there is another important factor - Local Links. That is to say local identities linking to your site. So if you are a local business in New York for example and there is a sites that have posts about Central Park, Empire State Building, Times Square, Rockefeller Center etc linking to your business it can be more valuable than a link from Forbes, Huffington Post, or some other high authority site because it builds relevance to your website in terms of locality.
That is why I am now offering Local Links.
What I do is type in Places of Interest New York for example and Google now shows me all the Places of Interest and Things to Do in New York which you can see here https://rebrand.ly/places-of-interest-nyc
I then create a category for each Place of Interest and run a campaign to create the blogs. Typically this is 100+ blog post for each Place of Interest.
I then create structured content themed for that Places of Interest and submit out to the blogs. So for example there would be 100+ blog posts on different domains themed for Central Park.
At the bottom of each page will be some wording like "This page was created by our sponsor - Your Company. Here is an example http://centralpark64184.blogzet.com/central-park-new-york-zip-code-10754744.
I can spin keyword brand variations as well as domain variations as the anchor text. Meaning I can link out with different variations of your URL as well as your GMB URL.
Each time I create a Place of Interest campaign (100+ blog posts) I then backlink those Places of Interest links with social bookmarks and city relevant blogs. I also send those Places of Interest and all other links to my propriety crawling system. That is to say I have 10 VPS running 24/7 just to crawl all the links to let Google and Bing know they exist.
You might order 10 Places of Interest to be done over 1-2 months so the links are coming in over time. You can chose the Places of Interest you want me to create but typically I would start at the top of the list as these are the ones Google is showing as the most popular.
There is a lot of work in setting this up but I think you can understand how beneficial this will be in establishing your locality and showing Google and Bing you have local links.
Many folks get citations and directory links however many of those are also no follow and are typically just a citation with not much other information.
But this new service really makes Local Links possible for a local business.
I am calling this new service - Local Links Booster
You can order as many Places of Interest as you want. Typically there will be 25-50 or more for each city depending on population.