I have a background in psychology and without going super in-depth, there is no doubt a BIG difference if you tell people to like and subscribe. Understand that there are some people who are what I call "Action Now" people. You tell them to do something, especially if they like you or perceive you as someone of authority, they'll just listen and do it. Imagine being a kid and your parents are telling you to do something, or a person you have a crush on is telling you to do something. You just do it.
There is also the way you tell people to like and subscribe. If you simply beg them, that's usually not that effective. If you simply tell people, it's a little bit more effective. But if you use an IF statement like, "If you liked this video and like action games, then subscribe and like." An IF statement implies a value exchange. It's very powerful in marketing.
Also sometimes people have the intention of subscribing, but simply need a reminder. And some people are on the fence on whether to subscribe or not, and that simple call to action might get them to subscribe.
Another tip is to consider not giving people too many choices. Telling people to like, comment, subscribe, share this video, visit my website and watch my next might overwhelm them with choices causing them not to choose any. So choose only one or two. I'm able to bypass this by making a multiple choice and asking people, "If you like this video, then choose ONE of the following. a) subscribe and like, b) Listen to the share bear over there and show that you care, c) watch my latest video, or d) tell me to jump off a bridge." It's also a good tip to find a way to make it a no big deal if they don't subscribe. This is why I make option d), something that makes fun of myself.
I could talk all day on this topic. But believe me it makes a big difference. My subscribe rate multiplied by 5 when I started applying all this psychology.