How can I set a keyboard shortcut to paste text?

You could create this using AppleScript and run it using Automator.

Create a script:

tell application "System Events" to keystroke "Hello World."

Replace "Hello World." with your desired text, but make sure to keep the quotation marks around whatever text you input as that is what is making the data type a string.

Next, use Automator to trigger the above AppleScript:

1. Open Automator.
2. Create a new services workflow.
3. Set Service Recieves to no input.
4. Set in to any application.
5. Under "Actions" in the left pane, search for "Run AppleScript."
6. Once you find that, drag "Run AppleScript" over to the right pane, which enters it into your workflow.
7. Save the workflow.

Finally, use System Preferences to assign this workflow to a global hotkey.

1. Open System Preferences.
2. Click Keyboard.
3. Click Keyboard Shortcuts.
4. Scroll down to and select Services in the left pane.
5. In the right pane, search for the name of the Automator workflow that you just saved and click on the checkbox to the left of the file name.
6. Hold down your desired keyboard shortcut and it will automatically assign this workflow to your selected hotkeys.

This is probably the easiest way of accomplishing your desired task while writing the least amount of code as possible.

There is also a tool called Alfred that is outstanding; I use it many times on a daily basis. At this point I would probably be lost without it. It can completely take over spotlight for you (in fact I deleted the hotkey to bring up spotlight search (cmd + space) and assigned that hotkey to open Alfred instead. Within Alfred you can do things such as copy text from one place, then copy more text from somewhere else and append them together, do anything that you can do in Spotlight search, plus much, much more. The reason that I bring up Alfred is because you can create this same exact workflow within Alfred and assign it to a system wide hotkey all within the same application without writing and code at all (if you consider the example that I just gave to actually be writing code). In fact, the types of workflows you can create in Alfred is essentially limitless and there are even already built recipes online, for different applications that you can download.

If you are fine with installing 3rd party software, one feature of BetterTouchTool does what you are looking for

http://docs.bettertouchtool.net/docs/key_sequences.html

According to the creators at https://www.boastr.net/ BetterTouchTools is available as a trial version.

This is not a keyboard shortcut per se but you can define letters to represent a word or phrase. I have set my email address to be represented by jj. Whenever I type that followed by a space it prints my email address. You can define as many as you like. Go to system preferences, keyboard. Click on the text tab and you can define your shortcuts.