Is a shop security guard legally permitted to persue a theif once they have left the shop?

Today I saw a security gaurd chasing a shoplifter down the street, and the shoplifter had left the shop ages ago and was a good distance away from the shop, and the security gaurd was still giving chace. I've heard somewhere that security guards have no power outside the shop they're working in and thus there is little more they can do than call the police.

Security guards have no rights that an ordinary citizen doesn't have, so issues that apply to cops such as "hot pursuit" don't apply here.
However, ANY citizen who witnesses a criminal offense is legally allowed to chase the suspect and affect a citizen's arrest. A security guard (any ANYONE ELSE) has the same power within the store as well as outside the store.

There are two concepts here. The first is "hot pursuit." If the security cop saw the shoplifting and is in hot pursuit of the thief, he can continue chasing even outside the store.

Think of it like this, a cop in Nevada sees a car theft and starts giving chase. The thief drives across into California where the Nevada cop does not have jurisdiction. Does the thief get away? No. The Nevada cop can continue the chase until such time as a California cop comes on scene and he takes over the chase. The security guard can continue the chase until a cop comes on scene and takes over.

The second concept is "citizen's arrest." If even an average every day citizen with no police powers at all sees a felony, he can attempt to place the felon under citizen's arrest. The security guard could be considered a citizen attempting such an arrest.

The only caveat to this is the citizen or guard must take exceptional care that their actions do not cause harm to bystanders. In most cases that means giving up the pursuit sooner rather than later.

The job of a Security Guard is to "observe" and "report". They do not (for the most part) have arrest authority except like you or me would have as citizens. If they think someone has stolen something, they observe the persons info and they report it to the Police who have arresting authority. Some stores give consent to search authority in which they could stop a person before they leave the store and ask if they could search their bags. If the person agrees then cool but if they don't there is not a thing they can do about it. Also, you are right, any authority given to the Security Guard resides within that store. I wonder what that Security Guard would have done if they caught the person, probably go to jail for assault or get sued.

I know a girl that has chased shoplifters outside, across a super busy street. I have heard that once they leave the parking lot, the theif is ok. It might be a scare tactic, but I'm not sure. I worked at a store, had the girl stealing on video, she wrote a check, and I knew her so it was a real check with her name, and there was nothing they could do but tell her not to come in anymore because I didn't notice stuff was missing til she was gone.

The security guard cant do anything in the store because they are not stealing until they try to leave the store without paying. So yes, they can chase the thief down.

In Los Angeles, they have to call the police, even if they have eyewitnesses.

It really depends on the state laws, but in most if there was more than one witness to the theft then the guard can give chase.

In my state they can pursue.