When I take my dog on walks, sometimes there will be loud noises that scare her (e.g. thunder, construction, large vehicles driving by). When this happens her flight response kicks in and she wants to take off running. She's securely on leash and won't get away, but I often will just start running with her. I usually try to jog with her anyway, and it's more often that I'm going too fast for her than the opposite, so I don't mind running for a little while when she gets scared like this.
She also likes to run, more often when she's off-leash at the dog park or the beach, so it's not something she only does when she's scared. I partially hope that by running with her when she's scared she might forget she's scared and just be happy running.
I'm wondering, is it okay to let her run when she's scared? Would it be better to not move and try to calm her down? On the one hand, I think it might be good to let her get out that energy to help calm her down some. On the other hand, I could see the argument that it encourages the fear response and might make her more likely to run away at loud noises in the future. I'm not worried about owner/pet dominance and her being in control of the pace - we only go as fast as I want, and I don't always let her run when she wants.