I'm kind of tired of hearing bad bad dog and kill it. Lets give the owners, who love their dogs, a chance. This dog may not normally roam around and got loose by accident. I would go to the neighbor and tell them in a nice way that their dogs hunting instinct is to prominent. Tell then that the dog charged at the birds and rammed into the fence, leaving a dent, and scarring the heck out of you. The owner may not know about their dog's bad behavior. Ask him kindly to take care of this situation, since you would like to have a nice neighbor relationship. I'm saying this because we have a dog that is aggressive and we did not know about it for almost 1.5 years. She is the sweetest dog to her 3 dog mates, our cat, us, our ducks, and people visiting. We found out by accident when we put her in the kennel, which we do frequently when going on business trips. The clerk mentioned oh yeah she is the aggressive one. We said what? She is the sweetest dog, who even loves strange children. Turned out she is aggressive towards other dogs, not the handlers in the kennel. We had no clue since we live away from other dogs. Ironically she never shows that behavior when we go hiking and meet other dogs. It's only in the kennel when she is stressed out. So this owner may not know that his dog is doing it, and may be shocked to find out. I agree that something more needs to be done, if the dog has been doing it over and over. Especially when the owner does not take control over the situation. So talk to your neighbor nicely, do not threat him about what you can and will do. Get their sympathy and they may even work on it. I would even offer to help them with my labor if they want to build a kennel.
Katharina