If estimating the amount of time to design a new product, should you err on the high side or the low side?

In general, you should err on the high side when making an estimate. Now the question is why? Consider what happens when the design is finished. If your error was on the low side and management created a schedule based upon your estimate, that means that your design is finished later than the schedule management made. So the production schedule slips, and people who were scheduled to handle your new design are left idle. And trust me, when the schedule slips, a lot of attention and pressure are brought to bear in order to attempt to "make up" for lost time. Overall, the adverse effects are quite large and sometimes quite expensive. If your error was on the high side, that means that the design is finished ahead of schedule. Management is happy. And more time is available for testing and possible refinement of the design. Or as a pithy bit of wisdom a craftsman once told me. "If you tell the customer it will take a week and it takes 8 days, they're gonna be mad and scream at you, but if you tell them that it's going to take 2 weeks and you deliver in 10 days, they're gonna kiss you."