If I give my employees shorter Friday workdays during the summer, how can I be sure productivity won't drop?

You can't be sure it won't. Your best bet would be to leave Friday workdays the way they are, and not make them shorter.

You can’t.

Work by objectives

I wouldn't think it would .They would be excited to get off early.

if your employees are good employees then it shouldnt effect productivity

you have to trust your employees

The only thing shorter workdays accomplishes is less hours, less pay, so time away from work just means needing another job (which many need now) just to afford insurance anyway.

ask for a few hours on a weekend day or ask everyone stay 1 extra hour the rest of week

You are more likely to improve productivity, as most employees are going to be more productive to assure the early releases happen, rather than not getting to leave early because their productivity dropped off.

Productivity drops when employees feel as if they would rather be somewhere else. Let them bee somewhere else as a reward for a solid X hours instead of the regular shift.

Trust works both ways. If you are honest and forthright and fair with your employees and they know this and feel the same, then you can depend on their working just as hard in return. Sometimes they’ll work even harder, trying to get a full day’s work crammed into a half day’s time.

Is there no other way to gauge their productivity besides making sure they’re sitting at their desk? Being a good boss is as much about trusting your employees as anything else. As long as their individual responsibilities are getting done, it shouldn’t matter whether they’re working a full 8 hours or not—assuming you have some way of measuring that productivity.

No way to be sure, but expectations must be disclosed before hand. Reduced Friday schedule will continue as long as productivity isn't affected.

As an employee, I would say that you make the shorter Friday hours a tentative agreement on the basis of maintaining productivity. That should provide the incentive needed for them to take on more ownership of their duties. I will also add that if you as an employer are expecting to maintain an 8 hour productivity standard in a 5 or 6 hour day, you will be met with resistance. So you should evaluate (if procedures are not already implemented) how your productivity is calculated, be it hourly or on a standard 8 hour shift.

You can't be completely sure of course but that is trust and good management skills come into play. I'm not sure what the productivity standard is now but if it's possible to flex from a daily standard to a weekly standard, that might be one way to go. Another idea would be to stagger staff so that not everyone is working a shorter Friday at the same time. You could try flexing 1/2 the team every other week or every other month. You could also solicit ideas from the team or let them vote on what they think would work best. This could go a long way and get their buy in. If you stress that making deadlines and meeting productivity standards is the main focus, I'm sure they will have lots of ideas on how to meet those standards as a team while earning the flexibility that they want.

That's the wrong question. Whether productivity drops or not is a function of how motivated your employees are, it has little to do with how long your workday is. If you think and manage in these terms, productivity is already dropping.

Keep goals just as high

you can't, but if you don't they will probably look elsewhere

If you don't know what your employees are working on that is your first challenge, regardless of number of hours employees work.

Set a time on all projects to be complete before Friday

While your employees would be working fewer hours, you must also factor in the impact of having more time to relax and "unwind." It's similar to the studies where employee productivity increases when working one fewer day a week; by giving your employees more time away from work, they'll be more likely to be fully recharged on Monday and ready to work their hardest. One thing to take into account, however, would be how it would affect the pay of your employees. If the shorter workdays caused employees to be paid less, it has a distinct possibility of backfiring and causing lower morale and productivity than a full day of work.