In fact 13 of Glass’s Facts and Fallacies book he says that Jeffery and Lawerence (1985) found that projects where no estimates were prepared at all fared best on productivity versus projects where estimates were performed by technologists (next best) or their managers (worst). This was confirmed by Landsbaum and Glass (1992).
If estimates must be provided to upper lever management, then ask each developer to calculate it and use a fudge factor (by developer) to report it to management. Try to hold off until the design (pseudocode) is completed, which will provide the closest estimates. If management insists on earlier estimates, then try to convince them to do the estimates after the requirements document has been produced.