I have an American Standard heat pump with a Honeywell thermostat.

As I understand it, the aux heat should engage when you raise the
thermostat 3 or 4 degrees OR if the heat pump falls behind by 3 or 4
degrees. On my system, the aux heat engages at a MUCH touchier
threshold (possibly 1/2 degree). If I move my thermostat 1 degree,
the aux heat kicks in. If the heat pump falls behind by 1/2 degree,
the aux heat kicks in. The heat pump is not being given much of a
chance to keep up.

For economics, I want to give the heat pump a greater chance at
maintaining temperature. Is this a thermostat adjustment that I can
make? What controls the 3-4 degree differential between heat pump and
aux heat?