As I understand it, the “trickle down” theory says that if the top tax rates are reduced, those in the top brackets will put the money into business activities which will hire lower-bracket people. Those people, in turn will spend the money they get, which will support a growing economy. The increased wage and business income will lead to additional tax revenue which, it is claimed, will balance the revenue lost when taxes were cut.
Thus, the benefits are largely dependent on additional money finding its way into the pockets of those in the lower tax brackets. Lowering the top rates is a means to that end. It seems to me that, instead of the two step process of trickle down, it would make more sense to focus the tax cuts on the lower brackets and increase the refundable credits in order to benefit even those who have no tax liability.
Another thing which would help drive the expansion of the economy would be what is generally called “universal basic income:” a fixed amount, sufficient to provide necessities of life, given monthly to every resident (possibly less for minors living at home). For the unemployed and those living paycheck to paycheck, this would represent a significant increase in spending power, leading to a significant increase in spending, further stimulating the economy. Businesses would expand, producing the goods most people need and want.
Unlike “trickle down,” which depends on the wealthiest to use their tax savings in ways that put money in the hands of the less well off, lowering the taxes of the less well off and (or) providing a universal basic income will accomplish directly what trickle down can only accomplish indirectly and with a real possibility of some of the lost revenue going to other things (e.g., foreign travel, investment, or purchases).