Southern Dad, we've both understood U.S. dollar's purchasing power in higher minimum rate states are less than those of lower rate states. Minimum rate increases are only of direct benefit to workers and their dependents, and those benefits are greatly shifted to be of the the greatest benefits to lower wage rate employees; (i.e. those benefits are inversely related to the employees' wage's wage rate).Your first sentence sums it up. You cannot prove it. It is your conclusion. Here's the problem, data, shows that your conclusion is incorrect. Why do you think that the purchasing power of minimum wage isn't greater in states with higher minimum wage? Could it be because the cost of everything increases to pay those higher wages? The data, and I've provided it, already shows that increasing the minimum wage does not decrease spending on public assistance. When you increase the costs of labor, that cost gets passed on to the consumer through increased prices. Increase a gallon of milk by a dime, the price of a Whopper by fifteen cents, the price of a watermelon by... Then at the register, you understand where that additional money came from. Obviously, the dime, and fifteen cents are just example, and not exactly what the increase would be.
Few employers are paying minimum wage. At minimum wage, they cannot attract and keep employees. Without any laws being passed, market forces have caused employers to increase the starting wage that they pay.
The minimum wage rate is not among the primary causes of the dollar's inflation rate. The dollar loses purchasing power without regard for modifications of the minimum wage rate.
Regardless of U.S. dollar's lesser purchasing power, lower wage employees gain a net benefit due to any increase of effective minimum wage rate in their state. The purchasing power of the U.S. dollar doesn't explain why we have not statistically proven the minimum rate's greater benefits to lower wage and wage rate employees of higher, rather than lower wage state's are not greater.
Although it's not yet been statistically proven, I have no good reason not to believe actually increasing the minimum wage rate's purchasing power of all lower wage and wage rate employees does not reduce the poverty among the working poor more than otherwise.
The data you provided indicates lower minimum rate states spend lesser dollars of greater purchasing power for public assistance. Even if it should be shown that Georgia or other of those states spend a lesser portion of their states' budgets for public assistance, that's no more or less likely to indicate those states have lesser regard for their working poor.
What portion of state's population of employees earn lower wage rates are, and the portion of them earning their state's precise effective minimum rate are not germane to this discussion.