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Minimum Wage

My evidence based decision making on the question of should we raise minimum wage.

Point in favor of raise: Research looking at real world data indicates that min wage increases don't have much of an impact on employment prospects.
Strength of evidence: Medium because I didn't really dig into the data and the parts I skimmed were handwavy about the right level for min wage. Saying "moderate increases are good" can be reapplied to reach any level of min wage.

Point against raise: The government is inefficient. I assume most new laws are filled with earmarks and increasing complexity of our legal system which is a cost on everyone for the long terms.
Evidence: People say so. Reading about a few laws on various sites.
Strength of evidence: Weak.

Point against raise: Basic economic theory indicates that increased min wage increases the cost of producing goods and services (or the extra value to pay workers comes from somewhere). If the cost of products rises, the supply and demand equilibrium should shift to a level with (slightly?) less supply and demand. This would result in (slightly?) less work and therefore increased unemployment.
Strength: Weak. This economic model may be too simple to make predictions about this.

Point in favor of raise: 1. We have enough wealth in this country that people who work, should be able to live a decent, non-stressful life. 2. People at minimum wage, in at least some places, will have trouble living a fun life.
Evidence for 1: Intuition for combined wealth and moral compass for fairness.
Strength: Medium
Evidence for 2: Trying to come up with a budget given cultural norms about spending is difficult. Forces like Mr Money Moustache provide info and try to shift cultural norms, but it's still hard for me and likely even harder for poor people with lots of business and stress.
Strength: Strong

Neutral point: We should probably set minimum wage locally or otherwise adjust for location. Cost of living differs drastically from place to place. Different wages are needed in different places to have comparable lifestyles.
Evidence: Living in Binghamton vs NYC.
Strength of evidence: Strong

Conclusion: I'm 75% confident that the minimum wage should be a little higher in places with a cost of living similar to Binghamton and min wage should be higher than that in places with a cost of living similar to NYC.

Conclusion: I'm 95% confident that min wage should be pegged to an index that tracks cost of living so that the purchasing power of min wage stays the same over time and we don't have to wrangle with this question every few years.