You sentences are almost all questions, but you didn't answer mine:
For example, does the paper provide any critical analysis that provides empirical rebuke for the sources I've presented? Also is it published or merely an opinion piece?
With regards your questions:
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How do you describe the difference between maximization of skills, and certification?
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I've already referred to the difference. We have a dual role of education. First, its economic role. This is about productivity (be it pecuniary or non-pecuniary). Second, the use of education to discriminate. This can theoretically also refer to economic efficiency. For example, look up the “screening hypothesis” where education is used to signal one's innate ability. However, once we have wealth inequality, it is increasingly dominated by means to maintain family wealth. Certification becomes about justifying hierarchy and promoting artificial wage divides.
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How would you track the education systems ability to maximize skills?
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I'd refer to value added measures.
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How would you track the education system's "waste" on certification?
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In the current regime, I'd refer to a proxy such as social immobility.
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What is an example of regulation that ensures maximization of skills without certification?
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This isn't a meaningful question. Certification is vocab to distinguish from human capital investment.
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How is this regulation incompatible with providing education services via the private sector?
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The private sector feeds off wealth inequality. It minimises the human capital role.
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By contrast automobiles are provided via the private sector while adhering to (and often surpassing) the minimum safety regulations.
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Education is a classic example of how equity and efficiency are the same beast. We can't say the same about mundane consumer goods.