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In introductory microeconomics, when studying partial equilibrium, we are introduced to the idea that a price floor will cause excess supply and a price ceiling will cause excess demand.

How strong is the empirical evidence for these results?

I recently read this article: https://www.urban.org/urban-wire/strengths-and-weaknesses-new-study-seattles-minimum-wage-increases that discusses a paper that found that raising the minimum wage does cause labour sold to fall. It also focuses on the limitations of the paper's methodology while also remarking that the quality of the data used is extraordinarily high. It also comments that most of previous research find little evidence for a negative impact on labour sold.

What is the overall empirical consensus/ leaning in the empirical literature regarding price floors and ceilings? Are they found to be as inefficient as described in introductory textbooks? If not, do more advanced theoretical models take that into account?

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There is different evidence for price controls in labor market and different evidence for price controls in general.

Minimum Wage

When it comes to minimum wages there is evidence that they do not cause as much unemployment as was thought in the past. According to the literature review by Neumark & Wascher (2006):

Our review indicates that there is a wide range of existing estimates and, accordingly, a lack of consensus about the overall effects on low-wage employment of an increase in the minimum wage. However, the oft-stated assertion that recent research fails to support the traditional view that the minimum wage reduces the employment of low-wage workers is clearly incorrect. A sizable majority of the studies surveyed in this monograph give a relatively consistent (although not always statistically significant) indication of negative employment effects of minimum wages. In addition, among the papers we view as providing the most credible evidence, almost all point to negative employment effects, both for the United States as well as for many other countries.

However, at the same time there is evidence that at least some of the negative effects might be due to publication bias (see meta analysis of Doucouliagos and Stanley, 2009) so the problem might be even bit less severe than the above excerpt suggest.

Nonetheless, this is likely due to peculiarity of labor market imperfections. For example, there can be significant quasi rents that usually go to employers due to their better bargaining position, which means that rising minimum wage would have no effect on employment up to the point that all quasi rents are assigned the worker and only then it would start to have any employment impact. There are also further reasons for this, since your question is very broad I won't go into details but you can learn more in Borjas Labor Economics about these reasons.

In addition, there are also some further caveats. First, US (where most of the studies on minimum wage come from) has one of the lowest minimum wages relative to average wages in the world, the employment effects are larger in countries with relatively high minimum wage to average wage ratio. Second, it might have adverse effect on consumers, Peter Harasztosi and Lindner (2019) for example find that about 75% of effect of higher minimum wage in Hungary was passed onto consumers.

Despite of this it is fair to say that when it comes to minimum wage the effects are not as bad as it was originally thought and they can be even beneficial on net basis if set to appropriate level.

Other Price Controls

When it comes to price controls in general, for example on many goods and services markets the consensus still remains that they reduce overall welfare. There might be some exceptions, it is beyond the scope of economics stack exchange to provide literature review on every single price or category of prices there is, but generally speaking evidence shows that price controls either lead to lower quality of goods or scarcity.

For example, Davis and Kilian (2011) estimate that price controls in energy prices in US had allocative cost on averaged $3.6 billion annually. This, is just one example of course but generally speaking evidence points relatively large adverse effects in most markets (e.g. see discussions in Finley and Holt (2019); Glaeser, Edward, and Luttmer (2003); Rockoff 1984; Coyne et al (2015) and sources cited therein).

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