I worry that an elasticity of less than 1 can be abused by
people who try to calculate the net benefits of increasing the minimum wage. I’ve
seen a few studies that try to do this. They will take some estimate of the elasticity
of demand from the empirical literature, count up the costs to the losers
(those who lose their jobs) and the benefits to the winners (those whose wages
increase) and cheer the net social benefits of the minimum wage.
Try this on for size. Let’s increase the minimum wage by
10%, which will reduce total employment of affected workers by only 1%. (Assuming -0.1 as the elasticity of demand for low wage workers.) The net effect is a
benefit, because the gains to the winners are larger than the losses to the
losers. Total compensation changes by (1 + 10%) * (1 – 1%) = 1.09, in other words a 9% increase. (The first term is the increase in wages per worker, the second term is the decrease in the total number of workers. Multiplying these together should give you the change in total compensation. Try it with some actual values for the minimum wage and numbers of workers to convince yourself.) Okay. So let’s
keep going. Let’s raise the minimum wage by 100%. Net benefits to the affected
workers are (1+100%)*(1-10%) = 1.8. An 80% increase! To boot, maybe there’s
some way the winners can compensate the losers, such that everyone’s take-home pay increases! A 200% increase would yield an
even bigger 140% increase! This isn’t literally a perpetual motion machine; it
maxes out at a 450% increase in the minimum wage, then the net benefits start
coming back down. But the notion that someone could take the logic of small
increases and extrapolate them this far is alarming. It implies that there’s
something fundamentally wrong with this approach. That fundamental error is present even for small changes, but the smallness allows minimum wage advocates to paper over it.
(If you assume that the demand curve is actually curved rather than being linear, then it actually does become a
perpetual motion machine. Say, the quantity demanded for low wage workers is proportional
to the price raised to the power -0.1, a curve that roughly speaking yields an
elasticity of -0.1. Multiply the price times the quantity demanded to get total
compensation for low-wage workers: price times price^-0.1 yields price^0.9. This result absurdly implies that the total
compensation keeps going up forever, no matter how high you raise the minimum
wage. Consider this a reductio ad absurdum. Minimum wage advocates are welcome
to explain what special thing is happening at small increases that stops
happening at larger increases.)
I don't know how pro-minimum wage economists arrive at the conclusion that "the benefits of raising the minimum wage outweigh the costs". They might not be naively multiplying total wages by total employment the way I'm doing above, but they must be doing something like this. In an Intelligence Squared debate on the minimum wage, Jared Bernstein describes his correspondence with David Neumark to get the opinion of an anti-minimum wage economist. Bernstein wanted to know what value he should "plug in" for the elasticity of labor demand to fairly represent the anti-minimum wage folks, and with astonishment in his voice he says that Neumark told him -0.1. (I'll bet Neumark told him a range, minus 0.1 to minus 0.2, because that's what his book Minimum Wages says.) At some point in the debate, he says it's "nuts" to worry about these kinds of tiny job losses when you weigh them against the gains to those who remain employed. He's either doing the same back-of-the-envelope I'm doing above, or he's doing a sloppy hand-waving version of it in his head.
Here is an example of a calculation in which someone really is treating the minimum wage like a perpetual motion machine. This study (IMO a terrible one, more on that in a later post) by the Illinois Economic Policy Institute attempts to calculate the effects of a minimum wage on various economic outcomes. See Figure 4 and the associated discussion in the text. They claim that a literature review turns up a result that a 10% increase in the minimum wage results in a 1.1 percent increase in worker incomes and a 0.45 percent decrease in hours-worked (presumably this comes from the various studies measuring the elasticity of demand for low-skilled workers). They apparently think that you can extrapolate those numbers to arbitrarily high increases in the minimum wage, because that's exactly what Figure 4 is doing. I want to say, "Okay, show me what the result will be for a $50/hour minimum wage. Or $1,000/hour for that matter." They get that a $10/hour minimum wage will result in a 1% reduction in working hours and a 2.3% increase in worker incomes (from a starting point of an $8.25/hour minimum). They get this by calculating the change in the minimum wage, 10/8.25-1 = 21.2%, and simply multiplying through by the numbers above. So 21.2%* (1.1%/10%) = 2.3% for the change in worker incomes. 21.2% * (-0.45%/10%) = -1% for the reduction in worker hours. They do exactly the same thing for the $15/hour minimum wage: 15/8.25-1 = 81.8%. So 81.8% * (1.1%/10%) = +9.0% for the change in income and 81.8% * (-0.45%/10%) = -3.7% for the reduction in employment. If the 1.1% and 0.45% can really be extrapolated to arbitrarily high minimum wages, then they have a perpetual motion machine. The increase in incomes keeps going up forever. If asked about a $30 or $50 minimum wage, the authors might demur. "Oh, of course you'd start to see bigger disemployment effects at that point." But why wouldn't they also see it at $13 and $15/hour? The $13 and $15 are minimum wages far large than what the 1.1% and 0.45% numbers are calculated from, so even extrapolating this far is dubious.
This discussion so far mostly applies to people advocating for very large increases in the minimum wage. Many pro-minimum wage economists place reasonable bounds on what the minimum wage should be. (For example, Dube argues that it should be half the median wage.) Some economists and policy advocates are more reckless. They use a crude summary of the empirical work, something to the tune of: "Empirical work shows that there's no effect on unemployment no matter how high you raise the minimum wage, so we can raise it however high we wish."
There is a certain fuzziness and lack of candor in the arguments offered by pro-minimum wage economists, the careful ones and the reckless ones alike. It's notable that even the reckless ones who advocate $15/hour minimum give a finite number. All of these people are making some version of the argument that disemployment effects don't really matter for small increases, but at some point these effects become important and overwhelm any positive effects on income. It's all very hand-wavy. Most economists would argue that for small increases, employers and employees can make various adjustments and avoid laying off workers. I've heard pro- and anti-minimum wage economists make this kind of argument, so there is general agreement on this point. Employers can adjust along margins other than the "total employment" margin, whereby they start needing to lay people off. But ramp up the minimum wage too high, and you exhaust those other margins. There are only so many amenities to rake back, there is only so much extra productivity you can squeeze out of your workers with strict work protocols, etc. Those unemployment effects eventually start to bite. Here is what bothers me. We know that those adjustments along other margins must be happening. Most employers of low-skilled workers have very thin profit margins, so there just isn't a lot of extra money to simply pay out higher wages. We can infer using the standard tools of economics that those adjustments are probably bad for the workers and the employers. But when pro-minimum wage economists talk about these adjustments, when they explain why the disempoyment effects don't appear until you raise the wage higher, they either ignore these other adjustments (which are adverse to the interests of employees) or misleadingly describe them as benefits. For example, there is a tendency for workers who are subject to a binding minimum wage to hang on to their current jobs longer and search more intensely for work if they aren't currently employed. These are costs, but minimum wage advocates often misrepresent them as benefits which offset the tendency toward reduced employment. Let's stop counting costs as benefits and vice versa. Let's stop pretending that costs don't exist just because we can't measure them very well. Let's also stop pretending that we can take an elasticity calculated on a 20% increase in the minimum wage (typical of the small increases in the empirical literature) and extrapolate it to a 100% increase. Even the "reasonable" minimum wage advocates have been sloppy on these points.
Here is an example of a calculation in which someone really is treating the minimum wage like a perpetual motion machine. This study (IMO a terrible one, more on that in a later post) by the Illinois Economic Policy Institute attempts to calculate the effects of a minimum wage on various economic outcomes. See Figure 4 and the associated discussion in the text. They claim that a literature review turns up a result that a 10% increase in the minimum wage results in a 1.1 percent increase in worker incomes and a 0.45 percent decrease in hours-worked (presumably this comes from the various studies measuring the elasticity of demand for low-skilled workers). They apparently think that you can extrapolate those numbers to arbitrarily high increases in the minimum wage, because that's exactly what Figure 4 is doing. I want to say, "Okay, show me what the result will be for a $50/hour minimum wage. Or $1,000/hour for that matter." They get that a $10/hour minimum wage will result in a 1% reduction in working hours and a 2.3% increase in worker incomes (from a starting point of an $8.25/hour minimum). They get this by calculating the change in the minimum wage, 10/8.25-1 = 21.2%, and simply multiplying through by the numbers above. So 21.2%* (1.1%/10%) = 2.3% for the change in worker incomes. 21.2% * (-0.45%/10%) = -1% for the reduction in worker hours. They do exactly the same thing for the $15/hour minimum wage: 15/8.25-1 = 81.8%. So 81.8% * (1.1%/10%) = +9.0% for the change in income and 81.8% * (-0.45%/10%) = -3.7% for the reduction in employment. If the 1.1% and 0.45% can really be extrapolated to arbitrarily high minimum wages, then they have a perpetual motion machine. The increase in incomes keeps going up forever. If asked about a $30 or $50 minimum wage, the authors might demur. "Oh, of course you'd start to see bigger disemployment effects at that point." But why wouldn't they also see it at $13 and $15/hour? The $13 and $15 are minimum wages far large than what the 1.1% and 0.45% numbers are calculated from, so even extrapolating this far is dubious.
This discussion so far mostly applies to people advocating for very large increases in the minimum wage. Many pro-minimum wage economists place reasonable bounds on what the minimum wage should be. (For example, Dube argues that it should be half the median wage.) Some economists and policy advocates are more reckless. They use a crude summary of the empirical work, something to the tune of: "Empirical work shows that there's no effect on unemployment no matter how high you raise the minimum wage, so we can raise it however high we wish."
There is a certain fuzziness and lack of candor in the arguments offered by pro-minimum wage economists, the careful ones and the reckless ones alike. It's notable that even the reckless ones who advocate $15/hour minimum give a finite number. All of these people are making some version of the argument that disemployment effects don't really matter for small increases, but at some point these effects become important and overwhelm any positive effects on income. It's all very hand-wavy. Most economists would argue that for small increases, employers and employees can make various adjustments and avoid laying off workers. I've heard pro- and anti-minimum wage economists make this kind of argument, so there is general agreement on this point. Employers can adjust along margins other than the "total employment" margin, whereby they start needing to lay people off. But ramp up the minimum wage too high, and you exhaust those other margins. There are only so many amenities to rake back, there is only so much extra productivity you can squeeze out of your workers with strict work protocols, etc. Those unemployment effects eventually start to bite. Here is what bothers me. We know that those adjustments along other margins must be happening. Most employers of low-skilled workers have very thin profit margins, so there just isn't a lot of extra money to simply pay out higher wages. We can infer using the standard tools of economics that those adjustments are probably bad for the workers and the employers. But when pro-minimum wage economists talk about these adjustments, when they explain why the disempoyment effects don't appear until you raise the wage higher, they either ignore these other adjustments (which are adverse to the interests of employees) or misleadingly describe them as benefits. For example, there is a tendency for workers who are subject to a binding minimum wage to hang on to their current jobs longer and search more intensely for work if they aren't currently employed. These are costs, but minimum wage advocates often misrepresent them as benefits which offset the tendency toward reduced employment. Let's stop counting costs as benefits and vice versa. Let's stop pretending that costs don't exist just because we can't measure them very well. Let's also stop pretending that we can take an elasticity calculated on a 20% increase in the minimum wage (typical of the small increases in the empirical literature) and extrapolate it to a 100% increase. Even the "reasonable" minimum wage advocates have been sloppy on these points.
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