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Thursday, December 17, 2009

In Which I Disagree with Paul Krugman about the Minimum Wage

I winced typing that title, since it is not wise to disagree with Paul Krugman and since I am going to argue that cutting the minimum wage can cause increased employment. Before going on, I stress that I oppose cutting the minimum wage as the logic of my argument suggests making the tax code more progressive. I think what we need right now is a more progressive tax code. That's what I always think.

OK so first Krugman argues that, when in a liquidity trap cutting all wages equally will not cause increased employment. Only here does he respond to the obvious criticism.

1. Why did I go from minimum wages to overall wages? Clearly, a cut in minimum wages –which only apply to some workers — can raise the employment of those workers at the expense of other workers. But the advocates of a cut are claiming that they can raise overall employment. The only way that can happen is if a reduction in average wages raises employment.

I assert it depends on how you measure employment. Krugman is appealing to standard macro models in which employment is measured in "efficiency units" and the wage level ("wage unit" to Keynes) is the wage per efficiency unit.

The standard assumption is that labor is uniform and can be measured by a number. The plain fact that some people are paid more than others is handled by assuming that they are more able in every way so their wage per efficiency unit of labor is the same. Thus consider able Andy who has twice the wage of luckless Larry and of bad Brad so he is paid as much as the two of them. It is assumed that he can do everything just as quickly as the two of them working together.
This is clearly absurd and is not to be taken literally.

As Krugman does.

Worse than that, once you define labor in efficiency units, you define employment as the number of efficiency units of labor employed.

The public policy concern is about how many people are employed. These can't be the same. Measuring labor in efficiency units might be an OK approximation if we cared about GNP, but if we care about employment and unemployment (as Krugman regularly insists we should) we have to think about people not units of efficient labor.

For the sake of argument let's stick with the efficient labor assumption. Oh and assume wages are sticky (we need some nominal stickiness to avoid the price level falling a few hundred fold in a second making the real balances effect a real factor). Now assume 2 types of workers able and not so able (90% are able 10% not so able) . An able worker produces just as much as two not so able workers.

Back in 2007 all workers were employed, not so able workers were paid the minimum wag and able workers twice as much. Now the market clearing real wage is lower, able workers are paid 1.99 times the minimum wage. Not so able workers are all unemployed so the unemployment rate is 10%

What happens if the minimum wage is cut 1% ? Suddenly all the not so able workers are hired. For each two that are hired one able worker is fired. Now the unemployment rate is 5%.

See simple. The reduction of the minimum can "raise the employment of those workers at the expense of other workers." Under standard assumptions such a shift in relative demand for different types of workers "can raise overall employment." so long as employment is counted you know by counting how many people are employed.

The absurd "efficiency units of labor" assumption implies that this effect is huge. Able and not so able workers are perfect substitutes so the elasticity of substitution of not so able for able workers is infinite.

In the real world the effect would be much smaller. It might be smaller than the damage to employment caused by the reduced expected inflation and therefore increased real interest rates noted by Krugman.

I oppose cutting the minimum wage, because I support cutting payroll taxes on low wage workers and making up the money by raising the FICA ceiling. I think payroll income above a floor should be taxed, not payroll income up to a ceiling.

According to Krugman's argument this wouldn't cause increased employment.

To put it another way, he is arguing that the increase in taxes on the rich and of the EITC enacted in 1993 had nothing to do with the huge puzzling increase in employment (without accelerating inflation) of the 90s.

OK now that I have argued with Krugman what about Card and Krueger. Empirical estimates of the effect of the minimum wage on employment suggest that the effect is very small. One famous study by Card and Krueger showed a positive effect of an increase in the minimum wage. The logic used by Card and Krueger to understand how this could happen suggests that things are different now.

Their logic is basically that firms can choose to pay a low wage and have a high quit rate and take a long time to fill vacancies or pay a high wage and have fewer quits and fill vacancies more quickly. If they are forced to pay the higher wage, their desired level of employment will be lower, but that level is the sum of employment plus vacant jobs. A binding minimum wage can reduce the number of vacant jobs by more than it reduces the sum of employment plus vacant jobs. Thus more employment.

I think this is not relevant to the current situation. There are very few vacant jobs. Quit rates are low. According to their logic, the effect of the minimum wage on employment depends on the unemployment rate. The evidence of a small effect is almost all from periods of unemployment far below 10%. I don't think it is relevant to the current situation.


TK said...

Assuming a given level of production, you have explained how removing barriers to the redistribution of work can increase the number of people working - by hiring two not-so-able and firing one able we increase the number of workers.

But the argument (one of the arguments?) is that you cannot assume a given level of production. The two not-so-able workers only replace the able worker if they together cost less than the able worker. This means that total income to workers falls. This might mean that demand (and so the level of production) falls.

Anonymous said...

You are missing part of the dynamic. Because of minimum wage, the employer has been forced to invest in equipment and training to make the currently employed worker more productive. That investment is a sunk cost. There is no gain to hiring 2 workers to replace the one needed for the job. That causes increased training and management costs. The effect of reducing minimum wage is the opportunity to cut or freeze wages and benefits for the one worker because competition is non-existent. The idea of a tax holiday on FICA is no different from any other government subsidy.

It only makes sense to hire workers if the additional output can increase profits by supplying unmet demand. In this economy, demand has tanked. The most direct way to address demand is for the government to demand more. In this economy, the government can get more bang for its buck because every new employee is one less unemployed person drawing benefits. The cost of adding an employee is the cost MINUS the cost of paying the unemployment benefits.

Lowering the minimum wage would require government to subsidize those workers through taxes or borrowing (min wage workers are already subsidized by EITC as you point out). By privatizing and subsidizing the government makes bad investments in speculative adventures and bubbles possible.

OTOH, government can direct money to pay for goods and services that will give return on investment. This is a twofer. We borrow money from the future to hire excess labor in the present to do work today that will save money in the future. The borrowing can be paid out of future savings. For example the US spent over $400 billion on oil imports in 2008. If through conservation and alternative energy we can cut that cost in half, then our future economy has an extra $200 billion per year to pay back the debt.

-jonny bakho

Robert said...

Wow two authentic comments (all of my comments have been comment spam recently).

TK the full argument is that average nominal wages don't matter. According to Krugman's assumptions (which I follow) the reduction in the nominal wage bill will cause a reduction in prices so real labor income and real profits will stay the same.

This isn't exactly true, but it is a shared assumption -- shared for the sake of argument -- of Krugman's post and my criticism.

Jonny Bakho. Yes indeed in my super simple little model I ignored almost all of the real world dynamics. I assumed that 2 less able workers are a perfect substitute for 1 able worker. That means I assume no training costs.

I used the super simple model just to note that Krugman's argument is not valid as he wrote it unless you redefine employment to mean something other than the number employed.

I noted that, in the real world, the magnitude of the effect would be tiny compared to that in the silly simple model. So we agree.

We also agree on what should be done right now. I support further stimulus spending. I didn't mention that because I was writing on another topic -- not "what is to be done" but "what would the effect of cutting the minimum wage be".

DM said...

Johnny Bakho writes:

"ere is no gain to hiring 2 workers to replace the one needed for the job."

You're assume there aren't new jobs that can be done with the additional resource. This is a false assumption. There is always more/addition work that can be done around a company. If a company is going to hire new resources, it's likely to do the work they've been putting off because the previous cost exceeded the benefit.

Kaleberg said...

"Suddenly all the not so able workers are hired"

Actually, a more realistic assumption is that they would be turned into transcendental hyper-matter angels. At least there's some hard science behind that.

Why, exactly, would a business faced with a weak economy and a means of cutting its payroll by simply lowering the hourly wage want to hire anyone new or even increase hours? Yes, there will be a few business owners who are stupid and will hire more people and find themselves drifting deeper into the red. However, those business owners who are trying to maximize profits and stay in business won't hire, but will simply increase their profit margin and bank it as a cushion against further economic shocks.

Even if enough business owners were stupid and did hire, they wouldn't be business owners for long. The problem is a collapse in demand, not a surfeit of money in circulation.

As I said, I'll go with the transcendent hyper-matter angels theory.

Robert said...

Kaleberg I have a question. Did you actually read the post ?

Obviously the point of hiring the two less able workers is to fire the able worker and save his or her salary. The firm just can't pay that worker less because the minimum wage was cut, because that worker was never paid the minimum wage, but rather a higher wage for some reason.

Do you know that some workers are paid wages even higher than the minimum wage ? Quite a few actually.

A business faced with a weak economy will not cut employment to zero. We know that because, hey employment is not zero. If such a firm can cut costs without reducing output, that firm might do so. This is conceptually separate from the state of demand and the choice of the level of output.

Note my claim is true because I indluded the ultra weasel word "might". "Might" makes right. The only claim in my post about the real magnitude of the phenonomenon I discuss in the real world is that I think it is small. Recall I do not advocate cutting the minimum wage.

Now the silly simple little model I used to prove that Krugman's assertion is not valid as stated is completely unrealistic. It is unrealistic, because higher wage and lower wage workers are not perfect substitutes.

I'm quite sure I must explain the phrase "pefect substitutes" to you. Note it does not mean "identical". The efforts of two workers are perfect substitutes if production depends on a linear function of those two efforts. This is what I assumed in the model so simple that I didn't imagine that anyone would be capable of missing the point completely. As you did.

You obviously don't give a damn about economic theory. I donìt say you should. However, I think you should recognise that you have nothing to contribute to a debate about economic theory.

The point of my post was to point out a mathematical error made by Paul Krugman. He said that something must be true. I presented a counter example. He made a math mistake, because he was thinking of employment in efficiency units not of employment as the word is used in normal English. I pointed out his math mistake.

I don't think this post is of general interest. That's why I posted it here not at (until asked by a fellow angrybear to cross post).

Anonymous said...

Amazing as always