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This is a strawman argument.

What would a government policy look like that took money from one person and gave it to someone with identical characteristics?

Such a policy would need to name the people, since they could not be distinguished in any other way.

But actual redistribution is nothing like that.

Taxes and benefits are *defined* in terms of characteristics, either the amount of income earned, or age, or disability status, etc.

So this model is inapplicable to any sort of re-distribution policy that has ever been proposed.

You missed the point about *random* redistributions. These are by definition not correlated with characteristics such as income.

The results here don't hold for a redistribution policy that systematically gives more to those with low incomes.

And it's by no means a strawman argument. Lot of people think that increasing the minimum wage will reduce poverty.

Maybe I'm not understanding this post properly, but I think it isn't right. Under plausible assumptions, utility functions are close to linear for small changes in (permanent) income. So this effect of redistribution on welfare will be very small, unless a sizable fraction of the agents' income is affected.

Moreover, trying to redistribute income through minimum wage increases obviously has other costs which are far greater, so it seems weird to focus on this small effect.

Your model is closed and dense, that is why you can use Jensen's and get a nice algebra. Under that assumption there is no place for the politician to be exogenous. Relaxing the dense makes the algebra difficult but the politician is still part of the package. The only way out is to partition the economy, have a separate G with its own system.

anon: Is it small? There are proposals out there calling for $17/hr minimum wages.

And if the change is small enough so that the linear approximation is useful, then we're back to the case where the minimum wage is neutral. If that's the best case we can hope for, then maybe the policy agenda should be reconsidered.

Matt: I did, but I called it z instead of G.

So the minimum wages is like a lottery, with random winners and losers. Except, it's a compulsory lottery -- we can't refuse to play.

"You missed the point about *random* redistributions."

No, I didn't miss that point -- the assumption of randomness is what makes it a strawman argument.

When government passes laws to redistribute income -- e.g. fines for smoking, giving money from the poor to the rich or from the rich to the poor, tax breaks or tax penalties, the redistribution is *never* random -- it is always based on some characteristics -- e.g. being a smoker, being poor, being rich, etc, so that money does not flow from one person to an identical person.

Then you must have skipped over the paragraph the begins with "But if you are familiar with this file..."

OK, I'd be willing to support the end of minimum wage in exchange for, e.g. a cap on wealth.

So how do you feel about increasing the Working Income Tax Benefit, then?

Good idea; the WITB targets low-income earners.

Anecdotes, my sister and I worked in factories for a year after 1st year uni, she made minimum wage, I made a couple bucks more, put our family over lico. One went bankrupt in 2008 CAD/US exchange rate, the other is now slow/shut down, its sister plant out west uses, temp foreign workers.
We probably displaced some people who were poorer, but were glad for the work, we also undercut older/union workers. I'm not sure if lower min wage would have kept them going, wouldn't make the unions happy.
I'm pretty sure a 17$ min wage would screw a lot of people, but it would probably help older people with kids etc. and as for lottery, I then went west, made a lot of money and blew it on risky stocks, not a truck, which would have been a better investment.

Why do you think that minimum wage laws are a *random* re-distribution?

Just because being a minimum wage earner is an independent event from being in poverty?

That's not nearly enough to designate the policy as being a random redistribution.

For example, if the re-distribution was truly random, then being a minimum wage earner would be independent of earning more than X, for *any* X.

Do you really believe that this is the case?

I have a relative who has worked in minimum wage jobs his entire working life. He had learning problems and dropped out of high school. Most attempts to upgrade his skill set have not been successful. He is now in his 50s. He pays his rent and grocery bills, but that's it - travel and other luxuries are things he will never have. Cutting the minimum wage - or even freezing it and letting inflation erode it - has a very real impact on his standard of living. As in whether he gets to eat meat or live off baked beans.

If there were no minimum wage, I shudder to think what would happen to him. Yes, I suppose I and other relatives could support him if we had to, but why should he be forced to degrade himself like that when he is perfectly willing and able to to work and support himself? Whatever happened to the concept of dignity, of fair pay for a fair day's work?

Does the minimum wage cause unemployment? My relative has never been unemployed in his 24 years in Canada, including three recessions. Nor have his hours been cut; if anything, he has voluntarily worked fewer hours than offered in order to qualify for his government housing subsidy. No social program is better than a job.

Or another example. I know of another family of four that just received refugee status in Canada. The parents, in their 50s, are working minimum wage jobs. They have less than a high school education and no particular skills. Evidently the minimum wage did not price them out of the labour market. Their two children, aged 15 and 18, hope to enter university after they finish high school. Eliminate the minimum wage and these children might not even go to university; they'd drop out of school and enter the labour force in order to pay the rent.

So don't tell me the minimum wage doesn't help people in poverty. I'm not going to believe it, and neither will the majority of Canadians. My relatives don't want welfare and they don't want handouts and tax credits. They want jobs at a decent wage and education for their children.

I think you've actually been rather generous in your assessment - anecdotes aside.

We can be pretty sure that losses hurt a lot more than a gain of the same magnitude (using prospect theory instead of expected utility theory). Given we're talking about redistribution from those who were working for minimum wage to those who continue to work at the improved minimum wage we don't even get the benefit of taking from the rich to give to the poor.

I'd like to hear your take on a flat tax and guaranteed annual income instead of minimum wage and other welfare programs.

tyronen, I don't think Stephen (or any of the commenters) are proposing to just repeal min wage and go home. The point is that in aggregate it amount to a random redistribution of wealth, and that random redistributions of wealth a) doesn't do anything in particular to help the poor b) arguably make us ALL worse off (in aggregate). Ok, we can argue about the concavity of the utility function or if it really is a random redistribution, but why bother? Why not instead implement policies that unequivocally a) make the poor better off b) make us all better off.

tyronen - one more thing: re-read the last paragraph of the OP. I think that the reason why the anecdotes seem compelling is because they are cases where the incidence of earning min wage coincides with poverty - something which Stephen has pointed out is not well correlated (hence the random redistribution). In those cases, the transfer does increase welfare. But that wasn't the argument. Many people would agree that giving money to poor people is a good idea. The thing to think about are the case where the money goes to people who aren't poor and when it comes from people who are (or at least who are less rich).

Patrick, the point is that the redistribution is not random.

Yes, assume being a minimum wage earner is independent of earning less than, say, $20,000 per year (or whatever the LICO happens to be).

Nevertheless, unless you also demonstrate that the probability of being a minimum wage earner is independent of the probability of earning less than $25,000 per year, and $100,000 per year, and $5,000 per year, and *any* amount per year, then you cannot conclude that the redistribution is random.

If tax rates were determined by your birthday, that would be a good candidate for being a random redistribution.

Now there are a lot of problems with government redistribution programs, but being _random_ shufflings of income is not one of those problems.

Actually, independent of who proposes the policy, what their agenda is, and who is affected, the one thing you can be fairly confident of is that the resulting redistribution will *not* be random. It will take money from one group with a given distribution of incomes, endowments, and utilities, and give it to another group with a *different* distribution of incomes, endowments, and utilities. That's the whole point of the exercise. The redistribution may well be welfare reducing, but not because of Jensen's inequality.

As we are talking about syllogisms, looking at a single data point and concluding randomness is a good example of hasty generalization.

We can mostly agree that ,leaving aside middle-class studetns in temporary jobs aside, MW redistributes income from not-that-wealthy small business owners to definitely-not-wealthy workers.
MW meets H.L. Mencken dictum that "To every complex problem, there is a solution that is simple,obvious and completely wrong."
The efficient way would of course be free market + subsidies. For most voters , that policy is uncomprehensible.
So you take the least-bad route, hoping not too much low-qualified people are left out of the labor force and that you can build a mercy case for them.
Anyway, what same human being would believe that "We will abolish MW and then institute a better system of free market + subsidies"?. Especially from those who usually propose it? Was it Twain or Mencken again who said that "It is difficult to believe someone when in its place you would lie?"

RSJ, Revisiting the links in the OP above might prevent arguing at cross purposes.

Sure, increasing the MW will increase the wage of someone earning MW: it's entirely correlated. But that's not the point. The gist of the evidence provided by Stephen in the links in the OP is that the incidence of MW and being a member *of a poor household* is such that an increase in MW has the same probability of increasing the income of a poor household as random redistribution. You don't seem to be making that distinction between individuals and households.

And I don't think it really matters that that u(.) of poor households is perhaps not the same as u(.) of rich households - unless we make some assumptions about poor people that you (and I) probably don't want to make. We can just use u_rich(.) and not open that can of worms.

After they introduced the min wage in Britain I think the price of coffee went-up. Shame that.

Travis: I wonder if the income elasticity of demand for coffee (and the goods that went up in price) is less than or greater than one? My guess is that for coffee it's less than one, and so the price rise would be like a regressive tax.

I second RSJ’s point that minimum-wage increases are not “purely random redistributions of income.” It may be that the proportion of people making minimum wage is about the same among households below the poverty line and above it. But is the proportion also the same among rich households?

Also, have you seen this recent study?

No. Why do you think it's relevant? It makes no reference to the questions of inequality and poverty.

You recently argued:

The employment effects of the minimum wage might be safely ignored if the gains from doing so - in terms of reduced poverty and inequality - were “large enough”. But available evidence makes it clear that these gains are far too small to justify ignoring employment effects.

The study finds “no adverse employment effects.”

Erin, you being too literal. Think of it this way:

Take the existing distribution of households and wages of the members of those households. You have a dart board and you pin the households to it. Then you close your eyes and throw the dart. The household the dart lands on gets money taken from all the other households on the dart board. Maybe the household is poor and maybe the household has someone working for minimum wage. But probably not. So the policy doesn't help poor households very much. And Stephen's nifty bit of math shows that in fact it makes everyone worse off. Probably. :)

But “doesn’t help poor households very much” is not the same as “welfare-reducing.”

Stephen’s point about decreasing marginal utility only applies to redistribution between people who started with the same income. If the redistribution is from rich households to middle-class households, it’s welfare-enhancing.

Of course, the next step is to see if that 'if' is in fact borne out in the data.

Available evidence suggests that increasing the minimum wage increases poverty rates. If you have a story that explains why that's an acceptable consequence of increasing the minimum wage, I'd like to hear it.

The study finds “no adverse employment effects.”

Oh, come on. Studies that use Canadian data - which I find more convincing when it comes to discussing the minimum wage in Canada - consistently find significant employment effects. You should know that.

You seemed pretty happy to cite an American study on your side of this debate.

You also seem pretty happy citing studies based on non-Canadian data in support of slashing Canadian corporate tax rates.

the next step is to see if that 'if' is in fact borne out in the data.

So, you did not check the data before asserting that it is “purely random”?

And if Canadian studies had contradicted it, I would have had some explaining to do. But they don't, so I don't.

You do. Tell me why you're okay with an increase in poverty rates as the price we have to pay for an increase in the minimum wage.

So, you did not check the data before asserting that it is “purely random”?

And you did? In any case, you missed the point of the post if you thought I was asserting that.*

But if you're claiming that this is the case, it's for you to show it. And again, to explain why it somehow compensates for increasing poverty rates.

*eta: Apparently I have to explain the point: If you want to claim that a redistribution policy is helpful, then you have to show that it *significantly* redistributes income to those in the bottom part of the distribution. Policies that are purely random - or are close to purely random - will be welfare-decreasing.

Stephen, I'm also wondering why you are modeling the minimum wage as a transfer in the first place.

If you are assuming a competitive labor market, then total income would be reduced -- the poorest earners would just be lopped off, with no transfer.

Given the clustering of wages at the MW, we can tweak this and say that some rents are being transferred from owners of firms to their lower paying employees, as well as a reduction in incomes. To the degree that the transfer occurs, it wouldn't be between groups with the same income levels, unless you are arguing that the owners of firms have the same income distribution as the MW workers. But asset ownership patterns (as a function of income) make that unlikely. In that case, I don't see how you would model the combined effects as a transfer among identical income cohorts (i.e. why E_z(z|x) = 0). It might be that E_z(z|x) < 0 for the smallest x (if households lose income to the minimum wage), and E_z(z|x) < 0 for the highest x, as asset ownership is more concentrated than income, but that E_z(z|x) > 0 for those x in between.

On top of all that, you have the possibility of different consumption preferences among these groups.

And the big elephant of regressive taxation that might incentivize MW earners to reduce their labor supply when their wage goes up. I think this might be enough to explain a divergence between U.S. and Canada data. In which case, the solution might be to get rid of the tax hump rather than to freeze the MW.

There is really a lot going on here, but none of it seems to satisfy your three bullet points -- the ones after "Suppose that [...]".

Which is not to say that there aren't good arguments against raising the MW, but the existence of those arguments doesn't make this particular argument a good one.

RSJ, please read my last comment, where I explain my point again. You seem to be missing it.

Stephen, I see your point, but the math doesn't support your point.

Simple example.

Our population contains three income cohorts: C_1 = 1, C_2 = 10, C_3 = 100. There are 10 people in the first cohort, 85 people in the second cohort, and 5 people in the third cohort.

The population is also divided into two groups.

Group A has 10 people, and its distribution among the three cohorts is (1, 9, 0).
Group B is everyone else.

Now a policy that takes $2 from everyone in C_3 and gives $1 to each person in Group A will be welfare enhancing, and it will lower inequality.

And yet p(A | C_1) = p(A), and most of the income from this policy doesn't land in C_1 at all.

Now if you want to argue that this policy isn't "helpful", that's one thing, but I'm responding to the math and the assumptions of the post. What is helpful or worth doing is a different matter.

@ Nick,

Maybe some, although I suspect most of the goods that were affected were actually services (the price of coffee did not go up but the price of a brewed coffee in restaurant did) and thus above 1.

Match that with the fact that labour markets got tighter after the legislation was passed until S-11 and I am betting it was actually a progressive transfer. Anyway the UK is a great natural experiment which on the face of it makes a mockery of the just so 101 story.

RSJ: Okay, I think I get it. Yes, I agree that going from 'earning minimum wage and being in poverty are independent events' to 'the minimum wage is a purely random transfer' does not follow (although the reverse is true).

The thought experiment was inspired by the independence result, and I wanted to see what the effects on welfare would be from a purely random transfer. As I said at the end, the point is to raise the bar for progressive transfers. Purely random transfers are not welfare-neutral.

Yep. By the way, the reason why random transfers among a group with the same income are welfare reducing is that they create inequality.

You started with everyone having the same income and after the transformation they have different incomes.

On the other hand, random transfers strictly across groups with different incomes may be welfare enhancing or welfare reducing, depending on whether they reduce or increase in inequality.

And you make a good point in that if you start with a certain income distribution and apply a purely random transformation to it, then as that transformation will consist of some transfers across income groups and some transfers within the income group, then you are already behind, in the sense that the transfer within the group will be welfare reducing whereas the transformation across the group is ambiguous.

In my example, there were no transformations within groups so it was clear that the result was welfare enhancing, but in general this wont be the case.

But having said all of that, I don't think the right MW policy is going to boil down to these types of questions. I really would be interested in seeing a model of the effects of a minimum wage hike in the presence of the low income marginal tax wall that you pointed out in your basic income post. Perhaps it's just me, but it seems that the tax policy is going to be a game changer for any effort to increase wage income for the poor.


Anyway, what same human being would believe that "We will abolish MW and then institute a better system of free market + subsidies"?. Especially from those who usually propose it? Was it Twain or Mencken again who said that "It is difficult to believe someone when in its place you would lie?"

All these comments and nobody has noticed that the math is wrong?

Suppose for "economic agent" we write "molecule of an ideal gas", for "income", "energy", and for "convex utility function", "entropy." Then according to this reasoning, the 2nd law of thermodynamics is backwards: entropy is always decreasing.

What has gone wrong is that x is mis-specified. On the one hand, negative incomes are inadmissible; thus, for a given agent, x cannot be independent of y. On the other, the requirement that the sum of all x be zero is not equivalent to the assumption that the expectation of each x be zero; in fact, individual x will be biased.

That is not to say that I necessarily think raising the minimum wage is utility-increasing. That is because I agree with RSJ: the observation that there is little overlap between poor people and minimum wage earners is not equivalent to the assumption that income is randomly distributed. So the premise of the model is wrong.

A few comments:

Without offering proof, it seems to me that we can divide the minimum wage into a desired income transfer and an arbitrary transfer that does not target the best sources of funds or targets of the transfer. Given this, it seems that a reasonable intepretation of the author's point is that the arbitrary transfer -- which might be big compared to the desired transfer -- is welfare reducing.

I agree that the described negative effect is likely to be modest. But so is the positive effect.

I'm not a big fan of the minimum wage; I thought that economists commonly accepted that it is inferior to the earned income tax credit (EITC), which is a type of negative income tax policy (loosely) in the United States that actually exists, contrary to the cynical suggestions by Twain and Mencken.

@Erin, forgive me if I am completely unpersuaded by an article in REstat. By my careful count, there have been 6,497,245,765,296 empirical studies in similarly good journals and of these approximately 0 -- give or take 0 -- have actually settled an important empirical issue permanently. I don't expect the Dube et al article to be the first. I could criticize it substantively -- e.g., restaurants are likely to be less affected than the labor market as a whole -- but I will be content with observing that someone else will do a better job of criticizing it in a few months or a few years. Just like Neumark Wascher (2000) hammered Card and Kreuger 15 years ago.

I will note that Dube et al cannot really claim "no adverse employment impacts," at best they fail to reject the null that there are no adverse employment impacts. That is very likely a power problem. But one cannot say that the null is actually true, just because one fails to reject it.

Further, the long-term effects of a minimum wage increase are likely to be much bigger than the short-term effects as businesses consider wages in planning to replace their capital stock and decide on new production facilities. Further, a young person who is priced out of the labor market for any period will often become permanently detached or at least lose significant lifetime human capital.

@tyronen, I don't understand why your relative is more dignified because there is a law that mandates that some business pay him a certain wage. That is surely not a "fair wage," it is a government mandated wage.

There are very few people who work from their 20th to 50th birthday at minimum wage. Very few. Those who do so likely have significant problems and a more carefully targeted policy would do them much more good than the scattershot minimum wage.

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