« Twitter Followers and Canada's Federal Election | Main | Why did (Canadian) inflation-targeting work in 1996 but fail in 2008? »


Feed You can follow this conversation by subscribing to the comment feed for this post.

What is Sumner's logic behind "At that point, a further increase in wages does not appreciably change their total costs"?

If they have raised wages to a point where the cost is just balanced by the reduced bill for recruiting and motivating workers then won't a wage increase beyond that point add a positive cost (the greater wage bill) that is greater than the negative cost (the reduced hiring and motivation bill) and result in a net increase in costs ?


It is Summers (Larry) not Sumner (Scott).

Oops, yes, I got that when I read the post but apparently my fingers didn't !

If i'm to misunderstand your point correctly; you think executive compensation is too high?

Exactly Miami Vice. We do want some sort of maximum wage law for senior executives.

MF: when you are maximising profits, the derivative of profits with respect to a control variable is zero, and a small change in the control variable will cause a very small fall in profits.

Miami and Chris: if I'm to misunderstand your point correctly, you only like theories when they tell you what you want to hear?

Ha, not at all. I'm not invested emotionally or otherwise to any economic theory;)

Please do go on with your, gotcha, take on efficiency wages. Clearly you've thought hard about this post and it isn't some knee jerk reaction to something some more prominent economist said.

So let me get your theory straight.

If God set wages perfectly any adjustment from wages set by God would be sub optimal. I would have to agree. So what?

So in order for anyone to see at the movie theater everyone must stand... or is it sit?

too funny

I made the same point once on Daniel Kuehn's blog. People invoke efficiency wages, and monopsony caused by search frictions as a justification for min wages, but there isn't a single model out there that I'm aware of that support the argument.

I'm a bit more familiar with the monopsony/search connection. The argument works like this: under "classic" monopsony higher wages can lead to higher employment. But we don't really believe there's that many instances of "classa ic" monopsony, like company towns etc. So instead we have a search model where there's an outcome that is "like monopsony" in some respects. But one of these crucial respects that is missing is actually the fact "higher wages raise employment". In other words, mathiness and equivocation.

Miami: Larry Summers (who, obviously, is much smarter than me) gave what I interpret to be an efficiency wage model rationale for God to raise wages above where they would be set by individual profit-maximising firms. I'm saying it would plausibly go in the other direction.

notsneaky: monopsony would (generally) motivate minimum wage laws, wouldn't it? But search frictions create both monopsony and monopoly, so my guess is it could go either way.

I'm waiting for minimum interest rate laws. Seems to me, in an era of negative real interest rates, we need to protect the owners of capital from exploitation by the market. I'm thinking 15% per annum, as people seem to think of that as a fair number (see http://fightfor15.org/). Maybe it's because fifteen starts with an "f". Anyone else want to join my "fight for fifteen" campaign?

Nick, I understand you are a busy man but please bear with me:

Assume two 'players', a now-hiring-company and an employee-to-be.

Those players have preferences over triplets of alternatives {wage, recruitment cost, productivity}*.

*Each entry in the list assumes only two values namely 'high'(alternatively 1) or 'low' (alternatively 0). Therefore in such a setting, both players have preferences over the (2^3=) 8 triplets of ones and zeros (high/low states of the three variables 'wage', 'recruitment cost' and 'productivity').

Now assume that the way each player ranks those alternatives is dependent on what he/she values most.
So, let's further assume that the now-hiring-company player, when comparing two alternative triplets, will (strongly) prefer the one with a low state on the wage and recruitment cost variables (or a zero in positions 1 and 2) and a high state on the productivity variable (or a 1 in position 3).

On the other hand, assume that the employee-to-be player (strongly) prefers triplets with ones in position 1 (high state of the wage variable) and zeros in position 3 (low state of the productivity variable). As far as recruitment costs are concerned, I assume that they are an 'irrelevant alternative' to this player ie they do not affect the way in which he/she ranks triplets.

In such a setting, both players can rank the available triplets in a decreasing order of preference eg the employee-to-be prefers {110,100} to {010,000,111,101} to {011,001} or if he were to assign utility indexes to each triplet he would be content with a mapping like so: {110,100}->3 {010,000,111,101}->2 {011,001}->1.

On the other hand, the now-hiring-company would be satisfied with the following mapping: {001}->4 {011,000,101}->3 {010,111,100}->2 {110}->1 (the numbers obviously are not comparable between players, they are just for preserving rank of preference).

Now, if the rules of the game stipulate that
a) both parties have to reach an agreement on the levels of the three variables and
b) no party can bully the other into accepting an inferior choice
then it seems plausible that both players will agree to negotiate on their second best options (which are {010,000,111,101} for the company and {010,111,100} for the employee).

In this node of the game, the employee's preference schedule looks something like {100}->2 and {010,111}->1 while the company's schedule looks something like {000,101}->2 and {010,111}->1.
Again, both players will choose to settle for their second-best options which - this time - happen to coincide (their second best choice sets are {010,111} for both players).

If the no-bully clause survives up to this point then the employee-to-be has a strong preference for high pay-low productivity (110) while the now-hiring-company opts for low pay and high productivity (011). Unless, they can negotiate some compromise (lowER wage, highER productivity), they won't reach an agreement.

Also, if this whole game had been set up in such a way so as to ignore recruitment costs on the part of the company when forming preferences (if it were more symmetric, in a sense), then the outcome would have been the (second best) collection of states {0#0, 1#1} (either low wage-low productivity or high wage-high productivity)

When comparing those two alternative set-ups (the one with preference over recruitment costs and the one without such preference) we observe that the later scenario (devoid of a preference for low recruitment costs) tends to produce less favorable results for the company than the former.

In a situation where we can think of the company being more powerful than the employee in 'suggesting' a certain outcome over an alternative one, having a preference for low recruitment costs, allows a (possible, final, favorable) choice of a low pay-high productivity agreement, whereas, when the company disregards recruitment costs altogether, it ends up in a situation where a preferable outcome (probably) comes at a cost (high wage-high productivity agreement).

Given the above, is it warranted to propose that when observing high recruitment costs one should expect to find wages that are lower than they otherwise would have been?

Also, in the discussion above, no relationship was assumed between recruitment costs and wages-only counting arguments were essentially used. Yet, it seems that following fairly general assumptions we end up with a proposed (negative) correlation between the two variables.

Does any of this make sense?

The Summers claim doesn’t hold up very well empirically either: most studies show roughly 100% pass-through of higher minimum wages to prices. This means that the “second-order effect on total costs” argument doesn’t hold when wages are increased across the board (presumably because of the fallacy you’re pointing out) — unless, for some reason, firms consistently pick the moment of a minimum wage increase to inflate their markups.

This reflects an interesting internal tension among minimum wage advocates in economics. If clean identification is the standard, they have the empirical high ground on the direct policy question — “do minimum wages decrease unemployment?”. But once we move from direct estimates to the underlying mechanisms, very few of the ideas floating around have any empirical support, and most of them can easily be rejected. Neither the Summers story nor the simplest variant of the monopsony story (which would imply that a binding minimum wage lowers marginal costs) seem consistent with full pass-through to prices. Or, to take another example, search-based monopsony requires that marginal recruitment costs increase dramatically with the scale of a firm’s employee base — which is hard to rationalize either anecdotally or using the formal evidence in the literature.

So it’s an amusing contrast. By prevailing standards, the minimum wage itself has great empirical support — but then pretty much every single explanation that’s offered to rationalize these findings crashes and burns when you subject it to data and a little light theory.

An even more subtle but telling case of this disconnect is the following. The current empirical consensus among mainstream labor economists is that the employment effects of the minimum wage are close to zero. But most of the economic arguments offered to explain this finding do not specifically rationalize the zero — instead, they suggest some force that pushes opposite the traditional supply-and-demand logic, and could in principle offset it by 50% or 150%, rather than just 100%.

In general, if X is some positive value and Y is some negative value — with no a priori relationship between the magnitudes — it’s a remarkable coincidence for X+Y to always come out near zero. Yet, if we substitute “the traditional downward-sloping component of labor demand” for X and “the added effects of search-based monopsony” for Y, that’s exactly what the minimum wage consensus seems to believe. After all, cleanly identified studies aren’t giving sizable negative estimates in some settings and sizable positive estimates in others — they’re basically just giving zeros.

(Of course, one advantage of the Summers hypothesis is that — when drawn out under some very particular assumptions — it could explain a consistent zero. I’m curious whether this view is currently popular, despite its obvious other failings, because smart economists like Summers realize this advantage.

My guess is no, and that this is all a little too subtle. It will take a while for everyone to realize that proposing a negative Y to offset the neoclassical X isn’t good enough — you also need to explain why Y is so consistently of a magnitude that cancels out the neoclassical X. Or else you need to acknowledge that your point estimates might be driven by attenuation bias a la Sorkin, and that the Credibility Revolution isn’t always and everywhere as credible as it purports to be.)

The search models which are used to motivate this are "like" monopsony in that individual firms face upwards sloping "labor supply curves" (basically the no-shirking condition in efficiency wage models). But that's not sufficient for an increase in wages to increase employment. I don't know if this is because of monopoly power, I'd have to think about that. But I do know that if you take any kind of search or efficiency wage model that is out there, from Pissarides and Mortensen to Shapiro and Siglitz, and you add in a above equilbirium wage to it, you still get unemployment just like in the vanilla labor-supply/labor-demand model.

There might be some version of a search model that gets you the pro-minimum wage result out there, but I haven't come across it, and I've looked. All I've seen is "this search model shares some features with classic monoposony, under monopsony minimum wages can increase employment, therefore this is a justification for minimum wages"

Also, here’s a toy model for thinking about the Summers point.

Firms set wages so that, at the margin, the efficiency benefits of higher wages are offset by the costs. Suppose that a fraction ‘alpha’ of these efficiency benefits are stolen from other employers; this is the component of savings that comes from the higher wages themselves, rather than wages being higher relative to the competition.

Now, efficiency gains can take two forms. One is economizing on low-wage labor itself: you need fewer man-hours to obtain the same services from these workers, because the higher wages make them more productive, more experienced, etc. The other is economizing on managerial labor and other expenses: with less turnover and better-behaved workers, you spend less time overseeing and hiring people per hour of labor they provide. Suppose that, at the margin, a fraction ‘beta’ of efficiency gains comes from the first source, and ‘1-beta’ from the second.

Finally, suppose that the demand for low-wage labor services has negative elasticity ‘-e’ with respect to their overall cost. (Let’s keep this simple and in partial equilibrium.)

The elasticity of low-wage labor hours with respect to the minimum wage is then:

-e*alpha - (1-alpha)*beta

Explanation: the “stolen” component ‘alpha’ of private efficiency gains is irrelevant to an across-the-board minimum wage hike, so that the elasticity of the cost of labor services with respect to the minimum wage is ‘alpha’, leading to a ‘-e*alpha’ demand response. Meanwhile, even for the ‘1-alpha’ of legitimate efficiency gains, the ‘beta’ that comes from economizing on worker hours leads to a direct decline in demand for hours.

The only way for the elasticity above to be zero rather than negative is if we assume that alpha = 0 and beta = 0: i.e. that the entire efficiency benefit of higher wages comes from the absolute wages, independent of the wages being paid by other employers, and that the entire efficiency benefit comes from economizing on other expenses, rather than low-wage labor hours themselves.

This is, apparently, the implicit position of Summers and others arguing along similar lines. It doesn’t seem very plausible to me: in fact, I’d find alpha = 1 and beta = 1 more realistic, though (of course) intermediate values are the most likely of all.

"If God set wages perfectly..." ... just so we're clear, you're referring to Lakshmi here, correct? I wouldn't trust Kali with that task (or anything else for that matter!)

john: sorry, but you lost me there.

Matt R.: I'm with you on the alpha in your model.

But I'm not sure about beta. Is it kosher to just assume beta is a parameter?

In any case, my intuition is coming to a similar sort of conclusion as yours, I think. Take the simplest possible efficiency wage model, where efficiency at firm i is a function of Wi only (because of higher wage causing better nutrition causing better strength). Firm i sets Wi so that the elasticity of efficiency wrt Wi is exactly one (assume second order condition satisfied). A small increase in W has only a second order effect on profit, and a first order effect on worker's utility. But even here, there will be a first order drop in the number of workers employed (with only a second order drop in efficiency units of labour employed). So it is not at all obvious that workers as a whole will be better off. If workers are risk-averse, I think the expected utility of a worker would fall.

But I'm not sure about beta. Is it kosher to just assume beta is a parameter?

Well, not a fundamental parameter so much as a local average share, in the same way that alpha is a local average share.

But this was pretty sloppy on my part: for any given impulse, 'beta = the share of efficiency gains coming from reduced labor hours' is well-defined, but 'beta' for the case where all wages are raised (due to the minimum wage) and the case where only your own company's wages are raised might well be different. The formula above makes sense only if 'beta' is defined as the former, so I'll go with that.

A small increase in W has only a second order effect on profit, and a first order effect on worker's utility. But even here, there will be a first order drop in the number of workers employed (with only a second order drop in efficiency units of labour employed).

Exactly, this was my intuition too. If the efficiency gains from a higher wage are solely from more efficiency units of labor provided per hour of work, then even if alpha = 0 and the cost per efficiency unit (and therefore the quantity of efficiency units demanded) stays constant to first order, the number of hours needed to achieve these efficiency units will fall in inverse proportion to the productivity improvement. In other words, Costco doubles its productivity over Walmart by paying $20 rather than $10, and its demand for efficiency units of labor is unchanged, then it will just have half as many hours on the payroll.

Total wages * hours will remain constant, which could in principle benefit workers because they are working fewer hours for the same level of pay; but as you point out, if the rationing rule is not uniform and workers are risk-averse (both of which seem plausible), this can quickly go in the other direction.

Now, that's the case where beta=1, and it's obviously not a very favorable case for the minimum wage. I introduced 'beta' in the first place because I saw some other stories out there, which in principle could be more favorable. In the beta=0 case, the savings come from lower managerial effort (or something similar) rather than higher hourly productivity of the low-wage workers themselves; since the workers are not more productive, if you're set on achieving the same total efficiency units of labor, you don't lower their hours. A number of papers that try to make the case for the minimum wage have stories of this kind - for instance, Rebitzer and Taylor (1995).

What I don't find credible is the view that efficiency gains would come entirely from this source - i.e. that beta=1. I'm sure it's part of the story - but I suspect that a lot of the gains from efficiency wages come from, well, the workers themselves being more efficient too! And I suspect that most people, aside from this particular context, would have priors similar to mine: beta=1, like alpha=1, is just not a very credible claim.

The sad feature of the minimum wage debate is that virtually no advocates feel compelled to make the alpha=1 and beta=1 claims explicitly, even if that's implicitly their contention...

[sorry, meant beta=0 and alpha=0 in the last two paragraphs!]

Nick, I will admit to going for an easy snark. I am not an economist and am not really able to judge the validity of your argument, but...

There is a social cost to dramatic inequality. When top bosses live in different cities and send their kids to different schools than the workers who work at the same place there can be real problems. Maybe not so much on Canada now but there is a problem when the guilded are too rich.

And I fail to see how your argument does not apply to those at the top as much as those at the bottom.

"the simplest variant of the monopsony story (which would imply that a binding minimum wage lowers marginal costs)"

This is not true in the "simplest variant of the monopsony story". A binding minimum wage increases marginal cost. Given a constant price and diminishing marginal product of labor this has to be true if employment goes up. You can type "monospony minimum wage" into google and look at one of those graphs.

Ah yeah, Bryan Caplan's "Low Wage Interventionism"

Also Bob Smith's proposal for a reverse-usury law is the most hilarious thing I've heard all day.


I'm not sure I follow you. Are you ultimately arguing that there are two negative externalities but that they exactly cancel out?

In any event, I don't think the fallacy of composition is the fundamental problem with Summer's analysis. Suppose there is just a bilateral negotiation. Did Summers just prove that we can increase the amount A gives B, by more than the reduction in what A is left with?

Matt R: off-topic (sort of). Did you graduate and get a job? Because you deserve one of the very best academic jobs out there. That is clear to me just from your comments here on these last two posts (which I'm still digesting).

I'm not sure why beta matters. Can't we just lump workers and supervisors together, for this purpose? Getting the same amount of output with fewer supervisors looks like getting the same amount of output with fewer workers. Plus efficiency wages presumably apply to supervisors too (quis custodiet eo ipso whatevers)?

Chris: "There is a social cost to dramatic inequality."

OK. Then base your argument for min and max wage laws on that argument, if that's what's really underlying your position. That's legit (at least in principle, though whether min and max wage laws would in fact help reduce inequality, or whether there might be better ways, could be argued). I'm just attacking people who use theories when it suits them, without really believing them.

"And I fail to see how your argument does not apply to those at the top as much as those at the bottom."

I think it would apply to both (if it applies at all). Which is one reason it would be almost impossible to implement well in practice, even if the theory made sense. And the same would go for any minimum wage argument based on the same theory. You would need a specific maximum (or minimum) wage applied to each type of worker.

notsneaky: "This is not true in the "simplest variant of the monopsony story". A binding minimum wage increases marginal cost."

That seems wrong to me. Assume Q=L, for simplicity. Under monopsony, MC is a markup over W, where the markup is inversely related to elasticity of labour supply. With a binding minimum wage, MC is just Wbar, with no markup. As long as Wbar is set only a little bit above W, MC falls for a given L.

Bob: "Are you ultimately arguing that there are two negative externalities but that they exactly cancel out?"

No. I'm arguing that Larry Summers missed the second externality. (Whether he got the first externality right depends on the model.) I reckon you could rig the model to go either way, but I think my way is more plausible.

"Did Summers just prove that we can increase the amount A gives B, by more than the reduction in what A is left with?"

That is generally true in efficiency wage models. I pay you more than the market wage, but threaten to fire you if I catch you cheating me, and because you now have something to lose if I fire you, you stop cheating me. And if cheating causes bigger losses to me than gains to you (if it didn't I would want you to "cheat" and just cut your wages by an equal amount) we can both gain. But there's a separate question of whether the equilibrium wage that results in this sort of model is (second-best) too high or too low.

"Assume Q=L, for simplicity"

Perhaps I should have said "in the textbook variant of monopsony" rather than "the simplest". I clarify that in the next sentence: "... and diminishing marginal product of labor"

Actually I'm not sure if your example works, I think, for the same reason that you can't have a monopoly with perfectly elastic demand. With Q=L, VMPL is constant. Hence, the competitive wage is the same as the monopsony wage (just like for a monopolist facing perfectly elastic demand, the competitive price is the same as the monopoly price).

The quantity of labor hired by a monopsonist is where the VMPL crosses the MC curve. We then find the monospony wage by "coming down" to the labor supply curve. In your example the MC curve is either constant (it's a bit late here and I have to think about this) in which case... well, the MC is always constant, or the MC curve is upward sloping (absent economies of scale or other funky stuff). Which means that if L goes up MC goes up.

In particular, this:

"MC falls for a given L."

makes no sense. MC is a function of L, no? Are you saying that somehow the MC curve shifts when the minimum wage is imposed?

Q=L, p=1, labor supply is w=(1/2)*L

No min wag:


Max --> L=1 and w=1/2, MC=1

Min wage = 3/4 (or just between 1/2 and 1)


Max --> p>wbar implies you hire as much labor as you can, so L determined by labor supply

(3/4)=(1/2)*L --> L=3/2 (min wage increases employment), w=3/4, MC=3/2

So MC rises, even without diminishing returns to labor, due to the upward sloping nature of the labor supply curve.

and yes, I was wrong about the example not working due to inelastic VMPL. The analogous problem to elastic/inelastic demand for monopoly would be inelastic/elastic labor supply for monopolist. But hey, you're still wrong about the MC.

However, a thought occurred to me ... maybe I should really turn in for the night. Suppose you don't have a monopsony, you got a duopsony. Both firms recognize that the w in their profit equation is a function of L (they're facing an upward sloping labor supply). Then it might matter whether or not the two duopsonists choose L or w, just like it matters whether duopolistic firms are Bertrand or Cournot. And their choices are going to shift each other's MC curves, just like duopolistic firms' choices shift each other's MR curves. And then maybe you can get the result that in equilibrium MC falls. I'd work it out, but I got to go to sleep now.

notsneaky: "Are you saying that somehow the MC curve shifts when the minimum wage is imposed?"

Yes. It shifts down. (You were talking about slopes, and I thought you were talking about shifts. You are right that it may still slope up, with a minimum wage, though it will be flatter than before.)

I'm off canoeing for a day or two.

Not clear on how that happens. With the minimum wage, wbar becomes your new "labor supply curve" but MC is just MC. See the numerical example.

Anyway, have fun canoeing.

If I understand Summers argument it is that a $1 increase in wages will mean more to the worker who receives it (since they get the full $), than it will to the employer who pays it (for whom it will represent only a small reduction in profit.).

The problem with this argument is that it seems to ignore the fact that the reduction in profit (while small) will at the margin lead to some employers choosing not to hire.

I think I see Nick's logic now he has added the update - just can't quite see (yet!) how that applies to Summer's model where no involuntary employment necessarily exists.

@Nick @notsneaky, it isn't about shifts vs slopes is it? In notsneaky's example, the marginal cost equals Wbar = 3/4 when the monopsony buyer is buying less than the optimal amount of labor. It jumps up only at that point. If this producer faces a competitive product market, isn't the relevant side of the MC curve the one to the left? i.e. he produces as long as p > 3/4, not as long as p > 3/2.

Nick, my first two lines were meant as a snarky joke. Too much control of wages is a bad idea. To reduce inequality I would turn to economists and from what I understand a negative income tax + a wealth tax of some sort is best. The American EITC is a huge experiment that seems to have worked. Wealth tax: trickier. A second home tax gets everyone with a camp. Too much capital gains discourages investment. I don't have an understanding of how that might work.

Having been involved in small business, it's a common complaint among proprietors that paying people more seems to have no effect on their performance or job satisfaction. I'm curious if this has been studied, given that small business is the supposed backbone of the Canadian economy.
I guess what I'm saying is that once someone is spaced out or unmotivated by nature, raising their wage by 5 or 10 bucks ain't gonna do a dang thing.

I also wonder about this: If you live in a country with even mild egalitarian wage controls among management in, say, the EU, where borders are open, would it not create a strong incentive for those who are ambitions to move next door where there are no such controls? I understand this is how Germany gets much of it's talent from other European countries, and that the damage caused by this outmigration of talent is suspected to be seriously damaging to small nations like Denmark and Holland. I'm sure you economist have a word for this, and I'd love to know what it is so I can Google it. Thank you.

@Peder, Your "by nature" in the first paragraph is the weak presumption. At the aggregate, there is always slack between ability and job requirements. Or in other words, they (workers) ain't all the "hippies" you describe.

And the maybe-not-so-technical term is "brain drain" perhaps?

@Nick, I can't follow all the math in comments to know if this objection to your reasoning/model was raised but: Surely "recruitment and motivation" is NOT zero-sum as you have modeled it in a slack labor market. Firm A raising wages does not automatically demotivate firm B's existing employees in any case. It only adds to aggregate motivation. (Setting aside second-order effects of course.)

@Jeff, so what's the theory say about how to use wages to reduce this "slack"? It must be different for those who do menial work at $15 / hr vs. managers who earn $60 / hr. ...?

Lastly, if the wage difference between a medium level manager and a higher level manager is relatively smaller, wouldn't there be less incentive for someone to take on the greater responsibility and stress, and thus remain simply content to stay where they are on the "corporate ladder", regardless of talent. It could make the ambitious yet rational person less productive, and thus hurt the company as a whole. So this is also the sort of "slack" you are referring to, correct?

@Peder, I believe the theory says that "carrot plus stick" are both needed to take out (some) slack. The "stick" part would require more from management, so carrots and sticks of appropriate type would need to spread up and down the chain, yes. The trick is to know the point of diminishing returns (i.e. human nature). One firm appears to be currently pushing the envelope in that regard:


"But if all firms were forced to cut wages a small amount, so relative wages stay the same, "recruitment and motivation" would stay the same at the existing level of unemployment, but the lower wages would lead firms to choose to increase employment .]"

Do firms have to lower prices too? Otherwise the aggregate demand will take the hit. Firms will anticipate this and will not choose to increase employment after all? I think failing to notice this is committing to fallacy of composition?

If raising the minimum wage is the purported solution (or part of it), what is the perceived problem? I doubt that it is firms "setting their relative wages too high." (Relative to other firms, that is.) Really? We need to raise wages because firms are in a race to the top in setting wages? Who is making that argument?

If we don't know what the problem is, how can we assess different proposed solutions?

Now, if the problem is unemployment, who is arguing that raising the minimum wage is the solution to that? Summer is talking about increasing long term thinking in business.

The comments to this entry are closed.

Search this site

  • Google

Blog powered by Typepad