Thursday, February 16, 2017

Why You Should Never Use a Supply and Demand Diagram for Labor Markets

You would know this if you read your Cahuc, Carcillo and Zylberberg, but you probably won’t, so read this instead.

A standard S&D diagram for the labor market might look like this:


It’s common to use W (wage) on the price axis and N (number of workers) on the quantity axis.  Equilibrium is supposed to occur at the W where quantity supplied equals quantity demanded.  From here you might introduce statutory minimum wage laws, or jobs with different nonpecuniary benefits and costs, etc.  The default conclusion is that free markets are best.

But hold on a moment.  S and D don’t tell you how many workers actually have jobs or how many jobs are actually filled—these are offer curves.  The S curve tells you how many workers would be willing to accept a job at various wages, and the D curve tells you how many jobs would be made available to them.  That’s not the same as employment.

They would be the same in a world in which labor markets operated according to a two-sided instantaneous matching algorithm, something designed by Google with no human interference at any stage of the process.  In such a world all offers would enter a digital hopper, and all deemed acceptable by someone else’s algorithm would be accepted immediately.  Maybe not Google but Priceline.

But that’s not the world we live in.  Finding out about job openings and job applicants is somewhat haphazard and time-consuming.  Applicants and jobs differ from one another in lots of obscure, subtle but crucial ways.  You really wouldn’t want an algorithm to make these decisions.  And so only some workers who offer their labor, even at what might be an equilibrium wage rate, are taken on, and only some job openings workers willingly apply for are filled.  When we measure unemployment and vacancies à la JOLTS, we are not seeing offers but changes in actual employment and disemployment.

So let’s redraw that diagram.


To the left of N*, the equilibrium number of employment offers, we find N**, the number of workers whose offers have actually been accepted and are now on the job.  A little reflection should be enough to indicate that S&D is a lousy way to frame this distinction.

First of all, what determines this gap between wanting to work (or fill a job) and actually working (or filling it)?  What does this apparatus tell you about N*–N**?  Nothing.  It isn’t built to answer that question, and it doesn’t answer it.

But it’s worse.  The apparatus indicates that N*–N** is the same on both sides of the market: the number of workers looking for work is exactly equal to the number of jobs looking for workers.  But why would we expect that to happen?  What reason is there to think that it’s equally easy for workers to find jobs and jobs to find workers?  On the contrary, the ratio of unemployed workers to job openings never falls to 1.0, or hasn’t since we’ve had JOLTS to inform us.

S&D is simply the wrong model, based on a failure to distinguish between offers and transactions.  Fortunately, there’s a better model out there, search theory, with fairly straightforward intuitions and tons of available data.

Anyone who waves an S&D model at me and makes claims about the labor market is simply advertising that they know less about economics than they think they do.

13 comments:

ProGrowthLiberal said...

That is one shortcoming of the Econ 101 model. As others have noted - the real world may also include markets where monopsony power exists. Add to this the realization that workers may care about things other than wages. Thanks for the hat tip on a labor economics text.

George H. Blackford said...

In addition to adding monopoly elements to the model, it is also necessary to add the fact that the labor demand curve assumes minimum wage employers pay wages that are comparable to what their compaction pays. When the minimum wage is increased all minimum wage employers costs are increased by the same amount, and all are able to pass their increased costs on through comparable increases in prices.

While the higher prices may decrease output somewhat in minimum wage industries, at the same time the increase in the minimum wage redistributes income in a way that affects the demands for output throughout the economic system that are not accounted for in the simple S and D diagram, and there is reason to believe that the more egalitarian distribution will reduce saving and, thereby, increase total demand, hence, total employment.

Anti said...

Who would expect a partial equilibrium model to be complete? We know, for example, that immigrant labor doesn't necessarily lower wages.

Denis Drew said...

Look; labor is bought more or less — or something like — “on margin.”

As long as labor is a fraction (usually small) of the price of a product or service (exception: baby sitting?), then, employees of (super efficient) Walmart for instance could swing themselves a 100% pay raise and the price of their end product would only go up 7% — leading to relatively little loss of demand.

You could say the price of labor is “hard-linked” or something (make up your own phrase) to the price of the product.
******************
My minimum wage angle is to suppose the wage is priced so as to sell fewer hours for more overall dollars (the right way to sell potatoes). By definition jobs will be lost (the first week) in higher paying firms -- diverted demand. Come first payday, if newly flush min wagers spend their extra bucks back at the exact same higher wage businesses the end result will be fewer min wage employees making more up scale purchases than they did before.

In real life people tend to spend more proportionately at firms employing people at their own wage level. Likely end result (found in Card's and Krueger's seminal study): minimum wage employment increases.
********************
http://www.forbes.com/sites/groupthink/2016/08/03/the-minimum-wage-hike-is-good-for-business/#d8512ea34bcd
The Minimum Wage Hike Is Good for Business
Guest post written by
Bill Phelps

"As the CEO of Wetzel’s Pretzels, a company with more than 3,000 employees system-wide—many of them in California—I’ve paid very close attention to our business as California has raised the minimum wage over the past couple of years. And what I found was stunning.

"When California increased the state minimum wage from $8 to $9 an hour in July 2014, our same-store sales doubled in the next two weeks and stayed that way for six months. When the minimum increased again in January of this year to $10, the same thing happened; our same-store growth rate more than doubled. In fact, I recently received an email from a multi-unit Wetzel’s Pretzels franchisee who said his business has never been better and he’s convinced the minimum wage increase has a lot to do with it."

Hat tip to Wetzel’s Pretzels. :-)

AXEC / E.K-H said...

Why you should NEVER use supply-demand-equilibrium
Comment on Peter Dorman on ‘Why You Should Never Use a Supply and Demand Diagram for Labor Markets’

As can be seen in every textbook, economists answer any question by painting the triad SS-function―DD-function―equilibrium. Leijonhufvud called this analytical tool totem of the micro/totem of the macro. What economists do not understand until this day is that there is NO such thing as an economic equilibrium and NO such thing as SS and DD functions. The totem of micro/macro is a NONENTITY like the Tooth Fairy or the Easter Bunny.

After economists have applied their standard analytical workhorse supply-demand-equilibrium for more than a century self-doubts arise, at least with regard to the labor-market: “S&D is simply the wrong model, based on a failure to distinguish between offers and transactions.” (see intro)

But economists never bury one self-delusion without advertising the next: “Fortunately, there’s a better model out there, search theory, with fairly straightforward intuitions and tons of available data.”

What the representative economist fails to realize is that the foundational error/mistake/blunder of the supply-demand-equilibrium approach lies in the microfoundations.#1 The lethal methodological blunder can be stated as an impossibility theorem: NO way leads from the explanation of individual behavior to the explanation of how the economic system works. Because of this, the microfoundations approach has already been dead in the cradle 140 years ago.

What the representative economist fails to realize is that the economy as a system is defined by the interrelationship of a number of elementary variables. Every model, no matter how differentiated, must contain these OBJECTIVE SYSTEMIC interrelationships as its formal hard core. In other words, the false microfoundations have to be replaced by the true macrofoundations. This in turn leads to an objective systemic theory of the labor market.#2

All this is forever beyond the horizon of the representative economist who can easily drop his true model of yesterday but not methodological individualism because: “It is a touchstone of accepted economics that all explanations must run in terms of the actions and reactions of individuals.” (Arrow)

The commitment to microfoundations is the ultimate reason why economics in general and labor market theory in particular is false. The search theory of the labor market is no exception.

Egmont Kakarot-Handtke

#1 The microfoundations approach is defined with these hard core propositions, a.k.a. axioms: “HC1 economic agents have preferences over outcomes; HC2 agents individually optimize subject to constraints; HC3 agent choice is manifest in interrelated markets; HC4 agents have full relevant knowledge; HC5 observable outcomes are coordinated, and must be discussed with reference to equilibrium states.” (Weintraub)

#2 See ‘The one stone that kills orthodox and heterodox employment theory’
http://axecorg.blogspot.de/2016/12/the-one-stone-that-kills-orthodox-and.html

Stephen Williamson said...

Well, if I go into any food store, I see milk on the shelf - there's a stock of the stuff being offered for sale. And there are always some people who have run out of milk and are looking for it. So is supply and demand the wrong paradigm to think about how the market for milk works?

AXEC / E.K-H said...

Stephen Williamson

Already Schumpeter found it necessary to diffuse doubts about the scientific content of the supply-demand-equilibrium approach: “The primitive apparatus of the theory of supply and demand is scientific. But the scientific achievement is so modest, and common sense and scientific knowledge are logically such close neighbors in this case, that any assertion about the precise point at which the one turned into the other must of necessity remain arbitrary.”

As a matter of fact, the ‘primitive apparatus of the theory of supply and demand’ is a thoroughly faulty construct: “There is little or nothing in existing micro- or macroeconomics texts that is of value for understanding real markets. Economists have not understood how to model markets mathematically in an empirically correct way.” (McCauley, 2006)

For the methodologically correct approach see: ‘Essentials of Constructive Heterodoxy: The Market’
https://papers.ssrn.com/sol3/papers2.cfm?abstract_id=2547098

Egmont Kakarot-Handtke

ProGrowthLiberal said...

"We know, for example, that immigrant labor doesn't necessarily lower wages."

(a) Certainly not a lot. Standard Econ 101er reply? That's because the labor demand schedule is very elastic.

(b) Also higher minimum wages lead to very few reductions in employment. Standard Econ 101er reply? That's because the labor demand schedule is very inelastic.

Note (a) and (b) contradict each other.

ProGrowthLiberal said...

Stephen Williamson. Two points. In my Brooklyn neighborhood, there are competing stores a few blocks apart. So if I cannot buy milk in one I go to the other. And even if neither does not have milk on the same day, a day without milk is not exactly the same thing as going months without a decent job. I would say apples and oranges but both types of fruit are subpar in NYC this time of the year.

Peter Dorman said...

Actually, Stephen Williamson (unintentionally) points to an extremely important question. Just as it is typical to have an unemployment/vacancy ratio greater than one, it is also typical to have excess supply in goods markets in capitalists countries, at least at the retail level. I think if you estimated a standard optimal inventory model for most retail establishments you would find that the actual inventory exceeds the optimum for most products. This regularity was first pointed out by Janos Kornai, who contrasted it with excess demand in state-managed economies. He regards this a key distinguishing feature of capitalism, and I agree.

Of course, I am just surmising this pattern; I don't have real evidence. It seems right though.

And the question is why. My hunch is that asymmetric costs of under- and oversupply derive from a model in which consumers face search costs and satisfice by continuing to shop at establishments that have a prior record of keeping their desired items in stock. Thus the cost of undersupplying a particular good is not only missing that one sale but also future sales. That hypothesis has consequences that are testable. I've fantasized about doing just that, maybe with the help of an class full of econ students.

Peter T said...

"if I go into any food store, I see milk on the shelf - there's a stock of the stuff being offered for sale. And there are always some people who have run out of milk and are looking for it"

There's a stock of parks, and people looking for a park to play in. Is supply and demand a good way to think about parks? Not really.

Notice that the price of milk does not vary with the flows of stock and customers. If milk is in short supply, the store puts up a notice limiting the amount customers can buy. If customers do not arrive, the milk is dumped, or given away. If supply is really tight, rationing will be imposed, or priority given to children. And so on (we've just had some interesting negotiations over milk here in Australia).

In short, outside a few rather special domains, people employ a range of strategies to deal with shortages or over-supply, not just one. As an intrinsically highly socially-embedded domain, labour is an area where the strategies are many and complex.

AXEC / E.K-H said...

ProGrowthLiberal

You say: “In my Brooklyn neighborhood, there are competing stores a few blocks apart. So if I cannot buy milk in one I go to the other.”

That is rather smart, but it escaped your attention that this thread is about the LABOR market and neither about the goods market in general nor the Brooklyn milk market in particular.

The SS-function―DD-function―equilibrium approach is false for BOTH the goods and the labor market because ALL microfounded approaches are methodologically false. The macrofounded approach delivers the following testable macro employment equation = true Phillips curve
https://commons.wikimedia.org/wiki/File:AXEC46.png

Explanations haven been given elsewhere.

Egmont Kakarot-Handtke

derrida derider said...

"there's always a stock of the stuff [milk] being offered for sale. And there are always some people who have run out of milk and are looking for it. So is supply and demand the wrong paradigm to think about how the market for milk works?" - Stephen Williamson

A static S&D diagram certainly is the wrong paradigm if we are trying to work out how many people at a given time are actually out of milk and looking for it, rather than what the equilibrium price of an homogenous commodity like milk would be in an economy where all other goods are at their equilibrium price.

In fact this is a good example of a real world effect - modest changes in the wholesale price of milk will make little difference to the stock of people who have run out of milk. But changes in the nature and use of milk would. That all depends on the changed search dynamics.