Believe those who are seeking the truth. Doubt those who find it. Andre Gide

Saturday, November 15, 2014

Roger Farmer on labor market clearing.

While I'm a huge fan of Roger Farmer's work, I think he gets this one a little wrong:  Repeat After Me: The Quantity of Labor Demanded is Not Always Equal to the Quantity Supplied. I am, however, sympathetic to the substantive part of his message. Let me explain.

The idea of "supply" and "demand" is rooted in Marshall's scissors (a partial equilibrium concept). The supply and demand framework is an extremely useful and powerful way of organizing our thinking on a great many matters. And it is easy to understand. (I have a pet theory that if you really want to have an idea take hold, you have to be able to represent it in the form of a cross. The Marshallian cross. The Keynesian cross. Maybe even the Christian cross.)

The Marshallian perspective is one in which commodities are traded on impersonal markets--anonymous agents trading corn and human labor alike in sequences of spot trades. Everything that you would ever need to buy or sell is available (absence intervention) at a market-clearing price. The idea that you may want to seek out and form long-lasting relationships with potential trading partners (and that such relationships are difficult to form) plays no role in the exchange process--an abstraction that is evidently useful in some cases, but not in others.

I think what Roger means to say is that (repeat after me) the abstraction of anonymity, when describing the exchange for labor services, is a bad one. And on this, I would wholeheartedly agree (I've discussed some of these issues in an earlier post here).

Once one takes seriously the notion of relationship formation, as is done in the labor market search literature, then the whole concept of "supply and demand" analysis goes out the window. That's because these well-defined supply and demand schedules do not exist in decentralized search environments. Wage rates are determined through bargaining protocols, not S = D. To say, as Roger does, that demand does not always equal supply, presupposes the existence of Marshall's scissors in the first place (or,  more generally, of a complete set of Arrow-Debreu markets).

And in any case, how can we know whether labor markets do not "clear?" The existence of unemployment? I don't think so. The neoclassical model is one in which all trade occurs in centralized locations. In the context of the labor market, workers are assumed to know the location of their best job opportunity. In particular, there is no need to search (the defining characteristic of unemployment according to standard labor force surveys). The model is very good at explaining the employment and non-employment decision, or how many hours to work and leisure over a given time frame. The model is not designed to explain search. Hence it is not designed to explain unemployment. (There is even a sense in which the neoclassical model can explain "involuntary" employment and non-employment. What is "involuntary" are the parameters that describe an individuals' skill, aptitude, etc. Given a set of unfortunate attributes, a person may (reluctantly) choose to work or not. Think of the working poor, or those who are compelled to exit the labor market because of an illness.)

Having said this, there is nothing inherent in the neoclassical model which says that labor market outcomes are always ideal. A defining characteristic of Rogers' work has been the existence of multiple equilibria. It is quite possible for competitive labor markets to settle on sub-optimal outcomes where all markets clear. See Roger's paper here, for example.

The notion that supply might not equal demand may not have anything to do with understanding macroeconomic phenomena like unemployment. I think this important to understand because if we phrase things the way Roger does, people accustomed to thinking of the world through the lens of Marshall's scissors are automatically going to look for ways in which the price mechanism fails (sticky wages, for example). And then, once the only plausible inefficiency is so (wrongly) identified, the policy implication follows immediately: the government needs to tax/subsidize/control wage rates. In fact, the correct policy action may take a very different form (e.g., skills retraining programs, transportation subsidies, job finding centers, etc.)


  1. Bob,
    This is the way labour markets work: v(s, y, λ) max{λ, R(s, y) min[ λ, β ∫ v(s′, y, λ) f(s′, s)ds′]}.


    Robert Lucas went on to explain in his professional memoir about this exchange in the early 1970s that:

    "we had agreed on notation: s stood for the state of product demand at a particular location, y stood for the number of workers who were already at that location, R(s, y) was the marginal product of labour implied by these two numbers, and v(s, y) stood for the present value of earnings that one of these workers could obtain if he made his decision whether to stay at this location or leave optimally.

    Other features of the equation were as novel to me as they are (I imagine) to you…a single parameter—Ed’s λ—stood for two different things: the present value of earnings that all searching workers would have to expect in order to leave a location and the present value that a particular location would need to offer to receive new arrivals…If I had to pick a single day to represent what I like about a life of research, it would be this one.

    Ed’s note captures exactly why I think we value mathematical modelling: it is a method to help us get to new levels of understanding the ways things work."

    1. The paper you refer to can be found here:

  2. Thanks, Alchian (1969) lists three ways to adjust to unanticipated demand fluctuations:
    • output adjustments;
    • wage and price adjustments; and
    • Inventories and queues (including reservations).

    Alchian (1969) suggests that there is no reason for wage and price changes to be used regardless of the relative cost of these other options:
    • The cost of output adjustment stems from the fact that marginal costs rise with output;
    • The cost of price adjustment arises because uncertain prices and wages induce costly search by buyers and sellers seeking the best offer; and
    • The third method of adjustment has holding and queuing costs.

    There is a tendency for unpredicted price and wage changes to induce costly additional search. Long-term contracts including implicit contracts arise to share risks and curb opportunism over sunken investments in relationship-specific capital.

    These factors lead to queues, unemployment, spare capacity, layoffs, shortages, inventories and non-price rationing in conjunction with wage stability.

    Alchian and Woodward’s 1987 ‘Reflections on a theory of the firm’ says:

    “… the notion of a quickly equilibrating market price is baffling save in a very few markets.

    Imagine an employer and an employee. Will they renegotiate price every hour, or with every perceived change in circumstances? If the employee is a waiter in a restaurant, would the waiter’s wage be renegotiated with every new customer? Would it be renegotiated to zero when no customers are present, and then back to a high level that would extract the entire customer value when a queue appears?

    … But what is the right interval for renegotiation or change in price? The usual answer ‘as soon as demand or supply changes’ is uninformative.”

    Alchian and Woodward then go on to a long discussion of the role of protecting composite quasi-rents from dependent resources as the decider of the timing of wage and price revisions.

    Alchian and Woodward explain unemployment as a side-effect of the purpose of wage and price rigidity, which is the prevention of hold-ups over dependent assets.

    They note that unemployment cannot be understood until an adequate theory of the firm explains the type of contracts the members of a firm make with one another.

    Benjamin Klein’s theory of rigid wages in American Economic Review in 1984 is one of the few that explored rigid wages as an industrial organisation issue. Klein treated rigid wages as a response to opportunism and hold-up problems over specialised assets and are forms of exclusive dealership or take-or-pay contracts.

  3. The fake cross of AD(p, y, t) and AS (p, y, t) lines is deadly sin, which is widely spread in “theoretical” economics. The fake cross has the following property:

    3-dimension AD/AS lines do not cross simultaneously in all 2-dimension projection planes (i.e. p-y, p-t, y-t).

    In temporal logic, we have 8 different logic assertions for describing AD/AS cross
    1. ALL t, ALL p, ALL y AD(p,y,t) = AS(p,y,t)
    2. EXIST t, ALL p, ALL y AD(p,y,t) = AS(p,y,t)
    3. ALL t, ALL p, EXIST y AD(p,y,t) = AS(p,y,t)

    Only the true cross (the first one above) gets redemption. My pet theory is that if you really want to have a true cross, you have to derive it from NIPA/FOF accounting identity since it requires AD-AS function equivalence (congruence). We cannot axiomatically assume it as equivalent function values by using a math sign “=”.

    As a reminder, the following AS/AD lines have fake crosses if thinking them in 3-dimension space-time in the economy.
    AS(p,y,t) = MV,
    AD(p,y,t) = PQ

    AS(p,y,t) = Nominal Interest Rate
    AD(p,y,t) = Real interest rate + inflation rate