Wages = MRP?

Stephen Gordon is wondering whether demographic changes account for concentration of income distribution.

I’ve never bought the wages = MRP story, for many reasons.

First, productivity is a function of the firm or industry, whereas wages are determined by the occupation. And most occupations are complementary.

From the BLS FAQ:

Why don’t we measure productivity for particular groups, such as white-collar workers?

BLS productivity measures are based on aggregate national measures of outputs and inputs. These data sources do not provide the information BLS would need to construct occupational measures. There are also conceptual obstacles to disaggregating these national measures. For example, the output of a factory may require both white-collar and blue-collar inputs, and it is therefore unclear how to allocate the output to the two groups separately.

Imagine a tech firm that has a QA department, an engineering department, technical writers, marketing staff, system administrators, accountants, lawyers, customer support, sales staff, sales engineers, human resources, and executives.

That is a simple firm.

Now the firm’s revenues increase (or decrease). How to allocate this change in revenue among the different occupations?

The notion that some form of MRS can determine relative wages is a bit odd. It suggests that the firm would engage in a series of experiments — say laying off some engineers and hiring more lawyers, to see which adds more to revenue in order to efficiently determine the wages paid to each occupation.

There is a reason why firms don’t do this. First, assume the firm has 100 occupations, so it engages in 100 100! = 9.33262154 × 10157 layoff/hire shifts and then monitors its own revenue. Next,  the firm would need to determine whether, after a staffing change, the change in revenue was attributable to market forces, to the laid off individual being genuinely more or less productive, or to the occupation as a whole being more or less productive.  Therefore to separate signal from noise, it would need to gather a lot of data, and to keep gathering this data as the market or the firm’s own product line up changed. But there are costs (e.g. hiring and firing costs) that make such a wage determination exercise prohibitive.

Therefore the first obstacle is that gathering data about the MRP of occupations is too expensive.

The second obstacle is that it takes time, whereas the MRP of workers is state-contingent. When the firm decides to layoff some human resources staff and hire more technical writers, the effects of this decision are revealed over long time periods. And of course the market conditions will be different then, so you need to repeat this experiment over the whole business cycle. But firms, at one stage of development, need more engineers than sales staff, whereas at another stage of development they need more sales staff than engineers.

By the time you’ve gathered all the data you need, your data is obsolete.

More or less, firms understand which employees are high performing and which business functions are critical. But that general understanding does not translate into a specific “MRP” number that is stamped on someone’s forehead. There are problems of attribution. Business units fight over credit for performance, and it pays to know how to cover your ass or how to take credit. These skills wouldn’t be valuable if there wasn’t deep ambiguity about who contributed to the bottom line and who didn’t.

One could argue, even if firms do not engage in useful experimentation, that mere competition among firms will ensure that firms that accurately judge the MRP of workers will survive whereas firms that do not will fail. This is a type of evolutionary argument. But there is no “right” way to survive, and the organisms that exist are not perfectly optimized in all respects. Moreover, evolution requires millions of years, whereas firms and occupations are constantly changing, as is relative compensation of occupations.

Firms need to only be as efficient as their peers, and there are many different solutions to the competition problem, just as there are many different configurations of compensation that are “good enough” for firms to survive. In Germany, executives don’t earn huge salaries relative to their employees, whereas in the U.S. they do. Both are good enough to allow firms to survive. Which pseudo-equilibrium is selected depends on custom, culture, power relations, and reservation wages.


Added BLS quote and link to Shapley Value.

Wages = MRP?

5 thoughts on “Wages = MRP?

  1. Man, that Stephen Gordon post is awful. One nonsense claim after another.

    “Greater demand for financial assets” cannot increase the present value of a given firm’s future earnings, except insofar as those earnings are discounted at a lower interest rate. That’s the mechanism by which greater demand for saving increases the value of corporate equity. And obviously it doesn’t work here.

    Second, insofar as greater demands for financial assets does drive up the market value of firms, the marginal product of their output hasn’t changed.

    Third, even if you somehow convinced yourself that a purely demand-driven increase in the value of claims on firms’ future earnings somehow represented a marginal product, why would you attribute it all to the CEO?

    At this point Gordon has tied himself into such a knot that he can assert that “CEOs are just being paid their marginal product” and then, two paragraphs later, “high executive salaries are best thought of as rents” without even noticing the contradiction.

    Just some silly special pleading on behalf of the overclass. Not worth your time.

    1. yeah, this is really history. We had some big debates a while ago about MRP = wages in relation to the minimum wage and union power. I was arguing that unions play a helpful role in counteracting the market power of executives. So this is part of an on-going discussion, and I just wanted to set it down here. This post took all of 5 minutes to write.

  2. bro-del says:

    I’m not sure if there’s a technical term for this but of course certain firms pay general groups of workers a particular wage. This is, I’m sure, more persistent in low-wage industries but it’s still worth thinking about.

    I think the MRP theory also misleads about how firms actually decide to pay wages — workers are paid wages ‘to attract them to work there’ or at least ‘to prevent them from joining the competition’ — but the bosses don’t consult some ‘theory of just deserts.’ So the argument that competition pushes in the direction paying people the value of MRP has some merit, but it is contingent on degree of monopoly/resemblance to perfect-market conditions — if the other guys are paying horrible wages, well, we only need to go a smidge better than that.

    On a highly abstract level, even duopolistic competition would theoretically push those wages up to the highest possible level but that could take a very long time in reality, especially given costs of retraining, job switching, etc. — and as you point out, it also depends on how much managers and bosses (who may persistently overrate their own value and underrate their workers’) think certain work is worth given the difficulty in measuring it. Theoretically, say in a oligopolistic industry, there could be an equilibrium where, wages being in the hands for a select few upper-level employees, it wouldn’t be unreasonable to suppose that they all might underrate employees’ value. Or there could be strategic-competition induced (I barely know any game theory so forgive if this is reaching) lower equilibria that ‘clear’ but are not paying the MRP.

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