A Good Paper Could Be Better

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“The compensating wage differentials [CWD] model is widely regarded as one of the core models of wage determination in labor economics.” The quote is from Kurt Lavetti’s “Compensating Wage Differentials in Labor Markets: Empirical Challenges and Applications,” Journal of Economic Perspectives (Summer 2023). If his CWD assessment is correct and the analysis is sound – I believe both to be true – his paper should interest readers of the GEM Blog. The objective of this essay, however, is more far-reaching, i.e., showing how Lavetti’s good paper could have been important. It could have been a must-read companion to Sherwin Rosen’s (1974, 1986) fundamental contribution to understanding wage differentials.

Lavetti lays out what the paper does: “In this article, I begin with an overview of the Rosen model, which emphasizes that compensating wage differentials result from workers with different preferences for amenities sorting between firms with different costs of providing amenities. I then present a chronology of the empirical approaches used to estimate compensating differentials, highlighting the new lessons learned as data quality and methods advanced over time and how these advances in turn revealed new challenges and setbacks.

“I begin with basic cross-sectional wage models, and then discuss how panel data models were used to alleviate bias caused by unobserved worker skills. Attempts to extend the theory of compensating wage differentials to markets with imperfect competition or search frictions led to grave concerns about  the applicability of the Rosen model to realistic labor market settings and sowed doubt about the reliability of empirical estimates. Recent progress in responding to these concerns has involved using newly available matched worker-firm data and settings with quasi-random variation in levels of job amenities.”

Rosen on Wage Differentials

Again from Lavetti: ” The Rosen (1986) model provides a theoretical framework for understanding tradeoffs between wages and amenities in labor markets. Consider a competitive labor market in which workers choose between jobs that offer different levels of wages, W, and amenities, A, to maximize utility ui(W,A). A includes both good and bad job characteristics, where a reduction in disamenities can be expressed as an increase in amenities, and vice versa. The subscript on ui indicates that different workers, denoted by i, have different preferences for amenities relative to wages.

“In this model, all workers are assumed to have the same productivity—the model abstracts from factors other than A that might cause wages to vary, making it important to control these other factors in empirical estimation. Workers choose whether to sell their services in the labor market at wage rate W and also choose how much A to buy, where the price of A is an implicit reduction in the wage rate. In this sense, a worker’s decision to accept a job can be viewed as a simultaneous selling and buying choice. The observed wage is the sum of these two transactions that are tied together but conceptually distinct.”

Lavetti’s paper is  concerned with the importance of and great difficulty in controlling the “factors other than A that might cause wages to vary… in empirical estimation”. The value of  his contribution is the care with which he works through the minefield of problems in controlling other-than-A factors that are ubiquitous in market-centric modeling.

How To Be Better

Despite my admiration of Lavetti’s article, I have a critical issue. Had he been more ambitious, he could have made a fundamental contribution. The major shortcoming of the Rosen literature is its market-centric modeling excludes a significant determinant of wage differentials in modern, highly specialized economies: the worker’s industry of employment. There are two related reasons for omitting worker location. First, while the evidence for the importance of the industry location is readily available, it is overlooked largely because (until recently) its use had never been made consistent with rational behavior. – a requirement of mainstream modeling enshrined in the New Neoclassical Synthesis. Second, the new model that emphasizes location is rooted in the generalization of rational exchange from the marketplace to workplaces restricted by asymmetric employer-employee information. Many mainstream theorists are deeply resistant to nonmarket analysis.

Evidence. The best, still relevant empirical analysis of U.S. wage rent occurred decades ago, a lapse that reflects the inattention paid to wage rigidities during the mainstream run of the New Keynesians. Katz and Summers (1989), hereafter K&S, used the Current Population Survey to demonstrate that many employees receive substantial wage rents as a result of working in particular industries. K&S estimated the average rent in industries that pay premiums to be 28%. Controlling for a range of worker characteristics reduces their estimate to 15%, but that adjustment requires caution. If firms use existing wage rent to cream job applicants, as they surely would, 15 percent significantly underestimates of the true pure wage rent (PWR). K&S additionally show that accounting for fringe-benefit or occupational differences tends to increase, not reduce, the wage differential.

Wage rents are also not caused by unionization. K&S find similar-magnitude rents are paid to nonunion workers. How about Adam Smith’s famous argument, i.e., relatively difficult working conditions being a cause of relatively high labor pricing? K&S present evidence indicating that industries paying wage rents tend to have better working conditions.

Probing more deeply, K&S use longitudinal evidence, focusing on worker movement from low- to high-wage industries, to identify another interesting fact. Relocating employees immediately pocket 60 to 100% of the industry wage differential. That new hires’ quickly capture most or all the existing rent undermines the argument that higher labor pricing reflects undetected differences in specific human capital. K&S finally investigate the nature of rent-paying industries. They are capital-intensive, experience relatively high rates of return, and invest more heavily in R&D. They are easily recognized as the large establishment venue (LEV) that in GEM modeling is inherently restricted by costly asymmetric workplace information and routinized jobs.

There is little reason to believe that the K&S findings do not hold today. As already noted, the analysis of industry wage rent largely dried up as mainstream research became dominated by friction-augmented general market-equilibrium (FGME) modeling, which is infertile ground for PWR. Some attention, especially in Europe, continues to be paid to firm-size wage effects, producing results consistent with K&S and the generalization of exchange. Relevant studies include Brown and Medoff (1989), Lallemand, et al. (2005), Plasman and Rycx (2005), Cardiff-Hicks et al. (2014), and Colonnelli et al. (2018).  

Rationality. The generalized-exchange model that microfounds industry location as a critical determinant of the nature and size of wage differentials will be compactly described below. Lavetti’s short account of the late Robert Lucas’s foray into wage estimation helps the transition to the two-venue theory. “In a classic example, Lucas (1977) estimates a cross-sectional wage model that controls for age, gender, schooling, and union membership and estimates compensating differentials for a set of amenities, including workplace hazards, whether the job requires repetitive tasks, is physically demanding, or requires supervising workers (among other amenities). Lucas finds that among workers with a high school degree, jobs that require highly repetitive tasks pay around 10–25 percent higher hourly wages. An instructive if perplexing finding, however, is that the coefficient on physically demanding jobs is negative—that is, it suggests that workers are willing to sacrifice wages to obtain physically demanding jobs. As Lucas (p. 218) explains: ‘[I]t is highly probable this effect may be explained by the omission of some ability, other than schooling, which is possessed by people in sedentary occupations’.”

Lucas errs in adopting the mainstream excuse for whatever compromises the market-centric modeling of wage differentials. The generalized-exchange theory, in which routinized jobs play an important role. easily explains Lucas’s perplexing findings 

Generalized-Exchange Modeling

Generalized-exchange theory, rooted in optimization and equilibrium, is the focus of the GEM Project. It is shown to be consistent with the relevant evidence as well as the descriptive analysis of practitioners and inside-the-firm labor economists. It provides a much more accurate treatment of large-establishment wage setting than market-centric NK modeling.

  • As already noted, the model intuitively generalizes rational exchange from the labor market (with its full slate of NK frictions) to workplaces restricted by inherent employer-employee information asymmetries. Such workplaces have accounted for a great deal of the total labor force since  the Second Industrial Revolution.
  • Generalized-exchange labor pricing is motivated by optimizing employer-employee interaction organized by general decision-rule equilibrium. It is consistent with perfectly competitive labor markets. It is fundamentally consistent with the 1990s New Neoclassical Synthesis, which provides standards for macro modeling accepted by New Keynesian, New Classical, and Real Business Cycle theorists.
  • That grand compromise paid particular attention to rational behavior. Indeed, if faced with a choice between rationality and the evidence, the jump ball goes to the former. While that always being the correct selection is debatable, a long career making sense out of difficult, high-stakes macro problems has persuaded me that close, not perfunctory, attention should be paid to rational behavior. Substituting assumptions of convenience, especially in wage analysis, almost always misleads, typically badly. At a minimum, such convenience – frequently used in NK modeling – must be carefully justified.
  • Information-challenged workplace equilibrium produces two classes of rational wage rigidities (WR), downward nominal inflexibility over stationary business cycles and chronic wage rent.
  • Generalized-exchange WR combines with adverse disturbances in nominal demand to produce two classes of mass involuntary job loss: temporary layoffs that occur in the millions in recessions (consistent with stationary spending disturbances) and permanent job downsizing that occurs in the millions in depression (consistent with nonstationary spending collapse).

The fundamental mistake made by NK theorists deserves emphasis. Rational marketplace exchange is inadequate to the task of usefully modeling macro instability. Standard theory must be cojoined with rational workplace exchange restricted by information asymmetries.

It is crucial to understand that the second venue is not some kind of elaborate market friction. What goes on in LEV workplaces differs greatly from SEV (small establishment venue) market activity. Preferences motivating worker conduct are especially unique to each sector. Detailed rules and systems of jurisprudence always constructed by profit-seeking LE firms exist only in their most rudimentary forms in SEV businesses. Moreover, LEV labor pricing rations high-wage jobs, forcing SEV workers into chronic market disequilibrium and creating (explicit and implicit) queues of SEV workers wanting LEV jobs. It makes no sense to try to understand information-challenged workplace equilibrium and the role it plays in macroeconomics by thinking of it as some kind of elaborate market friction. The hard fact is that stabilization-relevant theory requires two distinct venues of exchange, and any attempt to advise policymakers using analysis rooted in only one (always the marketplace) is akin to malpractice.  

Critical Puzzle

A recurrent theme of this Blog is that the casual scrapping of rationality, particularly in labor pricing, has robbed NK modeling of powerful guidance. Carefully pursued, rational behavior has a record of opening up analyses to important, sometimes unanticipated, results. In that context, the progression of NK research illustrates a consequential puzzle in the 21st century development of macro theory.

The GEM Project sets up the puzzle. As noted, it has successfully modeled and made available rigorous rational-behavior wage determination that is consistent with the available evidence. The two-venue approach generalizes rational exchange from the marketplace to information-challenged workplaces. The powerful results of the workplace-marketplace synthesis can be incorporated into NK research, making mainstream analyses much more consistent with both the New Neoclassical Synthesis and ever-accumulating macro facts at almost no cost. In so doing, and perhaps this is the rub, New Keynesians would be acknowledging that a fundamental requirement of the adequate treatment of labor pricing after the Second Industrial Revolution is the intuitive cojoining of a second (workplace) venue of rational exchange to textbook market-centric modeling. The new venue is comprised of firms in which workplace employer-employee information is inherently asymmetric. That commonplace condition characterizes a substantial share of the total labor force in any modern, highly specialized economy.

Here is the puzzle. Why would mainstream market-centric theorists choose to exclude millions of workers in large, highly specialized firms from their analysis? Paying attention to the fact of information-challenged workplaces would immediately upgrade a great deal of NK research to the elite status of macro modeling rooted in neoclassical tenets of optimization and equilibrium while aligning with a full range of stabilization-relevant evidence. More particular to this post, Lavetti’s analysis of wage differentials could draw on generalized-exchange findings and make the first fundamental contribution to CWD literature since Rosen. 


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