Guidance from a Better Model

John Haltiwanger has done important research on economic behavior inside complex, highly specialized firms. This post takes a look at a relatively recent entry in that scholarship, “Cyclical Job Ladders by Firm Size and Firm Wage”, American Economic Journal: Macroeconomics (2018), coauthored with Henry R. Hyatt, Lisa B. Kahn, and Erika McEntarfer. What follows complements the authors on their careful gathering and clever use of obscure inside-the-firm data while lamenting their misleading rejection of a long-standing labor-market fact.

From the HHKM abstract: “We study whether workers progress up firm wage and size job ladders, and the cyclicality of this movement. Search theory predicts that workers should flow toward larger, higher paying firms. However, we see little evidence of a firm size ladder, partly because small, young firms poach workers from all other businesses. In contrast, we find strong evidence of a firm wage ladder that is highly procyclical. During the Great Recession, this firm wage ladder collapsed, with net worker reallocation to higher wage firms falling to zero.” 

Two related difficulties damage the HHKM paper:

• Their interpretation of firm-size ladders;
• The inadequacy of ubiquitous mainstream search theory as a guide to explaining the job-transfer evidence.

After a brief overview of the data sources and critical findings, each difficulty is examined in turn.

Data Sources

From HHKM: “We use linked employer-employee data from the Longitudinal Employer Household Dynamics (LEHD) program at the US Census Bureau to examine the flows of workers across firms. The LEHD data consist of a link between two datasets: (i) quarterly worker-level earnings submitted by employers for the administration of state unemployment insurance (UI) benefit programs and (ii) establishment-level data collected for the Quarterly Census of Employment and Wages (QCEW) program. The UI wage data are associated with “firms” in the form of a state-level employer identification number (SEIN). SEINs typically capture the activity of a  firm within a sample used in this state in a specific industry…. The LEHD paper is a balanced panel of 28 states spanning 1998:I to 2011:IV. We choose this start date and sample of states trading off the need for a long time series with the desire for broad coverage across the United States.”

“Our goal is to measure worker flows across firm wage and size ladders. Firm size in the LEHD data is defined using the US Census Bureau’s Longitudinal Business Database (LBD). Firm size is the national size of the firm in March of the previous year. We use three size categories: “large” firms employ 500 or more employees, “medium” firms employ 50–499 employees, and “small” firms employ 0–49 employees.”

Critical Findings

“In this paper, we test whether workers tend to move up a firm job ladder via job-to-job moves, and the cyclicality of such moves. We explore firm ladders along two dimensions, size and wage, since both are linked to job quality and productivity in theory and empirical work.” The HHKM central conclusions are three-fold:

• “… we find strong evidence of a firm wage ladder in that workers tend to flow, on net, from low wage to high wage firms via direct job-to-job moves.
• “Furthermore, this movement is strongly procyclical, slowing to almost zero in recessionary periods.
• “Surprisingly, we see little evidence of a firm size ladder. Workers do not tend to move from small to large firms. (Italics mine) This is partly because small, young firms are a net attractor of workers making job-to-job moves.”

Of interest to readers of this Blog, the first two conclusions are consistent with – and significantly elaborated upon by – the  GEM Project’s generalization of rational exchange from the labor market to workplaces restricted by inherent information asymmetries. The two-venue theory, however, rejects the third conclusion that a firm-size wage ladder does not exist. On that finding, generalized-exchange modeling implies HHKM badly misinterpret their job-transfer evidence.

Interpreting the Firm-Size Ladders

HHKM conclude their job-to-job transfer evidence rejects the long-standing maxim that workers move from small to large firms. A great deal of other empirical work has demonstrated that large firms pay higher wages for workers with general human capital equivalent to workers in small firms, enabling the poaching of labor from those small establishments. HHKM are aware of the substance and conviction of the literature they are rejecting, citing the extensive evidence review of Burdett and Mortensen (1998) indicating that large firms pay higher wages. They also cite Foster et al. (2008) for evidence that firm size and productivity are positively linked. 

A more persuasive story, easily accommodated in GEM modeling but not in the FGME (friction-augmented general-market-equilibrium) framework, goes like this. High labor productivity, high wages, and substantial size are joint characteristics of LEV (large-establishment-venue) firms. Large establishments share those characteristics as a result of the access provided by size to powerful specialization and scale economies. The GEM Project elaborates on this process by demonstrating that within LEV firms size and high labor pricing are jointly determined outcomes of the Second Industrial Revolution. Given that size and wage rent cannot be separated, it makes no sense to conclude that workers move to high-wage but not to large-scale establishments. (See below.)

HHKM identify a likely explanation for the failure of the evidence to demonstrate the independent flow of workers from small to large establishments. “Firms are born small and then exhibit an up-or-out dynamic that takes some time to unfold. This pattern suggests there are young firms that are highly productive and fast growing but small. Consistent with this notion, we find that small, young firms poach workers on net from all along the size distribution. This can help explain why we see little evidence of a firm size ladder.” A significant number of high-productivity, high-wage, small businesses poaching from the range of small to large firms is not inconsistent with the important macro fact that workers tend to move from small to large firms.

Guidance from a Better Model

The HHKM headline conclusion (“workers do not tend to move from small to large firms”) results from their faulty interpretation of the job-to-job transfer data. The core problem is that search theory, the ubiquitous guide to almost all New Keynesian (NK) labor research, is inadequate to the task of explaining rational behavior of large, highly specialized firms. How can it surprise that adequate interpretation of the HHKM data requires a better model, i.e., one that accommodates the huge changes in production since the Second Industrial Revolution? Mainstream market-centric search theory is too rudimentary to support any such accommodation.

The two-venue analysis featured in the GEM Project is, by contrast, constructed on useful accommodation. It has no difficulty rationally interpretating findings that stump search theory. As noted above, its keystone innovation is the generalization of rational exchange from the marketplace to workplaces inherently restricted by costly, asymmetric information. Such workplaces are inherent to the large-establishment venue (LEV), while less complex firms populate the market-centric small-establishment venue (SEV) featured in FGME theory. 

The workplace-marketplace synthesis is rooted in the neoclassical tenets of optimization and equilibrium, microfounding two varieties of LEV nominal wage rigidities: downward-rigid labor pricing over stationary business cycles and, especially relevant to this post, chronic wage rent. The generalized-exchange theory powerfully enables LEV firms’ poaching workers from SEV firms. Be clear, the workers do not seek transfer to LEV firms because they are large; instead, they seek LEV rationed jobs (for which their general human capital qualifies them) because they pay significantly higher wages. Adequate theory here requires a fundamental step missing in FGME modeling: Identifying the capacity of large size to induce the rational payment of wage rent that in turn induces job-to-job transfer from smaller firms that do not pay such rent. The linkage shows up loud and clear in the wage ladder.    

Moreover, rational LEV wage rigidities interact with periodic adverse demand disturbances to produce mass involuntary job loss, which is almost wholly located in larger-scale firms and has now been made consistent with continuous general decision-rule equilibrium. The generalization of exchange makes employment at large firms more sensitive to the unemployment rate than small firms. It also explains the substantial incidence of job transfer from nonemployment as recalls occur during the persistence (caused by LEV payment of wage rent) of elevated unemployment into cyclical recoveries. HHKM should be pleased that the two-venue model, restricted by powerful wage rigidities, rationally explains the incidence and nature of the collapse of the wage ladder during the Great Recession.

Of particular importance to this critique, however, GEM modeling frees HHKM from rejecting the useful macro fact that large firms (necessarily paying wage rent) do attract workers from small, market-wage-paying small businesses. Rejection of what is broadly known about actual job-to-job transfer casts doubt on the entire article’s interpretation of its novel data source.

Blog Type: New Keynesians