A Structural Model of Human Capital and Leverage - Duke ...

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1 Introduction Quantitatively, human capital is the most important factor of production. On average roughly two-thirds of firm output is used to compensate its labor force. Yet despite its quantitative significance, labor has received relatively little attention in the corporate finance literature. When explicitly modeled, labor typically takes the form of a manager who controls a project and must be properly incentivized by the project’s owners. The study of the problem of the separation of ownership and control is central in corporate finance and has led to, among other things, a large literature on executive compensation. This focus on key managerial employees, however, ignores a much larger group of employees who have neither significant ownership nor control individually, but who collectively are tremendously important to the success of the firm. Typically, labor is implicitly treated as a purely variable factor of production. When labor markets are frictionless employees can be hired and fired costlessly and always earn their marginal product. In such a setting labor has no effect on firm value or firm policies. In the presence of labor market frictions, however, labor becomes a quasi-fixed factor of production and contributes to firm value. Such frictions may include the inability of workers to insure their labor income, costly search and matching, or the acquisition of firm- specific human capital. With frictional labor markets there is a match-specific surplus associated with the employment relationship, which must be divided between workers and employees. Workers are better off if they can keep their current jobs, and firms are better off if they can keep their current employees. When part of the value of the firm comes from rents earned from labor, a value maximizing firm will consider the effect of its policies on labor. Corporate policies may affect the firm’s labor expenses and its ability to retain workers, which in turn affect firm value. Such policies may include capital structure, dividend policy, cash management, corporate governance, investment, mergers and acquisitions, etc. Recently a literature has emerged that studies the interaction between labor markets and corporate finance. This literature presents mounting evidence that human capital has an important impact on corporate policies. Despite this evidence, to the best of my knowledge no dynamic model of labor and corporate finance currently exists. The purpose of this paper is to fill this gap, formalizing the way in which we think about the effect of labor markets on corporate finance and providing a lens through which to interpret recent contributions to this literature. I focus on the interaction between human capital and capital structure. I augment a standard neoclassical model of the firm to include a simple model of job search. Since workers who are laid off cannot find alternative employment immediately, unemployment is costly to workers. Leverage exposes workers to unemployment risk, for which they are compensated ex ante through higher wages. 1
Additionally, I assume that labor adjustment is costly to the firm. The firm incurs hiring and training costs per employee hired, and also pays a severance to any employees dismissed outside of default. In the spirit of the tradeoff models of capital structure, firms in my model can be financed either with debt or equity, with debt enjoying a tax advantage. Default is endogenous, with firms choosing to default whenever their equity value falls to zero. The model features deadweight costs of default that are proportional to the firm’s capital stock. This direct cost of financial distress has been studied in the previous literature, with many concluding that the costs appear too low to rationalize debt levels observed in the data. My model adds an important cost of financial distress that has mostly been ignored in the literature. In default, a proportion of the firm’s employees lose their jobs, and the human capital investment embodied in these employees is lost. I argue that this cost can be quantitatively large and should not be ignored by models of capital structure. Firms who rely more heavily on human capital in the production process will have lower leverage ratios because they face higher costs of financial distress. I calibrate the model and perform simulations to assess the quantitative significance of human capital for capital structure. The model produces leverage levels consistent with those in the data. Furthermore, the model is able to match the cross-sectional pattern of leverage and labor intensity. Leverage in the model decreases monotonically in labor intensity, closely matching the pattern in the data. A move from the lowest to the highest decile of labor intensity is associated with a drop in leverage of 21 percentage points in the model, very close to the 27 percentage point drop in the data. In addition to matching the cross-section of labor intensity, the model is able to match the cross-sectional relationship between leverage and several other previously recognized predictors of capital structure, including the market to book ratio, profitability, and cash flow volatility. Overall, I conclude that human capital is quantitatively significant and should not be ignored by capital structure researchers. 2 Related Literature My paper is primarily related to a new and growing literature that studies the interaction between labor markets and corporate finance. This literature provides mounting evidence that labor markets are important factors in determining corporate policies. Yet few models exist which help to formalize the analysis of the interaction between labor markets and corporate finance. I help fill this gap by deriving a dynamic model in which labor, investment and leverage can be studied jointly. To the best of my knowledge, this is the first paper that allows the joint study of these three important corporate policies. Such a model will help with 2
Page 1: A Structural Model of Human Capital
Page 5 and 6: ecoming unemployed drops, so it bec
Page 7 and 8: Rampini and Viswanathan (2010) deve
Page 9 and 10: is on the market to book ratio. Mov
Page 11 and 12: Positive dividends are subject to t
Page 13 and 14: 4.1 Labor Market Equilibrium In thi
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Page 17 and 18: is increasing in the probability of
Page 19 and 20: Note that the critical value for de
Page 21 and 22: Substituting in the solution for ω
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Page 25 and 26: long-run mean, the dotted line fixe
Page 27 and 28: ottom half of the panel shows the l
Page 29 and 30: References Acemoglu, Daron, 2002, T
Page 31 and 32: Jermann, Urban, and Vincenzo Quadri
Page 33 and 34: Table 2: Book Leverage and Labor In
Page 35 and 36: Table 5: Leverage and the Cross-Sec
Page 37 and 38: Mean Market Leverage .15 .2 .25 .3
Page 39 and 40: Firm Value 3 2.5 2 1.5 1 0.5 Panel
Page 41: Marginal Cost 2.5 2 1.5 1 0.5 Margi

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