A Labor Capital Asset Pricing Model

The standard model of stock returns has a blind spot the size of the entire labor market. That's the claim Kuehn, Simutin, and Wang make flat out, and they back it with a number. Firms on the wrong side of a single labor market variable underperform by six percent a year. Not because they're smaller or riskier by conventional measures or loaded with debt. It's because of how they're exposed to the job market. The authors built a model from scratch to explain why hiring frictions are a priced risk, and the evidence, from stock returns down to firm-level vacancy rates, holds together in a way that's hard to dismiss. The variable at the center of everything is labor market tightness, denoted theta. It's simple in concept: the ratio of aggregate vacancy postings to unemployed workers. When there are many open jobs relative to unemployed people, tightness is high. When few vacancies face many unemployed workers, tightness is low. In practice, the authors construct the unemployed pool as the unemployment rate times the labor force participation rate, and they use a composite Help Wanted series for vacancies covering both print and online postings. The monthly tightness factor is then the change in the log of that vacancy-to-unemployed ratio. It's strongly procyclical, correlated with industrial production, and its mean is 0.11 percent per month with a standard deviation of 5.43 percent over the sample period from 1954 to 2014. Tightness is a macro variable. What makes it useful for asset pricing is the question of how much each individual firm's stock return moves with it. Kuehn, Simutin, and Wang estimate that sensitivity — what they call beta-theta — using a rolling two-factor regression. At the end of each month, they take the prior thirty-six months of a stock's excess returns and regress them on two things: the market excess return and the monthly change in labor market tightness. Any stock with at least twenty-four valid months gets a beta-theta estimate. Those estimates are then used to rank stocks into ten decile portfolios, skipping a month to let data be reported, and holding the resulting value-weighted portfolios for a year. The spread is large and clean. The lowest-loading decile posts an average excess return of 1.14 percent per month. The highest-loading decile posts 0.66 percent. The long-short spread, which is low minus high, is 0.48 percent per month, with a t-statistic of 3.66. Annualized, that's the six percent figure. And it survives the standard controls. After adjusting for the market, size, value, and momentum factors using the Carhart four-factor model, the alpha is still 0.44 percent per month with a t-statistic of 3.31. Conditional alpha estimates using the Ferson-Schadt method come in around 0.50 percent per month. Fama-MacBeth regressions, which weight by market capitalization and test the loading's predictive power stock by stock, confirm the story: a one-standard-deviation increase in beta-theta — that's 0.49 units — implies at least a 1.2 percent decline in subsequent annual returns. The authors run robustness checks across different portfolio formation timings, alternative definitions of the tightness factor, different beta-estimation windows, and excluding microcaps. The result holds throughout. So the empirical pattern is solid. The question is why. Why would a firm's sensitivity to aggregate labor market tightness predict its expected stock return? This is where the model comes in. Kuehn, Simutin, and Wang build a partial equilibrium model in which firms cannot instantly hire workers. They have to post vacancies, and those vacancies get filled through a matching process — an aggregate technology that converts open positions and unemployed workers into filled jobs. The efficiency of that matching process fluctuates. A matching efficiency shock is a surprise change in how productively the economy converts vacancies and unemployed workers into filled jobs. The matching function has an estimated elasticity of 1.27, governing how responsive the vacancy-filling rate is to changes in tightness. Wages are set by Nash bargaining, with workers' bargaining power calibrated at 0.115. When matching efficiency rises, most firms want to expand — they post more vacancies because it's now easier to fill them. But some firms, those hit by adverse idiosyncratic productivity shocks, optimally refrain from hiring even when matching improves. Their dividends don't rise when efficiency rises — they stay flat or fall. Those are the low-beta-theta firms. They're countercyclical with respect to matching efficiency: lower vacancy rates, lower hiring, lower wages, and higher firing when efficiency is high. The pricing logic follows directly. The job-creation Euler equation says firms post vacancies until the marginal cost of posting equals the expected marginal benefit of filling a job, discounted by the pricing kernel. Because matching efficiency shocks carry a negative price of risk, meaning investors dislike states when matching is difficult, firms that suffer most in those states command higher expected returns. Low-beta-theta firms are exactly those firms. They're more exposed to adverse matching efficiency, and investors price that exposure. The result is a two-factor asset pricing structure: the usual market factor plus a labor market tightness factor, and expected returns rise as a firm's loading on tightness falls. The model then has to prove it can actually match the data. The calibration is demanding. Labor parameters are pinned to empirical targets: a monthly quit rate of 0.022, an outside value of unemployment at 0.71, and a labor share of 0.75. The pricing kernel parameters are set to match financial moments: a monthly risk-free rate of 0.001, a price of productivity risk of 0.28, and a price of matching-efficiency risk of negative 1.015. The model reproduces an unemployment rate of 5.9 percent, an aggregate hiring rate of 3.5 percent, a layoff rate of 1.3 percent, and labor market tightness of 0.65 against an empirical value of 0.63. Solving the model at this scale requires a shortcut. Instead of tracking the full distribution of firms at every point in time, the authors use a Krusell-Smith approximation: they replace the distributional law of motion with a simple log-linear forecasting rule for aggregate tightness, solve each firm's dynamic hiring and firing problem on a discretized state space, run a simulation across ten thousand firms over ten thousand three hundred months, and update the forecasting rule by regression until it converges. At convergence, the R-squared on that forecasting rule exceeds 0.995. That's a remarkably tight fit. The payoff: the simulated portfolio spread is 0.45 percent per month against 0.48 percent in the data. The unconditional Capital Asset Pricing Model alpha in the model is 0.54 percent per month, matching the empirical 0.54 percent almost exactly. The spread arises from a combination of priced matching-efficiency risk and the cash-flow exposures that hiring frictions create. When matching efficiency improves, the cash-flow effect dominates at the aggregate level — hiring gets cheaper and firms want to expand. But low-beta-theta firms are constrained; wages rise before they can benefit, making their dividends more countercyclical. That's the mechanism, and the model quantifies it with numbers that land on the empirical targets. The final test is whether the model's predicted mechanism shows up in actual firm behavior. Theory says low-beta-theta firms should respond differently to the labor market cycle than high-beta-theta firms — not in their average levels of hiring or wages, but in their cyclical sensitivity. The authors link each portfolio to five labor data sources, including the Job Openings and Labor Turnover Survey, Mass Layoff Statistics, and the Quarterly Census of Employment and Wages, matching by industry and state. The empirical correlations line up with the model. The correlation between aggregate labor market tightness and a portfolio's vacancy rate runs from negative 0.02 for the lowest-beta-theta decile to positive 0.20 for the highest. Hiring rates, employee growth, wages, and profitability all show the same monotonic pattern across deciles. Firing rates go the other way. And crucially, average levels of these labor characteristics don't vary significantly across beta-theta portfolios. What varies is the cyclicality. These firms aren't structurally different in size or labor intensity. They're different in how they respond to aggregate matching conditions. That distinction matters because it connects the Labor Capital Asset Pricing Model to something observable and intuitive. A standard factor model would tell you that low-beta-theta firms earn more because they load differently on statistical factors. The Labor Capital Asset Pricing Model tells you they earn more because they can't easily expand when hiring gets hard, and that inability to hire when matching efficiency deteriorates is precisely the source of the risk that investors are compensating them for. Labor market frictions, Kuehn, Simutin, and Wang conclude, are not a background condition of the economy. They're a priced systematic risk, and the job market and the stock market are, in that sense, speaking the same language. This lecture was created by ennepō. 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