the expected profit derived from a new worker rises. Firms increase their hiring; stock prices surge as employment and the expected firm surplus rise.
The third panel documents the negative correlation of separations and asset prices. Adverse news about productivity raises the number of terminated jobs and depresses stock prices at the same time.
Why do labour market flows and stock prices co-move in the DMP frame-work? Just like equity, a new hire is a risky asset that is priced with the
“fundamental asset pricing equation”: in the case of equity, the equilibrium stock price equals the present value of future dividends; in the case of em-ployment, the equilibrium price of a hire (cost of hiring and training) equals the present value of the firm’s share of the product of labour.
Solving the equity premium puzzle remains a challenge for consumption-based asset pricing models. Going back to Rietz (1988), Barro (2006), Barro (2009), Gourio (2012), and Ghosh and Anisha (2012), a small probability of deep and persistent drops in output and consumption (=disasters) can generate sizeable risk premia. Disasters can be interpreted as a Peso problem:
ex post the researcher observes a low volatility of fundamentals, but ex ante investors assigned a positive probability to a disaster. The Sharpe ratio observed by the researcher appears largeex post, but merely reflects the positive probability of a rare event. In a DMP framework, Wachter and Kilic (2018) assume a time-varying probability of exogenous disasters.
Relatedly, Petrosky-Nadeau et al. (2018) solve the DMP model globally with cyclical fluctuations, calibrate to long-term data and show that the model can generate disasters endogenously. In their standard framework, labour market frictions amplify the effect of cyclical shocks on employment and production.1 They claim that endogenous disasters and wage inertia generate a large equity premium. In contrast, I show that the DMP model with wage rigidity and cyclical TFP solves the Shimer puzzle, but fails to generate a large equity premium, even though the model is capable of generating endogenous disasters. I show that the parametrization used by Petrosky-Nadeau et al. (2018) does not match labour market transition rates and predicts disasters far too frequently. A careful parametrization falsifies the endogenous disaster story.
As emphasized by Bansal and Yaron (2004), Bansal et al. (2012), and
1See Hairault et al. (2010), Jung and Kuester (2011) and Den Haan et al. (2020).
Schorfheide et al. (2018), long-run consumption risk and recursive prefer-ences can generate large risk premia. Croce (2014) shows that a production-based asset pricing model with capital-adjustment costs and a small pre-dictable component of productivity growth can generate sufficiently large risk premia. Convex capital-adjustment costs reduce the volatility of invest-ment and give rise to a time-varying Tobin’s q. The volatile Tobin’s q raises the volatility of equity prices, which leads investors to demand a risk pre-mium. In contrast to Croce (2014), my long-run risk model (LRR) assumes a frictional labour market in an economy without capital. The time-varying cost of filling a vacancy takes the place of convex capital-adjustment costs:
the time-varying filling rate translates into time-varying vacancy-posting costs, which generate a volatile Tobin’s q. This point has been made by Merz and Yashiv (2007), who establish that equity prices reflect employ-ment and labour-adjustemploy-ment costs in a frictional labour market. To my knowledge, the long-run risk model with a frictional labour market has not yet been studied extensively.2 This paper shows that a small persistent component of productivity growth raises the equity premium marginally, but simulated unemployment volatility and the equity premium fall short of their empirical counterparts. In the LRR model, wage rigidity must be very strong to solve the Shimer puzzle. This makes the LRR model less robust:
very rigid wages affect separations and may turn them pro-cyclical.
This paper makes two additional contributions. Firstly, I use the models’
policy functions together with employment and output time series to esti-mate processes for cyclical fluctuations and the long-run growth component.
Using the estimated productivity series, I simulate the U.S. economy from 1929 to 2018 and study the goodness-of-fit of the generated series to the data. Endogenous separations improve the model’s goodness of fit, especially in turbulent times. The canonical model with a constant separation rate will fail to replicate large hikes in unemployment, for example the Great Depression. Endogenous separations allow the model to match such hikes.
Comparing time series reveals that the long-run risk model is better suited for the moderate post-1950s U.S. economy than the volatile years prior to the
2A working paper version of Kehoe et al. (2019) argues that the long-run risk model with recursive preferences, solved by perturbation, does not generate sufficiently strong volatility in the discount factor to drive a volatility of unemployment as large as observed empirically.
After solving the model globally, I agree.
1950s. This model puts the burden of matching fluctuations completely on a component that is assumed to besmall and highly-persistent. Deep recessions and quick recoveries, e.g. the Great Depression, are difficult to match with this component alone.
Secondly, I study why my models fail to generate a risk premium: Al-though investors dislike the pro-cyclical nature of equity returns, they do not demand a large premium because the conditional variance of marginal utility is too small. I show that the variance is larger in the long-run risk model (LRR) than the RBC model because small shocks can have long-lasting effects. But, neither cyclical nor long-run risk shocks suffice to introduce enough risk in the model, calibrated to post-war U.S. data. In the calibration by Petrosky-Nadeau et al. (2018), the prospect of (too) frequent disasters raises the volatility of marginal utility and a premium follows. I conclude that a habit model might be a step towards solving the equity premium puz-zle in this framework: with habits, the variance of marginal utility rises even though consumption and output volatility remain at empirically plausible levels.
The paper proceeds as follows: The next section outlines the model. The subsequent sections Section 2.3 and Section 2.4 analyze two different ver-sions of this model. First, Section 2.3 parametrizes the DMP model with endogenous separations and wage rigidity (RBC), simulates and matches the 1928-2018 time series. Second, Section 2.4 parametrizes the model with a small persistent component of productivity growth (LRR), simulates and matches time series. Section 2.5 studies the transmission of shocks in the models and their failure to replicate the equity premium.
1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 -100
-50 0 50 100
pct.deviationfromlineartrend Unemployment and Equity Prices
unemployment rate (left scale) S&P 500, inverted (right scale)
-100 -50 0 50 100
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 -40
-30 -20 -10 0 10 20 30 40
pct.deviationfromlineartrend Job-nding rate and Equity Prices
Job finding rate S&P 500 (right scale)
-80 -60 -40 -20 0 20 40 60 80
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 -50
pct.deviationfromlineartrend Separation rate and Equity Prices
separation rate S&P 500, inverted (right scale)
-100 0 100
Figure 2.1:Equity prices and labour market data. S&P 500 vs unemployment (inverted), the job-finding rate and the separation rate (inverted) in percentage deviations from a linear trend. U.S. quarterly data. Grey bands denote NBER recessions. These correlations are remarkable compared to other time series: as shown by Hall (2017), the correlation between TFP and unemployment is low. Appendix 2.A shows the comparatively low correlations of wages and dividends to equity prices and unemployment.