Risk Premium Shocks Can Create Inefficient Recessions
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
Why do recessions hit employment, consumption, and investment at once? This paper argues recessions are episodes when business owners become more exposed to risk they cannot insure, and the premium they demand acts like a tax on hiring. Capital, unlike labour, is a durable store of value, so a precautionary urge to save offsets that drag on investment; calibrated to U.S. data the two roughly cancel, leaving labour to bear the hit -- which is why the three fall together. The slump is inefficiently deep, because nobody internalises how their own belt-tightening worsens risk-sharing for everyone else, so optimal policy would subsidise employment and consumption in downturns rather than investment.
What this paper finds — and why it matters
This paper proposes a flexible-price model of business cycles driven by spikes in uninsurable idiosyncratic risk, built by adding one friction – entrepreneurs’ inability to insure the idiosyncratic risk in their own production – to an otherwise standard neoclassical growth model with workers and entrepreneurs. When aggregate shocks raise idiosyncratic risk, entrepreneurs demand a risk premium to compensate for bearing it, which shows up as a countercyclical wedge that effectively taxes both labour and capital; but because capital is a long-duration store of value, a concurrent precautionary-saving motive lowers interest rates and offsets the risk premium’s drag on investment demand, while labour, having no such store-of-value role, is left depressed by the risk premium alone. The paper derives a sufficient statistic showing that, calibrated to U.S. data, these two offsetting forces on capital roughly cancel, so risk shocks act almost purely as a tax on labour – generating recessions in which employment, consumption, and investment decline together, quantitatively broadly consistent with U.S. business-cycle facts. This competitive-equilibrium response is shown to be inefficient: because individual agents take interest rates and the market price of risk as given, they do not internalize that their own consumption choices affect aggregate idiosyncratic risk sharing, so a fall in aggregate consumption during a downturn worsens risk sharing and pushes risk premiums higher still, in a self-reinforcing spiral. A constrained-efficient planner who faces the same limits on idiosyncratic risk sharing responds very differently – lowering labour taxes and raising capital taxes during downturns, which stimulates employment and raises consumption on impact rather than letting it fall – so that optimal policy calls for subsidizing employment and consumption, not investment, during recessions.
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Questions & answers
Q1. What is the paper’s central departure from the traditional risk-premium view of business cycles?
The paper explicitly “flips the emphasis” of the traditional risk-premium literature, which dates to Keynes (1936) and “focuses on the negative impact of higher risk premiums on investment demand,” toward the negative impact of higher risk premiums on labour demand instead (Introduction, p. 1). The authors give two reasons: “employing workers is a risky endeavour carrying a countercyclical risk premium that acts like a tax on labour,” while “in contrast to labour, capital is a long-duration store of value, so while the risk premium depresses investment demand, a concurrent precautionary saving motive depresses interest rates and stimulates investment” (p. 1).
Q2. What is the model’s core friction, and why is it central to generating business cycles at all?
The only friction added to a standard neoclassical growth model is that entrepreneurs cannot insure the idiosyncratic risk in their own production, while workers and entrepreneurs can still trade Arrow securities contingent on aggregate shocks (Section 2, “Overview of the model,” p. 2). The authors are explicit that “the assumption that entrepreneurs cannot insure their idiosyncratic shocks plays a central role – with insurance, there would be no aggregate fluctuations because full risk sharing would occur” (p. 2); the only aggregate driving force is a mean-reverting process for the cross-sectional dispersion of idiosyncratic shocks, with “no TFP shocks or nominal rigidities” (p. 2).
Q3. Quantitatively, what happens to consumption, employment, and investment after a risk shock?
In the paper’s calibrated impulse response to a one-standard-deviation risk shock, consumption falls by about 1%, employment by about 3%, and investment by about 5%, all declining together and then slowly recovering – which the authors describe as “broadly in line with stylized facts about U.S. business cycles” (Section 3.1, pp. 9-10). Wages fall by around 2% on impact, “reflecting weaker labour demand,” as entrepreneurs demand a larger risk premium and the economy moves along workers’ labour-supply curve (p. 10).
Q4. What is the “sufficient statistic” for whether the risk premium acts as a net tax or a net subsidy to capital, and what does calibration to U.S. data say?
Comparing the planner’s capital-market condition to the competitive-equilibrium condition, the paper derives that the capital wedge equals the labour wedge (the risk premium) scaled by a damping factor built entirely from observable ratios – the consumption share of output, the capital income share, and the capital-output ratio – plus the entrepreneurs’ impatience rate (equation 20, Section 3.2, pp. 11-12). The authors state the calibrated result directly: the risk premium’s effect on capital investment and the offsetting precautionary-saving effect “roughly cancel out when calibrated to U.S. data. Risk depresses labour demand but leaves investment demand unaffected because of the different duration of labour and capital” (Introduction, p. 1). This is why “a constant labour wedge” alone would force consumption and employment to move in opposite directions (equation 17, p. 11), but the model’s countercyclical labour wedge, combined with a roughly neutral capital wedge, produces the observed parallel comovement of consumption, employment, and investment.
Q5. Is the recession generated by this mechanism efficient, and if not, what specific externality causes the inefficiency?
No: comparing the competitive equilibrium to a planner facing the identical inability to insure idiosyncratic risk, the paper shows “the response of the competitive-equilibrium economy to a risk shock is inefficient. Employment and output fall too much, and consumption should rise instead of falling” (Section 4, p. 15). The source is an aggregate consumption externality (Section 4.3, pp. 17-18): “private agents follow their Euler equations and aggregate risk sharing equations, which take the interest rate and the price of risk as given, without an incentive to consider the fact that their consumption also affects idiosyncratic risk sharing,” whereas the planner recognizes that raising aggregate consumption reduces entrepreneurs’ exposure to idiosyncratic risk (because it raises their net worth relative to the risk they bear) and so improves risk sharing for everyone.
Q6. Mechanically, why does higher aggregate consumption improve idiosyncratic risk sharing in this model?
Idiosyncratic risk borne by entrepreneurs’ consumption, v_cet, is expressed as a function of output relative to entrepreneurial net worth (proportional to consumption), so that a planner contemplating a small increase in employment recognizes that the resulting extra output raises consumption “and this reduces entrepreneurs’ exposure to idiosyncratic risk v_cet through the larger denominator,” an effect that “dominates because aggregate output is larger than aggregate consumption” (Section 4.3, p. 18). By contrast, raising investment requires diverting resources away from current consumption, which “makes risk sharing worse,” so investment is “particularly unappealing when idiosyncratic risk is high,” precisely the opposite of what the competitive equilibrium’s precautionary-saving channel would suggest in isolation.
Q7. How does the planner’s optimal response to a risk shock differ concretely from the competitive equilibrium’s?
In the planner’s numerical solution to the identical shock, employment falls only about 1% (versus 3% in competitive equilibrium) and consumption rises on impact rather than falling, while investment falls by a similar magnitude to the competitive case; the planner implements this “by lowering labour taxes during recessions to stimulate employment and raising the capital tax to reduce investment and free more resources for consumption… equivalent to a temporary subsidy to consumption” (Section 4.2, pp. 16-17). The authors note the resulting allocation “does not look like a recession at all” in employment and consumption terms, though investment still declines by a comparable amount to the market outcome – the efficient response redistributes the burden of the shock rather than eliminating a fall in investment.
Q8. What kind of firms does the model’s mechanism apply to most directly, and how do the authors defend its empirical relevance?
The authors argue the mechanism applies most directly to private, closely held firms where insiders retain concentrated equity exposure, citing evidence that “private U.S. firms account for 69% of private employment and 59% of sales” (Asker et al. 2015), and note that even at public firms, “large investors and upper management often retain large risk exposures through equity, bonuses, and stock options,” with a median inside-ownership fraction of 19% at U.S. public firms (Himmelberg et al. 2004) (Introduction, “Uninsurable idiosyncratic risk,” pp. 3-4). The paper also documents empirical spikes in idiosyncratic risk in stock returns “especially during the Great Depression and the 2008 financial crisis” using data from Herskovic et al. (2016) as motivation for the countercyclical risk process assumed in the model (Figure 1, p. 3).
Key terms in this paper
Definitions below follow the paper's own usage.
- Labour and capital wedges (the sufficient statistic for investment)
- the paper's decomposition (Section 3.2) of the effect of a risk shock into a labour wedge ω_ℓt, shown to equal exactly the idiosyncratic risk premium v_cet·v_t, which "acts like a tax on labour," and a capital wedge ω_kt that equals the same risk premium scaled by a damping factor: ω_kt = ω_ℓt × [(1 − ρ_e·y_t/c_t) × (1/α) × (k_t/y_t)]. Because this damping factor mixes a positive risk-premium effect with a negative precautionary-saving effect, the capital wedge can be positive, negative, or (as the paper's calibration to U.S. data finds) close to zero, whereas the labour wedge is unambiguously a tax.
- Risk premium as a tax on labour, not on capital
- the paper's account of why a risk shock depresses employment and investment asymmetrically even though the risk premium taxes both symmetrically: "employing workers is a risky endeavour carrying a countercyclical risk premium that acts like a tax on labour," but "capital is a long-duration store of value, so while the risk premium depresses investment demand, a concurrent precautionary saving motive depresses interest rates and stimulates investment" -- the two forces on capital "roughly cancel out when calibrated to U.S. data," while labour, having no store-of-value role, is left with only the tax-like effect of the risk premium.
- Aggregate consumption externality
- the source of inefficiency the paper identifies (Section 4.3): private agents take interest rates and the market price of risk as given when choosing consumption, so they do not internalize that higher aggregate consumption improves everyone's idiosyncratic risk sharing (by raising entrepreneurs' net worth relative to the risk they bear). In the competitive equilibrium, "lower consumption in turn makes risk sharing even worse and raises the risk premium even more, further reducing employment and output in a negative feedback loop" -- a vicious cycle the constrained-efficient planner breaks by stimulating consumption and employment during downturns.
- The constrained-efficient planner's allocation
- the paper's finding (Section 4, Figure 4) that the constrained-efficient planner's response to the same risk shock looks nothing like a recession: employment falls only about a third as much as in the competitive equilibrium (1% versus 3%), and consumption rises on impact instead of falling, while investment still falls by a similar amount to the competitive equilibrium; the planner implements this by lowering labour taxes (an implicit employment subsidy) and raising capital taxes during the downturn, "equivalent to a temporary subsidy to consumption."