Risk Premia and the Real Effects of Money

The paper asks how money can have large real effects on investment even when prices are completely flexible, by showing that money changes equilibrium risk sharing rather than working through nominal rigidities (Introduction, pp. 1995-1997). Conventionally, money’s real effects are attributed to sticky prices and the zero lower bound in New Keynesian models: “If there is money in the economy the nominal interest rate cannot be negative. So if the natural interest rate…is very negative, the central bank must either abandon its inflation target or allow the economy to operate with an output gap” (p. 1997). This paper instead shows that “in this paper prices are flexible, and the zero lower bound is not binding and does not play any role. Low investment does not reflect an output gap, but rather the equilibrium real effects of money” (p. 1997).

The baseline is a simple AK growth model with a continuum of agents who have log utility over consumption and real money balances, who can continuously trade capital exposed to idiosyncratic “quality” shocks that cannot be fully insured (Section I.A, pp. 1998-2000). Idiosyncratic risk washes out in the aggregate, so aggregate capital still evolves deterministically given investment, but individual agents bear undiversifiable risk in their own capital holdings. Money is introduced via money-in-the-utility, printed and distributed lump sum by the government to hit an inflation target, with “no taxes, government expenditures, or government debt” in the baseline so there is no fiscal channel (p. 1999).

The paper explains the mechanism in two steps (Section I.D, pp. 2005-2006): first, for a given level of risk, money’s liquidity premium lets it serve as a safe store of value that improves idiosyncratic risk sharing and weakens agents’ precautionary saving motive relative to the risk premium on capital, which keeps real rates higher and investment lower than in a moneyless economy; second, the value of money – the liquidity share of wealth – itself rises endogenously with risk, because “liquidity is discounted only with the risk-free rate, which must fall when idiosyncratic risk is large,” while capital is discounted with a large and rising risk premium. Formally, the paper’s equilibrium conditions for the real interest rate and investment are both written as functions of the liquidity share λ and idiosyncratic consumption risk, and the paper states directly that “a larger liquidity share λ raises the real interest rate and reduces investment” (equations 14-15, p. 2006).

Because both are in zero net supply: “safe assets without a liquidity premium must be backed by payments with equal present value. Agents own the assets but also the liabilities, so the net value is zero” (p. 1997, p. 2007). Only assets whose yield is pushed below the risk-free rate by a genuine liquidity premium – such as deposits or short-term Treasuries – have net value equal to the present value of that premium, which is what lets them function as a safe store of value that improves risk sharing in general equilibrium. The paper shows this formally by allowing agents to issue outside equity that can be diversified into a safe index: equity improves risk sharing somewhat, but because it too is in zero net supply, “after an increase in idiosyncratic risk real interest rates fall and investment remains stable” – it does not reproduce money’s stabilizing/depressing effect on investment (p. 1997).

Using a calibration in which checking/savings accounts (about 50 percent of GDP with a 2 percent average liquidity premium) plus Treasuries’ liquidity premium (per Krishnamurthy and Vissing-Jorgensen 2012) imply an expenditure share on liquidity services of about 1.7 percent of consumption, the liquidity share stays small when real rates are high relative to growth, but “when the real interest rate becomes persistently very low, such as in the aftermath of the 2008 financial crisis, the net value of liquid assets can become very large” (pp. 1996, 2007-2008, and Proposition 1). Proposition 1 formalizes this: for any positive expenditure share on liquidity, the liquidity share ranges from 0 as idiosyncratic risk goes to zero up to 1 as idiosyncratic risk goes to infinity, and the paper shows the real effects of money survive “even in the cashless limit where expenditures on liquidity services vanish” (as the expenditure share itself goes to zero).

Incomplete idiosyncratic risk sharing is derived, not assumed, from a moral-hazard contracting environment with hidden trade (Section II.A, based on Di Tella and Sannikov 2016): agents can misreport their own idiosyncratic capital returns and secretly save, invest, and consume from a hidden account, so incentive compatibility requires a “skin in the game” constraint tying each agent’s consumption volatility to his exposure to his own idiosyncratic shock (equations 19-25, pp. 2018-2020). The paper proves (Proposition 7) that the competitive equilibrium of the baseline portfolio problem coincides exactly with the outcome of privately optimal long-term contracts in this hidden-trade environment, so the earlier analysis can be read as the result of optimal private contracting rather than an ad hoc friction.

No: comparing the competitive equilibrium to a planner facing the same hidden-trade environment, the paper shows that “when idiosyncratic risk is low, money provides too little insurance and investment is too high. When idiosyncratic risk is large, money provides too much insurance and investment is too low” (Section II.C, p. 2022, and Proposition 8). The reason the planner can do better is that the local incentive-compatibility constraints that bind individual private contracts (requiring different agents to be treated identically or else they would trade among themselves) are not binding for the planner, who already wants to treat all agents symmetrically – only the aggregate skin-in-the-game constraint linking investment and idiosyncratic consumption risk remains binding for the planner (p. 2020-2021).

The optimal allocation is implemented with the Friedman rule (a nominal interest rate of approximately zero) together with a tax or subsidy on capital – a tax when idiosyncratic risk is low and the competitive equilibrium over-invests, a subsidy when risk is high and it under-invests (Section II.E, Proposition 10, pp. 2026-2027). Money is fully superneutral in this model – “doubling the amount of money would just double prices, leaving all real variables unaffected” – and Ricardian equivalence holds, so “changing the amount of government debt can only affect the liquidity premium on government debt and other assets, but not the real side of the economy” (pp. 1998, 2007). This is why the inefficiency cannot be corrected through the money supply or inflation target: “monetary policy cannot correct this… The optimal allocation requires the Friedman rule and a tax/subsidy on capital” (abstract, p. 1995).

The paper frames its mechanism as complementary to, but conceptually distinct from, the sticky-price ZLB channel: “under both views, money prevents the real interest rate from falling to stabilize investment and creates a slump. In the New Keynesian setting, because of sticky prices and the ZLB; in this paper, because it provides a store of value that improves risk sharing, even though prices are flexible” (Section IV.B, p. 2035). A key implied result for New Keynesian modeling is that introducing money doesn’t just impose a floor on nominal rates – it also raises the natural (flexible-price) real interest rate, so “it is perfectly possible for the natural interest rate to be negative without money but positive with money,” which can make the zero lower bound non-binding even in models where it otherwise would be (p. 2035). The paper explicitly credits Werning (2011) – the Werning “Managing a Liquidity Trap” manuscript in this same course’s reading list – for characterizing optimal monetary policy in the New Keynesian setting when the ZLB does bind (footnote 52, p. 2036).

The paper explicitly contrasts itself with the bubble literature, identifying Brunnermeier and Sannikov’s incomplete-risk-sharing bubble-money model as “the closest paper” but stressing that “here bubbles are explicitly ruled out” (Section IV.A, pp. 2034-2035; introduction, p. 1998). Under the liquidity view, money’s value derives from a genuine liquidity premium (it enters the utility function or a cash-in-advance constraint) and the no-Ponzi condition pins down a unique price; under the bubble view, money pays no dividend and has value purely because “the last term [of the valuation equation] doesn’t vanish,” which in a balanced growth path forces the real interest rate to equal the growth rate exactly, and requires the nominal interest rate to be exactly zero rather than merely low. The author argues the liquidity view is empirically more defensible because “money does have a liquidity premium… the bubble view cannot explain why people hold money when they can hold safe nominal bonds that pay interest” (p. 2035), while noting the two views share the qualitative logic that a safe store of value improves risk sharing and depresses investment, and that the liquidity-view economy converges to a bubbly equilibrium of the nonmonetary economy in the cashless limit.

Section III generalizes the model to a fully dynamic setting with a mean-reverting idiosyncratic-risk process and an aggregate TFP shock, both spanned by complete aggregate-risk markets, which yields a general closed-form expression for the liquidity share highlighting the role of the stochastic discount factor in pricing liquidity (Section III.A, pp. 2027-2028). The exercise clarifies that what matters for the mechanism is specifically incomplete idiosyncratic risk sharing – aggregate risk is assumed fully shareable via complete markets throughout – so the dynamic model isolates money’s role as an idiosyncratic-risk-sharing device even once time-varying aggregate shocks and a stochastic discount rate are present, rather than introducing any additional aggregate-risk-sharing role for money.