A Macroeconomic Model with a Financial Sector

Questions & answers

Q1. What is the paper’s central methodological departure from prior macro-finance models with financial frictions?

The paper explicitly departs from the log-linearization-around-the-steady-state approach used in Bernanke-Gertler-Gilchrist (1999) and Kiyotaki-Moore (1997), instead solving for the full global equilibrium dynamics of a continuous-time model, “not just near the steady state” (Introduction, p. 2). The authors state their central finding directly: “while the system is characterized by relative stability, low volatility and reasonable growth around the steady state, its behavior away from the steady state is very different and best resembles crises episodes as large losses plunge the system into a regime with high volatility” (p. 2) – a distinction the authors argue is invisible to linear approximations by construction.

Q2. Who are the “experts” and “households,” and what specifically constrains experts’ balance sheets?

Experts are more productive at managing capital (producing output at a higher rate per unit than households, with slower depreciation), so households lend to experts at the risk-free rate and experts may also issue limited outside equity, but experts “are required to hold at least a fraction of total risk of the capital they hold” (an equity/skin-in-the-game constraint) and must keep net worth nonnegative (a solvency constraint) (Section 2, pp. 6-9). Both constraints jointly determine how much capital experts can hold and how exposed they remain to their own asset-price risk, and the paper shows in Section 7 that these constraints can be derived from an explicit double moral-hazard contracting problem between entrepreneurs and monitoring intermediaries.

Q3. What generates “endogenous risk,” and why is it different from the exogenous cash-flow shocks the paper also allows for?

Endogenous risk is asset-price volatility caused “not by shocks to fundamentals, but rather by adjustments that institutions make in response to shocks” (Section 4.1, p. 20) – formally, total volatility in the price of capital is the sum of exogenous risk σ and an endogenous component σ^q_t that depends on the state. The paper derives (Proposition 2) that this endogenous volatility is governed by a nonlinear amplification term built from experts’ leverage and the sensitivity of the price of capital to the state variable: when the price function is flat (as it is near the steady state), a shock to net worth barely moves prices and amplification is small; but when that price sensitivity is large, a drop in net worth depresses prices, which depresses net worth further, in a loop the authors describe and illustrate as an “adverse feedback loop” (Figure 4, p. 20).

Q4. Why does the model produce a sharp distinction between “normal times” and “crisis times” rather than a single, uniformly stable regime?

Because experts choose their capital buffers endogenously: near the payout boundary η they are relatively unconstrained and absorb ordinary losses “through reduced payouts to raise capital cushions… without a significant effect on their demand for assets and market prices,” so amplification is small, but once losses are severe enough to push net worth well below η, experts become constrained and “shocks to their net worth’s immediately feed into their demand for assets”** (Section 4.1, pp. 20-22). The resulting stationary distribution of the state variable is bimodal – high density near η* and at very depressed values, thin in between – which the authors term “ergodic instability”: “the system spends most of the time around the extreme points… [and] moves fast through regions of high volatility, and so the time spent there is very short,” but “these excursions below the steady state… occasionally may take the system very far below the steady state,” producing what the paper identifies with systemic risk (Section 4.1, pp. 22-23).

Q5. What is the “volatility paradox,” and why might a period of low fundamental risk make a subsequent crisis worse?

Proposition/Section 5.1’s central result is that “a reduction in exogenous cash flow risk σ reduces financial frictions [but] paradoxically… can make the economy less stable” because “a decline in cash flow volatility encourages experts to increase their leverage by reducing their net worth buffer” (Section 5.1, p. 27). In their numerical example, lower exogenous risk lowers the payout point η* (experts pay out bonuses sooner and hold thinner buffers) and results in “higher systemic risk reflected by greater amplification below steady state,” which the authors explicitly connect to the fact that “the current crisis was preceded by a low volatility environment, referred to as the ‘great moderation’” (p. 27).

Q6. Does allowing experts to hedge idiosyncratic risk (e.g., through securitization) make the financial system safer?

No – Proposition 3 (Section 5.2) shows that when hedging within the financial sector is possible, experts fully hedge idiosyncratic risk (which then carries a zero risk premium), which lowers their effective cost of borrowing from the risk-free rate plus a default-risk spread down to simply the risk-free rate; “lower cost of borrowing leads to higher leverage and quicker payouts. As a result, the financial system becomes less stable” (Section 5.2, pp. 29-30). The authors summarize the tension directly: “even though in principle securitization is a good thing, as it allows financial institutions to share idiosyncratic risks better and avoid bankruptcy costs, it can lead to greater leverage and the amplification of endogenous systemic risks” (p. 30).

Q7. Is the competitive market outcome efficient, and if not, what specific externality breaks efficiency?

The market outcome is not even constrained efficient (efficient given the same financing frictions a planner would face), because of pecuniary externalities that work through prices: “individual market participants take prices as given, but as a group they affect them” (Section 6.3, p. 34). The paper singles out the fire-sale externality: “when levering up ex-ante, financial experts do not take into account that in crisis, its own fire sales will depress prices that other institutions are able to sell at. This effect leads to excess leverage since they take fire-sale prices as given, i.e. a social planner would lever up less” (p. 34). The paper also shows (Proposition 4, Section 6.2) that a constrained-feasible planner using transfers – or, equivalently, price-stabilization policy that reduces the volatility of experts’ net worth – could in principle attain the unconstrained first-best outcome, underscoring that the inefficiency in the market equilibrium stems from the externality rather than from the financing frictions being unfixable in themselves.

Q8. How does the model connect endogenous risk to asset pricing, even though all agents in the model are risk-neutral?

Despite risk-neutral preferences, the model generates time-varying risk premia because “excess volatility increases the experts’ precautionary motive, leading to a higher required expected return on capital” (Section 4.2, p. 24) – the precautionary motive arises from experts’ concern about becoming financially constrained, not from risk aversion per se. The paper’s Conclusion states this explicitly as a headline result: the model produces “interesting asset pricing implications with time-varying risk premia even though all agents in the economy are risk-neutral” (Section 8, p. 43), and Section 4 further shows that endogenous risk raises cross-sectional asset-price correlation in downturns, since feedback effects (unlike idiosyncratic cash-flow shocks) move the prices of all assets experts hold simultaneously.