A Theory of Macroprudential Policies in the Presence of Nominal Rigidities

The dominant prior justification rested on pecuniary externalities arising from frictions inside financial markets; this paper supplies an alternative foundation in which financial markets are frictionless and the only frictions are nominal rigidities plus, possibly, constraints on monetary policy (Introduction, pp. 1-2). The authors summarise the pecuniary-externality logic they are departing from: when asset markets are incomplete and there is more than one commodity, “a redistribution of asset holdings generically induces relative price changes in spot markets,” which changes the spanning properties of the available assets and is not internalised, so equilibrium is “generically constrained inefficient” (p. 2, citing Hart, Stiglitz, Geanakoplos–Polemarchakis and others). Their own route is explicitly different: “in our baseline model, the only frictions are nominal rigidities and, possibly, constraints on monetary policy such as the zero lower bound or a fixed exchange rate. Instead of pecuniary externalities, our theory emphasizes aggregate demand externalities” (p. 2). They are direct about why this matters beyond novelty: a framework built on nominal rigidities and monetary constraints “is well posed for the joint study of monetary and macroprudential policy” (p. 2). They also distinguish themselves from Woodford (2011), who studies nominal rigidities together with pecuniary externalities but whose case for macroprudential intervention is, “in contrast to our theory, entirely driven by the presence of pecuniary externalities” (fn. 1).

It is the gap between private and social marginal utility of income that arises because ex-post wealth distribution moves aggregate demand while ex-ante portfolio choice ignores that effect. The abstract states it compactly: “Ex post, the distribution of wealth across agents affects aggregate demand and output. Ex ante, however, these effects are not internalized in private financial decisions” (Abstract). The paper’s own gloss on the mechanism: “financial decisions determine the wealth distribution across states s. When agents have different spending patterns, changes in the distribution of wealth affect demand. These changes in demand can improve efficiency, but infinitesimal agents do not internalize the macroeconomic consequences of their financial decisions” (Section 3.1, p. 12). The authors note that Blanchard and Kiyotaki (1987) isolate “a different form of aggregate demand externality,” running through firms’ price-setting and real money balances rather than through the wealth distribution (fn. 5).

A static-in-spirit general-equilibrium economy with heterogeneous agents, commodities indexed by a state s and a within-state good j, a two-stage budget structure, and rigidity imposed as a constraint on the price vector (Section 2, pp. 6-10). Technology is a convex aggregate constraint F({Y_{j,s}}) <= 0; agent i has concave state-dependent utility. The dichotomy between s and j is load-bearing: “we allow the government to use taxes or quantity restrictions to influence financial transactions across states, but rule out such policy tools to influence spot transactions within a state” (p. 7), precisely so that the exercise is about intervening in financial markets rather than about undoing price stickiness with commodity taxes. Agents first trade a complete set of Arrow-Debreu claims at prices Q_s, facing an agent- and asset-specific tax or subsidy tau^i_{D,s}, then trade in spot markets at rigid prices. Heterogeneity is there for a reason the authors state: it is needed “to generate meaningful financial transactions and to allow differences in spending patterns” (p. 6). They are also careful about when monetary policy can and cannot fix things: even unconstrained monetary policy may not reach the first best, since the divine-coincidence result does not extend to open economies, multi-sector models, or models with nominal wage rigidity, where the first best “would require the adjustment of various relative prices” (fn. 9).

Proposition 2 states that the constrained-efficient allocation can be implemented with financial taxes tau^i_{D,s} equal to the sum over goods of that agent’s marginal propensity to spend on the good times that good’s wedge, with wedges satisfying the weighted-average conditions that also characterise optimal monetary policy (Section 3.1, p. 12). The authors emphasise measurability: “the taxes tau^i_{D,s} can be expressed in terms of two sufficient statistics: the marginal propensities to spend P_{j,s} X^i_{I,j,s} and wedges tau_{j,s}. Both of these variables are well-known concepts, that can in principle be measured from the data or calibrated from standard models, and are the focus of large applied literatures” (p. 12). The economic reading they give: “financial taxes should encourage an agent to shift wealth towards a state if this agent tends to spend relatively more (at the margin) than others on goods with positive wedges” (p. 12). Two qualifications travel with the result. Only relative taxes across agents are pinned down – “the relative financial taxes (1 - tau^i_{D,s}) faced by two agents i and i’ in any given state s are uniquely determined,” while the level depends on how state prices are normalised (p. 12). And the choice between price and quantity instruments is outside the theory: equivalent implementations exist “with quantity restrictions (caps and floors on portfolio holdings) instead of taxes… Our theory is silent on the relative desirability of these two forms of intervention” (fn. 14).

The claim is generic, not universal: Proposition 3 shows that if a non-first-best constrained-efficient allocation happens to be implementable without financial taxes, an arbitrarily small perturbation of preferences makes financial taxes necessary (Section 3.2, pp. 14-15). The construction perturbs utility so that individual demand functions, Slutsky matrices and social marginal utilities of income at the original incomes and prices are all unchanged – so the original allocation still solves the perturbed planning problem – while the income derivatives of demand are changed enough to break the no-tax condition (8). The authors flag the binding hypothesis: “The requirement that the allocation not be first best is important,” because with no restrictions on prices all wedges are zero and the perturbation cannot be constructed (p. 15). Their own summary of the pair of results is that non-first-best constrained-efficient allocations “cannot generically be implemented without financial taxes” (p. 15) – a statement about genericity in the space of preferences, not a claim that every economy with sticky prices calls for macroprudential taxes.

Only the set of goods entering the tax formula changes: Proposition 4 replaces the sum over all goods with a sum over non-rationed goods (Section 3.3, pp. 15-16, and p. 20). In the baseline, agents are on their demand curves, so if leisure is a good then agents are on their labor supply curve. To handle sticky nominal wages, the authors allow rationing of a subset of goods, of which underemployment is the leading case. The reason the formula narrows is stated plainly: “only the goods that are chosen (instead of rationed) appear in the formula. This is natural as for a given agent, wealth in a particular state only influences spending on these goods” (p. 20); in the introduction’s words, “marginal propensities to spend on rationed goods are effectively zero” (p. 3).

No – Proposition 5 and the surrounding argument establish that the optimum with commitment is time consistent, provided the right set of ex-ante macroprudential instruments exists. Ex post, the government “equalizes social marginal utilities of income across agents, rather than the private marginal utilities of income,” where the gap between private and social marginal utility of income for an agent is exactly the optimal financial tax in that state (Section 3.4, pp. 21-22). Because the allocation that arises in the ex-post stage of the no-commitment policy game – analysed as anonymous symmetric perfect Bayesian equilibria, following Chari and Kehoe (1990) – coincides with the commitment optimum, “the optimal allocation under commitment is an equilibrium allocation of the policy game, and the corresponding equilibrium financial taxes are the same as those required under commitment” (p. 22). The authors also note the direction of the redistribution logic: there are “macroeconomic stabilization benefits from redistribution” toward agents with a higher marginal propensity to spend on depressed goods, and financial taxes are needed “in order to prevent agents from undoing the desired ex-post wealth distribution through financial markets” (pp. 3-4, 22).

The formula for optimal macroprudential policy is unchanged; only the monetary-policy system acquires new forcing variables. Section 4 builds a unified model with market incompleteness and price-dependent borrowing constraints alongside nominal rigidities. The authors’ statement is explicit: “Remarkably, however, our formula for optimal macroprudential policy is unchanged in the unified model. To be sure, the presence of pecuniary externalities affects wedges, but does not affect the mapping from wedges to macroprudential policy” (p. 4; Proposition 6, p. 25, and the discussion at p. 25 noting the formula “is exactly the same as in Proposition 2 and its corollary for arbitrary securities” and “is independent of the exact frictions”). For optimal monetary policy, by contrast, “the system of linear equations in wedges describing optimal monetary policy now acquires new forcing variables, due to market incompleteness and the presence of prices in borrowing constraints” (p. 4).

No. Proposition 8 finds that at the optimum the average labor wedge in the boom period is exactly zero – perfect macroeconomic stabilisation – while the financial-stability objective is handled by a binding macroprudential borrowing limit. The model is a three-period version of Eggertsson and Krugman (2012) with savers (type 1) and more impatient borrowers (type 2), sticky wages, equal rationing in the labor market, and an exogenous period-1 borrowing constraint; the authors add period 0, in which the debt is contracted. Proposition 8 gives average labor wedges bar-tau_0 = 0, bar-tau_1 >= 0 and bar-tau_2 <= 0, “with strict inequalities if the zero lower bound constraint binds in period 1,” and in that case it is optimal to impose a binding borrowing constraint on type-2 agents in period 0, with an explicit implicit tax on borrowing tau^B_0 > 0 (p. 27). The policy reading is stated directly: “there is no need to sacrifice macroeconomic stability by tightening monetary policy to improve financial stability. It is better to tighten macroprudential policy instead” (p. 5), and “it is not optimal to implement tighter monetary policy in period 0 because of financial stability concerns” (p. 27). The authors immediately qualify this. The conclusion “rests on the availability of macroprudential instruments and the assumption that these can be implemented effectively,” and they note the practical concern that macroprudential policy “confront[s] different agents with different interest rates” whereas monetary policy “gets in all the cracks,” quoting Federal Reserve governor Jeremy Stein’s February 7, 2013 speech (p. 27, fn. 22). They also note that absent macroprudential instruments, optimal monetary policy in period 0 can go either way: “both bar-tau_0 > 0 or bar-tau_0 < 0 are then possible, depending on whether engineering a recession by increasing nominal interest rates increases and reduces borrowing” (fn. 22).

Under-insurance. With uncertainty added, the optimal macroprudential tax is zero on borrowing against the good state and positive only on borrowing against the bad state in which the zero lower bound binds. In the stochastic version, a date-1 shock is good or bad, complete Arrow-Debreu markets are available at date 0, and the borrowing limit is looser in the good state. Under optimal policy, when the good state occurs “the economy is perfectly stabilized,” while in the bad state there is a liquidity trap and recession; in period 0 the average wedge is still zero. Optimal policy “imposes no macroprudential tax on state-contingent borrowing against state omega_G, but a positive macroprudential tax on state-contingent borrowing against state omega_B” – hence “the problem can be seen as one of under-insurance, rather than over-borrowing” (p. 29). Non-contingent borrowing still carries a positive tax, because it “embeds a component of borrowing against the bad state of the world,” and that tax “is commensurate with the probability” of the bad state (p. 29).

It produces the hybrid case, where an aggregate demand externality and a pecuniary externality amplify each other, and the optimal tax is the sum of two corrective terms. With housing as collateral and a borrowing constraint that depends on house prices, the loop runs: extra date-0 borrowing lowers borrowers’ date-1 wealth; because they have a high marginal propensity to spend, aggregate demand falls; lower consumption lowers house prices; the collateral constraint tightens; demand falls further. The authors describe it as a “negative feedback loop [that] has the potential to greatly amplify the negative effects of the deleveraging shock,” none of it internalised by borrowers (p. 30). Correspondingly, “the macroprudential tax on period-0 borrowing by agents of type 2 now corrects for two externalities: an aggregate demand externality as before (the first term) and a new pecuniary externality (the second term)” (p. 30).

Under a fixed exchange rate, capital controls are optimal and function as a second-best substitute for interest-rate autonomy; but the paper also shows capital controls can be warranted with a flexible exchange rate, which qualifies the Mundellian reading. In the fixed-rate application (Section 5.2, drawing on Farhi and Werning 2012a), the small open economy could attain perfect stabilisation with a floating rate “just as envisioned by Friedman (1953),” but with the rate pegged by a hard peg or currency union it is optimal to use macroprudential capital controls – “a second-best way of regaining monetary policy autonomy, that is, control over the interest rate,” with “taxes on inflows… deployed to cool down booms, and taxes on outflows to mitigate recessions” (pp. 5-6). Proposition 11 states the optimum has labor wedges tau_0 and tau_1 “of opposite signs” and gives the inflow tax as an explicit ratio in those wedges (p. 35). The authors are careful that this application is deliberately stylised: “we stop short of developing and explaining this application in full… However, Farhi and Werning (2012a) address a number of specific issues that arise in the context of this application using a richer model” (fn. 7). The third and fourth applications drop the constraint on monetary policy entirely and still find a role for capital controls, which the authors present as “an important qualification to the Mundellian paradigm that ties the benefits of capital controls to fixed exchange rate regimes” (p. 6). With terms-of-trade-dependent collateral constraints, Proposition 13 gives an inflow tax in which “tau_t > 0 if and only if the collateral constraint is binding at t,” so taxes on inflows “should be imposed preemptively in anticipation of binding collateral constraints” (pp. 6, 43).

Because with incomplete markets limited to non-contingent local- and foreign-currency debt, the optimal inflow taxes on the two instruments differ, and the paper’s fourth application finds the foreign-currency instrument should be taxed more heavily. Proposition 15 gives separate expressions for the optimal tax on foreign-currency and local-currency borrowing, each an expectation of the wedge ratio plus an additional term reflecting how that instrument’s real payoff covaries with the price of non-traded goods (p. 45). The authors state the direction of the result and connect it to policy discussion: “capital controls should differentiate between local- and foreign-currency borrowing, with higher taxes on foreign-currency debt. This is consistent with common wisdom within policy circles arguing that international credit booms fueled by foreign-currency debt are especially problematic” (p. 6).

It does not offer empirical magnitudes, does not rank taxes against quantity restrictions, and does not claim its results are robust to every form of nominal rigidity. The conclusion is framed entirely in analytical terms: competitive equilibria are “constrained inefficient,” the market failures “can be traced to aggregate demand externalities,” and optimal interventions are “characterized by simple and interpretable formulas expressed in terms of empirically measurable sufficient statistics” (Section 6, p. 46) – measurable in principle, not measured here. The instrument-choice silence is explicit (fn. 14). And the authors flag one mechanism their baseline misses: in Schmitt-Grohé and Uribe (2012), where nominal wages are downward-sticky according to an ad hoc norm, the fact that “wages are not set in a forward looking manner in good times… introduces an additional rationale for macroprudential policy,” a motive that “could account for significant welfare effects” but “is not captured in our baseline model” (fn. 8). They also note that two applications from an earlier version – risk sharing in currency unions and capital controls under flexible rates in anticipation of a liquidity trap – were cut “to economize on space” (fn. 6).