Iván Werning | Macro Paper Warehouse

A Theory of Macroprudential Policies in the Presence of Nominal Rigidities

This is a theory paper, with no calibration or empirical estimates: its output is a set of analytical formulas rather than numbers. It asks what justifies macroprudential intervention in financial markets, and answers that nominal rigidities alone – without the incomplete markets or price-dependent borrowing constraints that earlier work relied on – are enough. In the baseline model financial markets are complete and frictionless; the only imperfections are sticky goods and labor prices and, in the cases the authors care most about, a constraint that stops monetary policy from undoing them, such as the zero lower bound or a fixed exchange rate. The mechanism is what the authors call an aggregate demand externality: once a state of the world is realised, who holds the wealth matters for how much the economy spends, because agents differ in their marginal propensities to spend, but no atomistic agent takes that macroeconomic consequence into account when choosing a portfolio ex ante. Two sets of results follow. First, using a perturbation argument in the spirit of Geanakoplos and Polemarchakis (1985), any equilibrium that is not first best can be improved by intervening in financial markets “except in non-generic knife-edged cases” – the constrained-inefficiency claim is a genericity claim, not a claim that intervention always helps. Second, optimal monetary and macroprudential policy are characterised jointly by explicit formulas in three sufficient statistics: elasticities of substitution, marginal propensities to spend, and good-specific wedges. The optimal financial tax on an agent’s claim in a given state is the marginal-propensity-weighted sum of that state’s wedges, so wealth should be tilted toward states where the goods an agent buys heavily are depressed. Monetary policy, in parallel, targets weighted averages of wedges, adapting the standard New Keynesian targeting rules. The framework is then extended to include pecuniary externalities as well, and – a result the authors call remarkable – the macroprudential formula is literally unchanged: market incompleteness and price-dependent constraints alter the wedges but not the mapping from wedges to taxes. Four applications illustrate the theory: household deleveraging into a liquidity trap, where the optimal policy mix restricts pre-crisis borrowing (in practice a loan-to-value or debt-to-income limit) while monetary policy still delivers perfect stabilisation during the boom; capital controls under a fixed exchange rate, read as a second-best way of regaining interest-rate autonomy; and two cases with a flexible exchange rate where capital controls are still warranted, one with terms-of-trade-dependent collateral constraints and one with non-contingent local- and foreign-currency debt.

Incomplete Markets and Aggregate Demand

This paper studies aggregate consumption dynamics in an economy populated by a continuum of households facing idiosyncratic income uncertainty and incomplete markets, focusing on the relationship between aggregate consumption and the path of real interest rates. Rather than solving a fully specified quantitative model, Werning derives a general “demand block” relation for aggregate consumption by exploiting the general-equilibrium requirement that aggregate consumption equal aggregate income. Under the extreme case of vanishing liquidity (no borrowing, no outside assets), the equilibrium coincides with financial autarky and aggregate consumption and interest rates are shown to satisfy a generalized Euler relation involving only current and future aggregate consumption and the current interest rate; for an important benchmark specification – power utility with multiplicative taste shocks and household income proportional to aggregate income – this relation collapses exactly to a standard representative-agent Euler equation, with market incompleteness affecting only a (state- and time-varying) discount factor rather than the responsiveness of consumption to interest rates. An immediate corollary is that forward guidance (a commitment to lower future interest rates) is exactly as powerful as in representative-agent models whenever this representation holds – a result the paper explicitly contrasts with McKay, Nakamura, and Steinsson (2015). Werning shows the same representative-agent representation survives with positive liquidity (borrowing and a positive-net-supply outside asset) when utility is logarithmic and income and borrowing limits are proportional to aggregate income. Moving away from these benchmark cases – for instance, when idiosyncratic risk is countercyclical, illustrated with an example based on a varying employment margin – the paper shows consumption is likely to become more sensitive to interest rates, and especially to future interest rates, which would strengthen rather than weaken the power of forward guidance. Finally, the paper extends its approach to a real business cycle model with capital and shows that, under logarithmic utility and full depreciation (the Brock-Mirman case), aggregate capital and labor dynamics are exactly identical to the representative-agent economy regardless of how large or persistent idiosyncratic risk is at the household level – an exact analytical counterpart to the approximate aggregation results Krusell and Smith (1998) found numerically.

Managing a Liquidity Trap: Monetary and Fiscal Policy

Working with a continuous-time version of the standard New Keynesian model, this paper studies optimal monetary and fiscal policy in a liquidity trap, where the zero lower bound on the nominal interest rate binds because the natural rate of interest is temporarily negative. Without commitment, a benevolent but discretionary central bank produces deflation and a depressed output gap that worsen, without bound, as the trap’s duration grows – and, perhaps counterintuitively, more flexible prices make both problems strictly worse rather than better, because faster deflation raises the real interest rate further and deepens the slump in a self-reinforcing spiral. Committing to future policy overturns this: the paper proves that optimal policy holds the nominal rate at zero for longer than current inflation alone would justify, which promotes future inflation and a future output boom that (via forward-looking expectations) raises consumption and narrows the output gap today; output must nonetheless start out below its efficient level even under the optimal commitment, and the exit from the trap features a discrete upward jump in the nominal rate even though the underlying natural-rate path is continuous. Adding government spending as a second instrument, the paper shows optimal spending is front-loaded – positive at the start of the trap and negative by its end – but that once spending is decomposed into a purely static, cost-benefit “opportunistic” component (spend more when the shadow cost of resources is low in a slump) and a residual “stimulus” component aimed at managing aggregate demand, stimulus spending is exactly zero at the start of every trap and, for a specific parameter configuration, can be identically zero throughout, so that observed front-loaded spending need not reflect deliberate demand management at all. When monetary policy instead lacks commitment while fiscal policy retains it, stimulus spending becomes unambiguously positive and rising through the trap, substituting for the missing monetary commitment.