E5 | 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.

Capital flows and the risk-taking channel of monetary policy

Bank leverage is the linchpin of a risk-taking channel through which monetary policy travels across borders: in a pre-crisis quarterly VAR a tighter US policy rate raises the VIX, lowers broker-dealer leverage, appreciates the dollar and shrinks cross-border bank flows, and an accompanying contracting model delivers the result that bank leverage rises with the expected appreciation of the borrower’s currency. The empirical work is a recursive VAR on quarterly data from 1995Q4 to 2007Q4 in the real fed funds target rate, the log VIX, the leverage of the US broker-dealer sector from the Flow of Funds, and the log change in the dollar’s real effective exchange rate, estimated with two lags and 90 percent bootstrapped confidence bands from 1,000 replications. Three links appear. A positive fed funds shock raises the VIX from quarter 4, consistent with Bekaert, Hoerova and Lo Duca’s finding of an effect between months 9 and 11. A rise in the VIX lowers broker-dealer leverage. And a positive fed funds shock lowers leverage after a lag of around 10 quarters, remaining significant to quarter 17, with a maximum response of minus 0.47 at quarter 12 – against a sample average leverage of 21.94, a decline to about 21.5. Leverage in turn moves the exchange rate: an increase in broker-dealer leverage lowers the dollar’s real effective exchange rate by 0.42 percent by quarter 3, with an effect that stays significantly negative across the whole 20-quarter horizon, which the paper offers as a complement to the delayed overshooting puzzle of Eichenbaum and Evans (1995). Adding the first difference of the BIS series for dollar liabilities of banks outside the US shows that higher broker-dealer leverage raises cross-border bank flows after 11 quarters, peaking at 17, and that a fed funds tightening lowers those flows from quarter 8 to quarter 17. Variance decompositions show monetary policy shocks accounting for almost 30 percent of VIX variance and 10 to 20 percent of leverage variance beyond 10 quarters, while leverage shocks account for over 20 percent of exchange rate variance and almost 40 percent of fed funds variance. The theory then rationalises this with a contracting problem in which a bank funds dollar loans from the wholesale market and its local borrowers hold local-currency assets: moral hazard over the correlation of the loan portfolio yields a unique solution with a binding leverage constraint, zero bank default, and the paper’s main proposition that leverage is increasing in expected currency appreciation. Two scope conditions are load-bearing and the authors state both. The sample stops in 2007 because extending it through the zero lower bound produces “markedly weaker VAR impulse responses,” with many fed funds responses insignificant, so “the results reported in this paper should be seen as applying mainly for the boom period preceding the onset of the crisis.” And the amplification story relies on capital inflows coinciding with appreciation, which conflicts with uncovered interest parity; the paper notes UIP’s empirical failure but says plainly that “uncovering the precise mechanism for the failure of UIP is beyond the scope of our paper.”

Expectation Traps and Monetary Policy

Embedding the Kydland-Prescott/Barro-Gordon time-inconsistency logic into a standard sticky-price, cash-credit-goods general equilibrium model, this paper shows the resulting model generically has either two Markov equilibria – a high-inflation and a low-inflation one – or none at all, with no trigger strategies (repeated-game punishments) required to sustain the multiplicity. In the model, monopolistically competitive firms produce inefficiently low output; some firms preset prices before the monetary authority chooses the money growth rate, so unanticipated monetary expansion raises output and, because output is inefficiently low to begin with, can raise welfare. Households simultaneously choose, before the money growth rate is set, how much to purchase with previously accumulated cash (costly in forgone interest) versus credit (costly in labor time); realized inflation forces substitution away from cash goods, which lowers welfare. The paper’s key insight is that both sticky-price firms and cash-using households take defensive actions that depend on their expectations of inflation: if either expects high inflation, their optimal defensive response (high preset prices, or lower cash use) lowers the marginal cost to a benevolent monetary authority of actually delivering high inflation, making validation optimal; the reverse defensive choices under low-inflation expectations sustain low inflation instead. The paper proves formally that the model has at least two Markov equilibria whenever it has at least one, labels the resulting persistent multiplicity an “expectation trap,” and shows the two equilibria have starkly different comparative statics: the interest rate’s response to a technology shock switches sign between them, implying the output-interest-rate correlation should be systematically more negative in high-inflation regimes. Examining cross-country and within-country data from the IMF’s International Financial Statistics, the paper finds support for this prediction (correlations of roughly −0.45 versus −0.08 within high-inflation countries’ high- and low-inflation episodes, and −0.33 versus −0.20 across high- and low-inflation countries) as well as for the model’s prediction of higher nominal-variable volatility under high inflation.

Review of Milton Friedman and Anna J. Schwartz's 'A Monetary History of the United States, 1867-1960'

Writing for the 30th anniversary of Milton Friedman and Anna Schwartz’s A Monetary History of the United States, 1867-1960, Lucas argues that the book’s enduring contribution is not merely its “beautiful time series on the money supply and its components” but a coherent normative narrative: nearly a century of U.S. monetary history, organized around two principles – long-run monetary neutrality and a short-run non-neutrality operating through unexplained but transient price rigidities – in which every major depression is traced to an avoidable policy mistake or an unchecked banking panic, so that the whole period “might have evolved, with stable prices and smoothly growing real output” had the monetary authority acted differently. Lucas states he finds this normative argument “wholly convincing,” particularly for the 1929-33 contraction, but presses on what a model-free narrative history cannot do: answer how much smoother money growth would have helped, since the book’s own conclusions are, in his words, not “a verbal summary of tables describing the results of a numerical simulation” but “the simulation” itself. He then surveys three later research programs against this yardstick – 1970s rational-expectations models that reconciled the book’s two neutrality principles but reached opposite normative conclusions about optimal policy depending on how price rigidity is modeled; Christopher Sims’s atheoretical statistical approach and Romer and Romer’s “natural experiments,” each proposing a different, non-equivalent notion of monetary “independence” from Friedman and Schwartz’s own; and real-business-cycle theory, which Lucas judges incapable of explaining the Depression’s actual magnitude – the Solow residuals for 1928-1933 are far too small to map into a 40% decline in output – while nonetheless reshaping how the discipline reads the comparatively small role of money in accounting for postwar fluctuations, not as evidence money is unimportant but as evidence postwar monetary policy has been close to efficient.

Taper Tantrums: Quantitative Easing, Its Aftermath, and Emerging Market Capital Flows

Identifying US monetary policy shocks from daily moves in five-year Treasury futures around FOMC announcements, this paper shows that during the unconventional-policy years those shocks largely represent revisions to required risk compensation rather than to the expected short-rate path, and that their effects on emerging market portfolio positions run mainly through valuations rather than physical flows – with by far the largest effects during the taper period. The shock measure follows Rogers, Scotti and Wright (2014): the daily change in the implied yield of the five-year Treasury futures contract on FOMC announcement dates, plus the additional policy events in Gagnon et al. (2011) and the taper-tantrum date of 22 May 2013. Its average value is a fall of 2.0 basis points during the QE period and a rise of 1.6 basis points during the taper period, against minus 0.6 for the full sample and minus 0.5 pre-crisis, with the period differences statistically significant. Feeding the shock through the Kim and Wright (2005) affine term structure decomposition shows it moves both the expected short rate and the term premium in the conventional period, but that in the unconventional periods the largest effects are on term premia and those effects rise monotonically with maturity – a one-standard-deviation shock raises the ten-year yield by 4.7 basis points pre-crisis but 12.2 basis points during QE, against unconditional daily ten-year standard deviations of 5.8 and 7.1 basis points respectively. The capital-flow analysis uses Bertaut-Tryon and Bertaut-Judson monthly estimates built from US Treasury International Capital data, covering 15 emerging markets monthly from 1994 to 2014, with positions, flows and valuation changes for debt and equity separately scaled by annual GDP, estimated in a random-effects panel with lagged dependent variables, an extensive set of lagged push and pull controls, and country-clustered robust standard errors. Three kinds of heterogeneity emerge. Flows versus prices: “in nearly every specification, the effect of monetary policy shocks on asset returns is larger than that for physical flows,” which the authors read as consistent with the shocks capturing revisions in required risk compensation. Debt versus equity: during QE the coefficient on equity valuations is ten times that on debt valuations, and during the taper period equity effects are double or triple debt effects. QE versus tapering: during QE the significant responses are confined to debt and equity valuations and equity positions, whereas after tapering was first mentioned the coefficients are inversely signed and significant at the 1 percent level across essentially every variable, and an order of magnitude larger than pre-crisis for debt positions, debt valuations and equity flows. Because the shock has a magnitude, the paper can price these effects: a mean-sized QE shock corresponds to roughly a $153.5 million monthly increase in US emerging market equity positions per country, a mean-sized taper shock to a $144.1 million monthly outflow, with one-standard-deviation ranges of roughly minus $672 million to plus $979 million during QE. The paper is explicit that its estimates are associations from a controlled panel regression rather than structural effects: coefficients are described throughout as correlations, the shock’s channel is inferred from coefficient signs rather than separately identified, and the exchange rate results, while statistically significant, are reported as economically modest against an unconditional monthly bilateral exchange rate standard deviation of 3.57 percent.

Term structure evidence on interest rate smoothing and monetary policy inertia

Estimated Taylor-type policy rules typically find the Fed adjusts the funds rate only 20-30 percent of the way to its desired level each quarter, widely read as deliberate “interest rate smoothing.” Reviewing estimates of both a backward-looking Taylor rule and the forward-looking Clarida-Galí-Gertler variant on 1987-1999 U.S. data, the paper confirms the standard result: partial-adjustment coefficients around 0.7-0.9, fitting the data far better than a version with no lagged rate at all. The paper then tests the interest-rate-smoothing interpretation against an implication it must carry: if the funds rate genuinely adjusts only partially each quarter, a large share of its future path should be predictable from information already available, and rational financial markets should price that predictability into the term structure. Using eurodollar futures rates to construct real-time forecasts, the paper finds an R² of 0.57 for the funds-rate change one quarter ahead, but only 0.11 two quarters ahead and 0.03 three quarters ahead – essentially no forecastable variation beyond about three months, sharply at odds with what a highly inertial policy rule implies. The paper then shows that a policy rule with immediate, full adjustment (no smoothing at all) but a persistent, serially correlated shock term fits the historical funds-rate data just as well as the standard partial-adjustment rule on conventional goodness-of-fit measures, and formal tests cannot reliably distinguish the two specifications within available samples. Because only the serially-correlated-shock version is consistent with the term structure’s near-total unpredictability of the policy rate beyond a quarter, the paper concludes that the large lag coefficients found throughout the policy-rule literature are largely a statistical illusion generated by omitted persistent shocks to policy, not evidence that central banks deliberately smooth interest-rate changes over multiple quarters.

Understanding policy in the great recession: Some unpleasant fiscal arithmetic

This paper uses the government-debt valuation equation – the requirement that the real value of outstanding money plus nominal government debt equal the present value of expected future primary surpluses – together with a money-demand equation, to interpret U.S. fiscal and monetary policy during and after the 2008-2009 financial crisis and to think through the possible paths to inflation or deflation that follow it. Cochrane argues that the depth of the 2008-2009 recession is best understood not as a shortage of money relative to money demand, but as a “flight to quality”: a surge in demand for all government debt, at the expense of private debt and of goods and services, corresponding in the fiscal equation to a fall in the discount rate applied to government liabilities. He argues that conventional “fiscal stimulus” reasoning is upended once government debt is recognized as nominal rather than real: a deficit is stimulative if and only if people do not expect future taxes or spending cuts to pay it off, and if so, future deficits are just as stimulative as current ones, so the standard “stimulus spending arrives too late” objection does not apply in this framework – though credibly communicating that debt will not be paid off is itself difficult, since most fiscal institutions are built to signal the opposite. On monetary policy, Cochrane contends that once nominal interest rates hit zero, “quantitative easing” that merely swaps money for short-term government debt does nothing, because the two are close to perfect substitutes at the margin; purchases of long-term debt can shift the timing but not the total magnitude of eventual inflation; and purchases of private debt can help only by relieving a genuine liquidity premium, an effect that is necessarily exhausted once that premium is satisfied. Extending the valuation equation to long-maturity debt, Cochrane argues that a plausible future “fiscal inflation” – one triggered by a reassessment of the government’s capacity or willingness to run future surpluses – would not appear as a sudden price-level jump but as a gradual process beginning with rising long-term interest rates, and that because credit guarantees, nominal government commitments, and growth effects on the present value of tax revenue can move the effective “fiscal limit” much closer than raw debt-to-GDP ratios suggest, such an event could arrive well before large current deficits, elevated debt/GDP, or overt debt monetization materialize. Finally, because in his account the fiscal valuation equation is itself what anchors inflation expectations, Cochrane argues a fiscal inflation is likely to act as a shift of the Phillips curve rather than a movement along it, so that – as illustrated in a calibrated New-Keynesian simulation in which output falls throughout an anticipated fiscal-inflation episode – such an event is more likely to resemble the stagflation of the 1970s than an inflationary boom, with correspondingly little that the Federal Reserve, legally barred from taking fiscal actions on its own, can do to prevent either outcome.