Martín Uribe | Macro Paper Warehouse

Avoiding Liquidity Traps

Because a Taylor-type interest-rate rule must be consistent with the zero nominal-interest-rate bound, it always admits a second, unintended steady state with low or negative inflation alongside the intended target – and this paper shows that steady state is itself indeterminate, allowing the economy to slide into it via a self-fulfilling, gradually decelerating inflation path. Setting up a flexible-price, continuous-time monetary model in which the nominal rate is an increasing, nonnegative function of inflation and the Fisher equation pins the steady state relationship between the real rate, inflation, and the nominal rate, the paper shows this second intersection is unavoidable given the zero bound: inflation and the nominal rate are both low there, and “monetary policy is passive” in the technical sense long associated with equilibrium indeterminacy. Extending prior work (Benhabib, Schmitt-Grohé, and Uribe 2001b), the paper shows equilibrium paths exist that start arbitrarily close to the intended, Taylor-rule-consistent target and converge gradually to this unintended low-inflation trap – a self-fulfilling deflationary spiral driven by nothing but revisions in expectations, with all the hallmarks of a liquidity trap in which the central bank cannot reverse falling prices by cutting rates further, since rates are already near zero. The paper’s contribution is to design remedies that preserve the Taylor rule’s appealing local properties (including unique local determinacy near the inflation target) while ruling out the global liquidity-trap equilibrium: first, a fiscal policy in which government revenue’s sensitivity to outstanding liabilities rises with inflation, making the low-inflation path fiscally unsustainable via a transversality-condition violation (a Pigou-style wealth-effect channel, not the Keynesian multiplier); second, a conditional switch to a money-growth-rate target once inflation nears the trap, which the paper shows succeeds or fails depending critically on the accompanying fiscal regime. The paper’s flexible-price results extend, per the authors, to environments with sticky prices and to discrete time, though a distinct chaotic-dynamics failure mode of Taylor rules (identified in companion work) is not addressed by these remedies.

Deep Habits

Habit-formation models, internal or external, standardly assume households form habits over a single aggregate good, which means habits change macroeconomic propagation only through aggregate demand and possibly labour supply. This paper asks what changes if habits are instead formed variety by variety – over clothing, vacation destinations, music, cars – a specification the authors call “deep habits” and argue is the more compelling reading of the evidence, citing Houthakker and Taylor’s classic demand work and the marketing literature finding that brand choices depend on past brand choices. Two consequences follow. The demand side is unaffected: the consumption Euler equation is indistinguishable from the superficial-habit case, so existing Euler-equation estimates of habit strength carry over. The supply side changes fundamentally, because firms now recognise that today’s sales raise tomorrow’s demand through habit, making the pricing problem dynamic. Demand for an individual variety splits into a price-elastic term and a perfectly inelastic term coming from habitual consumption of that good, so the short-run price elasticity is a weighted average of the elasticity of substitution and zero – smaller than the elasticity of substitution, and rising when aggregate demand rises because the inelastic component shrinks in relative weight. Since the mark-up is inversely related to the elasticity, mark-ups fall in expansions: the “price-elasticity effect.” A second, “intertemporal” channel operates because firms invest in customer base by cutting mark-ups when the present value of future per-unit profits is high, which also makes the mark-up rise with the real interest rate. Together these deliver a central result – mark-ups are countercyclical in response to preference, government-spending and productivity shocks – which matters because ad hoc general equilibrium customer-market and switching-cost models had been criticised by Rotemberg and Woodford precisely for implying procyclical mark-ups; the authors’ answer is that once demand is derived from optimising households rather than assumed, the prediction reverses. Embedding the mechanism in a full real-business-cycle model with capital, labour supply and government, and estimating the habit parameters by nonlinear GMM on U.S. quarterly data for 1967:Q1-2003:Q1 (exploiting supply-side restrictions absent from Euler-equation-only estimation) gives a habit strength of 0.86, a habit-stock persistence of 0.85, an elasticity of substitution across varieties of 5.3 and a curvature parameter of 2, with the remaining calibration targets taken from Rotemberg and Woodford to make the comparison direct; the implied steady-state mark-up is 1.32, which the authors describe as “somewhat high,” against 1.23 in the no-deep-habit case. Quantitatively, a preference shock worth 1% of steady-state habit-adjusted consumption cuts the mark-up by about 0.4% and raises wages by about 0.3%, where under superficial or no habits wages fall. A 1% government-spending shock cuts mark-ups by about half a per cent, raises real wages, and – against the standard neoclassical prediction – raises private consumption, in line with evidence from Fatás-Mihov, Blanchard-Perotti and Galí-López-Salido-Vallés, though the authors are explicit that “the deep-habit model underpredicts the magnitude of the consumption increase.” The model’s conditional correlation between labour productivity and output is 0.33 under government-purchases shocks and 0.72 under preference shocks, against an unconditional figure of 0.34 reported by Cooley and Prescott, where the superficial-habit model gives -0.1 and -0.85. Three extensions separate the mechanisms: good-specific subsistence points isolate the price-elasticity effect and still give countercyclical mark-ups, but the movements are too small to deliver procyclical wages or procyclical consumption after a government-spending shock; relative deep habits isolate the intertemporal effect, whose sign then depends on whether a shock raises the habit-forming or the non-habit-forming component of demand; and internal deep habits make the monopolist’s pricing problem time inconsistent, a case the authors flag as “beyond the scope of this paper” and “perhaps, the most relevant next step in this research programme.”

Optimal fiscal and monetary policy under sticky prices

This paper resolves a contradiction between two branches of optimal monetary policy theory. Ramsey models with flexible prices (Calvo and Guidotti; Chari, Christiano, and Kehoe) find that an optimizing government, restricted to distortionary income taxation and nominal non-state-contingent debt, should make inflation highly volatile and serially uncorrelated, using unanticipated price-level changes as a non-distorting, state-contingent tax on nominal wealth so that regular tax rates can stay smooth; New Keynesian models with sticky prices, by contrast, typically find optimal inflation should be zero or near-zero at all times – but usually by assuming the government can also rely on lump-sum taxes, eliminating any need for inflation to double as a fiscal instrument. Schmitt-Grohé and Uribe build a single model that combines the empirically relevant assumptions of both literatures – only distortionary income taxation and nominal non-state-contingent debt available to the fiscal authority, plus monopolistic competition and Rotemberg-style costly price adjustment on the supply side – and solve for the Ramsey-optimal fiscal and monetary policy under full commitment. Their central finding is that the tradeoff between using inflation as a shock absorber and avoiding the real costs of price adjustment is overwhelmingly resolved in favor of price stability: calibrating price stickiness to even one-tenth of available U.S. estimates already reduces the optimal standard deviation of inflation from about 7% per year under full price flexibility to well under 1%, and at their full baseline calibration it falls to just 0.17% per year. They trace this fragility to Aiyagari et al.’s result that the welfare gain from being able to issue real state-contingent debt (which flexible-price surprise inflation effectively replicates) is itself small, so even minor price-adjustment costs are enough to make the Ramsey planner abandon front-loading altogether. In its place, the government relies on ordinary tax-rate and debt adjustments, smoothed over time to minimize distortion – which induces near-random-walk behavior in both taxes and public debt, reproducing the Barro (1979)/Aiyagari et al. finding usually derived by assuming the government can issue only real (not nominal) non-state-contingent debt, but here obtained instead from a purely nominal, non-state-contingent debt structure plus even minimal price rigidity. The paper further shows that price stickiness induces a systematic, quantitatively significant deviation from the Friedman rule (roughly half of it attributable to stickiness itself, the rest to an existing monopoly-profit-taxation channel), and that a regression of the Ramsey-optimal nominal interest rate on inflation and output, estimated on simulated data, produces an inflation coefficient statistically indistinguishable from zero (and negative in point estimate) – the opposite of what an actual Taylor rule requires – a result the authors present as a cautionary finding about inferring policy rules from optimal-policy time series, not as a claim that a passive rule can implement the Ramsey outcome.