Habit Formation in Consumption and Its Implications for Monetary-Policy Models

The argument starts from a complaint about method: a model used to rank monetary policies must be trusted to represent how consumers and firms actually behave over the policy horizon, and the author contends that most optimisation-based sticky-price models of the late 1990s had not been validated in a way that would earn that trust. Matching first and second unconditional moments is not enough, and neither is matching a single impulse response – especially the response to a monetary policy shock, since the unanticipated component of policy accounts for only a small share of the variance of output, inflation or interest rates. Instead the paper advocates likelihood-based evaluation, comparing the full vector autocovariance function of a structural model against that of an unconstrained VAR in which the structural model is nested. Judged that way, the standard life-cycle consumption model fails in a specific and diagnosable manner: consumption behaves like a “jump variable,” front-loading its entire response to a shock, whereas identified VARs show a gradual hump-shaped response peaking around a year out. Adding Campbell-Mankiw rule-of-thumb consumers does not fix this. The paper’s proposed fix is habit formation in the Carroll-Overland-Weil form, in which utility depends on consumption relative to a reference level built from past consumption; the author’s own explanation of why it works is that this “mixes utility from the level of consumption with utility from the change in consumption,” so consumers acquire a motive to smooth changes as well as levels. He deliberately rules out the alternative repair – assuming serially correlated structural errors – on the grounds that a model with its dynamics hidden in the errors “becomes vulnerable to a Lucas critique of its errors.” Estimating the linearised consumption function by numerical maximum likelihood on U.S. quarterly data for 1966:1-1995:4, the habit parameter comes in at 0.80 with a standard error of 0.19, the rule-of-thumb income share at 0.26, the curvature parameter at 6.11 (implying a small intertemporal elasticity of substitution), and the forward-looking discount parameter at 0.99 per quarter. The restriction that habit formation is unimportant is rejected with a chi-squared statistic of 21.4 and a p-value of 4 times ten to the minus six; the restriction that rule-of-thumb behaviour is unimportant is rejected with a statistic of 12.6 and a p-value of 4 times ten to the minus four. Notably, the full set of cross-equation and zero restrictions implied by the structural model and rational expectations yields a test statistic of 32.8, “not significant at even the 10 percent level” – which the author calls “one of relatively few cases” where an optimisation-based rational-expectations model survives against the VAR that nests it. One estimate comes out lower than expected: the memory parameter in the habit reference level is essentially zero, implying the reference level is simply last quarter’s consumption, and the author defends this at length by showing that a single lag suffices to deliver the smoothing and that substituting a long memory changes the model’s disinflation dynamics only slightly. In a disinflation simulation that cuts the inflation target from about 5% to 2% unexpectedly, consumption in the habit model responds gradually with a peak at about a year and a full response over three to four years, and the author shows that the counterfactually fast real-side response in the no-habit model also significantly damps the persistence of inflation – so misspecifying the real side corrupts the nominal side. He declines to compute optimal policy in the model, giving three reasons: with empirically significant rule-of-thumb consumers it is unclear whose utility to maximise; the model contains no explicit cost of inflation, so the consumer-optimal policy degenerates to minimising consumption fluctuations; and the representative-agent structure is a poor vehicle for welfare costs that arguably fall on discrete employment shifts for a small fraction of the population. He is also explicit that the specification “might not be robust across shifts in monetary or other policy regimes,” and that only testing across regime shifts can settle that.

Jeffrey C. Fuhrer | Macro Paper Warehouse

Habit Formation in Consumption and Its Implications for Monetary-Policy Models