RDP 9812: An Optimising Model for Monetary Policy Analysis: Can Habit Formation Help? 2. Problems with Standard Models

In Fuhrer (1997a) I document the inability of standard optimising models of consumer and investment behaviour to replicate the dynamic interactions among real and nominal variables found in the data. Here I briefly summarise these results, and motivate the exploration of a less standard description of consumer behaviour that involves habit formation.

The key results uncovered in my earlier work include both perverse parameter estimates and empirically contradicted dynamic behaviour. For consumption, I use a standard life-cycle model of consumption, augmented to include rule-of-thumb behaviour by a fraction of consumers that is empirically determined.[2] The problems with this specification include extremely significant unexplained serial correlation in the consumption-income ratio, parameter estimates that indicate very little or no forward-looking behaviour, and excessive sensitivity of consumption to current income arising from the rule-of-thumb behaviour.

For investment, I employed a model that allows for both time-to-build and costs of adjustment. In this sector, the problems included very significant unexplained serial correlation in the investment-capital ratio, extreme sensitivity of model stability and uniqueness to small perturbations in parameter estimates, and a negative estimate of the capital share in income.

Equally important for the purposes of monetary policy analysis are the dynamic implications of these specifications when embedded in a model with sticky prices and an explicit federal funds rate policy rule. The dynamic correlations implied by the model, summarised by the ACF, are seriously at odds with those from an unconstrained vector autoregression that nests the restricted model. A set of disinflation simulations identify an important source of the discrepancy: both consumption and investment act like ‘jump variables’, completely front-loading or pulling forward in time their responses to shocks. This stands in contrast to exercises with identified VARs (e.g. Christiano, Eichenbaum and Evans (1994); Leeper, Sims and Zha (1996)), in which these variables demonstrate a gradual response over several years, with the peak response at one year or so. Thus the problem, broadly speaking, is that the standard models imply a strongly counterfactual immediate response of consumption and investment to all shocks, but particularly to monetary policy shocks.

This paper attempts a solution to the problems for the consumer sector, developing and econometrically testing a habit formation model. The intuition behind this approach is simple: If the standard life-cycle model implies a too-rapid or ‘jump’ response to shocks, then a model is required in which the utility function implies a smoother, more hump-shaped response to shocks. The specification explored below achieves this goal by employing a utility function that implies a smoothing motive for the change in consumption as well as its level.

2.1 A Non-behavioural Solution to the Problem

In this paper and in my earlier work, I begin with the assumption that the structural innovations in the econometric model are uncorrelated across time, although they may be correlated across equations. The rationale behind the first assumption is that we should first attempt to model the dynamic behaviour evident in the data as the outcome of the behaviour of consumers and firms. While some of the correlations in the data may arise from somewhat correlated shocks, it would be unsatisfying to attribute most or all of the fluctuations in key variables to shocks; this would in essence be admitting that consumption and investment fluctuate for reasons that we do not understand and cannot model as economic processes. This seems to take all the fun out of dynamic macroeconomic modelling.

However, in principle, one can augment a structural model that is dynamically deficient with an arbitrary error structure so as to exactly replicate the dynamic structure in the data. This approach is taken in Rotemberg and Woodford (1997), for example. A key problem with this approach, however, is that the error processes so identified cannot be considered ‘structural’ in any meaningful sense. We have no idea in what way the errors are linked to underlying behaviour, and thus we can have no more confidence about their policy invariance than we have for reduced-form VARs or 1960s structural models sans explicit expectations. In essence, by putting the dynamic structure in the errors, the model becomes vulnerable to a Lucas critique of its errors.[3]

For these reasons, I find the augmentation of the error structure an unappealing solution to the problem of finding a dynamically satisfying monetary policy model. The next section describes an attempt to modify the behavioural assumptions underlying the consumer sector to better capture the dynamics in the data.


Strictly speaking, the rule-of-thumb model suggests that a fraction of total income accrues to consumers who follow a rule of thumb. [2]

For more on this point, see my discussion of Rotemberg and Woodford in the 1997 NBER Macroeconomics Annual (Fuhrer 1997b). [3]