Modelling heterogeneous consumers: De Grauwe versus Woodford

Over the last few weeks, I have covered some highly relevant applied economic work on credit and financial frictions (see here and here). Taking a different approach to these topics, but still using the knowledge gained by these studies, it is necessary to move from the applied to the theoretical. As economists, we should be able to build on existing models, or even build new ones, that incorporate credit and other financial frictions. Two leading academic economists in this area are Michael Woodford and Paul de Grauwe. While subsequent posts will have to look at other areas of these theoretical models, this post will limit itself to the modelling of heterogeneous households or consumers. Theoretical economics is moving away from the ‘representative’ consumer in these models, which is allowing more richness in the analysis.

The heterogeneous households of Curdia & Woodford (2009)[1]

The exposition of heterogeneous households begins with the following objective intertemporal form:

intertemporal objective

Each household aims to maximise this function in each period. The left hand side in main brackets refers to the utility that each household gets from consumption, while the right hand side is the disutility from working. There is a distinction between households as indexed by μs and μb, where s and b refers to the household type of either a saver or a borrower.

Household type is derived in each period by a two-state Markov chain, where each period, with probability 1-δ a random event occurs that results in the draw of a new type for that household. This means that a change in the household type changes its relative impatience to consume.

Households are assumed to also differ in their marginal utility of additional expenditure, with borrower households having a marginal utility that varies less with current expenditure. This is shown in the figure below. This results in a greater degree of intertemporal substitution of expenditures due to interest rate changes for these households.

marginal utilities of income

De Grauwe’s endogenous consumer behaviour

As discussed in another post (see here), Paul De Grauwe has provided an intriguing approach to modelling consumer or household heterogeneity. He begins this differentiation by articulating two types of heuristics based on forecasting rules – shown below. Some agents in the model use a ‘fundamentalist’ rule for expectations of the future. In this case, the first expression here displays this fundamentalist expectation of the output gap in the next period, which is expected to be zero. In other words, these agents expect the economy to be at it’s natural or fundamental level next period.

The second expression refers to the ‘extrapolative’ rule, used by agents who extrapolate the state of the economy to be the same next period as it is this period.

forecasting heuristics

The market forecast of next period is a weighted average of these two forecasts, where αft and αet are the probabilities that agents use a fundamentalist or extrapolative rule respectively. Hence, the aggregate expectation of the economy is influenced by the proportion of agents using these different forecasting rules.

 aggregate expectations

The selection of these forecasting rules is something that I think really makes sense from a social psychological perspective. Agents in the De Grauwe model are willing to learn and constantly evaluate their performance. Even this simple point is important – it implies that agents in the economy react to changing events around them – which is something that I think is really needed in macro models.

De Grauwe then specifies how these rules are compared and evaluated in terms of their performance. Forecast performance is evaluated by the following two rules:

 forecast performance utility

These are utilities, representing how the forecast heuristic has performed. For example, within the brackets of the first expression, we see that the actual output performance of the economy is assessed compared to the expectation of that period by the fundamentalist rule in the previous period. These are then calculated as mean squared errors. The ω’s represent declining weights, implying that agents tend to forget output performance the greater the distance in time from the present period.

Whilst it might seem that agents would choose the rule with the best performance, De Grauwe notes that things are not so simple. Bringing human psychology into the analysis, De Grauwe notes that our state of mind also plays a role, meaning that there’s an unpredictable element to our behaviour. Mathematically, this suggests that there is a deterministic component to our behaviour, shown below as U ( the utilities shown above), and a random component, shown as ε.

 probability

This reveals that it is not just the performance utility of the rule that matters for which of the two rules are selected by agents – there is a random aspect of human behaviour that also plays a role.

Comparison of the two types of heterogeneity

Both of these attempts at modelling consumer or household heterogeneity are an important step forward. Woodford’s model has enabled these different household to interact with a financial intermediary, whilst also facing different interest rates, which allows the financial and credit frictions to be explored. De Grauwe’s framework is encouraging as it endogenises human behaviour, allowing agents to react to the environment around them. This model also generates non-normal output gaps, meaning it can generate the more realistic periods of economic downturns that we are currently experiencing.

I appreciate De Grauwe’s description of human interaction with the economy, as it feels more realistic than a random switching of households from borrower to saver in the Woodford model. The challenge would be combining De Grauwe’s behavioural model with the credit frictions in the Woodford model. If it was possible, it could make sense to use the financial frictions of the Woodford model to generate the random shocks in the De Grauwe model that then leads to an extended period of the output gap. I’m sure that’s easier said than done.


[1] Curdia, V & Woodford, M (2009). Credit frictions and optimal monetary policy.

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One response to “Modelling heterogeneous consumers: De Grauwe versus Woodford

  1. Pingback: Optimism, discounting & micro-foundations – lessons from Social Psychology | globalmacromatters

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