Whilst this is very challenging, and rather technical, I want to explore the point where we ended up last week. That was the question of how, or even if it is possible, to combine the models of De Grauwe and Woodford. To recap, I really appreciate the behavioural aspects of De Grauwe’s work, where households are endogenous and respond to the environment around them. On the other hand, the modelling of Woodford to bring in heterogenous households, two interest rates and financial frictions is an important step forward in these models.

Technically, we need to relate the ideas of De Grauwe – such as the responsive household evaluating heuristic performance from the actual economic outcome – with Woodford’s two interest rates and real resources used in the financial sector.

The first step in this exploration would be the question of whether we can reconcile the two types of heterogeneous households. If so, the second step would be the clarification of the intermediary sector and how this aligns with the revised household sector.

After spending time following Woodford’s equations, the first opportunity that I wanted to explore were the Euler equations in his model:

These are the descriptions of the evolution of real marginal utility of income for both household types. The utility for each household type depends on the interest rate that they face, as well as the probability of household type next period.

Now, is it possible to replace Woodford’s probabilities of household type with De Grauwe’s:

This doesn’t seem to be a satisfactory point for the integration of these two models. Firstly, by simply using De Grauwe’s probabilities, we have brushed over the ‘insurance agency’ aspect of Woodford’s model. There is also something amiss with the expectation of being a different household type – as in De Grauwe’s model, there is no expectation of being a different household type, one only shifts (with a deterministic and random component) to being a different type after observing the state of the economy. So the utility that a household tries to maximise in any period is independent of its probabilities of being a different type in the next period. If this is true, it bears the question of the structure of the Euler equation that each household type is trying to optimise.

Taking a step back and looking at one of the initial assumptions of the Woodford technology, it may be worth examining his proposition that the marginal utilities of consumption differ for each type. According to Olivier Blanchard, this is something worth questioning.

This begs an important question worth considering: How are borrowers different from savers, or fundamentalists different from extrapolators? Do they differ in their discounting of the future, or marginal utility of consumption? They need to differ in one of these respects so that there is a function for the intermediation of credit.

In De Grauwe’s model, these households differ in their expectations of the future, which provides a different forecast performance in each period. As De Grauwe notes, however, the utilities in his framework were not built from micro-foundations. Another model of heterogeneous households is my own Cubic IS curve (insert link). Again, this was not built with optimising agents in mind (and it was also static). In this model, households differed in their ‘propensity to take on debt’, meaning that an increase in house price expectations were needed to induce the marginal household to borrow.

Trying to find a dynamic blend of all of these ideas is challenging – at least for me! – but my impression is that it needs to be built from the bottom up. Whereas the integration attempted above was trying to impose De Grauwe’s parameters on Woodford’s model at an advanced point in the modelling, it seems that it might be preferable to adjust Woodford’s model from the initial steps.

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