Last week’s post finished with the need for theoretical considerations of credit booms. This work has been developing for a long time, but the best approach that I’ve found so far is from Paul De Grauwe, the same economist from this post . De Grauwe manages to model behavioural aspects of human nature in a way that accounts for ‘animal spirits’. 
Modelling Behavioural Economics in a New Keynesian Framework
In his fascinating book, De Grauwe examines the shortcomings of the New Keynesian model and lays the groundwork for behavioural factors to improve the fit of the model. He succeeds in providing a model that has sound psychological and behavioural underpinnings, which also improves on the non-behavioural New Keynesian framework. The steps he takes will be described in turn.
De Grauwe enables agent heterogeneity by introducing simple rules, or heuristics, into the model. The simplest example entails two heuristics: a fundamental rule, where agents estimate and forecast the steady state output gap, and an extrapolative rule, where agents extrapolate the current output gap into the future. This view differs starkly from the traditional ‘rational expectations’ modelling, where agents are all knowing and use this knowledge accordingly. These extrapolative agents, in contrast, have a kind of ‘bounded rationality’ as they do not know the entire model.
The market forecast of the output gap in the next period is a weighted average
Where αft and αet are the probabilities that agents use the fundamental and extrapolative rule.
De Grauwe then defines the success of these rules by utilities, or forecast performance. The forecast performance of each rule is as follows:
These utilities they are defined as mean squared forecasting errors and ωk are the geometrically declining weights. Thus, from a psychological or behavioural perspective, we have agents that are rationally bounded in their cognitions, but they also exhibit some level of memory loss over past events.
If the first step was defining the success of these heuristics, then the second step is evaluating them. Here, De Grauwe brings in another interesting step of the numerical representation of behaviour. As he describes, if agents were purely rational, they would simply compare these utilities and move to the best performing rule. Instead, he uses discrete choice theory to specify the evaluation process. As he notes in the paper, there is an element of unpredictability of human behaviour and decision making. Consequently, random variables εft and εet are the stochastic components of the decision process, leaving the actual ‘U’ as the deterministic components. As is customary in this literature, De Grauwe assumes that these random variables are logistically distributed. For example, the probability of choosing the fundamentalist rule is
De Grauwe uses λ to capture the ‘willingness to learn from past performance’, which is related to the variance of the ε components. As λ approaches zero, the variance is very high and agents choose each rule by ‘flipping a coin’ essentially. As λ approaches infinity, the variance of the random components is zero and utility is fully deterministic, making the probability of using the fundamentalist rule 0 or 1. Thus, when λ is zero, willingness to learn from past performance is zero, but the willingness increases with the size of λ.
De Grauwe provides a similar framework for inflation forecasts and solves the model in this extended New Keynesian approach. While this will not be elaborated upon here due to space, De Grauwe summarises his model with this description:
During some periods optimists (i.e. agents who extrapolate positive output gaps) dominate and this translates into above average output growth. These optimistic periods are followed by pessimistic ones when pessimists (i.e. agents who extrapolate negative output gaps) dominate and the growth rate of output is below average. These waves of optimism and pessimism are essentially unpredictable. Other realizations of the shocks (the stochastic terms in equations (3.1) – (3.3)) produce different cycles with the same general characteristics. These endogenously generated cycles in output are made possible by a self-fulfilling mechanism that can be described as follows. A series of random shocks creates the possibility that one of the two forecasting rules, say the extrapolating one, has a higher performance (utility), i.e. a lower mean squared forecast error (MSFE). This attracts agents that were using the fundamentalist rule. If the successful extrapolation happens to be a positive extrapolation, more agents will start extrapolating the positive output gap. The “contagion-effect” leads to an increasing use of the optimistic extrapolation of the output-gap, which in turn stimulates aggregate demand. Optimism is therefore self-fulfilling. A boom is created.
Introducing credit and asset markets
De Grauwe extends the basic model described above to explore how asset markets interact with output and inflation. He begins this section by outlining the two mechanisms through which stock prices affect aggregate demand. Firstly, a rise in stock prices increases consumers’ wealth, which encourages spending. Secondly, a rise in stock prices leads to the financial accelerator described by Bernanke and Gertler . When a firm wants to borrow from a bank, the bank does not have all of the information about the risks of the investment, so there is an external finance premium that the firm faces when borrowing from a bank. With a rise in stock prices, the firms’ net equity increases, reducing the risk that bank faces. This reduces the external finance premium, as banks are more willing to lend and this increases investment. (This sounds similar to the investment theory of Minsky )
De Grauwe outlines how a rise in stock prices also increases aggregate supply, again via these balance sheet effects. As the external finance premium declines with rising stock prices, the firm’s credit costs are reduced. As firms hold working capital to pay workers and other costs, the marginal cost for the firm has declined, thus increasing supply.
Using a discounted dividend model, De Grauwe adds a stock price term to the aggregate demand, supply and taylor rule equations in the model. The model is simulated again and the same ‘contagion effects’ result in a boom, as random shocks have the potential to make the payoff larger for one of the forecasting rules, attracting others in a self-fulfilling process. The introduction of the stock prices reinforces the interaction in the basic model as it adds more optimism to the boom phase.
In conclusion, De Grauwe notes the difficulties in testing the behavioural model empirically. Importantly, however, it passes the first test of explaining the data better than the more accepted DSGE model – mainly that the behaviour of the output gap is non-normally distributed. It seems quite clear that mainstream models like the DSGE were lacking and they limited the predictive power of economists to foresee something like the Global Financial Crisis. De Grauwe expects more exciting work to develop in this area. The challenge for my exploratory work is to see if the behavioural equations outlined here can strengthen the Cubic IS model.
 De Grauwe, P. (2010). Behavioral Macroeconomics. University of Leuven.