The Lucas Critique and Internal Consistency

For those interested in microfoundations macro. Unlike earlier posts, I make no judgement about the validity or otherwise of the microfoundations approach, but instead just try and clarify two different motivations behind microfoundations.

When I discuss the microfoundations project, I say that internal consistency is the admissibility criteria for microfounded models. I am not alone in stressing the role of internal consistency: for example in the preface to their highly acclaimed macroeconomics textbook, Obstfeld and Rogoff (1996) argue that a key problem with the pre microfoundations literature is that it “lacks the microfoundations needed for internal consistency”. However when others talk about microfoundations, they often say they are designed to avoid the Lucas critique. This post argues that the latter is just a particular case of the former.

What do we mean when we say a model is internally consistent? Most obviously, we mean that individual agents within the model behave consistently in making their own decisions. A trivial example is if the model contains a labour supply equation and a consumption function that are supposed to represent the behaviour of the same agent. In that case we would want the agent to behave consistently. An agent that became more impatient, and so wanted to consume more by borrowing, but also wanted to work more hours (and so exhibit less impatience in their consumption of leisure), would appear to behave inconsistently unless their preferences or prices also changed.

Suppose instead of a labour supply equation, we had wage setting by unions. In this case we have a consistency issue between two sets of agents: consumers and unions. If we wanted to model unions as representing consumers as workers, we would want to align their preferences, so we are back to the previous case. However, there may be reasons why we do not want to do this. If we did not, we would want to make sure these agents interrelated in a sensible way.

What is meant by a sensible way? Consumer’s decisions will almost certainly depend on expectations about the wages unions set. Lucas called rational expectations a ‘consistency axiom’. If, for example, the union started being more concerned about employment than wages, we might expect consumers to recognise this in thinking about how their future income might evolve.

The Lucas critique is just an example of consistency between agents. The question is whether the private sector agents in the model react in a sensible way to policy changes. The classical example of the Lucas critique is inflation expectations. If monetary policy changes to become much harder on inflation, then rational agents will incorporate that into the way they form inflation expectations. A model that did not have that feedback would be ‘subject to the Lucas critique’.

Discussion of the Lucas critique often involves the need to model in terms of ‘deep’ parameters. A deep parameter (like impatience) is one that is independent of (exogenous to) the rest of the model. Here the parameters of the rule agents’ use to forecast inflation are not deep parameters, because (under rational expectations) they depend on how policy is made. But we can have a similar discussion about workers and unions: if the latter aimed at representing the former, then union attitudes to the wage/employment trade off should not be independent of worker preferences. Internal consistency is again more general than the Lucas critique.

Now obviously the Lucas critique is a particularly important kind of inconsistency if you are interested in analysing policy. But it is not the only kind of inconsistency that matters. A very good example of this is Woodford’s derivation of a social welfare function from the utility function of agents. Before this work, macroeconomists had typically assumed that a benevolent policy maker would minimise some quadratic combination of excess inflation and output, but this was disconnected from consumers’ utility. This had no bearing on the Lucas critique, which applies to any policy, benevolent or not. However it was a glaring example of inconsistency – why wasn’t the policy maker maximising the representative agent’s utility? After Woodford’s analysis, nearly every macroeconomics paper followed his example: not because it did anything about the Lucas critique, but because it solved an internal consistency issue.

Why does putting the Lucas critique in its proper place matter? I can think of two reasons. First, if you believe that avoiding the Lucas critique means you necessarily have a microfounded model, you are wrong. (In contrast, an internally consistent model will avoid the Lucas critique.) Second, it has a bearing on the idea often put forward that microfounded models are just for policy analysis, but not for forecasting. If we think that microfoundations is all about the Lucas critique, then this mistake is understandable (although still a mistake). But if microfoundations is about internal consistency, then it is easier to see how a microfounded model could be much better at forecasting as well as policy analysis.