On microfoundation

There are two ways we can model the whole macroeconomy. We can model the aggregates directly, like aggregate consumption, price, and so forth. Alternatively, we could build from the bottom up, we start from people's decision making---solving their optimization problem, and then model their interaction, and finally the whole market. The second approach is a multi-layered approach in that in each layer you specify the rule, you study each layer separately, from the bottom up, and using the result you solved for in the previous layer as input. The idea of micro-founded economics is illustrated in the following diagram.

An Illustration of Microfoundation

A digression for the super serious: what the above diagram illustrates is a more hierarchical model where different groups of individuals make decisions sequentially. In reality, and in literature, different groups often make decisions simultaneously, and yet taking into account what other group will be doing (and other group will take into account of what that group is doing as well in an infinite loop) (for those who know game theory, we are looking at Nash Equilibrium). 

So an obvious observation is that the second approach is so complicated. After all, why bother to study from the bottom up if all you are interested is the top level? Indeed, economists have taken the first approach for a long time, until comes along the famous Lucas Critique:

"Given that the structure of an econometric model consists of optimal decision rules of economic agents, and that optimal decision rules vary systematically with changes in the structure of series relevant to the decision maker, it follows that any change in policy will systematically alter the structure of econometric models."

What in essence Lucas Critique says is that, when we model the top layer and decide to engineer some policy to bring out better outcomes, we have changed the environment the individuals face---and that change will pass through all those layers into the top layer---which means that our old model of the top layer becomes invalid. The most famous illustration is the Philipps Curve.

So we have turned to the second approach, with lots of added effort. The extra effort does not mean we are golden. Quite the contrary. The problem is when we model each layer, it will be highly imprecise. All those imprecision adds up and amplify each other, and when we get to the top, it is nothing like the the real world---that is how we get highly unrealistic models that very few has faith in. The standard approach in economics is that calibrate our model----find parameters (the very first inputs) to match our data.  Because of the problem I mentioned, to fit the macro data, our estimates of the parameters would be non-sensible in the micro level.  Not surprisingly, micro-level and macro-level data often give us highly different estimates.

Another Digression for the super-serious: Imprecision is a bad word choice as it suggests a mere error term that would be dealt with in statistical analysis. Instead, I mean the deviations of structures from the reality. For example, imposing homothetic utility does not just generate random errors. Another point is that, we can always tweak our models so that it will fit micro-level and macro-level data. But are we just telling stories so that the data will fit, or are we actually making the first several layers more precise? In some sense, the purpose deviates from the true spirit of micro-foundation, to spinning a story that resembles micro-foundation.

An example to illustrate. When I was young, I like to play with ship models. I liked those fancy ones where you build from very tiny parts. Those require very careful work, but I was clumsy. When I put together those little pieces in a less than perfect manner, I could no longer fit that giant chunk into the frame of the ship. I used brute force, squeezing here and there until it fits, more or less. But when I looked back at those little parts, it is so distorted now. Several parts were displaced, some parts fell off, and it was just a mess. I think that is very similar to the mess economists are dealing with.
While my modeling experience could be improved via better craftsmanship, the modeling experience of economists are in some sense hopeless----To mathematically model these layers, things get so complicated. To make things tractable, we have to make numerous simplifying assumptions, not all of which are innocuous. Further more, by imposing those assumptions, we limit the type of questions we could ask as well.

So which approach is better? I do not think there is a definitive answer yet, but I want to contribute my two cents. The critique against the first is that it is not robust to policy changes, but it could be fine in the absence of policy change/paradigm shift. The second approach is aimed to address this inadequacy. But it fails the job---the changes in policy/environment pass through the model highly distorted due to the imprecisions added at each layer.

Admittedly, if we take the first approach, we can be a scientist, but we can never be an engineer---the very attempt of engineering would destroy our model. However, could we ever aspire to be an engineer in those fields? There are always things we do not model, and those things might be irrelevant in the previous world, but matter a lot in an engineered world. If you think you can fine-tune the economy with DSGE, you are guilty of the pretense of knowledge.  As a conclusion, I want to be provocative and say that  mathematical thinking and careful judgements+intuition are not substitutes, and they as a whole make up rigorous thinking (though some arrogant people tend to view mathematical thinking is necessary and sufficient for rigor).


After Note: Micro-foundation is the mainstream in macroeconomics, or any branch of economics these days. I thought about this for a long time, but never wrote much about it. This blog came out of a discussion I had with a friend, and I feel I need to write it down to invite further discussion.