Every time you do optimal policy, Hayek sends you a greeting card

Whether you work as an economist, a management consultant, a computer scientist, an engineer, or indeed in any other profession in which you have to build some sort of mathematical model and solve some kind of optimality problem, you are often running into a very basic tradeoff. If you make a model that captures your object of study very realistically and in detail, you have a hard time figuring out how to optimise it. And if you make a model that you know to optimise, it is often in some important aspects oversimplified. So if you're an economist, you will be hopeless finding optimal policies in large-scale models of the macroeconomy, while nobody will believe the small-scale models you build to think about optimal policy. If you're a management consultant, you can fit some nonlinear model to explain your customer data very well, but good luck communicating a non-linear business strategy to the CEO of your client. If you're a computer scientist, you know the tradeoff as the curse of dimensionality. If you are an engineer, you know that versatility and precision of a machine usually run in opposite directions.

Essentially, we're facing a tradeoff between calibration and optimisation: models that fit the data or process we're looking at very well are hard to optimise well, and models that are easy to optimise usually don't fit the data well.

While this tradeoff exists almost anywhere, and is really just a consequence of the complexity of the world relative to the cognitive capacity of the human mind, I think it is carries a particular meaning in economics.

We know that under the standard assumptions we make (which are satisfied for example by the RBC model), the first welfare theorem holds. That's great, because the question of what the government should do is clear: nothing. The market allocates all resources efficiently. Okay, but that all markets are efficient is such an old joke that you can't even impress your grandmother with it. The world abounds with physical or pecuniary externalities, asymmetric information, bounded rationality or contract enforceability problems, and economics has demonstrated their existence both theoretically and empirically.

In principle, such market failures open the possibility of corrective government intervention. As economists, we often ask: What would an optimal policy intervention look like? As long as policy is not able to restore market efficiency completely (attaining the "first-best", as we say), this becomes quite a difficult problem. The computational complexity of solving a Ramsey problem is much higher than that of calculating a competitive equilibrium.

The reason that is so, at least in macroeconomics, is Hayek's insight that the market is successful because it distributes information decentrally. In the market, every individual need not know all the circumstances of some change which led to resources being allocated differently, as long as they see the prices in the market. I don't need to know that the implementation of some useful technological discovery requires extentive use of tin in order to give up some consumption of it to make room for that discovery; all I need to know is that the price of tin has gone up. By contrast, a central economic planner would need to aggregate all the dispersed information in the economy in order to know how resources should be allocated optimally. Collecting this dispersed information is very problematic, especially when it is about characteristics such as preferences, which are almost impossible to measure.

When we solve a competitive market equilibrium, we take the same position: we only need to solve optimisation problems for agents taking prices as given. Then we can solve for prices using resource constraints in a final step. By contrast, the Ramsey central planner takes into account the impact of policy on prices, and it is this which makes the Ramsey problem difficult. Now, of course solving for prices is also not always easy, especially with heterogenous agents such as in Krusell and Smith. But try to solve a Ramsey problem in the Krusell-Smith model!

And again, while we can calculate optimal policies elegantly in some models, those particular models are often so simplistic that, at least by my impression, people are more often than not very sceptical about the conclusions.

So every time you despair about a Ramsey or other optimal policy problem in economics, and you find yourself faced with a tradeoff of building a simple model nobody believes or not being able to calculate the optimal policy, Hayek is sending you a greeting card from the past: "Remember that the information contained in prices is difficult to centralise".