# Macroeconomics with Diffuse Priors

Below, I elaborate on two claims.

1. Macroeconometrics requires the imposition of prior beliefs.

2. If one has diffuse prior beliefs, the correct macroeconomic policies are not easily formulated.The proof that macroeconometrics requires strong prior beliefs is quite simple.

1. Macroeconomics in theory is a set of simultaneous equations. There are equations for interest rates, consumer spending, investment spending, and so on. What I call M70, the macroeconomic thinking of around 1970, was embodied in models with over one hundred equations.

2. Simultaneous equation systems face what is known as the “identification problem.” For example, in microeconomics, if you look at observations of price and quantity, you do not know whether you observing movements along a demand curve, along a supply curve, or a combination of both. To identify what you are looking at, you need at least one exogenous variable for each endogenous variable. Each exogenous variable can plausibly be excluded from one equation and included in another. For example, the cost of an input can plausibly be excluded from the demand curve and included in the supply curve. The exogenous variable allows you to identify shifts in the curves and to undertake estimation of the system. Thus, if there are r equations, you need at least r exogenous variables.

3. On the other hand, if you have k exogenous variables, you need the number of observations, n, to be larger than k. If you have more equations than observations, then you necessarily have more exogenous variables than observations, and the matrix will not invert.

4. In practice, macroeconometrics only works through the imposition of priors. In fact, M70 models are estimated in single-equation format, which implicitly imposes a prior belief that the equations are not truly simultaneous. In vector autoregression, the prior belief is that only a small subset of variables will summarize the entire system. VAR’s exclude most of the endogenous and all of the exogenous variables used in M70 models.

Overall, macroeconomics is problematic for those with diffuse priors. One can observe a Scott Sumner who is totally convinced that monetary expansion now is warranted. And one can observe a John Taylor who is equally adamant that monetary expansion now is not warranted. And, of course, one can observe Prad Krulong adamantly arguing that we are in a liquidity trap that requires more fiscal stimulus. Not to mention those of us who have doubts about the whole paradigm of aggregate supply and demand.

What should a policy maker do? In my view, a fiscal expansion is high risk, given the long-term debt outlook. A monetary expansion is lower risk. If we get more inflation, well, we were going to get it sooner or later, given the fiscal outlook. The worst case is that we get it sooner rather than later.

But, of course, my priors lean to the view that neither fiscal nor monetary expansion will do much good.