Identification rant!

Suppose you have an AD-AS model.

In math, that model is

  AD: y = a(m - p)

  AS: p = Ep + k(y - ybar)

Suppose you want to know the slopes of the AD or AS curves (in the toy example, the "a" and the "k"). How might you learn about them? Well, you gather up a bunch of data on inflation and output.

Suppose that all the fluctuations in the economy came from AD shifts. You observe the world for 3 years, so you observe 3 AD shifts. Then you'd get this AD-AS picture and this data. You'd be able to regress inflation on growth and get an estimate of the slope of the AS curve, like this, but wouldn't know anything about the slope of the AD curve.

Conversely, if the economy is mostly hit by AS shocks, you get the opposite story: you can estimate the slope of the AD curve, but are ignorant of the slope of the AS curve.

If there are both AS and AD shocks, no amount of (P,Y) data will get you the slopes: you just get a cloud of points! You need to do instrumental variables, or you need some way to isolate demand shocks, or you need some way to isolate supply shocks. You need more than just "model plus data." You cannot identify both supply and demand slopes just from (P,Y) data. You need more than that.

Canova's paper is showing that these problems are endemic in DSGE models: there are a lot of slope parameters that we just cannot identify using the normal data that we use. This is true even though the structure of DSGE models puts enormous discipline on what the various slope coefficients are. Cruelly, the parameters we can identify (the discount rate, the depreciation rate, the share of income going to capital) are parameters that we thought we knew anyway; the parameters we can't identify well (various slope parameters) are the ones we'd really like the data to identify for us. It's all terribly negative.

RBC guys get around it by calibrating. Just prax out the parameters! Let's just assume the AS curve has a slope of 0.5. Well, more specifically, let's pick parameters to match certain facts about the data. Example: we know that interest rates are, on average, about 4%. So we can pick a value of the discount factor that makes the model's interest rate 4%, on average. Continue doing this, picking parameters to hit certain features of the data. Can that get around the identification issue? Yes and no. The problem is: sometimes that calibration procedure isn't enough. No calibration procedure can tell us certain slope parameters, like the slope of the AS curve. Canova's paper is showing us that fancy estimation techniques also have a hard time of telling us about slope parameters. So we need even more advanced machinery.

In one sentence, identification is about whether the data you have are informative about the parameters you seek to understand. (Slightly more formally: identification has to do with the ability to draw inference about the parameters of a theoretical model from an observed sample. Intuitively [depending on your intuition] identification means not-flat likelihood functions. DSGE likelihood functions can have long flat bits, steep cliffs, local extrema, sinkholes, ridges, and all sorts of nasty features.)