Thanks psuet. I'm not one of those guys who goes around saying "mainstream economics is wrong and ignorant". Well, OK, we are often wrong and ignorant, but people who aren't in mainstream economics are usually even more wrong and ignorant!
This is just a particular beef I have. Because I keep on seeing examples where economists make mistakes by missing this point. Like when economists try to test whether headline or core inflation is better at forecasting future inflation, and use those results to give policy advice on whether inflation-targeting central banks should respond to core, headline, or both indicators. All they are modelling is the central bank's mistakes, in responding too strongly or too weakly to those indicators.
I think proper identification does require the econometrician be (in some sense) a "better" driver than the driver. If you can see the hills better than the driver can, then you can see the effects of a hidden hill that you know he doesn't see.
1. If the driver has as much information as the econometrician, setting both parameters on slope and gas equal to 0 will fit the data equally well.
2. If the econometrician observes slope and gas and speed with error (as will almost always be the case), then GMM will estimate both parameters on slope and gas as zero (if those 3 errors are independent of each other), even if the true parameters aren't.
3. If the driver observes gas or slope with error, and the econometrician doesn't, then the econometrician can indeed actually estimate the parameters.
How likely is 3? Only a stupidly arrogant econometrician would assume a priori that he knows better how to drive the car than the guy actually driving it. (OK, maybe the econometrician has final revised data, and the driver has only real time data, and the final revised data is better than the real time data. But even then the driver will be observing other indicators that the econometrician doesn't have data on, so the econometrician will interpret the driver's response to those omitted variables as "gas pedal shocks", and will screw up the estimation royally.
Yep, all that Sims VAR stuff is wrong. Here, read this.
This is just a particular beef I have. Because I keep on seeing examples where economists make mistakes by missing this point. Like when economists try to test whether headline or core inflation is better at forecasting future inflation, and use those results to give policy advice on whether inflation-targeting central banks should respond to core, headline, or both indicators. All they are modelling is the central bank's mistakes, in responding too strongly or too weakly to those indicators.
I think proper identification does require the econometrician be (in some sense) a "better" driver than the driver. If you can see the hills better than the driver can, then you can see the effects of a hidden hill that you know he doesn't see.