On Saturday I posted my views on why it is difficult to get good estimates of the effects of fiscal and monetary policy. On Sunday Greg Mankiw responded to (less than civil) criticism from Nate Silver.
Here is the very short version: Nate Silver criticised Greg Mankiw for looking at the effects of an exogenous change in fiscal policy, while the fiscal policy we are considering now is an endogenous response to the recession; Greg Mankiw replied that we need to identify an exogenous change in fiscal policy in order to estimate the effects. In this context, my point was that (nearly) all fiscal policy is endogenous, so we can't estimate the effects.
Andrew Gelman tries to salvage Nate Silver's criticism, arguing that while Greg Mankiw might be right about the econometrics, Nate Silver might have a valid point if there are interaction-effects between fiscal policy and other indicators of recession. In other words, the effects of fiscal policy might be different in a recession, which is when you normally get an endogenous fiscal policy response, than at other times.
I think Andrew Gelman's point is correct, but that he is asking too much of econometricians. Yes, it would be really nice if econometricians could estimate those non-linear interaction terms, because they might matter. But given the current state of knowledge, just getting a good estimate of the assumed linear effects of an exogenous change in fiscal policy is enough of a challenge.
If I wanted to salvage something from Nate Silver's criticism, I think I would invoke not interaction-effects, but the Lucas Critique. The effects of a change in fiscal (or almost any) policy depend on whether it was expected or unexpected. An endogenous policy change, an implementation of an ongoing policy regime, will be expected, and may have very different effects from an exogenous policy change, which is not part of an ongoing policy regime, and may change people's expectations of the policy regime.
But all this, like my previous post, is just so nihilistic. "We can only estimate the effects of exogenous changes in fiscal policy, and there aren't any exogenous changes, and even if there were, they wouldn't tell us what we need to know anyway, so let's just give up."
Here's a more constructive suggestion. Estimate the fiscal and monetary policy reaction functions. Pick a time period when those reaction functions seemed to be fairly stable. Then look at the target variables (inflation, unemployment?) over that period, and see whether they could be forecast at about a one year horizon (or however long you think is the policy lag). If they can't be forecast, then the policy regimes were right (or at least not demonstrably wrong) for stabilising those target variables. (This follows directly from the fact that forecast errors should be uncorrelated with the information set under rational expectations, as discussed in my previous post).
If the the target variable can be forecast, then the policy regimes were wrong, and failed to stabilise the target variables properly. If they can be forecast, what are the indicators which give the information useful in making those forecasts? If (say) the price of copper is useful, and has a (say) positive correlation with future inflation, and you want to target inflation, then the policy reaction functions should have tightened more strongly in response to an increase in the price of copper.