Why does a model that is used for policy analysis needs its shocks and parameters to be structural (= invariant) to the shock under consideration? In their paper, " New Keynesian Models: Not Yet Useful for Policy Analysis"

V. V. Chari, Patrick J. Kehoe, and Ellen R. McGrattan

argue that one needs a structural model in order to analyse the effect of economic policy. More specifically, they argue that it needs enough microfoundations consistent with the data such that both the models's shocks and parameters are structural. But in my opinion, they don't really explain why that is the case. 

I understand that IF it is the case, you can do policy analysis, and the results of this analysis will always apply, because the model is unchanged nevermind any policy. This was the Lucas critique, on models that used adaptive expectations.

Why is this the case? Isn't it reasonable to assume that, in addition to many economic variables, also many parameters that govern micro behaviour will be influenced by a policy shock? Which contradicts their claim? Or do they only say that those parameters related to the shock under consideration cannot change? Why not? Isn't it wishful thinking one can ever settle down on a structural, fixed, microfounded model, as too many parameters governing micro behaviour depend on too many things like institutions, policy, technology, ... ?

Additional question: expectation formation is a microfoundation I guess. So, if we use the adaptive/heterogeneous expectations approach instead of the rational expectation assumption: I guess if an agent switches from a fundamentalist rule to an trend following rule (see the book and papers by Cars Hommes and De Grauwe and Zi), this is a structural change to the model? Or is this not structural, because the switching is a structural part of the model? However, it is exactly this endogenous switching that happens in response to (policy) shocks. How does this switching relates to the condition that models should be structural in their shocks and parameters to be used for policy analysis?

Some more context below:

"We begin by clarifying the distinction between reduced form and structural shocks.
This distinction is critical in policy analysis. The reason is that in order to do policy analysis,
we need to predict the consequences of changes in policy both for outcomes of the standard
economic variables and for welfare. Such a prediction is possible only with a structural model.
Speci…cally, a structural model must have two ingredients. First, the relevant elements of
the model— including the shocks— must be invariant with respect to the policy interventions
considered. Second, the shocks must be interpretable, so that we know whether they are what
could be thought of as “good shocks”that policy should accommodate or “bad shocks”that
policy should o¤set. Shocks which have both of these properties are referred to as structural
shocks and ones that do not are referred to as reduced-form shocks.

Proponents of the New Keynesian model argue that it is promising for two reasons. It
represents a detailed economy that can generate the type of wedges we see in the data from
interpretable primitive shocks; and second, it has enough microfoundations that both their
shocks and parameters are structural, in that they can reasonably be argued to be invariant
to monetary policy shocks. A model with both of these features would potentially be useful
for monetary policy analysis."
This is due to the famous Lucas critique. 

To make long story short, in the past in the heyday of Keynesian macroeconomics it was quite normal for macroeconomists to just postulate some relationships based on relatively casual empirical observations like for example the Philips curve which says that there is positive relationship between inflation and employment. 

However, this ignores some fundamental facts that such relationship only holds as long as people do not expect inflation. The (original) version of Philips curve did not really postulate any deep relationship between the two variables just assumed that it holds.

In short Lucas harshly criticized such approach as the (old) Keynesian approach gives you the correct predictions only as long as you assume that people are passive agents that do not adjust their behavior when government changes its policy. But that is not really reasonable assumption as we know from microeconomics people are not just passive actors, when government changes its policy people try to find ways how to take the maximum advantage of the new policy regime. 

The Lucas critique is basically a generalisation of the Goodhart's law which states that "when a measure becomes a target, it ceases to be a good measure"

If you add structural microfoundations you create more rich model which actually has an ability to take account for peoples reaction to changes in policy.

For example, the New Keynesian version of Philips curve instead of assuming that there is positive relationship explicitly models peoples/firms expectations and shows that when  they do not expect inflation it is rational for them to increase employment but when they do it is rational for them to just adjust contracts in a way to account for inflation (for example linking pays to inflation). Hence in such model no matter what is the government policy (with respect to inflation) the answer will be always 'correct' in the sense that it does not just assumes there is a relationship but it explicitly models the reasons/mechanisms why there is sometimes positive and sometimes no relationship between inflation and employment. 


  Isn't it reasonable to assume that, in addition to many economic variables, also many parameters that govern micro behaviour will be influenced by a policy shock?


Not really in the sense the microfoundations are set in the New Keynesian macro models. In such models when we talk about microfoundations we talk about proving the results of the model assuming that for example people are rational, have rational expectations and interact in the markets. 

To affect such micro behavior the policy would have actually change fundamentally how people behave. 

I suppose from sociological perspective you could argue that in a long term policy can change how people behave (I am not expert on that). But from economic perspective it is completely valid to say that model with solid microfoundations is policy invariant. 

Moreover, note an extremely important caveat is what the authors from which you quote say here: 


  Must be invariant with respect to the policy interventions considered.


Hence, it is not even necessary to make structural model that is invariant to any conceivable policy that you can imagine but rather the policies that are important for the model, like in Philips curve transitioning from market economy to centrally planned economy where property rights are abolished would certainly invalidate many micro foundations and probably changed conclusions, but different monetary policy doesn't and thats what is important. 



Regarding your edit of a question, when it comes to microfoundations its not really about rational/adaptive expectations per se - it is about justifying people having such expectations based on some fundamental model of human behavior.  

De Grauwe (and others) in his recent work takes a lot of inspiration from behavioral economics. In a sense his models are microfounded they just tweak the classical rational choice theory by adding some behavioral flavor to it. But I used the word in 'a sense' on purpose because to my best knowledge there is no general behavioral theory of human behavior. Rather he takes the rational choice theory and tweaks it by assuming that people are sometimes rational but in other situations not (or many of his models can be also interpreted as saying some portion of population is rational while other not). 

Hence he uses some sort of microfoundations in a way that he has some model of fundamental human behavior based on which results are derived. But I would say there is some room for disagreement about that because since there is no general behavioral theory (at least not one accepted in macro for sure) you could argue that his assumptions on human behavior are ad hoc and not proper microfundations as he just assumes some behavioral regularities without really proving that they are not  policy dependent or giving some ‘deeper’ justification why some behavioral assumptions are made and not other other than showing that there is some support from them from behavioral economics or evidence (although I am just playing devils advocate - I actually really like the work of De Grauwe).