I think Simon Wren-Lewis's post
"Heterodox economics, mainstream macro and the financial crisis" is excellent even by his high standards. I advise you to just read it, but if you insist on staying here I attempt a brief summary and some comments.
1) Heterodox economists make two valid points about what the financial crisis showed us about inadequacies of 2008 vintage mainstream macro models.
2) The models did not include a financial sector. Banking and bank regulation was considered a sub field separate from macroeconomics. Thus macroeconomists such as Wren-Lewis (and I) didn't even know about the alarming increase in bank leverage. Since 2008 " there has been an explosion of DSGE and other microfounded analysis putting a financial sector into macromodels."
3) Heterodox economists also note that mainstream macro models failed to consider household finance and household balance sheets. Unfortunately while "heterodox economists also have a point, ... they tend not to put it very well and, perhaps as a result, it has not yet impacted on the mainstream " (here I have to note he means on mainstream theory as there is a very active largely empirical research program)
4) I think this [] was/is ignored because incorporating this analysis into microfounded models raises serious problems associated with heterogeneity across age and income. ... Playing around with habits or some ‘rule of thumb consumers’ is much easier. Blanchard has recently made a similar point in his critique of DSGE models.
5) This reveals a key problem with mainstream macro methodology which "allows you to be very selective about what empirical features you do or do not explain.
6) "As Jo Michell writes “The problem with heterdox economics is that it is self-definition in terms of the other”."
7) Macroeconomists might not have ignored bank and household balance sheets if they hadn't insisted on micro founding everything.
My effort to summarize shows why it is better to just click the link. The summary is almost as long as the post and consists mainly of quotes.
I do have some thoughts.
I think that point 5) is fundamental. Macroeconmists have a problem that there are few aggregate data points and no experimental data at all, but the standard approach makes this problem much worse by ignoring most of the available data. In particular, I think this applies to banking, prudential regulation and financial crises too. The 2008 financial crisis wasn't the first in human history, but it had been decided for some reason that macroeconomists could and should ignore data from long ago (the 30s) and far away (East Asia, Russia, Brazil and Argentina). One of Krugman's favorite boasts is that international macroeconomists weren't as blind as other macroeconomists, because they couldn't ignore those crises. Most macroeconomics was cut off not only from banking and finance but also from international -- that is from data from countries (including Korea and Japan) outside of Western Europe and North America. I have to add that, even aside from financial crises, data on unemployment rates collected east of the English Channel were neglected.
Personally, I think it is better to banish intertemporal optimization from models of aggregate consumption. Incorporation of realistic consideration of liquidity constraints and precautionary savings is, as Wren-Lewis notes, very difficult. I agree it is very costly to avoid such difficulties by assuming a representative consumer. but I think that there is no evidence that consideration of optimal intertemporal consumption choices adds anything useful to macroeconomic models. That is a very strong statement and I mean it literally. I fear that assuming consumers solve some sort of highly constrained optimization problem might be required to get papers published. That is I agree with Wren-Lewis that macro should cease to "shun what it calls policy models (models that use aggregate relationships justified by an eclectic mix of theory and data)", and, in particular, I think such models should include a simple empirical reduced form consumption equation. I am quite sure that, even if macroeconomists cease to shun policy models, it will shun the models I have in mind. Consumers' intertemporal optimization is the main dynamic aspect of DSGE. It won't be abandoned just because it leads to one false prediction after another.
I am sure that aggregate relationships justified by data will be accepted, if at all, only in less central equations in the model, and probably only in equations including a variable which was totally ignored in 2008. I agree that, for the forseable future, the best we can hope is that macroeconomists will accept mixed models which consider things totally excluded from existing models but do not micro found that consideration.