Wendy Carlin and David Soskice have an interesting post at Voxeu.org on "How should macroeconomics be taught to undergraduates in the post-crisis era." They explicitly follow, as in their manual, a New Keynesian framework. Which is an ISMP model with price rigidities, which are incorporated in a slow adjusting Phillips curve with imperfections (they refer to it as the ISPCMR model). Also, they add the financial system. I should make clear that in many respects it is an improvement on some of the newer manuals around, which since the 1990s have given less attention to the possibilities of crises, and have emphasized long term growth (presenting the Solow model in the initial chapters).
From a methodological point of view I would also agree with the notion that "undergraduates need a unified integrated model through which they can understand the major business cycle events of the past century and see how economic theories and policy regimes have evolved in response to these events." Mind you I would go further, it's not just the undergrads, but the profession that needs a unified integrated model to understand the functioning of the macroeconomy. The ad hoc nature of much of the macroeconomic field has been caused by the wrongheaded search for neoclassical microfoundations for macroeconomics. And the authors should be more forceful in denying the relevance of microfoundations.
Having said that, there are significant problems with their way of teaching macro, from my point of view. Carlin and Soskice suggest that "the most glaring absence in macroeconomic models and courses, [is] that of the financial sector." Mind you I would disagree, even if the financial sector is often an afterthought in most macro discussions for undergrads. The most glaring problem is the presence of a natural rate, which implies that in the absence of imperfections markets would produce full utilization of resources. Note that, in their model, Carlin and Soskice have a level of the rate of interest that equilibrates the goods market (IS) with stable inflation, and note that this would be for Woodford "the Wicksellian or natural rate of interest."
They think that they avoid the problem because in their model the equilibrium rate "changes whenever the IS curve shifts," which is of course a confusion, since that would be true of the Wicksellian rate of interest too. With changes in investment and savings (IS) behavior, that is, productivity and thrift the neoclassical natural rate must shift. The role of the central bank is to adjust the rate of interest to its natural level. Note that Carlin and Soskice confuse the fact that monetary and real shocks affect the economy with the notion that the economy described by their model is "an economy which is not self-stabilising."
In their view, the monetary authority can move the economy to the equilibrium rate, but the equilibrium rate is not controlled by the authorities. I would suggest that the central bank actually has control of the key variable, which is not natural at all, and as Keynes suggested is conventional, the normal rate of interest. And that could be set at a level which will not lead to full employment, particularly for distributive reasons. In my view the essential feature of a more relevant macro model would be the elimination of the natural rate, the idea that the system has a tendency to bounce back to the trend, and the notion still in the Carlin and Soskice model that the output gap, the deviation from optimal output, has significant impact on inflation.
Further, in order to introduce the effects of the financial system, while it is welcome that the behavior of banking is introduced, the most important development of the last three decades, the increased financialization, and the shadow banking system, would be better incorporated by introducing the effects of debt and income distribution on the consumption function, which remains based on the permanent income in their model. And by the way, the model says nothing about how income distribution affects spending.Yet, the main reason behind the crisis has been the fact that workers had to get indebted, since income has stagnated. So income distribution has to be brought back to macroeconomics. Not enough Kalecki, with their New (but still neoclassical) version of Keynesianism, that is the problem with Carlin and Soskice.