The IS-LM model is still not dead. Created to reflect the interaction of aggregate markets, it suffered from the rise of dynamics and microfoundations in macroeconomics, yet remained the staple of undergraduate macroeconomics because a generation of teachers knowing nothing else needs first to die out. Yet, even people in research have clung to it, trying to find the microfoundations of IS-LM, which seems to me completely backward. The scientific method should indicate that you build a theory from observations, then create its graphical representation (if possible), and not trying to justify a graphical representation with some theory.
But anyway, I was thinking about these vain efforts while reading a paper by Ingrid Größl and Ulrich Fritsche, whose goal is to show that the standard Neo-Keynesian DSGE model cannot be represented appropriately in the IS-LM framework. So what? Life is more complex than IS-LM, so deal with it and drop IS-LM. But anyway (again), let us see what their arguments is.
First, the claim is that a Taylor Rule is a poor substitute for the LM curve, because it neglects the store of value role of money. And the DSGE model cannot capture the IS curve because is assumes that savings always equal investment, and people never save in unproductive money. The final claim is that an overlapping generation model is better for the IS curve. Now let us see how these claims are formally made. The model starts with a standard Neo-Keynesian representative agent, who has intertemporal preferences over consumption, leisure and real money holdings. Real Money holdings? Why not question that while you are arguing about the role of money in a model? Why would I care about how much money I carry? Not because I need it for transactions, because current consumption is already there. Not because of the wealth it represents, because future consumption is also there. It is simply there because otherwise the LM curve would not exist. How wrong is that?
Then what about the firm? It produces goods proportionally to the number of employees. Where is capital? Are we now trying to derive an IS curve (where I stands for investment) without investment? Not very convincing. Does the resulting model have anything to do with observed facts? Nothing is offered by Größl and Fritsche. What do I take from this paper? To justify LM, one needs to force people to demand money just because, and to justify IS, one needs to assume away investment. Great.