I’m aware that for example, in general MIU, transaction costs and shopping time can be equivalent as shown by Feenstra (1986) and Croushore (1993) with certain conditions imposed in higher order derivatives of the utility function. Given that, to my understanding CIA models are fundamentally different than those mentioned (actually CIA can be represented by a Leontief utility function, but seems to me like a really different approach, although mathematically equivalent). My question is, with the purpose of making some rigorous, well-micro founded analysis on the effect of money with monetary policy analysis and nominal rigidities in an hypothetical economy, which approach is more robust between the first group (MIU, TC, ST) and CIA? Specially in the analysis of business cycles.
Also, I know that it fundamentally depends on what one wants to analyse, to that matter my focus would be the analysis of the demand of alternative types of money that coexist with Central Bank money.
Hope my point is legible, yet let me know if you need more information.