I find monetary models very frustrating. While there is empirical evidence that money is not completely neutral over the range of a couple of years, theory has so far not come up with a believable way to understand why this would happen. The models that come closest have completely outrageous assumptions, such as the infamous Calvo pricing hypothesis I was venting about just a few days ago. This is usually accompanied by money-in-the-utility-function (sure, we all love to walk around with a lot of cash) or with the cash-in-advance constraint. Let us consider the latter a bit more closely.
Essentially, this constraint assume that households have to carry cash for some purchases. Often these models are calibrated to quarterly frequency, because this is what the data bears. This implication is that people have to carry cash for all their purchases in the next three months! How reasonable is that? Or the constraint is imposed on firms for their investment or wage payments, which about as outrageous. Yet, cash-in-advance is used all over, either blindly or because it easily generates a money demand. Of course, as people are forced to demand money.
What monetary urgently needs is a better theory of money demand. People hold money in small amounts because it facilitates transactions. They also hold some as a store of value, as any principles of economics student can recite. But this is not a good solution, as money is dominated in return by almost any asset. People hold money due to some frictions on financial markets, and these holdings are temporary. Now having both these features makes it difficult for the model builder. Which one is more relevant?
Xavier Ragot tells us financial frictions are. For one, looking at data, the distribution of money across households looks much more like the distribution of financial assets than that of consumption. He tries to match both distributions using a model with cash-in-advance for consumption (slightly modified to account for the fact that the rich can buy more on credit), a fixed cost for financial transactions, borrowing constraints and idiosyncratic shocks to household productivity. The model has two degrees of freedom to match the distributions of money, consumption and financial assets: the fixed cost for adjusting your portfolio and the transaction technology parameter from the cash-in-advance constraint. Two values are then obtained, and by turning each of them to zero, Ragot concluded that 85% of money demand comes from financial frictions, and 15% from cash-in-advance transactions. Conclusion: if you want a simple model of money demand, do not rely on cash-in-advance.