How to model helicopter money in DSGE models?

Helicopter money refers to the money transferred to households provided the following two assumptions, among others, are satisfied:
– Households are awarethat this gift will not occur again.
– This gift is direct, that is, from the Central Bank (CB) to the households.

In other words, the CB prints money and directly sends it to the households, without issuing assets or financial products, and adds information to the effect, “Look, it’s a one-off event.” All these make it very different from quantitative easing.

Now that we have the basis for the money transfer, how should we model it? There are several ways. The following are certain:
– main assumption: households should receive utility from holding money, that is, the presence of money in the utility function is mandatory).
– main fact: households’ money holdings impact consumption behavior. Further, nonlinearities between real money and consumption are assumed.
– main difference : helicopter money.

We need to pay attention to the following:
– Money holdings (money in the utility function) constitute money demand. In addition, at each point in time, money demand equals money supply, that is, one cannot hold money one does not have and one cannot supply money that is not held). So, one can easily assume that impacting money demand is similar to impacting money supply.

– Money-in-the-utility (MIU), cash-in-advance (CIA), and transaction-cost (TC) approaches are similar. Money is demanded if: (i) it makes consumers happy (MIU); (ii) consumers cannot buy goods without it (CIA); or (iii) it saves transaction costs, including time (TC). Among these ways to introduce money in a model, MIU is the simplest and Feenstra (1986) succeeded in establishing a functional equivalence between the three approaches.

So how should this main difference, that is, helicopter money, be modeled? I think that first—and not only for simplifying purposes, as it is impossible to test it with data—this exercise should be a simulation of a well-calibrated model. Second, the model should contain a function where the CB controls a one-time shock on money holdings. I realized that such a model is very similar to that used in my paper. The difference is that it cannot be an estimation. In addition, the money shock should only be “one-time.”
Once these are addressed, it is possible to properly model helicopter money.

Incorporating money into a New Keynesian (NK) dynamic stochastic general equilibrium (DSGE) model should be the easiest way. The possible ways include a money-in-utility (Benchimol and Fourçans, 2012; Ireland, 2004), cash-in-advance, or shopping-time model.

Walsh. 2017. Monetary Theory and Policy, Fourth edition, MIT Press, is probably the best starting point.

However, any model that directly includes money in the household’s decision problem is basically a “helicopter drop,” as it is a representative agent model. So, the problem would be to compare a positive money supply shock that directly affects households, as above, with a money supply shock that is transmitted only through the banking sector (see below). This would require the modeling of an interest rate channel and/or a credit channel. This corresponds to the “classic” undergraduate Friedman/monetarist vs. Keynes, or a direct vs. indirect view.

One could simply compare a standard NKDSGE model, containing an interest rate shock, with a money-in-utility model but, typically, money tends not to have a big effect in the standard NKDSGE models unless the utility function is non-separable into consumption and money (e.g., see Benchimol and Fourçans, 2017.)

A more advanced way is to model a household’s bank accounts because the CB is unlikely to send money by post. If the CB runs a helicopter money policy, it would probably use the banking channel.
Including a banking sector makes things more complicated but there are many papers (including Ireland, 2014) that have done it successfully.

I am also in agreement with the idea that it could be a lump-sum transfer from the CB to the households’ budget constraint.

This option, which seems more like a “realistic” helicopter drop, is to simply have a lump-sum transfer (T) from the government (CB) to the household’s budget constraint (many models have this feature, which falls away). You can do this with CIA constraint as well (e.g., see Walsh, 2017).

However, this transfer must be financed by an equal increase in money supply, which will be the helicopter drop. Thus, money supply is controlled through lump-sum transfers represented as:
T_{t} = M_{t} – M_{t-1}

I would also like to point out that one can model a CB function that controls money supply instead of the interest rate, which is assumed to be zero. This is because helicopter money is generally run during the “zero lower bound,” or ZLB, and is linked to households’ money holdings.
This seems very interesting to me and is worth pursuing.