Incorporating Money - Money in Utility (MIU) and Cash in Advance (CIA) models

The Real Business cycle model, as discussed in another article, does not include monetary components in its analysis. This is because in the RBC models neither holding money gives utility nor it earns interest, thus there is no motivation to hold the same. However to understand the effect of monetary policy, impact of money on prices and comment on the optimal inflation rate we need to include monetary components into the model. Mainly two approaches are used to explicitly incorporate the frictions and motivate households to hold money - Money in utility approach and Cash in advance approach.  First, we will discuss the first model i.e. MIU.

Money in Utility (MIU) model:

In Money in Utility approach, holding money provides utility to the households since it eases the transactions and also reduces the transaction costs. The money is stuck to the household utility function in the form of real balances. The household budget constraint changes by the inclusion of real money balances. Frim still tries to maximize its profits as before. Further, we assume that the monetary authority sets the money supply exogenously using the money law of motion. The FOCs wrt consumption, labour and bond holdings remain the same as in the RBC, only the FOC wrt money balances change which now includes the additional term of the discounted utility households will obtain by holding real money balances. Solving the problem and by using the steady-state and log-linear strategies we observe that there is no effect of money or inflation on the real variables in long as well as short run. (To look into the math refer to [1])  The consumption behaviour remains unaffected because whatever effect inflation has on utility is only reflected via the holding of real money balances. So, when money does not impact the real variables like actual consumption, employment, real wages or real GDP  then the money is said to be "neutral". It was further investigated to find that non-neutrality can be obtained by using non-separable utilities. But this model after standard calibration suffers from several issues and thus has not been accepted widely. Also, the MIU approach comments that the optimal nominal interest rate should be zero. This is also known as Friedman rule.

Money neutrality and super-neutrality:

As discussed earlier, when the supply of money does not affect the real variables like output then the money is said to be neutral. In other words, changing the amount of money supply changes the nominal variables like prices and markets clear. The money supply, therefore, does not lead to changes in the aggregate supply. Its acceptance or rejection by different schools of thought has been shown in the figure.

Money super-neutrality is a stronger form which says that not only does the money supply independent of the real variables but even the growth of money supply does not affect the real variables. However, it has faced much stronger criticisms than money neutrality.

Friedman rule:

According to Friedman's rule, the net nominal interest rates should be near zero or inflation should equal the negative of real interest rates (i.e. deflation). Basically holding money saves time and reduces the hassles which the complex transaction via say credit card takes. Thus this becomes the incentives or benefits for the households to hold money. Also, it is basically costless for central banks to produce. CB's can simply print the money and transfer it to the households who would then have higher utilities as a result.

But on the downside, holding money unlike other financial assets like securities does not yield any interest. So, as per the expected inflation rates, households economize their cash holdings in order to keep them working in financial assets. The opportunity cost of holding money depends on the rate of interest. More is the interest rate, more is the cost of holding money (shoe-leather cost). Shoe leather cost refers to time, efforts and resources households take to minimize the effect of inflation on eroding the purchasing power of their money.  In a nutshell to save themselves from the risk of money erosion arising due to non-yielding asset forces households to minimize their cash holdings, and the efforts involved in reducing the cash and investing it in interest yielding assets can be thought of as the cost of holding money.

Thus, according to Friedman, central banks should try to remove the interest rate differential between monetary and non-monetary (securities) instruments.

Cash in Advance (CIA) model:

CIA model assumes that cash is necessary for certain types of transactions. Households derive utility from consumption. Households carry money, capital, bonds and profit dividends from the previous period, get lump-sum transfer from the government this period, and use it for consumption expenditure, invest in capital or bonds or save as money. This is their basic constraint as usual. The additional which is known as the CIA constraint follows that the goods markets open before the asset market or that the consumption expenditure depends on cash which has been carried from the previous period and the lump sum transfer from the government (assuming that here consumption goods can be bought only with cash). The main difference between the two models is that the MIU derives utility from money holdings, no matter how they spend that money on, however, the CIA gives a description of how the money flows.

After the FOC's have been derived the model is looked upon through the scenarios when (a) the CIA constraint binds and (b) the CIA constraint is slack or does not bind, and thus comments on the different issues.

References:

1. Lecture on Money in Utility function, Adam Spencer, University of Nottingham

2. Looking at the leather shoe cost of inflation, Michael R. Pakko, Federal Bank of St. Louis publication, Nov-Dec 1998

3. What is the optimal rate of inflation?, Timothy Cogley, FRBSF Economic letter, September 19th, 1997

4. Money neutrality: A central role in Monetary economics, Essays UK, November 2013, accessed on October 21st, 2018

5. http://econ.sciences-po.fr/sites/default/files/file/barany/grad_macro/CIA_cor.pdf, accessed on October 22nd, 2018