# Monetary Economics/Goals of Monetary Policy
## Overview: Objectives of Monetary Policy

Monetary policy is how a central bank acts in its economic environment. A central bank is a national (or, in the case of the European Central Bank, a supranational) institution. Mostly the primary goal is to maintain price stability. Another common goal is to support the economy if it does not inhibit the achievement of price stability to a risky extent. This chapter examines what different costs arise due to inflation (increasing prices) and why it makes sense to keep inflation at a moderate level, to maintain price stability respectively.
Monetary policy is subject to a so called “assignment”. It is the definition of the central bank’s objectives and its instruments. It is a precondition for basically two aspects: economic efficiency and the central bank's accountability. Economic efficiency is given because of the knowledge that economic agents have about the central bank. They know its objectives and its means to achieve these objectives. Although they do not know how the central bank will act in any given circumstance it will provide the grounds for a sound prediction of what could potentially happen (e.g. because the people are sure that the central bank will always make decisions against the background of price stability they are likely to save money.) The other aspect is accountability: the only possibility to held the central bank accountable for what it has done is the assignment, the guidelines to which the central bank needs to adhere. Whether what the central bank did was good or bad can only be ascertained by comparing the given objectives with what the central bank has achieved.
In order to plan monetary policy and to measure its success an objective function is used that accounts for the rate of inflation and economic output:
$f(\pi ^{*},Y^{*})={\frac {1}{2}}[(\pi _{t+1}-\pi ^{*})^{2}+\lambda (Y_{t+1}-Y^{*})^{2}]$
π* describes the targeted rate of inflation, $\pi _{t+1}$ the achieved rate of inflation in one year. Monetary policy's effects are time-shifted, the real effects are perceived later, that is why the rate of inflation in one year is of importance. The same way $Y_{t+1}$ is the economic output in one year whereas Y* is the targeted economic output. The difference of both is squared to get a positive result. That assures that there is no interpretative difference between a deviation downwards or a deviation upwards, both are not desired. For the sake of simplicity 1/2 is written in front of the formula because it simplifies the first mathematical derivative. λ has a special meaning: If it is equal to 0 then economic output does not matter to monetary policy, but if it is larger than 0, then economic output matters. The value of λ describes in how far the economic output matters relative to the rate of inflation. The two cases can be distinguished as follows:
λ = 0: strict inflation targeting
λ > 0: flexible inflation targeting
It is the central bank's task to find values for π* and Y* that create stability for the economy. Empirical evidence suggests that the rate of inflation should be between 0% and 3%. The target value for Y* should be equal to the economy's natural level of output $Y^{n}$. As a low rate of inflation, in the most cases, should be first priority, λ has a small value, which gives the economic output a slight significance, but does not exceed the rate of inflation in importance.
Theoretical background
The theoretical background for $Y^{*}=Y^{n}$ is the assumption that in the long-run the economy will equilibrate and the output of an economy in its equilibrium is called the natural level of output. Money cannot influence the natural level of output because in the long-run changes in the money supply only result in corresponding price changes. This is called the neutrality of money: prices will adjust to the quantity of money in circulation. Another important concept is the superneutrality of money: the growth rate of the money supply does not affect economic output. Therefore sustained economic growth is no goal of monetary policy as such, but, as in the short-run monetary policy has an effect on real variables, a stabilization around the natural level of output.
The central bank needs to give a target for π* because inflation is a monetary phenomenon: there exists no natural level of inflation, but inflation is dependent on the money supply and the central bank controls the money supply. Consequently inflation is the result of the central bank's way of proceeding and therefore the central bank needs to give a target value.

## Costs of Inflation: Anticipated Inflation

Even if everybody knows that inflation is coming and even if everybody knows the rate of inflation, it will result in costs for the economy. In what way costs are caused is examined in the subsequent parts.

### Liquidity Preference and the Utility of Money

One cost of inflation arises due to an individual's liquidity preference in connection with the money's utility. If the individual keeps cash then interest that could be earned on that money is forgone. The nominal interest rate i that is earned contains both, a real interest rate r and an additional π to compensate for inflation, the loss of purchasing power.
$i\approx r+\pi$
As a consequence of an increase in π the nominal interest rate i will increase (Fisher effect). That in turn will increase the opportunity costs to keep cash. Hence, higher inflation causes higher opportunity costs.
In order to circumvent these costs people renounce to keep cash and in that manner the money's utility as a medium of exchange decreases. If people anticipate the inflation, that means higher values for i, then they will automatically reduce the amount of cash they keep.
In the graphic to the right the utility is depicted by the area below the graph. The lower i gets, the bigger the area becomes. With i = r the sum of both areas, the orange and the red one, indicates the total utility of liquidity preference. The area gets larger as i decreases and because the user cost decreases people are more likely to keep cash than to deposit it. As a consequence more cash is in circulation, money increasingly serves as the medium of exchange. What the graphic also shows is the theoretically optimal rate of inflation:
$i=0$
$r+\pi =0$
$r=-\pi$
Money has the highest utility when i is equal to 0. i is equal to pi + r and r needs to be positive all the time because otherwise people would not deposit any money. Therefore π must be negative. Conclusion: the theoretically optimal rate of inflation is a deflation.
To summarize it: Anticipated inflation causes people to deposit their money instead of keeping it as cash. By depositing the money people aim at earning an interest i that compensates for the anticipated inflation. People will do so because to not deposit the money when inflation is anticipated causes costs equal to i. People do not get the real interest rate r, which they could always earn, and they do not get π, a compensation for inflation. The utility of money for the individual decreases as the user costs to keep cash, in order to be able to consummate transactions, increase.

### Menu Costs

The starting point for the argument of menu costs is the money's function as a unit of account. The term menu cost is derived from the metaphor of a menu card in a restaurant. Inflation would make it necessary to print new menu cards very often, resulting in additional costs.
However, the term menu cost does not only refer to menu cards, but also to all other things where regular price adjustments cause additional costs. That includes new wage negotiations, the adjustment of machines and the printing of new banknotes among others. The higher inflation is, the higher the fixed costs of price adjustments become. In extreme cases, if inflation is too high, money might lose its function as a unit of account.
In theory, indexation could be used as a countermeasure against menu costs, but in reality it is ineffective because never will all prices be linked to a price index. Either because people fail to do so or because before all would had done so, a currency reform would have been consummated.

### Bracket Creep and Oliveira-Tanzi Effect

The term bracket creep describes a phenomenon of taxation that occurs due to inflation. Because of inflation nominal wages increase and people get into higher tax brackets. That results in indirect costs because, although the nominal wages increase, in terms of real wages, nothing changes. The increase of the general price level neutralizes the increase of the nominal wage, but because tax brackets are not corrected for inflation, people will have to pay more taxes although their real purchasing power did not change.
With regard to taxation the Oliveira-Tanzi effect describes the devaluation of tax revenues due to the delay that occurs between the determination of taxes and the eventual payment. If the tax for something was 100$ last year and the rate of inflation up to now was 10%, then the government's real revenue will be 90$ instead of 100$.

## Costs of Inflation: Inflation Uncertainties
### The Risk Premium

In times of uncertainty regarding the monetary development capital suppliers often add a risk premium to the interest they would like to charge. The risk premium is supposed to compensate for possible inflationary developments that could potentially disadvantage the capital suppliers. That makes credits more expensive and in turn fewer credits are demanded. Due to the risk premium the price for credits is never in its natural equilibrium and consequently the market efficiency decreases.

### Volatility of Inflation

Empirical evidence suggests that there exists a relation between the rate of inflation and the volatility of inflation: The higher the average rate of inflation, the higher is its volatility. Example: If a country A has an average rate of inflation of approximately 3%, it might happen that the rate of inflation sometimes tends to be 1% or even 0% and sometimes a bit higher, like 5%. However it is very unlikely that country A will ever have inflation rates of 10% or 20%. In contrast to country A, country B has an average rate of inflation of 30%. When inflation has reached such a high level, it is inconceivable that inflation always fluctuates around 30% with rates of for example 28% or 33%. Instead the variance is much higher, country B could probably have inflation rates of 5% or 60%.
A possible explanation for this phenomenon is government intervention. Whether the government decides to take countermeasures against inflation or not can influence the expectations of inflation significantly. If the government decides to take countermeasures it depends on its success whether inflation rates decrease or if the situation even deteriorates. Therefore the result can vary tremendously and cause such great volatilities.

### Redistribution between Creditors and Debtors

The last cost to be mentioned here is the hazard of possible redistributions of wealth. Due to inflation the creditors are disadvantaged because the real value of their receivables decreases. Vice versa debtors are advantaged because inflation reduces the real value of the debts. The higher the rate of inflation the more significant the effect of redistribution becomes. In case of hyperinflation it might cause creditors to lose all their assets because their receivables need to be paid with monetary units. In contrast, if the debtors used the money to buy assets the values of which are not subject to inflation, then it is called redistribution of wealth. The risk premium (see above) mirrors the uncertainty of creditors of such a loss.

## Summary and Conclusion

In this chapter the costs of inflation, either anticipated or unexpected, were examined. It should become clear that inflation can cause high costs and that it is in the best interest of the people to keep inflation moderate. Therefore it is monetary policy's and consequently the central bank's primary concern to maintain price stability. If inflation arises once in an otherwise fairly stable economy, it is not so tremendously bad, but if it happens twice people might lose their confidence and the government might lose its credibility. It is worth mentioning at this point that the monetary system is based on trust and if people lose that trust, if their expectations about inflation are bad, it can cause severe damages to the economy.
The economic output plays a role too. In the short-run monetary policy can influence the output, that is why central banks usually do flexible inflation targeting instead of strict inflation targeting. It is the willingness to make compromises as long as it does not force the central bank to deviate from its goal of price stability, as a central bank that only pretends to be interested in price stability is not trustworthy. The distrust results in bad expectations and these could have serious repercussions for the economy.