Monetary economics - Appunti

Table of contents

• Lesson 1 – Introduction ...................................................................................................... 2
• Lesson 2 – Mp and fp without inflation ............................................................................... 6
• Lesson 3 – Mp and fp with inflation .................................................................................. 14
• Lesson 4 – Ad/as/pc model under adaptive expectations (monetarism 1.0) .............. 24
• Lesson 5 – Adaptive and rational expectations ............................................................ 33
• Lesson 6 – Ad/as/pc model under rational expectations (monetarism 2.0) ............. 40
• Lesson 7 - Staggered wage-price setting ........................................................................ 48
• Lesson 8 – Hyperinflation model under AEs and REs ..................................................... 58
• Lesson 9 – Monetary policy rule (MPR) ........................................................................... 66
• Lesson 10 – Interest rate rule (IRR) .................................................................................. 75
• Lesson 11 – Taylor rule & zero-lower bound ................................................................ 85
• Lesson 12 – Monetary policy in an open economy ........................................................ 99
• Lesson 13 – Interaction between monetary and fiscal policy .................................. 105
• Lesson 14 – Further topics about and ............................................................... 119
• Lesson 15 – Monetary and fiscal policies interactions in the EU.............................. 132
• Lesson 16 – Idiosyncratic shocks in the EU ................................................................... 141
• Lesson 17 – Demand and supply of bank reserves ....................................................... 154
• Lesson 18 - Unconventional monetary policy ............................................................. 166
• Lesson 19 – The economics of monetary union ........................................................... 178
• Lesson 20 – A critique on the OCA theory + costs and benefits of a MU ................... 190
• Lesson 21 – The fragility of incomplete monetary unions ........................................ 208

Lesson 1 – Introduction

There are different approaches to monetary policy that can be represented with this table, in which you have targets vertically and instruments horizontally.

Targets: output and inflation

Instruments: money growth and interest rate

The targets

• Inflation: the central bank controls it by fixing a target explicitly (as the ECB, FED, Bank of England do) usually at 2%. It’s an arbitrary choice, we will see why exactly 2% is reasonable.
• Output: this target may be seen as:
  • Output growth: difference between growth rates (actual output growth – potential output growth), a dynamic target.
  • Output gap (difference between actual output and potential output (both measured by GDP). This one is a more static target.

The CB is not concerned of the promoting growth/rising the potential growth rate, but it is rather concerned with the business cycle, which means that if output goes below its potential, the CB may increase it to bring it back to potential, or if it’s too much above and the economy is overheating, the CB may slow it by lowering the output. This is also called fine-tuning of the business cycle fluctuations.

The CB is not concerned as growth as such. The FED has a sort of blurred objectives, it’s not very sharply written as in the ECB case, and sometimes it says inflation and growth, full employment... Even if the goal is not as sharp as in the ECB case, the FED’s interpretation of its targets is also within the fine-tuning of the business cycle. The idea is that growth is a matter for the government to manage, and the CB is not concerned with that.

The ECB only targets inflation. We’ll also see an opposite case which is the fixed price model as the IS-LM in which only the interest rate is used to target output (IS-LM only target output, no inflation concerned).

The instruments

• Money growth: controlling money supply, determining a money growth rule.
• Interest rate targeting: the interest rate is an instrument (can also be seen as a lower-tier target) in order to pursue inflation and output.

There are also other targets which are not accounted for in the matrix. In the past, the CB had also an exchange rate target (when for instance we had a fixed exchange rate regime from the Bretton Woods agreements in 1944, where the exchange rate between the Italian Lira and the USD was 624 liras x 1$ and it was kept for over 20 years). So, at the time, the Central Banks had the exchange rate target which was to keep it fixed. Nowadays of course this target is no longer pursued within the Eurozone as there are no more national currencies, and with respect of external countries, we have a flexible exchange rate between the Euro and other currencies.

Operational framework

We can draw another matrix: Independent CB: operates within the boundaries of the law and it’s accountable as there’s a president of the CB which is appointed by elected politicians (FED president appointed by US Senate and ECB President appointed by the EU council). The president of the ECB is constrained by the EU parliament, as he/she has to address to them the CB operate. However, nobody can tell Lagarde what to do, she’s free to do what she wants of course within boundaries written in the Treaties of the EU.

The ECB is mentioned in the EU constitution, and it’s written that the ECB should only pursue price stability. The president of the ECB therefore can’t pursue whatever target, she has to declare in advance which is the target. As soon as the ECB was initiated in 1999, the target was fixed to a level lower but close to 2%.

Independent CB also means that the CB can’t be forced to purchase government bonds, which means that the monetarization of public debts is not allowed. The ECB can choose to buy bonds (Lagarde announced in March 2020 to buy up to 750 billions of government bonds), but it’s not the same thing as being forced by the government.

In Italy, up to 1982, the Bank of Italy was forced to buy old bonds issued by the government which were not sold, the Bank of Italy had to buy them on the primary market (issuing market). After 1982, this was not allowed anymore and the Bank of Italy was not forced to do so anymore, there was a divorce between the Treasury and the Italian CB.

The ECB by definition has a divorce with the Treasury, as the European Treasury does not actually exist, and in fact buying bonds means to buy Eurozone countries bonds. If the ECB was forced to buy bonds from states, it could buy Italian bonds with German or French money (which is not something liked by them), the ECB can choose to do that but cannot be forced. No EU government can ask the ECB to do that. This doesn’t happen in the UK/US: the Bank of England can be actually forced to buy the Treasury bills, and also the FED can be forced to buy T-bills.

Independence is a matter of degrees: among the CBs of relevant financial countries, the most independent one is the ECB, then we find that the CBs of Japan, UK, US are less independent.

Dependent CB: it means that the CB is a branch of the government and therefore the government direct the CB and can oblige it to purchase its bonds by definition. This is the least degree of independence.

What do ‘Rules’ and ‘Discretion’ mean?

Rules means that the CB is given a recipe, which is made public. Monetarism favors rules, favors the idea that the CB should set some rules, and then keep them as strict as possible (money growth rate 5% a year). Since CBs use the interest rates as an instrument, it may have an interest rate rule, that is to increase the interest rate if this happens by this much/decrease the interest rate if that happens by that much.

Discretion means that the CB does not have a rule to stick to, it will react to shocks or fixes its policy every time it needs to do so, it may change the interest rates or the money growth depending on its own discretion/assessment of the situation.

Generally:

• Independent CBs are meant to follow rules
• Dependent CBs are meant to use discretion

This statement finds ground both on logic and history:

Logic: if you have an independent CB, since the magnitude of its power, as a price for the independence it must respect some rules. For a dependent CB instead, discretion is reasonable as the government itself behaves discretionally, it reacts to situations by making decisions which are not constrained by rules but only by willpower.

History: CBs were born as the banks of the sovereign: Kings and Queen around Europe were hugely indebted with private banks. The king of France/Spain or whatever were indebted to the Italian and Dutch bankers (De medici, Pazzi...).

The Bank of England was the first central bank created, as the King of England was having his own bank, the bank which could finance the wars, the public buildings that the king was willing to make... The Bank of England was the instrument by means which the King could issue his own debt (most of Wars between England and France were bank-financed). The King issued debt which was purchased by the so-called gentry (people who had some lands, wealthy people as Lords, Dukes...) which were able to buy those Govt bonds which typical yield was 5%.

The gentry actually preferred to buy those bonds instead of paying taxes (taxes are a loss, bond is an investment). The debt/GDP in the early century in England was about 200%, and people were happy with that, to sustain that a high debt/gdp ratio is not always a bad thing (depends if people are willing to buy and sustain the Govt debt)

This brief story was to make the point that CBs were born dependent and have been that way for a long time. There has been a development of ideas. After WWII, the IS-LM and the early AS-AD model were the ruling models in Monetary Economics at the time, and so Monetary Policy was a sort of mix between money growth (Monetarism) but with an output target, and CBs were dependent.

Later on, there was a shift, inflation became more important (the only relevant target). Money growth was the instrument used at first when CBs started to become independent and to use rules. There’s a history of economic thought thread:

Monetarism prevailing → Inflation target → Independent CBs → Rules

Even if in the early 90s the instrument choices shifted from money growth to interest rate, this thread was still there, and it has been there up to the 2008 GFC. After that crisis there has been a re-thinking of many things.

Lesson 2 – MP and FP without inflation

Money demand: it is the desired holding of financial assets in the form of money, that is cash or bank deposits rather than investments. We’ll look at just one theory of money demand.

We first recall the quantitative theory of money (income version):

M × V = P × Y

V is the velocity of money: the number of times this quantity of money is used for buying things that belong to the GDP. This is an identity, must always hold. This equation has been interpreted as a money demand formula, which in equilibrium means that:

M_d = (1/V) × P × Y

We see that money demand depends inversely on velocity: increases as velocity decreases, because if the number of times a single currency unit circulates goes down, you need more money (more units) to buy the nominal GDP, and if the velocity of circulation tends to infinite, you’ll need very little money and M_d decreases, because every single unit can be used approximately an infinite number of times. The quantity of money x GDP can be very small in this case.

If this is the case, then apparently there’s no relation between monetary policy and interest rates. If you apply this simple equation, the only thing the CB can do is to manipulate M_s.

But if the interest rate enters into the formula, things change. Suppose that the velocity is a function of the interest rate: V(r). Then of course you’d have M_d = (1/V(r)) × P × Y and at that point you’d have a relationship between money demand and interest rate.

If we assume that the function is direct, then the velocity increases with the interest rate. Precisely, if V'(r) > 0 then M_d'(r) < 0, that is, we have an inverse relationship between money demand and interest rate: the higher the interest rate, the lower the money demand.

This is consistent with liquidity preference view of the money demand. What we have done is to transform a quantity equation into a liquidity preference equation by assuming that V is a direct function of r. This gives rise to an inverse relationship between money demand and the interest rate.

If r↑, V↑: If r is high, people prefer to use money to buy securities and stocks rather than using it into transactions: the velocity goes up, as fewer units of money are used into goods and services and more are used for financial/speculative purposes.

The money demand formula therefore becomes: M_d = (1/V(r)) × P × Y

Now we derive this function starting from maximizing the behavior of economic agents. We assume that people are able to maximize (as they are rational, self-interested):

We have a utility function:

U = ln(C) + ln(S/W)

Where

• C = consumption
• S = savings
• W = wealth

Income is a flow concept, real money/wealth is a stock.

Both income and wealth positively affect the utility, because both income and wealth can support consumption/expenditure from which agents draw their utility.

This is a log-linear utility function. Why? Given that it respects some fundamental concepts (people prefer more than less and people’s choices are transitive, consistent), utility functions are the representation of people’s preferences. We know that many forms of utility functions may represent the same preferences, indeed any monotonic transformation of the utility function is the same utility function and represents the same preferences. Therefore, we don’t really bother too much about the form of the utility function, we use the log-linear form simply because it’s convenient.

What we need to notice is that this utility function is separable (as income and wealth positively affect the utility separately) and it is concave, which means it has convex indifference curves (people prefer average over extremes). Concavity is a sufficient condition for maximization, that is very convenient. The parameters β and γ are constants.

Let’s define:

• L = Labor income
• W = money wage; P = price level; H = number of hours worked by employed people
• FW = Financial Wealth (sum of money wealth in real terms and securities wealth)

We’re assuming that all financial wealth is either kept in form of money or securities (people either have money or securities). What’s the difference between Money and Securities? The interest rate! By keeping money people give up the potential yields of securities.

FW = M + σ(PY - r)

M_max = L + rFW

The maximum level of income derives from summing the labor income and the financial wealth, given that all the financial wealth is kept as securities, so is made only of interest bearing securities, because for every unit of wealth kept as money corresponds some lost yield in securities.

M_actual = L + rFW - σ(PY - r)

The actual income is going to be our budget constraint. It depends on how much wealth we keep as money and how much we keep as securities.

So we have a utility function and a budget constraint:

U = ln(C) + ln(S/W)

Budget constraint: M_actual = L + rFW - σ(PY - r)

If we want to represent it graphically:

The budget constraint depends on the interest rate:

• The higher r, the steeper the budget constraint
• The lower r, the flatter the budget constraint

The labor income is given and if people keep some of their wealth in terms of securities, actual income will go beyond labor income. How much higher? It depends on the amount of wealth kept into interest bearing securities. The less the money (in proportion) held by people, the higher the income. This function gives rise to convex indifference curves. We can find the tangency point which is the geometrical solution of the maximization problem: rational economic agents will attempt to achieve the highest indifference curve which satisfies their budget constraint.

The solution of this problem provides the optimal quantity of money given a certain amount of labor income, total wealth and interest rate. This is a maximization problem. We can therefore solve it through the Lagrangian function, that is the merge of the utility function and the budget constraint.

U = ln(C) + ln(S/W) + λ[L + rFW - σ(PY - r)]