June 19, 2018

The Fisher Effect ― another piece of nincompoop-economics

Comment on David Glasner on ‘Keynes and the Fisher Equation’


Roughly speaking, the Fisher Equation is about the relationship between nominal and real interest rates under inflation and the Fisher Effect is about the effects of changes in expected inflation on the nominal interest rates.#1

In the following, it will be demonstrated that the Fisher Effect is due to a design flaw of the monetary economy. Neither Fisher nor Keynes has realized this because they never understood how the economic system works.#2

As the correct analytical starting point, the elementary production-consumption economy is defined with this set of macroeconomic axioms: (A0) The objectively given and most elementary configuration of the economy consists of the household and the business sector which in turn consists initially of one giant fully integrated firm. (A1) Yw=WL wage income Yw is equal to wage rate W times working hours. L, (A2) O=RL output O is equal to productivity R times working hours L, (A3) C=PX consumption expenditure C is equal to price P times quantity bought/sold X.

Under the conditions of market clearing X=O and budget balancing C=Yw in each period, the price is given by P=W/R (1). This is the most elementary form of the macroeconomic Law of Supply and Demand.

The price P is determined by the wage rate W, which takes the role of the nominal numéraire, and the productivity R. The quantity of money is NOT among the price determinants. This puts the commonplace Quantity Theory forever to rest.

What is needed for a start is two things (i) a central bank which creates money on its balance sheet in the form of deposits, and (ii), a legal system which declares the central bank’s deposits as legal tender.

Deposit money is needed by the business sector to pay the workers who receive the wage income Yw per period. The need is only temporary because the business sector gets the money back if the workers fully spend their income, i.e. if C=Yw. Overdrafts are needed by the household sector for consumption expenditures if the households want to spend before they get their income.

For the case of a balanced budget C=Yw, the idealized transaction sequence of deposits/overdrafts of the household sector at the central bank over the course of one period is shown on Wikimedia.#3

The household sector’s deposits/overdrafts are ZERO at the beginning and end of the period. Money is continually created and destroyed during the period under consideration. There is NO such thing as a fixed quantity of money. The central bank plays an accommodative role and simply supports the autonomous market transactions between the household and the business sector.

From this follows the average stock of transaction money as M=kYw, with k determined by the transaction pattern. In other words, the average stock of money M is determined by the autonomous transactions of the household and business sector and created out of nothing by the central bank. The economy NEVER runs out of money.

Monetary profit for the economy as a whole is defined as Qm≡C−Yw and monetary saving as Sm≡Yw−C. It always holds Qm+Sm=0, or Qm=−Sm, in other words, the business sector’s surplus = profit equals the household sector’s deficit = dissaving. Vice versa, the business sector’s deficit = loss equals the household sector’s surplus = saving. This is the most elementary form of the macroeconomic Profit Law.

When government is added, the Profit Law reads Qm=(G−T)−Sm. Legend: G government expenditures, T taxes.

In the initial period G, T, Sm are all zero. Hence macroeconomic profit Qm, too, is zero.

In period 1, there is a government sector deficit but it is exactly equal to the household sector saving. Hence Qm is again zero. The government’s debt consists of overdrafts at the central bank Ω. The household sector’s savings consist of deposits at the central bank Φ. Both sides of the central bank’s balance sheet are equal.

Now, the interest rate on deposits is zero and the interest rate on government debt is r. The rate r is set such that it covers exactly the central bank’s wage bill, i.e. rΩ=WL* (2).#4, #5

Under these simplified conditions, one has for the price of the consumption good P=W/R and for the rate of interest r=(W/Ω)L* (3).

In period 2, the wage rate W is doubled. All real variables remain unchanged. According to (1) the price P doubles. According to (2) either (a) the nominal rate of interest r doubles and the nominal debt Ω remains constant, or (b), the nominal rate of interest remains constant and the nominal debt doubles.

Needless to emphasize that (2b) is the correct solution. The institutional setting, though, is such that the nominal value of the debt does NOT move in lockstep with inflation.

In the correct institutional setting for the monetary economy, the nominal rate of interest does NOT move with inflation but nominal debt does. So, there is NO such thing as a Fisher Effect, the nominal rate r remains constant. And because of this, inflation expectations have NO effect on the nominal interest rate.

In a well-behaved inflation, the nominal interest rate r remains constant, the real interest rate r'=r/P falls and the nominal debt increases Ω'=ΩP such that nominal interest payments rΩ' increase and real interest payments r'Ω' remain constant.

Egmont Kakarot-Handtke

#1 Wikipedia, Fisher Equation
#2 Macroeconomics ― dead since Keynes
#3 Wikimedia, Idealized transaction pattern
#4 Essentials of Constructive Heterodoxy: Money, Credit, Interest
#5 The Emergence of Profit and Interest in the Monetary Circuit