A simple stock-flow consistent model with porfolio choice and a

government sector Chapter 4 of Godley and Lavoie 2007Monetary Economics: An Integrated Approach to Credit, Money, Income,

Production and Wealth

The model …• Can be found as E-views files or (soon)

Modler files on the web sites:– gennaro.zezza.it/software/models– http://www.modler.com/LearningTools.html

Preliminaries

• “I have found out what economics is; it is the science of confusing stocks with flows”

• Michal Kalecki (circa 1936), as told by Joan Robinson (1982).

Objective of the presentation

• To show what a SFC model is.• To show some of the main features of a

SFC model is within a simple framework• Provide some experiments (simulations)

with this simple model: changing some parameter values and draw charts.

What is the stock-flow consistent approach? SFC ?

• All sectors face budget constraints• Financial interdependence between

sectors• Stock variables arise from flows and

capital appreciation: historical time• There exist stock-flow norms (which may

change through time)• People react and adjust to disequilibria

SFC of some form in PKE and other heterodox economics

• Davidson, Minsky• Eichner 1985• Peter Skott 1989• Institutionalists: Copeland 1947

Origins

• Two strands of research linking stocks and flows:

• Godley and Cripps (1982) at Cambridge, • Cambridge Economic Policy Group, • New Cambridge school (1970’s). • Tobin (1982) and his associates at Yale,• the ‘pitfalls approach’ (1969)• the New Haven school.

General features• Tobin (1982, Nobel Lecture)• Models ought to track stocks;• Models should have several assets and

rates of return;• Models include financial and monetary

operations• Models include the sectoral budget

constraints • and the adding-up constraints in portfolio

equations

Other key features• There cannot be any black holes.• “The fact that money stocks and flows must

satisfy accounting identities in individual budgets and in an economy as a whole provides a fundamental law of macroeconomics analogous to the principle of conservation of energy in physics” (Godley and Cripps 1983).

• There are intrinsic dynamics, Turnovsky (1977)

• There are lag dynamics, to avoid telescoping time (Hicks, 1965)

The PC model• The PC Model (PC for Portfolio choice) is the second

model of our book, and the first to introduce portfolio choice.

• We find that it is the simplest model that can reproduce most of the main features of stock-flow consistency.

• It has four sectors: firms, households, government, and the central bank.

• The economy is highly simplified: firms have no fixed capital, and there are no commercial banks.

• As in all cases, it is best to start with the stock matrix and the transactions-flow matrix

The stock matrix (the balance sheet)

The transactions-flow matrix

• There cannot be any black holes (Godley 1996).

• Therefore, all columns and all rows must sum to zero.

• The economy is closed, and there is no investment (since there is no fixed capital)

The transactions-flow matrix

The PC model: national accounting equations and taxes

(4.1) Y C + G(4.2) YD Y - T + r-1.Bh-1

(4.3) T = .(Y + r-1.Bh-1)

Portfolio decisions, based on expected wealth and values:The Brainard-Tobin formula amended

(4.7E) Bd/Ve = 0 + 1.r - 2.(YDe/Ve)(4.6E) Hd/Ve = (1 - 0) - 1.r + 2.(YDe/Ve)(4.13) Hd = Ve - Bd

(4.14) Ve V-1 + (YDe - C)

Realized and expected valuesThe stock of money held by households is

the buffer

(4.4) V V-1 + (YD - C) (4.5) C = 1.YDe + 2.V-1 0 < 1 , 2 < 1(4.15) Bh = Bd

(4.6) Hh = V- Bh

(4.16A) YDe = YD-1

(4.16) YDe = YD.(1 + Ra)

The consumption function with propensities to consume out of income and out of wealth (the so-called Modigliani

consumption function) is equivalent to a wealth adjustement mechanism with a target wealth to disposable income ratio. The assumption of stable stock-flow norms (Godley and Cripps 1982) is derived from the assumption

of relatively stable propensities to consume

Vh = 2.( 3.YD - Vh-1) Vh = 2.( 3.VhT - Vh-1)where 3 = (1 - 1)/ 2.

The wealth to income ratio is: V/YD = 3

The government, the central bank, and the hidden equation

(4.8) Bs Bs - Bs-1 (G + r-1.Bs-1) - (T + r-1.Bcb-1)(4.9) Hs Hs - Hs-1 Bcb

(4.10) Bcb = Bs - Bh

(4.11) r = r

The hidden equation(4.12) Hh = H s

Money as a buffer against mistaken expectations (Here we assume that expectations about current income fluctuate randomly)

Money held changes more than money demand

Raising the interest rate: impact on portfolio shares

The surprising impact of an increase in interest rates !!!!!

An increase in the propensity to consume out of disposable income:Anti-Keynesian in the long run …

The impact of a higher propensity to consume

Higher interest rates must lead to higher income in this model

• Income is depends on a multiplier relationship, inversely tied to the tax rate, and where the multiplicand is government expenditure, which includes debt service.

*)1(*)1(*

3

3

rrGY

(4.30) 1 = 10 .r 1

The impact of a rise in interest rates is still positive in the long run even when higher interest rates have a short-run negative impact on income, Because they are assumed to induce lower propensities to consume

Evolution of tax revenues and government expenditures including net debt servicing,following an increase of 100 points in the rate of interest on bills, where the propensity to consume reacts negatively to higher interest rates

The hike in interest rates produces a recession, which pushes up the public debt to income ratio. Governments have little control over the evolution of the debt to GDP ratio, as long as households don’t modify their wealth to income ratio.

Alternative closuresIt is possible to have an alternative closure, a

neoclassical one, by assuming the following changes

• Replace the equation:• Bcb = Bs – Bh

• Delete the interest rate equation (where r was a constant)

• Set Bcb as a constant (through open market operations)

• Add the equation• Bh = Bs – Bcb

• We now have two equations that set Bh. The rate of interest must become a price-clearing variable (in the portfolio equation)

Neoclassical closure: Central bank sells T-bills on the open market in 1961

As an exercise …

• Go to the website of Gennaro Zezza• Introduce the neoclassical closure into the

PC model with expectations and random errors.

• Check what happens to interest rates and income with the random shocks.