Modify Model PC

Modify the PC model we covered in lectures to allow for the simulation of a stagflation-type episode in the economy

Stagflation occurs where there is a combination of rising prices (inflation) and stagnation (slow economic growth and rising unemployment) such as what occurred to the world economy in the late 70’s and early 80’s. The main cause of this is an adverse supply-side shock (eg. Increase in oil prices, natural disaster etc.) or inappropriate macroeconomic policies (wikipedia.org).

PC Model Transactions Matrix





Equation List for Model PC (endogenous system)

Y = G + C (1)
YD = Y − T + r−1 • Bh−1 (2)
T = θ• (Y + r−1 • Bh−1) (3)
V = V−1 + (YD − C) (4)
C = α1 • YD + α 2 • V−1, 0 < α 1 < α 2 < 1 (5)
Hh/V = (1 − λ0) − λ 1 • r + λ 2 • (YD/V) (6)
Bh/V = λ0 + λ 1 • r − λ 2 • (YD/V) (7) Hh = V − Bh (8)
ΔBs = Bs − Bs−1 = (G + r−1 • Bs−1) − (T + r−1 • Bcb−1) (9)
ΔHs = Hs − Hs−1 = ΔBcb (10)
Bcb = Bs − Bh (11)
r = r* (12)

α3 = α 2 • (1 − α 1)/ α 2 (13)
ΔV = α 2 • (α 3 − V−1) (14)
V*/YD*= α 3 (15)
R*= (B*h • r/V*) (16)

Modify to allow for possibility of stagflation

Inflation is given by π = (p1 - p0/p0), where p is the price level.

The PC model assumes that AD=AS. For stagflation to occur this implies the economy is in disequilibrium, due to the causes mentioned above. In the case of an adverse supply side shock this would imply shortage of supply and excess demand ie. AD>AS. To allow for this the model must be adjusted. Consumption (C) can be increased in nominal terms to become (C.π). This can be substituted into the model instead of C. This includes inflation in the model. Increased inflation will cause a decrease in C which, with G held constant,will lead to a decrease in output/GDP. In a stagflation environment this will lead to an increase in unemployment.

Adverse Supply Side Shock



Figure 1

Figure 1 shows an example of an adverse supply side shock. The AS curve shifts up to the left which results in a fall in GNP, a rise in unemployment (U) and an increase in inflation (π). The linear increase in U and π is contrary to that expected by the Phillips Curve. (Leddin and Walsh 2003, p.31)

Assignment Week 5

Question1

Chapter 4: Overview

The section entitled, Government money and portfolio theory, essentially introduces government bills, interest payments, and a central bank (as independent entity from the government sector) to the pre-existing Model SIM. However, unlike Model SIM the transactions flow matrix includes two financial assets and there is also interest payments due on debt. Finally, in Model SIM any change in total wealth is primarily a function of money, while in Model PC this is the difference between income and consumption. As a result of these additions Model PC undoubtedly strives to portray a more realistic picture of a modern macro-economy.

At the outset, Godley and Lavoie (2007, p.99) state “Agents make a portfolio choice between money and other possible financial assets”. It is important acknowledge the significance of this statement, as it is undoubtedly the premise upon which Model PC is developed.

Model PC
The opening equation (4.1) of the model basically states that production is equal to consumption plus government expenditure. Equations (4.2) and (4.3) define disposable income and taxable income respectively.

Y = C + G (4.1)
YD = Y – T + r-1. Bh-1 (4.2)
T = Ơ . (Y + r-1 . Bh-1) (4.3)

Households must make a two step decision: 1.determine how much of their income they will save and then 2. the proportion of their wealth to allocate between money and bills (V is total wealth), in the steady state, the public sector does not make any payments of interest on debt; nevertheless, household borrowers do. This means that the quantity of cash money kept by households equals the amount provided by the central Bank.

V = V-1 + (YD – C) (4.4)

Consumption now includes total wealth (as stated previously).

C = α1 . YD + α2 . V-1 0< α2< α1<1 (4.5)

Therefore, wealth is allocated between bills and money (Portfolio Choice). However, the allocation must sum to one in order to satisfy the following formulas;

Hh/V = (1- λ0) – λ1 . r + λ2 . YD/V (4.6A)
Bh/V = λ0 + λ1 . r - λ2. YD/V (4.7)

Households will hold a certain proportion (λ0) of wealth as bills and a certain proportion (1 - λ0 ) as money. This is a fundamental of the portfolio choice. The two primary factors that influence the allocation are: Interest rates and the liquidity preference. As illustrated in tutorials, higher interest rates results in higher bill coupon payments and consequently households will allocate more of their wealth to bills than money. Alternatively, the lower the households level of disposable income, the lower the proportion of wealth that will be held in bills. In this model, the rate of interest is assumed to be constant (so bill prices remain constant), therefore is an exogenous variable, stating the equilibrium point of the supply and demand for bills, if it were not constant, symmetry in the allocation decision would be impossible.
Following on, equations (4.8) to (4.11) concern the government and central bank.

∆Bs = Bs – Bs-1 = (G + r-1 . Bs-1) – (T + r-1 . BCB-1) (4.8)
∆Hs = Hs – Hs-1 = ∆Bcb (4.9)
Bcb = Bs - Bh (4.10)
R = r (4.11)

Equation (4.8) relates to the government budget constraint. Equation (4.9) depicts the capital account of the central bank. Equation (4.10) and (4.11) illustrates that the central bank is the residual purchaser of bills, the
Hh = Hs (4.12)
Consequently, in light of the above analysis and in accordance with equation (4.12) it is possible to ascertain that the cash held by households is equal to that supplied by the central bank.

Question 2

1. How does Keynes define liquidity-preference?

He defines it as:

“ a schedule of the amounts of his resources, valued in terms of money or of wage-units, which he will wish to retain in the form of money in different sets of circumstances” (Keynes 1936)

He essentially sees it as the degree and form a householder will want to keep command over future consumption of held income (ie. not already consumed). The choice is between immediate liquid command (money or some equivalent) or deferred command for a specified or indefinite period (ie. Future market conditions will determine any future conversion to liquidity). He analysed the reasons for holding money under three motives (Leddin and Walsh, 2003 p. 144):

1. transaction: where people need money for everyday use;
2.precautionary: which is the desire to hold money in case of emergencies, and;
3.speculative: which is where the object is to earn a profit by 'knowing better than the market what the future will bring forth' (Keynes 1936).

Keynes also says the interest rate is ‘the reward you get for parting with liquidity for a specified period’ and hence helps determine liquidity preference. When this is factored in along with the quantity of money, he defines liquidity-preference (demand for money) as:

“a potentiality or functional tendency, which fixes the quantity of money which the public will hold when the rate of interest is given; so that if r is the rate of interest, M the quantity of money and L the function of liquidity-preference, we have M = L (r)”
(Keynes 1936)

References:
Keynes, J.M. (1936) The General Theory of Employment, Interest and Money,Chapter 13. London: Macmillan.

Leddin, A. J. and Walsh, B. M. (2003) The Macroeconomy of the Eurozone: An Irish Perspective, chapter 8. Dublin: Gill & Macmillan.

2. Is PC a faithful representation of Keynes’ original vision of household decision-making? If so, why? If not, why?

Yes as the allocation decision process is based on Keynes’ liquidity-preference theory (see above). Similar to Keynes, the PC model splits the household consumption decision between (1) how much to save and (2) where to consume and on what (or in what form as Keynes states).

In both models the rate of interest is the equilibrium in the desire to hold wealth in cash form and the availability of cash.

Where they differ is the fact that the PC model does not include bonds whereas in Keynes analysis he uses bonds in conjunction with his 'normal rate of interest' in deriving the demand for money function incorporating the three afore-mentioned motives. keynes also considers uncertainty.

So depending on how strictly you define 'faithful' PC may not represent Keynes original vision, though it does initially to a large degree.