Blogwork 4 - PC and Keynes

Question 1

Godley and Lavoie combine the circular flow of money approach from the model SIM with the stock approach to create the model PC for portfolio choice. The SIM model is extended by adding a central bank which can issue T-bills. These bills will give an interest rate, r, and have the same price over their lifetimes. There is a need to endogenise money creation to close the model, as well as breaking the household’s decisions up into two stages:

- Consumption / saving decision
- Allocation decision.

The difference between model SIM and PC is the introduction of a central bank sector in the economy. This has two sections: capital and current. The current account describes the inflows and the outflows of the central bank, e.g. interest payments on existing assets or liabilities. The capital account describes changes in the balance sheet of the central bank, e.g. when it purchases new bills. The structure of model SIM is different to model PC as seen in figure 1 and figure 2.

Figure 1 Behavioural (transactions) matrix for Model SIM

Figure 2 Transaction – flow matrix of Model PC

The main assumption in Model PC is that producers sell whatever is demanded. Government bills and interest payments are in the PC model and not in the SIM model as seen in the equation below.

Y* = G + R-ı βң-ı (1- θ)

The disposable income and tax equations change from the model SIM versions to account for the interest received from holding bills as part of the households’ wealth as seen in equation 1 and the government taxes the interest received as it is added to the income of the household in equation 2.

1) YD = Y – T + r-1 . Bh-1
2) T = θ . (Y + r-1 . Bh-1)

A key behavioural assumption is that households make a two stage decision:

i) Households decide how much they will save out of their income.
ii) Households decide how they will allocate their wealth, including their newly acquired wealth.

The consumption decision determines the size of the expected end of period stock of wealth. The portfolio decision determines the allocation of the expected stock of wealth. The difference between disposable income and consumption is equal to the change in total wealth where:

V = V-1 + (YD-C)

The new consumption function now contains total wealth instead of money where:

C = α1.YD + α2.V-1 0 < α2 < α1 < v =" (1" v =" λ0" align="justify">
Households will hold a certain proportion (λ0) of wealth as bills and a certain proportion (1 - λ0) as money. The two factors which determine these proportions are: Interest rates and level of disposable income YD. Thus the sum of ‘constants’ ((1 - λ0) and λ0) must be unity because the decision to hold some proportion of wealth in the form of cash implies a decision to hold the rest in the form of bills.

If a change in interest rates (or incomes) causes people to wish to hold a higher proportion of their wealth in the form of money, they must simultaneously be wishing to hold an equivalently lower proportion in the form of bills. The interest rate must be fixed to stop the bills changing value during time periods to prevent capital gains which are not accounted for in the model PC. Therefore:

r = ŕ

r is endogenous as it reaches an equilibrium point of the supply and demand of bills for that period. If it varies no symmetry would be established in the allocation decision.

Question Two

1. How does Keynes define liquidity preference?

According to Keynes, liquidity preference refers to the decision made by households on what form they will hold the command over future consumption which they have reserved, whether out of current income or from previous savings (Keynes 1936). Households may want to hold the command over future consumption in immediate, liquid forms such as money or its equivalent, or in specific goods forms. This decision is made after specifying the propensity to consume, which determines how much of their income households will consume and how much they will reserve for future consumption.

Liquidity preference is given by a schedule of the amount of resources, valued in terms of money or of wage-units, which will be retained by households in the form of money in different sets of circumstances.

The quantity of money, when combined with liquidity preference, determines the interest rate. “Liquidity preference fixes the quantity of money which the public will hold when the rate of interest is given” (Keynes 1936). Thus the interest rate determines liquidity preference in part, as the interest rate is the bribe households get to give up liquidity. It is the reward for not “hoarding” cash. Where M is the quantity of money, L is the function of liquidity preference and r is the interest rate:

M = L(r)

Keynes states that liquidity preference exists because of the existence of uncertainty in relation to future interest rates. He defines three divisions of liquidity preference: the transactions-motive (the need of cash for current transactions), the precautionary-motive (the money held by individuals in case of emergencies), and the speculative-motive (to take advantage of a profit-making opportunity that may arise in the future).

As a rule, we can assume that the schedule of liquidity preference relation the quantity of money to the interest rate shows the rate of interest falling as the quantity of money increases, however Keynes points out that this does not always hold. For example, if the liquidity preference of the public is increasing faster than the increase in the quantity of money.

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

Yes, the PC model faithfully presents Keynes’ original vision of household decision-making. PC introduces the central bank. The central bank issues T-bills which are introduced as a part of wealth allocation and give a fixed interest rate, r. Thus, the household consumption decision must be split into two elements. This is consistent with the transactions-motive of Keynes’s liquidity preference theory and his idea of distinguishing between disposable income and consumption.

The first element is households’ propensity to consume, where they decide how much to save out of their income. Households should first consider how much to be used as consumption from income and how much to reserve in some form of command over future consumption.

In the second step, households decide how they will allocate their wealth, including their newly acquired wealth (Keynes 2007). Here, households can either allocate their wealth to cash or bills or both. This is again based on Keynes’ liquidity preference theory.

H_h/V= (1-λ₀)-λ₁*r+λ₂*(YD/V)

B_h/V=λ₀+ λ₁*r –λ₂ (YD/V)

These equations exhibit the following features: the cash holdings over the wealth (H_h/V) is negatively related to the interest rate and positively related to disposable income (YD), while the bill holdings over the wealth (B_h/V) is positively related to the interest rate and negatively related to disposable income. According to Keynes, the transaction and precaution motives for cash holdings have a positive correlation with income and the speculative motive has a negative correlation with interest rate. Hh/V+ Bh/V=1, which implies wealth is divided into cash and bills.

Thus it can be observed in the PC model that the difference between disposable income (YD) and consumption (C) is equal to the change in total wealth and not just money as in the Model SIM.

The consumption function now has total wealth instead of money:

V = V_-1 + (YD – C)

C = α_1. YD + α₂. V_-1

- where V_-1 represents past household wealth, α₁ is propensity to consume out of current income and α₂ propensity to consume out of current income.

The definition of YD is enlarged by adding interest payments on government debts. Taxable income is also enlarged by adding interest payments on government debt.

Furthermore, PC model assumes the money supply is endogenous and demand-led which can be expressed with these equations:

Bs= Bs-Bs-1= (G+r-1*Bs-1) - (T+r-1*Bcb-1);

ΔHs=Hs-Hs-1=ΔBcb;

Hcb=Bs-Bh;

The interest rate r is exogenous. It is clear that central bank acts as residual purchaser of bills. It purchases all the bills issued by the government that household are not willing to hold given the interest rate. In other words, the central bank is providing cash money to those who demand it. While introducing money into Keynes’ liquidity preference, we can also see autonomic mechanism would change the quantity of money supplied necessary to maintain a given rate of interest. In both models, the rate of interest is the equilibrium in the desire to hold wealth in cash form and the availability of cash. The quantity of money held depends on the rate of interest that can be obtained on other assets, in accordance with the speculative motive (the object of securing profit from knowing better than the market what the future will bring forth).

In conclusion, it’s reasonable to say that PC model faithfully present Keynes’ original vision of household decision-making.

References

Keynes, J. (1936)‘The General Theory of the Rate of Interest’, The General Theory of Employment, Interest and Money, [online] available at: http://www.marxists.org/reference/subject/economics/keynes/general-theory/ch13.htm

Accessed 29^th February 2008

Godley, W. & Lavoie, M. (2007) Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth, Palgrave Macmillan