PCEX Modification

Modify PCEX to accommodate the possibility of stagflation in this economy.

Stagflation is an economic phenomenon that occurs when increasing inflation rates are coupled with a period of stagnation, i.e. little or no economic growth in the economy.

One of the main causes of stagflation is the occurrence of an unfavourable supply-side shock which can have the effect of driving up prices in an economy while at the same time, slowing the economy by making production less profitable and thus having the effect of a drop in output.

(www.wikipedia.com)

For the purpose of this assignment, we will introduce a supply-side shock to the economy using Model PCEX to reflect the current stagflation concerns in the US economy brought on by the effects of the subprime mortgage crisis.

This model introduces expectations on household’s disposable income. The following is the equation list for the Model PC with expectations (PCEX)

• · Y = C + G (4.1)
• · YD = Y – T + r_-1 . B_h-1 (4.2)
• · T = Θ . (Y + r_-1 . B_h-1) Θ <>
• · V = V_-1 + (YD – C) (4.4)
• · C = α₁ . YD^e + α₂ . V_-1 (4.5E)
• · B_d/V^e = λ₀ + λ₁ . r - λ₂ . (YD^e/V^e) (4.7E)
• · H_d/V^e = (1 – λ₀) – λ₁ . r + λ₂ . (YD^e/V^e) (4.7E)
• · H_d = V^e – B_d (4.13)
• · V^e = V_-1 + (YD^e – C) (4.14)
• · H_h = V - B_h (4.6)
• · B_h = B_d (4.15)
• · ∆B_s = B_s – B_s-1 = (G + r_-1 . B_s-1) – (T + r_-1 . B_cb-1) (4.8)
• · ∆H_s = H_s – H_s-1 = ∆B_cb (4.9)
• · B_cb = B_s - B_h (4.10)
• · r = ȓ (4.11)
• · YD^e = YD . (1 + Ra)

The following is the modified version of model PCEX to accommodate the possibility of stagflation in this economy.

• · Y = C_s + G (4.1)
• · C_d > C_s (*1)
• · W.N_s = W.N_d (*2)
• · YD = Y – T + r_-1 . B_h-1 (4.2)
• · T = Θ . (Y + r_-1 . B_h-1) Θ <>
• · V = V_-1 + (YD – C_s) (4.4)
• · C_s = α₁ . YD^e + α₂ . V_-1 (4.5E)
• · B_d/V^e = λ₀ + λ₁ . r - λ₂ . (YD^e/V^e) (4.7E)
• · H_d/V^e = (1 – λ₀) – λ₁ . r + λ₂ . (YD^e/V^e) (4.7E)
• · H_d = V^e – B_d (4.13)
• · V^e = V_-1 + (YD^e – C_s) (4.14)
• · H_h = V - B_h (4.6)
• · B_h = B_d (4.15)
• · ∆B_s = B_s – B_s-1 = (G + r_-1 . B_s-1) – (T + r_-1 . B_cb-1) (4.8)
• · ∆H_s = H_s – H_s-1 = ∆B_cb (4.9)
• · B_cb = B_s - B_h (4.10)
• · r = ȓ (4.11)
• · YD^e = YD . (1 + Ra)

A supply side shock is introduced into the economy. This may take the form of a sudden scarcity of natural resources due to an event outside the control of the production firms in the economy i.e. war, natural disaster etc. This reduces the supply of goods and services in the economy. Equation *1 is introduced to accommodate the excess demand now evident in the economy. Households’ pay higher prices for the same goods and services to obtain the same level as consumption in period t_-1. This increases the level of inflation in the economy. In subsequent periods households’ will revise their expectations to account for the increased inflation. Equations 4.1, 4.4 and 4.14 have to be altered to account for the fact that the consumption demanded is no longer equal to consumption supplied.

Equation *2 is introduced to account for the stagnation influence on the model. Factor income is a function of national income and is used to account for changes in the wage agreements. In the long-term the households take into account the increased inflation when negotiating wage agreements. This increases the costs incurred by the production firms in the economy, thus making the firms less profitable, and as aforementioned, total output is reduced. As total output decreases, unemployment increases.

Therefore, the Model PCEX now accounts for stagflation as inflation and unemployment are increasing in conjunction with one another.

Homework 4

Question 1

Summary of Godley and Lavoie, chapter 4, pages 99-107, while answering the following questions:

1. Why is the interest rate on bills, B, fixed such that r = ȓ? What would it mean for the model if r could vary?
2. How does the household make its decisions with regard to cash balances?
3. How is PC different from SIM?

Chapter 4 introduces the stock approach to the circular flow of money approach from the model SIM to create the model PC. In the stock approach households have to decide how much of their stock of wealth is held in money and in other assets. This is dependent on the rate of interest that can be earned on the other assets. The households therefore have to make a portfolio choice, hence the model PC.

The model PC is different to model SIM as it separates the central bank from the government and introduces interest payments and government bills into the transactions-flow matrix. The price of the bills remains constant as it the interest rates do not change from t_-1 to t. The model PC assumes the principal and interest of the bills is paid at maturity (This is not like the real world where government bills often have periodic coupon payments during the life of the bill). The payoff from holding the bills at t is dependent on the interest rate at t_-1.

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.

• · YD = Y – T + r_-1 . B_h-1 (4.2)

• · T = Θ . (Y + r_-1 . B_h-1) (4.3)

The interest received from the bills is added to the households’ disposable income (4.2) and the government taxes the interest received as it is added to the income of the household. (4.3)

The households have to make a portfolio choice decision. Firstly, they must decide how much income to consume and save. From SIM, the households’ propensity to consume could be used to measure this. Then they must decide to allocate their savings to bills or cash holdings.

• · V = V_-1 + (YD – C) (4.4)

• · C = α₁ . YD + α₂ . V_-1 0 < α₂ < α₁ < style=""> (4.5)

In the model PC the wealth of households is a function of their wealth in the previous period plus disposable income (minus consumption). (4.4) SIM, wealth of households was just their stock of money. This can also true for the consumption function. (4.5)

Households hold a proportion of their wealth in money (1 – λ₀) and a proportion of their wealth in bills (λ₀). These sum to unity, therefore the amount of bills purchased by the household, will define the exact amount of wealth the household will retain in the form of money.

• · H_h/V = (1 – λ₀) – λ₁ . r + λ₂ . (YD/V) (4.6A)
• · B_h/V = λ₀ + λ₁ . r - λ₂ . (YD/V) (4.7)

Disposable income is positively related to money and negatively related to bills. Interest rates are positively related to bills and negatively related to money as interest is not paid on money held at the central bank.

Equation 4.6A is dropped for equation 4.6 which defines the money held by the household as the wealth not spent on bills. This means the households’ treat money as a residual.

• · H_h = V - B_h (4.6)
• · ∆B_s = B_s – B_s-1 = (G + r_-1 . B_s-1) – (T + r_-1 . B_cb-1) (4.8)
• · ∆H_s = H_s – H_s-1 = ∆B_cb (4.9)
• · B_cb = B_s - B_h (4.10)
• · r = ȓ (4.11)

Equation 4.8 describes the government budget constraint.

Equation 4.9 describes the capital account of the central bank.

Equations 4.10 and 4.11 explain how the demand for bills by the central bank is determined. The central bank purchases the government bills not bought by the households at the given interest rate. 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. If the interest rate varies over time, it would no longer be treated as an exogenous variable. The demand for bills by the central bank would be treated as exogenous instead.

Question 2

1. How does Keynes define liquidity preference?

“... [liquidity preference] is given by 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”

In this case when with regard to liquidity preference, Keynes is trying to determine whether or not the individual will retain money for future consumption by holding that money in cash and risk-free form or is the individual willing to give up that current liquidity and invest in illiquid assets in order to earn a given interest rate r. The interest rate r is the compensation received by the investor for parting with that immediate liquidity and holding less of his/her stock of wealth in cash form.

Keynes' stated that the public holds money for three distinct purposes:

1. Transaction motive: people have a need for cash for current transactions. This may be for personal or business transactions.
2. Precautionary motive: this is the desire for security and the holding of cash for extraordinary situations e.g. Sickness.
3. Speculative motive: this is the opportunity to take advantage of a profit making opportunity.

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

It would seem that the PC model is a faithful representation of Keynes’ original vision of household decision making. This is true for a number of reasons:

• · The PC model encompasses the 3 divisions of liquidity preference that Keynes discusses, namely; the transactions motive, the precautionary motive and the speculative motive.

• · Further to this, the PC decision has two steps:

1. Households make a decision regarding their propensity to consume, i.e. they decide what proportion of their disposable income they will consume.

2. The remainder of the disposable income that is not spent is allocated to savings. Therefore a decision is made whether or not to keep these savings in cash form or alternative assets. Keynes’ also discusses the allocation of savings (see Question 2.1).

• · The PC model distinguishes between disposable income and consumption. This idea is also inherent in Keynes’ writings.

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

• · Also in both models, the quantity of money held depends on the rate of interest that can be obtained on other assets.

Furthermore, the PC model assumes that the money supply is endogenous and demand-led with the interest rate r being exogenous

An interesting take on the sub-prime mortgage crisis:

"It turned out that the smartest guys in the world weren’t as smart as they thought!

In developing the collateralised loan obligation, they hadn’t developed the goose that laid the golden egg. It turned out they’d developed the financial equivalent of an infectious haemorrhoid!"

(How Banks Bet Your Money - Dispatches)

Lecture 4 Assignment

1. A change in interest rate on bonds from 0.07 to 0.1. What effect does this have in u-vh space?

As is evident from the graphical representations below; capital output decreases only slightly more than when in its original state. Correspondingly however, it increases at a faster rate in the long term when shocked.

The value of households also has a similar outcome. The value of the household begins at a lower figure but increases steadily to over double the value of the non-shocked state.

2. Show a change in the value of α from 0.3 to 0.7.

The shock in the accelerator effect impacts negatively on both output and the households values. The capital output increases initially but subsequently reduces slighlty to the constant value of 0.92.


The shock to the value of households is quite drastic as the household value quickly falls below 1.

Homework 3

Question 1

1. Explain the differences between SIM and SIMEX when both models are in their steady states.

The model SIM omits growth, with the steady state assuming that both the stocks and flows in the model change at the same rate and remain constant over time. The SIM model assumes:

· ΔH_h = YD – C = 0

· ΔH_g = G - T = 0

The SIM model assumes there is no change in the stock of money.

The government do not have a surplus or deficit as their expenditure is equal to the income they receive through taxation.

Household savings converge to zero as consumption must equal disposable income.

The SIM model is based on the assumption that consumers have perfect foresight and are completely certain of their future income. Wealth is the equilibrium mechanism in the SIM model.

This differs from the SIMEX model due to uncertainty. Consumers have to develop fixed expectations for their future disposable income.

• YD^e = YD_-1

The role of money is the equilibrium mechanism in the SIMEX model. The SIMEX model takes longer to converge to the steady state than the SIM model, but both equilibriums remain the same.

The SIMEX has four more equations to consider in its steady state in comparison to the SIM model. This is due to role of money in the SIMEX model and the fixed expectations of future disposable income rather than perfect foresight.

2. What does it mean for the stability of the model when the presence of mistakes allow household’s incomes suffer? Can you draw any conclusions about the real world from this model?

The stability of the model will remain intact when the presence of mistakes allow household’s incomes to suffer.

For example, if the household underestimates its disposable income in a given period, their savings will increase at a greater rate than expected if their expectations were met. The household will continually have fixed expectations towards disposable income and you use their stock of money as a buffer when expectations are not met. This process continues until expected disposable income equals actual disposable income:

• YD^e = YD

In a real world sense, if people continually underestimate their expected future disposable income, their wealth would grow faster than if they were correct in their expectations at every time period. If people continually overestimate their expected disposable income, their stock of wealth would fall considerably as they would have to use their savings to fund consumption.

3. Solve SIMEX for the following values for 3 periods: G = 30, α₁ = 0.6, α₂ = 0.4, Θ = 0.2.

Question 2

1. Is it possible to specify a version of SIM that replicates the ISLM model?

The version of SIM that replicates the ISLM model is that where

C = α₀ + (α₁ * YD) (1)

where; α₀ represents autonomous consumption, α₁ represents the marginal propensity to consume and YD is the disposable income.

This is so because ISLM is representative of that state which does not take account of stocks of money from previous periods.

2. Write one down and comment on the stability of this model.

First, we will look at the consumption function which is not stable in order to provide a more comprehensive explanation as to why equation (1) is stable.

C = α₁ * YD (2)

This model is not stable over time because it does not take account of cash money from previous periods. According to Godley and Lavoie (2007), this representation of the consumption function does not allow for growth in the model. In order for the model to be stable, there would have to be a “stock disequilibrium”, i.e. if income and consumption remain constant, then the money stock and government debt must be rising for ever (by an amount equal in each period to YD – C)

C = α₀ + (α₁ * YD)

α₀ represents autonomous consumption in this model, i.e. consumption that is independent of income. This consumption function is admissible as the constant term α₀ corrects for the problem in equation (2).

Homework 2

Q1.1. Why must the Vertical Columns sum to zero?

"The vertical columns must necessarily sum to zero, because the change in the amount of money held must always be equal to the difference between households' receipts and payments." (Godley & Lavoie, 2007: p.62)

Households for example, -ΔH_h = W.N_s-C_d-T_s

The household’s factor income is the total amount of money supplied to the household through the wage bill from supplying labour to the production element of the behavioural matrix. The government in turn demand taxes which is supplied by the household through income tax (-Ts). Households demands goods and services from the economy, they therefore use their income (minus taxes) to satisfy this demand.

The consumption of the household is therefore also deducted from their income (-C_d). That amount of money not consumed can be defined as the change in the money stock (ΔH_h). The vertical column must therefore equal zero.

Q1.2. Why must the horizontal Rows sum to zero?

"The matrix shows that every component of the transaction-flow matrix must have an equivalent component, or a sum of equivalent components, elsewhere." (Godley & Lavoie, 2007: p.60)

Every demand in the behavioural matrix can be fully satisfied by the supply in the economy. For example, producers supply the goods and services to the households and are able to satisfy their demand. It is assumed that if the households demand increases, the producers have the capacity to satisfy this demand instantaneously.

Total production (Y) is the only component which does not have an exact opposite in the matrix. This is due to the fact that it is not a transaction akin to the other components in the matrix.

Q2. Write out an explanation for each row.

1. Consumption: “sales are always equal to demand because it is assumed that inventories are always large enough to absorb any discrepancy between production and demand” (Godley and Lavoie, 2007: p.64). Consumption is that percentage of the household's income which is spent on purchasing the goods and services they demand that are supplied by the producers in the economy. The producers supply a level of goods and services that exactly offsets that demanded by the household.

2. Government Expenditure: The principle is the same as that of the consumption element of the transaction matrix in that the producers are supplying goods and services in return for payment. The difference is that the government is the recipient of the service in this case and this represents an outflow of money from the government.

3. Output: The output is the total production in the economy. "the sum of all expenditures on goods and services or [as] the sum of all payments of factor income"(Godley and Lavoie, 2007: p.61).

Y = C + G = WB

4. Factor Income: The producer pays the household a wage rate for employment services rendered. It is assumed that there is an unlimited amount of labour to satisfy demand and there is a willingness to work at the fixed wage rate.

5. Taxes: The income of the household is taxed at a rate -T_s. This in turn, is a source of income generated for the government in the amount +T_d which is used to fund government expenditure going forward.

6. Change in Money Stock: The change in the money stock represents changes from one period to the next resulting from the household not consuming all of their disposable income. When this happens and households have a surplus of money, they use this to purchase financial assets from the government.

References

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

2. Lavoie, M. (2001) “Endogenous Money in a Coherent Stock-Flow Framework” available: http://129.3.20.41/eps/mac/papers/0103/0103007.pdf [accessed 16 Feb 2008].

3. Leddin, A., and B. Walsh (2003) The Macroeconomy of the Eurozone: An Irish Perspective, Dublin: Gill and Macmillan.

Group 11 Members

KAREN WHELAN 0370673
MENGLAN DONG 0705012
MICHAEL BREEN 0229334