Blogwork 5---Modifying the PCEX Model to accommodate the possibility of stagflation in the economy

Stagflation

Stagflation is thought to occur when there is an adverse supply shock (a sudden increase in the price of oil or a new tax, for example) that causes a subsequent jump in the “cost” of goods and services (often at the wholesale level). In technical terms, this results in contraction or negative shift in an economy's aggregate supply curve. Stagflation results when economic growth is inhibited by a restricted supply raw materials. That is, when the actual or relative supply of basic materials (fossil fuels (energy), minerals, agricultural land in production, timber, etc.) decreases and/or cannot be increased fast enough in response to rising or continuing demand. The resource shortage can be caused either by an actual physical shortage of a resource or because other factors such as taxes or bad monetary policy have affected the “cost” or availability of raw materials and created a “relative scarcity” of resources. This is consistent with the “cost-push” inflation factors in neo-Keynesian theory.

Below is the PC Model where the circular flow approach to money and the stock approach are combined. While the PC model is not suitable for simulation the event of stagflation, it can assist in establishing how policy can be modified to deal with the event. Analysing the PC Model with expectations provides a way to study the possible effects of stagflation.

PC Model



PCEX Model

Y = C + G (4.1)

In stagflation times then Ywill remain the same, or decrease. Government Expenditures remain the same or decrease in stagflation times; however the government must try to battle stagflation maintain or increase Y.

YD = Y – T + r-1 . Bh-1 (4.2)

Stagflation is a period of inflation combined with stagnation. The disposable income of households remains the same or decreases marginally.

T = Ø . (Y + r-1 . Bh-1) (4.3)

The personal income tax rate remains the same but if Y and r-1 decrease and Bh-1 increase, taxes fall.

V = V-1 + (YD – C) (4.4)

The wealth of households will remain the same or decrease as consumers start to save in stagflation times. However consumers have to spend more for domestic products, i.e. groceries, since inflation rises C (consumption) increases. Therefore less wealth is saved in the present period and so less wealth saved overall.

C = α1 . YDe + α2 . V-1 (4.5E)

The consumption during stagflation will increase since inflation rises in stagflation - the consumer has to spend more for to get the same amount of goods as before.

Hh = V - Bh (4.6)

The money held by households will be the same or less since households invest more in Treasury bills since they benefit from higher interest rates. However a liquidity trap may arise if the interest rates are so low that there is no difference between household cash and household bonds e.g. treasury bills.

Bh/Ve = λ0 + λ1 . r - λ2 . (YDe/Ve) (4.7E)

The amount held in bonds depends on the marginal propensity to consume, the marginal propensity to consume out of regular income and the marginal propensity to consume out of past wealth (λ0, λ1 and λ2). Due to stagflation the proportion to consume out of past wealth and regular income will rise due to inflation and decreasing interest rates.

∆Bs = Bs – Bs-1 = (G + r-1 . Bs-1) – (T + r-1 . Bcb-1) (4.8)

This equation describes the government budget constraint, which is an identity illustrated by column 3 as shown in the PC model above. The equation simply says that the government deficit is financed by bills newly issued by the Treasury department (over and above bills which are renewed as they mature). The first term (G + r-1 . Bs-1) represents the total outlays of the government expenditures on services, purchased from the production sector and interest payments that must be made on the overall outstanding debt. The second term of the equation (T + r-1 . Bcb-1) represents the revenues of the government: its income tax revenue, and the profits which it receives from the central bank. Government expenditure will increase as many households invested in bonds while tax revenue will decrease so as to remain a growing economy to battle stagflation.

∆Hs = Hs – Hs-1 = ∆Bcb (4.9)

This equation describes the capital account of the central bank, as given in column 4 of the PC Model above. The additions of the stock of high powered money ∆Hs is equal to the additions in the demand for bills by the central bank ∆Bcb. The government issues bills to cover debt and so the amount issued in bills will be equivalent to the amount of money placed to cover all bills.

Bcb = Bs - Bh (4.10)

The demand for bills by the central bank is determined. The central bank is the residual purchaser of bills: it purchases all the bills issued by the government that households are not willing to hold given the interest rate. At present, this will be very small since mostly all households would have purchased the bills since they would be giving a greater interest rate than the nominal interest in the bank.

Hd = Ve - Bd (4.13)

This equation simply says that the money holdings are the discrepancy between the total household wealth and the demand for bills by households.

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

Total expected wealth accumulated depends on the expected current income and wealth accumulated in the previous period. During stagflation expectations will probably be never right as it is difficult to determine income in times of constant rising inflation and a stagnant economy. Therefore the expected wealth accumulated will be small due to rising inflation, and so very little income generated to save.

Bh = Bd (4.15)
Households invest in bills on the basis of their expectations with respect to disposable income that were made at the beginning of the period. The amount of bills held by households at the end of the period is exactly the same as the amount of bills demanded by households at the beginning of the period. Since interest rates are falling, there will be a hugh demand by households to invest their savings in bills. Also during stagflation the best households can do to battle this is through saving, so as to be prepared in hard times.

An Adverse Supply Shock
Below is an example of an adverse supply shock like a sudden doubling of the world price of oil, hits an economy and the dilemma of stagflation. Firstly here is the simple aggregate supply and demand curve given the potential output and the expected price level.

Such an adverse supply shock moves the economy up and to the left on the AS – AD diagram.

If the central bank wants to keep the supply shock from causing a recession, it increases the money supply and so pushes the aggregate demand curve up and to the right. Therefore it keeps production at a new equilibrium equal to potential output.

However increasing the money supply and pushing the aggregate demand curve up and to the right allows the price level to jump and inflation to accelerate.

If the central bank wants to keep inflation from accelerating in response to the supply shock, it must contract the money supply, raise interest rates and so shift the aggregate demand curve down and to the left (Bradford DeLong, 1998).

Although, trying to keep inflation from accelerating at the price of sharp fall in output, a deep recession and high unemployment is then likely.

Neither alternative is attractive. Being a central banker in a time of adverse supply shocks is not much fun.

Stagflation occurs when the economy isn’t growing but prices are, which is not a good situation for a country to be in (Investopedia ULC, 2008). The economy will first try to maintain momentum - that is, consumers and businesses will begin paying higher prices in order to maintain their current level of demand. The central bank may exacerbate this by increasing the money supply in an effort to combat a recession, for example by lowering interest rates. The increased money supply props up the demand for goods and services when it would normally drop during a recession. The solution to stagflation is to restore the supply of materials. In the case of a physical scarcity, stagflation is mitigated either by finding a replacement for the missing resource(s) or by developing ways to increase economic productivity and energy efficiency so that you can produce more with less input.
If the resource scarcity is being caused by flawed market intervention (i.e., bad government, etc.) then the solution is to eliminate the disrupting force on the market (e.g., better monetary policy, changes in tax laws) (Wikipedia, 2008).

The real factors that determine output and unemployment affect the aggregate supply curve only. The nominal factors that determine inflation affect the aggregate demand curve only. When some adverse changes in real factors are shifting the aggregate supply curve left at the same time that unwise monetary policies are shifting the aggregate demand curve right, the result is stagflation. Therefore so as to adjust to stagflation one must create a balance between the aggregate supply and aggregate demand so that the economy is neither in a recession or in stagflation. Therefore by modifying the PCEX model as discussed above and the simulation of a sudden shock to the system such as a double increase in oil, one can accommodate for the possibility of stagflation. The recessionary situation is exacerbated when a central bank expands the money supply as a means of fighting the recession - for example by lowering interest rates. The economy borrows more money to pay for defaults in loans and rise of oil but because oil is a non renewable resource and that it is very scrace, oil prices rise still further but only over the short-run (Wikipedia, 2008).

The economy must firstly restore the supply of materials, find a replacement for the missing resources, for example oil, and develop new ways to increase productivity and energy efficiency so as to produce more with less input so as to accommodate the possibility of stagflation. The economy must have better monetary policies and changes in the tax laws. If the economy increases government expenditure by enhancing skills in the workplace, the economy will start to boom by been more efficient, creating more exports and less unemployment and so the aggregate supply curve will move down and to the right. Furthermore being more efficient in the workplace creates cheaper output which contains only value added and not at the price of the inclusion of non value added. Therefore supplies will increase along with competition since been more skillful than other countries and so the aggregate demand will move down and to the right and so inflation will drop. If the aggregate demand moved down and to the left it would be in a recession.

Due to the subprime mortgage crisis, many banks and finacial service institutions are writing off huge amounts of debt since many loans are defaulting rapidly. To restore the money back in the economy that the banks have lost, banks must increase production by selling more products yet these products have to be to an extent riskfree, by taking on the correct client that has good credit ratings and will not default on their loans. Furthermore by increasing the sale of many of their products, they must take on more employees and decrease the price of their products, e.g. less interest paying rates, and so end the rise in inflation and stagflation. Governments must increase growth at the expense of giving grants to institutions to enhance workplace skills, i.e. skillnet, forfas and also decrease taxes. However at the expense of decreasing taxes, jobs in the government sector would be a concern.


References:

Bradford DeLong, J. (1998) “Supply Shocks: The Dilemma of Stagflation” [Online] available at: http://econ161.berkeley.edu/multimedia/ASAD1.html (accessed 20th March 2008)

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

Investopedia ULC. (2008) Stagflation [Online] available at:
http://www.investopedia.com/terms/s/stagflation.asp (accessed 20th March 2008)

Wikipedia (2008) Stagflation [online] available at: http://en.wikipedia.org/wiki/Stagflation (accessed 20th March 2008)

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