Homework

Q1 (1)

SIM
• Households know the multiplier process and the parameters of the economy – perfect knowledge.
• Wealth is the equilibrium mechanism.
• Quick convergence rate
• Consumption function: Cd = α1*YD + α2*H-1
SIMEX
• Slow convergence rate – delayed expectations, it takes longer to approach to a steady state solution.
• Introduces imperfect knowledge/uncertainty into the model.
• Households must estimate the income they will receive and the amount of money they wish to hold.
• Households are assumed to have mistaken expectations – if realized income > expected income they will hold the difference in the form of larger cash balances.
• Role of money is the equilibrium mechanism. Money acts as a buffer and provides flexibility when expectations turn out to be incorrect.
• Consumption function: Cd = α1*YDe + α2*H-1

Despite expectations both models achieve the same stationary state.

(2)

Steady state: Y*=G/ Θ
If households’ realized income is higher than expected (W.Nse – W.Nd), households will hold the difference in larger than expected cash balances ΔHs – ΔHd. They will give up more money in the form of taxes (Td – Tse).

Expectations about income will remain unchanged before and after a shock. If actual income is higher than expected, the increase in wealth will be higher than anticipated which will make consumption grow.

In the model, if expected income is lower than realized income, the stock of wealth will grow until the consumption lost through mistaken expectations about income equals the additional consumption out of wealth. Conversely, if expected income is less than realized income, the stock of wealth will fall.

In the real world, people have mistaken expectations and there is a high level of uncertainty particularity in times of recession where people may consume less and save more. When the economy begins to recover, people may then start to consume more than they save. This demonstrates the flexibility people have with their income.


(3)

In period one there is no economic activity and none has existed. The government has injected no money into the economy and households have no income.

In period two the government spends $30, which initiates the economy and circulates within the system.
• Producers pay households 30units of cash
• Households pay 20% in taxes (6 units => YDe=24)
• Households consumption: C = α1.YDe + α2.H-1 (0.6)(24)+(0.4)(0) = 14.4

In period three the government has not injected any extra money into the economy, therefore government expenditure remains at $30.
• Households consumption: C = α1.YDe + α2.H-1 (0.6)(35.52)+(0.4)(21.12) = 30
• Expected income = realized income YDe = YD-1

In the infinite period
• GDP (Y) = G/ Θ = 30/0.2 = 150 Fiscal stance: the stationary level of income
• Taxes 150*0.2 = 30

Question 2.

It is possible to specify a version of SIM that replicates the ISLM model


The IS Curve – Saving & Investment (Goods Market)
Examining the IS curve with the SIM model in mind, we make the assumption that supply must always equal demand. Therefore, the below income equation will fit for supply and demand.

Y = C(Y-T) + I(Y, i) + G

An increase in the supply, Y, would indicate that there is and excess supply of goods. To return this equation to equilibrium, an opposite reaction would have to take place such as a fall in interest rates, i.
The fall in interest rates would be used to encourage a rise in consumption as high interest rates encourage investors to save money due to the high expense of loans or the advantages of investing in bonds.
This relationship is best displayed in the IS curve graph diagram. It can be seen in the graph that as the interest rate (i2) is increased, the output (Y2) decreases i.e. output is a decreasing function of the interest rate.

Given the above equation, and a set interest rate, we can establish that changes in consumption and taxes will shift the IS curve to the left or the right to remain in equilibrium. This is evidenced in the diagram for an increase in taxes.



Increase in Taxes: IS shift left
Decrease in Taxes: IS shift right
Increase in Consumption: IS shift right
Decrease in Consumption: IS shift left

Y: Income
C(Y-T): Consumer spending as a function of disposable income
I(Y, i): Investment as a function of real interest rate
G: Government spending


The LM Curve – Financial Markets
The below equation fits for money supply equals money demand in the SIM model.

M/P = YL (i)

An increase in Y would lead to an increase in the demand for money by households. To maintain equilibrium, it would be necessary for an increase in interest rates to bring the level of demand back to that of supply. This is best illustrated in the diagram of the LM curve where the interest rates are raised to i2 to maintain equilibrium.

Additionally, if there was an increase in the money supply, a cut of interest rates would be required. This would cause the LM curve to shift down.

Increase in Money Supply: Cut in interest rates & shift down of LM curve
Decrease in Money Supply: Increase in interest rates & shift up of LM curve.

Y: Real income
P: Price level
I: Interest rate

The IS-LM Model and some function in SIM

For the IS-LM model, we take the two graphs and combine them. The point at where they meet is the point at which both models achieve equilibrium. The basic theory behind this model is that, as a factor of either model changes, say the IS model for example, the IS model will move up or down along the axis of the LM model to maintain equilibrium.

Td = θ. W.Ns θ<1

From the previous diagram, we can see what happens as taxes are increased. Disposable income is affected which leads to and affect on output, thus the IS curve shifts to the left. As there is no tax function in the LM model, the model is not affected.

However, the change in taxes will have caused a change (decrease) in the interest
rates, as a result of the decrease in income (Y), so the IS model will move along the LM curve to equilibrium. Similar results would show for changes in money supply and consumption.

Stability

We can see from this example that a change in one factor has a direct affect on the IS model to which it is a function of and an indirect impact on the LM model. This shows how difficult it is to use just one policy to have the desired affect on the overall economy (and of course SIM).

Td :Tax demand
W.Nd :Wage rate times employment demand
Θ: proportion of change

References
Macroeconomics, Blanchard. Chapter 5
Monetary Economics, Godley & Lavoie. Chapter 3
Wikipedia
Egiwald
Roubini & Backus
MIT (.pdf)

Here Comes Another Bubble!

Homework 2

Fill in the blanks.

1.1 Why must the vertical columns sum to zero?
The difference between the inflows of income and outflows of expenditure for each sector must match the sum of the transactions in stocks and financial assets.

For each sector the change in the amount of money held must equal the difference between the sector’s receipts and payments. For households, the change in their end of period holdings of cash must equal their wages minus taxes minus consumption. Similarly, government expenditure should equal the taxation supplied by households plus their end of period holdings of high powered money. It is assumed that producers hold no cash and therefore receipts from sales must equal their outlays on wages. This results in a zero sum rule for each column.

[Reference] Chapter 3, Monetary Economics, Godley & Lavoie

1.2 Why must the horizontal columns sum to zero?
In order to ensure that the horizontal rows sum to zero, the equalizing mechanisms must be specified. The fundamental economic principles of supply and demand help describe the behaviour of agents at the time of the transactions. In order for the horizontal rows to sum to zero four equations must be specified that imply whatever will be demanded will always be supplied in that period.

Cs = Cd Sales of consumption services will equal purchases of consumption services.

Gs = Gd Sales of government services will equal purchases of government services.

Ts = Td Taxes supplied will equal the taxes demanded.

Ns = Nd There is a reserve of unemployed workers willing to work at the going wage.

For sales to equal purchases we use the Keynesian quantity adjustment mechanism which states that production is flexible and producers produce what is demanded. This is the most suitable approach for a demand led economy without any supply constraints and will ensure all rows sum to zero.

For row 6 ∆Hh = ∆Hs

Under Keynesian economics investment = saving. In model SIM there is no investment therefore the saving of the overall economy equals zero. ∆Hs is the government’s fiscal deficit. The two terms are equal in order for overall saving to equal zero.

Total production is not a transaction between two sectors and therefore does not sum to zero. It is used in national accounts to denote the sum of expenditure on goods and services. Y = C + G

The equations have now been satisfied so that all rows, except output, sum to zero.

[Reference] Chapter 3, Monetary Economics, Godley & Lavoie

2.1. Consumption
Within the behavioural transaction matrix, consumption represents the purchase of goods by the household. The source of funds can come from current disposable income, YD, and from savings H[t-1]. Using the Keynesian quantity adjustment mechanism, the production sector will have a consumption of Cd which is exactly equal to Cs :

Cd = Cs

Note: the level of consumption demand has a direct link to the source of government revenue from the production sector and the level of employment.


2.2. Government Expenditure
This relates to the purchase of goods and services, Gd, and is used to provide essential facilities to the nation i.e. roads & schools. The source, Gs, of income is from "revenues collected by the production sector."[1]

Gd = Gs

[1] p.63 Monetary Economics, Godley & Lavoie

2.3. Output
Output is used to describe the end result in the production sector for the given period.
This can be used to measure the productivity of the nation. The measurement can be taken in the form of "the sum of all expenditure on goods and services (C + G)or, as the sum of all payments of factor income (WB)."[1]


[1] p.61 Monetary Economics, Godley & Lavoie

2.4. Factor Income
This refers to the flow of wages for services provided by the household for the production sector.
W.Ns = wage rate times the employment supplied by the household.
W.Nd = wage rate times the employment demanded by the production sector.

W.Ns = W.Nd; factor income rises and falls as the demand/supply for labour rises or falls in the production sector.

2.5. Taxes
A government use taxes as a source of money supply, Td, to enable it to influence the direction of the economy. In order to maintain a relatively steady flow of money, a “fixed proportion of money income”[1], θ, is levied as taxes. In the behavioural transaction matrix, the supply must equal demand;

Ts = Td.

Td = θ. W.Ns θ<1

[1] p.66 Monetary Economics, Godley & Lavoie




2.6. Change in Money Stock
The change in money stock relates to the supply that the government has as a result of income and expenditure. In real terms, this is usually a surplus or deficit. A deficit may occur due to the income from taxes, Td, not meeting the required government expenditure, Gd. This would lead to the government issuing debt in the form of treasury bonds to cover the excess.

In the behavioural transaction matrix, this deficit can be explained by households saving a proportion of their income to accumulate wealth. In theory, these savings should match the deficit.

Hh = Hs

Hh = YD - Cd

Hs = Gd - Td

Key to equations

Cs :Consumption supply
Cd :Consumption demand
Gs :Government supply
Gd :Government demand
Ts :Tax supply
Td :Tax demand
W.Ns :Wage rate times employment supply
W.Nd :Wage rate times employment demand
∆Hh :Change in cash held by households
∆Hs :Change in the supply of money
H[t-1] :Cash held from the previous period
Y :Total production
YD :Disposable income

Helicopter Ben

"In a speech in November 2002, early in his first stint with the Fed, Bernanke approvingly mentioned a Milton Friedman parable about how a "helicopter drop" of cash could push prices upward. It was simply an attempt to reassure then-skittish markets that the Fed had ways to stave off deflation, but the image of a man willing to dump bills out of helicopters stuck. In hard-money circles, Bernanke is still known as "Helicopter Ben.""
Article link.

Excercise 3

Q: What do you think will happen to the steady state value(s) of output when θ changes?
Why does this happen?

Eqn : Y* = G/θ
Y* = National Income in Nominal Terms
G = Pure Government Expenditure in Nominal Terms
θ = Personal Income Tax Rate

A : To maintain a steady state, the values of Y* and G must also change in the same direction at the same ratio.

If θ was to decrease, and both Y* and G were to remain the same, additional funds would have to be borrowed to maintain the level of G. This would result in a trade deficit.

If θ was to increase with both Y* and G remaining the same, there would be a surplus. In such an event, it is likely that the surplus would be used to enhance the incumbent governments standing by budget cuts that appeal to the masses.

Members

WEI.XIONG
HEATHER.FEENEY
CONOR.DIGGINS

Definitions

1. Aggregate Demand Relation

The aggregate demand relation captures the effect of the price level on output.

It is derived from the equilibrium conditions in the goods and financial markets.

Reference - (.ppt)

AD = (1/(1 - C1)) . (C0 + I + G - C1T)

AD = Aggregate demand

C0 = Consumption yesterday

C1 = Consumption today

I = Fixed investment

G = Pure government expenditure in nominal terms

T = Taxes

2. Animal Spirits

A spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities.

Reference - "The General Theory"

A possible example of this would be the era of the dot com bubble which saw investors & speculators rush to buy shares in technology companies (even companies with just a technological name). There was a confidence in the sector and market that was not justified by fundamentals.

3. Bank run

A situation in which a relatively large number of bank's customers attempt to withdraw their deposits in a relatively short period of time, usually within a day or two.

Reference

Click for an example of the share price plummet of Northern Rock during a bank run in 2007.

Picture of a bank run in the early 19th century.




4. Bond
A debt investment in which an investor loans money to an entity(corporate or governmental) that borrows the funds for a defined period of time at a fixed interest rate.

Reference.

An example of a bond would be a five year zero-coupon bond which might be worth €1,000,000 upon maturity. The entity would sell this type of bond to avoid having to pay coupons on a semi-annual basis and pay the full amount upon maturity so as to plough all its resources into the entities development.
The present price of the bond would be calculated as follows :

Z = M / ((1 + i)^n)

Zero-coupon bond price : Z
Value at maturity : M = 1,000,000
Yield required : i = 0.1 / 2 = 0.05
(taking i as if it was semi-annual)
Number of payments : n = 5 * 2 = 10
(taking it as though there would be semi-annual payments)

Z = €613,913

5. Capital Account
The net result of public and private international investments flowing in and out of a country.

The net results includes foreign direct investment, plus changes in holdings of stocks, bonds, loans, bank accounts and currencies.

Reference.

A prime example of foreign investment is that of the sovereign wealth funds taking stakes in financial companies in the US during the present market turbulence.

6. Debt to GDP Ratio
A measure of a country's federal debt in relation to its gross domestic product (GDP). It indicates the country's ability to pay back its debt.

Reference.

Ratio = (National Debt / GDP ) * 100


7. Effective Demand
The notion that the actual demand for aggregate output in the macroeconomy is based in the actual income or other existing economic conditions and not on income and conditions existing in equilibrium.

Reference.

8. Deflation
A decline in prices caused by a reduction in the supply of money or credit. It can also be caused by a reduction in government, personal or investment spending. Used by Classical economists to refer to a decrease in the money supply.

Reference.


Example: Japan CPI

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
3.3% 1.7% 1.3% 0.6% -0.1% 0.1% 1.8% 0.6% -0.3% -0.7% -0.7%

Reference.

9. Consumption function:
The amount of total consumption in an economy. It is made up of induced consumption and autonomous consumption. Its slope is the marginal propensity to consume and is assumed to be positive. It explains how consumption expenditures depend on the level of income.

C = co + c1*Yd

C = Consumer expenditure
co = autonomous consumption
c1 = marginal propensity to consumeYd = disposable income

Reference.

Example:

If a person’s expected income increased by €2000 and their consumption then increased by €1,600, then their mpc would be 0.8.




10. Consumer price index
Measures the percentage change in the average level of prices paid for consumer goods and services by all households and visitors to a country. It is the official measure of inflation in Ireland. It does not explain the actual price level.

Reference.

Example: Price of bread

December 2001 = base period

Dec 2001 - 100.0
Jan 2002 - 100.0
Dec 2002 - 105.4 (Source: Central Statistics Office, Ireland)

105.4
100.0 x 100 = 105.4 – 100 = 5.4%

The price of bread increased by 5.4%

11. Investment function
A model of income and interest rates. An increase in income promotes higher investment, while an increase in the interest rate may discourage investment. I = f(Y, r).

Reference.

Example: ECB interest rates:

Nov2001 Dec2002 Jun2003 Dec2005
3.25% 2.75% 2% 2.25%
Average weekly earnings of industrial workers Ireland €:

2001 2002 2003 2004 2005
512.38 538.38 564.9 588.92 609.91


From 1996-2005 Irish housing prices rose 270% due to unprecedented low interest rates and corresponding rising incomes.

Reference.

12. Fiscal Expansion
It is an increase in government spending or a decrease in taxation or a combination of both in an effort to change the direction of the economy. This will lead to a larger budget deficit or smaller budget surplus. The aggregate demand curve shifts right, real GNP increases and unemployment decreases.

Example:




13. GDP Deflator
A measure of the changes in the prices of all new, domestically produced, final goods and services in an economy. It is used to calculate real GDP. Changes in consumption patterns or the introduction of new goods and services are automatically reflected in the deflator.

Reference.

Example:

GDP Deflator – 1996=100



Reference.

14. Imports
Goods or commodities brought into one country from another country for use in trade. Inhibits the competitiveness of a country’s domestic products and services. A country will experience a trade deficit if imports exceed exports.

Example:

Ireland has experienced a trade surplus from 1996-2006. Exports have exceeded imports.


(Source: Central Statistics Office, Ireland)

15. Monetary Contraction
Contractionary monetary policy is monetary policy that seeks to reduce the size of the money supply. In most nations, monetary policy is controlled by either a central bank or finance ministry.

Reference.

16. Nominal GDP
Nominal GDP is a gross domestic product (GDP) figure that has not been adjusted for inflation.

GDP = consumption + gross investment + government spending + (exports - imports)
or,
GDP = C+I+G+(X-M)

Reference.

17. Propensity to Consume
In economics, the proportion of total income or of an increase in income that consumers tend to spend on goods and services rather than to save. The ratio of total consumption to total income is known as the average propensity to consume; an increase in consumption caused by an addition to income divided by that increase in income is known as the marginal propensity to consume.

APC = C/ (Y-T)

C = the amount spent
Y = pre-tax income
T = taxes

MPC = dC/dY

C = consumption
Y = disposable income

Reference 1.

18. Short Run
In economics, the concept of the short run refers to the decision-making time frame of a firm in which at least one factor of production is fixed. Costs which are fixed in the short-run have no impact on a firm's decisions.

Land : Fixed factor of production. A farmer can change the amount of capital or labout very easily. He can't change the amount of land owned. The length of time it would take him to buy new land is an example of the short run.

Reference 1.
Reference 2.

19. Real Exchange Rate
The real exchange rate(RER) is defined as:

RER = e(P*/P)

P = Domestic price level
P* = foreign price level

P and P* must have the same arbitrary value in some chosen base year. Hence, in the base year, RER = e.

The RER between two countries is the product of the nominal exchange rate and the ratio of prices between the two countries. If the Irish price of a good was € and the same good was priced at $3.40 in the US and e = 3.6

1.36 * 3/3.4 = 1.2

Reference 1. (.pdf)
Reference 2.

20. Trade Surplus
A positive balance of trade i.e. exports exceed imports.
The opposite is a trade deficit.

Reference.
Ireland : trade surplus 2000-2006

Understand The Market?