MULTIPLIERSin Theory and Practice

David A. Anderson

Centre College

AGENDA Multipliers in Depth

Colleges want itTeachers want itStudents want us to have it It provides roots for better understanding

Delivery Active LearningTheoryApplicationsPractice

FOR MORE DEPTH

Anderson, D. (1997), “The Multiplier Effect,” An Encyclopedia of Keynesian Economics, ed. Thomas Cate, Cheltenham, UK: Edward Elgar 450-453.

Kahn, R. (1931), “The Relation of Home Investment to Unemployment,” The Economic Journal 41:162 173-198.

Jeong J. Rhee and John A. Miranowksi (1983), “Determination of Income, Production, and Employment Under Pollution Control: An Input-Output Approach,” The Review of Economics and Statistics 66 146-150.

Clark, Colin M. (1938), “Determination of the Multiplier from National Income Statistics,” The Economic Journal 48:191 435-48.

Keynes, John M. (1973), The Collected Writings of John Maynard Keynes (30 vols.), ed. Donald Moggridge, London: Cambridge University Press.

THE BANKING MULTIPLIERSEEING IS BELIEVING

Required Reserve Ratio = 20%

We start with 100 Pennies

MONEY CREATION IN ACTIONDeposit Required Reserves Loan100 20 8080 16 6464 13 5151 10 4141 8 3333 7 2626 5 2121 4 1717 4 1313 2 1111 2 99 2 77 2 55 1 44 1 33 1 22 1 11 1 0Total ≈ 500 Total ≈ 100 Total ≈ 400

WHAT IF THE 1ST DEPOSIT WASN’T NEW MONEY?

Deposit Required Reserves Loan100 20 8080 16 6464 13 5151 10 4141 8 3333 7 2626 5 2121 4 1717 4 1313 2 1111 2 99 2 77 2 55 1 44 1 33 1 22 1 11 1 0Total ≈ 500 400 Total ≈ 100 Total ≈ 400

WHAT IF BANKS HOLD EXCESS RESERVES?OR THE RESERVE REQUIREMENT IS HIGHER?

Deposit Reserves = 40% Loan100 40 6060 24 3636 14 2222 9 1313 5 88 3 55 2 33 1 22 1 11 1 0Total ≈ 250 Total ≈ 100 Total ≈ 150

THE BANKING (MONEY) MULTIPLIER

= 1/Reserve Requirement = 1/0.2 = 5

It tells us the total increase in the money supply created from a deposit of $1 of new money IF banks hold no excess reserves and borrowers deposit all of their money in banks.

THE BANKING (MONEY) MULTIPLIER

= 1/Reserve Requirement = 1/0.2 = 5

5 × 100 = 500

Our exercise proves the result!

The Multiplier

The Initial Deposit

The Total

Increase in the Money Supply

THEORY AND APPLICATIONS

Kahn, Richard. (1931), “The Relation of Home Investment to Unemployment,” The Economic Journal 41:162 173-198.

The Employment Multiplier

The number of jobs ultimately created as the result of each new position.

“[The multiplier indicates] the cumulative effect of increased additional individual incomes because the expenditure of these incomes improves the incomes of a further set of recipients and so on.”

THEORY AND APPLICATIONS

John Maynard Keynes

Leakage: Money Held as Reserves

The Banking Multiplier

Leakages: Savings, Taxes, and Expenditure Elsewhere

The Spending Multiplier

Keynes referred to an investment multiplier, k, the ratio of an increase in real income to the increase in aggregate investment that caused it.

Suppose when $100 is spent, $25 of the resulting income (25%) leaks into savings (or taxes or imports). The other 75%, $75 is re-spent. Of that $75, 75% or $56.25 is again re-spent. That is, .75 × .75 × $100 = $56.25. …

Call the initial spending S.The fraction re-spent is m. After S is spent, m × S is re-spent. Of that, m × m × S is re-spent.

DERIVING THE MULTIPLIER

The ultimate change in income and output, ΔQ, is

ΔQ = S + mS + m2S + m3S + … + mnS (1)

where n is the is the number of the last round that produces a nonzero income increment.

DERIVING THE MULTIPLIER

Multiplying both sides by –m

-mΔQ = -mS - m2S - m3S - m4S - … - mn+1S (2)

Add equations (1) and (2):

ΔQ = S + mS + m2S + m3S + … + mnS (1)-mΔQ = -mS - m2S - m3S - … - mnS - mn+1S (2)

DERIVING THE MULTIPLIER

Add equations (1) and (2), noting that mn+1S = 0, yields

ΔQ = S + mS + m2S + m3S + … + mnS (1)-mΔQ = -mS - m2S - m3S - … - mnS - mn+1S (2)

(1 - m)ΔQ = S

or equivalently,

ΔQ = S / (1 - m)

ΔQ = S / (1 - m)

= S × 1 / (1 – m)

= S × 1 / Leakage

= S × Multiplier

Multiplier = 1 / Leakage

Multiplier = 1 / Leakage

Banking Multiplier = 1 / Reserve Requirement

Simple Spending Multiplier = 1 / Marginal Propensity to Save

Keynes:• No crowding out • Horizontal AS

Full multiplier effect.

This led him to advocate adjustments in G to help control Real GDP.

BALANCED BUDGET MULTIPLIER

The spending multiplier when taxes and government spending increase by the same amount.

BALANCED BUDGET MULTIPLIER

Consider $1 that is taxed and spent.

The $1 increase in spending eventually increases income by k. The $1 increase in taxes cuts spending, initially by m (the fraction of each dollar that is spent), and ultimately by -mk.

The combined effect is k - mk = k(1-m) = [1/(1-m)](1-m) = 1.

OTHER SIMILAR MULTIPLIERS

Foreign trade multiplier (change in AD is in the form of net exports)

Government spending multiplier (change in AD is change in government purchases).

LESS SIMILAR MULTIPLIERS

Jeong J. Rhee and John A. Miranowksi (1983) describe a pollution control multiplier

Total Reduction / Initial Reduction = 1 / % Reduction

IN PRACTICE

MULTIPLIERS IN PRACTICE

THE DATA

1048 Employees

$39.8 million in Direct Expenditures

$1.3 million in Visitor Expenditures

THE MULTIPLIER?

Study Multiplier

Indiana University of Pennsylvania, Indiana County, PN 2.31

Xavier University, Cincinnati 2.16

Shadyside Hospital, Allegheny County, PN 1.60

Toyota Motor Manufacturing, U.S.A 2.32

Consolidated Health Systems 2.00

Department of Commerce Estimate for Kentucky Health

Services

2.20

Centre College 3.50

Average 2.30

THE MULTIPLIER?

Figure 3Locations of Spending by Associates

Boyle, $15,882,440

Casey, $2,167,959

Garrard, $997,664

Lincoln, $2,229,041

Mercer, $2,850,036

Washington, $188,335

Other, $1,771,362

Leakages:

Federal Taxes: 24% (average not marginal)Savings: 21% of after-tax incomeSpending Elsewhere: 7% of after-tax income

THE MULTIPLIER?

Taxes = $24 Savings = (.21)($76) = $15.96

“Imports” = (.07)($76) = $5.32

$54.72 spent locally

THE MULTIPLIER?

1 1 1Multiplier = 2.21

% leakage 1 - % spent locally 1 .5472= = =

-

(I used 2 to be conservative)

THE RESULTSDirect Indirect Total

Local Expenditures in DollarsEMRMC Associates 24,315,513 24,315,513 48,631,025EMRMC - All Other Expenses 2,445,133 2,445,133 4,890,267Physicians’ Offices* - Payroll 11,710,196 11,710,196 23,420,393Physicians’ Offices* - Office Space 1,296,429 1,296,429 2,592,858Visitors’ Local Expenditures 924,310 924,310 1,848,620Gift Purchases 407,948 407,948 815,896Total 41,099,529 41,099,529 $82,199,058

Employment in FTE PositionsEMRMC 1048 1572 2620Physicians’ Offices* 497 745 1242Total 3,862 Jobs

Charity Donations in DollarsValue of Charity Care 5,665,086Donations by EMRMC Associates 1,458,887Donations by Physicians* 558,699Total $7,682,672

Volunteer Work in HoursHours of Volunteer Work by EMRMC Associates

41,377

Hours of Volunteer Work by Physicians* 17,144Total 58,521

Hours * Only those who would not be here if it were not for EMRMC.

MULTIPLIERS IN PRACTICE

AMENITIES125-ACRE PARK

WALKING, JOGGING, AND BIKING TRAILS

PICNIC AREAS

PLAYGROUND AREAS

BASEBALL

SOFTBALL

FOOTBALL

SOCCER FIELDS

BASKETBALL COURTS

LARGE POND

AMPHITHEATER

MULTI-PURPOSE BUILDING

BMX COURSE

Possible future GYMNASIUM and AQUATIC CENTER

COSTS

Development: $7.3 million dollars.

Optional gymnasium and aquatic center: $3.3 million.

Annual operating costs: $350,000

Total for future: $8.75 million.

Development and Operation Total: $16 million

Also

Noise

Light

Parking

Traffic

DIRECT BENEFITS

Value to Visitors

$3.00 per visit

950 (summer) / 50 (winter) visitors per day

237,000 total visits

$711,000 annual benefits

Total: $17.8 million

DIRECT BENEFITS

Additions to Commerce

15% day visitors or retained flee-ers

1 in 200 stay overnight

Kentucky Department of Travel Estimates:

$35.87 per day

$95.26 for overnight

(gas, meals, shopping, snacks, attractions, lodging, etc.)

35,550 day visitors

1,185 overnight visitors

1.4 million direct annual dollars

Total direct: $34.7 million

HERE COMES THE MULTIPLIER

Total direct = $34.7 million

If half of expenditures are spent locally, the

multiplier is _______

Total Increased Spending = $69.4 million

Value to visitors = $17.8 million

Total Benefit = $87.2 million

Total Cost = $16 million

BUILD!

NOTE ADDITIONAL BENEFITS

Additional Benefits

Attract and retain valued workers and community members

Avoid brain drain

Green Space