# Slide 1 - Moody's Math Challenge

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```					 Moody's M3 Challenge:
Modeling the Stimulus Plan

STAPLES HIGH SCHOOL, TEAM #143
KYLE BEATTY, JASON GANDELMAN, JUSTIN SHERMAN,
NAVEEN MURALI, JONATHAN CHOI
American Recovery and Reinvestment Act

 \$787 billion stimulus package
 More disposable income  consumer spending 
more employment
 Goal: 3 million jobs by 2010 end
Problem

1. Which elements of this \$787 billion package are
most likely to produce the greatest improvements
in employment?
2. How quickly can they be expected to produce
results?
3. There is considerable discussion about a second
stimulus package. If it is needed, how large should
it be, and how should it be structured?
Assumptions

1. All multipliers & MPC are constant with time

2. Population is constant during 11 years.

3. GDP deflator is constant for base year of 2000

4. There is no lag effect between spending, GDP, &
employment
Categorization

 Title I – Agriculture, Rural Development, Food and Drug Administration,
and Related Agencies
   Title II – Commerce, Justice, Science and Related Agencies
   Title III – Department of Defense
   Title IV – Energy and Water Development
   Title V – Financial Services and General Government
   Title VI – Homeland Security
   Title VII – Interior, Environment, and Related Agencies
   Title VIII – Departments of Labor, Health and Human Services, and
Education, and Related Agencies
   Title IX – Legislative Branch
   Title X – Military Construction and Veterans Affairs and Related Agencies
   Title XI – State, Foreign Operations and Related Programs
   Title XII – Transportations and Housing and Urban Development
   Title XIV – State Fiscal Stabilization Fund
Planning our Approach

Spending: ARRA

?
GDP

?
Employment Rate
Connecting GDP to Employment

Change in Employment Rates vs. Change in Real GDP per capita (Base year 2000)
3.00%
y = 0.4222x - 0.0091
R² = 0.7733
2.00%
% Change in Employment Rate

1.00%

0.00%
-4.00%         -2.00%            0.00%           2.00%           4.00%            6.00%   8.00%

-1.00%

-2.00%

-3.00%

-4.00%
% Change in Real GDP per Cap.
Keynesian Economics: Multiplier Effect

 Multiplier Effect: increase in government spending
creates multiplied increase in GDP
 Why this works:
   Marginal propensity to consume (MPC): fraction of every \$1
received that is used for consumption
Spending Round   Spending        Consumption =     Cumulative GDP
(MPC)(Spending)   Effect

Round 1          \$100            100*.8 = \$80      \$100
Round 2          \$80             80*.8 = \$64       \$180
Round 3          \$64             64*.8 = \$51       \$244
Round 4          \$51                               \$295
Round ∞                                            \$500
Infinite Geometric Series

Multiplier Effect Can be Modeled by an Infinite Geometric Series


1
Multiplier   MPC                       n

n0     1  MPC
Applying Geometric Series Model

 According to Council of Economic Advisors and
Office of the Vice President-Elect:
   Tax Relief multiplier: 0.98
   Infrastructure government spending multiplier: 1.75
   Non-infrastructure government spending multiplier: 1.30
 Multipliers were maximized after 8 quarters
 Length of a spending round is approximately one quarter
Calculating MPC

Non                     8                    
1
infrastructure   1.30   MPC n   MPC n                    MPC  0.231
n0                 n0       1  MPC
8                    
1
Infrastructure   1.75   MPC   MPC 
n
 MPC  0.429
n

n0     n0     1  MPC
8              
1
Tax Relief       0.98   MPC  MPC n 
n
 MPC  MPC  0.495
n 1           n 1       1  MPC
MPCs in Categorization

 6 Categories of ARRA
1.   Tax Cuts Uses Tax Cut MPC = 0.495
2.   Aid for State and Local Governments Uses Non Infrastructure MPC
3.   Relief                                              = 0.231
4.   Infrastructure Spending Uses Infrastructure MPC = 0.429
5.   Energy Efficiency
Uses Non Infrastructure MPC = 0.231
6.   Human Capital
Single GDP Multiplication

x
(1  MPC x )
G(x)   a(MPC)n  a
n0            1  MPC
Multiple Spending Installments

C(x)  G (x)  G (x)      Gy (x)
0
Linear Conversion Factor: 0.422 1
Percent Change in Employment Rate
Number of in Real GDP or Capita
Percent ChangeJobs Created perSaved
Cumulative Benefit to GDP

x x    x
(1 MPC x  4 )
(1  MPC x 4 y
y (x) )    MPC
(1 MPC )
x 0  y (MPC         n4
GG1 (G( x) aa1 (a0 ( MPC)))aa0
n 4 y n
a1
n n  4 n  0
4y
y
1  MPC
1  MPC
MPC
Jobs Created/Saved Through Tax Relief
Jobs Created/Saved Through Infrastructure
Spending
Jobs Created/Saved Through Non-Infrastructure
Spending

700

600
Jobs Created/Saved (Thousands)

500

400

300

200

100

0
0   5          10       15            20            25            30             35        40   45
Fiscal Quarters

Human Capital   Aid for State & Local Gov        Relief        Energy Efficiency
Effectiveness of Different Spending

 Tax cuts
 Very inefficient (Multiplier=0.98)

 Large amount of spending

 Infrastructure
 Most efficient (Multiplier: 1.75)

 Low amount of spending
Total Effectiveness

2010
Second Stimulus?

Government Spending       Will not meet goal (3
million jobs by 2010): only
2.26 million jobs created
GDP                  by 2010
 0.74 million jobs must be
saved
Employment Rate          \$176.2 billion would have

Number of Jobs
Second Stimulus Plan

 Goal: to achieve required GDP increase with least
amount of Government Spending

 Spending Priorities:

1.   Infrastructure Spending (Multiplier=1.75)   Maximum Possible Spending

2. Non-Infrastructure Spending      Maximum Possible Spending
(Multiplier=1.30)

3. Tax Cuts (Multiplier=0.98)     Leftover
Second Stimulus Plan

 Finite amounts of Infrastructure & Non-Infrastructure
spending possible
 Maximum spending must be determined by Congress

Hypothetical Second Stimulus Plan
Spending Type             Amount         Effect on GDP
Infrastructure       \$17.2 billion     \$30.1 billion
Non-infrastructure   \$73.4 billion     \$95.5 billion
Tax Cuts             \$51.6 billion     \$50.6 billion
Total                \$142.3 billion    \$176.2 billion
Conclusion

 After 11 years, total 3.61 million jobs created/saved
 Tremendous tax relief leads to greatest job creation
(1.16 million)
 Most efficient job creation: Infrastructure spending
(1.75 multiplier)
 Will not meet President Obama’s goal (3 million jobs
by 2010): only 2.26 million created
 Need 2nd stimulus plan: between \$100 billion and
References

1.    http://www.recovery.gov/?q=content/our-mission
2.    http://otrans.3cdn.net/ee40602f9a7d8172b8_ozm6bt5oi.pdf
3.    http://www.measuringworth.org/usgdp/
4.    http://data.bls.gov/PDQ/servlet/SurveyOutputServlet?data_tool=latest_numbers&series
_id=LNS14000000
5.    Bade, Robin. Foundation of Economics: AP Edition. Pages: 770
7.    The Job Impact of the American Recovery and Reinvestment Plan - Romer, Bernstein
8.    http://kennebecjournal.mainetoday.com/view/columns/4738602.html
9.    http://www.washingtonpost.com/wp-
dyn/content/graphic/2009/02/01/GR2009020100154.html
10.   http://www.bea.gov/newsreleases/national/pi/pinewsrelease.htm
11.   http://www.usnews.com/articles/opinion/2008/12/31/us-population-2009-305-
Tax Multiplier

 First round does not contribute to GDP
 Tax Multiplier = MPC / (1-MPC)

Spending Round   Spending      Consumption =     Cumulative GDP
(MPC)(Spending)   Effect

Round 1          \$100          \$0                \$0
Round 2          \$100          100*.8 = \$80      \$80
Round 3          \$80           80*.8 = \$64       \$144
Round 4          \$64           64*.8 = \$51       \$208
Round ∞                                          \$400
Why doesn’t the intercept matter?

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