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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
                          to be added to GDP

  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
  $180 billion in additional spending
                                  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
6.    http://economistsview.typepad.com/economistsview/2008/12/woodward-and--1.html
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-
      million-and-counting.html?s_cid=rss:us-population-2009-305-million-and-counting
                        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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