# Methodology

In order to accurately project and personalize the cost of federal government expenditures, the Government Cost Calculator uses a variety of data sources and assumptions in creating the estimates. The Calculator uses data from the Congressional Budget Office (CBO) and the Office of Management and Budget (OMB) to construct accurate estimates of projected federal expenditures. To determine how these expenditures affect American citizens specifically, the Calculator then draws on data from the U.S. Bureau of Labor Statistics and U.S. Census Bureau to create a detailed picture for the individual. The model we use relies on some simplifying assumptions both implicit and explicit, which we have summarized in the following outline. Have more questions? Contact us for more information or more details regarding the estimates provided by the Calculator.

FS(y) = Projected federal spending in year y
FT(y) = Projected federal taxes to be collected in year y
GDP(y) = Projected GDP of the United States in year y
I(y) = The individual’s projected annual income in year y
ST(y) = The individual’s share of taxes in year y
SS(y) = The individual’s share of spending in year y

ST(y) = (FT(y)/ GDP(y)) * I(y)

SS(y) = (FS(y)/ GDP(y)) * I(y)

The lifetime share of taxes and spending are the totals of the shares in every future year of an individual’s remaining lifespan.

CY = The current year
LY = The last projected year of the individual’s life
STL = The lifespan share of taxes for the individual
SSL = The lifespan share of spending for the individual

STL = (y=CY to LY) ST(y)

SSL = (y=CY to LY) SS(y)

The Centers for Disease Control and Prevention (CDC) projects the life expectancy of individuals based on their current age. [1]

From this data, we derive a polynomial equation of degree 6 to model the number of years of remaining life based on a person’s current age:

Remaining Years = 78.663 – 9.4767*(10-1) * (age) – 8.558*(10-3) * (age2) + 1.3257*(10-4) * (age3) + -2.6701*(10-6)*(age4) + 2.8509*(10-8)* (age5) – 1.0328* (10-10)*(age6)

Life Expectancy = Round (Current Age + Remaining Years)

[1] United States Life Tables. Table A.
http://www.cdc.gov/nchs/data/nvsr/nvsr56/nvsr56_09.pdf (Accessed 2/2/11)

Calculations for federal spending, tax revenue, and debt in the current year are based on data from the White House’s Fiscal Year 2014 budget, released April 10, 2013. (Accessed 5/7/2013)

Federal expenditures are based on the CBO’s “Alertantive Fiscal Scenario” from the CBO’s June 2012 The Long-Term Budget Outlook, June 2012. (accessed 10/29/2012) Data Underlying Scenarios and Figures. (Accessed 4/12/2013)

After 2023, the federal expenditure data split into two categories: discretionary spending and mandatory spending. For the discretionary spending categories, we use the baseline with a trend. For mandatory items (Social Security, Medicare, Medicaid, and Net Interest in the Debt) we use the CBO projections of each item as a percentage share of GDP up to 2085. The mandatory items make up the largest share of the federal budget, so the Calculator attempts to be most accurate with regard to these areas of the budget.

We use the CBO’s projections as the source of tax revenue as a percentage of GDP from FY 2010 to 2012. [1] Because of the uncertainty of future tax law, from 2014 on, we use a value of tax revenue of 18.5% of GDP, a level consistent with the average since World War II, and a level consistent with the policies of recent Congresses.

[1] The Budget and Economic Outlook: Fiscal Years 2013 to 2023
http://www.cbo.gov/publication/43907. (Accessed 4/10/2013)

The total federal debt at the end of fiscal year 2012 was \$16.0662 trillion. Estimates for future levels of debt at the end of a fiscal year y are estimated by adding the projected levels of federal spending (including interest) to the previous year’s debt and then subtracting projected tax revenue.

Debt(y) = Debt(y-1) + Spending (y) – Tax Revenue (y)

The estimate of the alternative value of tax contributions considers a scenario where all the money an individual is projected to pay in future taxes is instead deposited into an account and earns a standard rate of return. The assumed real rate of return is 6.09%, the average since 1871.
This model is based on the regression analysis of the S&P 500 in the period from January 1871 through May 2009. The average compound annualized rate of return is adjusted for the effects of inflation, which is taken as the average annualized rate of change for the Consumer Price Index for All Urban Consumers since 1913. [4] This real rate of inflation is estimated according to the Fisher equation. [5]

These models for each level of stock market performance are based on historic S&P 500 data [2], whose original source is maintained by Yale’s Robert Shiller. [3]

[1] Political Calculations. Remapping S&P 500 Performance Since 1871. http://politicalcalculations.blogspot.com/2009/06/remapping-s-500-performance-since-1871.html. Accessed 11 December 2009.

[2] Political Calculations. The S&P at Your Fingertips. http://politicalcalculations.blogspot.com/2006/12/sp-500-at-your-fingertips.html. Accessed 11 December 2009.

[3] Shiller, Robert. Stock Market Data Used in Irrational Exuberance. http://www.econ.yale.edu/~shiller/data/ie_data.xls. Accessed 11 December 2009.

[4] Political Calculations. Mapping Inflation Extremes Since 1913. http://politicalcalculations.blogspot.com/2006/11/mapping-inflation-extremes-since-1913.html. Accessed 1 January 2010.

[5] Wikipedia. Fisher Equation. http://en.wikipedia.org/wiki/Fisher_equation. Accessed 1 January 2010.

CY = Current Year
DY = Death Year
AR = Alternative return
ST(y) = Share of taxes in year y
RR = 1.0609 (real rate of return)

AR = (y=CY to DY) ST(y) * RR^(DY – y)

GDP Projections for 2013 through 2023 are based Congressional Budget Office’s Budget and Economic Outlook: Fiscal Years 2013 to 2023. February 2013. Table B-1. CBO’s Economic Projections, by Calendar Year and Data Underlying Figures (Accessed 12 April 2013).

After 2023, we use a modeled nominal GDP from 2024 through 2087 of 2.2% Real GDP Growth plus 2.0% inflation for a nominal growth rate of 4.2%.

Total tax receipts are calculated as a percentage of GDP. For the years from 1946 through 2008, and forecast into 2014 using White House projections [5], the long-term stable average percentage of total tax receipts as a percentage of annual GDP is 17.8% with a standard deviation of 1.2% [4]. The annual data appears to adhere to a normal distribution about this central tendency, falling with recessions and rising in economic expansion.

We should note that periods in which the federal government’s total tax receipts have risen above a one standard deviation difference with the mean has coincided with unique circumstances, such as in 1968-1969, where a 10% income surtax was applied to top income earners, 1980-1981 where tax revenues were inflated due to the hyperinflation of the period (prior to indexing tax brackets for inflation) and the period from 1997-2000 which coincides with the Dot-Com Bubble. We observe that none of these factors could be sustained and were often followed by significant drops in tax receipts as a percentage share of annual GDP.

We also note that the federal government’s personal income tax receipts demonstrate the same phenomenon, being very stable with as an average percentage share of GDP of 8.0% with a standard deviation of 0.8%. This is all the more remarkable given the extreme variation in the maximum tax rates that have applied throughout the period, from as high as 92% to as low as 28%. [6]

In addition to Personal Income Taxes, Federal Total Tax Receipts are supplemented by Corporate Income Taxes, Social Security and other Payroll Taxes, Capital Gains Taxes and various Excise Taxes. We note that Corporate Income Tax Rates have generally fallen throughout the period since 1946, offset by significant increases in Social Security and other Payroll Taxes, for which corporations match their employees tax payments. Excise taxes have also generally risen throughout the period. The combination of these taxes add up to a 9.8% share of GDP, with a standard deviation of 0.5% for the period from 1946 through the present.

We make no additional assumptions about inflation except those built into the CBO projections through 2023. The CBO assumes that inflation will average 2.0% annually after 2023.

[4] Political Calculations. Hauser’s Law.
http://politicalcalculations.blogspot.com/2009/12/hausers-law.html. Accessed 9 December 2009.

[5] White House Office of Management and Budget. Table 1.2. Summary of Receipts, Outlays, and Surpluses or Deficits as Percentages of GDP: 1930-2015.
http://www.gpoaccess.gov/usbudget/fy11/sheets/hist01z2.xls. Accessed 29 November 2009.

[6] National Taxpayers Unions. History of Federal Individual Income Bottom and Top Bracket Rates. http://www.ntu.org/main/page.php?PageID=19. Accessed 8 December 2009.

The projections for the future share of spending and share of taxes on an individual basis depend on the income the person is projected to earn in future years. This future income trajectory is modeled as polynomial equations based on data from the US Census Bureau. The Calculator makes no assumptions about retirement.

The Calculator uses generalized income patterns for educational degree level by using Census data 1997-2007 to project individualized income trajectories. These are estimates and users should interpreted these figures broadly.

U.S. Census Bureau. Current Population Survey (CPS). Annual Social and Economic (ASEC) Supplement. PINC-01. Selected Characteristics of People 15 Years Old and Over by Total Money Income in 2008, Work Experience in 2008, Race, Hispanic Origin, and Sex. Both Sexes, All Races.
http://www.census.gov/hhes/www/cpstables/032009/perinc/new01_001.htm. Accessed 2 February 2011.

U.S. Census Bureau. Current Population Survey (CPS). Annual Social and Economic (ASEC) Supplement. PINC-01. Selected Characteristics of People 15 Years Old and Over by Total Money Income in 2007, Work Experience in 2007, Race, Hispanic Origin, and Sex. Both Sexes, All Races.
http://pubdb3.census.gov/macro/032008/perinc/new01_001.htm. Accessed 2 February 2011.

U.S. Census Bureau. Current Population Survey (CPS). Annual Social and Economic (ASEC) Supplement. PINC-01. Selected Characteristics of People 15 Years Old and Over by Total Money Income in 2006, Work Experience in 2006, Race, Hispanic Origin, and Sex. Both Sexes, All Races.
http://pubdb3.census.gov/macro/032007/perinc/new01_001.htm. Accessed 2 February 2011.

U.S. Census Bureau. Current Population Survey (CPS). Annual Social and Economic (ASEC) Supplement. PINC-01. Selected Characteristics of People 15 Years Old and Over by Total Money Income in 2005, Work Experience in 2005, Race, Hispanic Origin, and Sex. Both Sexes, All Races.
http://pubdb3.census.gov/macro/032006/perinc/new01_001.htm. Accessed 2 February 2011.

U.S. Census Bureau. Current Population Survey (CPS). Annual Social and Economic (ASEC) Supplement. PINC-01. Selected Characteristics of People 15 Years Old and Over by Total Money Income in 2004, Work Experience in 2004, Race, Hispanic Origin, and Sex. Both Sexes, All Races.
http://pubdb3.census.gov/macro/032005/perinc/new01_001.htm. Accessed 2 February 2011.

U.S. Census Bureau. Current Population Survey (CPS). Annual Social and Economic (ASEC) Supplement. PINC-01. Selected Characteristics of People 15 Years Old and Over by Total Money Income in 2003, Work Experience in 2003, Race, Hispanic Origin, and Sex. Both Sexes, All Races.
http://pubdb3.census.gov/macro/032004/perinc/new01_001.htm. Accessed 2 February 2011.

U.S. Census Bureau. Current Population Survey (CPS). Annual Social and Economic (ASEC) Supplement. PINC-01. Selected Characteristics of People 15 Years Old and Over by Total Money Income in 2002, Work Experience in 2002, Race, Hispanic Origin, and Sex. Both Sexes, All Races.
http://pubdb3.census.gov/macro/032003/perinc/new01_001.htm. Accessed 2 February 2011.

U.S. Census Bureau. Current Population Survey (CPS). Annual Social and Economic (ASEC) Supplement. PINC-01. Selected Characteristics of People 15 Years Old and Over by Total Money Income in 2001, Work Experience in 2001, Race, Hispanic Origin, and Sex. Both Sexes, All Races.
http://pubdb3.census.gov/macro/032002/perinc/new01_001.htm. Accessed 2 February 2011.

U.S. Census Bureau. Current Population Survey (CPS). Annual Social and Economic (ASEC) Supplement. PINC-01. Selected Characteristics of People 15 Years Old and Over by Total Money Income in 2000, Work Experience in 2000, Race, Hispanic Origin, and Sex. Both Sexes, All Races.
http://pubdb3.census.gov/macro/032001/perinc/new01_001.htm. Accessed 2 February 2011.

U.S. Census Bureau. Current Population Survey (CPS). Annual Social and Economic (ASEC) Supplement. PINC-01. Selected Characteristics of People 15 Years Old and Over by Total Money Income in 1999, Work Experience in 1999, Race, Hispanic Origin, and Sex. Both Sexes, All Races.
http://pubdb3.census.gov/macro/032000/perinc/new01_001.htm. Accessed 2 February 2011.

U.S. Census Bureau. Current Population Survey (CPS). Annual Social and Economic (ASEC) Supplement. PINC-01. Selected Characteristics of People 15 Years Old and Over by Total Money Income in 1998, Work Experience in 1998, Race, Hispanic Origin, and Sex. Both Sexes, All Races.
http://pubdb3.census.gov/macro/031999/perinc/new01_001.htm. Accessed 2 February 2011.

U.S. Census Bureau. Current Population Survey (CPS). Annual Social and Economic (ASEC) Supplement. PINC-06A. Selected Characteristics of People 15 Years Old and Over by Total Money Income in 1997, Work Experience in 1997, Race, Hispanic Origin, and Sex. Both Sexes, All Races.
http://pubdb3.census.gov/macro/031998/perinc/06A_001.htm. Accessed 2 February 2011.

Bureau of Labor Statistics. â€œTable 2. Income before taxes: Average annual expenditures and characteristics, Consumer Expenditure Survey, 2008â€. Accessed 16 November 2009.

Bureau of Labor Statistics. â€œTable 3. Age of reference person: Average annual expenditures and characteristics, Consumer Expenditure Survey 2008â€. Accessed 16 November 2009.

Bureau of Labor Statistics. â€œTable 2301. Higher income before taxes: Average annual expenditures and characteristics, Consumer Expenditure Survey, 2008â€. Accessed 16 November 2009.

Congressional Budget Office. The Long-Term Budget Outlook, June 2009. Accessed 4 December 2009.

Henry, Tamara. Report: Greater percentage of Americans educated. USA Today. Accessed 2 December 2009.

National Taxpayers Unions. History of Federal Individual Income Bottom and Top Bracket Rates. Accessed 8 December 2009.

National Center for Health Statistics. United States Life Tables 2004. Accessed 11 December 2009

Political Calculations. A Different Kind of Bracketology, Part 2. Accessed 7 December 2009.

Political Calculations. Age and Income Driven Spending. Accessed 19 November 2009.

Political Calculations. Hauser’s Law. Accessed 9 December 2009.

Political Calculations. How Much Longer Can You Expect to Live? Accessed 11 December 2009.

Political Calculations. Mapping Inflation Extremes Since 1913. Accessed 1 January 2010.

Political Calculations. Remapping S&P 500 Performance Since 1871. Accessed 11 December 2009.

Political Calculations. The S&P at Your Fingertips. Accessed 11 December 2009.

Political Calculations. The Trigger Point for Taxes. Accessed 10 December 2009.

Shiller, Robert. Stock Market Data Used in Irrational Exuberance. Accessed 11 December 2009.

Social Security Administration. 2009 OASDI Trustees Report. Table VI.F6. Selected Economic Variables, Calendar Years 2008-85. Accessed 7 December 2009.

Social Security Administration. 2009 OASDI Trustees Report. Principal Economic Assumptions. Accessed 7 December 2009.

U.S. Census Bureau. Detailed Income Tabulations from the Current Population Survey, 1997-2008. Accessed 31 May 2009

U.S. Census Bureau. 2008 National Population Projections. Table 3. Resident Population Projectons: 2008 to 2050. Accessed 11 December 2009.

U.S. Census Bureau. 2009 ASEC (2008 Income) Person Table PINC-01. Accessed 2 December 2009.

White House Office of Management and Budget. Budget of the United States Government Fiscal Year 2008. Accessed 4 December 2009.

White House Office of Management and Budget. Table 1.2. Summary of Receipts, Outlays, and Surpluses or Deficits as Percentages of GDP: 1930-2014. Accessed 29 November 2009.

White House Office of Management and Budget. Table 1.2. Summary of Receipts, Outlays, and Surpluses or Deficits as Percentages of GDP: 1930-2014. Accessed 24 July 2010.