Sunday, June 12, 2011

Federal Debt Model

Below are the results of running a linear regression model on various economic data (obtained from the Bureau of Economic Analysis [BEA] government site) from 1947 to the present solving for the U.S. federal government Debt economic parameter:

n 64

R2 1.00
Adjusted R2 1.00
SE 121.5

Term Coefficient 95% CI SE t statistic DF p
Intercept 1376 941 to 1812 216.9 6.35 50 <0.0001
Population -3.83 -6.69 to -0.97 1.422 -2.69 50 0.0096
Unemployment -100.6 -131.4 to -69.8 15.33 -6.56 50 <0.0001
Inflation -26.64 -37.48 to -15.81 5.396 -4.94 50 <0.0001
GDP -0.7892 -1.4687 to -0.1097 0.33831 -2.33 50 0.0237
Tax Receipts 0.6127 -0.6578 to 1.8831 0.63251 0.97 50 0.3374
Gov Spending 1.05 -0.34 to 2.44 0.691 1.52 50 0.1353
Budget -0.0545 -1.6863 to 1.5773 0.81244 -0.07 50 0.9468
Trade Deficit 1.971 1.122 to 2.819 0.4225 4.66 50 <0.0001
Consumer Spending 1.742 0.176 to 3.307 0.7794 2.23 50 0.0300
State Deficit 2.745 -1.113 to 6.603 1.9209 1.43 50 0.1593
State Social Payment -0.6712 -9.5954 to 8.2530 4.44307 -0.15 50 0.8805
Gov Social Benefits 5.672 2.969 to 8.374 1.3455 4.22 50 0.0001
Personal Income -0.9377 -2.0603 to 0.1849 0.55891 -1.68 50 0.0996

The economic parameters used to model Debt over the past 64 (n) years are: the U.S. population, the unemployment rate, the inflation rate, the U.S. Gross Domestic Product (GDP), federal government tax receipts, federal government spending, the federal government budget size, the trade deficit, consumer spending, state government deficits, state government spending on social benefits, federal government spending on social benefits, and personal income. The intercept value in the above table is not a parameter – it is the value of the Debt (in billions of dollars) if all other parameters equal zero. These economic parameters are denoted in the above table.

The R² statistic illustrates how closely the linear regression model resembles a straight line (the ideal condition). If R² equals one then the model is 100% linear and the parameters correlate 100%. On the other hand, if R² is equal to zero then there is no correlation and the data in the linear regression model is completely random. T statistics reveal which of the economic parameters has the best correlation to the parameter being tested (Debt in this case). The higher the absolute value of the t statistic, the better the correlation the corresponding economic parameter has to the tested variable (Debt in this case). If a coefficient value of an economic parameter is positive then it trends in the same direction of the tested variable (Debt in this case). If a coefficient value is negative then the corresponding variable trends in the opposite direction of the tested variable (Debt in this case). It is time to do some math to prove higher taxes and government spending cripple economies. What economic parameters have the biggest effect on the U.S. federal government Debt?

The trade deficit has the biggest negative impact on our debt (importing oil) as does both federal and state government spending (in particular spending on government social benefits). Increased inflation and GDP can drive the federal government debt lower. The odd statistic is that increased unemployment tends to lower debt and increased tax receipts raise the debt. Actually, this is not that odd since the federal government tends to spend money than it receives regardless as to whether or not they raise more tax revenue. Thus, the federal debt continues to go up even when consumer spending is high.

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