Friday, June 17, 2011

Federal Tax Receipts 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 Tax Receipts economic variable:

n 64

R2 1.00
Adjusted R2 1.00
SE 26.91

Term Coefficient 95% CI SE t statistic DF p
Intercept -16.14 -145.72 to 113.43 64.513 -0.25 50 0.8034
Population -0.03525 -0.71208 to 0.64159 0.336976 -0.10 50 0.9171
Unemployment -1.122 -10.425 to 8.181 4.6316 -0.24 50 0.8095
Inflation 1.511 -1.386 to 4.407 1.4421 1.05 50 0.2998
GDP -0.03242 -0.19065 to 0.12582 0.078782 -0.41 50 0.6825
Debt 0.03006 -0.03228 to 0.09240 0.031038 0.97 50 0.3374
Gov Spending 0.5752 0.3063 to 0.8441 0.13389 4.30 50 <0.0001
Budget -0.7547 -1.0457 to -0.4636 0.14492 -5.21 50 <0.0001
Trade Deficit 0.07679 -0.14733 to 0.30092 0.111584 0.69 50 0.4945
Consumer Spending 0.008488 -0.355196 to 0.372171 0.1810668 0.05 50 0.9628
State Social Payment 0.2803 -1.6954 to 2.2560 0.98365 0.28 50 0.7768
Gov Social Benefits -0.776 -1.437 to -0.115 0.3292 -2.36 50 0.0224
Personal Income 0.442 0.219 to 0.665 0.1108 3.99 50 0.0002
State Deficit 2.557 2.075 to 3.039 0.2402 10.65 50 <0.0001

The economic parameters used to model Tax Receipts 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 debt, 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 Tax Receipts (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 (Tax Receipts 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 (Tax Receipts in this case). If a coefficient value of an economic parameter is positive then it trends in the same direction of the tested variable (Tax Receipts in this case). If a coefficient value is negative then the corresponding variable trends in the opposite direction of the tested variable (Tax Receipts 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 U.S. federal government Tax Receipts?

As personal income, federal government spending, and state government debt increase so does the amount of tax receipts received by the federal government. This, once again, proves the federal government will spend more if it receives more revenue. The federal deficit continues to increase even as the government receives more tax revenue. Interestingly, the only thing that will help reduce federal government tax revenues is to reduce the budget, and in particular, government social benefit spending. Our current government is following the opposite strategy.

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