Thursday, June 23, 2011

Federal Government Budget 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 budget economic variable:

n 64

R2 1.00
Adjusted R2 1.00
SE 21.1

Term Coefficient 95% CI SE t statistic DF p
Intercept -4.498 -106.370 to 97.375 50.7193 -0.09 50 0.9297
Population 0.06869 -0.46284 to 0.60022 0.264634 0.26 50 0.7963
Unemployment -1.457 -8.760 to 5.845 3.6357 -0.40 50 0.6903
Inflation -0.1558 -2.4562 to 2.1447 1.14532 -0.14 50 0.8924
GDP -0.02328 -0.14766 to 0.10109 0.061921 -0.38 50 0.7085
Debt -0.001651 -0.051092 to 0.047789 0.0246149 -0.07 50 0.9468
Tax Receipts -0.4659 -0.6457 to -0.2862 0.08948 -5.21 50 <0.0001
Gov Spending 0.6586 0.4970 to 0.8203 0.08049 8.18 50 <0.0001
Trade Deficit 0.1724 0.0024 to 0.3425 0.08465 2.04 50 0.0469
Consumer Spending 0.2863 0.0124 to 0.5603 0.13639 2.10 50 0.0408
State Deficit 1.382 0.821 to 1.944 0.2796 4.94 50 <0.0001
State Social Payment -2.45 -3.84 to -1.06 0.692 -3.54 50 0.0009
Gov Social Benefits 0.5422 0.0167 to 1.0677 0.26165 2.07 50 0.0434
Personal Income -0.02417 -0.22488 to 0.17654 0.099928 -0.24 50 0.8099

The economic parameters used to model Government Budget levels 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 tax receipts, federal government spending, 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 Government Budget (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 (Government Budget 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 (Government Budget in this case). If a coefficient value of an economic parameter is positive then it trends in the same direction of the tested variable (Government Budget in this case). If a coefficient value is negative then the corresponding variable trends in the opposite direction of the tested variable (Government Budget 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 budget?

Not surprisingly, government spending, state deficits, government social benefits, the trade deficit, and consumer spending have the biggest impact on the budget size. The only thing that will significantly lower the federal budget size is if states increase their share of social payments. If tax receipts go up, the government can also control the federal budget from going further into debt.

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