Tuesday, July 26, 2011

A Federal Government Social Benefits 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 federal government social benefit economic parameter:

n 64

R2 1.00
Adjusted R2 1.00
SE 10.97

Term Coefficient 95% CI SE t statistic DF p
Intercept -55.01 -105.49 to -4.53 25.133 -2.19 50 0.0333
Population 0.09296 -0.18166 to 0.36757 0.136724 0.68 50 0.4997
Unemployment 5.535 2.082 to 8.987 1.7190 3.22 50 0.0023
Inflation 1.905 0.842 to 2.969 0.5296 3.60 50 0.0007
GDP -0.0464 -0.1096 to 0.0168 0.03149 -1.47 50 0.1469
Debt 0.04623 0.02420 to 0.06826 0.010967 4.22 50 0.0001
Tax Receipts -0.1289 -0.2387 to -0.0191 0.05468 -2.36 50 0.0224
Gov Spending 0.03361 -0.09428 to 0.16151 0.063674 0.53 50 0.5999
Budget 0.1459 0.0045 to 0.2873 0.07039 2.07 50 0.0434
Trade Deficit -0.1554 -0.2358 to -0.0749 0.04006 -3.88 50 0.0003
Consumer Spending -0.2064 -0.3426 to -0.0703 0.06778 -3.05 50 0.0037
State Deficit 0.2576 -0.0902 to 0.6053 0.17314 1.49 50 0.1431
State Social Payment 2.005 1.435 to 2.575 0.2839 7.06 50 <0.0001
Personal Income 0.2481 0.1713 to 0.3248 0.03820 6.49 50 <0.0001

The economic parameters used to model federal government social benefit payments 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 federal government budget levels, the federal trade deficit, consumer spending, state government budget levels, state government spending on social benefits, and personal income. The intercept value in the above table is not a parameter – it is the value of federal government social benefit payments (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 (Federal Social Benefits 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 (Federal Social Benefits in this case). If a coefficient value of an economic parameter is positive then it trends in the same direction of the tested variable (Federal Social Benefits in this case). If a coefficient value is negative then the corresponding variable trends in the opposite direction of the tested variable (Federal Social Benefits 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 federal government social benefit expenditures?

It should come as no surprise that as unemployment, inflation, federal debt, the federal budget, state deficits, and state social benefit payments all increase then federal social benefit payments also increase. As economic times improve and GDP, federal tax receipts, the trade deficit, and consumer spending increase then federal social benefit payments decrease.

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