Monday, August 8, 2011

Personal Income 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 personal income economic parameter:

n 64

R2 1.00
Adjusted R2 1.00
SE 29.91

Term Coefficient 95% CI SE t statistic DF p
Intercept 65.45 -77.45 to 208.35 71.144 0.92 50 0.3620
Population -0.3092 -1.0563 to 0.4380 0.37199 -0.83 50 0.4098
Unemployment -2.761 -13.077 to 7.554 5.1358 -0.54 50 0.5932
Inflation -1.952 -5.159 to 1.255 1.5966 -1.22 50 0.2272
GDP 0.142 -0.030 to 0.313 0.0854 1.66 50 0.1026
Debt -0.05684 -0.12488 to 0.01121 0.033877 -1.68 50 0.0996
Tax Receipts 0.5459 0.2709 to 0.8209 0.13691 3.99 50 0.0002
Gov Spending -0.2901 -0.6300 to 0.0498 0.16921 -1.71 50 0.0927
Budget -0.04835 -0.44988 to 0.35318 0.199910 -0.24 50 0.8099
Trade Deficit 0.4869 0.2783 to 0.6955 0.10385 4.69 50 <0.0001
Consumer Spending 0.9265 0.6197 to 1.2333 0.15274 6.07 50 <0.0001
State Social Payment -5.385 -6.963 to -3.807 0.7856 -6.85 50 <0.0001
Gov Social Benefits 1.845 1.274 to 2.415 0.2840 6.49 50 <0.0001
State Deficit -1.496 -2.367 to -0.625 0.4336 -3.45 50 0.0011

The economic parameters used to model personal income 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 federal government social benefit payments. The intercept value in the above table is not a parameter – it is the value of personal income (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 (Personal Income 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 (Personal Income in this case). If a coefficient value of an economic parameter is positive then it trends in the same direction of the tested variable (Personal Income in this case). If a coefficient value is negative then the corresponding variable trends in the opposite direction of the tested variable (Personal Income 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 personal income?

It should come as no surprise when economic times are good and GDP, federal tax receipts, the trade deficit, and consumer spending are all increasing then so is personal income. Generally, when state and federal government spending and debt levels increase then personal income is declining. It is interesting to note that personal income levels have been decreasing with population increases.

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