Monday, July 11, 2011

State 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 individual state budget economic parameter:

n 64

R2 0.96
Adjusted R2 0.95
SE 8.77

Term Coefficient 95% CI SE t statistic DF p
Intercept -23.78 -65.48 to 17.91 20.759 -1.15 50 0.2573
Population 0.08521 -0.13397 to 0.30439 0.109125 0.78 50 0.4386
Unemployment 1.997 -0.982 to 4.975 1.4831 1.35 50 0.1843
Inflation 0.1056 -0.8478 to 1.0591 0.47469 0.22 50 0.8249
GDP 0.0491 -0.0006 to 0.0988 0.02475 1.98 50 0.0528
Debt 0.01429 -0.00580 to 0.03439 0.010003 1.43 50 0.1593
Tax Receipts 0.2714 0.2202 to 0.3226 0.02549 10.65 50 <0.0001
Gov Spending -0.2278 -0.3073 to -0.1483 0.03958 -5.76 50 <0.0001
Budget 0.2375 0.1410 to 0.3341 0.04805 4.94 50 <0.0001
Trade Deficit -0.05445 -0.12616 to 0.01725 0.035701 -1.53 50 0.1335
Consumer Spending -0.03384 -0.15193 to 0.08425 0.058793 -0.58 50 0.5675
Gov Social Benefits 0.1646 -0.0576 to 0.3867 0.11062 1.49 50 0.1431
State Social Payment -0.3374 -0.9744 to 0.2996 0.31713 -1.06 50 0.2925
Personal Income -0.1285 -0.2034 to -0.0537 0.03726 -3.45 50 0.0011

The economic parameters used to model state government deficit 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 federal government budget levels, the federal trade deficit, consumer spending, 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 state government budget levels (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 (State Budgets 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 (State Budgets in this case). If a coefficient value of an economic parameter is positive then it trends in the same direction of the tested variable (State Budgets in this case). If a coefficient value is negative then the corresponding variable trends in the opposite direction of the tested variable (State Budgets 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 state budgets?

It should come as no surprise as the federal government raises more tax revenues, spends more on entitlements, and increase their budget and deficit levels – so do the individual states. On the other hand, increased levels in personal income, consumer spending, and federal government spending can lead to lower budget deficits (states can collect more in sales taxes).

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