Progressive tax rates motivate higher taxed individuals to seek higher investment returns and further increase US income inequality.

**An example**

Suppose you have two investors, T and F, who each would like to have another $700 in income to spend per year, but T is in the lowest income tax bracket of 10 percent and F is in the highest income tax bracket of 40 percent. (The actual highest US tax bracket is 39.6 percent, ignoring increases in marginal tax rates due to lost benefits and deductions.)

Each invests $10,000. T invests at 8 percent (assume the economy has fully recovered and the Fed no longer is pushing short-term rates to zero) to get $800 before tax and $720 after the 10 percent tax. T is happy because the income from the investment provides the desired $700.

An 8 percent investment for F in the 40 percent tax bracket will provide only an additional $480. An amount far short of the $700 target.

F's only choice is to seek an investment that provides greater income, somewhere around $1200 instead of $800. A 12 percent investment for F will provide the same next of taxes amount, $720 (.12 X $10,000 = $1,200 less tax of 480 (1200 X .40) = $720) as T receives.

**Investment choices**

F has two choices on how to increase an investment's return to 12 percent. F can choose a riskier investment that has an expected return of 12 percent or F can use leverage (borrowed funds) to increase the amount invested in the 8 percent investment provided the cost of the loan is below 8 percent. Leverage also increases the risk of the investment since it includes the risk of default on the loan and increases the volatility of the investment returns. If F could borrow at 6 percent, F would need to borrow $20,000 for a total of $30,000 to invest to achieve the same after tax return as T. ($30,000 x .08= 2,400 less loan interest of 1,200 ($20,000 X .06) = $1200 less income tax of 480 (1200 X .4) = $720). From a financial theory point of view, both the leveraged 8 percent investment and the unleveraged 12 percent investment must be of equal risk to yield the same expected return, otherwise, there would be arbitrage opportunities.

**How much risk does F's investment have in comparison to T's investment.**

Let's assume that the average investment, a diversified portfolio of stocks, with typical stock market risk (standard deviation of 16 percent) has an expected return of 8 percent, which is comprised of a 2 percent risk free rate and a 6 percent risk premium for its average stock market risk. (See Capital Asset Pricing Model, aka CAPM for financial theory behind this methodology.)

F's investment has to be 67 percent riskier than T's. T's expected 8 percent investment is 2 percent risk-free rate plus 6 percent risk premium. F's expected 12 percent investment is 2 percent risk-free rate plus 10 percent risk premium. 10 percent is 1.67 times 6 percent. T's investment has a yearly volatility (std. dev.) of its return of 16 percent. F's investment has a yearly volatility of 26.7 percent. (1.67 X .16.) (Financial theory, CAPM, says the risk premium is proportional to the volatility (standard deviation) of the investment.)

**Shift In Investment Return Distribution**

F's investment has greater volatility than T's, 26.7 percent versus 16 percent. which means that F has a greater chance of earning both more and less money than T. The statistical distribution of F's investment returns becomes more spread out and flatter than T's, that is fewer returns close to the average or expected return and more higher and lower returns farther away from the average return.

By investing in a riskier investment, F has a 50 percent higher expected return than T, 12 percent versus 8 percent. The riskier investment also has a greater chance of producing a return much higher than 12 percent. The top five percent of the higher risk (F's) investment returns (two standard deviations) will make about 18 percent, and the top 1 percent (a little less than 3 standard deviations) will make about 21 percent. By comparison, a 3 standard deviation return for T is less than 12 percent.

The distribution of the higher risk returns is more spread out than the distribution of the lower risk investments and there is a greater probability of a higher risk investment paying out more than the lower risk investment. Over time, there will be a few higher taxed investors who have successfully invested and reinvested at a much higher return

**Magic of compounding**

Over a lifetime of 72 years, $1 at 8 percent with reinvestment will become $255, at 12 percent will become $3,500, at 18 percent will become $150,000 and at 21 percent will become over $900,000. The disparity in investment returns and income, motivated in part by progressive tax rates, exacerbates income inequality over time.

**Progressive tax rate effect**

The progressive tax rates push some investors seeking modest returns into riskier investments with the greater potential to achieve very high returns. Over time, the higher tax rates for high income individuals will produce very rich investors in the top 5 percent and top one percent of income.

In fact, IRS data shows that since 1970, investment income compared to labor income comprises a much greater share of the income of high income individuals. Progressive tax rates, which have become more progressive since the 1970s, are a likely reason.

Also see my post, "Progressive Taxation And Redistribution Reduce Human Capital Investment, Reduce Future Wage Income, Reduce Work Hours: Reduction In Tax Progressivity Can Increase Economic Growth: Federal Reserve Board Research" of April 11, 2013, for a discussion of Federal Reserve research on the reduction in pre-tax labor income due to progressive tax rates.

Your figures are in error. The taxes for both Clinton and Bush were calculated using the maximum rate for that selected income. For instance the Clinton 1999 tax rate on 30K was 28%, which is what they used to get the 8400 figure. However taxes are not calculated that way. The first 25K of income would have been 2013 tax brackets at the lower 15% bracket first, thus yielding a much lower figure than what you show.I am not arguing that Bush doesn't have lower taxes. He certainly does. Of course he obtained his lower tax brackets by using deficit spending and increasing the national debt. Add back in the interest payments we'll be making and I bet Bush actually cost taxpayers far more than Clinton ever did.

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