Regression Analysis – What It is and How It is Used

Have you ever wondered whether the Internal Revenue Service (IRS) has too many auditors, whether tax rates are too high for anticipated spending levels, how much money taxing marijuana would generate, or whether a governmental entity could close certain operations to improve its bottom line? These examples, and thousands of others, represent a few of the uses of regression analysis within the Government sector.

For example, the IRS employs thousands of individual income and corporate income tax auditors, each of which comes at a cost of around $150,000 (salaries, benefits, travel, office supplies, apportioned rent, etc.). The employer of the auditors, the IRS, is always clamoring for more tax auditors. Why? Because, as a general rule, IRS administrators think there’s more money out there that individuals and corporations potentially owe in taxes, but the IRS is unaware of it.

What does this have to do with regression analysis? Suppose you are asked to evaluate whether hiring more tax auditors would improve the Federal Government’s balance sheet. Further assume that you do some simple calculations and find that the average auditor imposes tax penalties and assessments of $250,000 per year. With an average cost of $150,000 per year, how could it not be a good idea to hire more tax auditors – they pay for themselves, right?

Here’s where regression analysis comes in handy. The issue is not the average, but the marginal impact of each auditor. For instance, the first auditor may assess $2 million in taxes because this auditor ends up with easy high dollar, red flag taxpayers. Suppose the next auditor is able to assess $1 million in unpaid taxes by seeking out medium dollar, red flag taxpayers. The average is $1.5 million, although the second auditor was really only worth $1 million less any salary and benefit costs. Suppose a third auditor only assessed $50,000 because all the “easy” delinquent tax accounts have been taken by the first two. When looking at the bottom line, the average auditor assesses $1.017 million in unpaid taxes, although, the third auditor isn’t worth it.

In practice, estimating whether there are too many tax auditors comes down to some form of regression analysis. This is done by looking at the correlation between auditor employment, assessments, actual collections, and other meaningful economic variables.  Essentially, regression analysis gives policymakers an idea of where one is along the marginal benefit/marginal cost curve, as shown in the figure. 

As a second example of the usefulness of regression analysis to improve Government operations, consider an example of closing a liquor store.  In 18 states, the sale of liquor is entirely controlled by State Governments.  With State Governments eliminating competition in the liquor consumption business, the Government becomes a monopolist of liquor products. As such, the Goverment can set the price of a product at a level that maximizes profit with little regard for competitive forces.

What’s the optimal price level and how many stores should the Government open?  Well, a good portion of the answer could be determined using regression analysis.

Overall, regression analysis is a useful tool in a number of different settings to evaluate the effectiveness of certain policy or business decisions.



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