# CBO’s Revenue Forecasting Record

CBO's revenue projections since 1982 have, on average, been a bit too high—more so for projections spanning six years than for those spanning two—but their overall accuracy has been similar to that of the projections of other agencies.

## Summary

To prepare the baseline budget projections on which much of its analysis is based, the Congressional Budget Office must regularly produce revenue forecasts. As a part of that process, the agency assesses the accuracy of its past projections and continually refines its methods for projecting revenues to attempt to make them more accurate. This report examines the accuracy of CBO's revenue projections since 1982, the earliest year for which the information necessary to assess the forecasts is available. On average, the agency's projections have been a bit too high—more so for projections spanning six years than for those spanning two—owing mostly to the difficulty of predicting when economic downturns will occur. The overall accuracy of CBO's revenue projections has been similar to that of the projections of other government agencies.

#### How Accurate Have CBO's Two-Year Revenue Projections Been?

On average, CBO has overestimated total revenues by 1.1 percent in its two-year projections—those that provide estimates of revenues for the fiscal year following the year in which they are released. A misestimate of that size in its January 2015 baseline projection, for example, would amount to $37 billion out of the roughly $3.5 trillion in total revenues that CBO projected for fiscal year 2016. Overestimates and underestimates offset one another in the mean error measure, so that average overestimate of 1.1 percent over the past three decades includes projections for years in the latest recession for which CBO overestimated revenues by as much as 25 percent and projections for the late 1990s and the mid-2000s for which CBO underestimated revenues by nearly 10 percent (see the figure below). The calculation of those errors—and of all such measures cited in this report—includes an adjustment to remove the estimated effects of legislation enacted after the projections were produced. That adjustment is necessary because the baseline projections incorporate the assumption that current laws governing taxes will generally not be modified by future legislation.

In addition to the mean error, CBO employs two other commonly used measures to evaluate the accuracy of revenue projections: the root mean square error (RMSE) and the mean absolute error. Unlike the mean error, the mean absolute error is the average of the errors without regard to direction (the negative signs are removed from underestimates before averaging), so errors in different directions do not offset one another. The RMSE, the calculation of which involves squaring the errors (thus removing the negative signs), also measures the size of errors without regard to direction, but by squaring the errors, it places a greater weight on larger deviations. The mean absolute error is an easier measure to understand, but the RMSE may be a more useful measure of forecast errors for revenue projections because larger forecast errors may have a disproportionately greater cost for policymaking than smaller ones.

For CBO's two-year revenue projections made since 1982, the mean absolute error is 5.2 percent, and the RMSE is 7.4 percent (see the table below). A mean absolute error of that magnitude would correspond to an error of about $180 billion in the revenue estimate for 2016 that CBO released in its January 2015 baseline projections. Because a disproportionate share of the misestimates occurred in projections made in years immediately preceding recessions, both the RMSE and the mean absolute error are roughly one-third smaller when the four two-year projections (out of the 32 included in this analysis) that were produced at or near peaks in the business cycle are excluded.

The RMSE provides a useful guide for assessing the distribution of CBO's past two-year projection errors. If the errors of a given set of forecasts are normally distributed around a mean error of zero—that is, if the misestimates are roughly symmetrically distributed around zero and there are more relatively small errors than large ones—about two-thirds of the forecasts will have misestimates within a range of plus or minus one RMSE. CBO's twoyear projections have had a small mean error, and they have misestimated revenues by small amounts more often than they have misestimated by large amounts. Thus, about two-thirds of those projections could be expected to have misestimated revenues by 7.4 percent (the RMSE of CBO's two-year projections) or less in either direction; indeed, three-quarters of the misestimates fell into that range. Because the sample size of historical forecasts is relatively small, however, it is not possible to know the true distribution of the forecast errors.

By CBO's calculation, the Administration's forecast errors for revenues have been very similar to CBO's. In its two-year forecasts over the same period (adjusted to exclude the effects of its proposed policy changes), the Administration also overestimated revenues, on average—by 1.7 percent, a little more than CBO's average overestimate of 1.1 percent; the RMSE of its forecasts is 7.8 percent, very close to CBO's RMSE of 7.4 percent. Likewise, the accuracy of revenue projections by state governments has also been very similar to CBO's for comparable sources of revenues.

#### How Accurate Have CBO's Six-Year Revenue Projections Been?

The projection errors have tended to be larger for longer horizons than shorter ones. CBO's six-year revenue projections—those that estimate revenues for the fifth fiscal year after the year in which they are released—have, on average, overestimated revenues by 5.3 percent. The mean absolute error of those projections is 10.4 percent, and the RMSE is 12.1 percent. A mean absolute error of that magnitude would correspond to an error of about $420 billion in the revenue estimate for 2020 that CBO released in its January 2015 baseline projections. The preponderance of overestimates over that longer horizon results in part from the fact that many of the six-year periods encompassed a recession that reduced economic activity and tax revenues below projected amounts.

The RMSE is not as helpful for analyzing the distribution of the errors for CBO's six-year projections as it is for the two-year projection errors because the six-year projections have a larger mean error than the two-year projections and have resulted in about as many relatively large errors as small ones. The mean absolute error and the RMSE show some signs of stabilizing at the six-year horizon, measuring not much higher than those calculated for the five-year horizon. However, the general accuracy of CBO's forecasts extending beyond six years may not become clearer until well into the future, when enough such forecasts have been produced to allow for a comprehensive assessment.

CBO's six-year forecasts of revenues as a share of gross domestic product (GDP) have an RMSE of 1.1 percentage points and a mean absolute error of 0.9 percentage points. In CBO's January 2015 baseline projections, revenues for 2020, the sixth year of the projection, total 18.0 percent of GDP. On the basis of the mean absolute error of past forecasts, revenues for that year might be expected to be as low as 17.1 percent of GDP or as high as 18.9 percent if there are no changes to current law. (The actual error for that particular projection might still fall outside that range.)

#### How Efficiently Has CBO Incorporated New Information?

CBO has tended to revise consecutive revenue forecasts in the same direction, suggesting that the agency does not efficiently incorporate new information into its forecasts. That tendency was less pronounced in the past 15 years than it was in the previous period, although the limited number of forecasts that can be assessed makes it difficult to conclude that CBO has improved its use of new information. That tendency, furthermore, has varied significantly over the entire history of CBO's forecasts, and CBO's forecast accuracy would not have been systematically improved had the agency incorporated into its forecasts what was known at the time about that tendency; such modifications would have over adjusted the forecasts in many cases.

#### What Factors Have Contributed to Forecast Errors in CBO's Revenue Projections?

All revenue forecast errors can be attributed either to errors in projections of GDP or to errors in projections of revenues raised as a percentage of GDP. The largest forecast errors are associated with revenue projections produced for years during which recessions occurred and GDP ended up being significantly lower than expected. Those substantial revenue shortfalls have also stemmed from other factors, including unexpected declines relative to GDP in certain types of income—most notably wages and salaries, corporate profits, and capital gains realizations—and declines in the share of overall income earned by the highest-earning taxpayers, which push down the effective tax rate (that is, total taxes as a percentage of total income). To a lesser extent, those same factors and others, working in both directions, have contributed to forecast errors in years without recessions.

At the two-year horizon, the RMSE for revenues as a percentage of GDP has been a little over twice as large as the RMSE for GDP. By the six-year horizon, the RMSE of each of those two measures is very similar. The projection errors for GDP have tended to be larger for longer forecast horizons, increasing steadily with each additional year of the horizon through the six-year horizon, whereas forecast errors for revenues as a percentage of GDP have tended to be larger for each year added to the horizon through the first four years but then to decline slightly at the five- and six-year horizons. It is unclear whether those patterns would continue in projections extending beyond six years.

Errors in revenue forecasts can also be broken down by source of revenues, and the projection errors for each of those specific sources vary widely. Of the seven categories of revenue sources, the forecasts of corporate income taxes exhibited the largest errors (measured as percentages of the actual revenues from the specific source), and those of payroll taxes, the smallest. Although the misestimates for projections of individual income taxes fall in the middle of the range of errors for the source categories, the projections of such taxes, which were the largest source of federal revenues each year over the historical period, have contributed the most to CBO's forecast errors for total revenues, followed by those of corporate income taxes (the third largest revenue source) and payroll taxes (the second largest). The Administration's forecasts for those revenue sources have had errors similar to those in CBO's forecasts, as have states' projections for individual income taxes and corporate income taxes, the main comparable sources of states' revenues.