Estimating and Forecasting Capital Gains with Quarterly Models: Technical Paper 2004-14

Working Paper
September 1, 2004

Jangryoul Kim, Preston Miller, and Larry Ozanne

At the end of each year, the Congressional Budget Office (CBO) estimates capital gains for the year ending and forecasts them for the next decade. The decade forecast is made using CBO’s forecast of GDP and an assumption that gains revert from their current size to their historical size relative to GDP. Our objective in this paper is to describe methods to improve CBO’s forecasts, particularly for the first year ahead.

We settled on two procedures. The first is similar to CBO’s method for forecasting gains. It uses an equation to forecast gains given forecasts of economic and financial variables. This procedure requires a prior step to forecast the economic and financial variables. The second procedure integrates the forecasting of gains and other variables into a single model. In this model we found it advantageous to work with quarterly data, so we interpolate the reported annual series on capital gains to a quarterly frequency. Forecasting in the prior step of the two-step method and the integrated quarterly method was based on Bayesian-restricted vector autoregressions.

Both of the procedures abstract from the effects of tax changes on forecasts of realizations. CBO’s baseline is required to assume that current law continues. We abstract from tax changes by constructing a series of capital gains realizations that assumes taxes remained at their 1998 level throughout the 1948-2000 period used for model development. This tax-adjusted series retains much of the volatility in the growth rate of actual capital gains. Between 1971 and 2000, the period used to test the models, the annual growth rate of tax-adjusted gains ranged from a high of 44 percent to a low of -18 percent. Its mean growth rate was 12 percent with a standard deviation of 16 percent.

We base our model comparisons on their root mean squared errors (RMSE) in 1-year-ahead out-of-sample forecasts of the growth rate of tax-adjusted gains. Our application of CBO’s mean reversion method found a RMSE of 18.7 percentage points. The two-step forecasting method reduced the RMSE to 14.8 percentage points, and the integrated quarterly method reduced the error to 11.9 percentage points.

Two additional findings from this investigation suggest improvements to CBO’s methods. First, the models we developed may help CBO improve its estimates of gains in the year ending. Second, the models may provide some help in forecasting a second year ahead, but after that, either mean reversion or a simple random walk model with drift appears to be as good or better.